raw_data/tabular_datasets/c6/c6-test.csv

Student ID;Student Country;Question ID;Type of Answer;Question Level;Topic;Subtopic;Keywords
1023;Lithuania;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
692;Portugal;204;1;Basic;Statistics;Statistics;Student distribution,Hypothesis testing
955;Lithuania;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
57;Portugal;184;1;Basic;Statistics;Statistics;Frequency,Sample,Stem and Leaf diagram,Variance,Standard deviation,Relative frequency
598;Italy;134;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
986;Portugal;430;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
415;Portugal;336;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Modulus of a complex number,Imaginary part
37;Portugal;608;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector
1271;Portugal;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
175;Italy;1110;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
28;Portugal;566;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Orthogonality,Locus
1420;Portugal;278;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
181;Italy;920;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1289;Italy;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
411;Portugal;412;0;Basic;Integration;Integration Techniques;Power of trigonometric functions
855;Italy;239;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
155;Spain;147;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
1517;Portugal;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1023;Lithuania;454;0;Basic;Linear Algebra;Vector Spaces;Basis
1220;Slovenia;436;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1045;Lithuania;266;1;Basic;Differentiation;Partial Differentiation;First order,Second order
625;Russian Federation;458;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Geometric transformations,Geometrical figures
1300;Italy;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1340;Portugal;1116;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
1557;Portugal;688;1;Advanced;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
985;Romania;253;1;Basic;Differentiation;Derivatives;Logarithmic rule,Trigonometric rules
1322;Italy;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
91;Lithuania;494;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1087;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
483;Portugal;108;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
128;Lithuania;645;1;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Linearly independent rows
851;Italy;860;0;Basic;Optimization;Nonlinear Optimization;Saddle point,Optimal solution,Minimum,Maximum,Stationary point
1353;Portugal;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
81;Lithuania;583;1;Advanced;Graph Theory;Graph Theory;Path,Simple graph,Cycle and circuit
840;Italy;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1149;Portugal;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
1339;Portugal;783;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
1564;Portugal;919;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
380;Portugal;155;1;Basic;Optimization;Nonlinear Optimization;Lagrange multipliers,Maximum,Minimum
1087;Portugal;780;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
1157;Portugal;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1252;Portugal;455;0;Basic;Linear Algebra;Vector Spaces;Basis
1282;Portugal;454;1;Basic;Linear Algebra;Vector Spaces;Basis
955;Lithuania;1111;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
1322;Italy;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
666;Portugal;181;0;Basic;Statistics;Statistics;Quantile,Frequency,Sample,Mean,Variance,Standard deviation,Median,Mode
198;Italy;495;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1565;Portugal;401;0;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
1220;Slovenia;454;1;Basic;Linear Algebra;Vector Spaces;Basis
1130;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
37;Portugal;360;1;Basic;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
974;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
420;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
1220;Slovenia;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
483;Portugal;441;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1219;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
203;Lithuania;613;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1219;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
972;Portugal;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
913;Ireland;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1148;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
641;Italy;80;0;Basic;Statistics;Statistics;Population,Variance,Median,Standard deviation,Mode,Quantile,Sample,Mean
958;Lithuania;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
884;Italy;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1517;Portugal;439;0;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
509;Portugal;507;0;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry
181;Italy;925;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Planar graph
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;319;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
493;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
625;Russian Federation;366;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids,Geometrical figures,Classification of geometric solids
1220;Slovenia;454;0;Basic;Linear Algebra;Vector Spaces;Basis
1146;Portugal;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
625;Russian Federation;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
1087;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
378;Portugal;701;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product,Distance
1525;Portugal;770;0;Advanced;Probability ;Probability ;Bayes' Theorem,Conditional probability
91;Lithuania;509;1;Advanced;Fundamental Mathematics;Elementary Geometry;Symmetry
634;Italy;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
972;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1517;Portugal;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
340;Portugal;301;0;Basic;Probability ;Probability ;Sample space,Event
176;Italy;658;1;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
1252;Portugal;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
175;Italy;1114;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
1157;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
448;Portugal;485;1;Advanced;Probability ;Probability ;Bayes' Theorem,Conditional probability
351;Portugal;104;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1147;Portugal;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
419;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;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
422;Portugal;134;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
71;Portugal;308;1;Basic;Probability ;Probability ;Axioms of probability,Event,Addition, multiplication, and total probability rules,Sample space
509;Portugal;776;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
81;Lithuania;573;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Locus,Scalar product,Cross product,Collinearity
91;Lithuania;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
986;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
633;Italy;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
955;Lithuania;1096;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
693;Portugal;191;0;Basic;Statistics;Statistics;Median,Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance
599;Italy;601;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Eigenvalue
1517;Portugal;781;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
91;Lithuania;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
524;Portugal;796;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Logarithmic function,Exponential function,Simplify expressions
376;Portugal;359;1;Advanced;Complex Numbers;Complex Numbers;Principal argument,Trigonometric form,Modulus of a complex number,Algebraic form
664;Portugal;202;1;Basic;Statistics;Statistics;Student distribution,Confidence interval,Point estimate,Hypothesis testing
91;Lithuania;503;0;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry,Geometric transformations
174;Portugal;661;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
675;Portugal;78;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
524;Portugal;789;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
91;Lithuania;461;1;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
592;Portugal;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
394;Portugal;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
91;Lithuania;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1220;Slovenia;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
600;Italy;640;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
1044;Lithuania;148;1;Basic;Differentiation;Partial Differentiation;First order
1146;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
168;Portugal;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
966;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
91;Lithuania;497;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
1322;Italy;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
419;Portugal;330;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number
1219;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
394;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1322;Italy;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
26;Portugal;487;1;Basic;Probability ;Probability ;Axioms of probability,Event,Independence,Addition, multiplication, and total probability rules,Sample space
986;Portugal;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
551;Lithuania;695;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product
1505;Portugal;280;1;Basic;Optimization;Linear Optimization;Linear programming
1379;Portugal;918;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
591;Portugal;569;1;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance,Scalar product,Cross product,Orthogonality,Collinearity
551;Lithuania;353;0;Basic;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
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
80;Lithuania;602;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector,Spectrum,Characteristic polynomial
359;Portugal;796;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Logarithmic function,Exponential function,Simplify expressions
26;Portugal;697;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Distance,Cross product
374;Portugal;346;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
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
1331;Portugal;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
81;Lithuania;118;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
913;Ireland;1113;1;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
1022;Lithuania;281;0;Basic;Optimization;Linear Optimization;Linear programming
71;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
1220;Slovenia;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
741;Ireland;942;0;Basic;Graph Theory;Graph Theory;Spanning tree,Shortest path,Path,Tree
28;Portugal;563;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
1543;Portugal;1093;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1044;Lithuania;266;0;Basic;Differentiation;Partial Differentiation;First order,Second order
69;Portugal;572;1;Basic;Analytic Geometry;Analytic Geometry;Locus,Scalar product,Cross product,Distance,Collinearity,Orthogonality
1076;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
972;Portugal;782;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
426;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1557;Portugal;683;0;Advanced;Real Functions of a single variable;Domain, Image and Graphics;Domain
591;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
776;Portugal;574;0;Advanced;Analytic Geometry;Analytic Geometry;Collinearity,Orthogonality,Distance,Scalar product
972;Portugal;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1332;Portugal;432;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
28;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
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
955;Lithuania;1213;1;Basic;Numerical Methods;Numerical Methods;Mean,Median,Outliers,Interquartile range
1143;Portugal;323;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
899;Lithuania;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
473;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
851;Italy;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
890;Portugal;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
898;Portugal;1004;1;Basic;Optimization;Nonlinear Optimization;Minimum,Stationary point,Maximum,Saddle point,Optimal solution
840;Italy;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1244;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
200;Lithuania;401;1;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
853;Italy;243;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
36;Portugal;639;0;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Determinant computation,Determinant properties,Matrix operations
1163;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1076;Portugal;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
28;Portugal;390;0;Basic;Integration;Integration Techniques;Direct inspection,Simple integration
175;Italy;142;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
1220;Slovenia;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
71;Portugal;695;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product
988;Portugal;917;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
451;Portugal;487;0;Basic;Probability ;Probability ;Axioms of probability,Event,Independence,Addition, multiplication, and total probability rules,Sample space
695;Portugal;80;0;Basic;Statistics;Statistics;Population,Variance,Median,Standard deviation,Mode,Quantile,Sample,Mean
1487;Portugal;327;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
37;Portugal;253;1;Basic;Differentiation;Derivatives;Logarithmic rule,Trigonometric rules
473;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
851;Italy;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
37;Portugal;327;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1026;Lithuania;268;0;Basic;Differentiation;Partial Differentiation;First order,Second order
473;Portugal;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1194;Portugal;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
899;Lithuania;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
986;Portugal;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
80;Lithuania;219;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
851;Italy;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
26;Portugal;558;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
1220;Slovenia;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
71;Portugal;604;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector,Spectrum,Characteristic polynomial
1517;Portugal;627;1;Advanced;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue,Diagonalization
1481;Portugal;982;1;Basic;Real Functions of a single variable;Limits and Continuity;Limits
26;Portugal;829;1;Basic;Differential Equations;Differential Equations;Linear differential equation
988;Portugal;384;1;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
91;Lithuania;512;1;Basic;Fundamental Mathematics;Elementary Geometry;Triangles
80;Lithuania;304;0;Basic;Probability ;Probability ;Addition, multiplication, and total probability rules,Sample space,Event,Axioms of probability
1146;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
178;Italy;275;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
37;Portugal;1033;1;Basic;Differentiation;Partial Differentiation;Power rule,Trigonometric rules,Logarithmic rule,First order
1173;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1252;Portugal;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
699;Portugal;201;0;Basic;Statistics;Statistics;Chi square distribution,Student distribution,Quantile,Hypothesis testing
351;Portugal;252;1;Basic;Differentiation;Derivatives;Quotient rule,Product rule,Power rule,Trigonometric rules
1091;Lithuania;779;0;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
1080;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
411;Portugal;229;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
890;Portugal;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
91;Lithuania;733;0;Basic;Integration;Integration Techniques;Simple integration,Direct inspection
473;Portugal;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
741;Ireland;191;0;Basic;Statistics;Statistics;Median,Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance
426;Portugal;356;0;Advanced;Complex Numbers;Complex Numbers;Operations with complex numbers
955;Lithuania;439;0;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
509;Portugal;592;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Logarithmic rule,Product rule,Trigonometric rules
349;Portugal;735;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
1557;Portugal;687;0;Advanced;Real Functions of a single variable;Limits and Continuity;Indeterminate forms,Limits
1220;Slovenia;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
351;Portugal;102;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
36;Portugal;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
955;Lithuania;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
855;Italy;951;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
955;Lithuania;428;0;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
693;Portugal;202;1;Basic;Statistics;Statistics;Student distribution,Confidence interval,Point estimate,Hypothesis testing
639;Italy;183;1;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
972;Portugal;424;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
955;Lithuania;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
689;Portugal;960;0;Basic;Optimization;Nonlinear Optimization;Linear programming
524;Portugal;104;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1156;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
376;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
633;Italy;449;1;Advanced;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis
1080;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1332;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
168;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
81;Lithuania;290;0;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1288;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
510;Portugal;853;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Continuity,Limits
168;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1157;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
91;Lithuania;381;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
91;Lithuania;368;1;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids,Regular polygon
1247;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
1044;Lithuania;912;0;Basic;Differentiation;Partial Differentiation;Minimum,Stationary point,Maximum,Saddle point,Optimal solution
986;Portugal;306;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
473;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
174;Portugal;369;0;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Geometrical figures,Classification of geometrical figures
1292;Italy;306;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
1420;Portugal;385;1;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1243;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
913;Ireland;432;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
1411;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1247;Portugal;639;0;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Determinant computation,Determinant properties,Matrix operations
1220;Slovenia;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
972;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
80;Lithuania;552;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product
387;Portugal;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1044;Lithuania;878;1;Basic;Differentiation;Partial Differentiation;Second order,First order
582;Lithuania;702;0;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Intersection,Cartesian equations of a line
168;Portugal;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
634;Italy;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1288;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
483;Portugal;461;0;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
168;Portugal;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1331;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1093;Portugal;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
151;Portugal;112;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
71;Portugal;614;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1427;Portugal;778;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
168;Portugal;724;1;Advanced;Integration;Integration Techniques;Trigonometric substitution
1322;Italy;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
175;Italy;1096;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1543;Portugal;1092;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1023;Lithuania;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1076;Portugal;277;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
525;Portugal;367;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometrical figures
64;Portugal;794;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
178;Italy;94;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
91;Lithuania;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1220;Slovenia;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
982;Portugal;439;0;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
1252;Portugal;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
986;Portugal;446;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
890;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
979;Portugal;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
91;Lithuania;354;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
634;Italy;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
972;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
166;Portugal;134;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
1087;Portugal;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
175;Italy;1106;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
351;Portugal;667;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1087;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
509;Portugal;629;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Eigenvalue
1220;Slovenia;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
509;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
36;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1363;Portugal;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1023;Lithuania;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
28;Portugal;568;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
200;Lithuania;667;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
168;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
626;Italy;919;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
473;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
851;Italy;820;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Maximum,Stationary point,Saddle point
470;Portugal;347;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
751;Lithuania;568;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
1173;Portugal;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
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
1331;Portugal;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1481;Portugal;565;1;Basic;Analytic Geometry;Analytic Geometry;Distance,Scalar product,Cross product,Orthogonal projection,Orthogonality,Collinearity,Locus
966;Portugal;291;0;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
1179;Portugal;778;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
625;Russian Federation;521;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Regular polygon
524;Portugal;102;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
913;Ireland;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
1219;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
414;Portugal;239;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
1146;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
81;Lithuania;558;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
751;Lithuania;885;0;Basic;Differentiation;Partial Differentiation;Second order,First order
898;Portugal;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
691;Portugal;177;0;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
448;Portugal;307;1;Basic;Probability ;Probability ;Event,Addition, multiplication, and total probability rules,Independence
168;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1353;Portugal;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1147;Portugal;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
411;Portugal;255;1;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Logarithmic rule
167;Portugal;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1284;Italy;457;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
972;Portugal;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
415;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
1543;Portugal;1090;0;Basic;Numerical Methods;Numerical Methods;Nonlinear equation,Newton’s method
1077;Portugal;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
468;Portugal;333;0;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
913;Ireland;1139;1;Basic;Set Theory;Set Theory;Subset
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
1319;Italy;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1517;Portugal;420;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
524;Portugal;667;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1322;Italy;381;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
966;Portugal;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
776;Portugal;703;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Scalar product
1220;Slovenia;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
966;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
509;Portugal;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
41;Portugal;118;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1163;Portugal;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1252;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
510;Portugal;138;0;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Determinant computation,Determinant properties,Inverse matrix 
719;Portugal;177;0;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
854;Italy;239;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
91;Lithuania;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
918;Portugal;192;0;Basic;Integration;Integration Techniques;Trigonometric substitution,Simple integration
955;Lithuania;1120;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
406;Portugal;114;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
81;Lithuania;697;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Distance,Cross product
1043;Lithuania;270;0;Basic;Differentiation;Partial Differentiation;First order,Second order
1093;Portugal;418;0;Advanced;Linear Algebra;Vector Spaces;Basis,Dimension
624;Portugal;524;0;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Rhombus
1288;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
625;Russian Federation;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;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1230;Portugal;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
411;Portugal;640;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
890;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1288;Portugal;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1171;Portugal;1053;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
1288;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
67;Portugal;189;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
393;Lithuania;354;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
1049;Lithuania;661;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
1444;Portugal;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,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
174;Portugal;274;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules
52;Portugal;130;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
1288;Portugal;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
71;Portugal;130;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
913;Ireland;1213;1;Basic;Numerical Methods;Numerical Methods;Mean,Median,Outliers,Interquartile range
1525;Portugal;316;0;Basic;Probability ;Probability ;Axioms of probability,Event,Addition, multiplication, and total probability rules,Sample space
1557;Portugal;674;1;Advanced;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
69;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
483;Portugal;461;1;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids
1109;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;455;1;Basic;Linear Algebra;Vector Spaces;Basis
311;Ireland;134;1;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
1340;Portugal;1106;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
552;Portugal;569;0;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance,Scalar product,Cross product,Orthogonality,Collinearity
1286;Italy;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
986;Portugal;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1179;Portugal;777;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1289;Italy;382;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
26;Portugal;951;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
750;Portugal;919;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
189;Portugal;519;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
955;Lithuania;455;0;Basic;Linear Algebra;Vector Spaces;Basis
91;Lithuania;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;444;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
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
165;Portugal;730;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
168;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
71;Portugal;114;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1220;Slovenia;455;1;Basic;Linear Algebra;Vector Spaces;Basis
91;Lithuania;522;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Triangles
1146;Portugal;378;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
988;Portugal;223;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;510;1;Advanced;Fundamental Mathematics;Elementary Geometry;Symmetry
351;Portugal;668;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1487;Portugal;930;0;Basic;Graph Theory;Graph Theory;Planar graph
378;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
85;Lithuania;480;1;Basic;Graph Theory;Graph Theory;Planar graph
455;Portugal;507;1;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry
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
168;Portugal;380;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
966;Portugal;325;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;454;1;Basic;Linear Algebra;Vector Spaces;Basis
748;Portugal;386;0;Basic;Graph Theory;Graph Theory;Shortest path,Tree,Spanning tree,Path
885;Italy;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
972;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1029;Lithuania;267;0;Basic;Differentiation;Partial Differentiation;First order,Second order
1379;Portugal;922;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
91;Lithuania;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
1288;Portugal;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1561;Portugal;410;0;Advanced;Integration;Integration Techniques;Rational functions
91;Lithuania;427;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
37;Portugal;258;1;Basic;Differentiation;Partial Differentiation;First order,Gradient
41;Portugal;576;0;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
1081;Portugal;424;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1219;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
625;Russian Federation;802;0;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1253;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
510;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1219;Portugal;421;0;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
37;Portugal;719;1;Basic;Integration;Integration Techniques;Integration by parts
175;Italy;329;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
71;Portugal;612;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1505;Portugal;957;0;Basic;Optimization;Linear Optimization;Linear programming
470;Portugal;555;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality,Locus,Distance
984;Romania;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
374;Portugal;603;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector,Spectrum,Characteristic polynomial
1220;Slovenia;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1044;Lithuania;879;1;Basic;Differentiation;Partial Differentiation;First order,Second order
624;Portugal;666;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1291;Italy;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
415;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
26;Portugal;308;1;Basic;Probability ;Probability ;Axioms of probability,Event,Addition, multiplication, and total probability rules,Sample space
1087;Portugal;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
731;Portugal;189;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
625;Russian Federation;666;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
177;Italy;795;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
376;Portugal;347;0;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Modulus of a complex number,Operations with complex numbers,Conjugate number,Real part
168;Portugal;382;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
26;Portugal;552;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product
884;Italy;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
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
1076;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1077;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1158;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
972;Portugal;780;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Range,Kernel,Isomorphism
955;Lithuania;454;0;Basic;Linear Algebra;Vector Spaces;Basis
167;Portugal;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
91;Lithuania;506;0;Basic;Fundamental Mathematics;Elementary Geometry;Symmetry
827;Italy;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
988;Portugal;246;1;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
71;Portugal;720;1;Basic;Differentiation;Derivatives;Quotient rule,Trigonometric rules,Logarithmic rule,Product rule
1220;Slovenia;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
645;Italy;184;1;Basic;Statistics;Statistics;Frequency,Sample,Stem and Leaf diagram,Variance,Standard deviation,Relative frequency
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
91;Lithuania;324;1;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1179;Portugal;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
884;Italy;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
890;Portugal;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
37;Portugal;412;0;Basic;Integration;Integration Techniques;Power of trigonometric functions
1219;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1150;Portugal;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
524;Portugal;793;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
1220;Slovenia;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
407;Portugal;275;0;Basic;Differentiation;Derivatives;Logarithmic rule,Product rule,Trigonometric rules
163;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
776;Portugal;702;1;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Intersection,Cartesian equations of a line
1220;Slovenia;785;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
81;Lithuania;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
411;Portugal;602;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector,Spectrum,Characteristic polynomial
1292;Italy;596;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Eigenvalue
510;Portugal;667;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1080;Portugal;435;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
576;Ireland;560;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality
1229;Portugal;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
986;Portugal;427;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1080;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
720;Portugal;77;1;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
1022;Lithuania;958;0;Basic;Optimization;Linear Optimization;Linear programming
91;Lithuania;467;1;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Polygons,Classification of geometrical figures,Geometrical figures
1271;Portugal;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
426;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
1291;Italy;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
483;Portugal;522;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Triangles
524;Portugal;368;1;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids,Regular polygon
1272;Portugal;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
380;Portugal;1015;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
1288;Portugal;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1196;Slovenia;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
91;Lithuania;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
71;Portugal;487;1;Basic;Probability ;Probability ;Axioms of probability,Event,Independence,Addition, multiplication, and total probability rules,Sample space
1252;Portugal;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
1220;Slovenia;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1289;Italy;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1150;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
72;Portugal;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
956;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
414;Portugal;242;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
576;Ireland;562;0;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Orthogonality
1220;Slovenia;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;375;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1557;Portugal;919;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
524;Portugal;798;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
674;Ireland;79;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
37;Portugal;569;0;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance,Scalar product,Cross product,Orthogonality,Collinearity
1505;Portugal;182;1;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
473;Portugal;419;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Dimension
131;Lithuania;365;1;Advanced;Graph Theory;Graph Theory;Adjacency matrix,Simple graph
91;Lithuania;455;0;Basic;Linear Algebra;Vector Spaces;Basis
965;Portugal;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
633;Italy;785;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
552;Portugal;570;0;Advanced;Analytic Geometry;Analytic Geometry;Distance,Orthogonal projection,Orthogonality
1300;Italy;433;0;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
899;Lithuania;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
166;Portugal;567;0;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a line,Orthogonality,Collinearity
1411;Portugal;292;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
61;Portugal;159;0;Basic;Differential Equations;Differential Equations;Linear differential equation,Integral curve,Cauchy problem
1077;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
380;Portugal;350;0;Advanced;Complex Numbers;Complex Numbers;Complex plane 
1220;Slovenia;421;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
80;Lithuania;131;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties,Inverse matrix ,Matrix operations
1219;Portugal;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
80;Lithuania;1248;1;Basic;Integration;Double Integration;Iterate integrals,Cartesian coordinates
1191;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1135;Portugal;785;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1087;Portugal;444;0;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
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
899;Lithuania;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1220;Slovenia;436;1;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
91;Lithuania;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
625;Russian Federation;371;1;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Geometrical figures
524;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
1350;Portugal;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1163;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
1220;Slovenia;431;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1284;Italy;443;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
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
966;Portugal;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1219;Portugal;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
28;Portugal;697;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Distance,Cross product
155;Spain;164;1;Basic;Differential Equations;Differential Equations;Separable variables equation
899;Lithuania;454;0;Basic;Linear Algebra;Vector Spaces;Basis
1375;Portugal;292;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism
415;Portugal;329;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
85;Lithuania;1136;0;Basic;Set Theory;Set Theory;Subset
535;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
91;Lithuania;497;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
899;Lithuania;437;1;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
376;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
166;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
91;Lithuania;500;0;Advanced;Fundamental Mathematics;Elementary Geometry;Geometrical figures,Triangles,Classification of geometrical figures
473;Portugal;348;1;Advanced;Complex Numbers;Complex Numbers;Imaginary part,Complex plane ,Real part
551;Lithuania;332;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1331;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
840;Italy;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
1543;Portugal;1107;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1538;Portugal;1091;0;Basic;Numerical Methods;Numerical Methods;Nonlinear equation,Newton’s method
913;Ireland;446;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1292;Italy;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1220;Slovenia;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
91;Lithuania;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1339;Portugal;448;1;Advanced;Linear Algebra;Vector Spaces;Subspace
61;Portugal;172;0;Basic;Differential Equations;Differential Equations;Linear differential equation
1220;Slovenia;450;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1286;Italy;432;0;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
683;Ireland;179;0;Basic;Statistics;Statistics;Sample,Population,Mean,Variance,Standard deviation,Median,Mode,Quantile
80;Lithuania;314;1;Basic;Probability ;Probability ;Event,Sample space
28;Portugal;559;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
972;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
1505;Portugal;1003;0;Basic;Optimization;Linear Optimization;Linear programming
168;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
37;Portugal;147;0;Basic;Differentiation;Derivatives;Product rule,Trigonometric rules,Logarithmic rule
853;Italy;950;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1087;Portugal;324;0;Basic;Linear Algebra;Linear Transformations;Linearity,Linear application
626;Italy;254;0;Basic;Differentiation;Derivatives;Logarithmic rule,Power rule,Trigonometric rules
1543;Portugal;1120;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
176;Italy;93;1;Basic;Differentiation;Derivatives;Product rule,Logarithmic rule,Trigonometric rules
955;Lithuania;1093;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
576;Ireland;557;0;Basic;Analytic Geometry;Analytic Geometry;Locus,Distance
1044;Lithuania;1000;1;Basic;Differentiation;Partial Differentiation;First order
576;Ireland;597;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvector,Spectrum,Characteristic polynomial,Diagonalization,Eigenvalue
419;Portugal;331;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1185;Portugal;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1350;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
840;Italy;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
695;Portugal;81;1;Basic;Statistics;Statistics;Mean,Median,Mode
657;Ireland;182;0;Basic;Statistics;Statistics;Quantile,Population,Sample,Mean,Variance,Standard deviation,Median,Mode
972;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1543;Portugal;1111;0;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
168;Portugal;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
661;Portugal;190;1;Basic;Statistics;Statistics;Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance,Median
72;Portugal;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1146;Portugal;777;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1252;Portugal;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
378;Portugal;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1087;Portugal;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
359;Portugal;440;1;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Subspace,Linear combination,Dimension
168;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1352;Portugal;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1220;Slovenia;423;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
414;Portugal;326;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part
85;Lithuania;1140;0;Basic;Set Theory;Set Theory;Subset
1095;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
753;Italy;296;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
175;Italy;1251;0;Basic;Numerical Methods;Numerical Methods;Newton’s interpolation,Polynomial interpolation
168;Portugal;319;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation,Linear application,Linearity
168;Portugal;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
982;Portugal;430;1;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
851;Italy;1015;1;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
72;Portugal;90;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1032;Lithuania;875;0;Basic;Differentiation;Partial Differentiation;Gradient,First order
1244;Portugal;431;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1487;Portugal;946;0;Basic;Graph Theory;Graph Theory;Spanning tree,Shortest path,Path,Tree
378;Portugal;573;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Locus,Scalar product,Cross product,Collinearity
457;Portugal;328;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
955;Lithuania;426;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
972;Portugal;452;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1220;Slovenia;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
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
1220;Slovenia;443;1;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Range,Kernel,Isomorphism
1220;Slovenia;317;0;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1543;Portugal;1106;1;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1219;Portugal;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
955;Lithuania;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1557;Portugal;918;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
625;Russian Federation;246;0;Basic;Linear Algebra;Linear Systems;Consistent system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
1291;Italy;289;0;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
955;Lithuania;1097;0;Basic;Numerical Methods;Numerical Methods;Lagrange's interpolation,Polynomial interpolation
510;Portugal;647;1;Basic;Linear Algebra;Matrices and Determinants;Matrix multiplication,Symmetric matrix,Matrix operations
625;Russian Federation;92;1;Basic;Linear Algebra;Linear Systems;Consistent system,Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system
28;Portugal;245;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1077;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
524;Portugal;645;1;Basic;Linear Algebra;Matrices and Determinants;Matrix rank,Linearly independent rows
899;Lithuania;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1080;Portugal;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
899;Lithuania;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
890;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
374;Portugal;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
359;Portugal;377;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel,Matrix of a linear transformation
1220;Slovenia;421;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
426;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
1557;Portugal;831;0;Basic;Differential Equations;Differential Equations;Linear differential equation
913;Ireland;1101;1;Basic;Numerical Methods;Numerical Methods;Polynomial interpolation,Newton’s interpolation
91;Lithuania;520;1;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
626;Italy;271;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule
41;Portugal;172;1;Basic;Differential Equations;Differential Equations;Linear differential equation
956;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1077;Portugal;306;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel,Isomorphism,Injective linear application
374;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
64;Portugal;414;0;Basic;Integration;Integration Techniques;Substitution,Direct inspection,Integration by parts,Rational functions
511;Portugal;234;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
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
426;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
1043;Lithuania;264;0;Basic;Differentiation;Partial Differentiation;Chain rule
851;Italy;784;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
697;Portugal;211;1;Basic;Statistics;Statistics;Linear regression
128;Lithuania;328;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
1049;Lithuania;879;0;Basic;Differentiation;Partial Differentiation;First order,Second order
1229;Portugal;783;0;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Isomorphism
80;Lithuania;729;1;Basic;Differentiation;Derivatives;Quotient rule
695;Portugal;189;1;Basic;Statistics;Statistics;Mode,Quantile,Population,Data type,Sample,Mean,Standard deviation,Variance,Median
953;Lithuania;211;1;Basic;Statistics;Statistics;Linear regression
1300;Italy;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
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
1557;Portugal;927;1;Advanced;Real Functions of a single variable;Domain, Image and Graphics;Planar graph
414;Portugal;216;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
890;Portugal;381;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
899;Lithuania;429;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
80;Lithuania;364;0;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids,Geometrical figures,Classification of geometric solids
90;Lithuania;326;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part
851;Italy;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
851;Italy;1053;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
81;Lithuania;547;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Orthogonality,Scalar product
1308;Italy;426;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1247;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
986;Portugal;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1286;Italy;455;0;Basic;Linear Algebra;Vector Spaces;Basis
57;Portugal;79;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
1286;Italy;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
91;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
913;Ireland;217;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
426;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
91;Lithuania;380;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
178;Italy;753;0;Basic;Differentiation;Derivatives;Exponential rule
1146;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
624;Portugal;467;1;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Polygons,Classification of geometrical figures,Geometrical figures
457;Portugal;336;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Modulus of a complex number,Imaginary part
979;Portugal;415;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1256;Portugal;287;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
151;Portugal;104;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
181;Italy;922;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
41;Portugal;190;1;Basic;Statistics;Statistics;Frequency,Mode,Quantile,Population,Data type,Sample,Relative frequency,Mean,Standard deviation,Variance,Median
840;Italy;288;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
483;Portugal;998;1;Basic;Differentiation;Partial Differentiation;First order
91;Lithuania;606;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector,Diagonalization
71;Portugal;254;1;Basic;Differentiation;Derivatives;Logarithmic rule,Power rule,Trigonometric rules
1220;Slovenia;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
218;Lithuania;665;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
973;Portugal;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
470;Portugal;355;1;Advanced;Complex Numbers;Complex Numbers;Nth root,Polar representation,Operations with complex numbers,Principal argument,De Moivre formulas
175;Italy;1493;1;Basic;Complex Numbers;Complex Numbers;Imaginary part,Conjugate number,Modulus of a complex number,Algebraic form,Real part,Equations involving complex numbers
1220;Slovenia;321;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
64;Portugal;616;0;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Eigenvector
509;Portugal;916;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Square linear system,Consistent system
41;Portugal;366;1;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids,Geometrical figures,Classification of geometric solids
91;Lithuania;368;1;Basic;Fundamental Mathematics;Elementary Geometry;Platonic solids,Regular polygon
1334;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1271;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
91;Lithuania;439;0;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
1220;Slovenia;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
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
967;Portugal;289;1;Advanced;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
651;Ireland;202;0;Basic;Statistics;Statistics;Student distribution,Confidence interval,Point estimate,Hypothesis testing
168;Portugal;672;1;Basic;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
524;Portugal;496;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons
378;Portugal;548;1;Basic;Analytic Geometry;Analytic Geometry;Collinearity,Distance,Locus,Cross product,Orthogonality,Scalar product
168;Portugal;446;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
470;Portugal;561;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Cartesian equations of a line
1375;Portugal;288;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
359;Portugal;366;0;Basic;Fundamental Mathematics;Elementary Geometry;Geometric solids,Geometrical figures,Classification of geometric solids
741;Ireland;475;1;Basic;Graph Theory;Graph Theory;Adjacency matrix
576;Ireland;702;0;Advanced;Analytic Geometry;Analytic Geometry;Cartesian equations of a plane,Intersection,Cartesian equations of a line
1148;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
80;Lithuania;701;1;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Cross product,Distance
1220;Slovenia;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
181;Italy;920;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1352;Portugal;380;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1173;Portugal;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1087;Portugal;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1179;Portugal;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
405;Portugal;788;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions,Exponential function
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
1319;Italy;437;0;Basic;Linear Algebra;Linear Transformations;Linear application,Composition of linear applications
311;Ireland;138;0;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Determinant computation,Determinant properties,Inverse matrix 
36;Portugal;233;1;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
851;Italy;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
855;Italy;217;0;Basic;Linear Algebra;Linear Systems;Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system,Inconsistent system
80;Lithuania;243;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
855;Italy;90;1;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1428;Portugal;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
986;Portugal;385;0;Advanced;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
851;Italy;1012;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Stationary point,Minimum,Maximum,Saddle point
511;Portugal;118;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1324;Italy;438;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
510;Portugal;227;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
884;Italy;383;0;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1244;Portugal;417;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
71;Portugal;307;0;Basic;Probability ;Probability ;Event,Addition, multiplication, and total probability rules,Independence
415;Portugal;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
525;Portugal;795;1;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Square roots,Simplify expressions
41;Portugal;573;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonality,Locus,Scalar product,Cross product,Collinearity
955;Lithuania;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1252;Portugal;459;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1220;Slovenia;433;1;Basic;Linear Algebra;Vector Spaces;Subspace,Dimension
884;Italy;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
181;Italy;920;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
1146;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
470;Portugal;547;1;Basic;Analytic Geometry;Analytic Geometry;Cross product,Orthogonality,Scalar product
215;Lithuania;868;1;Basic;Differential Equations;Differential Equations;Separable variables equation
1334;Portugal;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
415;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
1557;Portugal;983;0;Advanced;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
178;Italy;720;0;Basic;Differentiation;Derivatives;Quotient rule,Trigonometric rules,Logarithmic rule,Product rule
1023;Lithuania;317;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1220;Slovenia;313;1;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
753;Italy;885;0;Basic;Differentiation;Partial Differentiation;Second order,First order
855;Italy;241;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
899;Lithuania;776;0;Basic;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
1076;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1047;Lithuania;261;0;Basic;Differentiation;Partial Differentiation;First order,Gradient
1543;Portugal;1106;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
956;Portugal;416;0;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
600;Italy;215;1;Basic;Linear Algebra;Linear Systems;Undetermined solution of linear system,Consistent system,Inconsistent system,Solution of linear system
1220;Slovenia;415;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
986;Portugal;432;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Subspace,Linear combination,Linear dependence,Span
509;Portugal;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1402;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
525;Portugal;114;0;Basic;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
1132;Portugal;777;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1220;Slovenia;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
28;Portugal;77;0;Basic;Statistics;Statistics;Stem and Leaf diagram,Relative frequency,Sample,Frequency
1044;Lithuania;877;1;Basic;Differentiation;Partial Differentiation;Second order
176;Italy;920;0;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
411;Portugal;331;0;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1286;Italy;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
85;Lithuania;1148;1;Basic;Set Theory;Set Theory;Subset
1182;Portugal;376;0;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
85;Lithuania;1124;0;Basic;Set Theory;Set Theory;Integration by parts,Substitution,Simple integration,Direct inspection
387;Portugal;430;0;Advanced;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1220;Slovenia;291;1;Basic;Linear Algebra;Linear Transformations;Kernel,Isomorphism,Injective linear application,Range
884;Italy;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
376;Portugal;350;0;Advanced;Complex Numbers;Complex Numbers;Complex plane 
1517;Portugal;782;0;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
168;Portugal;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
713;Portugal;81;0;Basic;Statistics;Statistics;Mean,Median,Mode
510;Portugal;639;0;Basic;Linear Algebra;Matrices and Determinants;Inverse matrix ,Determinant computation,Determinant properties,Matrix operations
422;Portugal;328;0;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
28;Portugal;567;1;Basic;Analytic Geometry;Analytic Geometry;Cartesian equations of a line,Orthogonality,Collinearity
1023;Lithuania;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1308;Italy;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1081;Portugal;439;0;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
1220;Slovenia;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
414;Portugal;917;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
966;Portugal;296;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
176;Italy;98;0;Basic;Differentiation;Derivatives;Trigonometric rules,Product rule,Sum rule,Logarithmic rule,Power rule
380;Portugal;1007;0;Basic;Optimization;Nonlinear Optimization;Optimal solution,Minimum,Stationary point,Maximum,Saddle point
374;Portugal;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1044;Lithuania;875;0;Basic;Differentiation;Partial Differentiation;Gradient,First order
1565;Portugal;679;0;Basic;Real Functions of a single variable;Limits and Continuity;Limits,Indeterminate forms
1135;Portugal;454;1;Basic;Linear Algebra;Vector Spaces;Basis
1242;Portugal;454;0;Basic;Linear Algebra;Vector Spaces;Basis
854;Italy;225;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system,Square linear system
80;Lithuania;542;1;Basic;Integration;Double Integration;y-simple region (type I),Cartesian coordinates,Area ,Iterate integrals
128;Lithuania;330;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number
986;Portugal;325;1;Basic;Linear Algebra;Linear Transformations;Range,Kernel
967;Portugal;293;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
57;Portugal;185;1;Basic;Statistics;Statistics;Frequency,Quantile,Mean,Variance,Median,Mode
1305;Italy;278;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
840;Italy;779;1;Advanced;Linear Algebra;Linear Transformations;Rotation,Linear application
898;Portugal;785;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
972;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
898;Portugal;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
876;Italy;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1331;Portugal;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
552;Portugal;558;0;Basic;Analytic Geometry;Analytic Geometry;Cross product,Cartesian equations of a plane,Orthogonality,Cartesian equations of a line
1271;Portugal;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1557;Portugal;920;1;Basic;Real Functions of a single variable;Domain, Image and Graphics;Domain
979;Portugal;1094;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
1023;Lithuania;417;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
1077;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
982;Portugal;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
168;Portugal;323;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
422;Portugal;648;1;Advanced;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
1220;Slovenia;457;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
1420;Portugal;781;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1220;Slovenia;379;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
168;Portugal;434;0;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
955;Lithuania;1105;1;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
378;Portugal;379;0;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
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
885;Italy;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
899;Lithuania;459;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Subspace,Span
509;Portugal;434;1;Basic;Linear Algebra;Vector Spaces;Subspace,Basis,Dimension
509;Portugal;141;1;Basic;Linear Algebra;Matrices and Determinants;Matrix operations,Matrix multiplication
1324;Italy;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
667;Portugal;204;1;Basic;Statistics;Statistics;Student distribution,Hypothesis testing
955;Lithuania;435;0;Basic;Linear Algebra;Vector Spaces;Euclidean spaces,Orthogonal basis,Basis
986;Portugal;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
37;Portugal;1084;1;Advanced;Differentiation;Partial Differentiation;First order,Second order
1219;Portugal;423;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
840;Italy;453;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
625;Russian Federation;662;0;Advanced;Fundamental Mathematics;Algebraic expressions, Equations, and Inequalities;Simplify expressions
470;Portugal;333;1;Advanced;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1220;Slovenia;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
26;Portugal;903;1;Basic;Differential Equations;Differential Equations;Separable variables equation
457;Portugal;341;1;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers
855;Italy;244;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
884;Italy;422;0;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
1322;Italy;378;1;Basic;Linear Algebra;Linear Transformations;Invertible linear operator,Isomorphism,Injective linear application
1275;Lithuania;446;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span,Change-of-basis matrix
1253;Portugal;452;0;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
37;Portugal;332;1;Basic;Complex Numbers;Complex Numbers;Conjugate number,Real part,De Moivre formulas,Operations with complex numbers,Imaginary part
1220;Slovenia;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
166;Portugal;637;0;Basic;Linear Algebra;Matrices and Determinants;Determinant computation,Determinant properties
1288;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1023;Lithuania;454;1;Basic;Linear Algebra;Vector Spaces;Basis
1252;Portugal;290;0;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1557;Portugal;396;0;Advanced;Integration;Integration Techniques;Power of trigonometric functions
1044;Lithuania;263;0;Basic;Differentiation;Partial Differentiation;First order
509;Portugal;428;1;Basic;Linear Algebra;Vector Spaces;Change-of-basis matrix,Span,Basis,Dimension
1173;Portugal;384;0;Basic;Linear Algebra;Linear Transformations;Linearity,Invertible linear operator,Composition of linear applications,Linear application
661;Portugal;184;0;Basic;Statistics;Statistics;Frequency,Sample,Stem and Leaf diagram,Variance,Standard deviation,Relative frequency
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
91;Lithuania;369;0;Basic;Fundamental Mathematics;Elementary Geometry;Quadrilaterals,Geometrical figures,Classification of geometrical figures
1487;Portugal;1186;1;Basic;Integration;Definite Integrals;Fundamental theorem of Calculus,Partial fractions decomposition
1023;Lithuania;450;1;Basic;Linear Algebra;Vector Spaces;Subspace,Span,Linear combination
1023;Lithuania;429;0;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
753;Italy;1001;0;Basic;Differentiation;Partial Differentiation;Power rule,Trigonometric rules,Logarithmic rule
1044;Lithuania;261;1;Basic;Differentiation;Partial Differentiation;First order,Gradient
1192;Portugal;453;1;Basic;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
1148;Portugal;313;0;Basic;Linear Algebra;Vector Spaces;Span,Linear combination,Subspace
854;Italy;916;0;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Square linear system,Consistent system
986;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
641;Italy;181;1;Basic;Statistics;Statistics;Quantile,Frequency,Sample,Mean,Variance,Standard deviation,Median,Mode
1256;Portugal;422;1;Basic;Linear Algebra;Vector Spaces;Linear combination,Span
913;Ireland;441;0;Advanced;Linear Algebra;Vector Spaces;Basis,Span
1332;Portugal;448;0;Advanced;Linear Algebra;Vector Spaces;Subspace
898;Portugal;288;1;Advanced;Linear Algebra;Linear Transformations;Range,Kernel
1023;Lithuania;454;1;Basic;Linear Algebra;Vector Spaces;Basis
167;Portugal;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
1135;Portugal;290;0;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
1197;Slovenia;438;1;Basic;Linear Algebra;Vector Spaces;Subspace,Linear combination,Span
1353;Portugal;380;1;Advanced;Linear Algebra;Linear Transformations;Matrix of a linear transformation
411;Portugal;326;0;Basic;Complex Numbers;Complex Numbers;Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number,Real part
1288;Portugal;425;1;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
483;Portugal;439;1;Advanced;Linear Algebra;Vector Spaces;Span,Subspace,Linear combination
751;Lithuania;546;0;Basic;Analytic Geometry;Analytic Geometry;Orthogonal projection,Distance,Cross product,Orthogonality
419;Portugal;329;1;Basic;Complex Numbers;Complex Numbers;Real part,Operations with complex numbers,Imaginary part,Modulus of a complex number,Conjugate number
511;Portugal;89;0;Basic;Linear Algebra;Linear Systems;Square linear system,Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1147;Portugal;425;0;Basic;Linear Algebra;Vector Spaces;Subspace,Change-of-basis matrix,Linear combination,Span,Basis
1292;Italy;617;1;Basic;Linear Algebra;Eigenvalues and Eigenvectors;Eigenvalue,Spectrum,Eigenvector,Characteristic polynomial
1308;Italy;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
576;Ireland;521;0;Basic;Fundamental Mathematics;Elementary Geometry;Polygons,Regular polygon
414;Portugal;949;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
1158;Portugal;376;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
913;Ireland;1094;0;Basic;Numerical Methods;Numerical Methods;Newton’s method,Nonlinear equation
510;Portugal;129;0;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
167;Portugal;784;1;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
64;Portugal;394;1;Basic;Integration;Integration Techniques;Substitution
91;Lithuania;382;1;Advanced;Linear Algebra;Linear Transformations;Injective linear application,Invertible linear operator,Isomorphism
473;Portugal;287;1;Basic;Linear Algebra;Linear Transformations;Matrix of a linear transformation
524;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
633;Italy;140;1;Advanced;Linear Algebra;Matrices and Determinants;Matrix operations,Inverse matrix 
80;Lithuania;532;1;Basic;Integration;Double Integration;Cartesian coordinates,Iterate integrals,x-simple region (type II)
890;Portugal;277;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
509;Portugal;950;1;Basic;Linear Algebra;Linear Systems;Inconsistent system,Solution of linear system,Undetermined solution of linear system,Consistent system
955;Lithuania;290;1;Advanced;Linear Algebra;Linear Transformations;Linear application,Linearity
966;Portugal;321;0;Basic;Linear Algebra;Linear Transformations;Linear application,Linearity
1080;Portugal;383;1;Basic;Linear Algebra;Linear Transformations;Linearity,Matrix of a linear transformation,Linear application
1220;Slovenia;416;1;Basic;Linear Algebra;Vector Spaces;Basis,Dimension
986;Portugal;424;1;Advanced;Linear Algebra;Vector Spaces;Linear independence,Span,Linear dependence
80;Lithuania;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
1135;Portugal;293;0;Advanced;Linear Algebra;Linear Transformations;Range,Kernel