Student ID;Student Country;Question ID;Type of Answer;Question Level;Topic;Subtopic;Keywords
473;Portugal;346;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
351;Portugal;796;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Logarithmic function,Exponential function,Simplify expressions
967;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1557;Portugal;87;0;Advanced;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
394;Portugal;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
509;Portugal;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
884;Italy;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
955;Lithuania;385;0;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1126;Portugal;288;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
69;Portugal;551;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality
955;Lithuania;424;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
411;Portugal;82;0;Basic;Differentiation;Derivatives;Logarithmic rule,Power rule,Exponential rule,Trigonometric rules,Product rule
1182;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1322;Italy;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1252;Portugal;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
851;Italy;864;1;Basic;Optimization;Nonlinear Optimization;Lagrange multipliers,Optimal solution,Minimum,Maximum
1220;Slovenia;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1026;Lithuania;82;0;Basic;Differentiation;Derivatives;Logarithmic rule,Power rule,Exponential rule,Trigonometric rules,Product rule
414;Portugal;228;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
168;Portugal;732;0;Advanced;Integration;Integration Techniques;Trigonometric substitution
1220;Slovenia;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1533;Portugal;561;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
1220;Slovenia;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
982;Portugal;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
1350;Portugal;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
712;Portugal;181;0;Basic;Statistics;Statistics;Quantile,Frequency,Sample,Mean,Variance,Standard deviation,Median,Mode
473;Portugal;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
52;Portugal;463;0;Basic;Fundamental Mathematics;Elementary Geometry;Polyhedrons,Geometric solids,Classification of geometric solids
966;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1252;Portugal;779;1;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
552;Portugal;837;1;Basic;Differential Equations;Differential Equations;Linear differential equation
576;Ireland;567;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a line,Orthogonality,Collinearity
956;Portugal;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
163;Portugal;335;1;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
890;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
483;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
69;Portugal;568;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
509;Portugal;122;1;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication,Determinant properties,Symmetric matrix
1029;Lithuania;264;0;Basic;Differentiation;Partial Differentiation;Chain rule
840;Italy;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
913;Ireland;424;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
956;Portugal;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1288;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1505;Portugal;743;0;Basic;Optimization;Linear Optimization;Duality theory,Linear programming
1220;Slovenia;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
890;Portugal;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
1011;Portugal;271;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
1299;Italy;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
175;Italy;95;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule,Exponential rule
1220;Slovenia;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
913;Ireland;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
36;Portugal;142;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
979;Portugal;1252;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
717;Portugal;204;0;Basic;Statistics;Statistics;Student distribution,Hypothesis testing
64;Portugal;560;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality
955;Lithuania;1115;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
840;Italy;278;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
626;Italy;920;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
91;Lithuania;462;1;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
1219;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
57;Portugal;204;1;Basic;Statistics;Statistics;Student distribution,Hypothesis testing
1087;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1509;Portugal;922;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1220;Slovenia;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1047;Lithuania;261;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
1219;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1081;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
168;Portugal;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
634;Italy;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
175;Italy;1061;0;Basic;Complex Numbers;Complex Numbers;Complex plane 
986;Portugal;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
625;Russian Federation;462;0;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
876;Italy;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1080;Portugal;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1171;Portugal;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
913;Ireland;1105;1;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
876;Italy;448;1;Advanced;Linear Algebra;Vector Spaces;Subspace
451;Portugal;305;0;Basic;Probability ;Probability ;Event,Axioms of probability,Addition, multiplication, and total probability rules,Sample space
1220;Slovenia;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
591;Portugal;556;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line,Collinearity
551;Lithuania;359;1;Advanced;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
697;Portugal;190;1;Basic;Statistics;Statistics;Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance,Median
657;Ireland;201;0;Basic;Statistics;Statistics;Chi square distribution,Student distribution,Quantile,Hypothesis testing
1220;Slovenia;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
81;Lithuania;464;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Geometrical figures
1420;Portugal;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
851;Italy;821;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Maximum,Second derivative test,Stationary point,Unconstrained optimization,Saddle point
700;Portugal;177;0;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
1322;Italy;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
155;Spain;888;1;Basic;Differential Equations;Differential Equations;Linear differential equation
576;Ireland;695;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product
840;Italy;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1220;Slovenia;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1292;Italy;595;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Eigenvalue
1322;Italy;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
67;Portugal;179;1;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
1286;Italy;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
633;Italy;126;0;Advanced;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Solve matrix equation
988;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1322;Italy;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1331;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
64;Portugal;559;0;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
1023;Lithuania;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
890;Portugal;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
91;Lithuania;451;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
351;Portugal;84;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Indeterminate forms,Limits
598;Italy;223;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
986;Portugal;439;1;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
1363;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
473;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1517;Portugal;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
41;Portugal;183;1;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
1299;Italy;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1146;Portugal;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
359;Portugal;352;1;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Operations with complex numbers
988;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1122;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1339;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1044;Lithuania;268;0;Basic;Differentiation;Partial Differentiation;First order,Second order
1324;Italy;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1284;Italy;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
37;Portugal;399;1;Basic;Integration;Integration Techniques;Substitution,Direct inspection,Simple integration
1220;Slovenia;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
535;Portugal;333;1;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1481;Portugal;734;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Exponential rule
1083;Portugal;385;1;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
986;Portugal;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
1286;Italy;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1561;Portugal;732;0;Advanced;Integration;Integration Techniques;Trigonometric substitution
28;Portugal;700;1;Basic;Analytic Geometry;Analytic Geometry;Collinearity,Locus,Orthogonality,Orthogonal projection,Scalar product,Distance
1023;Lithuania;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1220;Slovenia;455;1;Basic;Linear Algebra;Vector Spaces;Basis
1049;Lithuania;100;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Power rule
1256;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
884;Italy;424;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
359;Portugal;359;0;Advanced;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
378;Portugal;558;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
1312;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
426;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
91;Lithuania;432;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
1220;Slovenia;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1525;Portugal;751;0;Advanced;Optimization;Linear Optimization;Sensitivity analysis,Postoptimality analysis,Duality theory,Excel solver add-in,Simplex method,Linear programming
311;Ireland;134;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
1081;Portugal;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
1147;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
899;Lithuania;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
985;Romania;100;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Power rule
1023;Lithuania;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
71;Portugal;353;1;Basic;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
80;Lithuania;744;0;Basic;Optimization;Linear Optimization;Excel solver add-in,Simplex method,Linear programming
168;Portugal;779;1;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
525;Portugal;494;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
473;Portugal;782;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1147;Portugal;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1248;Italy;91;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
898;Portugal;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
483;Portugal;275;1;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
723;Portugal;184;1;Basic;Statistics;Statistics;Frequency,Sample,Stem and Leaf diagram,Variance,Standard deviation,Relative frequency
394;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
625;Russian Federation;514;0;Basic;Fundamental Mathematics;Elementary Geometry;Triangle inequality,Triangles
1269;Portugal;432;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
411;Portugal;406;0;Basic;Integration;Integration Techniques;Direct inspection
1080;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1333;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1077;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
972;Portugal;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1143;Portugal;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1252;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1543;Portugal;1100;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
576;Ireland;575;1;Advanced;Analytic Geometry;Analytic Geometry;Orthogonality,Orthogonal projection,Cross product,Scalar product
689;Portugal;858;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Maximum,Stationary point,Saddle point
1220;Slovenia;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
548;Portugal;298;0;Basic;Probability ;Probability ;Event,Axioms of probability
81;Lithuania;468;1;Basic;Graph Theory;Graph Theory;Simple graph
1087;Portugal;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1542;Portugal;1111;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1147;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
576;Ireland;574;0;Advanced;Analytic Geometry;Analytic Geometry;Collinearity,Orthogonality,Distance,Scalar product
1070;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
380;Portugal;357;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
178;Italy;753;0;Basic;Differentiation;Derivatives;Exponential rule
1220;Slovenia;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
166;Portugal;141;1;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication
625;Russian Federation;507;0;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry
853;Italy;219;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1542;Portugal;309;1;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
853;Italy;216;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
1230;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
675;Portugal;188;0;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
1011;Portugal;877;0;Basic;Differentiation;Partial Differentiation;Second order
1220;Slovenia;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
80;Lithuania;285;1;Basic;Optimization;Linear Optimization;Linear programming
840;Italy;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
67;Portugal;187;0;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
1220;Slovenia;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
177;Italy;734;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Exponential rule
510;Portugal;789;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1286;Italy;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
376;Portugal;345;1;Advanced;Complex Numbers;Complex Numbers;Polar representation,Trigonometric form,Modulus of a complex number,Operations with complex numbers,Algebraic form,Principal argument,De Moivre formulas
37;Portugal;723;1;Basic;Integration;Integration Techniques;Substitution
175;Italy;1106;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
176;Italy;118;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
426;Portugal;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1252;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
422;Portugal;650;0;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties
898;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1269;Portugal;449;0;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
406;Portugal;916;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Square linear system,Consistent system
576;Ireland;562;0;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality
1194;Portugal;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
884;Italy;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
91;Lithuania;451;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1564;Portugal;413;0;Basic;Integration;Integration Techniques;Direct inspection
1427;Portugal;306;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
955;Lithuania;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
455;Portugal;850;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Continuity,Limits
753;Italy;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
972;Portugal;779;0;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
1517;Portugal;625;1;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Characteristic polynomial,Eigenvalue,Diagonalization,Eigenvector,Spectrum
1518;Portugal;489;0;Basic;Probability ;Probability ;Axioms of probability,Event,Addition, multiplication, and total probability rules,Sample space
468;Portugal;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1197;Slovenia;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
986;Portugal;430;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
37;Portugal;876;1;Basic;Differentiation;Partial Differentiation;Directional derivative,Gradient,First order,Second order
525;Portugal;112;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1271;Portugal;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1196;Slovenia;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
624;Portugal;112;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
979;Portugal;278;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
840;Italy;783;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
509;Portugal;454;1;Basic;Linear Algebra;Vector Spaces;Basis
28;Portugal;360;0;Basic;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
1321;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1024;Lithuania;874;0;Basic;Differentiation;Partial Differentiation;Power rule,Trigonometric rules,Logarithmic rule
1481;Portugal;686;1;Basic;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
633;Italy;419;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
1080;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
351;Portugal;753;1;Basic;Differentiation;Derivatives;Exponential rule
884;Italy;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
966;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1252;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
840;Italy;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1192;Portugal;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1557;Portugal;928;0;Advanced;Real Functions of a single variable;Domain, Image and Graphics;Planar graph
37;Portugal;612;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
26;Portugal;564;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonality
71;Portugal;142;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
967;Portugal;779;1;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
898;Portugal;420;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1044;Lithuania;874;0;Basic;Differentiation;Partial Differentiation;Power rule,Trigonometric rules,Logarithmic rule
1080;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
633;Italy;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
28;Portugal;554;0;Basic;Analytic Geometry;Analytic Geometry;Scalar product,Orthogonality,Orthogonal projection,Distance
552;Portugal;146;0;Basic;Differential Equations;Differential Equations;Separable variables equation
633;Italy;446;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1220;Slovenia;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
344;Portugal;735;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
876;Italy;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1322;Italy;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
511;Portugal;796;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Logarithmic function,Exponential function,Simplify expressions
551;Lithuania;569;0;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance,Scalar product,Cross product,Orthogonality,Collinearity
918;Portugal;1002;0;Basic;Differentiation;Partial Differentiation;First order
885;Italy;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
61;Portugal;164;1;Basic;Differential Equations;Differential Equations;Separable variables equation
986;Portugal;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
884;Italy;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1173;Portugal;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
890;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
855;Italy;221;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1023;Lithuania;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
168;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
219;Lithuania;667;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
168;Portugal;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1023;Lithuania;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
415;Portugal;131;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
890;Portugal;427;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1339;Portugal;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1427;Portugal;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;455;0;Basic;Linear Algebra;Vector Spaces;Basis
986;Portugal;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
986;Portugal;306;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
64;Portugal;796;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Logarithmic function,Exponential function,Simplify expressions
426;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
28;Portugal;189;0;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
457;Portugal;357;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
411;Portugal;617;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Spectrum,Eigenvector,Characteristic polynomial
851;Italy;1014;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
1220;Slovenia;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1286;Italy;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1557;Portugal;676;1;Advanced;Real Functions of a single variable;Domain, Image and Graphics;Domain,Image of a function
411;Portugal;360;1;Basic;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
599;Italy;618;1;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Spectrum,Eigenvector,Characteristic polynomial
1363;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1322;Italy;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1281;Portugal;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1158;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
986;Portugal;451;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
899;Lithuania;424;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
524;Portugal;788;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Exponential function
466;Portugal;359;1;Advanced;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
675;Portugal;77;1;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
91;Lithuania;460;1;Basic;Fundamental Mathematics;Elementary Geometry;Polyhedrons,Platonic solids,Geometric solids
71;Portugal;630;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue
1220;Slovenia;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
28;Portugal;353;0;Basic;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
511;Portugal;122;1;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication,Determinant properties,Symmetric matrix
955;Lithuania;448;0;Advanced;Linear Algebra;Vector Spaces;Subspace
394;Portugal;380;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
200;Lithuania;108;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1351;Portugal;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
552;Portugal;702;0;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Intersection,Cartesian equations of a line
411;Portugal;136;0;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
551;Lithuania;336;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Modulus of a complex number,Imaginary part
840;Italy;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
426;Portugal;333;1;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1171;Portugal;859;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Second derivative test,Minimum,Maximum,Stationary point,Saddle point
1299;Italy;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1056;Lithuania;876;0;Basic;Differentiation;Partial Differentiation;Directional derivative,Gradient,First order,Second order
712;Portugal;202;0;Basic;Statistics;Statistics;Student distribution,Confidence interval,Point estimate,Hypothesis testing
966;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
72;Portugal;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1220;Slovenia;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
167;Portugal;785;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
131;Lithuania;121;0;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
551;Lithuania;328;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1289;Italy;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1192;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
91;Lithuania;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1219;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1322;Italy;779;1;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
637;Italy;202;0;Basic;Statistics;Statistics;Student distribution,Confidence interval,Point estimate,Hypothesis testing
91;Lithuania;515;1;Advanced;Fundamental Mathematics;Elementary Geometry;Geometrical figures,Quadrilaterals,Rhombus
168;Portugal;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
1147;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
535;Portugal;357;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
1220;Slovenia;455;1;Basic;Linear Algebra;Vector Spaces;Basis
1109;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1286;Italy;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
411;Portugal;311;0;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
898;Portugal;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
511;Portugal;244;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
751;Lithuania;700;1;Basic;Analytic Geometry;Analytic Geometry;Collinearity,Locus,Orthogonality,Orthogonal projection,Scalar product,Distance
1023;Lithuania;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1557;Portugal;677;0;Advanced;Real Functions of a single variable;Domain, Image and Graphics;Domain,Image of a function
1079;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
239;Lithuania;878;1;Basic;Differentiation;Partial Differentiation;Second order,First order
972;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
90;Lithuania;329;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1286;Italy;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
972;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1220;Slovenia;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
71;Portugal;331;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
986;Portugal;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1538;Portugal;1116;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
1252;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
473;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
955;Lithuania;1102;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
972;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
1077;Portugal;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
955;Lithuania;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
898;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1158;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
41;Portugal;360;1;Basic;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
411;Portugal;141;0;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication
1220;Slovenia;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
41;Portugal;182;0;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
128;Lithuania;337;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form,Operations with complex numbers,Modulus of a complex number
1273;Portugal;439;0;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
176;Italy;612;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
393;Lithuania;349;1;Advanced;Complex Numbers;Complex Numbers;Complex plane 
913;Ireland;224;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
675;Portugal;193;1;Basic;Statistics;Statistics;Standard deviation,Variance,Median,Frequency,Mode,Outliers,Quantile,Interquartile range,Population,Data type,Sample,Relative frequency,Mean
1487;Portugal;476;1;Basic;Graph Theory;Graph Theory;Adjacency matrix
177;Italy;614;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;454;0;Basic;Linear Algebra;Vector Spaces;Basis
1146;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1179;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
349;Portugal;147;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
1220;Slovenia;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
986;Portugal;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1146;Portugal;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
349;Portugal;144;1;Basic;Differentiation;Derivatives;Trigonometric rules
1284;Italy;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1219;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1487;Portugal;1174;1;Basic;Integration;Definite Integrals; Integration by parts,Fundamental theorem of Calculus
1080;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1023;Lithuania;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
168;Portugal;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
974;Portugal;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
91;Lithuania;337;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form,Operations with complex numbers,Modulus of a complex number
854;Italy;952;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1244;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1252;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
311;Ireland;131;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
411;Portugal;337;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form,Operations with complex numbers,Modulus of a complex number
955;Lithuania;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1322;Italy;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
918;Portugal;722;0;Basic;Integration;Integration Techniques;Integration by parts
1146;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
91;Lithuania;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
884;Italy;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
37;Portugal;275;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
1220;Slovenia;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
90;Lithuania;327;1;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
168;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1023;Lithuania;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
840;Italy;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1095;Portugal;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
81;Lithuania;472;0;Advanced;Graph Theory;Graph Theory;Simple graph
576;Ireland;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
37;Portugal;1080;0;Basic;Differentiation;Partial Differentiation;First order
876;Italy;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1220;Slovenia;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
26;Portugal;892;0;Basic;Differential Equations;Differential Equations;Linear differential equation
1147;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
979;Portugal;1215;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Lagrange's interpolation
1126;Portugal;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1274;Portugal;795;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
174;Portugal;753;0;Basic;Differentiation;Derivatives;Exponential rule
913;Ireland;1160;1;Basic;Set Theory;Set Theory;Subset
1179;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1220;Slovenia;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1292;Italy;619;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Spectrum,Characteristic polynomial
1308;Italy;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1288;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
420;Portugal;643;0;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties,Hermitian matrix,Matrix multiplication,Linearly independent rows,Symmetric matrix,Matrix operations
1220;Slovenia;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1542;Portugal;1097;1;Basic;Numerical Methods;Numerical Methods;Lagrange's interpolation,Polynomial interpolation
695;Portugal;185;0;Basic;Statistics;Statistics;Frequency,Quantile,Mean,Variance,Median,Mode
91;Lithuania;329;1;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1220;Slovenia;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
168;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1288;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
633;Italy;427;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
41;Portugal;102;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
72;Portugal;289;0;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1543;Portugal;1086;0;Basic;Numerical Methods;Numerical Methods;First order,Second order
426;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1220;Slovenia;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1135;Portugal;779;0;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
984;Romania;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1269;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
91;Lithuania;494;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
175;Italy;339;1;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation
1043;Lithuania;262;0;Basic;Differentiation;Partial Differentiation;First order
1564;Portugal;682;0;Basic;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
26;Portugal;571;0;Basic;Analytic Geometry;Analytic Geometry;Intersection,Cartesian equations of a plane
1427;Portugal;781;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1081;Portugal;441;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span
28;Portugal;565;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonal projection,Orthogonality,Collinearity,Locus
1543;Portugal;1100;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
913;Ireland;771;0;Basic;Probability ;Probability ;Event,Sample space,Addition, multiplication, and total probability rules,Axioms of probability
1220;Slovenia;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1352;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
72;Portugal;446;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
625;Russian Federation;611;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
168;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
168;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
509;Portugal;604;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector,Spectrum,Characteristic polynomial
466;Portugal;333;0;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
81;Lithuania;471;1;Advanced;Graph Theory;Graph Theory;Simple graph
876;Italy;278;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1288;Portugal;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
750;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1023;Lithuania;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
176;Italy;730;1;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
1557;Portugal;890;1;Basic;Differential Equations;Differential Equations;Linear differential equation
986;Portugal;380;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
380;Portugal;1246;1;Basic;Optimization;Nonlinear Optimization;Unconstrained optimization,Second derivative test,Optimal solution
1274;Portugal;788;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Exponential function
599;Italy;619;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Spectrum,Characteristic polynomial
643;Italy;178;1;Basic;Statistics;Statistics;Mean,Variance,Standard deviation,Median,Mode
91;Lithuania;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
551;Lithuania;347;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
1220;Slovenia;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
168;Portugal;607;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector
634;Italy;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
969;Romania;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1220;Slovenia;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
985;Romania;730;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
1032;Lithuania;262;0;Basic;Differentiation;Partial Differentiation;First order
725;Portugal;188;0;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
1220;Slovenia;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1077;Portugal;278;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1517;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
41;Portugal;189;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
1146;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
351;Portugal;665;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1322;Italy;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
91;Lithuania;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
41;Portugal;336;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Modulus of a complex number,Imaginary part
1219;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
840;Italy;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
28;Portugal;564;0;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonality
750;Portugal;921;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
509;Portugal;848;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Continuity,Limits
576;Ireland;363;0;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
166;Portugal;138;1;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Determinant computation,Determinant properties,Inverse matrix 
1273;Portugal;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
974;Portugal;427;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1220;Slovenia;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1220;Slovenia;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
840;Italy;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1428;Portugal;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
26;Portugal;831;1;Basic;Differential Equations;Differential Equations;Linear differential equation
91;Lithuania;368;1;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids,Regular polygon
1324;Italy;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
91;Lithuania;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1079;Portugal;419;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
669;Portugal;77;1;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
966;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1284;Italy;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
175;Italy;1489;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Modulus of a complex number,Algebraic form,Real part,Equations involving complex numbers,Imaginary part
85;Lithuania;1150;0;Basic;Set Theory;Set Theory;Subset
26;Portugal;216;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
1077;Portugal;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
155;Spain;165;0;Basic;Differential Equations;Differential Equations;Linear differential equation,Homogeneous equation
625;Russian Federation;666;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
468;Portugal;349;1;Advanced;Complex Numbers;Complex Numbers;Complex plane 
168;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
576;Ireland;560;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality
1289;Italy;424;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
175;Italy;1087;0;Basic;Numerical Methods;Numerical Methods;First order,Second order
1334;Portugal;779;0;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
380;Portugal;861;1;Basic;Optimization;Nonlinear Optimization;Saddle point,Optimal solution,Minimum,Maximum,Stationary point
898;Portugal;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
876;Italy;419;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
180;Italy;342;1;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Modulus of a complex number,Algebraic form
509;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
509;Portugal;952;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
176;Italy;143;0;Basic;Differentiation;Derivatives;Trigonometric rules,Logarithmic rule
421;Portugal;328;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
634;Italy;94;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
1352;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
913;Ireland;1153;1;Basic;Set Theory;Set Theory;Subset
1273;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
71;Portugal;104;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
674;Ireland;188;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
776;Portugal;556;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line,Collinearity
41;Portugal;160;1;Basic;Differential Equations;Differential Equations;Linear differential equation
840;Italy;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
700;Portugal;187;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
1182;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
167;Portugal;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
1070;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
414;Portugal;244;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
91;Lithuania;516;1;Advanced;Fundamental Mathematics;Elementary Geometry;Symmetry
37;Portugal;701;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product,Distance
411;Portugal;141;0;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication
576;Ireland;574;1;Advanced;Analytic Geometry;Analytic Geometry;Collinearity,Orthogonality,Distance,Scalar product
1275;Lithuania;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
91;Lithuania;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
509;Portugal;495;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
955;Lithuania;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
750;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1146;Portugal;289;0;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
378;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1082;Portugal;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
57;Portugal;188;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
955;Lithuania;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1220;Slovenia;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
967;Portugal;424;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
176;Italy;274;1;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
969;Romania;451;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
200;Lithuania;613;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
155;Spain;172;1;Basic;Differential Equations;Differential Equations;Linear differential equation
91;Lithuania;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1130;Portugal;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
510;Portugal;221;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1220;Slovenia;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
168;Portugal;380;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1543;Portugal;1115;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
1220;Slovenia;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
524;Portugal;367;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometrical figures
965;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
189;Portugal;145;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
1291;Italy;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1220;Slovenia;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
955;Lithuania;1108;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Lagrange's interpolation
509;Portugal;949;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
885;Italy;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
511;Portugal;789;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
840;Italy;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
344;Portugal;787;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Logarithmic function
71;Portugal;1220;1;Basic;Differentiation;Derivatives;Trigonometric rules,Power rule
1322;Italy;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1147;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1149;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1182;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1044;Lithuania;259;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
634;Italy;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
168;Portugal;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
52;Portugal;503;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry,Geometric transformations
81;Lithuania;473;1;Advanced;Graph Theory;Graph Theory;Simple graph
91;Lithuania;369;1;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Geometrical figures,Classification of geometrical figures
636;Italy;202;0;Basic;Statistics;Statistics;Student distribution,Confidence interval,Point estimate,Hypothesis testing
1564;Portugal;250;0;Basic;Differentiation;Derivatives;Quotient rule,Product rule,Trigonometric rules
1252;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
853;Italy;244;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1271;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
470;Portugal;357;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
1132;Portugal;292;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
168;Portugal;292;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
81;Lithuania;566;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Orthogonality,Locus
37;Portugal;730;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
177;Italy;667;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1292;Italy;606;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector,Diagonalization
1350;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1220;Slovenia;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
168;Portugal;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1509;Portugal;685;0;Basic;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
525;Portugal;793;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
1080;Portugal;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
582;Lithuania;340;0;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers,Conjugate number
1517;Portugal;451;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1147;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1292;Italy;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
986;Portugal;419;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
152;Portugal;337;1;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form,Operations with complex numbers,Modulus of a complex number
876;Italy;420;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1274;Portugal;793;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
483;Portugal;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1219;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1220;Slovenia;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
91;Lithuania;393;1;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
1299;Italy;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
860;Italy;219;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1081;Portugal;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
240;Lithuania;918;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
26;Portugal;299;0;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Event,Axioms of probability
524;Portugal;458;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Geometric transformations,Geometrical figures
626;Italy;255;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Logarithmic rule
81;Lithuania;581;1;Basic;Graph Theory;Graph Theory;Tree,Spanning tree
720;Portugal;204;0;Basic;Statistics;Statistics;Student distribution,Hypothesis testing
645;Italy;202;0;Basic;Statistics;Statistics;Student distribution,Confidence interval,Point estimate,Hypothesis testing
470;Portugal;340;1;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers,Conjugate number
1427;Portugal;306;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
403;Portugal;352;1;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Operations with complex numbers
840;Italy;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
576;Ireland;572;0;Basic;Analytic Geometry;Analytic Geometry;Locus,Scalar product,Cross product,Distance,Collinearity,Orthogonality
1319;Italy;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
394;Portugal;432;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
72;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1427;Portugal;779;0;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
28;Portugal;563;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
525;Portugal;613;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1305;Italy;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1037;Lithuania;260;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
414;Portugal;334;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
1525;Portugal;861;0;Basic;Optimization;Nonlinear Optimization;Saddle point,Optimal solution,Minimum,Maximum,Stationary point
1220;Slovenia;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
174;Portugal;252;0;Basic;Differentiation;Derivatives;Quotient rule,Product rule,Power rule,Trigonometric rules
1081;Portugal;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1283;Italy;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
966;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1286;Italy;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
80;Lithuania;339;0;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation
81;Lithuania;929;1;Basic;Graph Theory;Graph Theory;Cycle and circuit,Shortest path,Path,Planar graph,Tree,Adjacency matrix,Chromatic number,Simple graph,Spanning tree,Incidence matrix 
1220;Slovenia;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
81;Lithuania;522;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Triangles
1023;Lithuania;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1375;Portugal;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1023;Lithuania;454;1;Basic;Linear Algebra;Vector Spaces;Basis
958;Lithuania;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1444;Portugal;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
91;Lithuania;514;0;Basic;Fundamental Mathematics;Elementary Geometry;Triangle inequality,Triangles
576;Ireland;556;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line,Collinearity
626;Italy;735;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
1517;Portugal;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
80;Lithuania;564;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonality
69;Portugal;551;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality
1049;Lithuania;257;1;Basic;Differentiation;Partial Differentiation;Gradient,First order
851;Italy;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
634;Italy;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1173;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1087;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1087;Portugal;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
349;Portugal;729;0;Basic;Differentiation;Derivatives;Quotient rule
1220;Slovenia;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
72;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1195;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1286;Italy;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
689;Portugal;960;0;Basic;Optimization;Nonlinear Optimization;Linear programming
853;Italy;89;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
966;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1284;Italy;455;1;Basic;Linear Algebra;Vector Spaces;Basis
393;Lithuania;333;0;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
866;Italy;233;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
1080;Portugal;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
91;Lithuania;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
776;Portugal;574;1;Advanced;Analytic Geometry;Analytic Geometry;Collinearity,Orthogonality,Distance,Scalar product
1284;Italy;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
986;Portugal;382;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
374;Portugal;348;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Complex plane ,Real part
592;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1095;Portugal;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
28;Portugal;326;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part
1308;Italy;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
855;Italy;228;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
67;Portugal;495;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
509;Portugal;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1332;Portugal;418;1;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
1338;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1049;Lithuania;268;0;Basic;Differentiation;Partial Differentiation;First order,Second order
1023;Lithuania;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
524;Portugal;518;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
28;Portugal;572;0;Basic;Analytic Geometry;Analytic Geometry;Locus,Scalar product,Cross product,Distance,Collinearity,Orthogonality
511;Portugal;612;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
969;Romania;448;1;Advanced;Linear Algebra;Vector Spaces;Subspace
979;Portugal;1099;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
351;Portugal;786;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
986;Portugal;418;1;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
955;Lithuania;1252;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
375;Portugal;348;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Complex plane ,Real part
524;Portugal;613;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
71;Portugal;1110;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
37;Portugal;300;0;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Event,Axioms of probability
80;Lithuania;137;1;Basic;Linear Algebra;Matrices and Determinants;Matrix equivalent - echelon,Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Linearly independent rows,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
1143;Portugal;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1044;Lithuania;262;0;Basic;Differentiation;Partial Differentiation;First order
1243;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
700;Portugal;190;0;Basic;Statistics;Statistics;Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance,Median
36;Portugal;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
509;Portugal;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
890;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
625;Russian Federation;795;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
955;Lithuania;1093;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
90;Lithuania;642;1;Basic;Linear Algebra;Matrices and Determinants;Symmetric matrix,Matrix multiplication,Matrix operations
599;Italy;854;1;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Diagonalization,Spectrum,Characteristic polynomial
1332;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
91;Lithuania;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1518;Portugal;642;1;Basic;Linear Algebra;Matrices and Determinants;Symmetric matrix,Matrix multiplication,Matrix operations
1220;Slovenia;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
176;Italy;255;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Logarithmic rule
1288;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1427;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
626;Italy;717;0;Basic;Differentiation;Derivatives;Trigonometric rules,Quotient rule
1043;Lithuania;912;0;Basic;Differentiation;Partial Differentiation;Minimum,Stationary point,Maximum,Saddle point,Optimal solution
1220;Slovenia;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
852;Italy;90;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1220;Slovenia;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1402;Portugal;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1481;Portugal;685;0;Basic;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
239;Lithuania;269;1;Basic;Differentiation;Partial Differentiation;First order,Second order
972;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
750;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1308;Italy;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
483;Portugal;380;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1271;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
956;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
394;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
966;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
91;Lithuania;419;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
1143;Portugal;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
854;Italy;230;1;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
979;Portugal;1103;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1220;Slovenia;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
972;Portugal;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1557;Portugal;694;0;Advanced;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
37;Portugal;1228;0;Basic;Differentiation;Partial Differentiation;First order,Second order
884;Italy;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1308;Italy;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
406;Portugal;92;1;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
986;Portugal;306;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
955;Lithuania;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
913;Ireland;761;0;Basic;Probability ;Probability ;Event,Sample space,Addition, multiplication, and total probability rules,Axioms of probability
71;Portugal;697;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Distance,Cross product
637;Italy;187;0;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
840;Italy;782;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1023;Lithuania;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
591;Portugal;334;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
91;Lithuania;121;1;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
967;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
979;Portugal;1103;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
176;Italy;665;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
591;Portugal;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1082;Portugal;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1220;Slovenia;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
851;Italy;1015;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
411;Portugal;89;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
509;Portugal;92;0;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
72;Portugal;288;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1149;Portugal;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
660;Portugal;204;1;Basic;Statistics;Statistics;Student distribution,Hypothesis testing
1044;Lithuania;876;0;Basic;Differentiation;Partial Differentiation;Directional derivative,Gradient,First order,Second order
1147;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
451;Portugal;314;1;Basic;Probability ;Probability ;Event,Sample space
1542;Portugal;1111;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1150;Portugal;289;0;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
168;Portugal;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
457;Portugal;337;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form,Operations with complex numbers,Modulus of a complex number
470;Portugal;349;1;Advanced;Complex Numbers;Complex Numbers;Complex plane 
956;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
349;Portugal;274;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
1047;Lithuania;1001;0;Basic;Differentiation;Partial Differentiation;Power rule,Trigonometric rules,Logarithmic rule
853;Italy;917;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
71;Portugal;793;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
91;Lithuania;524;1;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Rhombus
876;Italy;427;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
349;Portugal;735;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
510;Portugal;665;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
642;Italy;178;0;Basic;Statistics;Statistics;Mean,Variance,Standard deviation,Median,Mode
1322;Italy;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
1220;Slovenia;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
168;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
175;Italy;1475;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Real part,Equations involving complex numbers,Imaginary part,Conjugate number,Modulus of a complex number
1283;Italy;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
851;Italy;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
626;Italy;918;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1517;Portugal;385;0;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
473;Portugal;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
72;Portugal;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
464;Portugal;356;0;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers
638;Italy;177;0;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
986;Portugal;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1486;Portugal;787;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Logarithmic function
1220;Slovenia;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
840;Italy;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
422;Portugal;637;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
1311;Italy;306;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
168;Portugal;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1557;Portugal;86;1;Advanced;Real Functions of a single variable;Domain, Image and Graphics;Indeterminate forms,Limits
1122;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1273;Portugal;451;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
913;Ireland;1107;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1135;Portugal;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
409;Portugal;327;1;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1219;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
37;Portugal;887;1;Advanced;Differentiation;Partial Differentiation;First order
1173;Portugal;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
426;Portugal;349;0;Advanced;Complex Numbers;Complex Numbers;Complex plane 
625;Russian Federation;464;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Geometrical figures
1091;Lithuania;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1375;Portugal;278;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
71;Portugal;720;1;Basic;Differentiation;Derivatives;Quotient rule,Trigonometric rules,Logarithmic rule,Product rule
1256;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1157;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
966;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1252;Portugal;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
81;Lithuania;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
168;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1252;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
890;Portugal;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
1557;Portugal;670;0;Advanced;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
509;Portugal;512;0;Basic;Fundamental Mathematics;Elementary Geometry;Triangles
208;Lithuania;137;0;Basic;Linear Algebra;Matrices and Determinants;Matrix equivalent - echelon,Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Linearly independent rows,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
80;Lithuania;331;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1220;Slovenia;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1353;Portugal;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
684;Ireland;189;0;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
64;Portugal;557;0;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance
1334;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
128;Lithuania;326;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part
1565;Portugal;413;0;Basic;Integration;Integration Techniques;Direct inspection
855;Italy;90;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1220;Slovenia;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1248;Italy;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
576;Ireland;699;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Locus,Intersection,Cartesian equations of a line
37;Portugal;156;0;Basic;Differential Equations;Differential Equations;Linear differential equation
1220;Slovenia;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1411;Portugal;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1557;Portugal;918;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1505;Portugal;177;1;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
178;Italy;721;1;Basic;Differentiation;Derivatives;Quotient rule,Trigonometric rules
378;Portugal;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
451;Portugal;491;0;Advanced;Probability ;Probability ;Addition, multiplication, and total probability rules,Independence,Event
1044;Lithuania;1001;1;Basic;Differentiation;Partial Differentiation;Power rule,Trigonometric rules,Logarithmic rule
1220;Slovenia;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1543;Portugal;1091;0;Basic;Numerical Methods;Numerical Methods;Nonlinear equation,Newton’s method
359;Portugal;496;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1079;Portugal;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
57;Portugal;309;0;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
52;Portugal;635;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
988;Portugal;916;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Square linear system,Consistent system
1220;Slovenia;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1271;Portugal;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
974;Portugal;1102;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
167;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
576;Ireland;239;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1220;Slovenia;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
91;Lithuania;519;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
81;Lithuania;935;1;Basic;Graph Theory;Graph Theory;Chromatic number
414;Portugal;328;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
411;Portugal;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
80;Lithuania;134;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
80;Lithuania;530;0;Basic;Integration;Double Integration;Iterate integrals,Area ,y-simple region (type I),Cartesian coordinates
510;Portugal;102;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
955;Lithuania;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
483;Portugal;349;0;Advanced;Complex Numbers;Complex Numbers;Complex plane 
1252;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1481;Portugal;300;1;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Event,Axioms of probability
168;Portugal;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1150;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
851;Italy;1208;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
890;Portugal;420;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
852;Italy;229;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
972;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
37;Portugal;142;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
26;Portugal;890;1;Basic;Differential Equations;Differential Equations;Linear differential equation
1274;Portugal;112;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1049;Lithuania;658;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
1109;Portugal;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
91;Lithuania;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
411;Portugal;714;0;Basic;Integration;Integration Techniques;Simple integration,Direct inspection
201;Lithuania;613;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
411;Portugal;138;0;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Determinant computation,Determinant properties,Inverse matrix 
1273;Portugal;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
344;Portugal;100;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Power rule
840;Italy;779;1;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
955;Lithuania;451;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1543;Portugal;1095;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1150;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
679;Portugal;78;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
378;Portugal;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
175;Italy;98;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
411;Portugal;309;0;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
411;Portugal;275;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
168;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
37;Portugal;629;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue
986;Portugal;141;1;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication
1286;Italy;419;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
1379;Portugal;108;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1319;Italy;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
751;Lithuania;566;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Orthogonality,Locus
1525;Portugal;761;0;Basic;Probability ;Probability ;Event,Sample space,Addition, multiplication, and total probability rules,Axioms of probability
406;Portugal;665;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
91;Lithuania;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
509;Portugal;616;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector
71;Portugal;641;0;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties,Hermitian matrix,Symmetric matrix,Matrix multiplication,Linearly independent rows,Matrix operations
1286;Italy;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
1173;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
176;Italy;730;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
1292;Italy;604;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector,Spectrum,Characteristic polynomial
852;Italy;225;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
972;Portugal;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
510;Portugal;463;1;Basic;Fundamental Mathematics;Elementary Geometry;Polyhedrons,Geometric solids,Classification of geometric solids
1256;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
552;Portugal;564;0;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonality
151;Portugal;102;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1352;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
899;Lithuania;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1171;Portugal;863;1;Basic;Optimization;Nonlinear Optimization;Saddle point,Optimal solution,Minimum,Maximum,Stationary point
91;Lithuania;464;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Geometrical figures
380;Portugal;1007;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Stationary point,Maximum,Saddle point
582;Lithuania;574;1;Advanced;Analytic Geometry;Analytic Geometry;Collinearity,Orthogonality,Distance,Scalar product
898;Portugal;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
91;Lithuania;516;1;Advanced;Fundamental Mathematics;Elementary Geometry;Symmetry
1517;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
511;Portugal;647;1;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Symmetric matrix,Matrix operations
776;Portugal;547;0;Basic;Analytic Geometry;Analytic Geometry;Cross product,Orthogonality,Scalar product
682;Portugal;193;1;Basic;Statistics;Statistics;Standard deviation,Variance,Median,Frequency,Mode,Outliers,Quantile,Interquartile range,Population,Data type,Sample,Relative frequency,Mean
466;Portugal;346;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
200;Lithuania;397;1;Basic;Integration;Integration Techniques;Substitution
657;Ireland;185;1;Basic;Statistics;Statistics;Frequency,Quantile,Mean,Variance,Median,Mode
853;Italy;224;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1220;Slovenia;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1243;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
311;Ireland;125;1;Basic;Linear Algebra;Matrices and Determinants;Determinant properties,Symmetric matrix,Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication
71;Portugal;147;1;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
625;Russian Federation;113;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
524;Portugal;495;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1185;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1056;Lithuania;268;0;Basic;Differentiation;Partial Differentiation;First order,Second order
1135;Portugal;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1023;Lithuania;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
913;Ireland;303;0;Basic;Probability ;Probability ;Addition, multiplication, and total probability rules,Sample space,Event,Axioms of probability
455;Portugal;496;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1322;Italy;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
713;Portugal;188;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
465;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
81;Lithuania;781;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
414;Portugal;221;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
175;Italy;1486;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
81;Lithuania;569;0;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance,Scalar product,Cross product,Orthogonality,Collinearity
1079;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1044;Lithuania;875;1;Basic;Differentiation;Partial Differentiation;Gradient,First order
955;Lithuania;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
634;Italy;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1011;Portugal;658;1;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
598;Italy;249;0;Advanced;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Square linear system,Consistent system,Inconsistent system
1350;Portugal;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
175;Italy;1111;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
466;Portugal;355;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
1220;Slovenia;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
890;Portugal;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
91;Lithuania;309;0;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
175;Italy;1213;1;Basic;Numerical Methods;Numerical Methods;Mean,Median,Outliers,Interquartile range
1552;Portugal;406;0;Basic;Integration;Integration Techniques;Direct inspection
1220;Slovenia;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1182;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1332;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1135;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
966;Portugal;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
80;Lithuania;605;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Spectrum,Diagonalization,Characteristic polynomial
1220;Slovenia;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
955;Lithuania;1252;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
1109;Portugal;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1023;Lithuania;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
378;Portugal;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
591;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
511;Portugal;458;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Geometric transformations,Geometrical figures
1505;Portugal;1003;0;Basic;Optimization;Linear Optimization;Linear programming
1220;Slovenia;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
625;Russian Federation;798;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
37;Portugal;393;1;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
966;Portugal;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
197;Portugal;798;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1256;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1281;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
913;Ireland;80;1;Basic;Statistics;Statistics;Population,Variance,Median,Standard deviation,Mode,Quantile,Sample,Mean
202;Lithuania;668;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
690;Portugal;179;0;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
1379;Portugal;104;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
890;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
168;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
876;Italy;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
956;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
972;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1288;Portugal;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1148;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
81;Lithuania;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
884;Italy;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1146;Portugal;306;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
1279;Portugal;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
411;Portugal;243;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
633;Italy;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
591;Portugal;337;1;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form,Operations with complex numbers,Modulus of a complex number
913;Ireland;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1319;Italy;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1229;Portugal;454;1;Basic;Linear Algebra;Vector Spaces;Basis
128;Lithuania;336;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Modulus of a complex number,Imaginary part
151;Portugal;108;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
668;Portugal;81;1;Basic;Statistics;Statistics;Mean,Median,Mode
168;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1557;Portugal;677;1;Advanced;Real Functions of a single variable;Domain, Image and Graphics;Domain,Image of a function
1350;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1543;Portugal;1100;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
675;Portugal;185;0;Basic;Statistics;Statistics;Frequency,Quantile,Mean,Variance,Median,Mode
967;Portugal;419;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
972;Portugal;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
851;Italy;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
351;Portugal;679;0;Basic;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
376;Portugal;335;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
884;Italy;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
986;Portugal;446;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
69;Portugal;547;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Orthogonality,Scalar product
1140;Portugal;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
955;Lithuania;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
26;Portugal;906;0;Basic;Differential Equations;Differential Equations;Linear differential equation
731;Portugal;187;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
1279;Portugal;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
840;Italy;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
966;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
455;Portugal;647;1;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Symmetric matrix,Matrix operations
218;Lithuania;118;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1220;Slovenia;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
633;Italy;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
626;Italy;83;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain,Image of a function
511;Portugal;215;1;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Inconsistent system,Solution of linear system
1171;Portugal;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
876;Italy;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
80;Lithuania;168;0;Basic;Differential Equations;Differential Equations;Linear differential equation
28;Portugal;699;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Locus,Intersection,Cartesian equations of a line
1244;Portugal;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1517;Portugal;779;1;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
660;Portugal;201;1;Basic;Statistics;Statistics;Chi square distribution,Student distribution,Quantile,Hypothesis testing
955;Lithuania;446;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1289;Italy;380;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
582;Lithuania;348;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Complex plane ,Real part
626;Italy;142;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
1331;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
899;Lithuania;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1045;Lithuania;1000;0;Basic;Differentiation;Partial Differentiation;First order
37;Portugal;882;0;Advanced;Differentiation;Partial Differentiation;Gradient,First order,Directional derivative
311;Ireland;125;0;Basic;Linear Algebra;Matrices and Determinants;Determinant properties,Symmetric matrix,Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication
178;Italy;250;0;Basic;Differentiation;Derivatives;Quotient rule,Product rule,Trigonometric rules
189;Portugal;369;0;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Geometrical figures,Classification of geometrical figures
1288;Portugal;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
80;Lithuania;916;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Square linear system,Consistent system
1219;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1023;Lithuania;455;1;Basic;Linear Algebra;Vector Spaces;Basis
156;Lithuania;114;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1087;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
714;Portugal;186;0;Basic;Statistics;Statistics;Population,Sample
1271;Portugal;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1281;Portugal;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1557;Portugal;984;0;Advanced;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
80;Lithuania;1020;1;Basic;Optimization;Linear Optimization;Linear programming,Assignment problem,Excel solver add-in,Simplex method
956;Portugal;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1256;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1319;Italy;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
956;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1271;Portugal;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
511;Portugal;949;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1220;Slovenia;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
311;Ireland;138;0;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Determinant computation,Determinant properties,Inverse matrix 
1290;Italy;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
576;Ireland;697;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Distance,Cross product
955;Lithuania;1086;1;Basic;Numerical Methods;Numerical Methods;First order,Second order
552;Portugal;550;0;Advanced;Analytic Geometry;Analytic Geometry;Cross product,Orthogonality
41;Portugal;546;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonal projection,Distance,Cross product,Orthogonality
1244;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1288;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
198;Italy;497;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1220;Slovenia;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
979;Portugal;640;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
525;Portugal;520;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
380;Portugal;1010;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Maximum
1011;Portugal;145;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
80;Lithuania;955;0;Basic;Optimization;Linear Optimization;Linear programming
393;Lithuania;333;0;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
311;Ireland;134;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
955;Lithuania;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
753;Italy;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
91;Lithuania;496;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
344;Portugal;612;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1299;Italy;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
168;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
840;Italy;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
840;Italy;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
69;Portugal;558;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
1308;Italy;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
726;Portugal;188;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
168;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
37;Portugal;555;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality,Locus,Distance
1049;Lithuania;97;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
175;Italy;1496;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
511;Portugal;613;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
634;Italy;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1087;Portugal;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
972;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
955;Lithuania;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
57;Portugal;184;1;Basic;Statistics;Statistics;Frequency,Sample,Stem and Leaf diagram,Variance,Standard deviation,Relative frequency
1082;Portugal;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
853;Italy;949;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1173;Portugal;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
855;Italy;950;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
71;Portugal;614;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
890;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1087;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
884;Italy;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
885;Italy;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
175;Italy;327;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1291;Italy;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1282;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
376;Portugal;354;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
741;Ireland;933;0;Basic;Graph Theory;Graph Theory;Planar graph
359;Portugal;347;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
387;Portugal;449;1;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
1219;Portugal;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
1277;Portugal;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
852;Italy;241;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
956;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
378;Portugal;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
853;Italy;222;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
466;Portugal;333;0;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
913;Ireland;1151;1;Basic;Set Theory;Set Theory;Subset
483;Portugal;877;1;Basic;Differentiation;Partial Differentiation;Second order
1292;Italy;594;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Spectrum,Characteristic polynomial,Diagonalization,Eigenvalue
175;Italy;1485;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
1220;Slovenia;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
378;Portugal;573;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Locus,Scalar product,Cross product,Collinearity
1292;Italy;608;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector
466;Portugal;345;0;Advanced;Complex Numbers;Complex Numbers;Polar representation,Trigonometric form,Modulus of a complex number,Operations with complex numbers,Algebraic form,Principal argument,De Moivre formulas
414;Portugal;227;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
37;Portugal;911;0;Basic;Optimization;Nonlinear Optimization;Minimum,Stationary point,Maximum,Saddle point,Optimal solution
1543;Portugal;1110;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
470;Portugal;346;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
128;Lithuania;337;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form,Operations with complex numbers,Modulus of a complex number
1243;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
969;Romania;449;1;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
405;Portugal;611;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
509;Portugal;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1219;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
899;Lithuania;446;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
955;Lithuania;1097;1;Basic;Numerical Methods;Numerical Methods;Lagrange's interpolation,Polynomial interpolation
899;Lithuania;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1044;Lithuania;873;1;Basic;Differentiation;Partial Differentiation;First order
1525;Portugal;281;0;Basic;Optimization;Linear Optimization;Linear programming
965;Portugal;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
466;Portugal;340;0;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers,Conjugate number
240;Lithuania;920;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
890;Portugal;430;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1247;Portugal;355;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
626;Italy;717;1;Basic;Differentiation;Derivatives;Trigonometric rules,Quotient rule
85;Lithuania;1147;1;Basic;Set Theory;Set Theory;Subset
1220;Slovenia;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1252;Portugal;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
955;Lithuania;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
913;Ireland;244;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
175;Italy;1089;1;Basic;Numerical Methods;Numerical Methods;First order,Second order
576;Ireland;576;0;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
352;Portugal;657;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
1023;Lithuania;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
511;Portugal;524;1;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Rhombus
1518;Portugal;301;0;Basic;Probability ;Probability ;Sample space,Event
1517;Portugal;628;1;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue,Diagonalization
351;Portugal;145;1;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
394;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
411;Portugal;594;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Spectrum,Characteristic polynomial,Diagonalization,Eigenvalue
625;Russian Federation;793;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
913;Ireland;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1322;Italy;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
509;Portugal;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
955;Lithuania;1251;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
181;Italy;918;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
351;Portugal;101;0;Advanced;Differentiation;Derivatives;Trigonometric rules,Product rule,Logarithmic rule,Exponential rule
884;Italy;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
851;Italy;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1229;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
973;Portugal;950;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1340;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1518;Portugal;789;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
979;Portugal;1106;1;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
986;Portugal;90;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1148;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1029;Lithuania;998;0;Basic;Differentiation;Partial Differentiation;First order
426;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
1322;Italy;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
457;Portugal;347;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
1324;Italy;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
643;Italy;201;1;Basic;Statistics;Statistics;Chi square distribution,Student distribution,Quantile,Hypothesis testing
1220;Slovenia;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
988;Portugal;418;1;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
1220;Slovenia;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
204;Lithuania;796;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Logarithmic function,Exponential function,Simplify expressions
890;Portugal;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
426;Portugal;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
204;Lithuania;108;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
898;Portugal;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
525;Portugal;108;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1288;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1511;Portugal;551;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality
689;Portugal;821;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Maximum,Second derivative test,Stationary point,Unconstrained optimization,Saddle point
525;Portugal;523;0;Basic;Fundamental Mathematics;Elementary Geometry;Geometrical figures,Polygons
1093;Portugal;292;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
91;Lithuania;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
551;Lithuania;561;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
1219;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
840;Italy;446;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
660;Portugal;180;1;Basic;Statistics;Statistics;Mean,Median,Mode
198;Italy;368;0;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids,Regular polygon
986;Portugal;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
899;Lithuania;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1311;Italy;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
411;Portugal;336;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Modulus of a complex number,Imaginary part
511;Portugal;513;0;Basic;Fundamental Mathematics;Elementary Geometry;Triangle inequality,Triangles
664;Portugal;181;1;Basic;Statistics;Statistics;Quantile,Frequency,Sample,Mean,Variance,Standard deviation,Median,Mode
1444;Portugal;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
175;Italy;1102;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
41;Portugal;112;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
37;Portugal;860;0;Basic;Optimization;Nonlinear Optimization;Saddle point,Optimal solution,Minimum,Maximum,Stationary point
1487;Portugal;1052;0;Basic;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Conjugate number,Algebraic form,Operations with complex numbers,Real part,Equations involving complex numbers
80;Lithuania;215;1;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Inconsistent system,Solution of linear system
1220;Slovenia;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
1334;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
473;Portugal;381;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
81;Lithuania;385;0;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1220;Slovenia;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1047;Lithuania;885;0;Basic;Differentiation;Partial Differentiation;Second order,First order
1087;Portugal;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
988;Portugal;420;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1220;Slovenia;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1288;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
582;Lithuania;568;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
1023;Lithuania;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1274;Portugal;102;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
769;Portugal;339;0;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation
394;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
1252;Portugal;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1322;Italy;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
91;Lithuania;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
552;Portugal;146;0;Basic;Differential Equations;Differential Equations;Separable variables equation
509;Portugal;228;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
36;Portugal;1163;0;Basic;Set Theory;Set Theory;Subset
128;Lithuania;339;0;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation
972;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
643;Italy;181;0;Basic;Statistics;Statistics;Quantile,Frequency,Sample,Mean,Variance,Standard deviation,Median,Mode
175;Italy;339;1;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation
576;Ireland;559;0;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
407;Portugal;100;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Power rule
176;Italy;795;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
1220;Slovenia;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1029;Lithuania;1001;0;Basic;Differentiation;Partial Differentiation;Power rule,Trigonometric rules,Logarithmic rule
884;Italy;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
71;Portugal;337;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form,Operations with complex numbers,Modulus of a complex number
403;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
633;Italy;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
625;Russian Federation;662;1;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
483;Portugal;100;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Power rule
81;Lithuania;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
71;Portugal;271;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
1518;Portugal;297;0;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Event,Axioms of probability
168;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
41;Portugal;512;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangles
1091;Lithuania;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
973;Portugal;1109;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Lagrange's interpolation
1023;Lithuania;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1288;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1308;Italy;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
884;Italy;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
979;Portugal;1097;1;Basic;Numerical Methods;Numerical Methods;Lagrange's interpolation,Polynomial interpolation
625;Russian Federation;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1219;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
884;Italy;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
351;Portugal;118;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
26;Portugal;303;1;Basic;Probability ;Probability ;Addition, multiplication, and total probability rules,Sample space,Event,Axioms of probability
131;Lithuania;471;1;Advanced;Graph Theory;Graph Theory;Simple graph
359;Portugal;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
750;Portugal;925;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Planar graph
972;Portugal;449;0;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
1275;Lithuania;455;0;Basic;Linear Algebra;Vector Spaces;Basis
973;Portugal;951;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1256;Portugal;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
1147;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1143;Portugal;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
986;Portugal;447;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
958;Lithuania;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
64;Portugal;272;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
374;Portugal;350;1;Advanced;Complex Numbers;Complex Numbers;Complex plane 
91;Lithuania;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
633;Italy;439;0;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
181;Italy;919;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1220;Slovenia;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
71;Portugal;634;1;Basic;Linear Algebra;Matrices and Determinants;Determinant properties,Inverse matrix ,Solve matrix equation,Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Commuting matrices,Determinant computation
851;Italy;1208;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
591;Portugal;332;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1269;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
899;Lithuania;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1220;Slovenia;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
1023;Lithuania;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1543;Portugal;1088;0;Basic;Numerical Methods;Numerical Methods;First order,Second order
422;Portugal;137;0;Basic;Linear Algebra;Matrices and Determinants;Matrix equivalent - echelon,Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Linearly independent rows,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
876;Italy;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
852;Italy;221;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
168;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1281;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
91;Lithuania;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
168;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1081;Portugal;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
175;Italy;734;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Exponential rule
375;Portugal;345;1;Advanced;Complex Numbers;Complex Numbers;Polar representation,Trigonometric form,Modulus of a complex number,Operations with complex numbers,Algebraic form,Principal argument,De Moivre formulas
1087;Portugal;454;1;Basic;Linear Algebra;Vector Spaces;Basis
1220;Slovenia;455;0;Basic;Linear Algebra;Vector Spaces;Basis
524;Portugal;788;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Exponential function
483;Portugal;114;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
956;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1312;Portugal;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1087;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
956;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
625;Russian Federation;467;1;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Polygons,Classification of geometrical figures,Geometrical figures
414;Portugal;222;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
884;Italy;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1308;Italy;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1229;Portugal;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1220;Slovenia;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
524;Portugal;241;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
376;Portugal;341;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
1220;Slovenia;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
967;Portugal;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
420;Portugal;125;1;Basic;Linear Algebra;Matrices and Determinants;Determinant properties,Symmetric matrix,Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication
204;Lithuania;521;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Regular polygon
426;Portugal;359;1;Advanced;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
376;Portugal;358;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Conjugate number,Operations with complex numbers,Real part
967;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
913;Ireland;447;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1292;Italy;951;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
80;Lithuania;528;1;Basic;Integration;Double Integration;Changing order of integration,Cartesian coordinates
26;Portugal;560;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality
394;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1411;Portugal;306;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
176;Italy;97;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
91;Lithuania;449;1;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
407;Portugal;250;0;Basic;Differentiation;Derivatives;Quotient rule,Product rule,Trigonometric rules
37;Portugal;367;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometrical figures
1220;Slovenia;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
1023;Lithuania;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1334;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
175;Italy;1090;1;Basic;Numerical Methods;Numerical Methods;Nonlinear equation,Newton’s method
1194;Portugal;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
197;Portugal;113;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
71;Portugal;97;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
1075;Portugal;873;0;Basic;Differentiation;Partial Differentiation;First order
626;Italy;250;0;Basic;Differentiation;Derivatives;Quotient rule,Product rule,Trigonometric rules
91;Lithuania;493;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangles,Triangle inequality
351;Portugal;484;0;Advanced;Differentiation;Derivatives;Power rule,Product rule
699;Portugal;193;1;Basic;Statistics;Statistics;Standard deviation,Variance,Median,Frequency,Mode,Outliers,Quantile,Interquartile range,Population,Data type,Sample,Relative frequency,Mean
351;Portugal;118;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
178;Italy;147;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
712;Portugal;204;1;Basic;Statistics;Statistics;Student distribution,Hypothesis testing
1220;Slovenia;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
525;Portugal;512;0;Basic;Fundamental Mathematics;Elementary Geometry;Triangles
1220;Slovenia;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
411;Portugal;341;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
1351;Portugal;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1241;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1173;Portugal;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
483;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
473;Portugal;446;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
165;Portugal;524;0;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Rhombus
582;Lithuania;551;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality
374;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
91;Lithuania;420;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1071;Lithuania;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
692;Portugal;193;0;Basic;Statistics;Statistics;Standard deviation,Variance,Median,Frequency,Mode,Outliers,Quantile,Interquartile range,Population,Data type,Sample,Relative frequency,Mean
626;Italy;925;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Planar graph
374;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1036;Lithuania;998;0;Basic;Differentiation;Partial Differentiation;First order
311;Ireland;639;1;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Determinant computation,Determinant properties,Matrix operations
853;Italy;89;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1220;Slovenia;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1271;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1146;Portugal;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
61;Portugal;169;1;Basic;Differential Equations;Differential Equations;Linear differential equation
1146;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1075;Portugal;878;0;Basic;Differentiation;Partial Differentiation;Second order,First order
415;Portugal;339;0;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation
986;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1533;Portugal;559;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
36;Portugal;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1428;Portugal;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
700;Portugal;204;1;Basic;Statistics;Statistics;Student distribution,Hypothesis testing
1220;Slovenia;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
457;Portugal;348;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Complex plane ,Real part
71;Portugal;561;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
1288;Portugal;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
71;Portugal;717;1;Basic;Differentiation;Derivatives;Trigonometric rules,Quotient rule
1109;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
634;Italy;382;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
855;Italy;246;0;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
1322;Italy;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1179;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
376;Portugal;1054;1;Advanced;Complex Numbers;Complex Numbers;Equations involving complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Algebraic form,Real part
1288;Portugal;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1564;Portugal;918;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
511;Portugal;639;1;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Determinant computation,Determinant properties,Matrix operations
986;Portugal;430;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
731;Portugal;204;1;Basic;Statistics;Statistics;Student distribution,Hypothesis testing
483;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1075;Portugal;258;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
511;Portugal;636;0;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication
457;Portugal;340;1;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers,Conjugate number
1517;Portugal;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
403;Portugal;448;1;Advanced;Linear Algebra;Vector Spaces;Subspace
973;Portugal;239;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
986;Portugal;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
898;Portugal;1012;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
85;Lithuania;1142;1;Basic;Set Theory;Set Theory;Subset
853;Italy;218;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
576;Ireland;570;1;Advanced;Analytic Geometry;Analytic Geometry;Distance,Orthogonal projection,Orthogonality
1542;Portugal;1109;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Lagrange's interpolation
1220;Slovenia;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
657;Ireland;204;1;Basic;Statistics;Statistics;Student distribution,Hypothesis testing
511;Portugal;243;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1166;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
955;Lithuania;1117;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
884;Italy;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
142;Portugal;788;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Exponential function
1076;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
986;Portugal;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
966;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
731;Portugal;178;0;Basic;Statistics;Statistics;Mean,Variance,Standard deviation,Median,Mode
958;Lithuania;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1150;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
899;Lithuania;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1334;Portugal;782;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
168;Portugal;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
91;Lithuania;514;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangle inequality,Triangles
1543;Portugal;1099;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1286;Italy;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1049;Lithuania;874;0;Basic;Differentiation;Partial Differentiation;Power rule,Trigonometric rules,Logarithmic rule
1256;Portugal;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
524;Portugal;611;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1185;Portugal;385;1;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
913;Ireland;1099;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1290;Italy;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
509;Portugal;641;1;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties,Hermitian matrix,Symmetric matrix,Matrix multiplication,Linearly independent rows,Matrix operations
902;Lithuania;204;1;Basic;Statistics;Statistics;Student distribution,Hypothesis testing
464;Portugal;346;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
174;Portugal;730;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
638;Italy;180;0;Basic;Statistics;Statistics;Mean,Median,Mode
1428;Portugal;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
965;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
155;Spain;82;0;Basic;Differentiation;Derivatives;Logarithmic rule,Power rule,Exponential rule,Trigonometric rules,Product rule
1023;Lithuania;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
311;Ireland;650;0;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties
359;Portugal;612;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
151;Portugal;120;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
407;Portugal;512;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangles
351;Portugal;142;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
913;Ireland;204;0;Basic;Statistics;Statistics;Student distribution,Hypothesis testing
80;Lithuania;608;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector
509;Portugal;493;0;Basic;Fundamental Mathematics;Elementary Geometry;Triangles,Triangle inequality
155;Spain;169;1;Basic;Differential Equations;Differential Equations;Linear differential equation
1481;Portugal;85;0;Basic;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
1157;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
958;Lithuania;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
633;Italy;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
1253;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
349;Portugal;273;1;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
1220;Slovenia;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1220;Slovenia;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1289;Italy;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1244;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
349;Portugal;147;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
37;Portugal;1088;0;Basic;Numerical Methods;Numerical Methods;First order,Second order
1289;Italy;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1077;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1044;Lithuania;258;1;Basic;Differentiation;Partial Differentiation;First order,Gradient
85;Lithuania;387;0;Basic;Graph Theory;Graph Theory;Shortest path,Tree,Spanning tree,Path
374;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
90;Lithuania;648;1;Advanced;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
956;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1156;Portugal;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
181;Italy;981;0;Basic;Real Functions of a single variable;Limits and Continuity;Limits
1274;Portugal;787;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Logarithmic function
884;Italy;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
80;Lithuania;1061;0;Basic;Complex Numbers;Complex Numbers;Complex plane 
415;Portugal;133;1;Advanced;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
1219;Portugal;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
175;Italy;1111;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1220;Slovenia;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
26;Portugal;695;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product
414;Portugal;243;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1292;Italy;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
176;Italy;798;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
91;Lithuania;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
625;Russian Federation;520;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1150;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
349;Portugal;273;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
1039;Lithuania;998;0;Basic;Differentiation;Partial Differentiation;First order
1252;Portugal;454;1;Basic;Linear Algebra;Vector Spaces;Basis
1324;Italy;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
955;Lithuania;381;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
913;Ireland;446;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
175;Italy;1101;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
414;Portugal;245;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1273;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
175;Italy;339;1;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation
1517;Portugal;288;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
969;Romania;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
28;Portugal;566;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Orthogonality,Locus
675;Portugal;80;1;Basic;Statistics;Statistics;Population,Variance,Median,Standard deviation,Mode,Quantile,Sample,Mean
1220;Slovenia;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
955;Lithuania;1088;1;Basic;Numerical Methods;Numerical Methods;First order,Second order
509;Portugal;367;0;Basic;Fundamental Mathematics;Elementary Geometry;Geometrical figures
1525;Portugal;318;0;Advanced;Probability ;Probability ;Axioms of probability,Event,Addition, multiplication, and total probability rules,Sample space
1220;Slovenia;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1047;Lithuania;908;0;Basic;Differentiation;Partial Differentiation;Gradient,Directional derivative
1093;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
913;Ireland;193;1;Basic;Statistics;Statistics;Standard deviation,Variance,Median,Frequency,Mode,Outliers,Quantile,Interquartile range,Population,Data type,Sample,Relative frequency,Mean
91;Lithuania;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
852;Italy;217;0;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
415;Portugal;638;1;Advanced;Linear Algebra;Matrices and Determinants;Solve matrix equation,Matrix equivalent - echelon,Inverse matrix ,Determinant computation,Determinant properties,Matrix rank,Hermitian matrix,Matrix operations,Symmetric matrix,Matrix multiplication,Linearly independent rows,Commuting matrices
913;Ireland;234;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
890;Portugal;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
36;Portugal;1147;1;Basic;Set Theory;Set Theory;Subset
349;Portugal;730;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
955;Lithuania;1214;0;Basic;Numerical Methods;Numerical Methods;Mean,Median,Outliers,Interquartile range
1173;Portugal;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
1173;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
168;Portugal;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
218;Lithuania;114;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
853;Italy;222;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
851;Italy;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1517;Portugal;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1220;Slovenia;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
37;Portugal;394;1;Basic;Integration;Integration Techniques;Substitution
1322;Italy;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1080;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1283;Italy;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
71;Portugal;668;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
969;Romania;419;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
131;Lithuania;479;1;Advanced;Graph Theory;Graph Theory;Tree,Simple graph,Spanning tree,Path
1543;Portugal;1116;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
750;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
884;Italy;432;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
128;Lithuania;122;0;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication,Determinant properties,Symmetric matrix
510;Portugal;798;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1291;Italy;306;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
340;Portugal;488;0;Basic;Probability ;Probability ;Axioms of probability,Event,Addition, multiplication, and total probability rules,Sample space
1087;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1220;Slovenia;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
168;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1185;Portugal;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
359;Portugal;798;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1486;Portugal;796;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Logarithmic function,Exponential function,Simplify expressions
576;Ireland;547;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Orthogonality,Scalar product
1244;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
525;Portugal;666;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
855;Italy;917;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1256;Portugal;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1079;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
240;Lithuania;921;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
633;Italy;432;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
1220;Slovenia;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
972;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1322;Italy;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
851;Italy;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1252;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
641;Italy;193;0;Basic;Statistics;Statistics;Standard deviation,Variance,Median,Frequency,Mode,Outliers,Quantile,Interquartile range,Population,Data type,Sample,Relative frequency,Mean
1565;Portugal;686;0;Basic;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
972;Portugal;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
634;Italy;142;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
599;Italy;621;1;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Characteristic polynomial,Eigenvalue,Diagonalization,Eigenvector,Spectrum
1275;Lithuania;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
422;Portugal;132;0;Advanced;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
1505;Portugal;299;1;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Event,Axioms of probability
751;Lithuania;565;0;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonal projection,Orthogonality,Collinearity,Locus
91;Lithuania;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1543;Portugal;1089;0;Basic;Numerical Methods;Numerical Methods;First order,Second order
239;Lithuania;717;0;Basic;Differentiation;Derivatives;Trigonometric rules,Quotient rule
71;Portugal;1100;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
966;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
80;Lithuania;567;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a line,Orthogonality,Collinearity
414;Portugal;218;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1220;Slovenia;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
37;Portugal;1226;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Exponential rule
426;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
175;Italy;1489;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Modulus of a complex number,Algebraic form,Real part,Equations involving complex numbers,Imaginary part
1191;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
52;Portugal;458;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Geometric transformations,Geometrical figures
1322;Italy;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
974;Portugal;1251;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
884;Italy;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
966;Portugal;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
168;Portugal;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
885;Italy;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1308;Italy;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
80;Lithuania;342;0;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Modulus of a complex number,Algebraic form
1564;Portugal;982;1;Basic;Real Functions of a single variable;Limits and Continuity;Limits
176;Italy;1226;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Exponential rule
175;Italy;611;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
26;Portugal;489;0;Basic;Probability ;Probability ;Axioms of probability,Event,Addition, multiplication, and total probability rules,Sample space
1220;Slovenia;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1289;Italy;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1087;Portugal;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
168;Portugal;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
167;Portugal;451;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
509;Portugal;89;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
972;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1022;Lithuania;743;0;Basic;Optimization;Linear Optimization;Duality theory,Linear programming
750;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
890;Portugal;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
91;Lithuania;508;1;Advanced;Fundamental Mathematics;Elementary Geometry;Symmetry
1163;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
483;Portugal;524;1;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Rhombus
376;Portugal;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
80;Lithuania;652;1;Basic;Linear Algebra;Matrices and Determinants;Linearly independent rows,Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties
972;Portugal;289;0;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
625;Russian Federation;798;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
466;Portugal;358;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Conjugate number,Operations with complex numbers,Real part
1023;Lithuania;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1039;Lithuania;876;0;Basic;Differentiation;Partial Differentiation;Directional derivative,Gradient,First order,Second order
91;Lithuania;521;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Regular polygon
1219;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
967;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
851;Italy;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1517;Portugal;779;0;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
415;Portugal;338;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form
71;Portugal;1088;1;Basic;Numerical Methods;Numerical Methods;First order,Second order
411;Portugal;853;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Continuity,Limits
37;Portugal;467;1;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Polygons,Classification of geometrical figures,Geometrical figures
1557;Portugal;674;1;Advanced;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
201;Lithuania;612;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
409;Portugal;338;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form
411;Portugal;851;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Continuity,Limits
1079;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
69;Portugal;564;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonality
380;Portugal;357;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
451;Portugal;298;0;Basic;Probability ;Probability ;Event,Axioms of probability
1082;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
953;Lithuania;184;1;Basic;Statistics;Statistics;Frequency,Sample,Stem and Leaf diagram,Variance,Standard deviation,Relative frequency
1147;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
151;Portugal;120;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
464;Portugal;340;0;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers,Conjugate number
1220;Slovenia;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
80;Lithuania;698;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Orthogonal projection,Distance
1517;Portugal;288;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1220;Slovenia;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
643;Italy;80;0;Basic;Statistics;Statistics;Population,Variance,Median,Standard deviation,Mode,Quantile,Sample,Mean
1080;Portugal;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
576;Ireland;554;0;Basic;Analytic Geometry;Analytic Geometry;Scalar product,Orthogonality,Orthogonal projection,Distance
988;Portugal;244;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
26;Portugal;215;1;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Inconsistent system,Solution of linear system
576;Ireland;569;0;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance,Scalar product,Cross product,Orthogonality,Collinearity
1543;Portugal;1101;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
552;Portugal;159;0;Basic;Differential Equations;Differential Equations;Linear differential equation,Integral curve,Cauchy problem
349;Portugal;661;1;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
1284;Italy;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
239;Lithuania;661;1;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
899;Lithuania;454;0;Basic;Linear Algebra;Vector Spaces;Basis
1049;Lithuania;908;0;Basic;Differentiation;Partial Differentiation;Gradient,Directional derivative
913;Ireland;305;0;Basic;Probability ;Probability ;Event,Axioms of probability,Addition, multiplication, and total probability rules,Sample space
407;Portugal;519;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
91;Lithuania;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
168;Portugal;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
394;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
175;Italy;1096;1;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1334;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1080;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
175;Italy;332;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1363;Portugal;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1044;Lithuania;873;1;Basic;Differentiation;Partial Differentiation;First order
985;Romania;95;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule,Exponential rule
509;Portugal;136;0;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
1286;Italy;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
457;Portugal;350;1;Advanced;Complex Numbers;Complex Numbers;Complex plane 
1143;Portugal;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1023;Lithuania;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
525;Portugal;507;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry
1220;Slovenia;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
457;Portugal;348;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Complex plane ,Real part
1220;Slovenia;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1023;Lithuania;455;1;Basic;Linear Algebra;Vector Spaces;Basis
1157;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
700;Portugal;193;1;Basic;Statistics;Statistics;Standard deviation,Variance,Median,Frequency,Mode,Outliers,Quantile,Interquartile range,Population,Data type,Sample,Relative frequency,Mean
1564;Portugal;82;0;Basic;Differentiation;Derivatives;Logarithmic rule,Power rule,Exponential rule,Trigonometric rules,Product rule
1220;Slovenia;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
414;Portugal;948;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
1505;Portugal;283;0;Basic;Optimization;Linear Optimization;Excel solver add-in,Simplex method,Linear programming
81;Lithuania;502;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry,Geometric transformations
181;Italy;84;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Indeterminate forms,Limits
1087;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
37;Portugal;192;0;Basic;Integration;Integration Techniques;Trigonometric substitution,Simple integration
1220;Slovenia;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1080;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
175;Italy;1475;1;Basic;Complex Numbers;Complex Numbers;Algebraic form,Real part,Equations involving complex numbers,Imaginary part,Conjugate number,Modulus of a complex number
1043;Lithuania;999;0;Basic;Differentiation;Partial Differentiation;First order
509;Portugal;364;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids,Geometrical figures,Classification of geometric solids
1093;Portugal;451;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1044;Lithuania;908;0;Basic;Differentiation;Partial Differentiation;Gradient,Directional derivative
1517;Portugal;777;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1518;Portugal;138;1;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Determinant computation,Determinant properties,Inverse matrix 
876;Italy;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
1322;Italy;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
840;Italy;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
511;Portugal;917;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1182;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1076;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1219;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1256;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
966;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
422;Portugal;130;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
1219;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
510;Portugal;221;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
41;Portugal;468;0;Basic;Graph Theory;Graph Theory;Simple graph
1220;Slovenia;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1220;Slovenia;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1564;Portugal;97;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
91;Lithuania;419;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
483;Portugal;348;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Complex plane ,Real part
1220;Slovenia;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
511;Portugal;245;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1427;Portugal;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1024;Lithuania;256;0;Basic;Differentiation;Partial Differentiation;First order
1044;Lithuania;263;1;Basic;Differentiation;Partial Differentiation;First order
1283;Italy;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
455;Portugal;630;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue
1487;Portugal;936;1;Basic;Graph Theory;Graph Theory;Chromatic number
1220;Slovenia;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
956;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
175;Italy;614;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
36;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
1220;Slovenia;785;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1109;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1277;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1427;Portugal;385;1;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
511;Portugal;950;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1220;Slovenia;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
175;Italy;104;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1182;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
41;Portugal;146;0;Basic;Differential Equations;Differential Equations;Separable variables equation
406;Portugal;90;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1023;Lithuania;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1411;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
151;Portugal;108;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
175;Italy;611;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
851;Italy;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
483;Portugal;667;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1080;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
175;Italy;793;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
885;Italy;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
855;Italy;215;0;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Inconsistent system,Solution of linear system
151;Portugal;112;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
548;Portugal;492;0;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Axioms of probability,Event
1505;Portugal;1009;0;Basic;Optimization;Linear Optimization;Transportation problem,Excel solver add-in,Simplex method,Linear programming
510;Portugal;120;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1332;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
90;Lithuania;644;0;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Determinant computation,Matrix rank,Inverse matrix ,Determinant properties,Hermitian matrix,Matrix multiplication,Linearly independent rows,Symmetric matrix,Matrix operations
884;Italy;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1274;Portugal;113;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1517;Portugal;381;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
582;Lithuania;357;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
884;Italy;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1332;Portugal;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
90;Lithuania;338;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form
168;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
851;Italy;865;1;Basic;Optimization;Nonlinear Optimization;Lagrange multipliers,Minimum,Maximum,Stationary point
199;Lithuania;613;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1126;Portugal;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
81;Lithuania;553;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Distance,Scalar product
725;Portugal;191;0;Basic;Statistics;Statistics;Median,Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance
876;Italy;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1077;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
420;Portugal;337;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form,Operations with complex numbers,Modulus of a complex number
41;Portugal;332;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
876;Italy;424;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1334;Portugal;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
168;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
71;Portugal;134;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
1220;Slovenia;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1509;Portugal;981;1;Basic;Real Functions of a single variable;Limits and Continuity;Limits
378;Portugal;454;1;Basic;Linear Algebra;Vector Spaces;Basis
969;Romania;424;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1289;Italy;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
174;Portugal;788;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Exponential function
1220;Slovenia;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1220;Slovenia;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
750;Portugal;918;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1481;Portugal;773;0;Basic;Probability ;Probability ;Event,Sample space,Addition, multiplication, and total probability rules,Axioms of probability
1220;Slovenia;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
90;Lithuania;326;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part
1275;Lithuania;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1195;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1274;Portugal;668;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
510;Portugal;952;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
175;Italy;1110;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
699;Portugal;81;0;Basic;Statistics;Statistics;Mean,Median,Mode
41;Portugal;497;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1332;Portugal;446;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
359;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
26;Portugal;567;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a line,Orthogonality,Collinearity
468;Portugal;351;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Imaginary part,Complex plane ,Operations with complex numbers,Real part,Principal argument,De Moivre formulas
168;Portugal;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
552;Portugal;892;1;Basic;Differential Equations;Differential Equations;Linear differential equation
1220;Slovenia;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
969;Romania;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
1091;Lithuania;290;0;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1333;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
91;Lithuania;447;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1219;Portugal;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
378;Portugal;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
90;Lithuania;128;0;Advanced;Linear Algebra;Matrices and Determinants;Matrix multiplication,Determinant computation,Determinant properties,Symmetric matrix,Hermitian matrix,Inverse matrix ,Linearly independent rows,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Matrix equivalent - echelon
1286;Italy;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
176;Italy;919;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
884;Italy;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
852;Italy;89;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
37;Portugal;880;1;Advanced;Differentiation;Partial Differentiation;First order,Directional derivative,Gradient
1077;Portugal;419;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
1081;Portugal;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
851;Italy;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
201;Lithuania;120;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
511;Portugal;652;1;Basic;Linear Algebra;Matrices and Determinants;Linearly independent rows,Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties
394;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
165;Portugal;502;0;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry,Geometric transformations
966;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1220;Slovenia;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1044;Lithuania;885;0;Basic;Differentiation;Partial Differentiation;Second order,First order
380;Portugal;866;0;Basic;Optimization;Nonlinear Optimization;Stationary point,Maximum,Saddle point,Optimal solution,Minimum
1109;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1272;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
406;Portugal;89;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1518;Portugal;644;1;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Determinant computation,Matrix rank,Inverse matrix ,Determinant properties,Hermitian matrix,Matrix multiplication,Linearly independent rows,Symmetric matrix,Matrix operations
890;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
168;Portugal;424;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1044;Lithuania;260;1;Basic;Differentiation;Partial Differentiation;First order,Gradient
751;Lithuania;559;0;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
1093;Portugal;446;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1195;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1324;Italy;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
483;Portugal;349;1;Advanced;Complex Numbers;Complex Numbers;Complex plane 
1126;Portugal;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1148;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1147;Portugal;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1220;Slovenia;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1087;Portugal;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
913;Ireland;1252;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
455;Portugal;123;1;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication,Determinant properties,Symmetric matrix
422;Portugal;135;0;Basic;Linear Algebra;Matrices and Determinants;Symmetric matrix,Determinant computation,Determinant properties
853;Italy;241;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1220;Slovenia;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
853;Italy;952;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
890;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
913;Ireland;1125;1;Basic;Set Theory;Set Theory;Union of sets,Venn diagram,Complement of a set
455;Portugal;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
1220;Slovenia;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
168;Portugal;408;1;Advanced;Integration;Integration Techniques;Integration by parts
128;Lithuania;327;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
626;Italy;661;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
1242;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
986;Portugal;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
1194;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
899;Lithuania;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
633;Italy;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
378;Portugal;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
969;Romania;447;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1308;Italy;778;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
351;Portugal;720;1;Basic;Differentiation;Derivatives;Quotient rule,Trigonometric rules,Logarithmic rule,Product rule
415;Portugal;136;0;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
712;Portugal;191;0;Basic;Statistics;Statistics;Median,Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance
26;Portugal;566;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Orthogonality,Locus
455;Portugal;644;0;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Determinant computation,Matrix rank,Inverse matrix ,Determinant properties,Hermitian matrix,Matrix multiplication,Linearly independent rows,Symmetric matrix,Matrix operations
376;Portugal;345;1;Advanced;Complex Numbers;Complex Numbers;Polar representation,Trigonometric form,Modulus of a complex number,Operations with complex numbers,Algebraic form,Principal argument,De Moivre formulas
576;Ireland;699;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Locus,Intersection,Cartesian equations of a line
1271;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
524;Portugal;798;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
378;Portugal;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
1157;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
884;Italy;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
1481;Portugal;564;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonality
37;Portugal;331;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
168;Portugal;290;0;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
91;Lithuania;366;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids,Geometrical figures,Classification of geometric solids
1219;Portugal;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
37;Portugal;617;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Spectrum,Eigenvector,Characteristic polynomial
1322;Italy;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
899;Lithuania;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
175;Italy;1120;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
1220;Slovenia;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
344;Portugal;98;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
168;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
509;Portugal;120;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1244;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
451;Portugal;491;1;Advanced;Probability ;Probability ;Addition, multiplication, and total probability rules,Independence,Event
1220;Slovenia;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
988;Portugal;221;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
851;Italy;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
664;Portugal;79;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
1538;Portugal;1086;0;Basic;Numerical Methods;Numerical Methods;First order,Second order
1324;Italy;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
71;Portugal;593;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue
1557;Portugal;829;0;Basic;Differential Equations;Differential Equations;Linear differential equation
1284;Italy;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
979;Portugal;653;1;Basic;Linear Algebra;Matrices and Determinants;Linearly independent rows,Matrix rank
466;Portugal;347;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
510;Portugal;102;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1565;Portugal;85;0;Basic;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
250;Lithuania;246;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
1487;Portugal;475;1;Basic;Graph Theory;Graph Theory;Adjacency matrix
1220;Slovenia;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
855;Italy;952;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1146;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
956;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
36;Portugal;1157;1;Basic;Set Theory;Set Theory;Subset
1044;Lithuania;999;1;Basic;Differentiation;Partial Differentiation;First order
71;Portugal;338;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form
899;Lithuania;432;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
1557;Portugal;925;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Planar graph
985;Romania;788;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Exponential function
551;Lithuania;349;1;Advanced;Complex Numbers;Complex Numbers;Complex plane 
374;Portugal;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1271;Portugal;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1288;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
1300;Italy;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
91;Lithuania;364;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids,Geometrical figures,Classification of geometric solids
1157;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
80;Lithuania;951;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1322;Italy;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1350;Portugal;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1044;Lithuania;883;0;Basic;Differentiation;Partial Differentiation;First order,Directional derivative
683;Ireland;177;0;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
151;Portugal;112;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
175;Italy;1097;1;Basic;Numerical Methods;Numerical Methods;Lagrange's interpolation,Polynomial interpolation
855;Italy;245;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
219;Lithuania;786;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
625;Russian Federation;371;0;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Geometrical figures
202;Lithuania;108;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1487;Portugal;341;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
1564;Portugal;920;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1158;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1252;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1023;Lithuania;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1043;Lithuania;879;0;Basic;Differentiation;Partial Differentiation;First order,Second order
1220;Slovenia;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
751;Lithuania;551;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality
913;Ireland;418;1;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
69;Portugal;573;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Locus,Scalar product,Cross product,Collinearity
181;Italy;920;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
72;Portugal;328;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
422;Portugal;131;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
91;Lithuania;328;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1291;Italy;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
37;Portugal;252;1;Basic;Differentiation;Derivatives;Quotient rule,Product rule,Power rule,Trigonometric rules
1284;Italy;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
406;Portugal;104;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
422;Portugal;641;0;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties,Hermitian matrix,Symmetric matrix,Matrix multiplication,Linearly independent rows,Matrix operations
483;Portugal;717;0;Basic;Differentiation;Derivatives;Trigonometric rules,Quotient rule
955;Lithuania;1251;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
1252;Portugal;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
969;Romania;446;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1093;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
91;Lithuania;514;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangle inequality,Triangles
81;Lithuania;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
1557;Portugal;408;1;Advanced;Integration;Integration Techniques;Integration by parts
351;Portugal;102;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
509;Portugal;916;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Square linear system,Consistent system
1219;Portugal;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
1557;Portugal;693;1;Advanced;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
524;Portugal;635;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
37;Portugal;559;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
37;Portugal;261;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
645;Italy;180;0;Basic;Statistics;Statistics;Mean,Median,Mode
1272;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
37;Portugal;866;0;Basic;Optimization;Nonlinear Optimization;Stationary point,Maximum,Saddle point,Optimal solution,Minimum
969;Romania;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
177;Italy;98;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
1219;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
394;Portugal;358;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Conjugate number,Operations with complex numbers,Real part
200;Lithuania;668;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
37;Portugal;862;0;Basic;Optimization;Nonlinear Optimization;Saddle point,Optimal solution,Minimum,Maximum,Stationary point
955;Lithuania;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
1273;Portugal;419;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
72;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
966;Portugal;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
403;Portugal;333;1;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
176;Italy;720;0;Basic;Differentiation;Derivatives;Quotient rule,Trigonometric rules,Logarithmic rule,Product rule
175;Italy;97;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
1049;Lithuania;275;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
175;Italy;667;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
167;Portugal;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
853;Italy;92;1;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
174;Portugal;82;0;Basic;Differentiation;Derivatives;Logarithmic rule,Power rule,Exponential rule,Trigonometric rules,Product rule
1334;Portugal;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
1220;Slovenia;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1079;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
625;Russian Federation;611;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
511;Portugal;795;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
1146;Portugal;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
511;Portugal;218;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
91;Lithuania;446;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
378;Portugal;548;1;Basic;Analytic Geometry;Analytic Geometry;Collinearity,Distance,Locus,Cross product,Orthogonality,Scalar product
91;Lithuania;338;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form
36;Portugal;145;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
1195;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1311;Italy;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
64;Portugal;118;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
598;Italy;951;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
885;Italy;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1182;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1542;Portugal;1100;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
748;Portugal;947;1;Basic;Graph Theory;Graph Theory;Spanning tree,Shortest path,Path,Tree
751;Lithuania;717;0;Basic;Differentiation;Derivatives;Trigonometric rules,Quotient rule
955;Lithuania;1111;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1220;Slovenia;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1525;Portugal;859;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Second derivative test,Minimum,Maximum,Stationary point,Saddle point
725;Portugal;190;0;Basic;Statistics;Statistics;Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance,Median
852;Italy;245;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
175;Italy;1486;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
483;Portugal;620;1;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Characteristic polynomial,Eigenvalue,Diagonalization,Eigenvector,Spectrum
380;Portugal;904;0;Basic;Differential Equations;Differential Equations;Bernoulli equation,Linear differential equation
406;Portugal;501;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids
582;Lithuania;550;1;Advanced;Analytic Geometry;Analytic Geometry;Cross product,Orthogonality
199;Lithuania;104;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
168;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
956;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1173;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
898;Portugal;278;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1079;Portugal;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
378;Portugal;572;0;Basic;Analytic Geometry;Analytic Geometry;Locus,Scalar product,Cross product,Distance,Collinearity,Orthogonality
1271;Portugal;288;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
684;Ireland;78;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
633;Italy;446;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
41;Portugal;113;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
168;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
625;Russian Federation;787;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Logarithmic function
181;Italy;921;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
91;Lithuania;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
524;Portugal;653;1;Basic;Linear Algebra;Matrices and Determinants;Linearly independent rows,Matrix rank
725;Portugal;78;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
1324;Italy;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1023;Lithuania;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
380;Portugal;157;0;Basic;Differential Equations;Differential Equations;Homogeneous equation,Cauchy problem
1023;Lithuania;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1308;Italy;288;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
986;Portugal;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
468;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1289;Italy;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
128;Lithuania;330;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number
626;Italy;661;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
884;Italy;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1148;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
151;Portugal;113;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
854;Italy;92;1;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
552;Portugal;889;0;Basic;Differential Equations;Differential Equations;Linear differential equation
1080;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1087;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
600;Italy;129;1;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Determinant computation,Determinant properties,Symmetric matrix,Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank
28;Portugal;573;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Locus,Scalar product,Cross product,Collinearity
899;Lithuania;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
972;Portugal;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
689;Portugal;820;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Maximum,Stationary point,Saddle point
64;Portugal;714;1;Basic;Integration;Integration Techniques;Simple integration,Direct inspection
1109;Portugal;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
178;Italy;657;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
71;Portugal;326;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part
899;Lithuania;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
394;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1135;Portugal;777;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
697;Portugal;182;1;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
1487;Portugal;1198;0;Basic;Integration;Definite Integrals;Area of a planar region ,Fundamental theorem of Calculus
625;Russian Federation;663;0;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
166;Portugal;547;0;Basic;Analytic Geometry;Analytic Geometry;Cross product,Orthogonality,Scalar product
175;Italy;1087;1;Basic;Numerical Methods;Numerical Methods;First order,Second order
91;Lithuania;359;1;Advanced;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
1288;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
918;Portugal;401;0;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
1321;Portugal;241;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
176;Italy;113;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
918;Portugal;999;1;Basic;Differentiation;Partial Differentiation;First order
1034;Lithuania;912;0;Basic;Differentiation;Partial Differentiation;Minimum,Stationary point,Maximum,Saddle point,Optimal solution
955;Lithuania;1111;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1197;Slovenia;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
853;Italy;239;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
510;Portugal;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
986;Portugal;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
421;Portugal;326;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part
1542;Portugal;1101;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1525;Portugal;746;0;Advanced;Optimization;Linear Optimization;Duality theory,Excel solver add-in,Simplex method,Linear programming,Sensitivity analysis,Postoptimality analysis
913;Ireland;1100;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1220;Slovenia;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
633;Italy;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
176;Italy;921;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1276;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1220;Slovenia;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1044;Lithuania;1000;0;Basic;Differentiation;Partial Differentiation;First order
128;Lithuania;137;0;Basic;Linear Algebra;Matrices and Determinants;Matrix equivalent - echelon,Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Linearly independent rows,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
1171;Portugal;1015;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
411;Portugal;650;1;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties
986;Portugal;451;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
969;Romania;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
852;Italy;91;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
1322;Italy;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
855;Italy;224;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1220;Slovenia;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
953;Lithuania;202;0;Basic;Statistics;Statistics;Student distribution,Confidence interval,Point estimate,Hypothesis testing
884;Italy;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1081;Portugal;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
41;Portugal;387;0;Basic;Graph Theory;Graph Theory;Shortest path,Tree,Spanning tree,Path
178;Italy;734;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Exponential rule
380;Portugal;1012;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
394;Portugal;352;0;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Operations with complex numbers
37;Portugal;1087;0;Basic;Numerical Methods;Numerical Methods;First order,Second order
359;Portugal;112;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
625;Russian Federation;520;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
899;Lithuania;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1044;Lithuania;260;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
175;Italy;1485;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
625;Russian Federation;460;0;Basic;Fundamental Mathematics;Elementary Geometry;Polyhedrons,Platonic solids,Geometric solids
511;Portugal;789;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
168;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
510;Portugal;220;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
80;Lithuania;730;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
1402;Portugal;288;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
913;Ireland;227;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
91;Lithuania;331;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
166;Portugal;546;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonal projection,Distance,Cross product,Orthogonality
576;Ireland;234;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
409;Portugal;330;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number
1080;Portugal;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
483;Portugal;519;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1557;Portugal;673;0;Advanced;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
1322;Italy;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
168;Portugal;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1173;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
509;Portugal;666;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
955;Lithuania;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
448;Portugal;294;0;Basic;Probability ;Probability ;Event,Axioms of probability,Sample space
979;Portugal;1214;1;Basic;Numerical Methods;Numerical Methods;Mean,Median,Outliers,Interquartile range
524;Portugal;793;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
969;Romania;449;0;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
426;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
85;Lithuania;362;0;Basic;Graph Theory;Graph Theory;Simple graph
1557;Portugal;922;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
374;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1322;Italy;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
349;Portugal;720;0;Basic;Differentiation;Derivatives;Quotient rule,Trigonometric rules,Logarithmic rule,Product rule
406;Portugal;216;0;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
1324;Italy;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
378;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1274;Portugal;666;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
956;Portugal;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
525;Portugal;617;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Spectrum,Eigenvector,Characteristic polynomial
634;Italy;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1149;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1256;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1220;Slovenia;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1147;Portugal;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
625;Russian Federation;102;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1143;Portugal;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
168;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
625;Russian Federation;662;0;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1517;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
409;Portugal;339;0;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation
1289;Italy;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
380;Portugal;349;0;Advanced;Complex Numbers;Complex Numbers;Complex plane 
1082;Portugal;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1219;Portugal;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
913;Ireland;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
168;Portugal;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
168;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1147;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1056;Lithuania;883;0;Basic;Differentiation;Partial Differentiation;First order,Directional derivative
26;Portugal;573;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Locus,Scalar product,Cross product,Collinearity
689;Portugal;865;1;Basic;Optimization;Nonlinear Optimization;Lagrange multipliers,Minimum,Maximum,Stationary point
955;Lithuania;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
176;Italy;918;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
91;Lithuania;507;0;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry
1179;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
41;Portugal;157;1;Basic;Differential Equations;Differential Equations;Homogeneous equation,Cauchy problem
1197;Slovenia;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
311;Ireland;131;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
168;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1049;Lithuania;998;0;Basic;Differentiation;Partial Differentiation;First order
974;Portugal;420;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
81;Lithuania;455;0;Basic;Linear Algebra;Vector Spaces;Basis
80;Lithuania;142;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
26;Portugal;224;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
956;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
985;Romania;114;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1557;Portugal;922;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
415;Portugal;140;1;Advanced;Linear Algebra;Matrices and Determinants;Matrix operations,Inverse matrix 
406;Portugal;651;1;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties
1075;Portugal;1002;1;Basic;Differentiation;Partial Differentiation;First order
1288;Portugal;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
852;Italy;89;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
890;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
525;Portugal;102;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
28;Portugal;179;0;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
1561;Portugal;392;1;Advanced;Integration;Integration Techniques;Substitution
91;Lithuania;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
524;Portugal;229;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
175;Italy;1481;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
524;Portugal;92;0;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
415;Portugal;636;0;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication
509;Portugal;245;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
189;Portugal;250;0;Basic;Differentiation;Derivatives;Quotient rule,Product rule,Trigonometric rules
1220;Slovenia;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
890;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
349;Portugal;272;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
1256;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1023;Lithuania;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
840;Italy;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1312;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
250;Lithuania;640;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
986;Portugal;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1561;Portugal;408;0;Advanced;Integration;Integration Techniques;Integration by parts
151;Portugal;102;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1219;Portugal;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
37;Portugal;1203;0;Basic;Integration;Definite Integrals;Volume of revolution,Fundamental theorem of Calculus
1538;Portugal;1094;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
969;Romania;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
552;Portugal;677;0;Advanced;Real Functions of a single variable;Domain, Image and Graphics;Domain,Image of a function
1079;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
524;Portugal;363;1;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
1351;Portugal;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1292;Italy;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
57;Portugal;1212;1;Basic;Statistics;Statistics;Mean,Median,Outliers,Interquartile range
598;Italy;241;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1220;Slovenia;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
155;Spain;554;0;Basic;Analytic Geometry;Analytic Geometry;Scalar product,Orthogonality,Orthogonal projection,Distance
1135;Portugal;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
128;Lithuania;331;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
625;Russian Federation;612;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1557;Portugal;674;0;Advanced;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
72;Portugal;306;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
918;Portugal;720;0;Basic;Differentiation;Derivatives;Quotient rule,Trigonometric rules,Logarithmic rule,Product rule
175;Italy;1487;1;Basic;Complex Numbers;Complex Numbers;Modulus of a complex number,Algebraic form,Real part,Equations involving complex numbers,Imaginary part,Conjugate number
890;Portugal;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
1481;Portugal;465;0;Basic;Graph Theory;Graph Theory;Adjacency matrix,Simple graph
168;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
876;Italy;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
885;Italy;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1182;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
651;Ireland;79;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
1220;Slovenia;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
972;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
52;Portugal;523;0;Basic;Fundamental Mathematics;Elementary Geometry;Geometrical figures,Polygons
473;Portugal;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
890;Portugal;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1299;Italy;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
168;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
71;Portugal;314;0;Basic;Probability ;Probability ;Event,Sample space
1182;Portugal;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
979;Portugal;1117;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
85;Lithuania;1124;1;Basic;Set Theory;Set Theory;Integration by parts,Substitution,Simple integration,Direct inspection
1363;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
898;Portugal;1015;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
551;Lithuania;355;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
470;Portugal;701;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product,Distance
1230;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
840;Italy;292;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
168;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
36;Portugal;147;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
175;Italy;82;0;Basic;Differentiation;Derivatives;Logarithmic rule,Power rule,Exponential rule,Trigonometric rules,Product rule
91;Lithuania;369;1;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Geometrical figures,Classification of geometrical figures
642;Italy;80;0;Basic;Statistics;Statistics;Population,Variance,Median,Standard deviation,Mode,Quantile,Sample,Mean
852;Italy;916;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Square linear system,Consistent system
525;Portugal;788;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Exponential function
1087;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
81;Lithuania;566;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Orthogonality,Locus
465;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
28;Portugal;336;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Modulus of a complex number,Imaginary part
509;Portugal;597;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Diagonalization,Eigenvalue
890;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
378;Portugal;557;1;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance
81;Lithuania;701;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product,Distance
625;Russian Federation;612;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
884;Italy;449;0;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
1308;Italy;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1220;Slovenia;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
1305;Italy;292;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
840;Italy;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
91;Lithuania;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1322;Italy;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1050;Lithuania;263;0;Basic;Differentiation;Partial Differentiation;First order
374;Portugal;347;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
510;Portugal;787;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Logarithmic function
855;Italy;217;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
1242;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
202;Lithuania;667;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
511;Portugal;131;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
633;Italy;451;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
641;Italy;77;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
91;Lithuania;446;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
174;Portugal;657;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
913;Ireland;1096;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
374;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
625;Russian Federation;786;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
457;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
80;Lithuania;903;1;Basic;Differential Equations;Differential Equations;Separable variables equation
81;Lithuania;572;0;Basic;Analytic Geometry;Analytic Geometry;Locus,Scalar product,Cross product,Distance,Collinearity,Orthogonality
576;Ireland;574;1;Advanced;Analytic Geometry;Analytic Geometry;Collinearity,Orthogonality,Distance,Scalar product
1220;Slovenia;455;1;Basic;Linear Algebra;Vector Spaces;Basis
955;Lithuania;1214;1;Basic;Numerical Methods;Numerical Methods;Mean,Median,Outliers,Interquartile range
599;Italy;608;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector
1220;Slovenia;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1220;Slovenia;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
376;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1289;Italy;779;0;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
1023;Lithuania;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
81;Lithuania;560;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality
638;Italy;187;0;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
1402;Portugal;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
41;Portugal;338;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form
955;Lithuania;288;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1564;Portugal;406;0;Basic;Integration;Integration Techniques;Direct inspection
955;Lithuania;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1411;Portugal;779;1;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
1150;Portugal;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
91;Lithuania;494;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1079;Portugal;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
509;Portugal;668;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
175;Italy;145;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
374;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
535;Portugal;345;0;Advanced;Complex Numbers;Complex Numbers;Polar representation,Trigonometric form,Modulus of a complex number,Operations with complex numbers,Algebraic form,Principal argument,De Moivre formulas
689;Portugal;861;1;Basic;Optimization;Nonlinear Optimization;Saddle point,Optimal solution,Minimum,Maximum,Stationary point
80;Lithuania;796;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Logarithmic function,Exponential function,Simplify expressions
855;Italy;952;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1402;Portugal;381;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1109;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
378;Portugal;698;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Orthogonal projection,Distance
473;Portugal;290;0;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1093;Portugal;419;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
598;Italy;652;1;Basic;Linear Algebra;Matrices and Determinants;Linearly independent rows,Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties
1135;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
411;Portugal;123;0;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication,Determinant properties,Symmetric matrix
376;Portugal;356;0;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers
81;Lithuania;385;0;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
168;Portugal;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
1543;Portugal;1092;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1036;Lithuania;1000;0;Basic;Differentiation;Partial Differentiation;First order
510;Portugal;949;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1135;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
913;Ireland;1098;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1023;Lithuania;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
876;Italy;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
511;Portugal;644;0;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Determinant computation,Matrix rank,Inverse matrix ,Determinant properties,Hermitian matrix,Matrix multiplication,Linearly independent rows,Symmetric matrix,Matrix operations
1289;Italy;292;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
1351;Portugal;292;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
1286;Italy;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1143;Portugal;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
852;Italy;917;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
955;Lithuania;1094;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
91;Lithuania;462;1;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
1071;Lithuania;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
175;Italy;1102;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1284;Italy;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
80;Lithuania;592;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Logarithmic rule,Product rule,Trigonometric rules
250;Lithuania;594;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Spectrum,Characteristic polynomial,Diagonalization,Eigenvalue
359;Portugal;793;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
41;Portugal;494;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
72;Portugal;289;0;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1220;Slovenia;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1322;Italy;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
81;Lithuania;473;1;Advanced;Graph Theory;Graph Theory;Simple graph
142;Portugal;786;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
473;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1220;Slovenia;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
898;Portugal;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
913;Ireland;1086;0;Basic;Numerical Methods;Numerical Methods;First order,Second order
1283;Italy;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
128;Lithuania;141;1;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication
91;Lithuania;510;1;Advanced;Fundamental Mathematics;Elementary Geometry;Symmetry
966;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
511;Portugal;243;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
378;Portugal;697;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Distance,Cross product
376;Portugal;346;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
1077;Portugal;448;0;Advanced;Linear Algebra;Vector Spaces;Subspace
775;Portugal;761;0;Basic;Probability ;Probability ;Event,Sample space,Addition, multiplication, and total probability rules,Axioms of probability
1517;Portugal;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1080;Portugal;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
956;Portugal;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
414;Portugal;90;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1286;Italy;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
167;Portugal;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
979;Portugal;1091;0;Basic;Numerical Methods;Numerical Methods;Nonlinear equation,Newton’s method
239;Lithuania;661;1;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
1219;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
359;Portugal;785;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1308;Italy;278;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1191;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
689;Portugal;858;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Maximum,Stationary point,Saddle point
1487;Portugal;1207;1;Basic;Integration;Definite Integrals;Volume of revolution,Fundamental theorem of Calculus
1276;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
548;Portugal;301;0;Basic;Probability ;Probability ;Sample space,Event
854;Italy;961;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Homogeneous system,Consistent system
91;Lithuania;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1334;Portugal;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1219;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
776;Portugal;550;1;Advanced;Analytic Geometry;Analytic Geometry;Cross product,Orthogonality
1220;Slovenia;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
397;Portugal;354;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
69;Portugal;567;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a line,Orthogonality,Collinearity
576;Ireland;573;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Locus,Scalar product,Cross product,Collinearity
351;Portugal;666;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1286;Italy;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
36;Portugal;272;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
988;Portugal;951;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1095;Portugal;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
1230;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1517;Portugal;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
966;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
913;Ireland;183;1;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
913;Ireland;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
393;Lithuania;355;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
151;Portugal;118;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
411;Portugal;391;0;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
1291;Italy;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
208;Lithuania;129;1;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Determinant computation,Determinant properties,Symmetric matrix,Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank
890;Portugal;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
80;Lithuania;948;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
510;Portugal;90;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
311;Ireland;141;1;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication
509;Portugal;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
128;Lithuania;328;1;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
344;Portugal;611;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
349;Portugal;275;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
851;Italy;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1308;Italy;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
510;Portugal;113;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
349;Portugal;752;1;Basic;Differentiation;Derivatives;Power rule,Quotient rule,Product rule,Trigonometric rules
90;Lithuania;339;1;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation
1281;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
851;Italy;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
155;Spain;146;0;Basic;Differential Equations;Differential Equations;Separable variables equation
890;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
91;Lithuania;464;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Geometrical figures
1353;Portugal;779;1;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
80;Lithuania;611;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
394;Portugal;354;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
979;Portugal;634;0;Basic;Linear Algebra;Matrices and Determinants;Determinant properties,Inverse matrix ,Solve matrix equation,Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Commuting matrices,Determinant computation
91;Lithuania;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
851;Italy;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
638;Italy;81;1;Basic;Statistics;Statistics;Mean,Median,Mode
1518;Portugal;134;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
988;Portugal;239;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1375;Portugal;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
420;Portugal;329;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
28;Portugal;234;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
426;Portugal;340;1;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers,Conjugate number
91;Lithuania;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1173;Portugal;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
36;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1163;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1271;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1044;Lithuania;1000;1;Basic;Differentiation;Partial Differentiation;First order
509;Portugal;650;0;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties
1032;Lithuania;266;0;Basic;Differentiation;Partial Differentiation;First order,Second order
483;Portugal;504;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry,Geometric transformations
36;Portugal;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
91;Lithuania;510;0;Advanced;Fundamental Mathematics;Elementary Geometry;Symmetry
1091;Lithuania;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
464;Portugal;347;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
359;Portugal;505;0;Basic;Fundamental Mathematics;Elementary Geometry;Triangles
85;Lithuania;1139;0;Basic;Set Theory;Set Theory;Subset
913;Ireland;299;0;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Event,Axioms of probability
1109;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
80;Lithuania;742;0;Basic;Optimization;Linear Optimization;Duality theory,Linear programming
26;Portugal;869;0;Basic;Differential Equations;Differential Equations;Separable variables equation
177;Italy;97;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
969;Romania;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
57;Portugal;78;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
955;Lithuania;1104;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1252;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
582;Lithuania;349;1;Advanced;Complex Numbers;Complex Numbers;Complex plane 
1220;Slovenia;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
380;Portugal;891;0;Basic;Differential Equations;Differential Equations;Linear differential equation
1288;Portugal;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
751;Lithuania;142;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
455;Portugal;394;1;Basic;Integration;Integration Techniques;Substitution
422;Portugal;124;1;Advanced;Linear Algebra;Matrices and Determinants;Symmetric matrix,Inverse matrix ,Hermitian matrix,Commuting matrices,Linearly independent rows,Solve matrix equation,Matrix operations,Matrix rank,Matrix equivalent - echelon,Determinant computation,Matrix multiplication,Determinant properties
71;Portugal;147;1;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
1044;Lithuania;269;1;Basic;Differentiation;Partial Differentiation;First order,Second order
918;Portugal;259;1;Basic;Differentiation;Partial Differentiation;First order,Gradient
966;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1518;Portugal;643;1;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties,Hermitian matrix,Matrix multiplication,Linearly independent rows,Symmetric matrix,Matrix operations
473;Portugal;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
899;Lithuania;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
853;Italy;948;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
1351;Portugal;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
168;Portugal;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
91;Lithuania;345;1;Advanced;Complex Numbers;Complex Numbers;Polar representation,Trigonometric form,Modulus of a complex number,Operations with complex numbers,Algebraic form,Principal argument,De Moivre formulas
168;Portugal;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1126;Portugal;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
625;Russian Federation;120;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
918;Portugal;1000;0;Basic;Differentiation;Partial Differentiation;First order
1324;Italy;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
411;Portugal;603;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector,Spectrum,Characteristic polynomial
955;Lithuania;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
852;Italy;916;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Square linear system,Consistent system
393;Lithuania;357;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
426;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1332;Portugal;430;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
351;Portugal;255;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Logarithmic rule
168;Portugal;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
168;Portugal;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
483;Portugal;627;1;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue,Diagonalization
483;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
776;Portugal;576;0;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
1220;Slovenia;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
860;Italy;234;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
511;Portugal;794;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
876;Italy;454;1;Basic;Linear Algebra;Vector Spaces;Basis
1130;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
90;Lithuania;135;0;Basic;Linear Algebra;Matrices and Determinants;Symmetric matrix,Determinant computation,Determinant properties
979;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
664;Portugal;185;1;Basic;Statistics;Statistics;Frequency,Quantile,Mean,Variance,Median,Mode
72;Portugal;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
625;Russian Federation;524;1;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Rhombus
551;Lithuania;558;0;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
645;Italy;178;1;Basic;Statistics;Statistics;Mean,Variance,Standard deviation,Median,Mode
1284;Italy;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
775;Portugal;488;0;Basic;Probability ;Probability ;Axioms of probability,Event,Addition, multiplication, and total probability rules,Sample space
420;Portugal;647;0;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Symmetric matrix,Matrix operations
80;Lithuania;568;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
853;Italy;90;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
852;Italy;242;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
168;Portugal;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
200;Lithuania;112;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
91;Lithuania;640;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
1284;Italy;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1163;Portugal;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1282;Portugal;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
198;Italy;521;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Regular polygon
576;Ireland;575;1;Advanced;Analytic Geometry;Analytic Geometry;Orthogonality,Orthogonal projection,Cross product,Scalar product
406;Portugal;462;1;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
1135;Portugal;381;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
955;Lithuania;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
71;Portugal;253;0;Basic;Differentiation;Derivatives;Logarithmic rule,Trigonometric rules
1402;Portugal;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
625;Russian Federation;792;0;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Logarithmic function
851;Italy;963;0;Basic;Optimization;Nonlinear Optimization;Simplex method,Duality theory
1543;Portugal;1086;0;Basic;Numerical Methods;Numerical Methods;First order,Second order
899;Lithuania;454;0;Basic;Linear Algebra;Vector Spaces;Basis
1081;Portugal;451;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1081;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
525;Portugal;611;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1291;Italy;385;0;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
168;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
85;Lithuania;475;0;Basic;Graph Theory;Graph Theory;Adjacency matrix
1146;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1505;Portugal;305;1;Basic;Probability ;Probability ;Event,Axioms of probability,Addition, multiplication, and total probability rules,Sample space
1411;Portugal;306;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
1284;Italy;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
344;Portugal;272;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
1220;Slovenia;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
552;Portugal;673;0;Advanced;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
509;Portugal;90;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
890;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1220;Slovenia;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
175;Italy;795;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
966;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
751;Lithuania;701;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product,Distance
633;Italy;133;1;Advanced;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
647;Ireland;79;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
1516;Portugal;956;1;Basic;Optimization;Linear Optimization;Linear programming
1171;Portugal;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
411;Portugal;724;0;Advanced;Integration;Integration Techniques;Trigonometric substitution
525;Portugal;458;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Geometric transformations,Geometrical figures
37;Portugal;257;0;Basic;Differentiation;Partial Differentiation;Gradient,First order
376;Portugal;336;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Modulus of a complex number,Imaginary part
511;Portugal;225;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1248;Italy;243;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
663;Portugal;189;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
972;Portugal;446;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1220;Slovenia;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1543;Portugal;1093;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
91;Lithuania;513;0;Basic;Fundamental Mathematics;Elementary Geometry;Triangle inequality,Triangles
1147;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
81;Lithuania;943;1;Basic;Graph Theory;Graph Theory;Spanning tree,Shortest path,Path,Tree
1288;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
80;Lithuania;541;0;Basic;Integration;Double Integration;y-simple region (type I),Cartesian coordinates,Iterate integrals
985;Romania;789;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
71;Portugal;595;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Eigenvalue
1486;Portugal;613;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1291;Italy;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
311;Ireland;135;1;Basic;Linear Algebra;Matrices and Determinants;Symmetric matrix,Determinant computation,Determinant properties
1220;Slovenia;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
91;Lithuania;394;1;Basic;Integration;Integration Techniques;Substitution
167;Portugal;448;1;Advanced;Linear Algebra;Vector Spaces;Subspace
168;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
175;Italy;1052;0;Basic;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Conjugate number,Algebraic form,Operations with complex numbers,Real part,Equations involving complex numbers
1339;Portugal;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
600;Italy;245;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
511;Portugal;798;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1334;Portugal;454;1;Basic;Linear Algebra;Vector Spaces;Basis
483;Portugal;418;1;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
1076;Portugal;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
72;Portugal;339;0;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation
1557;Portugal;832;0;Basic;Differential Equations;Differential Equations;Separable variables equation
509;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1220;Slovenia;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1220;Slovenia;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1220;Slovenia;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
72;Portugal;432;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
1179;Portugal;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1146;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
465;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
37;Portugal;261;1;Basic;Differentiation;Partial Differentiation;First order,Gradient
1256;Portugal;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
378;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1091;Lithuania;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1289;Italy;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
80;Lithuania;337;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form,Operations with complex numbers,Modulus of a complex number
1076;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1352;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
525;Portugal;371;1;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Geometrical figures
380;Portugal;1004;0;Basic;Optimization;Nonlinear Optimization;Minimum,Stationary point,Maximum,Saddle point,Optimal solution
168;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
90;Lithuania;353;0;Basic;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
1220;Slovenia;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1220;Slovenia;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
403;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
890;Portugal;449;0;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
1220;Slovenia;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
403;Portugal;354;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
972;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1185;Portugal;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
884;Italy;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
448;Portugal;301;0;Basic;Probability ;Probability ;Sample space,Event
168;Portugal;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
167;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1288;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1324;Italy;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
175;Italy;353;1;Basic;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
955;Lithuania;1096;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
876;Italy;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1049;Lithuania;267;0;Basic;Differentiation;Partial Differentiation;First order,Second order
375;Portugal;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
524;Portugal;787;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Logarithmic function
375;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
535;Portugal;358;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Conjugate number,Operations with complex numbers,Real part
552;Portugal;568;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
1427;Portugal;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
625;Russian Federation;467;0;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Polygons,Classification of geometrical figures,Geometrical figures
1220;Slovenia;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
155;Spain;836;1;Basic;Differential Equations;Differential Equations;Linear differential equation
128;Lithuania;650;1;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties
1196;Slovenia;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1044;Lithuania;998;0;Basic;Differentiation;Partial Differentiation;First order
1352;Portugal;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1273;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
692;Portugal;182;1;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
1517;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1557;Portugal;928;0;Advanced;Real Functions of a single variable;Domain, Image and Graphics;Planar graph
1279;Portugal;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
1135;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
91;Lithuania;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
525;Portugal;512;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangles
165;Portugal;530;1;Basic;Integration;Double Integration;Iterate integrals,Area ,y-simple region (type I),Cartesian coordinates
37;Portugal;595;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Eigenvalue
37;Portugal;336;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Modulus of a complex number,Imaginary part
376;Portugal;349;0;Advanced;Complex Numbers;Complex Numbers;Complex plane 
1028;Lithuania;148;0;Basic;Differentiation;Partial Differentiation;First order
411;Portugal;92;1;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
966;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
375;Portugal;333;0;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
201;Lithuania;104;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
985;Romania;665;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1379;Portugal;919;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
637;Italy;191;1;Basic;Statistics;Statistics;Median,Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance
1163;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1283;Italy;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
986;Portugal;382;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
64;Portugal;1227;0;Basic;Differentiation;Derivatives;Exponential rule
349;Portugal;753;0;Basic;Differentiation;Derivatives;Exponential rule
509;Portugal;221;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1220;Slovenia;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
884;Italy;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
955;Lithuania;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1146;Portugal;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
175;Italy;1496;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
91;Lithuania;345;1;Advanced;Complex Numbers;Complex Numbers;Polar representation,Trigonometric form,Modulus of a complex number,Operations with complex numbers,Algebraic form,Principal argument,De Moivre formulas
168;Portugal;306;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
81;Lithuania;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
956;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1039;Lithuania;879;0;Basic;Differentiation;Partial Differentiation;First order,Second order
854;Italy;218;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
955;Lithuania;449;0;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
1220;Slovenia;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
637;Italy;78;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
80;Lithuania;529;0;Basic;Integration;Double Integration;Iterate integrals
1241;Portugal;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1256;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1109;Portugal;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
741;Ireland;81;0;Basic;Statistics;Statistics;Mean,Median,Mode
852;Italy;224;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1352;Portugal;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1082;Portugal;779;1;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
1158;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
457;Portugal;352;1;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Operations with complex numbers
1517;Portugal;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
1220;Slovenia;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
52;Portugal;511;0;Basic;Fundamental Mathematics;Elementary Geometry;Triangle inequality,Triangles
37;Portugal;661;1;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
85;Lithuania;1132;0;Basic;Set Theory;Set Theory;Subset
1044;Lithuania;887;1;Advanced;Differentiation;Partial Differentiation;First order
1252;Portugal;454;1;Basic;Linear Algebra;Vector Spaces;Basis
1135;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
979;Portugal;1090;1;Basic;Numerical Methods;Numerical Methods;Nonlinear equation,Newton’s method
455;Portugal;733;1;Basic;Integration;Integration Techniques;Simple integration,Direct inspection
1339;Portugal;418;1;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
700;Portugal;177;0;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
1130;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
175;Italy;335;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
741;Ireland;947;1;Basic;Graph Theory;Graph Theory;Spanning tree,Shortest path,Path,Tree
985;Romania;274;1;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
690;Portugal;180;1;Basic;Statistics;Statistics;Mean,Median,Mode
1220;Slovenia;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
466;Portugal;348;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Complex plane ,Real part
1135;Portugal;783;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
1220;Slovenia;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1044;Lithuania;176;0;Advanced;Differentiation;Partial Differentiation;Second order,First order
1516;Portugal;829;0;Basic;Differential Equations;Differential Equations;Linear differential equation
884;Italy;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
840;Italy;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
155;Spain;903;0;Basic;Differential Equations;Differential Equations;Separable variables equation
1379;Portugal;918;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1428;Portugal;278;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
80;Lithuania;594;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Spectrum,Characteristic polynomial,Diagonalization,Eigenvalue
1219;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
250;Lithuania;134;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
151;Portugal;120;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1135;Portugal;781;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
913;Ireland;441;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1149;Portugal;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1509;Portugal;925;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Planar graph
91;Lithuania;419;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
1220;Slovenia;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1486;Portugal;788;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Exponential function
202;Lithuania;614;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1543;Portugal;1118;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
918;Portugal;876;0;Basic;Differentiation;Partial Differentiation;Directional derivative,Gradient,First order,Second order
52;Portugal;793;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
860;Italy;89;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
509;Portugal;852;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Continuity,Limits
1341;Portugal;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
898;Portugal;860;0;Basic;Optimization;Nonlinear Optimization;Saddle point,Optimal solution,Minimum,Maximum,Stationary point
168;Portugal;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
351;Portugal;752;1;Basic;Differentiation;Derivatives;Power rule,Quotient rule,Product rule,Trigonometric rules
524;Portugal;363;0;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
1147;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1289;Italy;432;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
913;Ireland;952;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1444;Portugal;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
406;Portugal;634;0;Basic;Linear Algebra;Matrices and Determinants;Determinant properties,Inverse matrix ,Solve matrix equation,Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Commuting matrices,Determinant computation
955;Lithuania;1102;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
71;Portugal;1121;0;Basic;Differentiation;Derivatives;Trigonometric rules,Quotient rule
1077;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
165;Portugal;147;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
1076;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
750;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
955;Lithuania;1109;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Lagrange's interpolation
851;Italy;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
174;Portugal;250;1;Basic;Differentiation;Derivatives;Quotient rule,Product rule,Trigonometric rules
72;Portugal;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
636;Italy;178;0;Basic;Statistics;Statistics;Mean,Variance,Standard deviation,Median,Mode
1538;Portugal;1087;1;Basic;Numerical Methods;Numerical Methods;First order,Second order
26;Portugal;244;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
178;Italy;255;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Logarithmic rule
80;Lithuania;622;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Characteristic polynomial,Eigenvalue,Diagonalization,Eigenvector,Spectrum
1517;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
988;Portugal;246;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
1179;Portugal;385;0;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1219;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1080;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
1252;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
986;Portugal;288;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1281;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
626;Italy;94;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
1351;Portugal;289;0;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
967;Portugal;448;1;Advanced;Linear Algebra;Vector Spaces;Subspace
1256;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
80;Lithuania;221;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1023;Lithuania;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
956;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
876;Italy;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1274;Portugal;613;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
397;Portugal;355;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
64;Portugal;93;1;Basic;Differentiation;Derivatives;Product rule,Logarithmic rule,Trigonometric rules
473;Portugal;347;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
175;Italy;330;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number
411;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
979;Portugal;380;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
69;Portugal;565;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonal projection,Orthogonality,Collinearity,Locus
1286;Italy;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1080;Portugal;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
72;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
918;Portugal;260;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
1220;Slovenia;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1093;Portugal;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
349;Portugal;95;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule,Exponential rule
1150;Portugal;290;0;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1322;Italy;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
854;Italy;222;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1322;Italy;785;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1029;Lithuania;883;0;Basic;Differentiation;Partial Differentiation;First order,Directional derivative
1093;Portugal;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
181;Italy;921;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
985;Romania;612;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1517;Portugal;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
510;Portugal;786;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
524;Portugal;787;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Logarithmic function
1220;Slovenia;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1182;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
167;Portugal;432;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
666;Portugal;204;1;Basic;Statistics;Statistics;Student distribution,Hypothesis testing
966;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
181;Italy;919;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
166;Portugal;652;0;Basic;Linear Algebra;Matrices and Determinants;Linearly independent rows,Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties
1135;Portugal;290;0;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
91;Lithuania;495;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
181;Italy;923;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1220;Slovenia;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
470;Portugal;557;1;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance
1341;Portugal;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
91;Lithuania;517;0;Advanced;Fundamental Mathematics;Elementary Geometry;Symmetry
91;Lithuania;516;1;Advanced;Fundamental Mathematics;Elementary Geometry;Symmetry
1081;Portugal;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
91;Lithuania;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1312;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
411;Portugal;332;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
375;Portugal;349;1;Advanced;Complex Numbers;Complex Numbers;Complex plane 
448;Portugal;300;0;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Event,Axioms of probability
956;Portugal;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
473;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
626;Italy;143;0;Basic;Differentiation;Derivatives;Trigonometric rules,Logarithmic rule
1093;Portugal;306;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
1220;Slovenia;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
142;Portugal;114;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
986;Portugal;278;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
91;Lithuania;509;0;Advanced;Fundamental Mathematics;Elementary Geometry;Symmetry
913;Ireland;451;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1157;Portugal;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
853;Italy;215;0;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Inconsistent system,Solution of linear system
1135;Portugal;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
359;Portugal;441;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span
376;Portugal;355;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
1220;Slovenia;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
955;Lithuania;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
81;Lithuania;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
420;Portugal;639;0;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Determinant computation,Determinant properties,Matrix operations
509;Portugal;948;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
72;Portugal;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
692;Portugal;184;0;Basic;Statistics;Statistics;Frequency,Sample,Stem and Leaf diagram,Variance,Standard deviation,Relative frequency
142;Portugal;666;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
90;Lithuania;130;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
175;Italy;1089;1;Basic;Numerical Methods;Numerical Methods;First order,Second order
967;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
599;Italy;857;1;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Diagonalization,Spectrum,Characteristic polynomial
689;Portugal;865;0;Basic;Optimization;Nonlinear Optimization;Lagrange multipliers,Minimum,Maximum,Stationary point
986;Portugal;418;1;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
1487;Portugal;255;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Logarithmic rule
751;Lithuania;571;1;Basic;Analytic Geometry;Analytic Geometry;Intersection,Cartesian equations of a plane
524;Portugal;497;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
966;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1023;Lithuania;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
80;Lithuania;504;0;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry,Geometric transformations
90;Lithuania;633;0;Advanced;Linear Algebra;Matrices and Determinants;Matrix equivalent - echelon,Matrix rank,Matrix operations,Hermitian matrix,Matrix multiplication,Symmetric matrix,Linearly independent rows,Commuting matrices,Determinant computation,Determinant properties,Inverse matrix ,Solve matrix equation
667;Portugal;184;1;Basic;Statistics;Statistics;Frequency,Sample,Stem and Leaf diagram,Variance,Standard deviation,Relative frequency
394;Portugal;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
899;Lithuania;418;1;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
1148;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1173;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
748;Portugal;480;0;Basic;Graph Theory;Graph Theory;Planar graph
972;Portugal;781;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1252;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1079;Portugal;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
776;Portugal;555;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality,Locus,Distance
634;Italy;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1080;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1271;Portugal;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1087;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1049;Lithuania;875;0;Basic;Differentiation;Partial Differentiation;Gradient,First order
885;Italy;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1044;Lithuania;258;1;Basic;Differentiation;Partial Differentiation;First order,Gradient
1511;Portugal;549;0;Basic;Analytic Geometry;Analytic Geometry;Distance,Cross product,Orthogonality
1132;Portugal;779;1;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
128;Lithuania;341;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
1288;Portugal;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
359;Portugal;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
178;Italy;144;0;Basic;Differentiation;Derivatives;Trigonometric rules
1269;Portugal;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1289;Italy;432;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
1322;Italy;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1220;Slovenia;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1517;Portugal;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1150;Portugal;782;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
168;Portugal;405;1;Advanced;Integration;Integration Techniques;Rational functions
1024;Lithuania;260;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
1286;Italy;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
26;Portugal;159;1;Basic;Differential Equations;Differential Equations;Linear differential equation,Integral curve,Cauchy problem
26;Portugal;835;1;Basic;Differential Equations;Differential Equations;Exact differential form,Cauchy problem
510;Portugal;219;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
378;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
955;Lithuania;1103;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1220;Slovenia;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
769;Portugal;327;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1220;Slovenia;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1517;Portugal;624;1;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Characteristic polynomial,Eigenvalue,Diagonalization,Eigenvector,Spectrum
1565;Portugal;680;0;Basic;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
1564;Portugal;723;0;Basic;Integration;Integration Techniques;Substitution
1286;Italy;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
91;Lithuania;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
181;Italy;918;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1220;Slovenia;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
1146;Portugal;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
851;Italy;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
26;Portugal;157;1;Basic;Differential Equations;Differential Equations;Homogeneous equation,Cauchy problem
986;Portugal;448;1;Advanced;Linear Algebra;Vector Spaces;Subspace
1023;Lithuania;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
988;Portugal;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
525;Portugal;90;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1158;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
394;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
37;Portugal;495;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1085;Portugal;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1220;Slovenia;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1195;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1324;Italy;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
966;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
956;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1219;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1220;Slovenia;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
175;Italy;341;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
1146;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1182;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
26;Portugal;168;1;Basic;Differential Equations;Differential Equations;Linear differential equation
168;Portugal;289;0;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
899;Lithuania;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1291;Italy;777;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
625;Russian Federation;794;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
168;Portugal;781;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1334;Portugal;385;0;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
349;Portugal;94;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
81;Lithuania;554;0;Basic;Analytic Geometry;Analytic Geometry;Scalar product,Orthogonality,Orthogonal projection,Distance
403;Portugal;349;1;Advanced;Complex Numbers;Complex Numbers;Complex plane 
26;Portugal;888;0;Basic;Differential Equations;Differential Equations;Linear differential equation
1253;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1140;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1156;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
591;Portugal;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
966;Portugal;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
884;Italy;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
969;Romania;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1286;Italy;455;1;Basic;Linear Algebra;Vector Spaces;Basis
955;Lithuania;1098;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
411;Portugal;125;0;Basic;Linear Algebra;Matrices and Determinants;Determinant properties,Symmetric matrix,Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication
1157;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
592;Portugal;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1220;Slovenia;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1032;Lithuania;885;0;Basic;Differentiation;Partial Differentiation;Second order,First order
1517;Portugal;288;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
163;Portugal;332;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
853;Italy;949;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1333;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
1505;Portugal;959;1;Basic;Optimization;Linear Optimization;Linear programming
1220;Slovenia;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1483;Portugal;335;1;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
1220;Slovenia;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
884;Italy;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
37;Portugal;960;0;Basic;Optimization;Nonlinear Optimization;Linear programming
1252;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
524;Portugal;112;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1158;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
890;Portugal;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
174;Portugal;729;1;Basic;Differentiation;Derivatives;Quotient rule
176;Italy;102;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
37;Portugal;401;1;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
576;Ireland;567;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a line,Orthogonality,Collinearity
359;Portugal;345;1;Advanced;Complex Numbers;Complex Numbers;Polar representation,Trigonometric form,Modulus of a complex number,Operations with complex numbers,Algebraic form,Principal argument,De Moivre formulas
80;Lithuania;1003;0;Basic;Optimization;Linear Optimization;Linear programming
1024;Lithuania;999;0;Basic;Differentiation;Partial Differentiation;First order
351;Portugal;108;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1322;Italy;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1219;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
181;Italy;918;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
986;Portugal;385;1;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
168;Portugal;385;0;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
64;Portugal;698;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Orthogonal projection,Distance
1082;Portugal;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
69;Portugal;701;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product,Distance
175;Italy;337;1;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form,Operations with complex numbers,Modulus of a complex number
1179;Portugal;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1044;Lithuania;912;1;Basic;Differentiation;Partial Differentiation;Minimum,Stationary point,Maximum,Saddle point,Optimal solution
26;Portugal;146;1;Basic;Differential Equations;Differential Equations;Separable variables equation
884;Italy;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
419;Portugal;326;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part
1402;Portugal;306;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
592;Portugal;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
855;Italy;228;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
633;Italy;430;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
470;Portugal;568;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
351;Portugal;721;0;Basic;Differentiation;Derivatives;Quotient rule,Trigonometric rules
168;Portugal;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
91;Lithuania;455;1;Basic;Linear Algebra;Vector Spaces;Basis
972;Portugal;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
467;Portugal;357;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
1289;Italy;454;1;Basic;Linear Algebra;Vector Spaces;Basis
1220;Slovenia;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
422;Portugal;652;1;Basic;Linear Algebra;Matrices and Determinants;Linearly independent rows,Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties
552;Portugal;562;0;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality
448;Portugal;295;0;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Event,Axioms of probability
1029;Lithuania;256;0;Basic;Differentiation;Partial Differentiation;First order
1481;Portugal;553;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Distance,Scalar product
1322;Italy;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
168;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1505;Portugal;81;1;Basic;Statistics;Statistics;Mean,Median,Mode
1220;Slovenia;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
203;Lithuania;666;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
163;Portugal;326;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part
1150;Portugal;381;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
41;Portugal;104;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
457;Portugal;357;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
406;Portugal;368;1;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids,Regular polygon
151;Portugal;118;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
466;Portugal;354;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
91;Lithuania;364;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids,Geometrical figures,Classification of geometric solids
972;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
956;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1179;Portugal;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1147;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
511;Portugal;216;0;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
884;Italy;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1150;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1290;Italy;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
420;Portugal;326;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part
986;Portugal;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1533;Portugal;552;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product
966;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1288;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
966;Portugal;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
988;Portugal;89;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
91;Lithuania;334;1;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
1219;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
167;Portugal;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1340;Portugal;1092;1;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
969;Romania;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
625;Russian Federation;667;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
552;Portugal;889;1;Basic;Differential Equations;Differential Equations;Linear differential equation
1220;Slovenia;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
204;Lithuania;612;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
28;Portugal;337;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form,Operations with complex numbers,Modulus of a complex number
1079;Portugal;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1288;Portugal;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1080;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
899;Lithuania;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1023;Lithuania;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
483;Portugal;464;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Geometrical figures
69;Portugal;556;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line,Collinearity
1148;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
351;Portugal;794;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1289;Italy;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
966;Portugal;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1311;Italy;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
884;Italy;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
634;Italy;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1286;Italy;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1284;Italy;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
374;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1274;Portugal;796;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Logarithmic function,Exponential function,Simplify expressions
1542;Portugal;1107;1;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
394;Portugal;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
380;Portugal;1004;1;Basic;Optimization;Nonlinear Optimization;Minimum,Stationary point,Maximum,Saddle point,Optimal solution
1288;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
174;Portugal;143;0;Basic;Differentiation;Derivatives;Trigonometric rules,Logarithmic rule
625;Russian Federation;366;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids,Geometrical figures,Classification of geometric solids
1082;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
890;Portugal;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
80;Lithuania;741;0;Basic;Optimization;Linear Optimization;Graphical method,Linear programming
1220;Slovenia;454;1;Basic;Linear Algebra;Vector Spaces;Basis
426;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1420;Portugal;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1220;Slovenia;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1044;Lithuania;998;0;Basic;Differentiation;Partial Differentiation;First order
36;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
625;Russian Federation;612;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1290;Italy;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1150;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1023;Lithuania;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1289;Italy;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
200;Lithuania;118;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;455;0;Basic;Linear Algebra;Vector Spaces;Basis
899;Lithuania;446;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1557;Portugal;675;0;Advanced;Real Functions of a single variable;Domain, Image and Graphics;Domain,Image of a function
1352;Portugal;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
36;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
986;Portugal;292;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
1076;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
525;Portugal;120;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
37;Portugal;699;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Locus,Intersection,Cartesian equations of a line
1082;Portugal;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1146;Portugal;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
189;Portugal;512;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangles
972;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
955;Lithuania;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
898;Portugal;778;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
510;Portugal;102;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
61;Portugal;159;1;Basic;Differential Equations;Differential Equations;Linear differential equation,Integral curve,Cauchy problem
351;Portugal;793;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
1274;Portugal;789;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1026;Lithuania;269;0;Basic;Differentiation;Partial Differentiation;First order,Second order
181;Italy;922;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
965;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
311;Ireland;636;1;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication
1288;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
239;Lithuania;95;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule,Exponential rule
403;Portugal;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
776;Portugal;574;0;Advanced;Analytic Geometry;Analytic Geometry;Collinearity,Orthogonality,Distance,Scalar product
1220;Slovenia;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1324;Italy;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
168;Portugal;679;0;Basic;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
168;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
80;Lithuania;328;1;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
176;Italy;925;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Planar graph
884;Italy;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
876;Italy;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1286;Italy;455;0;Basic;Linear Algebra;Vector Spaces;Basis
91;Lithuania;513;0;Basic;Fundamental Mathematics;Elementary Geometry;Triangle inequality,Triangles
966;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
851;Italy;1005;1;Basic;Optimization;Nonlinear Optimization;Minimum,Stationary point,Maximum,Saddle point,Optimal solution
972;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1220;Slovenia;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
473;Portugal;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
483;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
876;Italy;455;0;Basic;Linear Algebra;Vector Spaces;Basis
1023;Lithuania;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1182;Portugal;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
394;Portugal;419;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
394;Portugal;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
69;Portugal;569;1;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance,Scalar product,Cross product,Orthogonality,Collinearity
387;Portugal;448;1;Advanced;Linear Algebra;Vector Spaces;Subspace
26;Portugal;834;1;Basic;Differential Equations;Differential Equations;Linear differential equation
1543;Portugal;1119;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
591;Portugal;330;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number
1220;Slovenia;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
598;Italy;122;1;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication,Determinant properties,Symmetric matrix
775;Portugal;773;0;Basic;Probability ;Probability ;Event,Sample space,Addition, multiplication, and total probability rules,Axioms of probability
1076;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1022;Lithuania;736;0;Basic;Optimization;Linear Optimization;Linear programming,Excel solver add-in,Simplex method
91;Lithuania;311;0;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
177;Italy;734;1;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Exponential rule
750;Portugal;922;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1444;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1147;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
576;Ireland;557;1;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance
1274;Portugal;114;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1143;Portugal;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
731;Portugal;202;0;Basic;Statistics;Statistics;Student distribution,Confidence interval,Point estimate,Hypothesis testing
1321;Portugal;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
1220;Slovenia;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1076;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
175;Italy;1114;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
854;Italy;216;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
1322;Italy;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1220;Slovenia;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
37;Portugal;1197;1;Basic;Integration;Definite Integrals;Area of a planar region ,Fundamental theorem of Calculus
972;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
853;Italy;961;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Homogeneous system,Consistent system
1481;Portugal;556;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line,Collinearity
1517;Portugal;380;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1049;Lithuania;93;0;Basic;Differentiation;Derivatives;Product rule,Logarithmic rule,Trigonometric rules
455;Portugal;122;0;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication,Determinant properties,Symmetric matrix
1516;Portugal;164;0;Basic;Differential Equations;Differential Equations;Separable variables equation
1195;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
168;Portugal;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
625;Russian Federation;497;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1143;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
753;Italy;998;0;Basic;Differentiation;Partial Differentiation;First order
1271;Portugal;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1256;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
483;Portugal;371;1;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Geometrical figures
1557;Portugal;87;0;Advanced;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
890;Portugal;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
26;Portugal;1128;1;Basic;Set Theory;Set Theory;Subset
851;Italy;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1220;Slovenia;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
657;Ireland;79;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
80;Lithuania;254;1;Basic;Differentiation;Derivatives;Logarithmic rule,Power rule,Trigonometric rules
1289;Italy;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1109;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
26;Portugal;701;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product,Distance
1109;Portugal;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
972;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
598;Italy;91;0;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
37;Portugal;353;1;Basic;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
1149;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
374;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
913;Ireland;1094;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1363;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1220;Slovenia;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
26;Portugal;1146;1;Basic;Set Theory;Set Theory;Subset
955;Lithuania;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1220;Slovenia;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
174;Portugal;611;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
955;Lithuania;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1525;Portugal;760;0;Basic;Probability ;Probability ;Event,Sample space,Addition, multiplication, and total probability rules,Axioms of probability
1322;Italy;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
37;Portugal;963;1;Basic;Optimization;Nonlinear Optimization;Simplex method,Duality theory
1179;Portugal;650;1;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties
1289;Italy;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
1044;Lithuania;267;0;Basic;Differentiation;Partial Differentiation;First order,Second order
1542;Portugal;1117;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
899;Lithuania;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
411;Portugal;328;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
176;Italy;721;1;Basic;Differentiation;Derivatives;Quotient rule,Trigonometric rules
1087;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1081;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1311;Italy;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1339;Portugal;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1557;Portugal;684;0;Advanced;Real Functions of a single variable;Domain, Image and Graphics;Domain
1338;Portugal;783;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
1291;Italy;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1272;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1220;Slovenia;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
840;Italy;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
411;Portugal;334;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
239;Lithuania;275;1;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
899;Lithuania;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
473;Portugal;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
913;Ireland;439;1;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
1044;Lithuania;881;1;Advanced;Differentiation;Partial Differentiation;Directional derivative,Gradient
1076;Portugal;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
455;Portugal;645;1;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Linearly independent rows
986;Portugal;419;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
955;Lithuania;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1244;Portugal;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1220;Slovenia;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
966;Portugal;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
163;Portugal;338;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form
1256;Portugal;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1022;Lithuania;861;0;Basic;Optimization;Nonlinear Optimization;Saddle point,Optimal solution,Minimum,Maximum,Stationary point
72;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1244;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
633;Italy;128;1;Advanced;Linear Algebra;Matrices and Determinants;Matrix multiplication,Determinant computation,Determinant properties,Symmetric matrix,Hermitian matrix,Inverse matrix ,Linearly independent rows,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Matrix equivalent - echelon
1147;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
176;Italy;922;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
955;Lithuania;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
91;Lithuania;359;1;Advanced;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
1291;Italy;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
913;Ireland;1086;0;Basic;Numerical Methods;Numerical Methods;First order,Second order
955;Lithuania;455;0;Basic;Linear Algebra;Vector Spaces;Basis
1135;Portugal;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
913;Ireland;1104;1;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1219;Portugal;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1149;Portugal;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
646;Ireland;187;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
913;Ireland;186;1;Basic;Statistics;Statistics;Population,Sample
465;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
955;Lithuania;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
876;Italy;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
840;Italy;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
380;Portugal;818;0;Basic;Optimization;Nonlinear Optimization;Minimum,Maximum,Stationary point,Second derivative test,Unconstrained optimization,Saddle point,Optimal solution
1256;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
741;Ireland;202;0;Basic;Statistics;Statistics;Student distribution,Confidence interval,Point estimate,Hypothesis testing
1150;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
71;Portugal;255;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Logarithmic rule
218;Lithuania;113;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
468;Portugal;355;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
1505;Portugal;744;1;Basic;Optimization;Linear Optimization;Excel solver add-in,Simplex method,Linear programming
1288;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
913;Ireland;231;1;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system,Solution of linear system
1220;Slovenia;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
151;Portugal;104;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
470;Portugal;348;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Complex plane ,Real part
1271;Portugal;381;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
394;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
1339;Portugal;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
168;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
468;Portugal;357;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
851;Italy;1016;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
1517;Portugal;777;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
511;Portugal;647;1;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Symmetric matrix,Matrix operations
483;Portugal;883;0;Basic;Differentiation;Partial Differentiation;First order,Directional derivative
1220;Slovenia;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
198;Italy;611;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1023;Lithuania;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
899;Lithuania;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
411;Portugal;192;0;Basic;Integration;Integration Techniques;Trigonometric substitution,Simple integration
85;Lithuania;1127;1;Basic;Set Theory;Set Theory;Union of sets,Venn diagram,Complement of a set
985;Romania;113;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
464;Portugal;351;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Imaginary part,Complex plane ,Operations with complex numbers,Real part,Principal argument,De Moivre formulas
876;Italy;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
359;Portugal;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
80;Lithuania;282;1;Basic;Optimization;Linear Optimization;Linear programming
1283;Italy;454;0;Basic;Linear Algebra;Vector Spaces;Basis
851;Italy;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1308;Italy;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
26;Portugal;1162;1;Basic;Set Theory;Set Theory;Subset
1557;Portugal;983;0;Advanced;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
524;Portugal;614;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
511;Portugal;646;1;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Commuting matrices,Solve matrix equation,Determinant computation,Inverse matrix ,Matrix rank,Determinant properties,Matrix multiplication,Symmetric matrix
80;Lithuania;334;1;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
1080;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1179;Portugal;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1220;Slovenia;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
988;Portugal;91;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
128;Lithuania;125;0;Basic;Linear Algebra;Matrices and Determinants;Determinant properties,Symmetric matrix,Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication
720;Portugal;186;1;Basic;Statistics;Statistics;Population,Sample
1179;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
376;Portugal;1056;0;Advanced;Complex Numbers;Complex Numbers;Complex plane 
969;Romania;430;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
955;Lithuania;1106;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
899;Lithuania;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
64;Portugal;668;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
72;Portugal;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1080;Portugal;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
128;Lithuania;335;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
898;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1487;Portugal;734;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Exponential rule
81;Lithuania;795;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
1322;Italy;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
175;Italy;330;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number
1428;Portugal;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1024;Lithuania;267;0;Basic;Differentiation;Partial Differentiation;First order,Second order
414;Portugal;243;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1220;Slovenia;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1023;Lithuania;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
483;Portugal;524;1;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Rhombus
576;Ireland;697;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Distance,Cross product
750;Portugal;920;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
407;Portugal;496;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1543;Portugal;1109;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Lagrange's interpolation
1564;Portugal;412;0;Basic;Integration;Integration Techniques;Power of trigonometric functions
986;Portugal;288;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1146;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
576;Ireland;335;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
827;Italy;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
376;Portugal;352;0;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Operations with complex numbers
80;Lithuania;552;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product
876;Italy;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1252;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
967;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
168;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
985;Romania;668;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
899;Lithuania;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
636;Italy;184;0;Basic;Statistics;Statistics;Frequency,Sample,Stem and Leaf diagram,Variance,Standard deviation,Relative frequency
1322;Italy;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1192;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
422;Portugal;329;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
351;Portugal;795;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
359;Portugal;418;1;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
465;Portugal;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
884;Italy;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1087;Portugal;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
860;Italy;230;0;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
1284;Italy;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
203;Lithuania;665;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1481;Portugal;294;0;Basic;Probability ;Probability ;Event,Axioms of probability,Sample space
1334;Portugal;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
351;Portugal;613;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
181;Italy;923;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
913;Ireland;177;1;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
37;Portugal;1105;1;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1195;Portugal;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1220;Slovenia;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1557;Portugal;688;1;Advanced;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
1220;Slovenia;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
380;Portugal;355;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
988;Portugal;430;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1150;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
483;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
884;Italy;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1291;Italy;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
683;Ireland;186;1;Basic;Statistics;Statistics;Population,Sample
956;Portugal;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1220;Slovenia;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1505;Portugal;957;1;Basic;Optimization;Linear Optimization;Linear programming
973;Portugal;948;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
1149;Portugal;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
751;Lithuania;558;0;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
466;Portugal;348;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Complex plane ,Real part
1220;Slovenia;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
1077;Portugal;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
351;Portugal;666;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1148;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
899;Lithuania;420;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1220;Slovenia;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1220;Slovenia;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1332;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1525;Portugal;747;0;Advanced;Optimization;Linear Optimization;Duality theory,Excel solver add-in,Simplex method,Linear programming,Sensitivity analysis,Postoptimality analysis
913;Ireland;187;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
175;Italy;1061;0;Basic;Complex Numbers;Complex Numbers;Complex plane 
26;Portugal;1149;0;Basic;Set Theory;Set Theory;Subset
955;Lithuania;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
511;Portugal;793;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
1146;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1517;Portugal;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
85;Lithuania;1163;1;Basic;Set Theory;Set Theory;Subset
37;Portugal;406;1;Basic;Integration;Integration Techniques;Direct inspection
876;Italy;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1077;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
311;Ireland;138;0;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Determinant computation,Determinant properties,Inverse matrix 
1273;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
840;Italy;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
91;Lithuania;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
1220;Slovenia;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1158;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1561;Portugal;403;0;Advanced;Integration;Integration Techniques;Rational functions
1220;Slovenia;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
41;Portugal;108;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1244;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
1509;Portugal;682;1;Basic;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
91;Lithuania;493;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangles,Triangle inequality
1220;Slovenia;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1269;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
851;Italy;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
972;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1179;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1220;Slovenia;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
913;Ireland;223;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1220;Slovenia;454;0;Basic;Linear Algebra;Vector Spaces;Basis
380;Portugal;862;1;Basic;Optimization;Nonlinear Optimization;Saddle point,Optimal solution,Minimum,Maximum,Stationary point
840;Italy;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
955;Lithuania;1089;1;Basic;Numerical Methods;Numerical Methods;First order,Second order
1252;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
128;Lithuania;342;1;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Modulus of a complex number,Algebraic form
457;Portugal;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1518;Portugal;644;1;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Determinant computation,Matrix rank,Inverse matrix ,Determinant properties,Hermitian matrix,Matrix multiplication,Linearly independent rows,Symmetric matrix,Matrix operations
827;Italy;644;0;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Determinant computation,Matrix rank,Inverse matrix ,Determinant properties,Hermitian matrix,Matrix multiplication,Linearly independent rows,Symmetric matrix,Matrix operations
37;Portugal;881;1;Advanced;Differentiation;Partial Differentiation;Directional derivative,Gradient
1071;Lithuania;455;1;Basic;Linear Algebra;Vector Spaces;Basis
71;Portugal;667;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
80;Lithuania;220;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
851;Italy;861;0;Basic;Optimization;Nonlinear Optimization;Saddle point,Optimal solution,Minimum,Maximum,Stationary point
1256;Portugal;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
465;Portugal;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
851;Italy;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
852;Italy;239;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1147;Portugal;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
200;Lithuania;399;1;Basic;Integration;Integration Techniques;Substitution,Direct inspection,Simple integration
667;Portugal;81;1;Basic;Statistics;Statistics;Mean,Median,Mode
81;Lithuania;779;0;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
955;Lithuania;292;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
969;Romania;448;0;Advanced;Linear Algebra;Vector Spaces;Subspace
510;Portugal;217;0;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
1486;Portugal;795;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
969;Romania;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1220;Slovenia;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
91;Lithuania;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
955;Lithuania;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1143;Portugal;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
660;Portugal;188;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
626;Italy;253;0;Basic;Differentiation;Derivatives;Logarithmic rule,Trigonometric rules
420;Portugal;644;0;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Determinant computation,Matrix rank,Inverse matrix ,Determinant properties,Hermitian matrix,Matrix multiplication,Linearly independent rows,Symmetric matrix,Matrix operations
91;Lithuania;522;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Triangles
600;Italy;224;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
509;Portugal;137;1;Basic;Linear Algebra;Matrices and Determinants;Matrix equivalent - echelon,Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Linearly independent rows,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
378;Portugal;701;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product,Distance
1339;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
91;Lithuania;358;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Conjugate number,Operations with complex numbers,Real part
918;Portugal;95;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule,Exponential rule
466;Portugal;354;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
1147;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
972;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
204;Lithuania;786;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1036;Lithuania;260;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
1289;Italy;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1339;Portugal;427;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
775;Portugal;304;1;Basic;Probability ;Probability ;Addition, multiplication, and total probability rules,Sample space,Event,Axioms of probability
913;Ireland;952;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
91;Lithuania;503;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry,Geometric transformations
1080;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
91;Lithuania;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
918;Portugal;391;0;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
1274;Portugal;788;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Exponential function
177;Italy;787;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Logarithmic function
1273;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
80;Lithuania;464;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Geometrical figures
1282;Portugal;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1543;Portugal;1098;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
167;Portugal;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
91;Lithuania;371;1;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Geometrical figures
1229;Portugal;288;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1538;Portugal;1117;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
85;Lithuania;1124;0;Basic;Set Theory;Set Theory;Integration by parts,Substitution,Simple integration,Direct inspection
884;Italy;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1179;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
647;Ireland;81;0;Basic;Statistics;Statistics;Mean,Median,Mode
1146;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1379;Portugal;611;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1271;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
509;Portugal;223;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1352;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
690;Portugal;186;0;Basic;Statistics;Statistics;Population,Sample
953;Lithuania;183;0;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
1220;Slovenia;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
359;Portugal;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
1043;Lithuania;412;0;Basic;Integration;Integration Techniques;Power of trigonometric functions
80;Lithuania;493;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangles,Triangle inequality
876;Italy;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
854;Italy;231;1;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system,Solution of linear system
524;Portugal;104;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
81;Lithuania;551;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality
1220;Slovenia;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1081;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
624;Portugal;114;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
351;Portugal;272;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
988;Portugal;91;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
625;Russian Federation;667;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
175;Italy;1112;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
387;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1197;Slovenia;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
955;Lithuania;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
468;Portugal;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1275;Lithuania;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1029;Lithuania;260;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
898;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1516;Portugal;903;1;Basic;Differential Equations;Differential Equations;Separable variables equation
1322;Italy;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1229;Portugal;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1275;Lithuania;424;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1299;Italy;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
525;Portugal;120;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
855;Italy;216;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
509;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
393;Lithuania;354;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
81;Lithuania;559;0;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
426;Portugal;350;0;Advanced;Complex Numbers;Complex Numbers;Complex plane 
311;Ireland;639;1;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Determinant computation,Determinant properties,Matrix operations
91;Lithuania;456;1;Advanced;Fundamental Mathematics;Elementary Geometry;Triangles
511;Portugal;243;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
455;Portugal;127;1;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Determinant computation,Determinant properties,Symmetric matrix,Inverse matrix ,Linearly independent rows,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank
1157;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
898;Portugal;1005;0;Basic;Optimization;Nonlinear Optimization;Minimum,Stationary point,Maximum,Saddle point,Optimal solution
1157;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
344;Portugal;102;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
41;Portugal;159;1;Basic;Differential Equations;Differential Equations;Linear differential equation,Integral curve,Cauchy problem
854;Italy;917;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1322;Italy;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
700;Portugal;185;1;Basic;Statistics;Statistics;Frequency,Quantile,Mean,Variance,Median,Mode
1023;Lithuania;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
411;Portugal;326;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part
426;Portugal;346;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
414;Portugal;234;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
168;Portugal;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
91;Lithuania;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1219;Portugal;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
913;Ireland;1090;1;Basic;Numerical Methods;Numerical Methods;Nonlinear equation,Newton’s method
71;Portugal;1087;1;Basic;Numerical Methods;Numerical Methods;First order,Second order
80;Lithuania;245;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
239;Lithuania;144;1;Basic;Differentiation;Derivatives;Trigonometric rules
955;Lithuania;1096;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
151;Portugal;112;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
988;Portugal;439;0;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
67;Portugal;185;1;Basic;Statistics;Statistics;Frequency,Quantile,Mean,Variance,Median,Mode
1319;Italy;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
852;Italy;233;0;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
1220;Slovenia;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
955;Lithuania;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
403;Portugal;357;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
769;Portugal;332;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1275;Lithuania;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1542;Portugal;1102;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
37;Portugal;604;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector,Spectrum,Characteristic polynomial
955;Lithuania;782;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
634;Italy;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
376;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1286;Italy;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
359;Portugal;367;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometrical figures
1271;Portugal;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
26;Portugal;952;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1252;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
414;Portugal;948;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
1093;Portugal;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
855;Italy;230;0;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
913;Ireland;204;1;Basic;Statistics;Statistics;Student distribution,Hypothesis testing
1220;Slovenia;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
168;Portugal;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1402;Portugal;777;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
422;Portugal;331;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1279;Portugal;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
898;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1140;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
509;Portugal;223;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
28;Portugal;557;1;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance
965;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
973;Portugal;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1479;Portugal;964;1;Basic;Optimization;Nonlinear Optimization;Simplex method,Duality theory
625;Russian Federation;514;0;Basic;Fundamental Mathematics;Elementary Geometry;Triangle inequality,Triangles
57;Portugal;185;0;Basic;Statistics;Statistics;Frequency,Quantile,Mean,Variance,Median,Mode
1552;Portugal;719;0;Basic;Integration;Integration Techniques;Integration by parts
1284;Italy;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
41;Portugal;79;1;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
26;Portugal;828;1;Basic;Differential Equations;Differential Equations;Linear differential equation
852;Italy;215;0;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Inconsistent system,Solution of linear system
524;Portugal;612;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1135;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
966;Portugal;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
378;Portugal;292;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
1130;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
675;Portugal;79;1;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
576;Ireland;556;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line,Collinearity
986;Portugal;446;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
81;Lithuania;362;1;Basic;Graph Theory;Graph Theory;Simple graph
1023;Lithuania;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
41;Portugal;342;1;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Modulus of a complex number,Algebraic form
1147;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1247;Portugal;642;0;Basic;Linear Algebra;Matrices and Determinants;Symmetric matrix,Matrix multiplication,Matrix operations
851;Italy;1208;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
406;Portugal;244;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
168;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1542;Portugal;1108;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Lagrange's interpolation
1023;Lithuania;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
91;Lithuania;364;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids,Geometrical figures,Classification of geometric solids
969;Romania;424;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
387;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
647;Ireland;77;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
483;Portugal;614;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
174;Portugal;255;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Logarithmic rule
955;Lithuania;1096;1;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
28;Portugal;573;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Locus,Scalar product,Cross product,Collinearity
91;Lithuania;522;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Triangles
1220;Slovenia;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1039;Lithuania;258;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
955;Lithuania;1112;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1220;Slovenia;454;0;Basic;Linear Algebra;Vector Spaces;Basis
851;Italy;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
700;Portugal;211;1;Basic;Statistics;Statistics;Linear regression
1194;Portugal;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
884;Italy;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1308;Italy;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
406;Portugal;640;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
91;Lithuania;504;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry,Geometric transformations
1286;Italy;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
28;Portugal;700;1;Basic;Analytic Geometry;Analytic Geometry;Collinearity,Locus,Orthogonality,Orthogonal projection,Scalar product,Distance
168;Portugal;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
175;Italy;798;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1308;Italy;292;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
851;Italy;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
26;Portugal;1151;0;Basic;Set Theory;Set Theory;Subset
128;Lithuania;329;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1220;Slovenia;455;1;Basic;Linear Algebra;Vector Spaces;Basis
913;Ireland;1099;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1173;Portugal;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
483;Portugal;624;1;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Characteristic polynomial,Eigenvalue,Diagonalization,Eigenvector,Spectrum
1308;Italy;454;0;Basic;Linear Algebra;Vector Spaces;Basis
651;Ireland;182;0;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
990;Portugal;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
509;Portugal;594;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Spectrum,Characteristic polynomial,Diagonalization,Eigenvalue
483;Portugal;447;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1564;Portugal;401;0;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
168;Portugal;392;1;Advanced;Integration;Integration Techniques;Substitution
1220;Slovenia;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1411;Portugal;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
167;Portugal;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1352;Portugal;306;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
72;Portugal;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1179;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1352;Portugal;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1525;Portugal;491;0;Advanced;Probability ;Probability ;Addition, multiplication, and total probability rules,Independence,Event
374;Portugal;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
168;Portugal;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
510;Portugal;92;0;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
979;Portugal;1113;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
693;Portugal;180;1;Basic;Statistics;Statistics;Mean,Median,Mode
36;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
411;Portugal;620;0;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Characteristic polynomial,Eigenvalue,Diagonalization,Eigenvector,Spectrum
168;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
415;Portugal;139;0;Advanced;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication,Determinant computation,Determinant properties
1150;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1146;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
979;Portugal;1113;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
359;Portugal;356;1;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers
600;Italy;222;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1220;Slovenia;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
986;Portugal;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
1185;Portugal;288;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
344;Portugal;796;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Logarithmic function,Exponential function,Simplify expressions
511;Portugal;952;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1379;Portugal;118;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1516;Portugal;165;1;Basic;Differential Equations;Differential Equations;Linear differential equation,Homogeneous equation
168;Portugal;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
598;Italy;229;0;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
411;Portugal;127;0;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Determinant computation,Determinant properties,Symmetric matrix,Inverse matrix ,Linearly independent rows,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank
1375;Portugal;779;1;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
1196;Slovenia;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1050;Lithuania;878;0;Basic;Differentiation;Partial Differentiation;Second order,First order
1481;Portugal;413;0;Basic;Integration;Integration Techniques;Direct inspection
1292;Italy;617;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Spectrum,Eigenvector,Characteristic polynomial
406;Portugal;89;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1220;Slovenia;455;1;Basic;Linear Algebra;Vector Spaces;Basis
509;Portugal;949;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
548;Portugal;304;0;Basic;Probability ;Probability ;Addition, multiplication, and total probability rules,Sample space,Event,Axioms of probability
1517;Portugal;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
151;Portugal;108;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1564;Portugal;721;0;Basic;Differentiation;Derivatives;Quotient rule,Trigonometric rules
509;Portugal;127;0;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Determinant computation,Determinant properties,Symmetric matrix,Inverse matrix ,Linearly independent rows,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank
986;Portugal;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
913;Ireland;179;1;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
1241;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1229;Portugal;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
466;Portugal;359;0;Advanced;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
378;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1322;Italy;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
988;Portugal;224;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
967;Portugal;778;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
851;Italy;1246;0;Basic;Optimization;Nonlinear Optimization;Unconstrained optimization,Second derivative test,Optimal solution
973;Portugal;88;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
72;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1241;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
175;Italy;1093;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1479;Portugal;1208;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
1220;Slovenia;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
890;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1146;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
387;Portugal;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
36;Portugal;278;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1352;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1525;Portugal;743;0;Basic;Optimization;Linear Optimization;Duality theory,Linear programming
1427;Portugal;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
168;Portugal;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
37;Portugal;1229;0;Basic;Differentiation;Partial Differentiation;First order
41;Portugal;572;1;Basic;Analytic Geometry;Analytic Geometry;Locus,Scalar product,Cross product,Distance,Collinearity,Orthogonality
1511;Portugal;567;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a line,Orthogonality,Collinearity
876;Italy;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
852;Italy;231;1;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system,Solution of linear system
1312;Portugal;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1525;Portugal;1010;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Maximum
483;Portugal;333;1;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
966;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1044;Lithuania;260;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
750;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
168;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
666;Portugal;177;0;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
151;Portugal;114;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
510;Portugal;113;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
600;Italy;645;0;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Linearly independent rows
91;Lithuania;714;0;Basic;Integration;Integration Techniques;Simple integration,Direct inspection
80;Lithuania;658;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
168;Portugal;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
359;Portugal;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
71;Portugal;729;0;Basic;Differentiation;Derivatives;Quotient rule
1087;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
168;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
986;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
634;Italy;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
91;Lithuania;496;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
972;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
860;Italy;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1037;Lithuania;148;0;Basic;Differentiation;Partial Differentiation;First order
37;Portugal;1072;1;Basic;Differentiation;Partial Differentiation;Power rule,Trigonometric rules,Logarithmic rule
448;Portugal;491;1;Advanced;Probability ;Probability ;Addition, multiplication, and total probability rules,Independence,Event
1220;Slovenia;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
982;Portugal;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1286;Italy;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
750;Portugal;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
851;Italy;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1292;Italy;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
913;Ireland;427;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
483;Portugal;752;1;Basic;Differentiation;Derivatives;Power rule,Quotient rule,Product rule,Trigonometric rules
913;Ireland;316;0;Basic;Probability ;Probability ;Axioms of probability,Event,Addition, multiplication, and total probability rules,Sample space
1220;Slovenia;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
69;Portugal;566;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Orthogonality,Locus
72;Portugal;451;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
852;Italy;243;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1219;Portugal;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
661;Portugal;181;1;Basic;Statistics;Statistics;Quantile,Frequency,Sample,Mean,Variance,Standard deviation,Median,Mode
465;Portugal;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
1487;Portugal;332;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
420;Portugal;332;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1023;Lithuania;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
411;Portugal;622;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Characteristic polynomial,Eigenvalue,Diagonalization,Eigenvector,Spectrum
679;Portugal;188;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
1220;Slovenia;455;1;Basic;Linear Algebra;Vector Spaces;Basis
420;Portugal;339;0;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation
634;Italy;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
168;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
598;Italy;136;1;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
840;Italy;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1564;Portugal;84;1;Basic;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
168;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
986;Portugal;439;0;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
967;Portugal;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
37;Portugal;665;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1564;Portugal;685;1;Basic;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
1220;Slovenia;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1146;Portugal;278;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
80;Lithuania;703;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Scalar product
988;Portugal;229;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
81;Lithuania;699;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Locus,Intersection,Cartesian equations of a line
853;Italy;948;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
411;Portugal;596;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Eigenvalue
1130;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
885;Italy;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1023;Lithuania;455;1;Basic;Linear Algebra;Vector Spaces;Basis
483;Portugal;788;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Exponential function
71;Portugal;571;1;Basic;Analytic Geometry;Analytic Geometry;Intersection,Cartesian equations of a plane
37;Portugal;1033;0;Basic;Differentiation;Partial Differentiation;Power rule,Trigonometric rules,Logarithmic rule,First order
351;Portugal;108;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
693;Portugal;177;1;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
1220;Slovenia;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
509;Portugal;125;1;Basic;Linear Algebra;Matrices and Determinants;Determinant properties,Symmetric matrix,Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication
885;Italy;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1077;Portugal;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
1095;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1087;Portugal;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
28;Portugal;223;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
750;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1561;Portugal;309;0;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
403;Portugal;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
80;Lithuania;571;1;Basic;Analytic Geometry;Analytic Geometry;Intersection,Cartesian equations of a plane
483;Portugal;352;0;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Operations with complex numbers
155;Spain;870;1;Basic;Differential Equations;Differential Equations;Homogeneous equation
457;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1504;Portugal;328;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1220;Slovenia;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1220;Slovenia;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
689;Portugal;866;1;Basic;Optimization;Nonlinear Optimization;Stationary point,Maximum,Saddle point,Optimal solution,Minimum
972;Portugal;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
81;Lithuania;481;0;Advanced;Graph Theory;Graph Theory;Path,Simple graph,Cycle and circuit
683;Ireland;182;1;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
851;Italy;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
552;Portugal;891;0;Basic;Differential Equations;Differential Equations;Linear differential equation
168;Portugal;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
37;Portugal;155;1;Basic;Optimization;Nonlinear Optimization;Lagrange multipliers,Maximum,Minimum
91;Lithuania;357;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
884;Italy;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1487;Portugal;720;1;Basic;Differentiation;Derivatives;Quotient rule,Trigonometric rules,Logarithmic rule,Product rule
599;Italy;623;1;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Characteristic polynomial,Eigenvalue,Diagonalization,Eigenvector,Spectrum
851;Italy;818;1;Basic;Optimization;Nonlinear Optimization;Minimum,Maximum,Stationary point,Second derivative test,Unconstrained optimization,Saddle point,Optimal solution
41;Portugal;506;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry
1220;Slovenia;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
986;Portugal;292;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
890;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
855;Italy;949;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
884;Italy;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
853;Italy;233;0;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
168;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
175;Italy;1526;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Linear equations,Quadratic equations,Simplify expressions
1087;Portugal;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
175;Italy;1104;1;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
71;Portugal;341;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
1109;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1252;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1322;Italy;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
669;Portugal;183;0;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
91;Lithuania;511;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangle inequality,Triangles
969;Romania;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
351;Portugal;730;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
80;Lithuania;514;0;Basic;Fundamental Mathematics;Elementary Geometry;Triangle inequality,Triangles
80;Lithuania;280;1;Basic;Optimization;Linear Optimization;Linear programming
1557;Portugal;684;1;Advanced;Real Functions of a single variable;Domain, Image and Graphics;Domain
1308;Italy;455;0;Basic;Linear Algebra;Vector Spaces;Basis
37;Portugal;887;1;Advanced;Differentiation;Partial Differentiation;First order
1219;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
658;Ireland;193;1;Basic;Statistics;Statistics;Standard deviation,Variance,Median,Frequency,Mode,Outliers,Quantile,Interquartile range,Population,Data type,Sample,Relative frequency,Mean
1220;Slovenia;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1244;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1146;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1525;Portugal;767;0;Basic;Probability ;Probability ;Event,Sample space
168;Portugal;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1147;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
387;Portugal;446;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
28;Portugal;546;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonal projection,Distance,Cross product,Orthogonality
407;Portugal;786;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
885;Italy;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
725;Portugal;185;0;Basic;Statistics;Statistics;Frequency,Quantile,Mean,Variance,Median,Mode
1022;Lithuania;1004;0;Basic;Optimization;Nonlinear Optimization;Minimum,Stationary point,Maximum,Saddle point,Optimal solution
1146;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
468;Portugal;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1271;Portugal;779;0;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
1081;Portugal;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
552;Portugal;576;0;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
1220;Slovenia;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
41;Portugal;193;0;Basic;Statistics;Statistics;Standard deviation,Variance,Median,Frequency,Mode,Outliers,Quantile,Interquartile range,Population,Data type,Sample,Relative frequency,Mean
26;Portugal;565;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonal projection,Orthogonality,Collinearity,Locus
1241;Portugal;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
67;Portugal;79;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
174;Portugal;342;1;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Modulus of a complex number,Algebraic form
1044;Lithuania;261;1;Basic;Differentiation;Partial Differentiation;First order,Gradient
1525;Portugal;750;0;Advanced;Optimization;Linear Optimization;Sensitivity analysis,Postoptimality analysis,Duality theory,Excel solver add-in,Simplex method,Linear programming
376;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
457;Portugal;346;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
26;Portugal;829;0;Basic;Differential Equations;Differential Equations;Linear differential equation
1279;Portugal;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
972;Portugal;783;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
1229;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
168;Portugal;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
37;Portugal;872;0;Basic;Differential Equations;Differential Equations;Linear differential equation
374;Portugal;853;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Continuity,Limits
378;Portugal;571;0;Basic;Analytic Geometry;Analytic Geometry;Intersection,Cartesian equations of a plane
380;Portugal;1015;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
885;Italy;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
509;Portugal;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
37;Portugal;1013;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
899;Lithuania;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
899;Lithuania;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
576;Ireland;554;0;Basic;Analytic Geometry;Analytic Geometry;Scalar product,Orthogonality,Orthogonal projection,Distance
625;Russian Federation;798;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
625;Russian Federation;102;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
37;Portugal;1203;1;Basic;Integration;Definite Integrals;Volume of revolution,Fundamental theorem of Calculus
1087;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1284;Italy;420;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
664;Portugal;204;1;Basic;Statistics;Statistics;Student distribution,Hypothesis testing
1132;Portugal;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1505;Portugal;965;0;Basic;Optimization;Linear Optimization;Excel solver add-in,Simplex method,Linear programming,Transportation problem
956;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
955;Lithuania;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1220;Slovenia;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
955;Lithuania;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1023;Lithuania;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1542;Portugal;1088;1;Basic;Numerical Methods;Numerical Methods;First order,Second order
1375;Portugal;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1093;Portugal;783;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
28;Portugal;547;0;Basic;Analytic Geometry;Analytic Geometry;Cross product,Orthogonality,Scalar product
955;Lithuania;1113;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
1538;Portugal;1086;0;Basic;Numerical Methods;Numerical Methods;First order,Second order
1281;Portugal;424;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1284;Italy;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
769;Portugal;326;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part
1517;Portugal;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1047;Lithuania;999;0;Basic;Differentiation;Partial Differentiation;First order
966;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
155;Spain;96;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
71;Portugal;629;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue
890;Portugal;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
175;Italy;613;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
181;Italy;925;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Planar graph
37;Portugal;1073;0;Basic;Differentiation;Partial Differentiation;Power rule,Trigonometric rules,Logarithmic rule
1220;Slovenia;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1023;Lithuania;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
982;Portugal;424;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
899;Lithuania;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1517;Portugal;439;0;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
1147;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1256;Portugal;385;1;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
511;Portugal;136;1;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
468;Portugal;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
913;Ireland;424;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
41;Portugal;550;0;Advanced;Analytic Geometry;Analytic Geometry;Cross product,Orthogonality
1269;Portugal;424;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1543;Portugal;1111;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
509;Portugal;641;1;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties,Hermitian matrix,Symmetric matrix,Matrix multiplication,Linearly independent rows,Matrix operations
509;Portugal;223;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
899;Lithuania;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1275;Lithuania;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
966;Portugal;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
1220;Slovenia;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
986;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1308;Italy;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
26;Portugal;220;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
28;Portugal;556;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line,Collinearity
1220;Slovenia;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1087;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
397;Portugal;356;0;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers
1543;Portugal;1101;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1195;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
28;Portugal;558;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
1271;Portugal;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
41;Portugal;341;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
411;Portugal;723;0;Basic;Integration;Integration Techniques;Substitution
80;Lithuania;837;0;Basic;Differential Equations;Differential Equations;Linear differential equation
674;Ireland;184;1;Basic;Statistics;Statistics;Frequency,Sample,Stem and Leaf diagram,Variance,Standard deviation,Relative frequency
69;Portugal;561;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
1194;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1077;Portugal;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
359;Portugal;454;1;Basic;Linear Algebra;Vector Spaces;Basis
1220;Slovenia;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1196;Slovenia;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1158;Portugal;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
168;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
175;Italy;1216;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
955;Lithuania;1214;0;Basic;Numerical Methods;Numerical Methods;Mean,Median,Outliers,Interquartile range
81;Lithuania;114;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
988;Portugal;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
633;Italy;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
552;Portugal;548;0;Basic;Analytic Geometry;Analytic Geometry;Collinearity,Distance,Locus,Cross product,Orthogonality,Scalar product
1504;Portugal;338;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form
176;Italy;729;0;Basic;Differentiation;Derivatives;Quotient rule
1565;Portugal;732;0;Advanced;Integration;Integration Techniques;Trigonometric substitution
26;Portugal;829;1;Basic;Differential Equations;Differential Equations;Linear differential equation
1299;Italy;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1150;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1147;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
913;Ireland;1215;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Lagrange's interpolation
85;Lithuania;477;0;Basic;Graph Theory;Graph Theory;Simple graph
1487;Portugal;328;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1220;Slovenia;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1351;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
625;Russian Federation;367;0;Basic;Fundamental Mathematics;Elementary Geometry;Geometrical figures
1197;Slovenia;447;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
625;Russian Federation;798;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
26;Portugal;555;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality,Locus,Distance
1271;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1171;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1375;Portugal;385;1;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1095;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
411;Portugal;339;0;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation
91;Lithuania;460;1;Basic;Fundamental Mathematics;Elementary Geometry;Polyhedrons,Platonic solids,Geometric solids
168;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
91;Lithuania;463;1;Basic;Fundamental Mathematics;Elementary Geometry;Polyhedrons,Geometric solids,Classification of geometric solids
988;Portugal;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1288;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
208;Lithuania;644;1;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Determinant computation,Matrix rank,Inverse matrix ,Determinant properties,Hermitian matrix,Matrix multiplication,Linearly independent rows,Symmetric matrix,Matrix operations
1220;Slovenia;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
80;Lithuania;848;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Continuity,Limits
1339;Portugal;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
178;Italy;147;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
1286;Italy;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
85;Lithuania;476;0;Basic;Graph Theory;Graph Theory;Adjacency matrix
986;Portugal;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
394;Portugal;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
90;Lithuania;645;1;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Linearly independent rows
1339;Portugal;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
1087;Portugal;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
218;Lithuania;611;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
168;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
972;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
64;Portugal;729;1;Basic;Differentiation;Derivatives;Quotient rule
1479;Portugal;1053;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
1565;Portugal;905;1;Advanced;Differential Equations;Differential Equations;Bernoulli equation,Linear differential equation
695;Portugal;183;1;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
349;Portugal;144;1;Basic;Differentiation;Derivatives;Trigonometric rules
91;Lithuania;502;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry,Geometric transformations
451;Portugal;490;1;Advanced;Probability ;Probability ;Addition, multiplication, and total probability rules,Independence,Event
1220;Slovenia;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1324;Italy;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
91;Lithuania;348;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Complex plane ,Real part
403;Portugal;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1244;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
913;Ireland;1251;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
634;Italy;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
340;Portugal;77;1;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
1351;Portugal;778;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
625;Russian Federation;496;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
483;Portugal;113;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1146;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1322;Italy;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
852;Italy;948;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
1427;Portugal;288;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
975;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
128;Lithuania;641;0;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties,Hermitian matrix,Symmetric matrix,Matrix multiplication,Linearly independent rows,Matrix operations
1557;Portugal;87;1;Advanced;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
1220;Slovenia;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
750;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
359;Portugal;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1487;Portugal;929;1;Basic;Graph Theory;Graph Theory;Cycle and circuit,Shortest path,Path,Planar graph,Tree,Adjacency matrix,Chromatic number,Simple graph,Spanning tree,Incidence matrix 
986;Portugal;447;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1220;Slovenia;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
407;Portugal;368;0;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids,Regular polygon
1146;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
69;Portugal;703;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Scalar product
376;Portugal;357;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
1247;Portugal;650;0;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties
1220;Slovenia;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
509;Portugal;141;1;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication
1340;Portugal;1095;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
168;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
202;Lithuania;611;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1334;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1220;Slovenia;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
972;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1147;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
918;Portugal;266;0;Basic;Differentiation;Partial Differentiation;First order,Second order
420;Portugal;127;1;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Determinant computation,Determinant properties,Symmetric matrix,Inverse matrix ,Linearly independent rows,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank
175;Italy;339;1;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation
913;Ireland;451;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1135;Portugal;779;0;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
1091;Lithuania;292;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
913;Ireland;1104;1;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
155;Spain;267;0;Basic;Differentiation;Partial Differentiation;First order,Second order
1220;Slovenia;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1288;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
509;Portugal;218;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
955;Lithuania;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
219;Lithuania;666;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
576;Ireland;696;0;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Intersection,Cartesian equations of a line
1220;Slovenia;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1300;Italy;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
168;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
483;Portugal;357;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
168;Portugal;278;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1023;Lithuania;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
26;Portugal;572;0;Basic;Analytic Geometry;Analytic Geometry;Locus,Scalar product,Cross product,Distance,Collinearity,Orthogonality
1135;Portugal;290;0;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
956;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
91;Lithuania;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
411;Portugal;623;0;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Characteristic polynomial,Eigenvalue,Diagonalization,Eigenvector,Spectrum
1081;Portugal;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1146;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
80;Lithuania;738;1;Basic;Optimization;Linear Optimization;Graphical method,Linear programming
28;Portugal;701;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product,Distance
1044;Lithuania;258;1;Basic;Differentiation;Partial Differentiation;First order,Gradient
690;Portugal;193;0;Basic;Statistics;Statistics;Standard deviation,Variance,Median,Frequency,Mode,Outliers,Quantile,Interquartile range,Population,Data type,Sample,Relative frequency,Mean
1070;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
378;Portugal;549;0;Basic;Analytic Geometry;Analytic Geometry;Distance,Cross product,Orthogonality
1487;Portugal;328;1;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
751;Lithuania;554;0;Basic;Analytic Geometry;Analytic Geometry;Scalar product,Orthogonality,Orthogonal projection,Distance
483;Portugal;359;1;Advanced;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
955;Lithuania;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1196;Slovenia;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
175;Italy;1095;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
700;Portugal;80;0;Basic;Statistics;Statistics;Population,Variance,Median,Standard deviation,Mode,Quantile,Sample,Mean
1220;Slovenia;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
750;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
899;Lithuania;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
1289;Italy;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
674;Ireland;179;0;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
71;Portugal;297;0;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Event,Axioms of probability
854;Italy;951;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
851;Italy;1053;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
851;Italy;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1219;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1079;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1220;Slovenia;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
625;Russian Federation;366;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids,Geometrical figures,Classification of geometric solids
85;Lithuania;1127;0;Basic;Set Theory;Set Theory;Union of sets,Venn diagram,Complement of a set
1195;Portugal;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1288;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
176;Italy;118;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
376;Portugal;357;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
876;Italy;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1308;Italy;380;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
71;Portugal;1120;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
511;Portugal;229;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
91;Lithuania;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
72;Portugal;451;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1248;Italy;217;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
91;Lithuania;500;0;Advanced;Fundamental Mathematics;Elementary Geometry;Geometrical figures,Triangles,Classification of geometrical figures
913;Ireland;1120;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
176;Italy;788;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Exponential function
956;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
28;Portugal;186;0;Basic;Statistics;Statistics;Population,Sample
1179;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
840;Italy;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1081;Portugal;418;1;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
1308;Italy;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
511;Portugal;91;0;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
695;Portugal;202;1;Basic;Statistics;Statistics;Student distribution,Confidence interval,Point estimate,Hypothesis testing
1543;Portugal;1115;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
91;Lithuania;371;0;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Geometrical figures
483;Portugal;363;1;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
599;Italy;617;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Spectrum,Eigenvector,Characteristic polynomial
352;Portugal;144;0;Basic;Differentiation;Derivatives;Trigonometric rules
1517;Portugal;446;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1288;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
483;Portugal;274;1;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
1247;Portugal;635;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
625;Russian Federation;802;1;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
36;Portugal;1150;0;Basic;Set Theory;Set Theory;Subset
576;Ireland;699;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Locus,Intersection,Cartesian equations of a line
406;Portugal;666;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
470;Portugal;700;0;Basic;Analytic Geometry;Analytic Geometry;Collinearity,Locus,Orthogonality,Orthogonal projection,Scalar product,Distance
1091;Lithuania;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
26;Portugal;837;1;Basic;Differential Equations;Differential Equations;Linear differential equation
250;Lithuania;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
884;Italy;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1135;Portugal;292;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
1081;Portugal;449;0;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
840;Italy;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
28;Portugal;569;1;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance,Scalar product,Cross product,Orthogonality,Collinearity
840;Italy;785;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1079;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
81;Lithuania;549;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Cross product,Orthogonality
1252;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
625;Russian Federation;792;1;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Logarithmic function
525;Portugal;513;0;Basic;Fundamental Mathematics;Elementary Geometry;Triangle inequality,Triangles
985;Romania;250;1;Basic;Differentiation;Derivatives;Quotient rule,Product rule,Trigonometric rules
151;Portugal;114;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1081;Portugal;420;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
852;Italy;233;0;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
1044;Lithuania;266;1;Basic;Differentiation;Partial Differentiation;First order,Second order
855;Italy;227;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
151;Portugal;118;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
37;Portugal;309;1;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
165;Portugal;98;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
1220;Slovenia;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1056;Lithuania;999;0;Basic;Differentiation;Partial Differentiation;First order
37;Portugal;657;1;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
1286;Italy;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1273;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1331;Portugal;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
91;Lithuania;507;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry
966;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
985;Romania;798;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
394;Portugal;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
128;Lithuania;353;1;Basic;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
1038;Lithuania;261;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
181;Italy;925;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Planar graph
176;Italy;253;0;Basic;Differentiation;Derivatives;Logarithmic rule,Trigonometric rules
899;Lithuania;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1220;Slovenia;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
72;Portugal;420;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
827;Italy;636;1;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication
91;Lithuania;493;0;Basic;Fundamental Mathematics;Elementary Geometry;Triangles,Triangle inequality
1292;Italy;778;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1077;Portugal;382;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
414;Portugal;241;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1292;Italy;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1487;Portugal;1052;1;Basic;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Conjugate number,Algebraic form,Operations with complex numbers,Real part,Equations involving complex numbers
91;Lithuania;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1350;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
411;Portugal;342;0;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Modulus of a complex number,Algebraic form
509;Portugal;637;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
1182;Portugal;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
168;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1322;Italy;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1146;Portugal;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
955;Lithuania;1117;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
552;Portugal;927;0;Advanced;Real Functions of a single variable;Domain, Image and Graphics;Planar graph
72;Portugal;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
468;Portugal;354;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
406;Portugal;363;1;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
898;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
37;Portugal;733;1;Basic;Integration;Integration Techniques;Simple integration,Direct inspection
426;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
426;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1220;Slovenia;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
985;Romania;613;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
457;Portugal;332;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1023;Lithuania;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
986;Portugal;427;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1023;Lithuania;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
37;Portugal;412;1;Basic;Integration;Integration Techniques;Power of trigonometric functions
851;Italy;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
397;Portugal;352;0;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Operations with complex numbers
1182;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
598;Italy;949;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
151;Portugal;118;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
913;Ireland;300;1;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Event,Axioms of probability
1220;Slovenia;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
204;Lithuania;666;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
913;Ireland;767;0;Basic;Probability ;Probability ;Event,Sample space
1284;Italy;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
28;Portugal;560;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality
625;Russian Federation;117;0;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1219;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
168;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
973;Portugal;246;0;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
1082;Portugal;278;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1026;Lithuania;263;0;Basic;Differentiation;Partial Differentiation;First order
181;Italy;679;0;Basic;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
1288;Portugal;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
633;Italy;420;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
352;Portugal;272;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
986;Portugal;306;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
1428;Portugal;781;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1039;Lithuania;885;0;Basic;Differentiation;Partial Differentiation;Second order,First order
90;Lithuania;354;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
967;Portugal;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
667;Portugal;183;1;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
1275;Lithuania;419;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
1220;Slovenia;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
411;Portugal;733;0;Basic;Integration;Integration Techniques;Simple integration,Direct inspection
28;Portugal;567;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a line,Orthogonality,Collinearity
1220;Slovenia;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
91;Lithuania;432;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
1291;Italy;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
955;Lithuania;1251;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
851;Italy;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
411;Portugal;610;0;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector,Spectrum,Characteristic polynomial
374;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
151;Portugal;113;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
85;Lithuania;1144;1;Basic;Set Theory;Set Theory;Subset
576;Ireland;699;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Locus,Intersection,Cartesian equations of a line
72;Portugal;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
913;Ireland;1100;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
61;Portugal;156;1;Basic;Differential Equations;Differential Equations;Linear differential equation
1543;Portugal;1087;0;Basic;Numerical Methods;Numerical Methods;First order,Second order
899;Lithuania;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1331;Portugal;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1023;Lithuania;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1220;Slovenia;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
899;Lithuania;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
67;Portugal;202;0;Basic;Statistics;Statistics;Student distribution,Confidence interval,Point estimate,Hypothesis testing
1353;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
973;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1244;Portugal;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1135;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
168;Portugal;388;0;Advanced;Integration;Integration Techniques;Rational functions
1185;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
974;Portugal;439;1;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
1080;Portugal;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
535;Portugal;351;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Imaginary part,Complex plane ,Operations with complex numbers,Real part,Principal argument,De Moivre formulas
85;Lithuania;1151;1;Basic;Set Theory;Set Theory;Subset
1308;Italy;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
986;Portugal;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1023;Lithuania;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
165;Portugal;542;0;Basic;Integration;Double Integration;y-simple region (type I),Cartesian coordinates,Area ,Iterate integrals
638;Italy;79;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
973;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1252;Portugal;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
37;Portugal;1173;1;Basic;Integration;Definite Integrals; Integration by parts,Fundamental theorem of Calculus
467;Portugal;354;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
155;Spain;493;0;Basic;Fundamental Mathematics;Elementary Geometry;Triangles,Triangle inequality
1428;Portugal;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
769;Portugal;334;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
840;Italy;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1148;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1220;Slovenia;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1023;Lithuania;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1487;Portugal;145;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
1289;Italy;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
725;Portugal;189;0;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
81;Lithuania;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
509;Portugal;227;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
80;Lithuania;736;1;Basic;Optimization;Linear Optimization;Linear programming,Excel solver add-in,Simplex method
1481;Portugal;671;0;Basic;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
1444;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1338;Portugal;289;0;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1126;Portugal;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1130;Portugal;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
91;Lithuania;522;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Triangles
1220;Slovenia;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1044;Lithuania;148;1;Basic;Differentiation;Partial Differentiation;First order
1411;Portugal;385;1;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
598;Italy;130;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
1427;Portugal;278;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
854;Italy;215;0;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Inconsistent system,Solution of linear system
625;Russian Federation;800;0;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Exponential function,Simplify expressions
1081;Portugal;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
394;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
913;Ireland;486;0;Basic;Probability ;Probability ;Event,Addition, multiplication, and total probability rules,Sample space
1179;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1163;Portugal;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
576;Ireland;951;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
91;Lithuania;508;1;Advanced;Fundamental Mathematics;Elementary Geometry;Symmetry
1517;Portugal;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
91;Lithuania;456;1;Advanced;Fundamental Mathematics;Elementary Geometry;Triangles
1171;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
851;Italy;964;1;Basic;Optimization;Nonlinear Optimization;Simplex method,Duality theory
699;Portugal;180;1;Basic;Statistics;Statistics;Mean,Median,Mode
1319;Italy;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
37;Portugal;1070;1;Basic;Differentiation;Partial Differentiation;First order
646;Ireland;80;0;Basic;Statistics;Statistics;Population,Variance,Median,Standard deviation,Mode,Quantile,Sample,Mean
197;Portugal;118;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
411;Portugal;592;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Logarithmic rule,Product rule,Trigonometric rules
1220;Slovenia;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
854;Italy;88;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
1276;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1050;Lithuania;908;0;Basic;Differentiation;Partial Differentiation;Gradient,Directional derivative
956;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
80;Lithuania;559;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
394;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
359;Portugal;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1220;Slovenia;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
52;Portugal;653;1;Basic;Linear Algebra;Matrices and Determinants;Linearly independent rows,Matrix rank
1049;Lithuania;260;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
1321;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1023;Lithuania;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
958;Lithuania;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1269;Portugal;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
510;Portugal;798;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1071;Lithuania;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
41;Portugal;181;0;Basic;Statistics;Statistics;Quantile,Frequency,Sample,Mean,Variance,Standard deviation,Median,Mode
1324;Italy;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1444;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
422;Portugal;643;0;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties,Hermitian matrix,Matrix multiplication,Linearly independent rows,Symmetric matrix,Matrix operations
625;Russian Federation;662;0;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
468;Portugal;350;0;Advanced;Complex Numbers;Complex Numbers;Complex plane 
1220;Slovenia;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
71;Portugal;650;0;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties
37;Portugal;1116;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
637;Italy;80;0;Basic;Statistics;Statistics;Population,Variance,Median,Standard deviation,Mode,Quantile,Sample,Mean
168;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
26;Portugal;217;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
465;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
414;Portugal;91;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
1220;Slovenia;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
168;Portugal;381;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1229;Portugal;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
1220;Slovenia;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
969;Romania;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1146;Portugal;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
483;Portugal;432;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
176;Italy;612;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
26;Portugal;146;1;Basic;Differential Equations;Differential Equations;Separable variables equation
37;Portugal;1014;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
1291;Italy;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
969;Romania;451;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1044;Lithuania;148;1;Basic;Differentiation;Partial Differentiation;First order
67;Portugal;181;0;Basic;Statistics;Statistics;Quantile,Frequency,Sample,Mean,Variance,Standard deviation,Median,Mode
876;Italy;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
374;Portugal;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1271;Portugal;385;0;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
352;Portugal;100;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Power rule
1220;Slovenia;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1543;Portugal;1094;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1135;Portugal;381;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
168;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
72;Portugal;782;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1219;Portugal;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
509;Portugal;793;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
1022;Lithuania;1005;0;Basic;Optimization;Nonlinear Optimization;Minimum,Stationary point,Maximum,Saddle point,Optimal solution
37;Portugal;1168;0;Basic;Integration;Definite Integrals;Direct integrals ,Fundamental theorem of Calculus
351;Portugal;795;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
168;Portugal;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
1220;Slovenia;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
168;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
626;Italy;274;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
57;Portugal;186;0;Basic;Statistics;Statistics;Population,Sample
639;Italy;177;0;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
1286;Italy;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
91;Lithuania;330;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number
168;Portugal;288;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1517;Portugal;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
168;Portugal;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
1334;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1082;Portugal;777;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
142;Portugal;667;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1286;Italy;420;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1173;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
972;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
203;Lithuania;102;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1324;Italy;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
988;Portugal;948;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
1023;Lithuania;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
664;Portugal;211;1;Basic;Statistics;Statistics;Linear regression
1427;Portugal;782;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
457;Portugal;330;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number
986;Portugal;781;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
37;Portugal;309;1;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
80;Lithuania;647;1;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Symmetric matrix,Matrix operations
890;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1049;Lithuania;876;0;Basic;Differentiation;Partial Differentiation;Directional derivative,Gradient,First order,Second order
854;Italy;215;0;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Inconsistent system,Solution of linear system
1220;Slovenia;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
625;Russian Federation;613;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
36;Portugal;1151;1;Basic;Set Theory;Set Theory;Subset
855;Italy;949;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
72;Portugal;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1023;Lithuania;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1023;Lithuania;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
552;Portugal;904;0;Basic;Differential Equations;Differential Equations;Bernoulli equation,Linear differential equation
37;Portugal;821;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Maximum,Second derivative test,Stationary point,Unconstrained optimization,Saddle point
524;Portugal;495;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
376;Portugal;346;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
827;Italy;602;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector,Spectrum,Characteristic polynomial
1276;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1023;Lithuania;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
751;Lithuania;703;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Scalar product
1322;Italy;454;1;Basic;Linear Algebra;Vector Spaces;Basis
972;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
974;Portugal;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
178;Italy;143;0;Basic;Differentiation;Derivatives;Trigonometric rules,Logarithmic rule
1334;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
913;Ireland;1138;1;Basic;Set Theory;Set Theory;Subset
1044;Lithuania;879;1;Basic;Differentiation;Partial Differentiation;First order,Second order
26;Portugal;557;1;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance
90;Lithuania;329;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
955;Lithuania;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
393;Lithuania;351;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Imaginary part,Complex plane ,Operations with complex numbers,Real part,Principal argument,De Moivre formulas
510;Portugal;646;0;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Commuting matrices,Solve matrix equation,Determinant computation,Inverse matrix ,Matrix rank,Determinant properties,Matrix multiplication,Symmetric matrix
1505;Portugal;488;1;Basic;Probability ;Probability ;Axioms of probability,Event,Addition, multiplication, and total probability rules,Sample space
1338;Portugal;778;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
422;Portugal;126;1;Advanced;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Solve matrix equation
176;Italy;752;1;Basic;Differentiation;Derivatives;Power rule,Quotient rule,Product rule,Trigonometric rules
1044;Lithuania;257;1;Basic;Differentiation;Partial Differentiation;Gradient,First order
625;Russian Federation;114;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
753;Italy;258;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
1564;Portugal;399;0;Basic;Integration;Integration Techniques;Substitution,Direct inspection,Simple integration
1487;Portugal;335;1;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
625;Russian Federation;789;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
37;Portugal;1067;0;Advanced;Differentiation;Partial Differentiation;Power rule,Trigonometric rules,Logarithmic rule
576;Ireland;565;0;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonal projection,Orthogonality,Collinearity,Locus
988;Portugal;229;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
1220;Slovenia;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1080;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
175;Italy;1496;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
1543;Portugal;1112;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
625;Russian Federation;117;0;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1479;Portugal;866;1;Basic;Optimization;Nonlinear Optimization;Stationary point,Maximum,Saddle point,Optimal solution,Minimum
155;Spain;904;0;Basic;Differential Equations;Differential Equations;Bernoulli equation,Linear differential equation
899;Lithuania;420;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1023;Lithuania;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1023;Lithuania;454;1;Basic;Linear Algebra;Vector Spaces;Basis
851;Italy;155;0;Basic;Optimization;Nonlinear Optimization;Lagrange multipliers,Maximum,Minimum
1039;Lithuania;885;0;Basic;Differentiation;Partial Differentiation;Second order,First order
1220;Slovenia;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
91;Lithuania;634;1;Basic;Linear Algebra;Matrices and Determinants;Determinant properties,Inverse matrix ,Solve matrix equation,Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Commuting matrices,Determinant computation
473;Portugal;288;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
876;Italy;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
91;Lithuania;513;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangle inequality,Triangles
898;Portugal;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
426;Portugal;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
200;Lithuania;733;1;Basic;Integration;Integration Techniques;Simple integration,Direct inspection
1179;Portugal;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
175;Italy;1474;1;Basic;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
511;Portugal;130;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
1023;Lithuania;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1288;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
91;Lithuania;508;1;Advanced;Fundamental Mathematics;Elementary Geometry;Symmetry
1252;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
91;Lithuania;367;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometrical figures
91;Lithuania;514;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangle inequality,Triangles
1277;Portugal;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1289;Italy;419;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
625;Russian Federation;950;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1352;Portugal;454;1;Basic;Linear Algebra;Vector Spaces;Basis
1143;Portugal;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1023;Lithuania;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
851;Italy;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
524;Portugal;794;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1252;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1340;Portugal;1090;0;Basic;Numerical Methods;Numerical Methods;Nonlinear equation,Newton’s method
1196;Slovenia;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
582;Lithuania;698;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Orthogonal projection,Distance
128;Lithuania;645;0;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Linearly independent rows
1070;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
28;Portugal;560;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality
64;Portugal;576;1;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
634;Italy;657;1;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
1322;Italy;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1256;Portugal;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
37;Portugal;1066;1;Advanced;Differentiation;Partial Differentiation;First order,Second order
1289;Italy;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
90;Lithuania;133;0;Advanced;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
175;Italy;1485;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
853;Italy;245;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
204;Lithuania;366;0;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids,Geometrical figures,Classification of geometric solids
28;Portugal;948;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
955;Lithuania;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1082;Portugal;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
967;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
167;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1220;Slovenia;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
71;Portugal;612;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1157;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
986;Portugal;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
852;Italy;215;0;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Inconsistent system,Solution of linear system
1487;Portugal;331;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1220;Slovenia;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
174;Portugal;519;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1322;Italy;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
853;Italy;230;0;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
420;Portugal;342;0;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Modulus of a complex number,Algebraic form
972;Portugal;779;0;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
1220;Slovenia;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
91;Lithuania;456;0;Advanced;Fundamental Mathematics;Elementary Geometry;Triangles
1308;Italy;292;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
1082;Portugal;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
80;Lithuania;327;1;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
91;Lithuania;424;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1049;Lithuania;1002;0;Basic;Differentiation;Partial Differentiation;First order
168;Portugal;420;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1081;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
351;Portugal;787;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Logarithmic function
351;Portugal;735;1;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
990;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
625;Russian Federation;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
174;Portugal;341;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
1219;Portugal;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
884;Italy;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
1332;Portugal;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
625;Russian Federation;513;0;Basic;Fundamental Mathematics;Elementary Geometry;Triangle inequality,Triangles
91;Lithuania;369;1;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Geometrical figures,Classification of geometrical figures
967;Portugal;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
1517;Portugal;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
91;Lithuania;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
642;Italy;191;1;Basic;Statistics;Statistics;Median,Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance
483;Portugal;665;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
890;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
884;Italy;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1282;Portugal;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1220;Slovenia;454;1;Basic;Linear Algebra;Vector Spaces;Basis
1351;Portugal;782;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
524;Portugal;494;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
741;Ireland;480;1;Basic;Graph Theory;Graph Theory;Planar graph
1122;Portugal;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
175;Italy;1106;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
374;Portugal;645;1;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Linearly independent rows
852;Italy;233;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
576;Ireland;567;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a line,Orthogonality,Collinearity
885;Italy;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1023;Lithuania;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
913;Ireland;222;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
625;Russian Federation;120;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
72;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
636;Italy;201;1;Basic;Statistics;Statistics;Chi square distribution,Student distribution,Quantile,Hypothesis testing
1220;Slovenia;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
986;Portugal;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1518;Portugal;767;1;Basic;Probability ;Probability ;Event,Sample space
168;Portugal;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
387;Portugal;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
979;Portugal;1251;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
1087;Portugal;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
71;Portugal;1107;1;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
840;Italy;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
524;Portugal;646;1;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Commuting matrices,Solve matrix equation,Determinant computation,Inverse matrix ,Matrix rank,Determinant properties,Matrix multiplication,Symmetric matrix
1277;Portugal;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
853;Italy;242;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1538;Portugal;1102;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
470;Portugal;552;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product
1147;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1341;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
426;Portugal;358;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Conjugate number,Operations with complex numbers,Real part
1220;Slovenia;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
69;Portugal;556;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line,Collinearity
1220;Slovenia;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
91;Lithuania;349;0;Advanced;Complex Numbers;Complex Numbers;Complex plane 
551;Lithuania;340;0;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers,Conjugate number
690;Portugal;78;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
898;Portugal;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
57;Portugal;187;0;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
28;Portugal;211;0;Basic;Statistics;Statistics;Linear regression
378;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1173;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
177;Italy;657;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
1291;Italy;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
351;Portugal;721;0;Basic;Differentiation;Derivatives;Quotient rule,Trigonometric rules
71;Portugal;567;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a line,Orthogonality,Collinearity
1308;Italy;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1505;Portugal;958;0;Basic;Optimization;Linear Optimization;Linear programming
28;Portugal;699;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Locus,Intersection,Cartesian equations of a line
376;Portugal;340;0;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers,Conjugate number
899;Lithuania;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1220;Slovenia;454;0;Basic;Linear Algebra;Vector Spaces;Basis
876;Italy;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
168;Portugal;419;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
876;Italy;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
524;Portugal;787;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Logarithmic function
41;Portugal;77;1;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
1081;Portugal;424;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1044;Lithuania;875;0;Basic;Differentiation;Partial Differentiation;Gradient,First order
524;Portugal;113;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
979;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
91;Lithuania;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
549;Portugal;703;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Scalar product
26;Portugal;92;1;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
387;Portugal;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
250;Lithuania;218;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
71;Portugal;328;1;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
166;Portugal;701;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product,Distance
426;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
168;Portugal;449;0;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
1220;Slovenia;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1081;Portugal;427;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1411;Portugal;778;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1122;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
625;Russian Federation;799;0;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
775;Portugal;301;0;Basic;Probability ;Probability ;Sample space,Event
1338;Portugal;782;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
80;Lithuania;363;1;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
359;Portugal;424;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
80;Lithuania;545;0;Basic;Integration;Double Integration;y-simple region (type I),Area ,Cartesian coordinates
1286;Italy;418;1;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
311;Ireland;125;0;Basic;Linear Algebra;Matrices and Determinants;Determinant properties,Symmetric matrix,Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication
1087;Portugal;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
414;Portugal;335;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
1286;Italy;306;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
956;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
473;Portugal;779;0;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
884;Italy;441;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span
462;Lithuania;272;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
1082;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1565;Portugal;412;0;Basic;Integration;Integration Techniques;Power of trigonometric functions
986;Portugal;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
1050;Lithuania;261;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
411;Portugal;88;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
1479;Portugal;821;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Maximum,Second derivative test,Stationary point,Unconstrained optimization,Saddle point
955;Lithuania;1119;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
387;Portugal;439;1;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
91;Lithuania;369;1;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Geometrical figures,Classification of geometrical figures
72;Portugal;342;0;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Modulus of a complex number,Algebraic form
956;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
483;Portugal;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1379;Portugal;921;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
582;Lithuania;573;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Locus,Scalar product,Cross product,Collinearity
1286;Italy;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1166;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1095;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
840;Italy;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
198;Italy;460;0;Basic;Fundamental Mathematics;Elementary Geometry;Polyhedrons,Platonic solids,Geometric solids
884;Italy;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1333;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1517;Portugal;448;0;Advanced;Linear Algebra;Vector Spaces;Subspace
421;Portugal;327;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
913;Ireland;1095;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
884;Italy;451;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1299;Italy;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
36;Portugal;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
625;Russian Federation;464;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Geometrical figures
683;Ireland;211;1;Basic;Statistics;Statistics;Linear regression
1018;Lithuania;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
91;Lithuania;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
91;Lithuania;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
160;Portugal;104;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
457;Portugal;351;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Imaginary part,Complex plane ,Operations with complex numbers,Real part,Principal argument,De Moivre formulas
41;Portugal;584;1;Basic;Graph Theory;Graph Theory;Adjacency matrix
1135;Portugal;278;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1220;Slovenia;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
967;Portugal;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1220;Slovenia;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
71;Portugal;735;1;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
455;Portugal;640;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
1518;Portugal;135;0;Basic;Linear Algebra;Matrices and Determinants;Symmetric matrix,Determinant computation,Determinant properties
525;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
41;Portugal;211;1;Basic;Statistics;Statistics;Linear regression
974;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1517;Portugal;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1411;Portugal;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
483;Portugal;371;0;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Geometrical figures
1220;Slovenia;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
1271;Portugal;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1080;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
955;Lithuania;455;0;Basic;Linear Algebra;Vector Spaces;Basis
80;Lithuania;281;1;Basic;Optimization;Linear Optimization;Linear programming
576;Ireland;702;0;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Intersection,Cartesian equations of a line
91;Lithuania;358;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Conjugate number,Operations with complex numbers,Real part
41;Portugal;185;1;Basic;Statistics;Statistics;Frequency,Quantile,Mean,Variance,Median,Mode
91;Lithuania;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
1308;Italy;778;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
80;Lithuania;765;1;Basic;Probability ;Probability ;Addition, multiplication, and total probability rules
411;Portugal;334;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
525;Portugal;612;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
689;Portugal;964;0;Basic;Optimization;Nonlinear Optimization;Simplex method,Duality theory
181;Italy;83;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain,Image of a function
151;Portugal;120;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
674;Ireland;186;0;Basic;Statistics;Statistics;Population,Sample
175;Italy;1119;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
884;Italy;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
509;Portugal;640;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
1220;Slovenia;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
91;Lithuania;505;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangles
1281;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
658;Ireland;189;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
1044;Lithuania;878;1;Basic;Differentiation;Partial Differentiation;Second order,First order
168;Portugal;393;0;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
1505;Portugal;742;0;Basic;Optimization;Linear Optimization;Duality theory,Linear programming
972;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
955;Lithuania;1099;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
851;Italy;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
168;Portugal;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
41;Portugal;570;1;Advanced;Analytic Geometry;Analytic Geometry;Distance,Orthogonal projection,Orthogonality
1244;Portugal;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
91;Lithuania;420;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1564;Portugal;922;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1049;Lithuania;253;0;Basic;Differentiation;Derivatives;Logarithmic rule,Trigonometric rules
197;Portugal;667;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1289;Italy;783;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
684;Ireland;204;0;Basic;Statistics;Statistics;Student distribution,Hypothesis testing
660;Portugal;182;0;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
979;Portugal;89;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
953;Lithuania;78;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
80;Lithuania;300;1;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Event,Axioms of probability
975;Portugal;603;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector,Spectrum,Characteristic polynomial
1379;Portugal;925;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Planar graph
168;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
175;Italy;1092;1;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
969;Romania;424;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
151;Portugal;114;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
840;Italy;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
625;Russian Federation;458;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Geometric transformations,Geometrical figures
753;Italy;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
393;Lithuania;351;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Imaginary part,Complex plane ,Operations with complex numbers,Real part,Principal argument,De Moivre formulas
168;Portugal;290;0;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
884;Italy;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1192;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
524;Portugal;794;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1080;Portugal;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
700;Portugal;193;1;Basic;Statistics;Statistics;Standard deviation,Variance,Median,Frequency,Mode,Outliers,Quantile,Interquartile range,Population,Data type,Sample,Relative frequency,Mean
1271;Portugal;454;1;Basic;Linear Algebra;Vector Spaces;Basis
625;Russian Federation;461;0;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
1509;Portugal;923;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
509;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
913;Ireland;193;1;Basic;Statistics;Statistics;Standard deviation,Variance,Median,Frequency,Mode,Outliers,Quantile,Interquartile range,Population,Data type,Sample,Relative frequency,Mean
1324;Italy;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
80;Lithuania;736;1;Basic;Optimization;Linear Optimization;Linear programming,Excel solver add-in,Simplex method
1219;Portugal;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
955;Lithuania;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
1322;Italy;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
91;Lithuania;448;1;Advanced;Linear Algebra;Vector Spaces;Subspace
898;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1334;Portugal;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1023;Lithuania;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
28;Portugal;558;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
851;Italy;821;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Maximum,Second derivative test,Stationary point,Unconstrained optimization,Saddle point
1220;Slovenia;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
168;Portugal;451;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
414;Portugal;222;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
625;Russian Federation;802;1;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1157;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1288;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
852;Italy;215;0;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Inconsistent system,Solution of linear system
509;Portugal;123;1;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication,Determinant properties,Symmetric matrix
349;Portugal;94;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
1158;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
576;Ireland;123;0;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication,Determinant properties,Symmetric matrix
71;Portugal;666;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
91;Lithuania;521;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Regular polygon
1286;Italy;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
387;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1379;Portugal;923;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1220;Slovenia;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
376;Portugal;355;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
899;Lithuania;449;1;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
626;Italy;275;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
986;Portugal;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1150;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
955;Lithuania;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1077;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
853;Italy;229;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
71;Portugal;294;0;Basic;Probability ;Probability ;Event,Axioms of probability,Sample space
359;Portugal;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
352;Portugal;93;0;Basic;Differentiation;Derivatives;Product rule,Logarithmic rule,Trigonometric rules
1109;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1564;Portugal;271;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
750;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
473;Portugal;351;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Imaginary part,Complex plane ,Operations with complex numbers,Real part,Principal argument,De Moivre formulas
1220;Slovenia;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1220;Slovenia;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
600;Italy;231;0;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system,Solution of linear system
168;Portugal;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1292;Italy;455;1;Basic;Linear Algebra;Vector Spaces;Basis
1044;Lithuania;875;0;Basic;Differentiation;Partial Differentiation;Gradient,First order
582;Lithuania;557;0;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance
1220;Slovenia;785;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
468;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1220;Slovenia;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
913;Ireland;1094;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
525;Portugal;495;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
851;Italy;911;1;Basic;Optimization;Nonlinear Optimization;Minimum,Stationary point,Maximum,Saddle point,Optimal solution
36;Portugal;273;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
359;Portugal;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
457;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
91;Lithuania;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
776;Portugal;562;0;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality
181;Italy;918;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1034;Lithuania;883;0;Basic;Differentiation;Partial Differentiation;First order,Directional derivative
72;Portugal;326;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part
1220;Slovenia;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1087;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1230;Portugal;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
699;Portugal;79;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
511;Portugal;92;1;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
884;Italy;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
979;Portugal;779;1;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
376;Portugal;331;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
80;Lithuania;565;0;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonal projection,Orthogonality,Collinearity,Locus
91;Lithuania;461;0;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
955;Lithuania;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1517;Portugal;779;1;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
899;Lithuania;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
91;Lithuania;368;0;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids,Regular polygon
1543;Portugal;1101;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1517;Portugal;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
168;Portugal;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
851;Italy;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1093;Portugal;381;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
524;Portugal;228;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
684;Ireland;182;1;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
913;Ireland;1213;1;Basic;Numerical Methods;Numerical Methods;Mean,Median,Outliers,Interquartile range
1029;Lithuania;262;0;Basic;Differentiation;Partial Differentiation;First order
380;Portugal;910;1;Basic;Optimization;Nonlinear Optimization;Minimum,Maximum,Lagrange multipliers,Saddle point,Unconstrained optimization,Second derivative test
1543;Portugal;1089;0;Basic;Numerical Methods;Numerical Methods;First order,Second order
1219;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
411;Portugal;593;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue
1171;Portugal;960;0;Basic;Optimization;Nonlinear Optimization;Linear programming
679;Portugal;79;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
1505;Portugal;962;1;Basic;Optimization;Linear Optimization;Simplex method,Duality theory
1070;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1543;Portugal;1107;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1080;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
661;Portugal;177;0;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
1277;Portugal;278;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
85;Lithuania;1128;1;Basic;Set Theory;Set Theory;Subset
91;Lithuania;517;1;Advanced;Fundamental Mathematics;Elementary Geometry;Symmetry
81;Lithuania;454;1;Basic;Linear Algebra;Vector Spaces;Basis
1220;Slovenia;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1023;Lithuania;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1487;Portugal;341;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
1402;Portugal;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
511;Portugal;239;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1308;Italy;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
422;Portugal;130;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
1256;Portugal;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
80;Lithuania;541;0;Basic;Integration;Double Integration;y-simple region (type I),Cartesian coordinates,Iterate integrals
1147;Portugal;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
91;Lithuania;367;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometrical figures
827;Italy;218;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1273;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
1077;Portugal;288;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1274;Portugal;794;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
175;Italy;147;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
1288;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1037;Lithuania;1001;0;Basic;Differentiation;Partial Differentiation;Power rule,Trigonometric rules,Logarithmic rule
1157;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1564;Portugal;414;0;Basic;Integration;Integration Techniques;Substitution,Direct inspection,Integration by parts,Rational functions
1561;Portugal;681;1;Basic;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
1561;Portugal;392;0;Advanced;Integration;Integration Techniques;Substitution
840;Italy;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1300;Italy;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1147;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
175;Italy;1103;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
407;Portugal;335;1;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
988;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1220;Slovenia;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1305;Italy;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
91;Lithuania;349;1;Advanced;Complex Numbers;Complex Numbers;Complex plane 
72;Portugal;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
535;Portugal;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1543;Portugal;1094;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1157;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1220;Slovenia;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1196;Slovenia;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
854;Italy;227;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
411;Portugal;414;0;Basic;Integration;Integration Techniques;Substitution,Direct inspection,Integration by parts,Rational functions
1220;Slovenia;454;0;Basic;Linear Algebra;Vector Spaces;Basis
64;Portugal;703;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Scalar product
1334;Portugal;278;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
913;Ireland;1088;0;Basic;Numerical Methods;Numerical Methods;First order,Second order
155;Spain;275;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
72;Portugal;548;0;Basic;Analytic Geometry;Analytic Geometry;Collinearity,Distance,Locus,Cross product,Orthogonality,Scalar product
1274;Portugal;614;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
380;Portugal;351;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Imaginary part,Complex plane ,Operations with complex numbers,Real part,Principal argument,De Moivre formulas
1148;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1286;Italy;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1077;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
411;Portugal;341;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
509;Portugal;640;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
1196;Slovenia;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1220;Slovenia;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
81;Lithuania;781;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
913;Ireland;1116;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
168;Portugal;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
965;Portugal;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1244;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1275;Lithuania;448;0;Advanced;Linear Algebra;Vector Spaces;Subspace
71;Portugal;639;0;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Determinant computation,Determinant properties,Matrix operations
197;Portugal;102;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
411;Portugal;593;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue
1557;Portugal;670;1;Advanced;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
1143;Portugal;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
967;Portugal;449;1;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
422;Portugal;133;1;Advanced;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
403;Portugal;306;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
1339;Portugal;446;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
71;Portugal;253;0;Basic;Differentiation;Derivatives;Logarithmic rule,Trigonometric rules
1173;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1279;Portugal;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1288;Portugal;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1081;Portugal;449;0;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
80;Lithuania;332;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
967;Portugal;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
81;Lithuania;783;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
576;Ireland;550;0;Advanced;Analytic Geometry;Analytic Geometry;Cross product,Orthogonality
913;Ireland;1119;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
1220;Slovenia;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
411;Portugal;596;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Eigenvalue
955;Lithuania;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
473;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
1023;Lithuania;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
551;Lithuania;358;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Conjugate number,Operations with complex numbers,Real part
913;Ireland;420;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
661;Portugal;81;1;Basic;Statistics;Statistics;Mean,Median,Mode
851;Italy;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
955;Lithuania;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1081;Portugal;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1080;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
956;Portugal;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
37;Portugal;399;1;Basic;Integration;Integration Techniques;Substitution,Direct inspection,Simple integration
72;Portugal;292;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
884;Italy;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
625;Russian Federation;460;0;Basic;Fundamental Mathematics;Elementary Geometry;Polyhedrons,Platonic solids,Geometric solids
91;Lithuania;346;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
1339;Portugal;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
966;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
956;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
598;Italy;635;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
411;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1291;Italy;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
72;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
898;Portugal;818;0;Basic;Optimization;Nonlinear Optimization;Minimum,Maximum,Stationary point,Second derivative test,Unconstrained optimization,Saddle point,Optimal solution
72;Portugal;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
411;Portugal;605;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Spectrum,Diagonalization,Characteristic polynomial
406;Portugal;230;0;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
1182;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
240;Lithuania;83;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain,Image of a function
1087;Portugal;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
776;Portugal;553;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Distance,Scalar product
197;Portugal;666;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
979;Portugal;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
876;Italy;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
956;Portugal;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1375;Portugal;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1271;Portugal;292;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
168;Portugal;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
918;Portugal;268;0;Basic;Differentiation;Partial Differentiation;First order,Second order
1271;Portugal;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
851;Italy;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
753;Italy;876;0;Basic;Differentiation;Partial Differentiation;Directional derivative,Gradient,First order,Second order
91;Lithuania;777;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1286;Italy;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
483;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1049;Lithuania;269;1;Basic;Differentiation;Partial Differentiation;First order,Second order
91;Lithuania;342;0;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Modulus of a complex number,Algebraic form
1220;Slovenia;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
876;Italy;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
166;Portugal;573;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Locus,Scalar product,Cross product,Collinearity
202;Lithuania;613;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
851;Italy;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
890;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1481;Portugal;546;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonal projection,Distance,Cross product,Orthogonality
470;Portugal;554;1;Basic;Analytic Geometry;Analytic Geometry;Scalar product,Orthogonality,Orthogonal projection,Distance
1220;Slovenia;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1481;Portugal;757;0;Basic;Integration;Double Integration;Iterate integrals,Cartesian coordinates,y-simple region (type I)
524;Portugal;108;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
853;Italy;222;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
524;Portugal;461;0;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
898;Portugal;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
165;Portugal;393;0;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
142;Portugal;613;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
884;Italy;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1126;Portugal;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1220;Slovenia;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
359;Portugal;665;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1286;Italy;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
203;Lithuania;112;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
509;Portugal;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
851;Italy;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
689;Portugal;862;0;Basic;Optimization;Nonlinear Optimization;Saddle point,Optimal solution,Minimum,Maximum,Stationary point
1517;Portugal;854;0;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Diagonalization,Spectrum,Characteristic polynomial
374;Portugal;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
405;Portugal;104;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1022;Lithuania;965;0;Basic;Optimization;Linear Optimization;Excel solver add-in,Simplex method,Linear programming,Transportation problem
511;Portugal;612;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1557;Portugal;676;0;Advanced;Real Functions of a single variable;Domain, Image and Graphics;Domain,Image of a function
1291;Italy;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1284;Italy;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
422;Portugal;326;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part
483;Portugal;142;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
965;Portugal;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
69;Portugal;564;0;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonality
1023;Lithuania;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
966;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1252;Portugal;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1158;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1026;Lithuania;878;0;Basic;Differentiation;Partial Differentiation;Second order,First order
1220;Slovenia;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1339;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1146;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1256;Portugal;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
91;Lithuania;505;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangles
1220;Slovenia;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
378;Portugal;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
1504;Portugal;330;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number
37;Portugal;787;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Logarithmic function
1271;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
80;Lithuania;233;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
890;Portugal;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
683;Ireland;188;0;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
840;Italy;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
344;Portugal;665;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1146;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1076;Portugal;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
72;Portugal;338;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form
411;Portugal;94;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
168;Portugal;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
986;Portugal;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1135;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
90;Lithuania;125;0;Basic;Linear Algebra;Matrices and Determinants;Determinant properties,Symmetric matrix,Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication
913;Ireland;773;1;Basic;Probability ;Probability ;Event,Sample space,Addition, multiplication, and total probability rules,Axioms of probability
551;Lithuania;335;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
956;Portugal;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
988;Portugal;952;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1220;Slovenia;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
405;Portugal;795;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
168;Portugal;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
853;Italy;244;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1324;Italy;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
91;Lithuania;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
168;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
81;Lithuania;568;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
1082;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1032;Lithuania;1000;0;Basic;Differentiation;Partial Differentiation;First order
898;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1135;Portugal;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
634;Italy;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
1505;Portugal;1021;0;Basic;Optimization;Linear Optimization;Simplex method,Linear programming,Assignment problem,Excel solver add-in
1182;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
200;Lithuania;723;0;Basic;Integration;Integration Techniques;Substitution
1156;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
750;Portugal;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
71;Portugal;645;0;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Linearly independent rows
1220;Slovenia;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1220;Slovenia;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1332;Portugal;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
349;Portugal;252;0;Basic;Differentiation;Derivatives;Quotient rule,Product rule,Power rule,Trigonometric rules
851;Italy;860;1;Basic;Optimization;Nonlinear Optimization;Saddle point,Optimal solution,Minimum,Maximum,Stationary point
966;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
637;Italy;204;1;Basic;Statistics;Statistics;Student distribution,Hypothesis testing
1334;Portugal;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
1135;Portugal;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
91;Lithuania;504;0;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry,Geometric transformations
1220;Slovenia;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1289;Italy;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1322;Italy;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1220;Slovenia;455;1;Basic;Linear Algebra;Vector Spaces;Basis
168;Portugal;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
457;Portugal;333;1;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
91;Lithuania;498;1;Advanced;Fundamental Mathematics;Elementary Geometry;Triangles,Classification of geometrical figures,Geometrical figures
1093;Portugal;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
854;Italy;949;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
168;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
239;Lithuania;143;1;Basic;Differentiation;Derivatives;Trigonometric rules,Logarithmic rule
37;Portugal;329;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1252;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1109;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
176;Italy;250;1;Basic;Differentiation;Derivatives;Quotient rule,Product rule,Trigonometric rules
175;Italy;1104;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
175;Italy;1216;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
913;Ireland;1105;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
61;Portugal;165;1;Basic;Differential Equations;Differential Equations;Linear differential equation,Homogeneous equation
168;Portugal;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
751;Lithuania;557;0;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance
511;Portugal;224;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
967;Portugal;288;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
985;Romania;794;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1256;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1182;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
986;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
524;Portugal;219;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
851;Italy;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1282;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1044;Lithuania;999;0;Basic;Differentiation;Partial Differentiation;First order
1252;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
913;Ireland;427;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
885;Italy;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
177;Italy;112;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
851;Italy;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1557;Portugal;835;0;Basic;Differential Equations;Differential Equations;Exact differential form,Cauchy problem
625;Russian Federation;517;0;Advanced;Fundamental Mathematics;Elementary Geometry;Symmetry
1109;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
26;Portugal;302;1;Basic;Probability ;Probability ;Addition, multiplication, and total probability rules,Sample space,Event,Axioms of probability
1146;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
394;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
37;Portugal;1198;0;Basic;Integration;Definite Integrals;Area of a planar region ,Fundamental theorem of Calculus
1288;Portugal;777;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1271;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1286;Italy;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1082;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1256;Portugal;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
201;Lithuania;786;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
37;Portugal;735;1;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
1109;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
421;Portugal;341;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
1339;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
990;Portugal;625;1;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Characteristic polynomial,Eigenvalue,Diagonalization,Eigenvector,Spectrum
176;Italy;254;0;Basic;Differentiation;Derivatives;Logarithmic rule,Power rule,Trigonometric rules
52;Portugal;137;1;Basic;Linear Algebra;Matrices and Determinants;Matrix equivalent - echelon,Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Linearly independent rows,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
1182;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1543;Portugal;1098;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
168;Portugal;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
918;Portugal;394;0;Basic;Integration;Integration Techniques;Substitution
175;Italy;720;0;Basic;Differentiation;Derivatives;Quotient rule,Trigonometric rules,Logarithmic rule,Product rule
1220;Slovenia;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
197;Portugal;120;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1271;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
913;Ireland;1107;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
91;Lithuania;357;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
91;Lithuania;367;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometrical figures
359;Portugal;506;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry
168;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
988;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1525;Portugal;749;0;Advanced;Optimization;Linear Optimization;Postoptimality analysis,Duality theory,Excel solver add-in,Simplex method,Linear programming,Sensitivity analysis
411;Portugal;646;1;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Commuting matrices,Solve matrix equation,Determinant computation,Inverse matrix ,Matrix rank,Determinant properties,Matrix multiplication,Symmetric matrix
658;Ireland;184;0;Basic;Statistics;Statistics;Frequency,Sample,Stem and Leaf diagram,Variance,Standard deviation,Relative frequency
72;Portugal;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
1220;Slovenia;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
69;Portugal;558;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
1194;Portugal;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
91;Lithuania;497;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
852;Italy;215;0;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Inconsistent system,Solution of linear system
1220;Slovenia;785;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
660;Portugal;177;1;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
625;Russian Federation;796;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Logarithmic function,Exponential function,Simplify expressions
1242;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
91;Lithuania;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
511;Portugal;796;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Logarithmic function,Exponential function,Simplify expressions
525;Portugal;102;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
725;Portugal;187;0;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
986;Portugal;777;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
955;Lithuania;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
899;Lithuania;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1082;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1542;Portugal;1087;1;Basic;Numerical Methods;Numerical Methods;First order,Second order
720;Portugal;181;1;Basic;Statistics;Statistics;Quantile,Frequency,Sample,Mean,Variance,Standard deviation,Median,Mode
1542;Portugal;1106;1;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1505;Portugal;79;1;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
876;Italy;785;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
311;Ireland;130;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
1044;Lithuania;257;1;Basic;Differentiation;Partial Differentiation;Gradient,First order
955;Lithuania;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
986;Portugal;424;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
988;Portugal;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1322;Italy;455;1;Basic;Linear Algebra;Vector Spaces;Basis
1543;Portugal;1091;0;Basic;Numerical Methods;Numerical Methods;Nonlinear equation,Newton’s method
57;Portugal;186;0;Basic;Statistics;Statistics;Population,Sample
1427;Portugal;778;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
965;Portugal;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
201;Lithuania;798;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
890;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1525;Portugal;744;0;Basic;Optimization;Linear Optimization;Excel solver add-in,Simplex method,Linear programming
1220;Slovenia;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
91;Lithuania;502;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry,Geometric transformations
955;Lithuania;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
840;Italy;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
717;Portugal;190;1;Basic;Statistics;Statistics;Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance,Median
1247;Portugal;130;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
1024;Lithuania;261;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
986;Portugal;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1080;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
411;Portugal;271;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
1322;Italy;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
406;Portugal;108;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
599;Italy;610;1;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector,Spectrum,Characteristic polynomial
91;Lithuania;432;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
1220;Slovenia;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
72;Portugal;338;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form
167;Portugal;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
1243;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1289;Italy;439;0;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
1044;Lithuania;266;1;Basic;Differentiation;Partial Differentiation;First order,Second order
91;Lithuania;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
751;Lithuania;275;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
128;Lithuania;341;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
177;Italy;665;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1481;Portugal;192;1;Basic;Integration;Integration Techniques;Trigonometric substitution,Simple integration
1288;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1087;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
64;Portugal;94;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
1319;Italy;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
483;Portugal;112;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1044;Lithuania;153;1;Advanced;Differentiation;Partial Differentiation;Stationary point,Minimum,Optimal solution,Lagrange multipliers
203;Lithuania;798;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1045;Lithuania;268;0;Basic;Differentiation;Partial Differentiation;First order,Second order
351;Portugal;660;0;Advanced;Differentiation;Derivatives;Product rule,Trigonometric rules,Quotient rule
1271;Portugal;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1150;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
483;Portugal;503;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry,Geometric transformations
669;Portugal;190;0;Basic;Statistics;Statistics;Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance,Median
473;Portugal;359;1;Advanced;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
885;Italy;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
359;Portugal;798;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
625;Russian Federation;363;0;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
375;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
473;Portugal;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
483;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
840;Italy;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1220;Slovenia;454;1;Basic;Linear Algebra;Vector Spaces;Basis
986;Portugal;448;0;Advanced;Linear Algebra;Vector Spaces;Subspace
1518;Portugal;123;1;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication,Determinant properties,Symmetric matrix
953;Lithuania;77;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
658;Ireland;202;0;Basic;Statistics;Statistics;Student distribution,Confidence interval,Point estimate,Hypothesis testing
1023;Lithuania;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
393;Lithuania;347;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
37;Portugal;143;1;Basic;Differentiation;Derivatives;Trigonometric rules,Logarithmic rule
1087;Portugal;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1220;Slovenia;455;1;Basic;Linear Algebra;Vector Spaces;Basis
1220;Slovenia;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
378;Portugal;561;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
1146;Portugal;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
37;Portugal;337;1;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form,Operations with complex numbers,Modulus of a complex number
72;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
641;Italy;182;0;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
1324;Italy;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
175;Italy;1052;0;Basic;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Conjugate number,Algebraic form,Operations with complex numbers,Real part,Equations involving complex numbers
551;Lithuania;329;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1247;Portugal;345;1;Advanced;Complex Numbers;Complex Numbers;Polar representation,Trigonometric form,Modulus of a complex number,Operations with complex numbers,Algebraic form,Principal argument,De Moivre formulas
972;Portugal;306;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
41;Portugal;165;1;Basic;Differential Equations;Differential Equations;Linear differential equation,Homogeneous equation
422;Portugal;335;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
988;Portugal;243;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
26;Portugal;1144;1;Basic;Set Theory;Set Theory;Subset
455;Portugal;192;0;Basic;Integration;Integration Techniques;Trigonometric substitution,Simple integration
71;Portugal;909;1;Basic;Differentiation;Partial Differentiation;Power rule,Trigonometric rules,Logarithmic rule
91;Lithuania;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
69;Portugal;559;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
1291;Italy;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
175;Italy;329;1;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1023;Lithuania;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1402;Portugal;278;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
876;Italy;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1220;Slovenia;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
473;Portugal;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1079;Portugal;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
683;Ireland;78;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
1242;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
576;Ireland;546;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonal projection,Distance,Cross product,Orthogonality
1143;Portugal;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
26;Portugal;560;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality
189;Portugal;363;0;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
359;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1081;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
91;Lithuania;350;0;Advanced;Complex Numbers;Complex Numbers;Complex plane 
988;Portugal;432;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
91;Lithuania;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1087;Portugal;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
72;Portugal;328;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1322;Italy;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1122;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1023;Lithuania;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1339;Portugal;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
985;Romania;668;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
600;Italy;234;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
409;Portugal;331;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
552;Portugal;566;0;Basic;Analytic Geometry;Analytic Geometry;Distance,Orthogonality,Locus
175;Italy;338;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form
913;Ireland;190;1;Basic;Statistics;Statistics;Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance,Median
1143;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1157;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
599;Italy;606;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector,Diagonalization
80;Lithuania;558;0;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
1026;Lithuania;148;0;Basic;Differentiation;Partial Differentiation;First order
470;Portugal;354;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
91;Lithuania;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1220;Slovenia;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
955;Lithuania;454;0;Basic;Linear Algebra;Vector Spaces;Basis
1023;Lithuania;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
351;Portugal;612;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
37;Portugal;97;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
979;Portugal;136;0;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
470;Portugal;563;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
851;Italy;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1247;Portugal;340;0;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers,Conjugate number
511;Portugal;229;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
1311;Italy;290;0;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
851;Italy;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
890;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1286;Italy;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
198;Italy;461;0;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
918;Portugal;94;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
91;Lithuania;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
956;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
80;Lithuania;297;1;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Event,Axioms of probability
415;Portugal;132;1;Advanced;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
700;Portugal;183;0;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
199;Lithuania;114;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
753;Italy;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
969;Romania;446;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
483;Portugal;795;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
1044;Lithuania;876;1;Basic;Differentiation;Partial Differentiation;Directional derivative,Gradient,First order,Second order
956;Portugal;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
975;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1252;Portugal;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1093;Portugal;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
552;Portugal;835;0;Basic;Differential Equations;Differential Equations;Exact differential form,Cauchy problem
1220;Slovenia;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
376;Portugal;347;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
1379;Portugal;920;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
168;Portugal;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1557;Portugal;920;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1517;Portugal;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1543;Portugal;1112;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1525;Portugal;304;0;Basic;Probability ;Probability ;Addition, multiplication, and total probability rules,Sample space,Event,Axioms of probability
37;Portugal;881;1;Advanced;Differentiation;Partial Differentiation;Directional derivative,Gradient
890;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
393;Lithuania;349;1;Advanced;Complex Numbers;Complex Numbers;Complex plane 
955;Lithuania;1110;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1023;Lithuania;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
972;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
311;Ireland;131;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
510;Portugal;497;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1284;Italy;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
177;Italy;735;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
1220;Slovenia;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
128;Lithuania;642;1;Basic;Linear Algebra;Matrices and Determinants;Symmetric matrix,Matrix multiplication,Matrix operations
28;Portugal;572;1;Basic;Analytic Geometry;Analytic Geometry;Locus,Scalar product,Cross product,Distance,Collinearity,Orthogonality
955;Lithuania;1216;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
913;Ireland;298;0;Basic;Probability ;Probability ;Event,Axioms of probability
91;Lithuania;494;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
376;Portugal;350;0;Advanced;Complex Numbers;Complex Numbers;Complex plane 
913;Ireland;948;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
913;Ireland;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
455;Portugal;135;1;Basic;Linear Algebra;Matrices and Determinants;Symmetric matrix,Determinant computation,Determinant properties
1220;Slovenia;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
955;Lithuania;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1229;Portugal;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
552;Portugal;870;0;Basic;Differential Equations;Differential Equations;Homogeneous equation
483;Portugal;522;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Triangles
1379;Portugal;102;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1196;Slovenia;455;1;Basic;Linear Algebra;Vector Spaces;Basis
1171;Portugal;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
407;Portugal;507;0;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry
1292;Italy;849;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Continuity,Limits
840;Italy;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1333;Portugal;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
90;Lithuania;342;0;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Modulus of a complex number,Algebraic form
1158;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
80;Lithuania;529;1;Basic;Integration;Double Integration;Iterate integrals
913;Ireland;916;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Square linear system,Consistent system
1244;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
61;Portugal;547;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Orthogonality,Scalar product
165;Portugal;94;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
1288;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
1244;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
71;Portugal;1061;1;Basic;Complex Numbers;Complex Numbers;Complex plane 
1023;Lithuania;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1163;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
552;Portugal;571;0;Basic;Analytic Geometry;Analytic Geometry;Intersection,Cartesian equations of a plane
91;Lithuania;523;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometrical figures,Polygons
91;Lithuania;446;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
26;Portugal;558;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
411;Portugal;629;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue
693;Portugal;181;0;Basic;Statistics;Statistics;Quantile,Frequency,Sample,Mean,Variance,Standard deviation,Median,Mode
91;Lithuania;515;1;Advanced;Fundamental Mathematics;Elementary Geometry;Geometrical figures,Quadrilaterals,Rhombus
91;Lithuania;456;0;Advanced;Fundamental Mathematics;Elementary Geometry;Triangles
899;Lithuania;424;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
168;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1220;Slovenia;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
625;Russian Federation;790;1;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Logarithmic function
1322;Italy;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1481;Portugal;492;0;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Axioms of probability,Event
956;Portugal;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1331;Portugal;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
71;Portugal;796;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Logarithmic function,Exponential function,Simplify expressions
176;Italy;112;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
411;Portugal;252;0;Basic;Differentiation;Derivatives;Quotient rule,Product rule,Power rule,Trigonometric rules
1109;Portugal;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1171;Portugal;1016;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
448;Portugal;320;1;Advanced;Probability ;Probability ;Axioms of probability,Event,Addition, multiplication, and total probability rules,Sample space
1179;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
168;Portugal;292;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
1220;Slovenia;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1284;Italy;447;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1284;Italy;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
457;Portugal;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
913;Ireland;1107;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
411;Portugal;595;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Eigenvalue
965;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
168;Portugal;381;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
899;Lithuania;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
189;Portugal;274;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
128;Lithuania;637;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
1135;Portugal;385;0;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
509;Portugal;793;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
511;Portugal;642;1;Basic;Linear Algebra;Matrices and Determinants;Symmetric matrix,Matrix multiplication,Matrix operations
1076;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
1292;Italy;852;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Continuity,Limits
852;Italy;227;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
168;Portugal;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1543;Portugal;1096;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1351;Portugal;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
422;Portugal;141;1;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication
26;Portugal;552;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product
551;Lithuania;700;0;Basic;Analytic Geometry;Analytic Geometry;Collinearity,Locus,Orthogonality,Orthogonal projection,Scalar product,Distance
1182;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
91;Lithuania;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
731;Portugal;179;0;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
1411;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1182;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
374;Portugal;357;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
415;Portugal;634;0;Basic;Linear Algebra;Matrices and Determinants;Determinant properties,Inverse matrix ,Solve matrix equation,Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Commuting matrices,Determinant computation
1179;Portugal;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
974;Portugal;441;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1353;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1533;Portugal;556;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line,Collinearity
625;Russian Federation;464;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Geometrical figures
1484;Portugal;667;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
986;Portugal;449;1;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
700;Portugal;190;0;Basic;Statistics;Statistics;Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance,Median
1147;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
643;Italy;185;1;Basic;Statistics;Statistics;Frequency,Quantile,Mean,Variance,Median,Mode
1288;Portugal;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1196;Slovenia;455;1;Basic;Linear Algebra;Vector Spaces;Basis
175;Italy;1215;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Lagrange's interpolation
967;Portugal;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
91;Lithuania;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
509;Portugal;108;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
175;Italy;1495;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
1140;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
966;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
91;Lithuania;504;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry,Geometric transformations
52;Portugal;123;0;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication,Determinant properties,Symmetric matrix
1077;Portugal;420;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1220;Slovenia;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1023;Lithuania;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
972;Portugal;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1256;Portugal;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
91;Lithuania;334;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
1352;Portugal;292;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
91;Lithuania;117;1;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
168;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
380;Portugal;864;0;Basic;Optimization;Nonlinear Optimization;Lagrange multipliers,Optimal solution,Minimum,Maximum
69;Portugal;560;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality
851;Italy;1246;0;Basic;Optimization;Nonlinear Optimization;Unconstrained optimization,Second derivative test,Optimal solution
693;Portugal;183;0;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
1163;Portugal;785;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
955;Lithuania;1099;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1565;Portugal;391;0;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
1185;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1312;Portugal;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
168;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
91;Lithuania;351;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Imaginary part,Complex plane ,Operations with complex numbers,Real part,Principal argument,De Moivre formulas
634;Italy;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
855;Italy;220;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1179;Portugal;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
37;Portugal;327;1;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
509;Portugal;496;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
985;Romania;786;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
890;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
722;Portugal;193;1;Basic;Statistics;Statistics;Standard deviation,Variance,Median,Frequency,Mode,Outliers,Quantile,Interquartile range,Population,Data type,Sample,Relative frequency,Mean
1044;Lithuania;259;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
720;Portugal;202;1;Basic;Statistics;Statistics;Student distribution,Confidence interval,Point estimate,Hypothesis testing
1324;Italy;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
91;Lithuania;513;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangle inequality,Triangles
1351;Portugal;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
37;Portugal;155;0;Basic;Optimization;Nonlinear Optimization;Lagrange multipliers,Maximum,Minimum
340;Portugal;299;0;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Event,Axioms of probability
1220;Slovenia;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
378;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
128;Lithuania;329;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
457;Portugal;333;0;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
26;Portugal;546;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonal projection,Distance,Cross product,Orthogonality
128;Lithuania;328;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1288;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1542;Portugal;1099;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1146;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
81;Lithuania;701;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product,Distance
36;Portugal;853;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Continuity,Limits
81;Lithuania;565;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonal projection,Orthogonality,Collinearity,Locus
311;Ireland;652;1;Basic;Linear Algebra;Matrices and Determinants;Linearly independent rows,Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties
552;Portugal;156;0;Basic;Differential Equations;Differential Equations;Linear differential equation
1220;Slovenia;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1070;Portugal;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
26;Portugal;231;0;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system,Solution of linear system
1331;Portugal;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
666;Portugal;186;0;Basic;Statistics;Statistics;Population,Sample
1080;Portugal;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
643;Italy;179;1;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
72;Portugal;451;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
91;Lithuania;358;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Conjugate number,Operations with complex numbers,Real part
1093;Portugal;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1288;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1324;Italy;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
37;Portugal;820;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Maximum,Stationary point,Saddle point
1220;Slovenia;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
899;Lithuania;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
918;Portugal;908;0;Basic;Differentiation;Partial Differentiation;Gradient,Directional derivative
71;Portugal;645;0;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Linearly independent rows
374;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
913;Ireland;771;0;Basic;Probability ;Probability ;Event,Sample space,Addition, multiplication, and total probability rules,Axioms of probability
1517;Portugal;306;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
1179;Portugal;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1557;Portugal;919;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
91;Lithuania;192;0;Basic;Integration;Integration Techniques;Trigonometric substitution,Simple integration
1220;Slovenia;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
90;Lithuania;360;0;Basic;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
1219;Portugal;454;1;Basic;Linear Algebra;Vector Spaces;Basis
636;Italy;77;1;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
851;Italy;1246;0;Basic;Optimization;Nonlinear Optimization;Unconstrained optimization,Second derivative test,Optimal solution
1244;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1080;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
851;Italy;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
776;Portugal;575;0;Advanced;Analytic Geometry;Analytic Geometry;Orthogonality,Orthogonal projection,Cross product,Scalar product
1087;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1505;Portugal;298;1;Basic;Probability ;Probability ;Event,Axioms of probability
71;Portugal;100;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Power rule
884;Italy;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
741;Ireland;478;0;Basic;Graph Theory;Graph Theory;Adjacency matrix
199;Lithuania;798;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1143;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
80;Lithuania;486;1;Basic;Probability ;Probability ;Event,Addition, multiplication, and total probability rules,Sample space
1292;Italy;288;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1023;Lithuania;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
689;Portugal;821;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Maximum,Second derivative test,Stationary point,Unconstrained optimization,Saddle point
376;Portugal;356;0;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers
200;Lithuania;393;0;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
91;Lithuania;501;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids
1220;Slovenia;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
591;Portugal;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1331;Portugal;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1220;Slovenia;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
840;Italy;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
218;Lithuania;667;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
626;Italy;82;0;Basic;Differentiation;Derivatives;Logarithmic rule,Power rule,Exponential rule,Trigonometric rules,Product rule
1220;Slovenia;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1071;Lithuania;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
658;Ireland;181;0;Basic;Statistics;Statistics;Quantile,Frequency,Sample,Mean,Variance,Standard deviation,Median,Mode
26;Portugal;565;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonal projection,Orthogonality,Collinearity,Locus
71;Portugal;326;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part
633;Italy;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1565;Portugal;394;0;Basic;Integration;Integration Techniques;Substitution
189;Portugal;144;0;Basic;Differentiation;Derivatives;Trigonometric rules
1220;Slovenia;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1543;Portugal;1088;0;Basic;Numerical Methods;Numerical Methods;First order,Second order
91;Lithuania;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1308;Italy;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
37;Portugal;1201;1;Basic;Integration;Definite Integrals;Fundamental theorem of Calculus,Volume of revolution
422;Portugal;128;1;Advanced;Linear Algebra;Matrices and Determinants;Matrix multiplication,Determinant computation,Determinant properties,Symmetric matrix,Hermitian matrix,Inverse matrix ,Linearly independent rows,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Matrix equivalent - echelon
1220;Slovenia;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1077;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
876;Italy;446;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1252;Portugal;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
91;Lithuania;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
80;Lithuania;545;1;Basic;Integration;Double Integration;y-simple region (type I),Area ,Cartesian coordinates
509;Portugal;795;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
72;Portugal;329;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1220;Slovenia;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1150;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
90;Lithuania;331;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1543;Portugal;1112;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1291;Italy;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
175;Italy;721;0;Basic;Differentiation;Derivatives;Quotient rule,Trigonometric rules
168;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
200;Lithuania;113;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
972;Portugal;278;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
181;Italy;921;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
91;Lithuania;368;1;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids,Regular polygon
967;Portugal;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1023;Lithuania;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
176;Italy;735;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
956;Portugal;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1299;Italy;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
218;Lithuania;120;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
638;Italy;78;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
1517;Portugal;419;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
1146;Portugal;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
80;Lithuania;215;1;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Inconsistent system,Solution of linear system
1220;Slovenia;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
851;Italy;860;1;Basic;Optimization;Nonlinear Optimization;Saddle point,Optimal solution,Minimum,Maximum,Stationary point
1109;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1565;Portugal;315;0;Advanced;Integration;Integration Techniques;Integration by parts
979;Portugal;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
483;Portugal;356;1;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers
1322;Italy;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
986;Portugal;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1517;Portugal;448;0;Advanced;Linear Algebra;Vector Spaces;Subspace
598;Italy;131;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
411;Portugal;849;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Continuity,Limits
176;Italy;1121;0;Basic;Differentiation;Derivatives;Trigonometric rules,Quotient rule
955;Lithuania;1088;0;Basic;Numerical Methods;Numerical Methods;First order,Second order
1561;Portugal;718;0;Advanced;Integration;Integration Techniques;Substitution
155;Spain;160;1;Basic;Differential Equations;Differential Equations;Linear differential equation
1291;Italy;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
168;Portugal;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1220;Slovenia;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
510;Portugal;141;0;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication
1543;Portugal;1095;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1220;Slovenia;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
986;Portugal;449;0;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
751;Lithuania;567;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a line,Orthogonality,Collinearity
151;Portugal;104;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
524;Portugal;217;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
955;Lithuania;1093;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1244;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
851;Italy;1007;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Stationary point,Maximum,Saddle point
407;Portugal;273;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
1241;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
465;Portugal;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
483;Portugal;345;1;Advanced;Complex Numbers;Complex Numbers;Polar representation,Trigonometric form,Modulus of a complex number,Operations with complex numbers,Algebraic form,Principal argument,De Moivre formulas
80;Lithuania;917;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1049;Lithuania;270;0;Basic;Differentiation;Partial Differentiation;First order,Second order
26;Portugal;88;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
1220;Slovenia;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
28;Portugal;573;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Locus,Scalar product,Cross product,Collinearity
510;Portugal;89;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
406;Portugal;218;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
899;Lithuania;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
91;Lithuania;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
351;Portugal;796;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Logarithmic function,Exponential function,Simplify expressions
975;Portugal;131;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
956;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1273;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
72;Portugal;553;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Distance,Scalar product
955;Lithuania;454;0;Basic;Linear Algebra;Vector Spaces;Basis
625;Russian Federation;794;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
198;Italy;666;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1080;Portugal;785;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
876;Italy;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
81;Lithuania;571;1;Basic;Analytic Geometry;Analytic Geometry;Intersection,Cartesian equations of a plane
1487;Portugal;1197;1;Basic;Integration;Definite Integrals;Area of a planar region ,Fundamental theorem of Calculus
633;Italy;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
189;Portugal;729;1;Basic;Differentiation;Derivatives;Quotient rule
1564;Portugal;142;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
1166;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1077;Portugal;439;0;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
776;Portugal;552;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product
1220;Slovenia;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1023;Lithuania;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1146;Portugal;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
397;Portugal;333;0;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
956;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1044;Lithuania;259;1;Basic;Differentiation;Partial Differentiation;First order,Gradient
351;Portugal;612;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1284;Italy;419;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
37;Portugal;879;1;Basic;Differentiation;Partial Differentiation;First order,Second order
128;Lithuania;326;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part
658;Ireland;179;1;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
1334;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1056;Lithuania;256;0;Basic;Differentiation;Partial Differentiation;First order
72;Portugal;449;0;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
840;Italy;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1143;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
967;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1220;Slovenia;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
175;Italy;1477;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
898;Portugal;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1281;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
753;Italy;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1220;Slovenia;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
972;Portugal;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1023;Lithuania;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1517;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1087;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
1564;Portugal;686;0;Basic;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
81;Lithuania;470;0;Advanced;Graph Theory;Graph Theory;Simple graph,Adjacency matrix
204;Lithuania;114;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
986;Portugal;292;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
890;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
600;Italy;89;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1505;Portugal;736;0;Basic;Optimization;Linear Optimization;Linear programming,Excel solver add-in,Simplex method
1076;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
176;Italy;613;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
411;Portugal;645;1;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Linearly independent rows
956;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1093;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
988;Portugal;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
1192;Portugal;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
582;Lithuania;354;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
168;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1220;Slovenia;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
85;Lithuania;374;0;Basic;Graph Theory;Graph Theory;Tree,Spanning tree
549;Portugal;230;1;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
422;Portugal;328;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1150;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
852;Italy;88;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
1182;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1026;Lithuania;147;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
1557;Portugal;983;0;Advanced;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
890;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
175;Italy;1108;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Lagrange's interpolation
509;Portugal;523;0;Basic;Fundamental Mathematics;Elementary Geometry;Geometrical figures,Polygons
684;Ireland;211;1;Basic;Statistics;Statistics;Linear regression
189;Portugal;371;0;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Geometrical figures
1079;Portugal;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
91;Lithuania;498;0;Advanced;Fundamental Mathematics;Elementary Geometry;Triangles,Classification of geometrical figures,Geometrical figures
311;Ireland;130;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
1256;Portugal;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
776;Portugal;702;0;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Intersection,Cartesian equations of a line
1087;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
175;Italy;1111;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
898;Portugal;419;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
1179;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
552;Portugal;683;0;Advanced;Real Functions of a single variable;Domain, Image and Graphics;Domain
1289;Italy;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1044;Lithuania;998;1;Basic;Differentiation;Partial Differentiation;First order
1220;Slovenia;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
625;Russian Federation;102;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
165;Portugal;828;0;Basic;Differential Equations;Differential Equations;Linear differential equation
986;Portugal;778;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
80;Lithuania;698;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Orthogonal projection,Distance
1542;Portugal;1100;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
72;Portugal;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1543;Portugal;1096;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
470;Portugal;563;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
986;Portugal;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
61;Portugal;889;0;Basic;Differential Equations;Differential Equations;Linear differential equation
378;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1093;Portugal;781;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
411;Portugal;616;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector
359;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1150;Portugal;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
71;Portugal;701;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product,Distance
1269;Portugal;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1182;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
853;Italy;221;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1244;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
81;Lithuania;572;0;Basic;Analytic Geometry;Analytic Geometry;Locus,Scalar product,Cross product,Distance,Collinearity,Orthogonality
81;Lithuania;564;0;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonality
91;Lithuania;520;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
91;Lithuania;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1289;Italy;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
955;Lithuania;432;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
168;Portugal;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1220;Slovenia;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1273;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
884;Italy;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
955;Lithuania;1110;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
483;Portugal;347;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
1135;Portugal;382;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
175;Italy;271;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
955;Lithuania;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
407;Portugal;82;0;Basic;Differentiation;Derivatives;Logarithmic rule,Power rule,Exponential rule,Trigonometric rules,Product rule
972;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
955;Lithuania;1099;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
175;Italy;144;0;Basic;Differentiation;Derivatives;Trigonometric rules
26;Portugal;244;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
426;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
582;Lithuania;548;1;Basic;Analytic Geometry;Analytic Geometry;Collinearity,Distance,Locus,Cross product,Orthogonality,Scalar product
855;Italy;231;0;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system,Solution of linear system
625;Russian Federation;367;0;Basic;Fundamental Mathematics;Elementary Geometry;Geometrical figures
855;Italy;239;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
470;Portugal;699;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Locus,Intersection,Cartesian equations of a line
380;Portugal;356;0;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers
163;Portugal;327;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1034;Lithuania;878;0;Basic;Differentiation;Partial Differentiation;Second order,First order
691;Portugal;190;1;Basic;Statistics;Statistics;Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance,Median
639;Italy;182;0;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
1564;Portugal;921;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
966;Portugal;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
351;Portugal;147;1;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
359;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
511;Portugal;230;1;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
1565;Portugal;678;1;Basic;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
1219;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
852;Italy;219;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
80;Lithuania;341;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
91;Lithuania;501;0;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids
26;Portugal;765;1;Basic;Probability ;Probability ;Addition, multiplication, and total probability rules
1557;Portugal;83;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain,Image of a function
1219;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1269;Portugal;439;0;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
1288;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
168;Portugal;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
176;Italy;923;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1150;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
26;Portugal;165;1;Basic;Differential Equations;Differential Equations;Linear differential equation,Homogeneous equation
1087;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1428;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
663;Portugal;77;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
719;Portugal;186;0;Basic;Statistics;Statistics;Population,Sample
181;Italy;922;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
657;Ireland;184;1;Basic;Statistics;Statistics;Frequency,Sample,Stem and Leaf diagram,Variance,Standard deviation,Relative frequency
1363;Portugal;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1340;Portugal;1106;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
524;Portugal;519;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1291;Italy;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
1543;Portugal;1120;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
966;Portugal;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
969;Romania;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
411;Portugal;127;0;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Determinant computation,Determinant properties,Symmetric matrix,Inverse matrix ,Linearly independent rows,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank
175;Italy;272;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
955;Lithuania;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1220;Slovenia;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
468;Portugal;357;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
643;Italy;177;0;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
1080;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
376;Portugal;352;1;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Operations with complex numbers
913;Ireland;492;0;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Axioms of probability,Event
717;Portugal;185;1;Basic;Statistics;Statistics;Frequency,Quantile,Mean,Variance,Median,Mode
1284;Italy;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
37;Portugal;262;0;Basic;Differentiation;Partial Differentiation;First order
549;Portugal;948;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
1334;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
551;Lithuania;553;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Distance,Scalar product
91;Lithuania;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1338;Portugal;290;0;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
876;Italy;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
697;Portugal;77;1;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
1220;Slovenia;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
955;Lithuania;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
986;Portugal;645;1;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Linearly independent rows
1543;Portugal;1104;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1505;Portugal;737;0;Basic;Optimization;Linear Optimization;Linear programming
91;Lithuania;385;0;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1185;Portugal;783;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
890;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
151;Portugal;120;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
986;Portugal;123;1;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication,Determinant properties,Symmetric matrix
91;Lithuania;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
986;Portugal;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
509;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1179;Portugal;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
414;Portugal;229;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
1093;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
374;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
80;Lithuania;338;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form
634;Italy;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
422;Portugal;331;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
483;Portugal;505;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangles
1252;Portugal;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
91;Lithuania;502;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry,Geometric transformations
1256;Portugal;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1292;Italy;292;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
64;Portugal;1123;1;Basic;Integration;Integration Techniques;Integration by parts,Substitution,Simple integration,Direct inspection
955;Lithuania;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
509;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
91;Lithuania;351;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Imaginary part,Complex plane ,Operations with complex numbers,Real part,Principal argument,De Moivre formulas
1220;Slovenia;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
378;Portugal;558;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
1220;Slovenia;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1292;Italy;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
851;Italy;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
651;Ireland;185;1;Basic;Statistics;Statistics;Frequency,Quantile,Mean,Variance,Median,Mode
1028;Lithuania;912;0;Basic;Differentiation;Partial Differentiation;Minimum,Stationary point,Maximum,Saddle point,Optimal solution
663;Portugal;78;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
1220;Slovenia;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
426;Portugal;333;0;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
973;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1087;Portugal;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
393;Lithuania;357;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
890;Portugal;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
1109;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1292;Italy;616;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector
958;Lithuania;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1275;Lithuania;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1220;Slovenia;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1516;Portugal;157;1;Basic;Differential Equations;Differential Equations;Homogeneous equation,Cauchy problem
168;Portugal;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
240;Lithuania;923;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
966;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
71;Portugal;1061;1;Basic;Complex Numbers;Complex Numbers;Complex plane 
1252;Portugal;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
955;Lithuania;1100;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
198;Italy;518;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
852;Italy;243;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1272;Portugal;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
468;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
913;Ireland;1114;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
64;Portugal;551;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality
175;Italy;331;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
552;Portugal;928;0;Advanced;Real Functions of a single variable;Domain, Image and Graphics;Planar graph
80;Lithuania;246;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
851;Italy;1247;0;Basic;Optimization;Nonlinear Optimization;Unconstrained optimization,Second derivative test,Optimal solution
853;Italy;230;1;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
1093;Portugal;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
855;Italy;225;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
41;Portugal;575;1;Advanced;Analytic Geometry;Analytic Geometry;Orthogonality,Orthogonal projection,Cross product,Scalar product
898;Portugal;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
455;Portugal;136;0;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
1076;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
855;Italy;234;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
651;Ireland;186;0;Basic;Statistics;Statistics;Population,Sample
969;Romania;439;1;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
1284;Italy;420;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1070;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1292;Italy;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
525;Portugal;789;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1324;Italy;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1481;Portugal;679;0;Basic;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
421;Portugal;331;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
37;Portugal;274;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
1352;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1080;Portugal;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
197;Portugal;614;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
91;Lithuania;347;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
955;Lithuania;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1518;Portugal;136;0;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
1076;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1229;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
511;Portugal;795;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
955;Lithuania;432;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
1487;Portugal;272;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
168;Portugal;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
979;Portugal;1101;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1196;Slovenia;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;454;0;Basic;Linear Algebra;Vector Spaces;Basis
393;Lithuania;347;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
168;Portugal;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1252;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1023;Lithuania;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1146;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
37;Portugal;304;0;Basic;Probability ;Probability ;Addition, multiplication, and total probability rules,Sample space,Event,Axioms of probability
85;Lithuania;1157;0;Basic;Set Theory;Set Theory;Subset
1179;Portugal;382;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1505;Portugal;181;0;Basic;Statistics;Statistics;Quantile,Frequency,Sample,Mean,Variance,Standard deviation,Median,Mode
374;Portugal;345;1;Advanced;Complex Numbers;Complex Numbers;Polar representation,Trigonometric form,Modulus of a complex number,Operations with complex numbers,Algebraic form,Principal argument,De Moivre formulas
359;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
41;Portugal;507;0;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry
176;Italy;108;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
71;Portugal;596;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Eigenvalue
525;Portugal;524;0;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Rhombus
41;Portugal;561;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
72;Portugal;451;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
667;Portugal;190;1;Basic;Statistics;Statistics;Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance,Median
1220;Slovenia;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1543;Portugal;1110;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
853;Italy;916;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Square linear system,Consistent system
1292;Italy;382;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
913;Ireland;449;1;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
524;Portugal;118;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
966;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
473;Portugal;355;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
131;Lithuania;586;1;Advanced;Graph Theory;Graph Theory;Adjacency matrix
448;Portugal;318;1;Advanced;Probability ;Probability ;Axioms of probability,Event,Addition, multiplication, and total probability rules,Sample space
1292;Italy;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
81;Lithuania;556;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line,Collinearity
41;Portugal;211;0;Basic;Statistics;Statistics;Linear regression
1220;Slovenia;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
986;Portugal;424;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
378;Portugal;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1087;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1148;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1220;Slovenia;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
155;Spain;274;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
1135;Portugal;781;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1076;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
340;Portugal;295;0;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Event,Axioms of probability
340;Portugal;320;0;Advanced;Probability ;Probability ;Axioms of probability,Event,Addition, multiplication, and total probability rules,Sample space
625;Russian Federation;108;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
753;Italy;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1256;Portugal;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1274;Portugal;108;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1146;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
913;Ireland;1110;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
626;Italy;274;1;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
1220;Slovenia;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1557;Portugal;694;1;Advanced;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
1197;Slovenia;446;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1518;Portugal;645;1;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Linearly independent rows
1273;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1093;Portugal;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
1220;Slovenia;455;1;Basic;Linear Algebra;Vector Spaces;Basis
311;Ireland;636;0;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication
168;Portugal;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
69;Portugal;556;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line,Collinearity
1023;Lithuania;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
524;Portugal;368;0;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids,Regular polygon
36;Portugal;288;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
986;Portugal;782;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1150;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
181;Italy;83;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain,Image of a function
394;Portugal;351;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Imaginary part,Complex plane ,Operations with complex numbers,Real part,Principal argument,De Moivre formulas
1331;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1150;Portugal;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1271;Portugal;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
90;Lithuania;328;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1219;Portugal;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
28;Portugal;242;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1140;Portugal;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
37;Portugal;1010;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Maximum
918;Portugal;273;1;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
1219;Portugal;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
81;Lithuania;938;1;Advanced;Graph Theory;Graph Theory;Chromatic number
26;Portugal;697;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Distance,Cross product
1220;Slovenia;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1248;Italy;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1517;Portugal;783;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
1271;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1146;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
898;Portugal;1053;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
599;Italy;856;1;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Diagonalization,Spectrum,Characteristic polynomial
853;Italy;948;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
72;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
81;Lithuania;611;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
168;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
955;Lithuania;419;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
1220;Slovenia;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
979;Portugal;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
1525;Portugal;740;0;Advanced;Optimization;Linear Optimization;Linear programming
80;Lithuania;282;0;Basic;Optimization;Linear Optimization;Linear programming
1543;Portugal;1105;1;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1087;Portugal;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1351;Portugal;306;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
855;Italy;217;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
174;Portugal;327;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
973;Portugal;635;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
37;Portugal;521;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Regular polygon
473;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1253;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
72;Portugal;653;0;Basic;Linear Algebra;Matrices and Determinants;Linearly independent rows,Matrix rank
311;Ireland;645;0;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Linearly independent rows
965;Portugal;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
91;Lithuania;505;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangles
1351;Portugal;781;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1271;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1197;Slovenia;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
394;Portugal;347;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
403;Portugal;345;1;Advanced;Complex Numbers;Complex Numbers;Polar representation,Trigonometric form,Modulus of a complex number,Operations with complex numbers,Algebraic form,Principal argument,De Moivre formulas
642;Italy;211;1;Basic;Statistics;Statistics;Linear regression
1077;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
966;Portugal;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1284;Italy;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
168;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
899;Lithuania;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
71;Portugal;327;1;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1023;Lithuania;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
37;Portugal;821;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Maximum,Second derivative test,Stationary point,Unconstrained optimization,Saddle point
1220;Slovenia;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1256;Portugal;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
426;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
693;Portugal;211;1;Basic;Statistics;Statistics;Linear regression
851;Italy;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
972;Portugal;289;0;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
380;Portugal;333;0;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1518;Portugal;635;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
1219;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
535;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
666;Portugal;190;1;Basic;Statistics;Statistics;Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance,Median
972;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
600;Italy;138;1;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Determinant computation,Determinant properties,Inverse matrix 
91;Lithuania;500;0;Advanced;Fundamental Mathematics;Elementary Geometry;Geometrical figures,Triangles,Classification of geometrical figures
1375;Portugal;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1080;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
72;Portugal;290;0;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
168;Portugal;292;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
1220;Slovenia;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
57;Portugal;79;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
851;Italy;1007;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Stationary point,Maximum,Saddle point
1351;Portugal;380;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;455;1;Basic;Linear Algebra;Vector Spaces;Basis
884;Italy;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
378;Portugal;289;0;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1517;Portugal;432;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
1023;Lithuania;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
151;Portugal;104;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1284;Italy;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1339;Portugal;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1252;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
26;Portugal;568;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
969;Romania;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1252;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
972;Portugal;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
1044;Lithuania;880;0;Advanced;Differentiation;Partial Differentiation;First order,Directional derivative,Gradient
1322;Italy;385;0;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
955;Lithuania;1099;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
955;Lithuania;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
411;Portugal;335;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
1034;Lithuania;264;0;Basic;Differentiation;Partial Differentiation;Chain rule
956;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1163;Portugal;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1319;Italy;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
448;Portugal;310;1;Advanced;Probability ;Probability ;Direct inspection,Simple integration
91;Lithuania;521;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Regular polygon
349;Portugal;271;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
1292;Italy;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
509;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
1220;Slovenia;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1220;Slovenia;454;1;Basic;Linear Algebra;Vector Spaces;Basis
483;Portugal;98;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
406;Portugal;215;1;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Inconsistent system,Solution of linear system
884;Italy;446;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1274;Portugal;120;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
751;Lithuania;697;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Distance,Cross product
91;Lithuania;519;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1517;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1220;Slovenia;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
955;Lithuania;449;0;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
26;Portugal;698;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Orthogonal projection,Distance
663;Portugal;187;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
1350;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
625;Russian Federation;664;0;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
166;Portugal;646;1;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Commuting matrices,Solve matrix equation,Determinant computation,Inverse matrix ,Matrix rank,Determinant properties,Matrix multiplication,Symmetric matrix
1022;Lithuania;959;0;Basic;Optimization;Linear Optimization;Linear programming
876;Italy;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
966;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
409;Portugal;341;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
72;Portugal;326;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part
468;Portugal;345;1;Advanced;Complex Numbers;Complex Numbers;Polar representation,Trigonometric form,Modulus of a complex number,Operations with complex numbers,Algebraic form,Principal argument,De Moivre formulas
955;Lithuania;1112;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1220;Slovenia;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
853;Italy;215;0;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Inconsistent system,Solution of linear system
692;Portugal;180;1;Basic;Statistics;Statistics;Mean,Median,Mode
1220;Slovenia;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
168;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
37;Portugal;192;0;Basic;Integration;Integration Techniques;Trigonometric substitution,Simple integration
1557;Portugal;925;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Planar graph
351;Portugal;102;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
422;Portugal;342;1;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Modulus of a complex number,Algebraic form
189;Portugal;798;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
524;Portugal;611;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
465;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
972;Portugal;439;0;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
552;Portugal;868;1;Basic;Differential Equations;Differential Equations;Separable variables equation
1109;Portugal;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
468;Portugal;358;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Conjugate number,Operations with complex numbers,Real part
890;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
91;Lithuania;516;1;Advanced;Fundamental Mathematics;Elementary Geometry;Symmetry
1179;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
913;Ireland;441;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1109;Portugal;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
955;Lithuania;1101;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
510;Portugal;608;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector
359;Portugal;501;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids
1557;Portugal;834;1;Basic;Differential Equations;Differential Equations;Linear differential equation
884;Italy;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1230;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
483;Portugal;496;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
552;Portugal;87;0;Advanced;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
669;Portugal;193;1;Basic;Statistics;Statistics;Standard deviation,Variance,Median,Frequency,Mode,Outliers,Quantile,Interquartile range,Population,Data type,Sample,Relative frequency,Mean
1427;Portugal;380;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
80;Lithuania;335;1;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
1276;Portugal;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
359;Portugal;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
985;Romania;798;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
890;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
967;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1350;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1341;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
239;Lithuania;273;1;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
91;Lithuania;349;1;Advanced;Complex Numbers;Complex Numbers;Complex plane 
1220;Slovenia;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1220;Slovenia;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1543;Portugal;1106;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
168;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
660;Portugal;202;0;Basic;Statistics;Statistics;Student distribution,Confidence interval,Point estimate,Hypothesis testing
741;Ireland;180;1;Basic;Statistics;Statistics;Mean,Median,Mode
634;Italy;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
972;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1023;Lithuania;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1194;Portugal;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
311;Ireland;644;1;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Determinant computation,Matrix rank,Inverse matrix ,Determinant properties,Hermitian matrix,Matrix multiplication,Linearly independent rows,Symmetric matrix,Matrix operations
151;Portugal;113;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
633;Italy;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1284;Italy;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1289;Italy;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
380;Portugal;871;0;Basic;Differential Equations;Differential Equations;Cauchy problem,Exact differential form
1511;Portugal;563;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
1220;Slovenia;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1220;Slovenia;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
525;Portugal;518;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
884;Italy;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
37;Portugal;153;1;Advanced;Differentiation;Partial Differentiation;Stationary point,Minimum,Optimal solution,Lagrange multipliers
411;Portugal;360;0;Basic;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
890;Portugal;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1284;Italy;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1039;Lithuania;258;1;Basic;Differentiation;Partial Differentiation;First order,Gradient
1220;Slovenia;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1220;Slovenia;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
955;Lithuania;1114;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
311;Ireland;653;1;Basic;Linear Algebra;Matrices and Determinants;Linearly independent rows,Matrix rank
851;Italy;858;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Maximum,Stationary point,Saddle point
851;Italy;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
672;Portugal;492;1;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Axioms of probability,Event
426;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
155;Spain;144;0;Basic;Differentiation;Derivatives;Trigonometric rules
510;Portugal;850;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Continuity,Limits
80;Lithuania;756;1;Basic;Integration;Double Integration;Cartesian coordinates,x-simple region (type II),Changing order of integration
1351;Portugal;382;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
556;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1143;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1135;Portugal;385;0;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1271;Portugal;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
625;Russian Federation;102;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
175;Italy;1521;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Quadratic equations,Simplify expressions,Linear equations
884;Italy;454;0;Basic;Linear Algebra;Vector Spaces;Basis
1289;Italy;439;1;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
986;Portugal;278;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
168;Portugal;678;0;Basic;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
1080;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1308;Italy;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1082;Portugal;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
1517;Portugal;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
535;Portugal;354;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
468;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
374;Portugal;359;1;Advanced;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
466;Portugal;333;0;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
80;Lithuania;307;1;Basic;Probability ;Probability ;Event,Addition, multiplication, and total probability rules,Independence
1023;Lithuania;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1487;Portugal;940;0;Basic;Graph Theory;Graph Theory;Spanning tree,Shortest path,Path,Tree
426;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1087;Portugal;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
986;Portugal;451;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
986;Portugal;643;1;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties,Hermitian matrix,Matrix multiplication,Linearly independent rows,Symmetric matrix,Matrix operations
1122;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1324;Italy;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
913;Ireland;916;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Square linear system,Consistent system
576;Ireland;575;0;Advanced;Analytic Geometry;Analytic Geometry;Orthogonality,Orthogonal projection,Cross product,Scalar product
1339;Portugal;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1140;Portugal;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
406;Portugal;787;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Logarithmic function
625;Russian Federation;517;1;Advanced;Fundamental Mathematics;Elementary Geometry;Symmetry
91;Lithuania;516;0;Advanced;Fundamental Mathematics;Elementary Geometry;Symmetry
80;Lithuania;234;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1220;Slovenia;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
81;Lithuania;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
91;Lithuania;463;1;Basic;Fundamental Mathematics;Elementary Geometry;Polyhedrons,Geometric solids,Classification of geometric solids
174;Portugal;337;1;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form,Operations with complex numbers,Modulus of a complex number
1411;Portugal;382;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
128;Lithuania;335;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
1525;Portugal;769;0;Advanced;Probability ;Probability ;Bayes' Theorem,Conditional probability
1256;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
91;Lithuania;336;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Modulus of a complex number,Imaginary part
1038;Lithuania;908;0;Basic;Differentiation;Partial Differentiation;Gradient,Directional derivative
69;Portugal;563;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
509;Portugal;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
576;Ireland;549;0;Basic;Analytic Geometry;Analytic Geometry;Distance,Cross product,Orthogonality
41;Portugal;463;1;Basic;Fundamental Mathematics;Elementary Geometry;Polyhedrons,Geometric solids,Classification of geometric solids
61;Portugal;888;1;Basic;Differential Equations;Differential Equations;Linear differential equation
1402;Portugal;288;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1284;Italy;432;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
1220;Slovenia;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
955;Lithuania;1114;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
1049;Lithuania;657;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
241;Lithuania;603;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector,Spectrum,Characteristic polynomial
91;Lithuania;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1220;Slovenia;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
397;Portugal;352;1;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Operations with complex numbers
1481;Portugal;714;1;Basic;Integration;Integration Techniques;Simple integration,Direct inspection
1271;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
411;Portugal;597;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Diagonalization,Eigenvalue
351;Portugal;614;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
168;Portugal;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
168;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1277;Portugal;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
634;Italy;273;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
633;Italy;139;0;Advanced;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication,Determinant computation,Determinant properties
91;Lithuania;495;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1023;Lithuania;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1229;Portugal;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
1428;Portugal;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
967;Portugal;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
525;Portugal;667;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
71;Portugal;275;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
406;Portugal;497;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1538;Portugal;1097;0;Basic;Numerical Methods;Numerical Methods;Lagrange's interpolation,Polynomial interpolation
955;Lithuania;1105;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
973;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
969;Romania;427;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1505;Portugal;1003;0;Basic;Optimization;Linear Optimization;Linear programming
351;Portugal;795;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
1269;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
72;Portugal;783;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
344;Portugal;734;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Exponential rule
1271;Portugal;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
394;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1220;Slovenia;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
854;Italy;89;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
240;Lithuania;922;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1487;Portugal;332;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
168;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1517;Portugal;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
913;Ireland;430;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
712;Portugal;185;0;Basic;Statistics;Statistics;Frequency,Quantile,Mean,Variance,Median,Mode
1150;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
394;Portugal;348;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Complex plane ,Real part
674;Ireland;183;0;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
90;Lithuania;951;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
690;Portugal;191;0;Basic;Statistics;Statistics;Median,Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance
966;Portugal;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
168;Portugal;420;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1256;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1543;Portugal;1112;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
753;Italy;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
406;Portugal;635;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
175;Italy;1487;1;Basic;Complex Numbers;Complex Numbers;Modulus of a complex number,Algebraic form,Real part,Equations involving complex numbers,Imaginary part,Conjugate number
380;Portugal;865;1;Basic;Optimization;Nonlinear Optimization;Lagrange multipliers,Minimum,Maximum,Stationary point
80;Lithuania;230;1;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
57;Portugal;190;1;Basic;Statistics;Statistics;Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance,Median
1194;Portugal;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
972;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
91;Lithuania;352;1;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Operations with complex numbers
1219;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
851;Italy;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
28;Portugal;571;1;Basic;Analytic Geometry;Analytic Geometry;Intersection,Cartesian equations of a plane
669;Portugal;184;1;Basic;Statistics;Statistics;Frequency,Sample,Stem and Leaf diagram,Variance,Standard deviation,Relative frequency
720;Portugal;193;1;Basic;Statistics;Statistics;Standard deviation,Variance,Median,Frequency,Mode,Outliers,Quantile,Interquartile range,Population,Data type,Sample,Relative frequency,Mean
626;Italy;752;1;Basic;Differentiation;Derivatives;Power rule,Quotient rule,Product rule,Trigonometric rules
1056;Lithuania;877;0;Basic;Differentiation;Partial Differentiation;Second order
1081;Portugal;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1157;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
91;Lithuania;458;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Geometric transformations,Geometrical figures
1220;Slovenia;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
91;Lithuania;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
91;Lithuania;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
198;Italy;364;0;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids,Geometrical figures,Classification of geometric solids
986;Portugal;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
451;Portugal;318;1;Advanced;Probability ;Probability ;Axioms of probability,Event,Addition, multiplication, and total probability rules,Sample space
1271;Portugal;782;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
411;Portugal;630;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue
1081;Portugal;447;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1023;Lithuania;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
851;Italy;862;1;Basic;Optimization;Nonlinear Optimization;Saddle point,Optimal solution,Minimum,Maximum,Stationary point
1487;Portugal;1060;0;Basic;Complex Numbers;Complex Numbers;Complex plane 
898;Portugal;864;1;Basic;Optimization;Nonlinear Optimization;Lagrange multipliers,Optimal solution,Minimum,Maximum
28;Portugal;180;0;Basic;Statistics;Statistics;Mean,Median,Mode
624;Portugal;364;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids,Geometrical figures,Classification of geometric solids
1091;Lithuania;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1243;Portugal;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1043;Lithuania;873;0;Basic;Differentiation;Partial Differentiation;First order
465;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1292;Italy;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
470;Portugal;359;1;Advanced;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
626;Italy;921;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1247;Portugal;349;1;Advanced;Complex Numbers;Complex Numbers;Complex plane 
81;Lithuania;783;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
965;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1334;Portugal;781;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1023;Lithuania;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1220;Slovenia;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
1220;Slovenia;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
176;Italy;104;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
457;Portugal;333;1;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1158;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
91;Lithuania;500;1;Advanced;Fundamental Mathematics;Elementary Geometry;Geometrical figures,Triangles,Classification of geometrical figures
1286;Italy;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
168;Portugal;432;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
41;Portugal;549;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Cross product,Orthogonality
1305;Italy;783;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
483;Portugal;340;1;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers,Conjugate number
155;Spain;157;1;Basic;Differential Equations;Differential Equations;Homogeneous equation,Cauchy problem
634;Italy;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1271;Portugal;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
28;Portugal;187;0;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
511;Portugal;130;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
448;Portugal;343;0;Advanced;Probability ;Probability ;Conditional probability,Bayes' Theorem
1220;Slovenia;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1557;Portugal;889;1;Basic;Differential Equations;Differential Equations;Linear differential equation
41;Portugal;168;1;Basic;Differential Equations;Differential Equations;Linear differential equation
168;Portugal;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
168;Portugal;441;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1158;Portugal;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
625;Russian Federation;795;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
1182;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
524;Portugal;368;0;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids,Regular polygon
37;Portugal;335;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
986;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1525;Portugal;860;0;Basic;Optimization;Nonlinear Optimization;Saddle point,Optimal solution,Minimum,Maximum,Stationary point
972;Portugal;375;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1080;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1185;Portugal;306;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
510;Portugal;668;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
988;Portugal;916;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Square linear system,Consistent system
407;Portugal;614;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
80;Lithuania;160;1;Basic;Differential Equations;Differential Equations;Linear differential equation
1487;Portugal;729;1;Basic;Differentiation;Derivatives;Quotient rule
972;Portugal;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
974;Portugal;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1292;Italy;622;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Characteristic polynomial,Eigenvalue,Diagonalization,Eigenvector,Spectrum
913;Ireland;1131;0;Basic;Set Theory;Set Theory;Subset
898;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
406;Portugal;467;0;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Polygons,Classification of geometrical figures,Geometrical figures
41;Portugal;328;1;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1338;Portugal;278;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
351;Portugal;112;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1542;Portugal;1096;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1026;Lithuania;729;1;Basic;Differentiation;Derivatives;Quotient rule
1543;Portugal;1109;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Lagrange's interpolation
1081;Portugal;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
219;Lithuania;795;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
625;Russian Federation;120;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1140;Portugal;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
1195;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1080;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1229;Portugal;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
403;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1081;Portugal;785;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
160;Portugal;118;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
81;Lithuania;557;0;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance
380;Portugal;890;0;Basic;Differential Equations;Differential Equations;Linear differential equation
1288;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
344;Portugal;720;0;Basic;Differentiation;Derivatives;Quotient rule,Trigonometric rules,Logarithmic rule,Product rule
1517;Portugal;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1077;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1351;Portugal;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1525;Portugal;763;0;Advanced;Probability ;Probability ;Conditional probability
697;Portugal;178;1;Basic;Statistics;Statistics;Mean,Variance,Standard deviation,Median,Mode
913;Ireland;1118;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
1253;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1557;Portugal;83;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain,Image of a function
1289;Italy;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
90;Lithuania;132;0;Advanced;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
913;Ireland;1112;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
168;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1486;Portugal;614;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
174;Portugal;364;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids,Geometrical figures,Classification of geometric solids
972;Portugal;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
71;Portugal;653;0;Basic;Linear Algebra;Matrices and Determinants;Linearly independent rows,Matrix rank
26;Portugal;549;0;Basic;Analytic Geometry;Analytic Geometry;Distance,Cross product,Orthogonality
1023;Lithuania;454;0;Basic;Linear Algebra;Vector Spaces;Basis
1299;Italy;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
511;Portugal;952;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
712;Portugal;177;0;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
1517;Portugal;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
524;Portugal;668;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1076;Portugal;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
64;Portugal;309;1;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
375;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1271;Portugal;385;1;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
311;Ireland;645;0;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Linearly independent rows
376;Portugal;358;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Conjugate number,Operations with complex numbers,Real part
91;Lithuania;507;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry
972;Portugal;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
448;Portugal;487;0;Basic;Probability ;Probability ;Axioms of probability,Event,Independence,Addition, multiplication, and total probability rules,Sample space
1333;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
468;Portugal;348;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Complex plane ,Real part
71;Portugal;786;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
979;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1241;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1185;Portugal;779;1;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
91;Lithuania;511;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangle inequality,Triangles
177;Italy;252;0;Basic;Differentiation;Derivatives;Quotient rule,Product rule,Power rule,Trigonometric rules
26;Portugal;567;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a line,Orthogonality,Collinearity
741;Ireland;187;0;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
638;Italy;193;0;Basic;Statistics;Statistics;Standard deviation,Variance,Median,Frequency,Mode,Outliers,Quantile,Interquartile range,Population,Data type,Sample,Relative frequency,Mean
1093;Portugal;278;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1291;Italy;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
37;Portugal;703;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Scalar product
1220;Slovenia;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
175;Italy;1096;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
852;Italy;91;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
1093;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1273;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
634;Italy;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
1289;Italy;449;1;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
1147;Portugal;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
414;Portugal;91;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
852;Italy;88;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
876;Italy;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1044;Lithuania;1002;1;Basic;Differentiation;Partial Differentiation;First order
1220;Slovenia;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
41;Portugal;81;0;Basic;Statistics;Statistics;Mean,Median,Mode
898;Portugal;1053;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
1077;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1173;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1319;Italy;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
204;Lithuania;614;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
885;Italy;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
625;Russian Federation;667;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
625;Russian Federation;799;1;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
80;Lithuania;136;0;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
411;Portugal;624;0;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Characteristic polynomial,Eigenvalue,Diagonalization,Eigenvector,Spectrum
468;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
986;Portugal;418;1;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
1091;Lithuania;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
750;Portugal;83;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain,Image of a function
177;Italy;254;0;Basic;Differentiation;Derivatives;Logarithmic rule,Power rule,Trigonometric rules
1087;Portugal;785;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
177;Italy;143;0;Basic;Differentiation;Derivatives;Trigonometric rules,Logarithmic rule
1324;Italy;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1244;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
576;Ireland;572;0;Basic;Analytic Geometry;Analytic Geometry;Locus,Scalar product,Cross product,Distance,Collinearity,Orthogonality
972;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
674;Ireland;81;0;Basic;Statistics;Statistics;Mean,Median,Mode
510;Portugal;652;0;Basic;Linear Algebra;Matrices and Determinants;Linearly independent rows,Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties
406;Portugal;123;0;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication,Determinant properties,Symmetric matrix
80;Lithuania;752;1;Basic;Differentiation;Derivatives;Power rule,Quotient rule,Product rule,Trigonometric rules
851;Italy;155;1;Basic;Optimization;Nonlinear Optimization;Lagrange multipliers,Maximum,Minimum
525;Portugal;112;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
955;Lithuania;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
973;Portugal;135;1;Basic;Linear Algebra;Matrices and Determinants;Symmetric matrix,Determinant computation,Determinant properties
1244;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
525;Portugal;668;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
913;Ireland;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1292;Italy;849;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Continuity,Limits
876;Italy;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1081;Portugal;449;1;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
37;Portugal;1063;1;Basic;Differentiation;Partial Differentiation;Second order,First order
349;Portugal;275;1;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
26;Portugal;948;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
689;Portugal;860;1;Basic;Optimization;Nonlinear Optimization;Saddle point,Optimal solution,Minimum,Maximum,Stationary point
72;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
36;Portugal;274;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
1146;Portugal;385;0;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1185;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1182;Portugal;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1157;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
26;Portugal;878;1;Basic;Differentiation;Partial Differentiation;Second order,First order
71;Portugal;1099;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1147;Portugal;454;1;Basic;Linear Algebra;Vector Spaces;Basis
168;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
455;Portugal;652;1;Basic;Linear Algebra;Matrices and Determinants;Linearly independent rows,Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties
473;Portugal;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
1147;Portugal;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1197;Slovenia;424;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1023;Lithuania;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1185;Portugal;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
913;Ireland;1105;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1220;Slovenia;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
591;Portugal;335;1;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
91;Lithuania;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
239;Lithuania;256;0;Basic;Differentiation;Partial Differentiation;First order
1076;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1220;Slovenia;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1079;Portugal;449;0;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
1147;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
958;Lithuania;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
553;Portugal;630;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue
582;Lithuania;562;0;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality
851;Italy;818;0;Basic;Optimization;Nonlinear Optimization;Minimum,Maximum,Stationary point,Second derivative test,Unconstrained optimization,Saddle point,Optimal solution
854;Italy;246;0;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
1288;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
986;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
168;Portugal;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
151;Portugal;120;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
890;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
376;Portugal;327;1;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
376;Portugal;357;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
986;Portugal;290;0;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
128;Lithuania;330;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number
524;Portugal;504;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry,Geometric transformations
1543;Portugal;1115;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
956;Portugal;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
41;Portugal;188;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
625;Russian Federation;792;1;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Logarithmic function
1543;Portugal;1110;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1093;Portugal;420;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
359;Portugal;351;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Imaginary part,Complex plane ,Operations with complex numbers,Real part,Principal argument,De Moivre formulas
81;Lithuania;561;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
1428;Portugal;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
470;Portugal;351;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Imaginary part,Complex plane ,Operations with complex numbers,Real part,Principal argument,De Moivre formulas
1220;Slovenia;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
175;Italy;1090;1;Basic;Numerical Methods;Numerical Methods;Nonlinear equation,Newton’s method
918;Portugal;399;0;Basic;Integration;Integration Techniques;Substitution,Direct inspection,Simple integration
174;Portugal;366;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids,Geometrical figures,Classification of geometric solids
1322;Italy;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1122;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
1044;Lithuania;883;0;Basic;Differentiation;Partial Differentiation;First order,Directional derivative
1023;Lithuania;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
26;Portugal;573;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Locus,Scalar product,Cross product,Collinearity
852;Italy;949;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1427;Portugal;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
955;Lithuania;1094;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
351;Portugal;796;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Logarithmic function,Exponential function,Simplify expressions
966;Portugal;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
1505;Portugal;308;1;Basic;Probability ;Probability ;Axioms of probability,Event,Addition, multiplication, and total probability rules,Sample space
175;Italy;1119;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
913;Ireland;1102;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
175;Italy;1115;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
979;Portugal;1093;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1146;Portugal;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
524;Portugal;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
168;Portugal;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
174;Portugal;336;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Modulus of a complex number,Imaginary part
1219;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
884;Italy;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1077;Portugal;292;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
394;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1195;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1252;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
168;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
591;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
776;Portugal;576;0;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
966;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1049;Lithuania;148;0;Basic;Differentiation;Partial Differentiation;First order
151;Portugal;114;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
91;Lithuania;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1241;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
419;Portugal;360;0;Basic;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
1076;Portugal;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
510;Portugal;789;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
465;Portugal;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
72;Portugal;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
380;Portugal;1012;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
397;Portugal;357;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
851;Italy;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
582;Lithuania;575;0;Advanced;Analytic Geometry;Analytic Geometry;Orthogonality,Orthogonal projection,Cross product,Scalar product
1220;Slovenia;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1516;Portugal;891;0;Basic;Differential Equations;Differential Equations;Linear differential equation
986;Portugal;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
979;Portugal;1093;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1032;Lithuania;877;1;Basic;Differentiation;Partial Differentiation;Second order
168;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
855;Italy;233;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
1334;Portugal;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1220;Slovenia;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
525;Portugal;613;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
979;Portugal;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
168;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
576;Ireland;553;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Distance,Scalar product
165;Portugal;391;0;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
955;Lithuania;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
511;Portugal;245;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
483;Portugal;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
884;Italy;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
913;Ireland;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1292;Italy;306;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
465;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
168;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
689;Portugal;867;0;Basic;Optimization;Nonlinear Optimization;Stationary point,Maximum,Saddle point,Second derivative test,Optimal solution,Minimum
956;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
91;Lithuania;360;0;Basic;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
1220;Slovenia;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
344;Portugal;253;0;Basic;Differentiation;Derivatives;Logarithmic rule,Trigonometric rules
1173;Portugal;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
1220;Slovenia;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1220;Slovenia;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
163;Portugal;329;1;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1284;Italy;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1150;Portugal;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1044;Lithuania;874;0;Basic;Differentiation;Partial Differentiation;Power rule,Trigonometric rules,Logarithmic rule
1147;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1288;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
175;Italy;342;1;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Modulus of a complex number,Algebraic form
625;Russian Federation;121;0;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1182;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1288;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1095;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
91;Lithuania;439;0;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
955;Lithuania;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
851;Italy;963;0;Basic;Optimization;Nonlinear Optimization;Simplex method,Duality theory
240;Lithuania;919;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1288;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1080;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
510;Portugal;137;0;Basic;Linear Algebra;Matrices and Determinants;Matrix equivalent - echelon,Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Linearly independent rows,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
956;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
898;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
986;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
483;Portugal;523;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometrical figures,Polygons
509;Portugal;244;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
840;Italy;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
80;Lithuania;917;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
175;Italy;330;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number
81;Lithuania;582;1;Advanced;Graph Theory;Graph Theory;Path,Cycle and circuit
509;Portugal;636;1;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication
979;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
972;Portugal;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1352;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
409;Portugal;329;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
955;Lithuania;1120;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
351;Portugal;798;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1487;Portugal;658;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
340;Portugal;300;0;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Event,Axioms of probability
1034;Lithuania;875;0;Basic;Differentiation;Partial Differentiation;Gradient,First order
969;Romania;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
852;Italy;242;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
633;Italy;132;0;Advanced;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
1087;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
1220;Slovenia;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
36;Portugal;292;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
986;Portugal;779;1;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
548;Portugal;300;1;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Event,Axioms of probability
689;Portugal;964;1;Basic;Optimization;Nonlinear Optimization;Simplex method,Duality theory
1543;Portugal;1116;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
199;Lithuania;120;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1282;Portugal;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
956;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1518;Portugal;637;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
85;Lithuania;1151;0;Basic;Set Theory;Set Theory;Subset
1288;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
885;Italy;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
175;Italy;1497;1;Basic;Complex Numbers;Complex Numbers;Imaginary part,Conjugate number,Modulus of a complex number,Algebraic form,Real part,Equations involving complex numbers
511;Portugal;112;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
642;Italy;189;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
985;Romania;143;0;Basic;Differentiation;Derivatives;Trigonometric rules,Logarithmic rule
956;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
36;Portugal;306;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
913;Ireland;1098;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1044;Lithuania;998;1;Basic;Differentiation;Partial Differentiation;First order
982;Portugal;432;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
1299;Italy;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1341;Portugal;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
91;Lithuania;462;1;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
151;Portugal;108;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
657;Ireland;211;0;Basic;Statistics;Statistics;Linear regression
1220;Slovenia;454;0;Basic;Linear Algebra;Vector Spaces;Basis
1230;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
899;Lithuania;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1319;Italy;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1047;Lithuania;259;1;Basic;Differentiation;Partial Differentiation;First order,Gradient
451;Portugal;344;1;Advanced;Probability ;Probability ;Event,Independence,Addition, multiplication, and total probability rules
986;Portugal;385;0;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
28;Portugal;557;1;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance
359;Portugal;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
524;Portugal;666;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
511;Portugal;364;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids,Geometrical figures,Classification of geometric solids
1220;Slovenia;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
966;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1516;Portugal;892;1;Basic;Differential Equations;Differential Equations;Linear differential equation
91;Lithuania;449;0;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
1220;Slovenia;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
898;Portugal;911;1;Basic;Optimization;Nonlinear Optimization;Minimum,Stationary point,Maximum,Saddle point,Optimal solution
576;Ireland;568;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
174;Portugal;98;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
1220;Slovenia;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
41;Portugal;79;1;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
91;Lithuania;515;1;Advanced;Fundamental Mathematics;Elementary Geometry;Geometrical figures,Quadrilaterals,Rhombus
175;Italy;1549;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Linear equations,Quadratic equations
1077;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
411;Portugal;225;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
176;Italy;796;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Logarithmic function,Exponential function,Simplify expressions
625;Russian Federation;614;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1229;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1339;Portugal;278;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
853;Italy;217;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
470;Portugal;345;0;Advanced;Complex Numbers;Complex Numbers;Polar representation,Trigonometric form,Modulus of a complex number,Operations with complex numbers,Algebraic form,Principal argument,De Moivre formulas
972;Portugal;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
855;Italy;231;1;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system,Solution of linear system
1081;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1046;Lithuania;998;0;Basic;Differentiation;Partial Differentiation;First order
91;Lithuania;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
684;Ireland;177;1;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
426;Portugal;359;1;Advanced;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
421;Portugal;360;0;Basic;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
378;Portugal;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
198;Italy;367;0;Basic;Fundamental Mathematics;Elementary Geometry;Geometrical figures
91;Lithuania;359;1;Advanced;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
37;Portugal;1032;1;Basic;Differentiation;Partial Differentiation;Power rule,Trigonometric rules,Logarithmic rule,First order
582;Lithuania;570;0;Advanced;Analytic Geometry;Analytic Geometry;Distance,Orthogonal projection,Orthogonality
1543;Portugal;1093;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1157;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1220;Slovenia;454;0;Basic;Linear Algebra;Vector Spaces;Basis
1248;Italy;234;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
168;Portugal;782;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1375;Portugal;278;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
465;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1256;Portugal;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
219;Lithuania;108;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
91;Lithuania;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
411;Portugal;144;0;Basic;Differentiation;Derivatives;Trigonometric rules
71;Portugal;136;0;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
1087;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1518;Portugal;141;1;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication
168;Portugal;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
189;Portugal;665;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
175;Italy;1116;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
1411;Portugal;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1075;Portugal;148;0;Basic;Differentiation;Partial Differentiation;First order
1244;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1291;Italy;292;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
1220;Slovenia;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
658;Ireland;79;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
913;Ireland;487;0;Basic;Probability ;Probability ;Axioms of probability,Event,Independence,Addition, multiplication, and total probability rules,Sample space
840;Italy;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
91;Lithuania;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
407;Portugal;97;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
37;Portugal;1230;1;Basic;Differentiation;Partial Differentiation;Second order,First order
884;Italy;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
72;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1037;Lithuania;998;0;Basic;Differentiation;Partial Differentiation;First order
72;Portugal;385;0;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1220;Slovenia;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1024;Lithuania;877;0;Basic;Differentiation;Partial Differentiation;Second order
457;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1220;Slovenia;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
899;Lithuania;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
986;Portugal;420;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
511;Portugal;230;1;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
1219;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
311;Ireland;131;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
378;Portugal;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1179;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1197;Slovenia;419;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
955;Lithuania;1099;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1220;Slovenia;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1220;Slovenia;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
972;Portugal;448;0;Advanced;Linear Algebra;Vector Spaces;Subspace
1305;Italy;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1081;Portugal;439;0;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
988;Portugal;216;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
1143;Portugal;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1505;Portugal;955;0;Basic;Optimization;Linear Optimization;Linear programming
175;Italy;334;1;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
71;Portugal;271;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
64;Portugal;253;1;Basic;Differentiation;Derivatives;Logarithmic rule,Trigonometric rules
311;Ireland;635;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
1517;Portugal;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
378;Portugal;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
91;Lithuania;424;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
91;Lithuania;506;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry
128;Lithuania;138;0;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Determinant computation,Determinant properties,Inverse matrix 
71;Portugal;852;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Continuity,Limits
1182;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
155;Spain;165;0;Basic;Differential Equations;Differential Equations;Linear differential equation,Homogeneous equation
551;Lithuania;352;0;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Operations with complex numbers
1220;Slovenia;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
483;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
41;Portugal;562;1;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality
913;Ireland;1108;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Lagrange's interpolation
667;Portugal;177;1;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
1135;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1290;Italy;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
599;Italy;628;1;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue,Diagonalization
967;Portugal;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1158;Portugal;454;1;Basic;Linear Algebra;Vector Spaces;Basis
840;Italy;292;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
625;Russian Federation;501;0;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids
1173;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1130;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
876;Italy;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1322;Italy;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1339;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
751;Lithuania;999;0;Basic;Differentiation;Partial Differentiation;First order
1171;Portugal;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
397;Portugal;358;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Conjugate number,Operations with complex numbers,Real part
1147;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1290;Italy;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
411;Portugal;856;1;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Diagonalization,Spectrum,Characteristic polynomial
1032;Lithuania;257;0;Basic;Differentiation;Partial Differentiation;Gradient,First order
1220;Slovenia;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
80;Lithuania;231;1;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system,Solution of linear system
876;Italy;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
986;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
473;Portugal;432;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
91;Lithuania;356;0;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers
69;Portugal;565;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonal projection,Orthogonality,Collinearity,Locus
1533;Portugal;564;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonality
988;Portugal;217;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
509;Portugal;635;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
175;Italy;1252;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
956;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
1564;Portugal;981;0;Basic;Real Functions of a single variable;Limits and Continuity;Limits
840;Italy;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1275;Lithuania;440;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
64;Portugal;564;0;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonality
37;Portugal;886;1;Advanced;Differentiation;Partial Differentiation;Second order,First order
1220;Slovenia;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
37;Portugal;394;1;Basic;Integration;Integration Techniques;Substitution
26;Portugal;217;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
204;Lithuania;668;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
80;Lithuania;951;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
340;Portugal;304;0;Basic;Probability ;Probability ;Addition, multiplication, and total probability rules,Sample space,Event,Axioms of probability
840;Italy;778;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
426;Portugal;351;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Imaginary part,Complex plane ,Operations with complex numbers,Real part,Principal argument,De Moivre formulas
1082;Portugal;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1179;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
511;Portugal;88;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Square linear system,Solution of linear system,Undetermined solution of linear system,Consistent system
1269;Portugal;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
91;Lithuania;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
851;Italy;911;0;Basic;Optimization;Nonlinear Optimization;Minimum,Stationary point,Maximum,Saddle point,Optimal solution
1288;Portugal;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1322;Italy;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1300;Italy;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1077;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1279;Portugal;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
548;Portugal;302;0;Basic;Probability ;Probability ;Addition, multiplication, and total probability rules,Sample space,Event,Axioms of probability
510;Portugal;368;0;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids,Regular polygon
1195;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
669;Portugal;81;0;Basic;Statistics;Statistics;Mean,Median,Mode
1269;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
28;Portugal;331;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
69;Portugal;571;1;Basic;Analytic Geometry;Analytic Geometry;Intersection,Cartesian equations of a plane
913;Ireland;243;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
168;Portugal;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
641;Italy;186;0;Basic;Statistics;Statistics;Population,Sample
1352;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
351;Portugal;788;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Exponential function
411;Portugal;616;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector
913;Ireland;761;1;Basic;Probability ;Probability ;Event,Sample space,Addition, multiplication, and total probability rules,Axioms of probability
1229;Portugal;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
91;Lithuania;504;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry,Geometric transformations
1517;Portugal;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
956;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1533;Portugal;557;0;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance
1185;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
468;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
966;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
36;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
876;Italy;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1220;Slovenia;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
769;Portugal;338;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form
250;Lithuania;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1248;Italy;90;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1194;Portugal;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
80;Lithuania;757;0;Basic;Integration;Double Integration;Iterate integrals,Cartesian coordinates,y-simple region (type I)
1076;Portugal;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
979;Portugal;1120;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
1271;Portugal;385;1;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
955;Lithuania;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
625;Russian Federation;614;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1487;Portugal;335;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
913;Ireland;211;0;Basic;Statistics;Statistics;Linear regression
1557;Portugal;923;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1517;Portugal;288;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
64;Portugal;406;0;Basic;Integration;Integration Techniques;Direct inspection
90;Lithuania;641;0;Basic;Linear Algebra;Matrices and Determinants;Commuting matrices,Solve matrix equation,Matrix equivalent - echelon,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties,Hermitian matrix,Symmetric matrix,Matrix multiplication,Linearly independent rows,Matrix operations
979;Portugal;1107;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1195;Portugal;785;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
168;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1379;Portugal;796;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Logarithmic function,Exponential function,Simplify expressions
1220;Slovenia;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1241;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
890;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
913;Ireland;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
422;Portugal;337;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form,Operations with complex numbers,Modulus of a complex number
697;Portugal;201;0;Basic;Statistics;Statistics;Chi square distribution,Student distribution,Quantile,Hypothesis testing
1220;Slovenia;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1220;Slovenia;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
351;Portugal;918;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1509;Portugal;83;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain,Image of a function
41;Portugal;114;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
966;Portugal;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1243;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1158;Portugal;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
483;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1276;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1517;Portugal;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
91;Lithuania;517;0;Advanced;Fundamental Mathematics;Elementary Geometry;Symmetry
525;Portugal;113;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
91;Lithuania;519;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
884;Italy;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
349;Portugal;734;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Exponential rule
625;Russian Federation;113;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1045;Lithuania;908;0;Basic;Differentiation;Partial Differentiation;Gradient,Directional derivative
1023;Lithuania;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1252;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1299;Italy;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
525;Portugal;795;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
967;Portugal;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1023;Lithuania;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
637;Italy;182;0;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
1286;Italy;454;0;Basic;Linear Algebra;Vector Spaces;Basis
91;Lithuania;136;1;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
1220;Slovenia;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
168;Portugal;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
166;Portugal;703;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Scalar product
509;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
851;Italy;861;1;Basic;Optimization;Nonlinear Optimization;Saddle point,Optimal solution,Minimum,Maximum,Stationary point
956;Portugal;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1087;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1291;Italy;781;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
168;Portugal;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
473;Portugal;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
61;Portugal;837;0;Basic;Differential Equations;Differential Equations;Linear differential equation
1332;Portugal;424;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
61;Portugal;870;1;Basic;Differential Equations;Differential Equations;Homogeneous equation
1135;Portugal;779;0;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
1023;Lithuania;455;0;Basic;Linear Algebra;Vector Spaces;Basis
403;Portugal;439;0;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
1479;Portugal;955;1;Basic;Optimization;Linear Optimization;Linear programming
168;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
175;Italy;794;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
175;Italy;1117;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
1219;Portugal;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1505;Portugal;189;0;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
168;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
775;Portugal;298;0;Basic;Probability ;Probability ;Event,Axioms of probability
634;Italy;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1229;Portugal;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1197;Slovenia;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1230;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1351;Portugal;126;1;Advanced;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Solve matrix equation
775;Portugal;308;1;Basic;Probability ;Probability ;Axioms of probability,Event,Addition, multiplication, and total probability rules,Sample space
1375;Portugal;306;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
1023;Lithuania;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
898;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1275;Lithuania;432;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
667;Portugal;202;1;Basic;Statistics;Statistics;Student distribution,Confidence interval,Point estimate,Hypothesis testing
351;Portugal;793;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
468;Portugal;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
359;Portugal;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
91;Lithuania;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
966;Portugal;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
1352;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
91;Lithuania;505;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangles
1352;Portugal;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1284;Italy;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1220;Slovenia;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1022;Lithuania;738;0;Basic;Optimization;Linear Optimization;Graphical method,Linear programming
1023;Lithuania;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
359;Portugal;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
91;Lithuania;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
91;Lithuania;345;1;Advanced;Complex Numbers;Complex Numbers;Polar representation,Trigonometric form,Modulus of a complex number,Operations with complex numbers,Algebraic form,Principal argument,De Moivre formulas
380;Portugal;169;0;Basic;Differential Equations;Differential Equations;Linear differential equation
986;Portugal;447;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1334;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1543;Portugal;1114;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
1220;Slovenia;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
852;Italy;246;0;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
1220;Slovenia;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
378;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
411;Portugal;342;0;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Modulus of a complex number,Algebraic form
913;Ireland;492;1;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Axioms of probability,Event
1308;Italy;782;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
359;Portugal;364;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids,Geometrical figures,Classification of geometric solids
1220;Slovenia;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1308;Italy;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
986;Portugal;427;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
71;Portugal;771;1;Basic;Probability ;Probability ;Event,Sample space,Addition, multiplication, and total probability rules,Axioms of probability
394;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
625;Russian Federation;800;0;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Exponential function,Simplify expressions
899;Lithuania;449;0;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
1143;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1286;Italy;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
91;Lithuania;346;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
851;Italy;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
351;Portugal;666;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1220;Slovenia;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
380;Portugal;868;0;Basic;Differential Equations;Differential Equations;Separable variables equation
36;Portugal;607;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector
1220;Slovenia;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1279;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1023;Lithuania;455;1;Basic;Linear Algebra;Vector Spaces;Basis
1171;Portugal;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1525;Portugal;295;0;Basic;Probability ;Probability ;Sample space,Addition, multiplication, and total probability rules,Event,Axioms of probability
1163;Portugal;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1220;Slovenia;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
966;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
81;Lithuania;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
81;Lithuania;288;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
462;Lithuania;645;1;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Linearly independent rows
1220;Slovenia;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1379;Portugal;798;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
972;Portugal;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
741;Ireland;935;0;Basic;Graph Theory;Graph Theory;Chromatic number
1288;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
351;Portugal;612;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
986;Portugal;449;1;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
26;Portugal;566;0;Basic;Analytic Geometry;Analytic Geometry;Distance,Orthogonality,Locus
168;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
955;Lithuania;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1135;Portugal;782;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1087;Portugal;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
591;Portugal;341;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
1220;Slovenia;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
876;Italy;385;1;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1219;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
420;Portugal;327;1;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1044;Lithuania;885;0;Basic;Differentiation;Partial Differentiation;Second order,First order
26;Portugal;1157;1;Basic;Set Theory;Set Theory;Subset
1220;Slovenia;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1195;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1543;Portugal;1092;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
827;Italy;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
168;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
535;Portugal;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
852;Italy;239;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
851;Italy;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1274;Portugal;787;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Logarithmic function
1350;Portugal;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1286;Italy;451;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
80;Lithuania;549;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Cross product,Orthogonality
776;Portugal;570;0;Advanced;Analytic Geometry;Analytic Geometry;Distance,Orthogonal projection,Orthogonality
1071;Lithuania;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1290;Italy;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1564;Portugal;680;0;Basic;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
1289;Italy;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
884;Italy;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
1077;Portugal;290;0;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
473;Portugal;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1093;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
239;Lithuania;255;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Logarithmic rule
958;Lithuania;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
422;Portugal;327;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1219;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1252;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
884;Italy;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
639;Italy;202;0;Basic;Statistics;Statistics;Student distribution,Confidence interval,Point estimate,Hypothesis testing
168;Portugal;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
972;Portugal;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
80;Lithuania;788;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Exponential function
451;Portugal;307;0;Basic;Probability ;Probability ;Event,Addition, multiplication, and total probability rules,Independence
1557;Portugal;926;0;Advanced;Real Functions of a single variable;Domain, Image and Graphics;Planar graph
625;Russian Federation;495;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
61;Portugal;831;0;Basic;Differential Equations;Differential Equations;Linear differential equation
37;Portugal;1084;1;Advanced;Differentiation;Partial Differentiation;First order,Second order
625;Russian Federation;522;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Triangles
1147;Portugal;455;1;Basic;Linear Algebra;Vector Spaces;Basis
376;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
986;Portugal;640;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
91;Lithuania;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1324;Italy;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1143;Portugal;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
955;Lithuania;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
988;Portugal;950;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1197;Slovenia;449;0;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
890;Portugal;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1352;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1157;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
177;Italy;730;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
91;Lithuania;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1080;Portugal;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
851;Italy;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1256;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
37;Portugal;1123;1;Basic;Integration;Integration Techniques;Integration by parts,Substitution,Simple integration,Direct inspection
1220;Slovenia;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1312;Portugal;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
913;Ireland;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
37;Portugal;1076;0;Basic;Differentiation;Partial Differentiation;Logarithmic rule,Power rule,Trigonometric rules
1241;Portugal;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
91;Lithuania;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1220;Slovenia;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1044;Lithuania;875;1;Basic;Differentiation;Partial Differentiation;Gradient,First order
311;Ireland;647;0;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Symmetric matrix,Matrix operations
1081;Portugal;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
411;Portugal;335;0;Basic;Complex Numbers;Complex Numbers;Algebraic form,Principal argument,De Moivre formulas,Polar representation,Operations with complex numbers,Modulus of a complex number,Trigonometric form
376;Portugal;356;0;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers
406;Portugal;91;0;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
81;Lithuania;481;1;Advanced;Graph Theory;Graph Theory;Path,Simple graph,Cycle and circuit
375;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1252;Portugal;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
168;Portugal;446;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
175;Italy;1514;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
1220;Slovenia;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
986;Portugal;419;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
1087;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1273;Portugal;418;1;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
128;Lithuania;338;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form
1220;Slovenia;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
986;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
422;Portugal;651;0;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Symmetric matrix,Matrix operations,Commuting matrices,Solve matrix equation,Inverse matrix ,Determinant computation,Matrix rank,Determinant properties
591;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
175;Italy;1093;1;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
899;Lithuania;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1028;Lithuania;268;0;Basic;Differentiation;Partial Differentiation;First order,Second order
376;Portugal;329;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
913;Ireland;432;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
884;Italy;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
374;Portugal;241;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1023;Lithuania;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
552;Portugal;869;0;Basic;Differential Equations;Differential Equations;Separable variables equation
1288;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1049;Lithuania;253;0;Basic;Differentiation;Derivatives;Logarithmic rule,Trigonometric rules
1543;Portugal;1086;0;Basic;Numerical Methods;Numerical Methods;First order,Second order
1288;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
483;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
414;Portugal;336;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Modulus of a complex number,Imaginary part
394;Portugal;447;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
913;Ireland;1103;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
509;Portugal;114;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
64;Portugal;120;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
131;Lithuania;117;0;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1220;Slovenia;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1269;Portugal;419;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
751;Lithuania;703;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Scalar product
1288;Portugal;289;0;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
511;Portugal;245;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1220;Slovenia;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
91;Lithuania;355;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
81;Lithuania;937;0;Advanced;Graph Theory;Graph Theory;Chromatic number
753;Italy;1000;0;Basic;Differentiation;Partial Differentiation;First order
202;Lithuania;798;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
376;Portugal;358;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Conjugate number,Operations with complex numbers,Real part
1220;Slovenia;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
651;Ireland;187;0;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
414;Portugal;227;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
855;Italy;218;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
965;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
36;Portugal;1133;1;Basic;Set Theory;Set Theory;Subset
1220;Slovenia;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
913;Ireland;1251;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
899;Lithuania;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
974;Portugal;424;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1087;Portugal;454;1;Basic;Linear Algebra;Vector Spaces;Basis
1299;Italy;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1517;Portugal;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
974;Portugal;1088;1;Basic;Numerical Methods;Numerical Methods;First order,Second order
155;Spain;148;1;Basic;Differentiation;Partial Differentiation;First order
1173;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1252;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
69;Portugal;353;1;Basic;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
1135;Portugal;288;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1023;Lithuania;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
955;Lithuania;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
524;Portugal;127;1;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Determinant computation,Determinant properties,Symmetric matrix,Inverse matrix ,Linearly independent rows,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank
1220;Slovenia;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
525;Portugal;120;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
91;Lithuania;355;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
1322;Italy;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1109;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
90;Lithuania;355;0;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
1087;Portugal;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
168;Portugal;595;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Eigenvalue
988;Portugal;233;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
1427;Portugal;380;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
700;Portugal;201;1;Basic;Statistics;Statistics;Chi square distribution,Student distribution,Quantile,Hypothesis testing
69;Portugal;548;1;Basic;Analytic Geometry;Analytic Geometry;Collinearity,Distance,Locus,Cross product,Orthogonality,Scalar product
349;Portugal;82;0;Basic;Differentiation;Derivatives;Logarithmic rule,Power rule,Exponential rule,Trigonometric rules,Product rule
387;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1487;Portugal;1164;1;Basic;Integration;Definite Integrals;Direct integrals ,Fundamental theorem of Calculus
411;Portugal;414;0;Basic;Integration;Integration Techniques;Substitution,Direct inspection,Integration by parts,Rational functions
1332;Portugal;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
394;Portugal;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
198;Italy;524;0;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Rhombus
599;Italy;594;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Spectrum,Characteristic polynomial,Diagonalization,Eigenvalue
91;Lithuania;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1082;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1220;Slovenia;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
57;Portugal;1212;1;Basic;Statistics;Statistics;Mean,Median,Outliers,Interquartile range
71;Portugal;123;1;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Commuting matrices,Solve matrix equation,Matrix operations,Matrix rank,Determinant computation,Matrix multiplication,Determinant properties,Symmetric matrix
71;Portugal;753;1;Basic;Differentiation;Derivatives;Exponential rule
1220;Slovenia;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1517;Portugal;292;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
1308;Italy;306;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
1220;Slovenia;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
986;Portugal;418;1;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
1220;Slovenia;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1505;Portugal;183;1;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
351;Portugal;100;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Power rule
1109;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
955;Lithuania;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
552;Portugal;575;1;Advanced;Analytic Geometry;Analytic Geometry;Orthogonality,Orthogonal projection,Cross product,Scalar product
899;Lithuania;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1075;Portugal;908;1;Basic;Differentiation;Partial Differentiation;Gradient,Directional derivative
956;Portugal;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1077;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1044;Lithuania;263;1;Basic;Differentiation;Partial Differentiation;First order
1557;Portugal;693;1;Advanced;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
1220;Slovenia;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1483;Portugal;327;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1305;Italy;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1081;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
468;Portugal;333;1;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
751;Lithuania;734;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Exponential rule
1039;Lithuania;264;0;Basic;Differentiation;Partial Differentiation;Chain rule
973;Portugal;630;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue
776;Portugal;564;0;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonality
1081;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
851;Italy;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
359;Portugal;432;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
28;Portugal;563;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
483;Portugal;368;1;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids,Regular polygon
1220;Slovenia;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
90;Lithuania;126;0;Advanced;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Solve matrix equation
641;Italy;187;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
854;Italy;243;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
972;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
1039;Lithuania;908;0;Basic;Differentiation;Partial Differentiation;Gradient,Directional derivative
840;Italy;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
511;Portugal;221;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
37;Portugal;399;1;Basic;Integration;Integration Techniques;Substitution,Direct inspection,Simple integration
840;Italy;306;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
407;Portugal;329;1;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
661;Portugal;193;0;Basic;Statistics;Statistics;Standard deviation,Variance,Median,Frequency,Mode,Outliers,Quantile,Interquartile range,Population,Data type,Sample,Relative frequency,Mean
1481;Portugal;681;0;Basic;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
387;Portugal;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
376;Portugal;357;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Algebraic form,Conjugate number,Real part,Equations involving complex numbers
1076;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
80;Lithuania;229;0;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
414;Portugal;951;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
551;Lithuania;342;0;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Modulus of a complex number,Algebraic form
71;Portugal;560;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality
1517;Portugal;451;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
175;Italy;1473;0;Basic;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
633;Italy;448;1;Advanced;Linear Algebra;Vector Spaces;Subspace
576;Ireland;561;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
175;Italy;327;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
80;Lithuania;756;1;Basic;Integration;Double Integration;Cartesian coordinates,x-simple region (type II),Changing order of integration
1146;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
37;Portugal;339;1;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation
1334;Portugal;290;0;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
80;Lithuania;836;1;Basic;Differential Equations;Differential Equations;Linear differential equation
483;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
955;Lithuania;1109;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Lagrange's interpolation
1135;Portugal;382;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
751;Lithuania;261;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
509;Portugal;136;1;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Matrix operations,Matrix multiplication,Symmetric matrix,Determinant computation,Commuting matrices,Determinant properties,Inverse matrix ,Solve matrix equation
988;Portugal;441;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1049;Lithuania;148;0;Basic;Differentiation;Partial Differentiation;First order
1219;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
898;Portugal;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1256;Portugal;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
898;Portugal;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
1341;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
376;Portugal;1056;1;Advanced;Complex Numbers;Complex Numbers;Complex plane 
956;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
91;Lithuania;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1095;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1256;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
966;Portugal;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1322;Italy;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1286;Italy;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1486;Portugal;611;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
966;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
199;Lithuania;108;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
165;Portugal;875;0;Basic;Differentiation;Partial Differentiation;Gradient,First order
1076;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
626;Italy;753;1;Basic;Differentiation;Derivatives;Exponential rule
969;Romania;427;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1220;Slovenia;454;1;Basic;Linear Algebra;Vector Spaces;Basis
473;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
91;Lithuania;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1220;Slovenia;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
168;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
840;Italy;778;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1244;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
405;Portugal;120;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
697;Portugal;177;1;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
1274;Portugal;104;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1533;Portugal;563;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
174;Portugal;501;0;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids
203;Lithuania;118;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1079;Portugal;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
525;Portugal;524;0;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Rhombus
411;Portugal;338;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Modulus of a complex number,Algebraic form,Principal argument,De Moivre formulas,Polar representation,Trigonometric form
1256;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1292;Italy;629;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue
394;Portugal;449;1;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
1220;Slovenia;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1220;Slovenia;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1564;Portugal;925;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Planar graph
81;Lithuania;779;0;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
1087;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1179;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
634;Italy;274;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
1081;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1273;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
972;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1220;Slovenia;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1093;Portugal;432;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
876;Italy;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;785;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
406;Portugal;223;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
979;Portugal;1096;1;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
899;Lithuania;424;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1229;Portugal;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
966;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
72;Portugal;779;0;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
168;Portugal;777;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
448;Portugal;322;1;Advanced;Probability ;Probability ;Conditional probability,Bayes' Theorem
198;Italy;613;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1163;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
451;Portugal;343;1;Advanced;Probability ;Probability ;Conditional probability,Bayes' Theorem
1091;Lithuania;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
394;Portugal;446;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
414;Portugal;331;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1050;Lithuania;268;0;Basic;Differentiation;Partial Differentiation;First order,Second order
71;Portugal;271;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
1194;Portugal;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1028;Lithuania;257;0;Basic;Differentiation;Partial Differentiation;Gradient,First order
1150;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
598;Italy;222;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1271;Portugal;779;0;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
600;Italy;131;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
72;Portugal;566;0;Basic;Analytic Geometry;Analytic Geometry;Distance,Orthogonality,Locus
689;Portugal;867;0;Basic;Optimization;Nonlinear Optimization;Stationary point,Maximum,Saddle point,Second derivative test,Optimal solution,Minimum
1411;Portugal;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
81;Lithuania;381;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
853;Italy;227;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1192;Portugal;454;1;Basic;Linear Algebra;Vector Spaces;Basis
1292;Italy;278;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
510;Portugal;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1076;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
633;Italy;424;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1322;Italy;455;0;Basic;Linear Algebra;Vector Spaces;Basis
359;Portugal;506;0;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry
552;Portugal;574;0;Advanced;Analytic Geometry;Analytic Geometry;Collinearity,Orthogonality,Distance,Scalar product
511;Portugal;227;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
983;Portugal;342;1;Basic;Complex Numbers;Complex Numbers;Trigonometric form,Modulus of a complex number,Algebraic form
457;Portugal;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1081;Portugal;439;1;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
918;Portugal;397;0;Basic;Integration;Integration Techniques;Substitution
955;Lithuania;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1171;Portugal;155;0;Basic;Optimization;Nonlinear Optimization;Lagrange multipliers,Maximum,Minimum
375;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
80;Lithuania;328;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
852;Italy;223;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
155;Spain;153;1;Basic;Differentiation;Partial Differentiation;Stationary point,Minimum,Optimal solution,Lagrange multipliers
1289;Italy;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1046;Lithuania;883;0;Basic;Differentiation;Partial Differentiation;First order,Directional derivative
1220;Slovenia;377;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
840;Italy;454;0;Basic;Linear Algebra;Vector Spaces;Basis
37;Portugal;1071;1;Basic;Differentiation;Partial Differentiation;First order
1023;Lithuania;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1220;Slovenia;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
913;Ireland;449;1;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
37;Portugal;851;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Continuity,Limits
509;Portugal;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
634;Italy;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
349;Portugal;142;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
741;Ireland;181;0;Basic;Statistics;Statistics;Quantile,Frequency,Sample,Mean,Variance,Standard deviation,Median,Mode
509;Portugal;602;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector,Spectrum,Characteristic polynomial
840;Italy;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
853;Italy;228;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1286;Italy;424;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
411;Portugal;401;0;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
468;Portugal;356;0;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers
967;Portugal;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1158;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
383;Portugal;352;1;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Operations with complex numbers
151;Portugal;102;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
168;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1220;Slovenia;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
448;Portugal;304;1;Basic;Probability ;Probability ;Addition, multiplication, and total probability rules,Sample space,Event,Axioms of probability
175;Italy;1088;1;Basic;Numerical Methods;Numerical Methods;First order,Second order
1220;Slovenia;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1292;Italy;853;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Continuity,Limits
414;Portugal;220;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
913;Ireland;294;0;Basic;Probability ;Probability ;Event,Axioms of probability,Sample space
1517;Portugal;419;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
426;Portugal;352;1;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Operations with complex numbers
840;Italy;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1087;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1273;Portugal;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1158;Portugal;785;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
510;Portugal;666;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
359;Portugal;668;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions