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Students explore a linear, a parabolic, and a log function. In this Algebra II/Pre-calculus instructional activity students investigate the graph a line, a parabola, and a log function. Students examine the three graphs as they compare and contrast the three in a problem solving context.
Students read about AP calculus online. In this calculus lesson, students learn real life usage for calculus. They read about instructors and their experience teaching and incorporating calculus into the real world.
Twelfth graders examine the Taylor Series. In this calculus activity, 12th graders explore the representation of a function as an infinite sum of terms calculated form the values of its derivatives at a single point, hence the Taylor Series. Students use a TI-89 to explore the patterns and the command to compute the Taylor series.
Students make mathematical argument using the concept of Limit. For this algebra lesson, student calculate the instantaneous rate of change from the linear graph. They use a TI-calculator to create a visual of the graphs.
Students explore graphs of polynomials. In this Pre-calculus/Calculus lesson, students investigate the problem of constructing the expression for a polynomial curve based on the dynamic properties of the curve. TI-Interactive is required to perform the algebraic manipulations.
In this physics 240:24 worksheet, students apply the concepts of wave, speed and sound, and oscillation to correctly answer the word problems provided. Students apply their understanding of pressure and molecular motion to calculate the speed of sound and oscillation in the given problems.
In this physics 210 worksheet, students answer the question of the predicted modes of oscillations heard based on the information provided in the word problems. Students apply their understanding of sound waves to answer the questions given. |
PUBLISHED
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Mathematics
Mathematics, "The Queen of Sciences" as called by Carl Friedrich Gauss, is the science of number, quantity, and space, either as abstract concepts or as applied to other disciplines (such as physics and engineering).
The distinguished authors of the top-quality books and textbooks listed under Research and Markets' Mathematics category are the world's leading researchers. These publications cover all the key areas in today's research. They are invaluable references, comprehensive and
readily accessible. When available, pre-publication titles are also included, so you can be sure not to miss the latest developments in your research field.
The readership of this category includes both graduate and undergraduate students, as well as researchers and mature mathematics.
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Mathematics for Physical Science and Engineering opens with an introduction to symbolic computing at a level designed to be accessible to an audience that is intellectually ready to study detailed mathematics...
An Introduction to Measure-Theoretic Probability, Second Edition, employs a classical approach to teaching students of statistics, mathematics, engineering, econometrics, finance, and other disciplines...
Differential forms are utilized as a mathematical technique to help students, researchers, and engineers analyze and interpret problems where abstract spaces and structures are concerned, and when questions...
Since its first volume in 1960, Advances in Computers has presented detailed coverage of innovations in computer hardware, software, theory, design, and applications. It has also provided contributors...
A UNIQUELY PRACTICAL APPROACH TO ROBUST DESIGN FROM A STATISTICAL AND ENGINEERING PERSPECTIVE Variation in environment, usage conditions, and the manufacturing process has long presented a challenge...
Computational Approaches to Studying the Co-evolution of Networks and Behaviour in Social Dilemmas shows students, researchers, and professionals how to use computation methods, rather than mathematical...
Explore and analyze the solutions of mathematical models from diverse disciplines
As biology increasingly depends on data, algorithms, and models, it has become necessary to use a computing language,...
An introduction to technical details related to the Physical Layer of the LTE standard with MATLAB®
The LTE (Long Term Evolution) and LTE-Advanced are among the latest mobile communications standards,...
The author's goal is a rigorous presentation of the fundamentals of analysis, starting from elementary level and moving to the advanced coursework. The curriculum of all mathematics (pure or applied)...
Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have...
Modern analysis of HEP data needs advanced statistical tools to separate signal from background. This is the first book which focuses on machine learning techniques. It will be of interest to almost...
The proposed book is the first comprehensive and methodologically rigorous analysis of earthquake occurrence. Models based on the theory of the stochastic multidimensional point processes are employed...
This book presents the main valuation approaches that can be used to value financial institutions. By sketching 1) the different business models of banks (both commercial and investment banks) and insurance... |
As most of you know, there has been a national
movement to "reform" the teaching and content of calculus and precalculus.
Michigan's Introductory Mathematics Program is being used as a model for colleges and
universities throughout the country. Our program takes a fresh approach which is designed
to help students learn to think about the fundamental ideas of mathematics.
The texts emphasize the underlying concepts and de-emphasize rote memorization. The
concepts are presented from a variety of symbolic, numeric, visual, and verbal points of
view. Since our goal is to prepare students for further study in all mathematical
subjects, there will be a strong emphasis on mathematics in everyday life and many of the
applications will come from the physical and social sciences.
We use a teaching style which expands on the traditional lecture format. It
incorporates cooperative learning into the classroom and organizes students into homework
teams. The focus in our classes is on student learning rather than teaching.
The purpose of this guide and our professional development program is to help accustom
you to the new program. Throughout the term the instructors will have a weekly staff
meeting to share ideas on what is working and what isn't working . Since our program is
still fairly new, the courses evolve with each year's infusion of new teachers; we will be
counting on you to help us make them successful.
Your class is often a student's first experience with a university math course, and
the quality of your teaching can make this first experience either rewarding or
distressing. In the coming days and weeks we will try to help you master some of the
principles and techniques of good teaching, but ultimately your success will depend on
your ability to interact productively with your class. Your class will respond to your
enthusiasm for the material and to your genuine efforts to help them understand. |
Free, professionally developed content designed to teach engineering fundamentals. Students use this material to explore and reinforce concepts, and instructors use it to supplement lectures, and as ase material for labs and assignments. Topics include:
The idea of powerful mathematics delivered through very visual, interactive, point-and-click methods has launched a new generation of teaching and learning techniques in mathematics. Video Demonstration: What is Clickable Math?
Maple T.A. users can take advantage of thousands of free questions on calculus, precalculus, algebra, physics, and more. Questions and assignments can be freely used, recombined, and modified. Browse all Maple T.A. Content
Precalculus
Each topic in the Precalculus classroom content includes Maple T.A. questions to test students understanding and provide extra practice.
Calculus 1
This content covers the complete first semester of an introductory honors calculus course, and provides weekly assignments. This material has been used at the University of Guelph for the last three years.
Calculus 2
This content covers the complete second semester of an introductory honors calculus course, and provides weekly assignments. This material has been used at the University of Guelph for the last three years. |
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define $5^{1/3}$ to be the cube root of $5$ because we want $(5^{1/3})^3 = 5^{(1/3)3}$ to hold, so $(5^{1/3})^3$ must equal $5$.illustrations
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
illustrations
Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
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Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
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Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.
illustrations
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Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., $\textbf{v}$, $|\textbf{v}|$, $||\textbf{v}||$, $v$).
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Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
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Solve problems involving velocity and other quantities that can be represented by vectors.
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Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
illustrations
Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
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Understand vector subtraction $\textbf{v} - \textbf{w}$ as $\textbf{v} + (-\textbf{w})$, where $-\textbf{w}$ is the additive inverse of $\textbf{w}$, with the same magnitude as $\textbf{w}$ and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.
illustrations
Compute the magnitude of a scalar multiple $c\textbf{v}$ using $||c\textbf{v}|| = |c|v$. Compute the direction of $c\textbf{v}$ knowing that when $|c|{v} \neq 0$, the direction of $c\textbf{v}$ is either along $\textbf{v}$ (for $c > 0$) or against $\textbf{v}$ (for $c < 0$).
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Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
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Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
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Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
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Work with $2 \times2$ matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.
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Interpret expressions that represent a quantity in terms of its context.
illustrations
Interpret parts of an expression, such as terms, factors, and coefficients.
illustrations
Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret $P(1+r)^n$ as the product of $P$ and a factor not depending on $P$.illustrations
Use the structure of an expression to identify ways to rewrite it. For example, see $x^4 - y^4$ as $(x^2)^2 - (y^2)^2$, thus recognizing it as a difference of squares that can be factored as $(x^2 - y^2)(x^2 + y^2)$.illustrations
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Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
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Factor a quadratic expression to reveal the zeros of the function it defines.
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Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
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Use the properties of exponents to transform expressions for exponential functions. For example the expression $1.15^t$ can be rewritten as $(1.15^{1/12})^{12t} \approx 1.012^{12t}$ to reveal the approximate equivalent monthly interest rate if the annual rate is $15\%$.illustrations
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Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.illustrations
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
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Know and apply the Remainder Theorem: For a polynomial $p(x)$ and a number $a$, the remainder on division by $x - a$ is $p(a)$, so $p(a) = 0$ if and only if $(x - a)$ is a factor of $p(x)$.
illustrations
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
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Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity $(x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2$ can be used to generate Pythagorean triples.illustrations
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Know and apply the Binomial Theorem for the expansion of $(x + y)^n$ in powers of $x$ and $y$ for a positive integer $n$, where $x$ and $y$ are any numbers, with coefficients determined for example by Pascal's Triangle.The Binomial Theorem can be proved by mathematical induction or by a com- binatorial argument.illustrations
Rewrite simple rational expressions in different forms; write $\frac{a(x)}{b(x)}$ in the form $q(x) + \frac{r(x)}{b(x)}$, where $a(x)$, $b(x)$, $q(x)$, and $r(x)$ are polynomials with the degree of $r(x)$ less than the degree of $b(x)$, using inspection, long division, or, for the more complicated examples, a computer algebra system.
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Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
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Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.illustrations
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Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
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Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.illustrations
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Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law $V = IR$ to highlight resistance $R$.illustrations
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
illustrations
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
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Use the method of completing the square to transform any quadratic equation in $x$ into an equation of the form $(x - p)^2 = q$ that has the same solutions. Derive the quadratic formula from this form.
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Solve quadratic equations by inspection (e.g., for $x^2 = 49$), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as $a \pm bi$ for real numbers $a$ and $b$.
illustrations
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
illustrations
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
illustrations
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line $y = -3x$ and the circle $x^2 + y^2 = 3$.illustrations
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Represent a system of linear equations as a single matrix equation in a vector variable.
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Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension $3 \times 3$ or greater).
illustrations
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
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Explain why the $x$-coordinates of the points where the graphs of the equations $y = f(x)$ and $y = g(x)$ intersect are the solutions of the equation $f(x) = g(x)$; find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where $f(x)$ and/or $g(x)$ are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
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Graph
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Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If $f$ is a function and $x$ is an element of its domain, then $f(x)$ denotes the output of $f$ corresponding to the input $x$. The graph of $f$ is the graph of the equation $y = f(x)$.
illustrations
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
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For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.illustrations
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Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function $h(n)$ gives the number of person-hours it takes to assemble $n$ engines in a factory, then the positive integers would be an appropriate domain for the function.illustrations
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Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
illustrations
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
illustrations
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
illustrations
Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as $y = (1.02)^t$, $y = (0.97)^t$, $y = (1.01)^{12t}$, $y = (1.2)^{t/10}$, and classify them as representing exponential growth or decay.illustrations
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.illustrations
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Write a function that describes a relationship between two quantities.
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Determine an explicit expression, a recursive process, or steps for calculation from a context.
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Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.illustrations
Compose functions. For example, if $T(y)$ is the temperature in the atmosphere as a function of height, and $h(t)$ is the height of a weather balloon as a function of time, then $T(h(t))$ is the temperature at the location of the weather balloon as a function of time. illustrations
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Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
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Identify the effect on the graph of replacing $f(x)$ by $f(x) + k$, $k f(x)$, $f(kx)$, and $f(x + k)$ for specific values of $k$ (both positive and negative); find the value of $k$ given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.illustrations
Solve an equation of the form $f(x) = c$ for a simple function $f$ that has an inverse and write an expression for the inverse. For example, $f(x) =2 x^3$ or $f(x) = (x+1)/(x-1)$ for $x \neq 1$.illustrations
Verify by composition that one function is the inverse of another.
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Read values of an inverse function from a graph or a table, given that the function has an inverse.
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Produce an invertible function from a non-invertible function by restricting the domain.
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Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
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Distinguish between situations that can be modeled with linear functions and with exponential functions.
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Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
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Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
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Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
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Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
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Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
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For exponential models, express as a logarithm the solution to $ab^{ct} = d$ where $a$, $c$, and $d$ are numbers and the base $b$ is 2, 10, or $e$; evaluate the logarithm using technology.
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Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
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Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
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Use special triangles to determine geometrically the values of sine, cosine, tangent for $\pi/3$, $\pi/4$ and $\pi/6$, and use the unit circle to express the values of sine, cosines, and tangent for $\pi - x$, $\pi + x$, and $2\pi - x$ in terms of their values for $x$, where $x$ is any real number.
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Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
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Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
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Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.
illustrations
Prove the Pythagorean identity $\sin^2(\theta) + \cos^2(\theta) = 1$ and use it to find $\sin(\theta)$, $\cos(\theta)$, or $\tan(\theta)$ given $\sin(\theta)$, $\cos(\theta)$, or $\tan(\theta)$ and the quadrant of the angle.
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Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
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Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
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Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
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Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
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Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
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Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
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Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
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Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
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Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
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Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.illustrations
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to $180^\circ$; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.illustrations
Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.illustrations
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copyingillustrations
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
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Verify experimentally the properties of dilations given by a center and a scale factor:
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A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
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The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
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Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
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Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
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Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.illustrations
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
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Identillustrations
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
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Construct a tangent line from a point outside a given circle to the circle.
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Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
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Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point $(1, \sqrt{3})$ lies on the circle centered at the origin and containing the point $(0, 2)$.illustrations
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
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Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
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Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
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Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments.illustrations
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Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.
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Represent data with plots on the real number line (dot plots, histograms, and box plots).
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Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
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Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
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Use
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Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
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Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
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Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.illustrations
Informally assess the fit of a function by plotting and analyzing residuals.
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Fit a linear function for a scatter plot that suggests a linear association.
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Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
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Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability $0.5$. Would a result of $5$ tails in a row cause you to question the model?illustrations
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Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").
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Understand that two events $A$ and $B$ are independent if the probability of $A$ and $B$ occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
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Understand the conditional probability of $A$ given $B$ as \(P(\mbox{$A$ and $B$})/P(B)\), and interpret independence of $A$ and $B$ as saying that the conditional probability of $A$ given $B$ is the same as the probability of $A$, and the conditional probability of $B$ given $A$ is the same as the probability of $B$.
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Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.illustrations
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Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.illustrations
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Find the conditional probability of $A$ given $B$ as the fraction of $B$'s outcomes that also belong to $A$, and interpret the answer in terms of the model.
illustrations
${}^{\huge\star}$
Apply the Addition Rule, \(P(\mbox{$A$ or $B$}) = P(A) + P(B) - P(\mbox{$A$ and $B$})\), and interpret the answer in terms of the model.
illustrations
$(+)$
${}^{\huge\star}$
Apply the general Multiplication Rule in a uniform probability model, \(P(\mbox{$A$ and $B$}) = P(A)P(B|A) = P(B)P(A|B)\), and interpret the answer in terms of the model.
illustrations
$(+)$
${}^{\huge\star}$
Use permutations and combinations to compute probabilities of compound events and solve problems.
illustrations
$(+)$
${}^{\huge\star}$
Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
illustrations
$(+)$
${}^{\huge\star}$
Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
illustrations
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${}^{\huge\star}$
Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.illustrations
$(+)$
${}^{\huge\star}$
Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?illustrations
$(+)$
${}^{\huge\star}$
Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
illustrations
Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant.illustrations
Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.illustrations
$(+)$
${}^{\huge\star}$
Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
illustrations
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${}^{\huge\star}$
Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
illustrations |
Waddell Calculus correct and offer suggestions for delet...When I was in high school, my father bought me disks with math programs on them. The math content on the disks were Algebra 1, Algebra 2, and Geometry. I practiced and mastered them all during my downtime after school |
Formats
Book Description
Publication Date: Jan. 1 2010 | Series: Algebra SurvivalProduct Description
About the Author
Josh Rappaport runs the Now I Get It! Tutoring Service in Santa Fe, New Mexico. As a longtime tutor, Josh has heard just about every question about math ever uttered. To help children, Josh relates math's complexities to life situations through playful analogies. Josh put his ideas together in the Algebra Survival Guide, winner of a Parents Choice commendation. The Guide has been used by individuals, schools and school districts across the United States.Trust me when I say this the best Alegbra guide on the market. I know because I tried them all(no joke.) As an adult, who never had Algebra in high school, I was not prepared for it in college. And there are few college courses that go all the way back to the beginning, mine expected that you already had basic algebra fundamentals. The guide along with the workbook, actually replaced my textbook. The textbook was simply put, confusing, and unrelatable. The guide, and workbook were lifesavers for me. The clear, precise and easy to understand examples clarified much of what confused me. And associating all of the properties and laws to analogies worked liked a charm. In fact, I soon learned I knew th properties and laws better than my classmates and began using the analogies to explain them so they to could remember all the little tricks this guide taught me. My teenage son, who has struggled with Algebra, now has his own copies and wonders why his teachers have never thought to make it so easy to learn.
48 of 51 people found the following review helpful
5.0 out of 5 starsHighly recommend the book and workbookAug. 27 2007
By T. Malnar - Published on Amazon.com
Format:Paperback
I purchased the Algebra Survival guide and the workbook for my sons who would be taking Algebra in 8th grade. They easily completed the entire book over the summer. The survival guide is easy to understand. The Emergency Fact sheet will be a great reference. They will sail through Algebra this year. I highly recommend these books as a prelude to classroom Algebra for all students.
53 of 62 people found the following review helpful
5.0 out of 5 starsA Classic Start!July 7 2004
By John D MacDonald - Published on Amazon.com
Format:Paperback31 of 35 people found the following review helpful
5.0 out of 5 starsAlgebra Survival GuideAug. 1 2005
By Learnability - Published on Amazon.com
Format:Paperback
Absolutely the best book we have found in working with students preparing for Algbra. Great foundational skills organized in a useful way with good explanations that are easy to follow.
13 of 14 people found the following review helpful
5.0 out of 5 starsThe Best EverFeb. 6 2010
By Mary O. Paddock - Published on Amazon.com
Format:Paperback|Verified Purchase
I'll bet a lot of mothers have hugged this author.
I'm a homeschooler with one boy in college and another in public high school. I'm also math challenged so teaching algebra was a nightmare and I felt that my very bright older boys suffered because of it (though they are now both near the top of their classes). I was fine with teaching basic math skills as I know exactly where math falls apart for most kids who learn to hate it. Algebra was an entirely different story. I simply didn't get it, and consequently, neither did my boys. What they did get was that algebra was a horrible subject that should be hated. This feeling was not on the list of things I wanted my sons to inherit from me.
I was determined that it would be better for my younger two and I went in search of a user friendly book that would break it down to manageable steps so that I could teach it effectively and they could master it comfortably.
Enter Algebra Survival Handbook and Workbook. Combined, these two are an unbeatable teaching tool. My third born (who dislikes math intensely) has grown confident enough to teach himself with only occasional help from me. When I do have to step in, I'm able to quickly scan the previous pages and explain what he's missing without feeling like I'm all thumbs. I am learning as much as he is.
Each lesson carefully builds on the concepts you learned previously, just a few problems at a time, with only one or two steps added. His "ohh this is so easy--watch this--" approach builds concepts in the student. He also admits when something is confusing and then goes on to make sure that the student doesn't stay that way. |
Trigonometry - 6th edition
Summary: This easy-to-understand trigonometry text makes learning trigonometry an engaging, simple process. The book contains many examples that parallel most problems in the problem sets. There are many application problems that show how the concepts can be applied to the world around you, and review problems in every problem set after Chapter 1, which make review part of your daily schedule. If you have been away from mathematics for awhile, study skills listed at the beginning of the first...show more six chapters give you a path to success in the course. Finally, the authors have included some historical notes in case you are interested in the story behind the mathematics you are learning. This text will leave you with a well-rounded understanding of the subject and help you feel better prepared for future mathematics49510835918.00 +$3.99 s/h
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Hardcover Fine 0495108359 Like New copy, without any marks or highlights. Might have minor shelf wear on covers. This is Student US Edition. Same day shipping with free tracking number. A+ Customer...show more Service! ...show less
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2007 Hard cover 6th ed. Brand New Student's Edition. ISBN-0495108359 as pictured. We also have great prices on the Solutions Manual! See ISBN 0495382582. Thks! ! 500 p. New Student Edition text. You...show more will be happy! ...show less
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helping students to develop both the conceptual understanding and the analytical skills necessary to experience success in mathematics, we present each mathematical topic in this text using a carefully developed learning system to actively engage students in the learning process. We have tried to address the diverse needs of today's students through a more open design, updated figures and graphs, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids. Students planning to continue their study of mathematics in calculus, trigonometry, statistics, or other disciplines, as well as those taking college algebra as their final mathematics course, will benefit from the text's student-oriented approach. We believe instructors will particularly welcome the new Annotated Instructor's Edition, which provides answers in the margin to almost all exercises, plus helpful Teaching Tips. |
5.0 out of 5 starsA must reading for any geometry enthusiast!30 Nov 1998
By Didier Bizzarri (D.Bizzarri@ulg.ac.be) - Published on Amazon.com
Format:Hardcover
After reading this book, no doubt Thomas Banchoff is a deeply experienced geometry enthusiast.Unlike many schoolbooks, his book shows the main ideas underlying a multi-faceted geometry with minimal technical complication nonsense, using simple concepts and a bright argumentation, almost without losing insight! He never misses an opportunity to connect geometry to other sciences like algebra, relativity, optics, mechanics and to arts. It is not only the 'Everything you desired to know about the 4th dimensions' but also a bunch of 2D and 3D geometry 'master tricks' as well as a historical narration (including recent discoveries). Examples: - how to find yourself the polytopes (4D 'polyhedra') with 3D representations - how to easily calculate vertex coordinates of the 5 polyhedra - how to draw a torus on a hypersphère! -.. and many others No way you could escape this reading with the same vision of geometry!
25 of 27 people found the following review helpful
5.0 out of 5 starsA book that helps us to leave the confines of 3 dimensions.30 Dec 1997
By A Customer - Published on Amazon.com
Format:Hardcover
I am a high school mathematics teacher, and often students ask about the fourth dimension. Usually their question takes the form, "What is the fourth dimension?" or "How can we see things in the fourth dimension?" This book answers both questions very clearly. Relying mainly on superb computer graphics and analogies of a two-dimensional being trying to perceive the third dimesion (as in Flatland), the author helps us to understand the fourth and higher dimensions. He uses the techniques of slices, projections, shadows, and of course, generalization. I found the most practical part of the book was learning to count the number of faces, vertices, and edges in a 4 (and higher)-D hypercube and also the number of 4 (and higher)-D polytopes (analogues of Platonic solids in 3-D). I also found it valuable to learn the process of folding an unfolded hypercube through the fourth dimension, although I cannot visualize this process, being a mere 3-D creature. Experimental design models in various sciences can involve four or more dimensions. The example from paleoecology was very helpful in that it showed how we can take a 4-D model and take various 3-D cross sections to study various interactions of variables. This is an important concept for a research-bound high school student to learn. Martin Gardner has suggested that we read this book for the computer graphics alone, if for no other reason. Actually there is much more of value, although I found some parts repetitive and boring. The next time a student asks about the fourth dimension, I'll hand her/him the book and say, "Here, kid, go read.
14 of 15 people found the following review helpful
5.0 out of 5 starsConcise Well-Written And Beautifully Illustrated Work23 April 2003
By Rahman - Published on Amazon.com
Format:Paperback
Mathematical ideas, when first learned, tend to undergo a curious inner transformation. At the outset, some tangible representation is necessary to effectively latch onto the concept. Thereafter, the symbolic elaboration using the language of mathematics is sufficient to encompass not only that particular figure, but limitless others like it as well. The underlying geometry is still there, but there are simply too many possibilities to illustrate in any amount of time. The first step of illustrating must be manifest, using ink or chalk or sand or digital pixels. In this way, even the finest geometric illustrations can be considered extremely crude and innacurate in comparison to rigorous mathematical precision. Consider, however, how extraordinarily difficult it would be to grasp trigonometric functions, vector spaces, or even the basic Cartesian coordinate system, without first observing supporting representative illustrations. Even if later forgotten, those initial images are crucial for understanding. This work provides a wide range of richly color-illustrated examples of the abstract geometric structures dealt with regularly in mathematics and the sciences. It is unique in its quality and affordability, and is supported with excellent prose, briefly describing the developmental history, and frequently how to reconstruct the figures from a sparse handful of assumptions. From an introductory description of dimension, this book then branches into numerous and diverse major topics: scaling, slices, regular polytopes, perspective, coordinate geometry, and non-euclidean geometry. While sparing in its level of mathematical description and precision, it never diverges into a fully artistic exposition on the subjects either. There is a careful balance, to guide the reader into better understanding the particular system under discussion. Certainly reading this book is merely the first step of a far longer term process. Symbolic computing programs, such as Mathematica, Maple or MatLab, will assist in visualization, as well as in understanding the pragmatic relation between the graphical and set-theoretic descriptions of the figures. Other books will also assist in this. Many of Rucker's works provide further descriptions of certain topics, specifically Geometry Relativity & The Fourth Dimension is admirable in its brevity and profundity. Abbott's classic Flatland is the foundational book on non-technical description of dimensions. The venerable What Is Mathematics? by Courant and Robbins combines illustration and mathematics as well as any work written since. Design science touches on these topics frequently as well, Kappraff's Connections is an extraordinary example of this. Deeper mathematical topics include set theory, algebraic groups, vector analysis, and too many others to list. However abstract the concepts diagrams and illustrations in this book may seem initially, most if not all have been utilized for practical application in recent times. You may very well be using devices on a daily basis, which have these concepts as a basis for their functionality. Keep this in mind while reveling in what the individual imagination can conjure.
8 of 9 people found the following review helpful
5.0 out of 5 starsThe royal road to geometry!26 Feb 2001
By Helmer Aslaksen - Published on Amazon.com
Format:Paperback
This book is a jewel! It contains a wide collection of visual geometry. Professor Banchoff is able to link geometry to many aspects of life. It's a treasure trove for anybody teaching geometry at any level. It's a book that can be read at many levels. If you're willing to skip a bit here and there, you can get a very good general idea. But if you want to really understand all the details, it can make for hours of challenging reading. I'm still reading it! :-) |
Eighth Grade Course Descriptions
810 Algebra
This course will develop the fundamental principals of algebra. Course topics will include algebraic symbolism, simplifying equations, solutions to elementary equations and graphic representations associated with variables. This course will introduce algebraic processes applied to word problems.
820 Accelerated Algebra I
This course, incorporating the consistent use of real numbers and a problem solving approach, emphasizes the principles of algebra, including algebraic symbolism, simplifying complex expressions, solutions to linear and quadratic equations, and graphic representations associated with variables. Students will apply algebraic representations to word problems and analyze the nature of changes in linear and non-linear relationships.
830 Accelerated Geometry
This accelerated course is a comprehensive study of plane and solid geometry including constructions, formulas for measurement and formal proofs. It is based on the axioms and theorems that relate points, lines, planes and solids. Many of the topics are covered in great depth, especially area and volume of solids. Additional emphasis is placed on the integration of algebraic techniques in solving geometric problems. |
Solving Exponential Growth Functions - Social Networking
Created:
Sunday, July 04, 2010
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Thursday, April 17, 2014
This article focuses on how to solve equations. An exponential growth function tells the stories of explosive growth. Four variables — percent change, time, the amount at the beginning of the...
Guide to Parent Functions
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Friday, June 03, 2011
Updated:
Wednesday, April 16, 2014
Use the Guide to Parent Functions to learn more about Algebra functions. Each family of Algebraic functions is headed by a parent. This article focuses on the traits of the parent functions.
The Quadratic Formula - One x-intercept
Created:
Sunday, March 13, 2011
Updated:
Wednesday, April 16, 2014
This tutorial focuses on the parabola that crosses the x-axis once -- the quadratic function with only 1 solution.
First Grade Math - 1st Grade Math Course of Study
Created:
Thursday, June 22, 2006
Updated:
Wednesday, April 16, 2014
The following list provides you with the basic concepts that should be attained by the end of the school year." itemprop="description">>
Sunday, July 11, 2010
Updated:
Wednesday, April 16, 2014
The measure of an angle with a measure between 0° and 90° Also Known As: A positive angle that measures less than 90°.
Updated Articles and Resources
Euclid of Alexandria
Created:
Sunday, June 27, 2004
Updated:
Wednesday, April 16, 2014
A biography of Euclid of Alexandria. All of the rules we use in Geometry today are based on the writings of Euclid, specifically 'The Elements'." itemprop="description" itemprop="description"<...
Math Disability
Created:
Saturday, December 27, 2003
Updated:
Wednesday, April 16, 2014
When referring to language difficulties, the term Dyslexia is used. However, for math the term Discalculia is used." itemprop="description">>
Sunday, April 03, 2011
Updated:
Wednesday, April 16, 2014
Be a problem solver and solve Algebra word problems. Learn to improve your problem solving skills. |
Hello there fellow student! I have been using Wiz kids algebra 2 help study tool for some time now and I am proud to say that it has been very effective for me as I have ...
AGS Pre-Algebra - Revised The bridge to algebra Help your students make a smooth transition from basic math to algebra. Pre-Algebra is written for the needs of the ...
In this series, host Sol Garfunkel explains how algebra is used for solving real-world problems and clearly explains concepts that may baffle many students.
PBS Teachers provides PreK-12 educational resources and activities for educators tied to PBS programming and correlated to local and national standards and professional ...
Catalog: UWC Materials for Educational Use (12-01-10) All of the materials available are listed here. Please use this reference to fill out the checklist you will ... Materials for Educational Use Catalog 12-01-10.doc
Insights Into Algebra 1: Teaching for Learning is an eight-part video, print, and Web-based professional development workshop for middle and high school teachers.
math. used teacher resources this page up-dated may 5, 2010. over 2,500 items are now listed, call for pricing and quantities available. 252 244 0728 |
Basic Math and Pre-Algebra - 2nd edition
Delivers the appropriate amount of expert coverage on basic math topics for consumers who need a supplement to a beginning basic math text or class; who need to prepare for exams; or who need to brush up on the fundamentals of basic math
Chapter Check-In gives readers an overview of what they'll learn in the chapter
Chapter Check-Out reviews the chapter to enforce the items learned and help with comprehensio...show moren
Review section is a summary test on all chapter topics in the book -- great tool for teachers and students
Resource Center directs reader to additional information available for the subject such as books and websites
500 practice questions available online at CliffsNotes.com and directly ties to each chapter in the bookGIANTBOOKSALE BAY SHORE, NY
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MODIS Snow Cover over Europe The Moderate Resolution Imaging Spectroradiometer (MODIS) provides data in 36 spectral bands, some of which are used in an algorithm to map global snow cover. The animation shows the dynamic behavior of the advance and retreat of continental snow cover over Europe for the winter of 2001-02 from MODIS-derived 8-day composite snow maps with a spatial resolution of about 5 km. Author(s): No creator set
How and why we do mathematical proofs This is a module framework. It can be viewed online or downloaded as a zip file.
As taught in Autumn Semester 2009/10
The aim of this short unit is to motivate students to understand why we might want to do proofs (why proofs are important and how they can help us) and to help students with some of the relatively routine aspects of doing proofs.
In particular, the student will learn the following:
* proofs can help you to really see why a result is true;
* problems that are easy to state |
Holt Spanish 2 Workbook Answer Key Book
Click your algebra 2 textbook below for homework help. our answers explain actual algebra 2 textbook homework problems. each answer shows how to solve a textbook.
Holt mcdougal online provides access to online books,assessments, and resources for students and teachers. you can register for the materials if you meet one of the.
We would like to show you a description here but the site won't allow us.. |
Find an East Elmhurst Algebra 1It is customary to include some introductory Geometry topics, such as the Pythagorean theorem. Additionally, Probability is introduced, including Permutations and Combinations, and an introduction to Statistics. The quadratic formula is presented, along with an introduction to complex numbers |
Mathematics for Elementary Teachers, Textbook with Hints and Solutions Manual: A Contemporary Approach
All the essential mathematics teachers need for teaching at the elementary and middle school levels! This best seller features rich problem-solving ...Show synopsisAll the essential mathematics teachers need for teaching at the elementary and middle school levels! This best seller features rich problem-solving strategies, relevant topics, and extensive opportunities for hands-on experience. The coverage in the book moves from the concrete to the pictorial to the abstract, reflecting the way math is generally taught in elementary classrooms. Mathematics for Elementary Teachers, Student Resource Handbook This invaluable resource handbook is designed to improve student learning and provide models for effective classroom |
Book Information"Algebra II For Dummies" is the fun and easy way to get a handle on this subject and solve even the trickiest algebra problems. This friendly guide shows you how to get up to speed on exponential functions, laws of logarithms, conic sections, matrices, and other advanced algebra concepts. In no time you'll have the tools you need to: Interpret quadratic functionsFind the roots of a polynomialReason with rational functionsExpose exponential and logarithmic functionsCut up conic sectionsSolve linear and non linear systems of equationsEquate inequalitiesSimplifyy complex numbersMake moves with matricesSort out sequences and sets
This straightforward guide offers plenty of multiplication tricks that only math teachers know. It also profiles special types of numbers, making it easy for you to categorize them and solve any problems without breaking a sweat. When it comes to understanding and working out algebraic equations, "Algebra II For Dummies" is all you need to succeed
Book descriptionAlgebra II For Dummies is the fun and easy way to get a handle on this subject and solve even the trickiest algebra problems.
This friendly guide shows you how to get up to speed on exponential functions, laws of logarithms, conic sections, matrices, and other advanced algebra concepts. In no time you'll have the tools you need to:
Interpret quadratic functions
Find the roots of a polynomial
Reason with rational functions
Expose exponential and logarithmic functions
Cut up conic sections
Solve linear and non linear systems of equations
Equate inequalities
Simplifyy complex numbers
Make moves with matrices
Sort out sequences and sets
This straightforward guide offers plenty of multiplication tricks that only math teachers know.
It also profiles special types of numbers, making it easy for you to categorize them and solve any problems without breaking a sweat. When it comes to understanding and working out algebraic equations, Algebra II For Dummies is all you need to succeed!
Customer Product Reviews
Rated 5 out of 5★ by ChiefPup Excellent resource for struggling students I'm a father who completed Algebra I many years ago and never took Algebra II, and I have an 11th grade daughter who is struggling with Algebra II. I bought this book with the expectation that it would help me quickly get up to speed so that I could help my daughter understand what to do when presented with a problem on an assignment, quiz, test, etc. I had to apply myself, but within a couple of weeks, I was able to be an effective tutor for my daughter. This book clearly explains how to do things; it shows the procedure for solving problems in a way that is easy to understand. I must add, however, that if I had not had a good grasp of Algebra I, I don't think this book would have been the right solution for me. (I would have first needed to buy Algebra for Dummies.) 11 |
More About
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Overview
This textbook, for an undergraduate course in modern algebraic geometry, recognizes that the typical undergraduate curriculum contains a great deal of analysis and, by contrast, little algebra. Because of this imbalance, it seems most natural to present algebraic geometry by highlighting the way it connects algebra and analysis; the average student will probably be more familiar and more comfortable with the analytic component. The book therefore focuses on Serre's GAGA theorem, which perhaps best encapsulates the link between algebra and analysis. GAGA provides the unifying theme of the book: we develop enough of the modern machinery of algebraic geometry to be able to give an essentially complete proof, at a level accessible to undergraduates throughout. The book is based on a course which the author has taught, twice, at the Australian National |
Algebra Glencoe Lesson BIGIDEA: NUMBERS, OPERATIONS AND EXPRESSIONS Students work with integer exponents, scientific notation, and radicals, and use variables and expressions to solve problems from purely mathematical as well as applied contexts.
Algebra: BIGIDEA2: Develop an understanding of and fluency with addition and subtraction of fractions and decimals. Represent addition and subtraction of decimals and fractions with like and unlike denominators using models, place value or properties.
BigIdea: The place values to the right of the decimal point in the base-ten system names numbers less than one. EQ: ... BigIdea: Properties and concepts of algebra are used to evaluate expressions and solve multiplication and division equations.
Algebra2 Ch 2 What is the impact of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ... BigIdea:(Every component at the course level has to reside in each unit individually so it collectively communicates the course's big picture.)
BigIdea2: Develop an understanding of and use formulas to determine surface areas and volumes of three-dimensional shapes. ... Supporting Idea: Algebra Supporting Idea: Geometry and Measurement Supporting Idea: Number and Operations
Hear about the big ideas behind this book. Do ... that remove the abstraction from algebra and give it meaning. Topics will be from algebra 1& 2, trigonometry, & pre-calculus ... Open the door to future mathematical learning for ALL students by making a unifying idea of mathematics a ...
Developing Big Ideas in Algebra thru Technology and Hands on Activities ... This idea was also a Classroom Grant Award winner from last year. ... We have examples for use in Algebra 1 & 2, geometry, and Calculus that we have copied for you and with a little preparation, ...
... with their college and career goals for 5 years as part of a non-profit program she developed called, TeenSpace. The idea ... Carol previously taught Algebra2, ... She has tutored for over five years in organizations such as Kids on Campus, Big Brothers Big Sisters of Athens County ...
Evaluate a linear combination of vectors [Algebra2] Determine a unit vector in the same direction as a given vector [Algebra2] Determine a quadratic function given the coordinates of two or three points [Algebra2]
GLE captures the bigidea (conceptual understanding) of magnitude of numbers. CCSS is ... a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a ... -- Use appropriate representations to solve problems or to portray, clarify, or extend a mathematical idea.
What's the BigIdea, Ben Franklin? What's Under My Bed? Where Do You Think You're Going, Christopher Columbus? Where the Wild Things Are ... Adventurous World of Algebra, The, Program 2: Functions Adventurous World of Algebra, The, Program 3: Linear Equations
JASPER PRE-ALGEBRA WORKING SMART X All 3 episodes help students see the power of As teenagers Jasper, ... THE BIG SPLASH X X X With 1 sample, 1 extrapolation to the population, ... A CAPITAL IDEA ACI involves a sample within a sample, making the
... How Big is 1 Million? 8A 12A 16A Expanded Notation 18A ... ALGEBRA & FUNCTIONS AF1.2...Expressions with Parenthesis AF1 ... the DSAT Exam and look over the CST "Released Questions" prior to planning the next 9 chapters so that you have a good idea of the level of teaching that needs to be ...
This session will focus on meaningful algebra activities ... without whose dirty unkempt rooms I never would have thought up this idea. calculus ... and instruction can impact student achievement.This session will focus on a curriculum organized around the "big ideas" of Algebra and help ... |
More About
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Overview
Supporting NCTM's call for a more visual approach to algebra, these supplementary exercises give students a concrete understanding of abstract algebra concepts! Students see everyday situations represented mathematically through exercises that ask students to picture a visual image (a graph) of a real-life relationship before tackling the equation |
Can you suggest me a comprehensive book to revise high school mathematics (up to besic calculus)? It should be extremely clear and complete and "scientific" (not like most high school books). Thank ...
I read the theorem stated below on Wikipedia
( But I do not understand how to prove the equivalence of these different definitions.Any hints ...
I'm a high school student who just finished elementary school.Though since I was into math I started going through advanced math while I was in elementary school and I pretty much finished most of the ...
I recently bought a good amount of math books, because I want to self teach math, and they are on their way--via U.P.S.--to my house. I was just wondering if someone would be kind enough to tell me in ...
I could prove that a four input butterfly network is planar. For that I simply drew it such that no two edges intersect. But I could not use the same approach for the 8-input butterfly network. So I ...
I am trying to understand how the very basic Markov Chain Monte Carlo approach works: We try to approximately calculate the expected value $E_{\pi(x)}[X]$ by drawing sequential samples from a Markov ...
A single sample $t$ test is only against a sample and a population correct? Can it test against a population and itself or two populations? ie $\mu_1$ vs. $\mu_2$....if not what tests would you use ...
I'm looking for a textbook or resources my younger brother could use. (He is in year 9, equivalent to US high school freshman) He is wanting to advance upon his math, he currently does exercises out ...
What would be a step by step sequence of learning mathematics from basic algebra to basic calculus? I pose this question because I am in the process of self-learning mathematics as a preparation for a4.5: If f is continuous on a closed set in $R^1$, prove there exist continuous functions $g$ on $R^1$ such that $g(x)=f(x)$ for all $x \in \mathbb{E}$.
4.6: Suppose $\mathbb{E}$ is compact, and prove ...
$Gal(\Bbb K/\Bbb F)\cong S$. Where $\Bbb K$ is extension of $\Bbb F$. And $S= G_1\times G_2\times\cdots\times G_K$ is a solvable group. Where each $G_i$ are groups of prime power order and $o(S)= n.$
...
Why is $[0,1]$ not homeomorphic to $[0,1]^2$? It seems that the easiest way to show this is to find some inconsistency between the open set structures of the two. It is clear that the two share the ...
I was never a very good math student and over the years, I simply forgot a lot of math. But sometimes it annoys me to no end, because I work in a mathematically related field (applied statistics) and ... |
North Plainfield, NJThank you for your consideration. Algebra 1 is a textbook title or the name of a course, but it is not a subject. It is often the course where students become acquainted with symbolic manipulations of quantities. |
MATH 104 or equivalent. Completes the study of algebraic and trigonometric skills necessary for successful study of calculus. Trigonometric functions and identities are applied to analytic geometry. Systems of equations and inequalities are solved using algebraic, graphical and matrix/determinant methods. Theory of equations including remainder, factor and De Moivre's theorem are used to study and help in graphing of equations. Introduces series and sequences (arithmetic and geometric), the binomial theorem, and mathematical induction. Assistance is available in the Center for Academic Success. A scientific calculator is required. Three class hours weekly. |
Algebra and Trigonometry and Useful Mathematical and Physical Formulae | 22 Mb Beecher, Penna, and Bittinger's Algebra and Trigonometry is known for enabling students to "see the math" through its focus on visualization and early introduction to functions. With the Fourth Edition, the authors continue to innovate by incorporating more ongoing review to help students develop their understanding and study effectively.
A compact volume of mathematical and physical formulae presented in a concise manner for general use.
Updating the Artech House bestseller, Fundamentals and Applications of Microfluidics, this newly revised second edition provides electrical and mechanical engineers with complete and current coverage of microfluidics – an emerging field involving fluid flow and devices in microscale and nanoscale. The second edition offers a greatly expanded treatment of nanotechnology, electrokinetics and flow theory |
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14 of 14 people found the following review helpful
5.0 out of 5 starsThe best 11+ maths bookPublished on 25 July 2011 by Busymum
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3.0 out of 5 starsGood guide
A good guide for those studying to take their eleven plus exam. My daughter found it easy & helpfull to use.
Got my kid out of kumon due to the repititive nature of assignments. Found this book very practical and useful in teaching my kid in a structured manner. Knowing Maths and Teaching Maths are 2 different things and this book helped bridge the gap.
A very well organised book going through all the topics needed for 11 plus exam. It taught me how to explain ratio in a simpler way. Key facts gather all the knowledge a child should have. Well worth the money. Plus a bonus: 1 practice test included.
This book is really well organised. It tackles each topic in turn. There is a short test at the beginning of each section so you can see how well your child understands the topic before you look at the information. It's very useful for identifying areas you need to work on and those you don't need to worry about. I would say this is a good bridging book for maths when your child is moving up to secondary school, regardless of whether they are sitting entrance tests or not.
I found this book to be very helpful for me to assist my son with his revision. The content is very clear and very easy to follow. I would recommend this to anyone following the Bonds 11+ 10 minute tests and the test papers.
An excellent resource for both parents, pupils and tutors preparing for the 11+/Entrance Exam for Grammar Schools. It is a very useful complement to the 11+ practice papers as it helps to identify pupils' strengths and weaknesses whilst revising the main topics required for the exam. It has been a godsend to us. Highly recommended.
A brilliant book for helping practice for the 11+. Use this right from the start to help guide KS2 maths revision. Start off slowly supporting the basics and warm up gradually to 11+ style questions, ensuring preparation is always within grasp of your child's ability. It covers everything needed for 11+ maths and questions are to a realistic standard. |
Math made easier: advice from experts
Many students struggle with various kinds of math, including positive and negative number signs, fractions, factoring, graphing and word problems, instructors in the department of mathematics and statistics said.
In fall 2011, the success rate for college algebra, a core math course, was 59 percent, said Mellisa Hardeman, senior instructor in the department. The success rate dropped anther percentage point the following year, she said.
In fall 2012, 50 to 60 percent of pre-core math students had difficulties solving math problems, said Denise LeGrand, director of the Mac I math lab.
Ike McPhearson, math tutor, explained why students may have trouble comprehending math. One reason is that students may come from a home where education is not valued, he said.
A bad experience with an instructor can also change students' attitudes about math.
"You can't take yourself too seriously as a teacher," said Hardeman. Instructors can never give a student too much help passing math, she said.
Students who took a math course in high school before going to college are less likely to struggle with math, Hardeman said. Some students go to college years after graduating high school, however, and may forget everything they learned in their math classes.
Fortunately, there are a number of strategies that can help students overcome these challenges and develop a better understanding of math.
"In order to make math easy for students, show different ways of how to understand it," said McPherson, who has tutored high school and college students. Another way of making math fun for students is to create different games, he said.
According to LeGrand, the most important way to become better at math is to practice math exercises for 20 to 30 minutes.
"They won't see the results right away," said LeGrand, " but if they go to class and focus on work required, they will be successful and they will build confidence."
In addition, students can get help from tutors at the math lab. Each semester, the lab hires 12 tutors, LeGrand said.
For the math-impaired, there is a new math course called Quantitative and Mathematical Reasoning. The course was designed for students who are not science, technology, engineering or mathematics majors. It focuses on practical math, for example, currency exchange rates. The course fulfills the core math requirement, in place of college algebra.
Pre-core math courses, developmental math courses students take if they do not have the prerequisites for college math classes, are becoming more successful, said Tracy Watson, coordinator for pre-core math. The success rate for those courses rose to 77 percent in fall 2012, she said. Previously, the success rate was 37 percent for a 4-year period, she said.
This semester, there are 80 math majors at the university.
"We all like how math works because it all fits together," Watson said.
"Students who major in math develop a sense of thinking and solving problems," said Thomas McMillan, department chair.
Once students better understand math, they will have the confidence to solve not only math problems, but problems in everyday life as well. |
II. Mathematics
Focus is on the mathematical understandings that middle school teachers must have, the ability to communicate these understandings,
and the ability to solve mathematical problems.
Because the emphasis is on assessing the examinee's ability to reason logically, to use mathematical techniques in problem
solving, and to communicate mathematical ideas effectively, examinees are not required to do much computation. Examinees may use non-programmable calculators while taking the test; a basic four-function calculator will be adequate.
The test questions do not require knowledge of advanced-level mathematics vocabulary but may require examinees to relate mathematics
to real-life situations. Mathematics is conceptualized as an integrated field; therefore, a single problem may test several
mathematical content areas.
Although few technical words are used in the test questions, terms such as area, perimeter, ratio, integer, factor, and prime
number are used because it is assumed that these are commonly encountered in the mathematics that all examinees have studied.
Number sense and numeration (20%)
understand the meaning/implication of number and number concepts as they relate to problem solving, using cardinal and ordinal
numbers, place value, ordering of fractions, decimals, whole numbers
Geometry (20%)
knowledge of relationships in both two and three dimensions
ability to draw inferences based on precepts/concepts of parallelism, perpendicularity, congruence and similarity, angle measures
and polygons
Measurement (5%)
knowledge and application of standard units of both the English and metric systems, nonstandard units, estimation, perimeter,
area, volume, mass, weight, angle measure, time, temperature
Algebraic concepts (10%)
recognize and apply algebraic concepts and properties
describe patterns by writing or identifying a formula
Number theory (10%)
problem solving that demonstrates an understanding of prime and composite numbers, divisibility rules, least common multiple,
greatest common divisor and set theory
The real number system and its subsystems (20%)
solve real-world situational problems
work with both standard and alternate algorithms
Probability and statistics (15%)
understand the organization, presentation, and interpretation of data in various forms |
A graphing applet with sliders for controlling a, b, h and k. Both the ellipse and hyperbola applets are on the same page. The hyperbola applet allows for horizontal and vertical hyperbolas. The "b... More: lessons, discussions, ratings, reviews,...
Flash introduction to finding the equation of an hyperbola centered on (0,0) and with its major axis on the x-axis. With step-by-step instructions and an illustrated glossary, students can learn how t... More: lessons, discussions, ratings, reviews,...
Flash introduction to finding the equation of an hyperbola centered on (0,0) and with its major axis on the y-axis. With step-by-step instruction and an illustrated glossary, students can learn how to... More: lessons, discussions, ratings, reviews,...
A very powerful graphing program that is also especially easy to use. You can graph functions in two or more dimensions using different kinds of coordinates. You can make animations and save as movies... More: lessons, discussions, ratings, reviews,...
On this online calculator calculate mathematical expressions and complex numbers. You can do matrix algebra and solve linear systems of equations and graph all 2D graph types. You can also calculate z...The user reviews some basic definitions and properties of real numbers. After viewing explanations and examples of the properties, users can interactively test their understanding of the properties o |
PLEASE SUBSCRIBE!!!!!!! Check out my BLOG at drewbutcher.wordpress.com where all the videos are much better organized by topic. The weight that a 2 inch wide piece of pine can support varies directly … [Read More...]
PowerPoint Math Lessons for Arithmetic, Beginning, Intermediate and College Algebra
1. Lessons are listed by topic.
2. Detailed Examples with explanation of each step as it appears.
3. Practice Problems given during lesson to enhance
comprehension.
Workbooks are available for the above courses. Homework problems with answers are included.
Performing all homework problems will help you gain proficiency on the various topics.
Videos on How-to use various useful features of your
calculator.
Videos on How to use various educational websites |
This book concerns the origins of mathematical problem solving at the internationally active Osram and Telefunken Corporations during the golden years of broadcasting and electron tube research. The woman scientist Iris Runge, who received an interdisciplinary education at the University of Gottingen, was long employed as the sole mathematical authority... more...
The 16th-Century intellectual Robert Recorde is chiefly remembered for introducing the equals sign into algebra, yet the greater significance and broader scope of his work is often overlooked. This book presents an authoritative and in-depth analysis of the man, his achievements and his historical importance. This scholarly yet accessible work examines... more...
Among the group of physics honors students huddled in 1957 on a Colorado mountain watching Sputnik bisect the heavens, one young scientist was destined, three short years later, to become a key player in America's own top-secret spy satellite program. One of our era's most prolific mathematicians, Karl Gustafson was given just two weeks to... more...
The Scottish mathematician Colin MacLaurin (1698-1746) is known for developing and extending Newton's work in calculus, geometry and gravitation; his "Treatise of Fluxions" was the first exposition of Newton's methods. This book presents these important works in translation, preceded by a translation of MacLaurin's MA dissertation... more...
Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions.... more...
Need to learn statistics as part of your job, or want some help passing a statistics course? Statistics in a Nutshell is a clear and concise introduction and reference that's perfect for anyone with no previous background in the subject. This book gives you a solid understanding of statistics without being too simple, yet without the numbing complexity... more... |
Algebra I am getting ready to start an Algebra class for the first time and I was wondering what challenges people have with learning and using algebra concepts. Also what are the best ways to over come math anxiety? The best way? Learn the language of algebra.
Tuesday, March 20, 2007 at 9:02am by jeff
what does pre-algebra mean?? pre algebra is like a bunch of math that comes before algebra in middle school.
Monday, August 25, 2008 at 9:11pm by Grace
English Grammar The only time you capitalize the M on "math" is when the word is part of the actual title of a course. Here are some examples: He is studying algebra. She is enrolled in Algebra I. They are working on their math homework. They are taking the Discrete Mathematics class. So ... ...
Friday, March 21, 2008 at 1:05am by Writeacher
algebra 2 They are conic sections. For a more detailed explanation, see: or post what details you need.
Tuesday, December 15, 2009 at 4:43pm by MathMateMath Algebra but im supposed to use algebra
Saturday, May 11, 2013 at 7:30pm by Hanah
algebra i need help with algebra 1A in Math/116
Wednesday, September 8, 2010 at 10:25pm by bessie
Math (Algebra/Pre-Algebra) so you get... 3x = 24... so x = 8!!! Yay!!! thanks soooo much for answering all my questions! =]=]=]
Thursday, June 4, 2009 at 9:13pm by Samantha
Math - Algebra This is a fraction algebra. n/24=25 (not divide sign). I don't know if I have to multifly and which number do i use.
Tuesday, March 2, 2010 at 11:40pm by Joe
Math 032 Algebra Before we can tell you the answer, what is the question? Are you adding them, multiplying them or what? The subject is not algebra, by the way.
Tuesday, May 18, 2010 at 12:25am by drwls
3rd grade math (not algebra!) can you post how you solved it...I can solve it using algebra.. but can't figure it out otherwise!!!
Wednesday, February 1, 2012 at 6:44pm by susan
Math 117 Algebra i want to learn algebra
Friday, June 18, 2010 at 5:50pm by ronald
Math-Algebra-1 (???) How does this relate to Algebra? What is the context?
Wednesday, September 5, 2012 at 11:53pm by PsyDAGAlgebra What are intersections and unions (in algebra). Also, what are complements? And what does MATH stand for in terms of sets? Please answer quickly. Thanks!
Wednesday, September 21, 2011 at 5:18pm by Jena
math? needs help (Algebra) Please select the School Subject carefully. With the label you have the correct teacher will probably never even open it. If you say Algebra or Math, you'll get the correct teacher. It is not I! Sra (aka Mme)
Tuesday, June 15, 2010 at 12:11pm by SraJMcGin
algebra 1 10(y^2 -9) What you have in parentheses is the difference of two squares. You should know how to factor that again. If you don't know how,
Sunday, June 5, 2011 at 2:31pm by drwlsMath Check this site. If it doesn't help you, please post one or two of your problems. We'll be happy to show you how to find the solutions.
Tuesday, July 29, 2008 at 9:27pm by Ms. SueAlgebra 1A This is for my math 116 algebra 1A. The question is homework. I'm having problems understand it myself...
Monday, November 24, 2008 at 9:41pm by Julissa
algebra with pizzazzi Is this REALLY the title of your post: algebra with pizzazzi? We would expect MATH problems. Sra
Friday, December 5, 2008 at 9:14am by SraJMcGinmath polynomials In google type: Algebra Solver and Math Simplifier that SHOWS WORK When you see list of results clik on: Algebra Solver and Math Simplifier that SHOWS WORK In rectacangle type your expresion and click option: SOLE OR SIMPLIFY You will se solution step by step
Sunday, April 3, 2011 at 12:14am by Bosnian
math Need help with algebra question If c= 5/9 (F-32)and F is 77 then what is c the 5/9 reprsents a fraction, I am no good in algebra and need help how to get the answer and the problem, thanks
Saturday, October 11, 2008 at 11:54am by chris
math 116 algebra 1A can someon help please. why is it important that you follow the steps rather than solve the problem from left to right?I have no clue. this is my first time taking algebra
Thursday, September 17, 2009 at 10:44am by Lea
Algebra maybe i should have put this under Algebra or just math..I have no clue.
Friday, August 20, 2010 at 2:51pm by Mary
algebra the population P(t) of a new residential development t years after 2010 is P(t)=8000(1-e^-0.3t). What is the population for 2015? * algebra - Reiny, Sunday, December 5, 2010 at 6:19pm replace t with 5 and evaluate using your calculator (I got 6215) I was the population to ...
Sunday, December 5, 2010 at 7:11pm by math helpmath 116 Should algebra be taught to everyone? Who should study algebra?
Friday, March 20, 2009 at 6:30pm by MeshelleALGEBRA How many ordered triples of complex numbers(a,b,c) are there such that a^3-b,b^3-c,c^3-a are rational numbers, and a^2(a^4+1)+b^2(b^4+1)+c^2(c^4+1)=2[{(a^3) b}+{(b^3)c}+{(c^3)a}]
Friday, October 11, 2013 at 10:54am by algebra,math
math Use algebra pieces and mental arithmetic to determine four consecutive odd numbers who sum is 64. Sketch and label your algebra piece model and explain how you solved the problem.
Saturday, June 2, 2012 at 7:37pm by marcus
Algebra 1A describe what the graph of interval -4, 10 looks like? This is for math 166 algebra 1A I dont understand how to answer this question, please help me!
Saturday, November 29, 2008 at 1:35am by Julissaalgebra honors I was placed into algebra honors instead of advanced math.. I am in 7th grade.. I have to maintain an 80% for the entire year or go to virtual school all summer.. My question is: Is there a special technique, formula, or very useful site that might help me grasp the concepts ...
Tuesday, October 5, 2010 at 11:24am by Jarrad
math The one that says that a (b + c) = ab + ac
Sunday, July 29, 2012 at 5:37pm by drwls
math, algebra what are some challenges about working with rational expressions? Math is a language. Getting it precisely right is a lot easier than describing it in a vague statement in English such as you ask. Is there a chance you can change teachers? If so, I recommend it. THe focus of ...
Tuesday, March 6, 2007 at 12:41am by jas20
math Can someone correct this for me please or help me out.... Why are variables useful in algebra? My answer: Variables are useful in algebra because they detemine an answer that anyone is trying to get to. Variables can represent a single number or a whole sub-equation. they make...
Monday, January 1, 2007 at 4:35am by jasmine20
Algebra I need help on doing a math problem for my algebra class so if u could help i would be really grateful any way please explain. : Find two consecutive negative integers with the product of 110
Wednesday, March 24, 2010 at 7:44pm by Please help
math 116 algebra 1A The language of Algebra is precise, and built into it is an expectation that the user will follow the order of operations rules. Going from left to right is not in those rule, and can lead to erroneous results.
Thursday, September 17, 2009 at 10:44am by bobpursley
College Algebra is this really algebra, im doing this now in freshman year algebra 2
Monday, February 21, 2011 at 1:06am by BOSS
Math What data do you have about Mr. Doodle's grading system? Does he grade strictly on a curve? Do the majority of his student receive at least a B?
Tuesday, July 19, 2011 at 5:27pm by Ms. Sue
Algebra I am going to take an Accuplacer math placement test later this week. It is to determine what math course I need to take in college. The school would like me to place in statistics.This will be my second time taking the test. The first time I placed in algebra. Does anyone ...
Tuesday, April 1, 2008 at 11:59am by Christian
Algebra If Literature, history and French are your life loves, then algebra probably will not be a great part of your life. But, life consists of a wide variety of experiences, and I guarantee you that some basic math know-how (yes, even including algebra) will make things easier. So...
Friday, March 28, 2014 at 4:38pm by Steve
Algebra 1A How is algebra a useful tool? what concepts investigated in algebra can be apply to personal and professional life? I need help answering this question. Please help?
Sunday, November 30, 2008 at 7:34pm by Julissa
MATH !! Get a common denominator, and combine. If you dont know how to do that,
Wednesday, September 7, 2011 at 9:02pm by bobpursley
algebra 2 thats part of algebra 2 thats easy were doing that now in pre algebra
Wednesday, April 29, 2009 at 1:14pm by Tanisha
7th grade math What i would say is work backwards. So if there are 44 students in Algebra 2, and it states that there are twice as many in Alg.1 then 2. So, then there are twice that amount in Algebra 1. It also states that there are at least 5 more than that, so you add another 5 students. ...
Thursday, November 20, 2008 at 8:37pm by Take it or Leave itmath/prealgebra what are the actual definitions to the word algebra itself? algebra? cubed? counter example? function table? function rule? can you help me find these definitions?
Friday, August 20, 2010 at 8:51am by alexis
math .26 (x) = 350 if you use algebra?? divide both sides by .26 If you don't use algebra, I can show you another way.
Thursday, February 21, 2013 at 6:11pm by JJ
Math (Algebra) if i have 3 algebra tiles(big size)and 2 regular size negative tiles what would the expression be?
Thursday, June 13, 2013 at 9:32pm by cake
College Algebra And yes this is College Algebra...some of us are better at things other than math. I'm doing great after being graduated for 17 years, a 9 year old, a husband and a full time job. I'm loving my A average thank you.
Saturday, November 6, 2010 at 11:27am by Kelly
math urgent help needed it's not that difficult I was not too good in probability and even in algebra i learnt from an online tutoring education company that's tcyonline this also give individual sessions for a particular topic i was enrolled for a package in algebra and probability
Saturday, October 25, 2008 at 3:15pm by preekan31pm by Ms. Sue
Math an algebra book weighs 6 oz less than twice as much as grammar book. if 5 algebra books weigh the same as 8 grammar books, how much does an algebra book weigh?
Thursday, September 19, 2013 at 10:37pm by Zoey
algebra 1 help fin the complement and the supplemnt of the angel measure 1) 130 complement-40 suplement-50 or vice versa if anyone can help me with some algebra work it would be greatly appreciated i am im algebra 1 and still on the second quarter and have until november to finsh thank you ...
Saturday, August 20, 2005 at 8:23pm by cristina
math Please explain in detail how to solve each question: At a certain high school, 350 students are taking an algebra course. The ratio of boys to girls taking algebra is 33:37. How many more girls are taking algebra than boys? How can you write a system of equations to model the ...
Wednesday, January 4, 2012 at 5:56pm by Jane
Maths-can someone explain something to me??? Here's another site that may help you.
Monday, February 18, 2013 at 12:48pm by Ms. Sue
DRWLS,MATH,ALGEBRA Drawls, How did you get 2h. and then the 2a/h from.Can you help me understand it when you get a chance. Directions: Solve each literal equation for the indicated variable. A=1/2h(B+b) (For b) Area of a trapezoid For Further Reading math,algebra - drwls, Monday, December 18, ...
Monday, December 18, 2006 at 1:30pm by jasmine20 |
Foundations of Real World Math
"Why is math important? Why do I have to learn math?" These are typical questions that you have most likely asked at one time or another in your education. While you may learn things in math class that you will not use again, the study of mathematics is still an important one for human development. Math is widely-used in daily activities (e.g. shopping, cooking, etc.) and in most careers (e.g. medicine, teaching, engineering, construction, business, statistics in psychology, etc.). Math is also considered a "universal language." One of the fundamental reasons why you learn math is to help you tackle problems, both mathematical and non-mathematical, with clear, concise, and logical steps. In this course, you will study important fundamental math concepts.
This course begins your journey into the "Real World Math" series. These courses are intended not just to help you learn basic algebra and geometry topics, but also to show you how these topics are used in everyday life. In this course, you will cover some of the most basic math applications, like decimals, percents, and even the dreaded "f-word"–fractions. You will not only learn the theory behind these topics, but also how to apply these concepts to your life. You will learn some basic mathematical properties, such as the reflexive property, associative property, and others. The best part is that you most likely already know them, even if you did not know the proper mathematical names.
Let's start with fractions. Have fractions ever been bothersome to you? Do you think that there is no purpose for them? In this course, you will learn that fractions are all around us in the forms of measurement, ratios, and proportions–and we think you might change your tune on the subject. You will see how to solve those sometimes troubling fraction problems, like the ones that use 1 ? and 3 ?, which don't divide as evenly as you'd like. In case you're not yet familiar with fractions, let's offer a common every day example: a recipe for making chocolate chip cookies. You see a recipe that calls for 2 ? cups of flour, ¾ cup of sugar, and ½ teaspoon of vanilla, and you need to make 2 ½ the recipe amount. Each of these measurements involves fractions. If you want to make the right amount of cookies, you have to determine how much you need of each ingredient.
This course will also introduce you to decimals and percentages, which are widely used in money, finances, and measurement. Decimals are all around you, including when you download applications for your smart phone. Say, for example, you've just purchased the newest Angry Birds application for $0.99. The number 0.99 is a decimal. If you want to spend no more than $10.00, then you will have to determine how many other applications you can download without going over budget. In this course, you will learn how to solve complex decimal problems, such as 13.4561 – 21.03 and 301.21 * 140.31.
You will also learn to write ratios and solve proportions in the course. You are probably already very familiar with ratios, even if you're not aware of it. A recipe that calls for "2 parts milk to 1 part flour," or a speed limit sign that reads "55 miles per hour," or a newspaper ad listing apples at a cost of $2.99 per pound — these are all examples of ratios. Ratios and proportions are particularly useful when doing an everyday activity like planning a party: "If I need two hams for nine guests, how many hams will I need for thirty guests?" Learning how to set up and solve problems like this is a very useful mathematical concept that is applicable to real life situations.
Finally, have you wondered how graph and charts are created with certain data? Data can be visually represented in various forms (bar graphs, circle graphs, etc.) to convey information to a reader. In this course, you will see data in common forms and will have to interpret data (for example, reading a chart of the most downloaded songs from iTunes or interpreting football statistics for your fantasy league). The final unit of the course pertains to charts and graphs and includes the interpretation and creation of various charts and graphs.
Requirements for Completion: In order to complete this course, you will need to work through each unit and all of its assigned materials. Please pay special attention to Units 1 and 2, as these lay the groundwork for understanding the more advanced, exploratory material presented in the latter units. Throughout the course, there are activities assigned from the Pre-Algebra Textbook that you will need to complete. You will also need to complete:
Subunit 1.4 Assessment
Sub-subunit 2.3.4 Assessment
Sub-subunit 2.4.2 Assessment
Sub-subunit 2.5.2 Assessment
Sub-subunit 3.2.1.5 Assessment
Sub-subunit 3.2.2.4 Assessment
Sub-subunit 3.2.6 Assessment
Sub-subunit 4.2.4 Assessment
Sub-subunit 5.2.2 Assessment
Sub-subunit 6.1.2.2 Assessment
Sub-subunit 6.3.2 Assessment
Subunit 7.2 Assessment
Subunit 7.3 Assessment
Subunit 7.4 Assessment
Subunit 7.5 Assessment
Subunit 7.7 Assessment
The Final Exam
Please note that you will only receive an official grade on your Final Exam. However, in order to adequately prepare for this exam, you will need to work through the readings, lectures, activities, and assessments listed above as well as all resources in each unit.
In approximately 140.5 hours to complete. Each unit includes a "time advisory" that lists the amount of time you are expected to spend on each subunit. It may be useful to take a look at these time advisories and determine how much time you have over the next few weeks to complete each unit and to then set goals for yourself. For example, Unit 1 should take approximately 9.75 hours to complete. Perhaps you can sit down with your calendar and decide to complete subunit 1.1 (a total of 4 hours) on Monday night; subunit 1.2 (a total of 3.5 hours) on Tuesday night; subunits 1.3 and 1.4 (a total of 2.25 hours) on Wednesday night; etc.
Tips/Suggestions: Please make sure to take comprehensive notes as you work through each resource. Complete all practice problems, because this will allow you to fully understand each concept. These notes will serve as a useful review as you study for your Final Exam
NOTE: Each of the learning outcomes listed below has been aligned with one or more of the Common Core standards in mathematics. This alignment is reflected in the numbered notation listed alongside each outcome below. For more information on Common Core standards, please read here.
Upon successful completion of this course, the student will be able to:
Apply properties of operations as strategies to add and subtract. (1.OA.B.3)
Apply properties of operations as strategies to multiply and divide. (3.OA.B.5)
Explain how negative numbers are used together to describe quantities having an opposite direction. (6.NS.C.5)
Solve real-world and mathematical problems involving the four operations(including fractions and decimals). (4.MD.A.2)
Find the greatest common factor and least common multiple of whole numbers. (6.NS.B.4)
Just as in life, there are certain things in math that make you shrug and say, "Well, duh. I knew that; it's common sense." This unit will discuss some of the basic algebraic properties which you already know, but may not necessarily know the names of, because they are what some math teachers refer to as the "common sense" properties.
The really neat thing about these properties is that you can see their uses in everyday, non-mathematical ways. For example, if you drive to work, you "commute." Whether you are driving to work from home, or to home from work, you are making the same trip. (Ignoring those times you take a back road because you do not want to spend two hours sitting on the interstate, of course!) In math, the commutative property tells us when we can move numbers around and still get the same answer. Another example is the associative property. The people you hang out with are also known as your "associates." If you are hanging out with two friends, but one of them is in a different room, you still have the same group of friends. The same applies to certain mathematical situations. If you are grouping numbers, depending upon the situation, the grouping is not going to change anything.
Instructions: Please click on the link above and take notes as you watch this video to learn about the Commutative Law of Addition (also known as the Commutative Property of Addition). Watch the presentation carefully two or three times until you are able to explain how changing the order of the addition of two numbers obtains the same result.
Watching this lecture and pausing to take notes should take less than 15 minutes.
Instructions: Please click on the link above and study the "Associative Property of Addition" on pages 15 and 16 of the textbook, stopping at "Grouping Symbols." The material may also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, "The Commutative Property of Addition"), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Commutative Property of Addition.
Reading these sections should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
Instructions: Please click on the link above and take notes as you watch this video to learn about the Associative Law of Addition (also known as the Associative Property of Addition). Watch the presentation carefully two or three times until you are able to explain how to associate the addition of three numbers to obtain the same result.
Watching this lecture and pausing to take notes should take less than 15 minutes.
Instructions: Please click on the link above and study the "Associative Property of Addition" on page 17 of the textbook, stopping at "The Additive Identity." The material may also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, "The Associative Property of Addition"), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Associative Property of Addition adding zero to any number is the original number.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Instructions: Please click on the link above and study "The Additive Identity" located on pages 17 and 18 of the textbook, stopping at "Adding Larger Whole Numbers." The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, "The Additive Identity"), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Additive Identity Property.
Reading this section should take less than 15 minutes.
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Instructions: Please click on the link above; complete the odd-numbered exercises for 11–27 on page 25 and the odd-numbered exercises for 67–79 on page recognize addition laws and properties and apply the conceptsApplications – Geometry" on pages 21 and 22 of the textbook. The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, "Applications - Geometry"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Example 5 on page 21 and Examples 6 and 7 on page 22. This reading provides applications to the properties and laws of addition 51–65 on pages 26 and apply addition laws and properties "Additive Inverse" located on page 120 of the textbook, including Example 8. The material can also be located through the bookmark on the left side (2 The Integers, 2.2 Adding Integers, "Properties of Addition of Integers"), which will take you directly to the reading. After you study and read this section, complete the "You Try It" problem next to Exercise 8. This reading provides an example of the property and the formal definition of the Additive Inverse Property Inverse Property of Addition results in zero changing the order of the multiplication of two numbers obtains the same result.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Instructions: Please click on the link above; study the introduction to "Multiplication and Division of Whole Numbers" on page 33 and continue through "The Commutative Property of Multiplication" on page 34. The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Commutative Property of Multiplication.
Reading this section should take approximately 15 minutes.
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Instructions: Please click on the link above and study "The Associative Property of Multiplication" on page 35 of the textbook. The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, "The Associative Property of Multiplication), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Associative Property of Multiplication.
Reading this section should take less than associate the multiplication of three numbers to obtain the same result multiplying any number by one results in the original number.
Watching this lecture and pausing to take notes should take less than 15 minutes.
Instructions: Please click on the link above and study "The Multiplicative Identity" on page 34 of the textbook. The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, "The Multiplicative Identity"), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Multiplicative Property 5–27 on page 44 recognize addition laws and properties and apply these concepts. The solutions to these problems are located in the "Answers" section on page 49 section titled "Application –Area" through Example 4 on pages 42 and 43 of the textbook. The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, "Applications - Area"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Example 4 on page 43. This reading provides applications to the properties and laws of multiplication.
Reading this section should take approximately 15 minutes.
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Instructions: Please click on the link above and complete the odd-numbered exercises for 49–59 on pages 45 and 46 find the area of rectangles as well apply multiplication such as if a math tutor was paid $20 per hour and worked 20 hours, how much would the tutor get paid? inverse property of multiplication results in one.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Instructions: Please click on the link above and study "The Multiplicative Inverse Property" through Example 1 on pages 266 and 267 of the textbook. The material can also be located through the bookmark on the left side (4 Fractions, 4.3 Reciprocals, "The Multiplicative Inverse Property"), which will take you directly to the material. After you read and study this section, attempt the "You Try It" problem beside Example 1. Check your answer on page 267. This reading provides an example of the property and the formal definition of the Multiplicative Inverse Property.
Reading this section should take approximately 15 minutes.
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Link: College of the Redwoods: Department of Mathematics' Pre-Algebra Textbook, 2nd Edition: "Multiplication by Zero" (PDF)
Instructions: Please click on the link above and study the section titled "Multiplication by Zero" on pages 34 and 35 of the textbook. You may stop when you reach the section titled "The Associative Property of Multiplication." The material can also be located through the bookmark on the left side (1 Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, "Multiplication by Zero"), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Multiplication by Zero.
Reading this section should take approximately 15 minutes.
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Instructions: Please click on the link above and study the section titled "Division by Zero Is Undefined" on page 40 of the textbook, stopping at "Dividing Larger Whole Numbers." The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, "Division by Zero is Undefined"), which will take you directly to the reading. This reading provides an example of the property and the formal definition of why division by zero is undefined 69–75 on page 46 of the textbook. The apply multiplication laws and properties. why dividing by zero is undefined.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Instructions: Please click on the links above and take notes as you watch these videos. Watch the first presentation carefully two or three times until you are able to explain how the distributive property applies with an addition expression. Watch the second presentation carefully two or three times until you are able to explain how the distributive property applies with a subtraction expression.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Instructions: Please click on the link above and read "The Distributive Property" section through "Sample Set A." Then, complete "Practice Set A," exercises 1-7. The solutions to the problems are revealed below each problem. These problems will allow you to practice using the distributive property to simplify algebraic expressions "Number Properties Assessment" multiple-choice assignment. These assignments incorporate concepts from the Associative, Commutative, Identity, Inverse, and Distributive Properties. You may want to review these concepts associated with the questions by revisiting the Khan videos in this unit.
Completing this assessment should take approximately 30 minutes.
Note: You must be logged into your Saylor Foundation School account in order to access this assessment. If you do not yet have an account, you will be able to create one, free of charge, after clicking the link.
Unit 2: Order of Operations
In life, we often have procedures that everybody uses to avoid problems. When driving a car, for example: if you want to change lanes, you have to first look to make sure the lane is clear, activate your turn signal, check the lane again, move into the lane, and deactivate your turn signal. You do not move into the lane, activate your signal, make sure the lane is clear, and deactivate your signal. That can, and eventually will, cause a serious accident. In order to avoid costly errors, mathematicians had to agree on the series of steps that are needed to simplify expressions involving the four basic operations, grouping symbols, and exponents. This series of steps is known as the "order of operations" and is more commonly known as either PEMDAS or "Please Excuse My Dear Aunt Sally, she Left to Right." This tells us in which order to simplify the expression. (Tip: it is multiply OR divide and add OR subtract– whichever you see first.)
Mathematicians also needed a way to quickly write out a repeated multiplication problem, like 2 x 2 x 2 x 2 x 2, so they invented the use of exponents. This unit will introduce you to the process of working with basic exponents. As you go higher, you will learn more about exponents.
Another topic you will learn about in this unit is the concept of "greatest common factor." Mathematically, the greatest common factor (GCF) is the largest number you can divide two or more numbers by. In real life, it also makes appearances, both mathematical and non-mathematical. A detective trying to make connections between an arrested criminal and a suspected accomplice is going to be less interested in the facts that they have both eaten at McDonald's and both like strawberry milkshakes than in the fact that the suspected accomplice has been the criminal's best friend for twenty years. That fact is far greater to the investigation.
The last topic you will cover is related to greatest common factor but is different. It is known as "least common multiple." Here, you are trying to determine the smallest number that two numbers can both divide into. Again, it appears in life. Let's say your favorite radio station is running a promotion: every fifth caller receives free concert tickets, and every twelfth caller receives a free gas card. How long will it take before they have a caller who receives both prizes on the same phone call? This is an example of using the least common multiple. (In case you are wondering, it would be the 60th caller who won both prizes.)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how to solve problems finding the greatest common divisor/factor.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Instructions: Please click on the link above and read the entire section on "The Greatest Common Factor (GCF)" through "Sample Set A." Look closely at the section titled "A Method for Determining the Greatest Common Factor." Then, complete "Practice Set A," exercises 1–4 and the even-numbered problems for 6–20. The solutions to the problems are shown below each problem. These problems will allow you to practice finding the greatest common factor between numbers.
Reading this section and completing this activity should take approximately 1 hour.
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Instructions: Please click on the link above and complete the "Greatest Common Divisor" assignment. This assignment incorporates concepts from the greatest common divisor solve problems finding the least common multiple.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Instructions: Please click on the link above and read the "Least Common Multiple" section. Start with the "Multiples" section, and then complete "Practice Set A," exercises 1–3. Continue with the "Common Multiples" section, and then complete "Practice Set B," exercises 6–8. Finish by reading "The Least Common Multiple (LCM)" section, and then complete "Practice Set C," exercises 11–13. Then, complete the even-numbered problems for 16–44. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to practice finding the least common multiple between numbers.
Reading this section and completing this activity should take approximately 2 hours.
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Instructions: Please click on the link above and complete the "Least Common Multiple" assignment. This assignment incorporates concepts from the least common multiple Click on the link above and watch this video, which consists of two least common multiple and greatest common factor word problems. Pause the video after each problem has been given, and try to work out the answer on your own before coming back to the video to check your answer. It may help to review the concepts associated with the questions by revisiting the Khan videos in Unit 2.
Instructions: Please click on the link above and study the section titled "Adding Integers with Like Signs" on pages 115–117 of the textbook. You may stop when you reach the section titled "Adding Integers with Unlike Signs" on page 117 Examples 1 and 2 on page 115 and Example 3 on page 116. This material provides examples of adding two positive and two negative integers add integers with different signs.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Instructions: Please click on the link above and study the section titled "Adding Integers with Unlike Signs" on pages 117–119 of the textbook. You may stop when you reach the section titled "Properties of Addition of Integers" on page 119 Example 4 on page 117 and Example 5 on page 118. This material provides examples of adding one positive and one negative integer35 and 65–83 on pages 124 and 125 of the textbook. The exercises can also be located through the bookmark on the left side (2 The Integers, 2.2 Adding Integers, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to recognize addition properties as well as determine the profit and loss for a company. The solutions to these problems are located in the "Answers" section on page 126 of the textbook. The solutions page can also be located through the bookmark on the left side (2 The Integers, 2.2 AddingSubtracting Integers" on pages 128 through 132. The material can also be located through the bookmark on the left side (2 The Integers, 2.3 Subtracting Integers, "Subtracting Integers"), which will take you directly to the reading. After reading and studying the "Subtracting Integers" section, complete the "You Try It" problems beside Example 1 on page 129 and Example 4 on page 131. This material provides examples of subtracting integers and 51–59 on pages 133 and 134 of the textbook. The exercises can also be located through the bookmark on the left side (2 The Integers, 2.3 Subtracting Integers, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to recognize subtraction and properties and apply the concepts when dealing with a temperature change and comparing highest and lowest points. The solutions to these problems are located in the "Answers" section on page 135 of the textbook. The solutions page can also be located through the bookmark on the left side (2 The Integers, 2.3 Subtracting "Adding Negative Numbers" assessment. This quiz quiz, you will compute your answer and type it into the answer box. You may then click on "Check Answer" to see if you were correct or if you need to try again.
Instructions: Please click on the link above and complete the "Negative Number Word Problems" assignment. This assignment multiply integers with different signs.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Instructions: Please click on the link above and study the sections titled "Multiplication and Division of Integers" on pages 137 and 138 as well as "Multiplying by Minus One" and "The Product of Two Integers" on pages 140–142 of the textbook. The material can also be located through the bookmark on the left side (2 The Integers, 2.4 "Multiplication and Division of Integers") and (2 The Integers, 2.4 Multiplication and Division of Integers, "Multiplying by Minus One"), which will take you directly to the readings. After reading and studying these sections, complete the "You Try It" problems beside Examples 1 and 2 on pages 141 and 142. This material provides examples of multiplication of integers and rules associated with each problem 17–47 as well as problem 85 on pages 145 through 147 multiplication divide integers with different signs.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Instructions: Please click on the link above and study the section titled "Division of Integers" on pages 143 and 144 of the textbook. The material can also be located through the bookmark on the left side (2 The Integers, 2.4 Multiplication and Division of Integers, "Division of Integers"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Example 4 on page 144. This reading provides examples of division of integers and rules associated with each problem.
Reading this section and completing the exercises should take approximately 20 minutes.
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Instructions: Please click on the link above and complete the odd-numbered exercises for 61–83 division "Multiplying and Dividing Negative Numbers" assignment. This assignment incorporates concepts from multiplying and dividing explain how to write a problem in exponential notation. Watch the second presentation carefully two or three times until you are able to explain how to simplify a problem in exponential notation.
Watching these lectures and pausing to take notes should take approximately 15 minutes.
Instructions: Please click on the link above and read the entire section titled "Exponential Notation." Read the introductory text on exponential notation through "Sample Set A." Then, complete "Practice Set A," exercises 1–6. Continue with the "Reading Exponential Notation" subsection. Then, complete the odd-numbered exercises for 15–29 and 31–57. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to understand the basics of exponential notation.
Reading this section and completing this activity should take approximately 1 hour and simplify exponents with a positive and negative bases as well as exponents to the zero power.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Instructions: Please click on the link above and study Example 3 located on page 142 of the textbook. After reading and studying this example, complete the "You Try It" problems beside Example 3. This material provides an example of exponential notation with negative signs and bases.
Studying this example and attempting the "You Try It" example should take approximately 15 minutes.
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Instructions: Please click on the link above and complete the odd-numbered problems for 49–59 simplify exponent problems with negative bases complete the assessment that tests your knowledge on positive and zero exponents. This incorporates concepts from positive exponents with a positive or negative base and zero exponents. You can review the concepts associated with the questions with the Khan videos in Unit 2. Answer each question by inputting your calculation into the answer box. You may click on "Check Answer" to check if your answers are correct or if you need to try again.
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to apply the process of the order of operations.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Instructions: Please click on the link above and read the section titled "Order of Operations with Integers" on pages 148–150 of the textbook, stopping at "Evaluating Fractions." The material can also be located through the bookmark on the left side (2 The Integers, 2.5 Order of Operations with Integers), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 2 and 4 on page 149. This material provides examples of order of operations with integers. Note that this reading also covers the topic outlined in sub-subunit 2.5.2 problems for 1–39 on page 152 of the textbook. These exercises can also be located through the bookmark on the left side (2 The Integers, 2.5 Order of Operations with Integers, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to apply the process of the order of operations The topic of this sub-subunit is covered by the reading assigned below sub-subunit 2.5.1. To apply your knowledge of this topic, also complete the "You Try It" problem beside Example 3 on page 149.
Completing this activity should take approximately 15 minutes.
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Instructions: Please click on the link above and complete the odd-numbered problems for 45–53 as well as 59, 61, 67, 69, 73, 75, and 77 on page 153 45 minutes.
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Instructions: Please click on the link above and review the section titled "Evaluating Fractions," including Example 6, on page 150 of the textbook. The material can also be located through the bookmark on the left side (2 The Integers, 2.5 Order of Operations with Integers, "Evaluating Fractions"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problem beside Example 6 on page 150. This material provides examples of order of operations while evaluating fractions problems for 81–103 on pages 153 and 154, which tests your knowledge on order of operations. You can review these concepts associated with the questions with the Khan videos in subunit 2.5. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.
The very word – fractions – often chills the bones of math students. Working with fractions is easily the most dreaded, most feared topic in any math class. However, fractions are actually very easy to work with, if you learn the rules. After all, you cannot escape fractions in life; they are everywhere.
Have you ever eaten a Hershey's chocolate bar? It is conveniently broken up into little pieces, allowing you the option to devour in big bites or to savor tiny little morsels. Let's say you have a Hershey's bar sitting on your dining room table. Your oldest child cheerfully announces that she has eaten half of the bar, and her younger brother has eaten a quarter of the bar. If you know how to work with fractions, you can quickly calculate how much of the bar is left.
Fractions appear in many other situations such as sale prices, measurements, money, gardening; the list of applications is virtually endless. In this unit, you will learn to work with fractions. You will learn how to reduce them, how to add/subtract/multiply/divide them, and how to apply them to real-world situations. One suggestion: never show fear. Fractions can smell fear.
Instructions: Please click on the links above and take notes as you watch these videos (3 minutes each). Watch the first presentation carefully two or three times until you are able to identify the numerator and denominator of a fraction. Watch the second presentation carefully two or three times until you are able to identify parts of a fraction.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Instructions: Please click on the link above and read "Fractions of Whole Numbers," "The Parts of a Fraction," and "Reading and Writing Fractions" sections. Then, complete "Practice Set A," exercises 1–5 and "Practice Set B," exercises 6–17. The solutions to the problems are shown directly below each problem. These problems will allow you to practice identifying numerators and denominators as well as writing fractions by using words every fourth problem for 18–46 and the even-numbered problems for 48-64. The solutions to the problems are shown directly below each problem. These problems will allow you to practice identifying numerators and denominators. This includes determining the numerator and denominator from problems such as "you need ¾ of a cup of sugar to make a batch of cookies."
Completing these exercises should take approximately 30 identify equivalent fractions. Watch the second presentation carefully two or three times until you are able to compare fractions.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Instructions: Please click on the link above and read the "Equivalent Fractions" section through "Sample Set A." Then, complete "Practice Set A," exercises 1–5. The solutions to the problems are shown directly below each problem. These problems will allow you to practice identifying if pairs of fractions are equivalent assignments, which test your knowledge on equivalent fractions. You can review the concepts associated with the questions the Khan videos in subunit 3 odd-numbered problems 11–25. The solutions to the problems are shown directly below each problem. These problems will allow you to determine a proper fraction, improper fraction, or a mixed number.
Completing these exercises mixed numbers and improper fractions.
Watching this lecture and pausing to take notes should take approximately 30 minutes 15 minutes.
Instructions: Please click on the link above and review the section titled "Changing Improper Fractions to Mixed Fractions" on pages 293–295 of the textbook, stopping at "Multiplying and Dividing Mixed Fractions." The material can also be located through the bookmark on the left side (4 Fractions, 4.5 Multiplying and Dividing Mixed Fractions, "Changing Improper Fractions to Mixed Fractions"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 4–6 on pages 294 and 295. This material provides examples of converting an improper fraction to a mixed fraction.
Reading this section and completing the exercises should take approximately 30 minutes.
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Instructions: Please click on the link above and read the "Converting Improper Fractions to Mixed Numbers" section. Then, complete "Practice Set A," exercises 1–6. The solutions to the problems are shown directly below each problem. These problems will allow you to practice converting an improper fraction to a mixed numbernumber exercises 27–39. The solutions to the problems are shown directly below each problem. These problems will allow you to practice converting an improper fraction to a mixed number.
Completing these exercises should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above 30 minutes 41–55. The solutions to the problems are shown directly below each problem. These problems will allow you to practice converting a mixed number and an improper fraction assignment that tests your knowledge of converting fractions. This assignment incorporates concepts from converting mixed numbers to improper fractions and vice versa. You can review the concepts associated with the questions with the Khan videos in sub-subunit 3.1.3Reducing Fractions to Lowest Term" section. Then, complete "Practice Set B," exercises 6–11 and "Practice Set C," exercises 12–17. The solutions to the problems are shown directly below each problem. These problems will allow you to practice reducing fractions to their lowest terms problems for 61–77 as well as the odd-numbered problems for 89–113. The solutions to the problems are shown directly below each problem. These problems will allow you to practice reducing fractions to their lowest terms as well as determine fractional parts of a day solve an application of raising fractions to highest terms.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Instructions: Please click on the link above and read the "Raising Fractions to Higher Terms" section. Then, complete "Practice Set D," exercises 18–22. The solutions to the problems are shown directly below each problem. These problems will allow you to find the missing numerator and denominator 39–53. The solutions to the problems are shown directly below each problem. These problems will allow you to practice reducing fractions to their lowest terms rewrite fractions with a least common denominator.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Instructions: Please click on the link above and read the "Addition of Fractions with Like Denominators" section. Then, complete "Practice Set A," exercises 1–4. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to practice adding fraction fn adding fractions. This assignment incorporates concepts from addingSubtraction of Fractions with Like Denominators" section. Then, complete "Practice Set B," exercises 5–9. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to practice subtracting fractions with like1. Please click on the link above and complete the odd-numbered problems for 11–35 and 39. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to practice adding and subtracting fractions and read the "Addition and Subtraction of Fractions" section stopping at "Sample Set A," Example 3. Then, complete "Practice Set A," exercise 1. The solutions to the problem can be revealed by the "Show Solution" link under each problem. This reading and exercise will allow you to practice adding fractions with unlike denominators assignment that tests your knowledge of adding fractions. This assignment incorporates concepts from adding starting at "Sample Set A," Example 3, read through the "Addition and Subtraction of Fractions" section. Then, complete "Practice Set A," exercises 2–5. The solutions to the problems are shown directly below each problem. These problems will allow you to practice subtracting fractions with unlike3. Please click on the link above and complete the even-numbered problems 6–36. The solutions to the problems are shown directly below each problem. These problems will allow you to add and subtract fractions with unlike denominators Fractions with Different Denominators" on pages 277–279 of the textbook. The material may also be located through the bookmark on the left side (4 Fractions, 4.4 Adding and Subtracting Fractions, "Adding and Subtracting Fractions with Different Denominators"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 4 and 5 on page 279. This material provides examples of subtracting fractions with different signs103 on pages 287 through 288 of the textbook. These exercises can also be located through the bookmark on the left side (4 Fractions, 4.4 Adding and Subtracting Fractions, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to add and subtract fractions with different signs. The solutions to these problems are located in the "Answers" section on page 289 of the textbook. The solutions page can also be located through the bookmark on the left side (4 Fractions, 4.4 Adding and Subtracting Fractions that tests your knowledge on adding and subtracting fractions. This quiz incorporates concepts from adding and subtracting fractions with like and View each presentation carefully two or three times until you are able add mixed numbers with common denominators.
Watching these lectures and pausing to take notes should take approximately 15 minutes.
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able subtract mixed numbers with common denominators.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Instructions: Please click on the links above and take notes as you watch these videos. View each presentation carefully two or three times until you are able add mixed numbers with unlike denominators.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Instructions: Please click on the link above and study the "Adding Mixed Fractions" section on pages 301–303 of the textbook. The material may also be located through the bookmark on the left side (4 Fractions, 4.6 Adding and Subtracting Mixed Fractions, "Adding Mixed Fractions"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 1, 2, and 3 on pages 301 and 302. This material provides examples of subtracting fractions with different signs.
Reading this section and completing the exercises should take approximately 1 hour.
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Instructions: Please click on the links above and take notes as you watch these videos. View each presentation carefully two or three times until you are able subtract mixed numbers with unlike denominators.
Watching these lectures and pausing to take notes should take approximately 45 minutes.
Instructions: Please click on the link above and study the "Subtracting Mixed Fractions" section 9 on pages 304–307 of the textbook, stopping at Example 9. The material may also be located through the bookmark on the left side (4 Fractions, 4.6 Adding and Subtracting Mixed Fractions, "Subtracting Mixed Fractions"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems next to Examples 5 through 8 on pages 304–306. This material provides examples of subtracting mixed fractions.
Reading this section and completing the exercises should take approximately 45 minutes.
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Instructions: This topic is covered by the reading and activity in sub-subunits 3.2.2.1, 3.2.2.2, and 3.2.2.3. Please click on the link above and complete the even-numbered problems for 6–36. The solutions to the problems are shown directly below each problem. These problems will allow you to practice with the addition and subtraction of mixed assignments that tests your knowledge of adding and subtracting mixed numbers. These assignments incorporate concepts from adding and subtracting mixed numbers with like and unlike denominators. You can review the concepts associated with the questions with the Khan videos in sub-subunit 3.2.2. Compute the answer to the given problem, and input your response View each presentation carefully two or three times until you are able understand applications where you add and subtract.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Instructions: Please click on the link above and review the "Adding and Subtracting Mixed Fractions" section through Example 9 on pages 301–307 of the textbook; you read this section in sub-subunits 3.2.1 and 3.2.2. The material may also be located through the bookmark on the left side (4 Fractions, 4.6 Adding and Subtracting Mixed Fractions), which will take you directly to the reading. After reviewing this section, complete the "You Try It" problem next to Example 4 on page 303 and Example 9 on page 307. This material contains applications of adding and subtracting fractions.
Reading this section and completing the exercises should take approximately 15 minutes.
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Instructions: Please click on the links above and complete the following problems: problem 39 for "Addition and Subtraction of Fractions with Like Denominators;" problems 50, 52, and 54 for "Addition and Subtraction of Fractions with Unlike Denominators;" problems 42, 44, and 46 for "Addition and Subtraction of Mixed Numbers." The solutions to the problems can be revealed by the "Show Solution" link below each problem, or may be found directly below the problem. These problems will allow you to practice adding and subtracting fractions with unlike denominators, which include finding amounts needed for recipes and finding the cost after an increase.
Reading this section and completing these exercises should take approximately 30 minutes.
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Instructions: Please click on the link above and study the "Multiply Fractions" section on pages 249–252, stopping at Example 5 on page 252 of the textbook. The material may also be located through the bookmark on the left side (4 Fractions, 4.2 Multiplying Fractions), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems next to Examples 2, 3, and 4 on pages 251 and 252. This material contains examples of multiplying 5–27 on page 260 multiply fractionsMultiplication of Mixed Numbers" section stopping at the "Powers and Roots of Fraction" section. Then, complete "Practice Set C," exercises 17–20. The solutions to the problems are shown directly below each problem. These problems will allow you to practice multiplying 25–47 on pages 297 and 298 multiplyDivision" section on pages 267 and 268 of the textbook. The material may also be located through the bookmark on the left side (4 Fractions, 4.3 Dividing Fractions, "Division"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems next to Examples 2, 3, and 4 on pages 267 and 268. This material contains examples of dividing 33–67 on page 271 of the textbook. These exercises can also be located through the bookmark on the left side (4 Fractions, 4.3 Dividing Fractions, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to divide fractions. The solutions to these problems are located in the "Answers" section on page 273 of the textbook. The solutions page can also be located through the bookmark on the left side (4 Fractions, 4.3 Dividing Examples 7–9 under "Division of Fractions" section, stopping at the "Powers and Roots of Fraction" section. Then, complete "Practice Set B," exercises 11–13. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to practice dividing 49–71 on pages 298 and 299 divide apply the multiplication of fractions to a word problem. Watch the second presentation carefully two or three times until you are able to apply the division of fractions to a word problem.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Instructions: Please click on the link above and study the "Parallelograms" and "Triangles" sections on pages 255–258 of the textbook, stopping at "Identifying the Base and Altitude." The material may also be located through the bookmark on the left side (4 Fractions, 4.3 Dividing Fractions, "Parallelograms"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 8 and 9 on pages 256 and 257. This material contains examples of dividing fractions 57–69 on page 262 apply multiplying fractions by finding the areas of parallelograms and triangles problems 73 and 75 on page 299 of the textbook. These exercises can also be located through the bookmark on the left side (4 Fractions, 4.5 Multiplying and Dividing Mixed Fractions, "Exercises"), which will take you directly to the material. These exercises will provide you with the opportunity to practice dividing fractions by dividing fields and cutting jewelry into pieces assessments that test your knowledge on applications of multiplying and dividing fractions. You can review the concepts associated with these questions with the Khan videos in sub-subunits 3.2.4 and 3.2 read "The Order of Operations" section, stopping at "Sample Set A," Example 5. Then, complete "Practice Set A," exercises 1–5 and 7. The solutions to the problems are shown directly below each problem. These problems will allow you to practice the order of operations with 17–35 on pages 321 and 322 of the textbook. These exercises can also be located through the bookmark on the left side (4 Fractions, 4.7 Order of Operations with Fractions, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to practice dividing fractions. The solutions to these problems are located in the "Answers" section on page 324 of the textbook. The solutions page can also be located through the bookmark on the left side (4 Fractions, 4.7 Order of Operations withSimple Fractions and Complex Fractions" and "Converting Complex Fractions to Simple Fractions" sections, stopping at "Sample Set A," Example 5. Then, complete "Practice Set A," exercises 1–6. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to practice the order of operations with complexnumber problems for 7–25. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to use order of operations to simplify complex fractions.
Reading this section and completing the exercises should take approximately 45 minutes.
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Unit 4: Decimals
Congratulations on surviving fractions! In this unit, you will turn your attention to the "fraternal twin" of fractions: decimals. Yes, decimals are really just fractions in disguise! Who knew? For example, look at (American) money. A dollar is 100 cents; a quarter is 25 cents, or in decimal form, $0.25. The fraction 25/100 reduces to ¼, which is read as "one-quarter." Decimals are fractions, and fractions are decimals. It's all in how you write them.
Decimals are everywhere, just like fractions. You cannot go shopping without encountering decimals. Whether you are adding up totals on your shopping list, calculating your change, or even just measuring the length of something, you will use decimals. If you add up all your purchases, find that your total comes to $17.31, and you hand the cashier $20, you need to know how to determine your change to make sure the cashier gives you back the correct amount of money. If you are measuring the length of your wall in order to fit a couch there, you might find that the wall's length is in between two lengths, measuring at, say, 11.5 ft. You have to know how to deal with decimals to approximate distances.
In this unit, you will learn how to add/subtract/multiply/divide decimals as well as how to convert between fraction and decimal form.
Instructions: Please click on the links above and take notes as you watch these videos. Watch the first presentation carefully two or three times until you are able to understand place value. Watch the second presentation carefully two or three times until you are able to write decimals in word form.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Instructions: Please click on the link above and study the "Introduction to Decimals," "Decimal Notation," and "Pronouncing Decimal Numbers" sections on pages 342–346 of the textbook, stopping at "Decimals to Fractions." The material may also be located through the bookmark on the left side (5 Decimals, 5.1 Introduction to Decimals), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 1–6 on pages 344–346. This material contains examples of decimal notation and pronouncing decimal numbers.
Reading these sections39 on pages 353 and 354 writing out decimals numbers in expanded form and words. The solutions to these problems are located in the "Answers read the "Rounding Decimal Numbers" section through "Sample Set A." Then, complete "Practice Set A," exercises 1–7. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to round decimals to various positions even-numbered problems for 8–22. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will help you practice rounding decimals to various positions.
Reading this section and completing the exercises should take approximately 45 minutes.
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Instructions: Please click on the link above and study the "Comparing Decimals" section on pages 350–352 of the textbook. The material may also be located through the bookmark on the left side (5 Decimals, 5.1 Introduction to Decimals, "Comparing Decimals"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 11 and 12 on pages 351 and 352. This material contains examples of comparing 81–91 on page 355 write out decimals numbers in expanded form and words. The solutions to these problems are located in the "Answers read the "Converting a Fraction to a Decimal" section, stopping at "Sample Set A," Example 5. Then, complete "Practice Set A," exercises 1–4. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to convert fractions into decimals 7–31 and 37–53. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to convert fractions into decimals assignment that tests your knowledge onf converting fractions to decimals. You can review the concepts associated with the questions with the Khan videos in sub-subunit 4.1.4Converting an Ordinary Decimal to a Fraction" section through "Sample Set A," and complete "Practice Set A," exercises 1–4 9–27 assignments that test your knowledge of converting decimals to fractions. You can review the concepts associated with the questions with the Khan videos in sub-subunit 4.1.4Instructions: Please click on the links above and take notes as you watch these videos. View these presentations carefully two or three times until you are able to convert repeating decimals to fractions.
Watching these lectures and pausing to take notes should take approximately 45 minutes.
Instructions: Please click on the link above and study the "Adding Decimals" section on pages 359–361 of the textbook, stopping at "Subtracting Decimals." The material may also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, "Adding Decimals"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 1–4 on pages 359–361. This material contains examples of adding decimal numbers11 adding decimal assignments that test your knowledge of adding decimals. You can review the concepts associated with the questions with the Khan videos in sub-subunit 4.2.1 subtract decimals. Watch the second presentation carefully two or three times until you are able to add and subtract decimals in application.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Instructions: Please click on the link above and study the "Subtracting Decimals" section on pages 361 and 362 of the textbook, stopping at "Adding and Subtracting Signed Decimal Numbers." The material may also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, "Subtracting Decimals"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 5 and 6 on pages 361 and 362. This material contains examples of subtracting23 and 81–87 apply the addition and subtraction of decimals assignments that test your knowledge of subtracting decimals. You can review the concepts associated with the questions with the Khan videos in sub-subunit 4.2 Signed Decimal Numbers" section on pages 362–364 of the textbook. The material may also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, "Adding and Subtracting Signed Decimal Numbers"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 7–10 on pages 362–364. This material contains examples of adding and subtracting signed 25–63 add and subtract signed decimalsMultiplying Decimals" section on pages 370–373 of the textbook, stopping at "Multiplying Signed Decimal Numbers." Then, read "The Circle" section on pages 376–380. The material may also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals) and (5 Decimals, 5.3 Multiplying Decimals, "The Circle"), which will take you directly to the readings. After reading and studying these sections, complete the "You Try It" problems beside Examples 1–3 on pages 370–373 and Examples 9 and 10 on pages 378–380. This material contains examples of multiplying decimal numbers and its applications-27 and 89-105 decimals numbers and study applications of multiplying decimals, which include finding the total cost of items. The solutions to these problems are located in the "Answers" section on page 384 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals the "Multiplying Signed Decimal Numbers" section on pages 373 and 374 of the textbook, stopping at "Order of Operations." The material may also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, "Multiplying Signed Decimal Numbers"), which will take you directly to the material. After reading and studying this section, complete the "You Try It" problems beside Examples 4 and 5 on pages 373 and 374. This reading contains examples of multiplying signed 29–55 signed decimals numbers. The solutions to these problems are located in the "Answers" section on page 385 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying multiplying decimals. You can review the concepts associated with the questions with the Khan videos in sub-subunit 4.2.2.1, and 4.2.2Dividing Decimals" on pages 386–390 of the textbook, stopping at "Dividing Signed Decimal Numbers." The material may also be located through the bookmark on the left side (5 Decimals, 5.4 Dividing Decimals), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 1–3 on pages 387–390. This reading contains examples and applications of dividing39 and 107–113 on page 395 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.4 Dividing Decimals, "Exercises"), which will take you directly to the material. These exercises will provide you with the opportunity to divide decimals numbers and study applications of dividing decimals, which include finding averages for a project "Dividing Signed Decimal Numbers" section on pages 390 and 391 of the textbook, stopping at "Rounding." The material may also be located through the bookmark on the left side (5 Decimals, 5.4 Dividing Decimals, "Dividing Signed Decimal Numbers"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Example 4 on page 390. This reading contains examples of dividing signed decimal numbers exercises for 41–63 on page 395 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.4 Dividing Decimals, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to divide signed decimals numbers dividing decimals. You can review the concepts associated with the questions with the Khan videos in sub-subunit 4.2.3.1, and 4.2.3.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.
Link: College of the Redwoods: Department of Mathematics' Pre-Algebra Textbook, 2nd Edition: "Order of Operations" (PDF)
Instructions: Please click on the link above and study the "Order of Operations" section on pages 374 and 375 of the textbook, stopping at "Powers of Ten." Then, read "Order of Operations" through Example 8 on pages 393 and 394. The material may also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, "Order of Operations")and (5 Decimals, 5.4 Dividing Decimals, "Order of Operations"), which will take you directly to the readings. Review only the processes involved with each problem and do not worry about substituting into the expression. This material contains examples of order of operations79 on page 382 and 89–99 on page 397 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, "Exercises") and (5 Decimals, 5.4 Dividing Decimals, "Exercises"), which will take you directly to the assignments. These exercises will provide you with the opportunity to apply order of operations to decimal numbers. The solutions to these problems are located in the "Answers" section on page 384 and page 399 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, "Answers") andUnit 5: Ratios and Proportions
In this unit, you will study ratios and proportions. These are mathematical concepts you use all the time, probably without even realizing it. Have you ever been in line at a donut store, comparing the number of chocolate donuts to the number of customers? That's a ratio. Perhaps you are telling your vet how many times a week your dog drags you outside for an extended walk. That's also a ratio. Have you ever been driving on a trip, going around 75 mph, and wanted to know how long it would take to reach your destination, which was only 35 miles away? You would find the answer using a proportion. In sports, statisticians use proportions to predict an athlete's production, based on what they've done up to that point. In this unit, you will learn how to write ratios, how to set-up and solve proportions, and how to apply these skills to real-world experiences.
Instructions: Please click on the link above and study the "Introduction to Ratios and Rates" section on pages 449–451 of the textbook, stopping at "Rates." The material may also be located through the bookmark on the left side (6 Ratio and Proportion, 6.1 Introduction to Ratios and Rates), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 1 and 2 on pages 449–451. This material contains examples on ratios write and simplify ratios these videos. Watch the first presentation carefully two or three times until you are able to find unit rates. Watch the second presentation carefully two or three times until you are able to find unit prices.
Watching these lectures and pausing to take notes should take approximately 15 minutes.
Instructions: Please click on the link above and study the "Rates" and "Unit Rates" sections on pages 451–453. The material may also be located through the bookmark on the left side (6 Ratio and Proportion, 6.1 Introduction to Ratios and Rates, "Rates"), which will take you directly to the reading. After reading and studying these sections, complete the "You Try It" problems beside Examples 3–6 on pages 451–453. This material contains examples on rates and unit rates 23–37 write and simplify rates, which includes comparing rates to see the better deal on an item assignment that tests your knowledge of ratio word problems. This assignment incorporates concepts of ratios. You can review the concepts associated with the questions with the Khan video in sub-subunit 5Introduction to Ratios and Rates" section on pages 456–459 of the textbook, stopping at "Example 4." The material may also be located through the bookmark on the left side (6 Ratio and Proportion, 6.2 Introduction to Proportions), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 1–3 on pages 457–459. This material contains examples on an introduction to proportions13, and 17, 19, 23, 27, 29, 31, and 35 on page 463 solve proportions review the "Introduction to Ratios and Rates" section through Example 4 on pages 456–459 of the textbook; note that you already studied this material in sub-subunit 5.2.1. The material may also be located through the bookmark on the left side (6 Ratio and Proportion, 6.2 Introduction to Proportions), which will take you directly to the reading. After reviewing this section, complete the "You Try It" problems beside Example 4 on page 459. This material contains examples on an introduction to proportions 37-53 on pages 464 and 465 write and solve proportions, which include finding the cost of an item the "Applications of a Proportion" section. Then, complete "Practice Set A," exercises 1–5. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to practice applications of proportions odd-numbered problems for 7–25. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to practice applications of proportions.
Reading this section and completing the exercises should take approximately 45 minutes.
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Instructions: Please click on the links above and complete the assignments that test your knowledge on proportion word problems. These assignments incorporate concepts of ratios and proportions. You can review the concepts associated with the questions with the Khan video in sub-subunit 5.2In this course, you have already studied fractions and decimals. In this unit, you will study the other "fraternal twin" of fractions: percents, which are actually fractions and decimals in disguise. (Perhaps we should call them "fraternal triplets.") Going back to our example with decimals: we established that a dollar is 100 cents, a quarter is 25 cents, and the fraction form would be 25/100, which reduces to ¼. A percentage is simply a fraction whose denominator is 100. Therefore, 25/100 becomes 25%. Because it is also 0.25, the percent is a fraction which is a decimal, which in turn is a percent. It's the Circle of Math. (Cue music from "The Lion King.")
Percents appear all over the place in life, especially when it comes to buying products. If you are considering whether to buy clothes at one store that has a sale with 65% off or a second store that has a sale with 50% off and an additional 15% discount off the sale price, you might be surprised to learn that the two sales are not the same. For those who follow the stock market, you might see the news talking about how your stock has had an increase of 70%. What does that mean?
In this unit, you will learn the rules of percentages and how to apply them. You will learn to convert percentages to and from fractions and decimals. You will learn about percent increase and decrease, which comes into play when you are out shopping. You will also learn (to the delight of shoppers everywhere) exactly how to calculate sale prices, restaurant tips, and other similar items.
Instructions: Please click on the link above and take notes as you watch this video. Watch this presentation carefully two or three times until you are able to understand how to convert a decimal to a percent and a percent to a decimal.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Instructions: Please click on the links above and study the "Changing a Percent to a Decimal" and "Changing a Decimal to a Percent" sections on pages 504 and 505 of the textbook. The material may also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, "Changing a Percent to a Decimal), which will take you directly to the reading. After reading and studying these sections, complete the "You Try It" problems beside Examples 4–7 on pages 504 and 505. This reading contains examples on changing a percent to a decimal and vice versa.
Reading this section should take approximately 30 minutes.
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Instructions: Please click on the link above and complete the odd-numbered exercises for 19–49 on pages 508 and 509 video. View these presentations carefully two or three times until you are able to understand how to convert a fraction to a percent and a percent to a fraction.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Instructions: Please click on the links above and study the "Changing a Percent to a Fraction" section on pages 502–504 of the textbook, stopping at "Changing a Percent to a Decimal." Then, study "Changing a Fraction to a Percent" on pages 506–508 of the textbook. The material may also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, "Changing a Percent to a Fraction"), and (7 Percent, 7.1 Percent, Decimal, Fractions, "Changing a Fraction to a Percent"), which will take you directly to the readings. After reading and studying these sections, complete the "You Try It" problems beside Examples 1–4 on pages 502–504 and Examples 8–10 on pages 506–508. This reading contains examples of changing a percent to a fraction and vice versa.
Reading this section and completing the exercises should take approximately 1 hour.
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Instructions: Please click on the links above and complete the odd-numbered exercises for 1–17 and 51–79 on pages 508–510 "Find a Given Percent of a Given Number" on pages 512–514 of the textbook, stopping at "Find a Percent Given Two Numbers." The material may also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, "Find a Given Percent of a Given Number), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 1–3 on pages 512–514. This reading contains examples of finding a given percent of a given a percent given two numbers.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Instructions: Please click on the link above and study "Find a Percent Given Two Numbers" on pages 514–516 of the textbook, stopping at "Find a Number That Is a Given Percent of Another Number." 4 and 5 on pages 514–516. This reading contains examples of finding a percent when given two numbers.
Reading this section should take approximately 30 minutes.
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Instructions: Please click on the link above and study "Find a Number That Is a Given Percent of Another Number" on pages 516 and 517 of the textbook. 6 and 7 on pages 516 and 517. This material contains examples of finding a number that is a given percent of another 1–49 on page 518 519 of the textbook. The solutions page can also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions "7.3 General Applications of Percent"on pages 521–524 of the textbook. The material may also be located through the bookmark on the left side (7 Percent, 7.3 General Applications of Percent), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 1–4 on pages 521–524. This material contains examples of percent applications37 on pages 525–527 of the textbook. These exercises can also be located through the bookmark on the left side (7 Percent, 7.3 General Applications of Percent, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to apply concepts of percent. This includes determining the percent that you earned on a test, finding the amount of a population who fall under certain criteria, and finding the sales tax on specific items. The solutions to these problems are located in the "Answers" section on page 528 of the textbook. The solutions page can also be located through the bookmark on the left side (7 Percent, 7.3 General Applications of Percent the amount that grows or decreases by a percent.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Instructions: Please click on the link above and study the "7.4 Percent Increase or Decrease" section on pages 529–537 of the textbook. The material may also be located through the bookmark on the left side (7 Percent, 7.4 Percent Increase or Decrease), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 1–6 on pages 529–537. This material contains applications of percent increase or decrease–37 on pages 538–541 of the textbook. These exercises can also be located through the bookmark on the left side (7 Percent, 7.4 Percent Increase or Decrease, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to apply the percent of increase or decrease, which includes how much an item is discounted at the store, the percent of increase in a salary, and finding the new cost of a product. The solutions to these problems are located in the "Answers" section on page 541 of the textbook. The solutions page can also be located through the bookmark on the left side (7 Percent, 7.4 Percent Increase or Decrease, "Answers").
Completing this activity should take approximately 1 hour.
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Instructions: Please click on the links above and complete these assignments, which test your knowledge of percent word problems. These assignments incorporate concepts of solving applications of percents. You can review the concepts associated with the questions with the Khan videos in sub-subunit 6.3.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.
The list of available graph and chart applications is endless. You may have seen applications such as trying to understand voting trends and demographics for presidential campaigns and elections. Or, a business may require graphs and charts to forecast employment growth for a specific time period. Or, you may belong to a fantasy football or baseball team, and you may need to analyze the history of points that players have against certain teams as well as other statistics. In reading a news article that provides a chart, you may want to determine what information the chart provides. Using graphs and charts is a way to convey data that is easy to understand for a specific audience. Knowing how to read and interpret these items is of utmost importance in life, because charts and graphs can be manipulated to misrepresent the data.
This unit discusses various topics when using graphs and charts in mathematics. For each type of graph in the unit, you will need to create a graph as well as interpret the results of this type of graph. You will learn to create charts and graphs (stem-and-leaf plots, line graphs, bar graphs, box-and-whisker plots, circle or pie graphs, and pictographs), read charts, and work with the measures of central tendency for a data set. (We promise it is not as scary as it sounds!)
Instructions: Please click on the links above and take notes as you watch these videos. Watch these presentations carefully two or three times until you are able to understand how to find the mean, median, mode, and range of a set of numbers.
Watching these lectures and pausing to take notes should take approximately 1 hour.
Instructions: Please click on the link above and read the "Summarizing Data" section, stopping at the "Percentiles" section, and complete the exercise associated with each topic. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to practice and understand terms related to the measure of central tendency exercises 1-4, 5b, 5c, 7-8. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to practice and understand terms related to the measure of central tendency stem-and-leaf plot.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Instructions: Please click on the link above and read the "Stem-and-Leaf Graphs" section, stopping at the "Line Graphs" section. Then, complete Example 2. The solution to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to practice how to read and create a stem-and-leaf graph 1m, 3m, and 23. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to read and create a stem-and-leaf graph on reading stem and leaf plots. You can review the concepts associated with the questions with the Khan videos in subunit 7 understand how to read line graphs. Watch the second presentation carefully two or three times until you are able to understand how line graphs can be misleading.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Instructions: Please click on the link above and complete the assignment on reading line charts. You can review the concepts associated with the questions with the Khan videos in subunit 7 take notes as you watch this video. Watch this presentation carefully two or three times until you are able to understand how to find information from a bar graph.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Instructions: Please click on the links above and complete these assignments, which test your knowledge of reading and creating bar graphs. These assignments incorporate concepts of reading and creating bar charts. You can review the concepts associated with the questions with the Khan videos in subunit 7.4 Watch the first presentation carefully two or three times until you are able to understand how to read a box-and-whisker plot. Watch the second presentation carefully two or three times until you are able to understand how to create a box-and-whisker plot.
Watching these lectures and pausing to take notes should take approximately 1 hour.
Instructions: Please click on the link above and read the "Box Plots" section. Then, complete Examples 1 and 2. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to practice how to read and create a box-and-whisker plot 5a-e, 17a, 17b, 17e, and 21. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to read and create a box-and-whisker plot assessment, which tests your knowledge on creating box-and-whisker plots. This quiz incorporates concepts of creating box-and-whisker plots, means, and quartiles. You can review the concepts associated with the questions with the Khan videos in subunit 7 take notes as you watch this video. Watch this presentation carefully two or three times until you are able to understand how to find information from a pie/circle graph.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Instructions: Please click on the link above and study the "Pie Charts" section on pages 552–559 of the textbook. The material may also be located through the bookmark on the left side (7 Percent, 7.6 Pie Charts), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 1 and 2 on pages 554 and 556. This material contains examples on how to interpret and represent data with a pie chart.
Reading this section and completing the exercises should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
Instructions: Please click on the link above and complete the odd-numbered exercises for 1–29 on pages 560–565 of the textbook. These exercises can also be located through the bookmark on the left side (7 Percent, 7.6 Pie Charts, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to interpret and represent data with a pie chart. The solutions to these problems are located in the "Answers" section on page 566 of the textbook. The solutions page can also be located through the bookmark on the left side (7 Percent, 7.6 Pie Charts, "Answers").
This activity will take approximately 2 hours to complete pictograph.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Instructions: Please click on the links above and complete the assignments, which test your knowledge of interpreting pictographs. You can review the concepts associated with the questions with the Khan videos in subunit 7.7 |
Elementary Statistics with CD : A Step by Step Approach with Formula Card and Data Cd
9780077460396
ISBN:
0077460391
Edition: 8 Pub Date: 2011 Publisher: McGraw-Hill Higher Education
Summary: Be guided through every step of the fundamentals of statistics. It is a great introduction to statistics for college students who have a basic grasp of algebra. It covers all the main concepts effectively and provides a lot of opportunity for practical application. Students are taught problem solving using detailed instructions and examples. It also focuses on the different digital applications used in statistics suc...h as Excel, graphing calculators and MINITAB. It also complements an online course so students can receive more from their course and excellent feedback from the online platform. We offer many top quality used statistics textbooks for college students.
Bluman is the author of Elementary Statistics with CD : A Step by Step Approach with Formula Card and Data Cd, published 2011 under ISBN 9780077460396 and 0077460391. Five hundred fifty eight Elementary Statistics with CD : A Step by Step Approach with Formula Card and Data Cd textbooks are available for sale on ValoreBooks.com, one hundred thirty nine used from the cheapest price of $38.94, or buy new starting at $170.078th Edition. Pre-loved books for the budget-conscious consumer. With more than 50 years' experience, we aim to please with immediate shipping and fast, friendly service. All Comes with CD only. This is an international edition. Brand New 8th Ed. Same Content High Quality Color and Paper as US Edition, International Softcover Edition. Ship within 2 [more]
ALTERNATE EDITION: Comes with CD only. This is an international edition. Brand New 8. Expedited shipping within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions.[less] |
Math 121 -- Calculus III
Calculus III is the third semester of calculus, taken by first-year students
who have sufficient calculus background from high school or by students who have taken
Calculus II (Math 114 and either 115 or 116). It covers both differential
and integral multivariable calculus,
Informal geometric arguments take the place of formal mathematical reasoning, so
students who desire a rigorous treatment of the subject should take Math 215-216 instead.
Math 121 includes a variety of applications in all disciplines, and is appropriate
for first-year students who have not yet decided on a major.
Depending on the instructor, the mix of applications may favor either the
natural or social sciences, and students choosing this course should be sure to determine
this emphasis.
Math 121 is accessible to students who have taken only a year of calculus in high school,
yet it has a visual appeal and wealth of applications that far surpasses single variable calculus.
It is excellent preparation for many 200-level electives in mathematics,
as well as courses in chemistry and physics. It may substitute for Math 216 in the requirements for
the math major and minor and as a prerequisite for Math 317 and Math 333,
but Math 216 provides better preparation for these courses.
Prerequisites: Math 114 and either 115 or 116, or advanced placement
Who should take this course?
Students considering a major in the natural sciences, or anyone else looking for
a thorough treatment of multivariable calculus
Students considering a major or minor in mathematics who want to take multivariable calculus
before linear algebra
Students who have wish to build on their knowledge of single-variable calculus to enjoy the
visual appeal and wealth of applications of functions whose graphs are in 3-space and beyond. |
As there are two basic types of data "continuous" and discrete. So, in discrete mathematics we study discrete data which is not continuous or in some regular pattern.Topics in discrete maths are integers,graphs and statements in logic. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. More simply,we can say that discrete maths deals with countable sets.
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Steps
1
Know what discrete mathematics is not. Discrete mathematics is more defined by what it is not, rather than what it is.[1] It encompasses anything except quantities that vary smoothly ("continuous mathematics") such as calculus and analysis.
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2
Determine whether the set of objects studied in discrete mathematics is finite or infinite.
For broader view of discrete mathematics
1
Research Theoretical computer science. Theoretical computer science includes areas of discrete mathematics relevant to computing. It is based on graph theory and logic. Computability studies what can be computed in principle, and has close ties to logic, while complexity studies the time taken by computations.
2
Research Information theory. Information theory involves the quantification of information. Closely related is coding theory which is used to design efficient and reliable data transmission and storage methods.
3
Research Logic. Logic is the study of the principles of valid reasoning and inference, as well as of consistency, soundness, and completeness. For example, in most systems of logic Peirce's law (((P→Q)→P)→P) is a theorem. For classical logic, it can be easily verified with a truth table.
4
Research Set theory and Graph theory. Set theory is the branch of mathematics that studies sets, which are collections of objects. In discrete mathematics, countable sets (including finite sets) are the main focus. Graph theory, the study of graphs and networks. Graphs can model many types of relations and process dynamics in physical, biological and social systems. In computer science, they represent networks of communication, data organization, computational devices, the flow of computation, etc. In Mathematics, they are useful in Geometry and certain parts of Topology.
5
Research Probability And Number theory. Discrete probability theory deals with events that occur in countable sample spaces. For example, count observations such as the numbers of birds in flocks comprise only natural number values {0, 1, 2, ...}. Discrete probability distributions can be used to approximate continuous ones and vice versa. Number theory is concerned with the properties of numbers in general, particularly integers. It has applications to cryptography, cryptanalysis, and cryptology, particularly with regard to prime numbers and primality testing.
6
Research Algebra. Algebraic structures occur as both discrete examples and continuous examples. Discrete algebras include: boolean algebra used in logic gates and programming; relational algebra used in databases; discrete and finite versions of groups |
On the Study and Difficulties of Mathematics
On the Study and Difficulties of Mathematics
One of the twentieth century's most eminent mathematical writers, Augustus De Morgan enriched his expositions with insights from history and psychology. On the Study and Difficulties of Mathematics represents some of his best work, containing points usually overlooked by elementary treatises, and written in a fresh and natural tone that provides a refreshing contrast to the mechanical character of common textbooks. Presuming only a knowledge of the rules of algebra and Euclidean theorems, De Morgan begins with some introductory remarks on the nature and objects of mathematics. He discusses the concept of arithmetical notion and its elementary rules, including arithmetical reactions and decimal fractions. Moving on to algebra, he reviews the elementary principles, examines equations of the first and second degree, and surveys roots and logarithms. De Morgan's book concludes with an exploration of geometrical reasoning that encompasses the formulation and use of axioms, the role of proportion, and the application of algebra to the measurement of lines, angles, the proportion of figures, and surfaces.
Unabridged republication of the edition published by The Open Court Publishing Company, La Salle, Illinois, 1943. |
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Summary
Focused on helping students develop both the conceptual understanding and the analytical skills necessary to experiencesuccess in mathematics, the authors present each mathematical topic in this text using a carefully developed learning system to actively engage students in the learning process. The book addresses the diverse needs of today's students through an open design, current figures and graphs, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids. |
I picked this book up, after a friend recommended it to me. I have done linear algebra before, probably the same way anyone else has done it at some point; via linear equations, matrix algebra, and a lot of exposure to the ubiquitous, yet strangely unmotivated, determinant. Contrary to many books on linear algebra, this book takes a more abstract look at linear algebra, and it gets to the heart of the subject very quickly. I consider myself somewhat of a purist, and I could therefore rather quickly find myself at home in this book. Axler starts off discussing vector spaces, and linear maps, trying to keep them as abstract and general as possible. This book adopts the standard theorem, proof, example, exercise way of describing mathematics. Something that may seem like a daunting way to learn mathematics to many people. Although I strongly believe that these people miss the point: Mathematics is not about remembering theorems and their proofs from the outside, it is about using theorems and definitions to construct proofs of other theorems, and to ponder these. The exercises might therefore seem a bit too difficult, but they are certainly not impossible to do. In fact, almost all the exercises in this book build upon material that was previously described, and unless you haven't understood something in the text, they are straightforward to solve. Axler has done a very good job at getting to the core of linear algebra with this book, and I can wholeheartedly recommend it to anyone who considers him or herself a serious mathematician.
This review is from: Linear Algebra Done Right (Undergraduate Texts in Mathematics) (Paperback)
A brief book on linear algebra that develops the theory by emphasizing vector spaces and linear maps; this leads to clearer, more elegant proofs than the traditional, matrix-based approach. This approach manages to be both more lucid and more abstract. Among the many fine features of this book are the author's marginal notes highlighting important points, commenting on strategy, and mentioning other names that a concept may go by (e.g., an injective mapping is also known as one-to-one, this is quite useful for beginning students).
4.0 out of 5 starsExcellent for a second course in Linear Algebra, 26 April 1998
By A Customer
This review is from: Linear Algebra Done Right (Undergraduate Texts in Mathematics) (Paperback)
The book does a better job of explaining what is happening at the heart of linear spaces and linear transformations than most. This is mostly due to the fact that linear maps and operators are used more often that matrices in the proofs, and that determinants are relegated to the end of the book. Overall a very good bare bones, gives you what you need book. |
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Starting at $52 Nuts and Bolts of Proofs instructs students on the primary basic logic of mathematical proofs, showing how proofs of mathematical statements work. The text provides basic core techniques of how to read and write proofs through examples. The basic mechanics of proofs are provided for a methodical approach in gaining an understanding of the fundamentals to help students reach different results. A variety of fundamental proofs demonstrate the basic steps in the construction of a proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems. * New chapter on proof by contradiction * New updated proofs * A full range of accessible proofs * Symbols indicating level of difficulty help students understand whether a problem is based on calculus or linear algebra * Basic terminology list with definitions at the beginning of the text |
Algebra for College Students: Early Graphing
An emphasis on the practical applications of algebra motivates readers and encourages them to see algebra as an important part of their daily lives. ...Show synopsisAn emphasis on the practical applications of algebra motivates readers and encourages them to see algebra as an important part of their daily lives. Strongly emphasizes good problem-solving skills, uses real-world applications. For anyone interested in Algebra |
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This site has has interactive explanations and simulations of math from alegrbra to trigonometry. Just click the "interactive" tab on the top left menu and you can choose different simulations. It includes, the complete definition of parabolas, reaching beyond the ability to graph into the realm of why the graph appears as it does. It also has vivid descriptions of angles including circle angles for geometry. It also has calculators for principal nth roots, gdc, matrices, and prime factorization. It's definitely worth checking out. Quote from site: "A parabola is actually a locus of a point and a line. The point is called the focus and the line the directrix. That means that all points on a parabola are equidistant from the focus and the directrix. To change the equation and the graph of the interactive parabola below just click and drag either the point A, which is the focus, or point B, which controls the directrix." This is an interactive site that allows people to change the graph to understand why directrix and focus dictate parabolic graphs. |
This is a booklet containing 37 space science mathematical problems, several of which use authentic science data. The problems involve math skills such as unit conversions, geometry, trigonometry, algebra, graph analysis, vectors, scientific...(View More) notation, and many others. Learners will use mathematics to explore science topics related to Earth's magnetic field, space weather, the Sun, and other related concepts. This booklet can be found on the Space Math@NASA website |
PBS Teachers: Math - PBS Teachers
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A pre-calculus investigation designed to enable students to discover each calculus power rule independently (albeit in simplified form), and hence their inverse relationship. Students are required only to do simple arithmetic and some elementary algebra,PreCalculus Problem of the Week - Math Forum
Math problems for students who had finished studying topics commonly covered in first-year algebra and high school geometry. From 2002 to 2003, problems involved probability, statistics, discrete math, and trigonometry. The goal was to challenge studentsProductive Struggle
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A blog about real life projects suitable for college math courses such as algebra, finite math, and business calculus. Most of these applied math projects include handouts, videos, and other resources for students, as well as a project letter. Graser,
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Blog by a high school math and learning specialist. Posts, which date back to June, 2011, have included "twitter math camp," "mathematical art," "i also want you to learn…," and "rational functions take two." |
0534453457
9780534453459
Beginning and Intermediate Algebra:BEGINNING AND INTERMEDIATE ALGEBRA is the ideal text for professors who want to eliminate the significant overlap of topics found in separate beginning and intermediate algebra texts. This best-selling text helps students develop the ability to synthesize and conceptualize material by thoroughly integrating coverage of graphing and problem solving without sacrificing manipulative skills. Students appreciate the non-technical writing and the Authors' Notes in worked examples, while instructors appreciate the realistic applications, mathematical accuracy, and the flexibility Gustafson/Frisk affords.
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Rent Beginning and Intermediate Algebra 3rd edition today, or search our site for Peter D textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Brooks Cole. |
Covers the main areas of mathematics used in the first years of a typical engineering, science or applied mathematics degree. This is a guide to what the important skills in mathematics are: the ones that need to be remembered. It includes the useful elements of MATLAB and Maple the two common computer tools used by students at university. |
books.google.com - Did... mathematics
Discrete mathematics: mathematical reasoning and proof with puzzles, patterns, and games
Did games, puzzles, patterns, magic tricks, and real-world problems. You will discover how new mathematical topics can be applied to everyday situations, learn how to work with proofs, and develop your problem-solving skills along the way.
Online applications help improve your mathematical reasoning. Highly intriguing, interactive Flash-based applications illustrate key mathematical concepts and help you develop your ability to reason mathematically, solve problems, and work with proofs. Explore More icons in the text direct you to online activities at
Improve your grade with the Student Solutions Manual. A supplementary Student Solutions Manual contains more detailed solutions to selected exercises in the text.
From inside the book
Review: Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns, and Games
User Review - Ashley - Goodreads
I would not want to teach myself from this book and you better have a good teacher when you do need to use this book. The concepts are not explained very clearly, sometimes missing portions of the concept. It's a real headache trying to learn from this book.Read full review
Review: Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns, and Games
About the author (2006)
Doug Ensley is a full professor at Shippenshburg University with a Ph.D. from Carnegie Mellon. He is an active participant in national and regional committees determining the future of the discrete math curriculum, and he regularly speaks at Joint Math and MathFest.
Winston Crawley is a full professor and chair of the math department at Shippensburg University. He has a Ph.D. from University of Tennessee-Knoxville. Crawley developed the undergraduate computer science curriculum at Shippensburg.
Bibliographic information
Title
Discrete mathematics: mathematical reasoning and proof with puzzles, patterns, and games |
1|Traditional Portfolio
On this page you'll get a formal synopsis of me – educational history, transcripts, and so forth. But for a lot more detailed & rich information, check out the tabs above. I think you'll like what you see!
TEACHING PHILOSOPHY (a work always in progress)
Enthusiasm about math is infectious. Students learn from both discovery and direct learning. I try to constantly show my students that I care about their learning. I always try to teach to just a little higher level than my students think they can accomplish, but give them the tools and infinite encouragement to reach that level. I know, not just believe, that having clear and consistent expectations for students works.
I want to respect the privacy of my students, so I don't feel comfortable scanning in documents, but here are some projects they have done/worked on.
1. My Multivariable Calculus class does a project in the 4th quarter — on a topic of their choice. In 2009, one of my students worked on creating a harmonograph which draws damped Lissajous Curves. He then explained the theory behind the harmonograph, and wy the parametric equations being drawn took the form that they did. A video of the Harmonograph is below.
2. For our Algebra II classes in 2007/8, the other Algebra II teacher and I created a "video project" which was used to promote student communication in mathematics. Each student signed up for a topic and created a video "teaching" the topic (with an example) to the rest of the students in Algebra II. They were put up on a blog called Logarithms, Rational Functions, and Trigonometry! Oh My! Feel free to click on the name to visit it, or to visit the post mortem (analysis) on my blog here.
EXAMPLES OF MY WORK
I teach most of my classes using SmartBoard, sometimes alongside worksheets I create.
1.You can read my paean to Smartboard here. But you probably just want to see samples.
2. In 2008/9, when studying quadratic regressions, my Algebra II class collected some data from pendulums of various lengths and analyzed them. The original idea for the "lab" is here, and a blow-by-blow for the lab, our thought processes, and our conclusion, is here.
3. In 2008/9, in Algebra II, I made a series of packets to teach linear and quadratic inequalities. The topic list is here. The packets are: |
Web Resources
Assessments
Title: Prerequsites for Calculus Quiz
Description:
Students will take this self-assessment to make sure they are prepared to take Calculus.
Standard(s): [MA2013] PRE (9-12) 13: (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined, for example, by Pascal's Triangle. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.) [A-APR5] [MA2013] PRE (9-12) 33: Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1, and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. [F-TF8] (Alabama) [MA2013] PRE (9-12) 3: (+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. [N-CN6] [MA2013] PRE (9-12) 14: (+) Represent a system of linear equations as a single matrix equation in a vector variable. [A-REI8] [MA2013] PRE (9-12) 20: Determine the inverse of a function and a relation. (Alabama) [MA2013] PRE (9-12) 22: (+) Read values of an inverse function from a graph or a table, given that the function has an inverse. [F-BF4c] [MA2013] PRE (9-12) 24: (+) Understand the inverse relationship between exponents and logarithms, and use this relationship to solve problems involving logarithms and exponents. [F-BF5] [MA2013] PRE (9-12) 25: Compare effects of parameter changes on graphs of transcendental functions. (Alabama) [MA2013] PRE (9-12) 26: Determine the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses. (Alabama) [MA2013] PRE (9-12) 27: Use the sum, difference, and half-angle identities to find the exact value of a trigonometric function. (Alabama) [MA2013] PRE (9-12) 34: (+) Prove the addition and subtraction formulas for sine, cosine, and tangent, and use them to solve problems. [F-TF9] [MA2013] PRE (9-12) 12: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.* (Extend to infinite geometric series.) [A-SSE4] (Alabama) |
Algebra 1
9780078738227
ISBN:
0078738229
Pub Date: 2007 Publisher: McGraw-Hill Higher Education
Summary: THE PROGRAM STUDENTS NEED; THE FOCUS TEACHERS WANT! "Glencoe Algebra 1" is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics scores on today's high-stakes assessments.
McGraw-Hill Staff is the author of Algebra 1, published 2007 under ISBN 9780078738227 and 0078738229. Seven hundred... thirty eight Algebra 1 textbooks are available for sale on ValoreBooks.com, five hundred thirty five used from the cheapest price of $8.96, or buy new starting at $56 [more student names and school markings on book and inside, minimal writing/highlighting with no detracting writing inside book, strong, solid binding.[less]
THE PROGRAM STUDENTS NEED; THE FOCUS TEACHERS WANT! "Glencoe Algebra 1" is a key program in our vertically aligned high school mathematics series developed to help all studen [more]
THE PROGRAM STUDENTS NEED; THE FOCUS TEACHERS WANT! "Glencoe Algebra 1" is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematic |
Calculus provides the language and some powerful tools for the study of change. As such, it is an essential subject for those interested in growth and decay processes, motion, and the determination of functional relationships in general. Using student-selected models from primary literature, we will investigate dynamical systems from economics, ecology, epidemiology and physics. Computers are essential tools in the exploration of such processes and will be integral to the course. No previous programming experience is required. Topics will include: 1) dynamical systems, 2) basic concepts of calculus-- rate of change, differentiation, limits, 3) differential equations, 4) computer programming, simulation, and approximation, 5) exponential and circular functions. While the course is self-contained, students are strongly urged to follow it up by taking NS 316-Linear Algebra or NS 261-Calculus II to further develop their facility with the concepts. In addition to regular substantial problem sets, each student will apply the concepts to recently published models of their choosing. |
This first-level mathematics course for engineering technology programs begins with a review of fundamental concepts, arithmetic operations, and units of measure. This is followed by an in-depth study of basic algebra, trigonometric and other functions, and quadratic equations.
...
Anyone operating in a decision-making environment.
Statistics consists of information, exercises, and knowledge quizzes geared towards more advanced problem solving. This course will provide a review and introduction of basic statistical methods. You will have 180 days to access this course.
For the examples, this course will utilize the Microsoft's Excel 'Analysis ToolPack'......
Basic Mathematics course is designed to prepare you for the basic math skills needed in the Fire Alarm Industry. For the exam, it is important that you be able to convert decimal feet and inches to fractional feet and inches and vice versa. Other vital testing elements this course covers are calculating length, area, volume and temperature. It also discusses the equations used in scientific and......
This course covers broad mathematical concepts, which can be applied to business, and prepares students for the required quantitative courses (statistics, economics, and finance) in their program. Topics include equations, inequalities and problem-solving, functions and graphs, counting techniques, probability, and basic statistics using the appropriate technology....
The Curriculum and Instruction Program is a graduate degree for bachelor prepared individuals who wish to develop and enhance their curriculum and instruction. The program encompasses the study of curricular planning and development with an integration of technology, assessment and evaluation practices, strategies for effective classroom instruction for a variety of learners and critical issues......
The Master of Arts in Education/Secondary Teacher Education- Math (MAED/TED-SM) is a graduate degree program preparing candidates for teacher licensure. The guiding philosophy of the MAED/TED-SM program is to provide the adult student, who already has a degree in a discipline other than education, with the skills and knowledge that will allow them to become a competent and effective educator. T...... |
Linear Algebra : Introduction - 2nd edition
Summary: In this appealing and well-written text, Richard Bronson gives readers a substructure for a firm understanding of the abstract concepts of linear algebra and its applications. The author starts with the concrete and computational, and leads the reader to a choice of major applications (Markov chains, least-squares approximation, and solution of differential equations using Jordan normal form).
The first three chapters address the basics: matrices, vector s...show morepaces, and linear transformations. The next three cover eigenvalues, Euclidean inner products, and Jordan canonical forms, offering possibilities that can be tailored to the instructor's taste and to the length of the course. Bronson's approach to computation is modern and algorithmic, and his theory is clean and straightforward. Throughout, the views of the theory presented are broad and balanced. Key material is highlighted in the text and summarized at the end of each chapter. The book also includes ample exercises with answers and hints. With its inclusion of all the needed features, this text will be a pleasure for professionals, teachers, and36.00 +$3.99 s/h
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Webe Books Rushville, IL
PAPERBACK New 0120887843 Excellent condition. Never been used. **FREE** Delivery tracking with every book purchased. |
Created by Jill Stevens of Illuminations: Resources for Teaching Mathematics, this activity allows students to look for functions within a given set of data. After analyzing the data, the student should be able to...
This online, interactive lesson on distributions provides examples, exercises, and applets which explore the basic types of probability distributions and the ways distributions can be defined using density functions,...
Exercises posted on this web site offer an opportunity for students to evaluate how much they have retained in various subjects of Algebra. Topics covered include geometry, functions, vectors, and statistics. There are...
Statistical Associates Publishing is a creation of Professor Dave Garson and hosts a number of free statistics e-books, and some low-cost Kindle versions as well. Use of the site is password-protected, so visit the...
This unit from Illuminations focuses on collecting data and using technology to find functions to describe the data collected. Students will learn to use a calculator to find the curve of best fit for a set of data and... |
Mathematics: Course 1 - 07 edition
Summary: The Student Edition develops skills that stretch beyond the classroom, such as higher-order thinking and the ability to read and write about math. All this is in a framework that begins to prepare students for algebra as soon as they open the book.
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Hardcover Very Good 0030385075 Book is in very good condition. Its clean with minimal to no writing.
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Hardcover Very Good 00303850759.45 +$3.99 s/h
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2007 |
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Ib math studies internal assessment final draft - SlideShareIB Math Studies Internal Assessment :<br />What is the Relationship ... two
classifications or factors from the same sample are independent of ...
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Intermediate Algebra Connecting Concepts Through Applications
Description: INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS shows students how to apply traditional mathematical skills in real-world contexts. The emphasis on skill building and applications engages students as they master concepts, problemMore...
INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS shows students how to apply traditional mathematical skills in real-world contexts. The emphasis on skill building and applications engages students as they master concepts, problem solving, and communication skills. It modifies the rule of four, integrating algebraic techniques, graphing, the use of data in tables, and writing sentences to communicate solutions to application problems. The authors have developed several key ideas to make concepts real and vivid for students. First, the authors integrate applications, drawing on real-world data to show students why they need to know and how to apply math. The applications help students develop the skills needed to explain the meaning of answers in the context of the application. Second, they emphasize strong algebra skills. These skills support the applications and enhance student comprehension. Third, the authors use an eyeball best-fit approach to modeling. Doing models by hand helps students focus on the characteristics of each function type. Fourth, the text underscores the importance of graphs and graphing. Students learn graphing by hand, while the graphing calculator is used to display real-life data problems. In short, INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS takes an application-driven approach to algebra, using appropriate calculator technology as students master algebraic concepts and |
Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities. It provides an excellent introduction to a timeless area of number theory that is still as widely researched today as it was when the book originally appeared. The three main themes of the book are Waring's problem and the representation of integers by diagonal forms, the solubility in integers of systems of forms in many variables, and the solubility in integers of diagonal inequalities. For the second edition of the book a comprehensive foreword has been added in which three prominent authorities describe the modern context and recent developments. A thorough bibliography has also been added. less |
Algebra for College Students / With CD-ROM - 2nd edition
Summary: Algebra for College Students is designed to provide students with the algebra background needed for further college-level mathematics courses. The unifying theme of this text is the development of the skills necessary for solving equations and inequalities, followed by the application of those skills to solving applied problems. The primary goal in writing the second edition of Algebra for College Students has been to retain the features that made the first edition s...show moreo successful, while incorporating the comments and suggestions of first-edition users. Many new features have been provided that will help instructors reach the goals that they have set for their students. As always, the author endeavors to write texts that your students can read, understand, and enjoy, while gaining confidence in their ability to use mathematics. While the essence of the text remains, the topics have been rearranged and new features added to reflect the current needs of instructors and students.
Features:
An increased emphasis on real-data applications that involve graphs is a focus for the third edition. Some exercises have been updated throughout the text to help demonstrate concepts, motivate students, and to give students practice using new skills. Many of the real data exercises contain data obtained from the Internet. Internet addresses are provided as a resource for both students and teachers. Because internet addresses frequently change, a list of addresses will also be available on the website so that they may be more effectively maintained. An Index of Applications listing applications by subject matter is included at the front of the text.
The third edition contains three new margin features that appear throughout the text: Calculator Close-Ups give students an idea of how and when to use a graphing calculator. Some Calculator Close-Ups simply introduce the features of a graphing calculator, but many are intended to enhance understanding of algebraic concepts. For this reason, many of the Calculator Close-Ups will benefit even those students who do not use a graphing calculator. Study Tips are included in the margins throughout the text. These short tips are meant to continually reinforce good study habits and keep reminding students that it is never too late to make improvements in the manner in which they study. Helpful Hints are short comments that enhance the material in the text, provide another way of approaching a problem, or clear up misconceptions.
Every section in the third edition generally begins with six simple writing exercises; these exercises appear in the exercise sets. These exercises are designed to get students to review the definitions and rules of the section before doing more traditional exercises. For example, the student might be simply asked what properties of equality were discussed in this section.
Each chapter begins with a Chapter Opener that discusses a real application of algebra. The discussion is accompanied by a photograph and, in most cases by a real-data application graph that helps students visualize algebra and more fully understand the concepts discussed in the chapter. In addition, each chapter contains a Math at Work feature, which profiles a real person and the mathematics that he or she uses on the job. These two features have corresponding real data exercises.
Every section begins with In This Section, a list of topics that shows the student what will be covered. Because the topics correspond to the headings within each section, students will find it easy to locate and study specific concepts.
Important ideas, such as definitions, rules, summaries, and strategies, are set apart in boxes for quick reference. Color is used to highlight these boxes as well as other important points in the text.
At the end of every section are Warm-up exercises, a set of ten simple statements that are to be answered true or false. These exercises are designed to provide a smooth transition between the ideas and the exercise sets. They help students understand that every statement in mathematics is either true or false. They are also good for discussion or group work.
The end-of-section Exercises follow the same order as the textual material and contain exercises that are keyed to examples, as well as numerous exercises that are not keyed to examples. This organization allows the instructor to cover only part of a section if necessary and easily determine which exercises are appropriate to assign. The keyed exercises give the student a place to start practicing and building confidence, whereas the non-keyed exercises are designed to wean the student from following examples in a step-by-step manner. Getting More Involved exercises are designed to encourage writing, discussion, exploration, and cooperative learning. Graphing Calculator Exercises require a graphing calculator and are identified with a graphing calculator logo. Exercises for which a scientific calculator would be helpful are identified with a scientific calculator logo.
Every chapter ends with a four-part Wrap-up, which includes the following: The Chapter Summary lists important concepts along with brief illustrative examples. Enriching Your Mathematical Word Power NEW! appears at the end of each chapter and consists of multiple choice questions in which the important terms are to be matched with their meanings. This feature emphasizes the importance of proper terminology. The Review Exercises contain problems that are keyed to the sections of the chapter as well as numerous miscellaneous exercises. The Chapter Test is designed to help the student assess his or her readiness for a test. The Chapter Test has no keyed exercises, thus enabling the student to work independently of the sections and examples.
At the end of each chapter is a Collaborative Activities feature which is designed to encourage interaction and learning in groups. Instructions and suggestions for using these activities and answers to all problems can be found in the Instructor's Solutions Manual.
The Making Connections exercises at the end of each chapter are designed to help your students review and synthesize the new material with ideas from previous chapters, and in some cases, review material necessary for success in the upcoming chapter. Every Making Connections exercise set includes at least one applied exercise that requires ideas from one or more of the previous chapters |
books.google.co.uk - Where,... Through the Ages
Math Through the Ages: A Gentle History for Teachers and Others
Where, easygoing style that's accessible to teachers, students, and anyone who is curious about the history of mathematical ideas. Each sketch contains Questions and Projects to help you learn more about its topic and to see how its main ideas fit into the bigger picture of history. The 25 short stories are preceded by a 56-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today. Reading suggestions after each sketch provide starting points for readers who want to pursue a topic further.
User ratings
Review: Math Through the Ages: A Gentle History for Teachers and Others, Expanded Edition (Mathematical Association of America Textbooks)
User Review - Lillian - Goodreads
Great overview, not too heavy, and fed to you in short chapters on widely varying topics. It includes some problems and projects to further investigate at the end of each chapter. Great for teachers. This may be inspiring to me for programs or just outreach to people facing math homework.Read full review
Review: Math Through the Ages: A Gentle History for Teachers and Others, Expanded Edition (Mathematical Association of America Textbooks)
User Review - Brian Carpenter - Goodreads
The collection of sketches on mathematical history contained in this book were, for the most part, interesting to read. Many of them provoked additional thoughts or drove me to look up new sources ...Read full review
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About the author (2004)
William Berlnghoff received his Ph.D in mathematics from Wesleyan University. He is a visiting professor of mathematics at Colby College. He is the author or co-author of several college texts for liberal arts mathematics.
Fernando Gouves received his Ph.D. in mathematics from Harvard University. He is currently a professor of mathematics at Colby College. |
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The Klahowya Secondary School ninth-grader's feet can't quite reach the ground when he sits in one of the heavy, cushy chairs in the main office. When the red-haired freshman was in sixth grade, upon teacher recommendation he sped up his math studies and by seventh grade, he was in algebra 1.
"Normally I'd be in geometry at this age," said Kevin Hassett who is enrolled in the first all-freshman algebra 2 class at KSS.
Hassett says he's always been a fan of functions and sequences and sitting in Ellen Kraft's algebra 2 classroom has proven to be a complementary occupation to his advanced physical science class.
One reason he takes math is because he looks ahead to where the numbers could figure into his career.
"I think in my future jobs which might include engineer or something in the realm of science (math would be useful) and again I take it because I like it," Hassett said.
An appreciation of math like Hassett's adds up to perfection in Dave Thielk's |
This best-selling guide from authors Elaine Weinmann and Peter Lourekas has been the go-to tutorial and reference book for photography/design professionals and the textbook of choice in college classrooms for decades. This edition includes their trademark features of clear, concise, step-by-step instructions; hundreds of full-color images; screen captures of program features; and supplemental tips and sidebars in every chapter.
Practice makes perfect-and helps deepen your understanding of algebra 1,001 Algebra I Practice Problems For Dummies, with free access to online practice problems, takes you beyond the instruction and guidance offered in Algebra I For Dummies, giving you 1,001 opportunities to practice solving problems from the major topics in algebra. You start with some basic operations, move on to algebraic properties, polynomials, and quadratic equations, and finish up with graphing. |
W. D. Wallis
This second edition of Wallis' concisely written textbook on finite mathematics can be a valuable resource for freshmen and sophomores. An economy of language lends elegance and clarity to this text, which is unusual among comparable texts that I work with. The sequence in which topics are presented convinces me, however, that it would be awkward in the classroom. Additional lectures would be required, and probably also reordering the sections. Such situations, I find, often confuse and unsettle a student already on the margins of his or her confidence and works against encouraging students to read ahead and do independent study. The book can nevertheless be helpful for parents or students seeking a resource to supplement a required textbook during the first couple of years of pre-calculus college algebra.
As usual with comparable works, the book leads off with set theory. I very much appreciate that Wallis immediately connects this to solution sets, instead of waiting until half-way into the text. However, a tangent is taken into summation notation and principles before returning to cover such set basics as union, intersection, and Venn diagrams. Arithmetic and geometric sequences are never explored in detail, or even introduced. Wallis also introduces probability sooner than most comparable textbooks. In his approach, standard deviation comes before the combinatorial basis of probability. Similarly, after a quick exhibition of probability measures, including the unnamed inclusion-exclusion principle, the text is into Bernoulli trials before counting basics. As a result, the student is confronted with determining the probability that a netted butterfly is striped or female sections prior to meeting the ideal urn and its monochrome marbles.
Wallis adds material that I believe is crucial to introduce to the target audience. For many business or liberal arts majors, this text contains most if not all of the mathematics they will learn before they enter the workforce with an Associate's Degree. Unlike many textbooks that may be chosen for them, Wallis includes a very good, not merely cursory, introduction to Bayes. There is also an entire chapter on Graph Theory going as far as Hamiltonian cycles and colorings. (This is perhaps further than is necessary for these students.) There is also an entire chapter on Game Theory. Wallis also ties together nicely the general form of the linear equation with the dot product by way of introducing matrix multiplication. I feel there was a missed opportunity to underscore the applicability to sales figures matrix examples previously presented, but I appreciate the rarely seen vector topics for students at this level.
Finally, there is the subject of graphical solutions to equations and systems. Wallis calls this The Geometric Method and largely relegates this to a later, dedicated chapter and rarely broaches the topic elsewhere. I feel this is a disservice to the student at this level, because very often the crucial "aha!" moment can be sparked with a Cartesian presentation. As a result, Wallis concludes the text with a chapter on exponential growth without comment or display of the unique curve, let alone having it come at the tail of an enlightening parade of fully explored basic graph forms.
Tom Schulte teaches finite mathematics and more at Oakland Community College in Michigan. |
with Applications and Visualization
The Rockswold/Krieger algebra series fosters conceptual understanding by using relevant applications and visualization to show students why math ...Show synopsisThe Rockswold/Krieger algebra series fosters conceptual understanding by using relevant applications and visualization to show students why math matters. It answers the common question â When will I ever use this?â Rockswold teaches students the math in context, rather than including the applications at the end of the presentation. By seamlessly integrating meaningful applications that include real data and supporting visuals (graphs, tables, charts, colors, and diagrams), students are able to see how math impacts their lives as they learn the concepts. The authors believe this approach deepens conceptual understanding and better prepares students for future math courses and life.Hide synopsis
Description:Hardcover. Instructor Edition: Same as student edition with...Hardcover. Instructor Edition: Same as student edition with additional notes or answers. New Condition. SKU: 97803217479691773302. |
...This applies especially to students with learning disabilities, or otherwise unique learning styles that may be less compatible with a traditional classroom learning environment.I use algebra extensively, from basic arithmetical manipulations to abstract topics such as rings and fields. Like mos...
...Having command of basic elementary mathematics - addition, subtraction, multiplication, division, fractions, decimals, exponents, roots, etc. - is essential to mastering the higher-level math disciplines that a student will encounter in high school and college. But 40 years as a working engineer... |
97815586059ometric Tools for Computer Graphics (The Morgan Kaufmann Series in Computer Graphics)
Do you spend too much time creating the building blocks of your graphics applications or finding and correcting errors? Geometric Tools for Computer Graphics is an extensive, conveniently organized collection of proven solutions to fundamental problems that you'd rather not solve over and over again, including building primitives, distance calculation, approximation, containment, decomposition, intersection determination, separation, and more. If you have a mathematics degree, this book will save you time and trouble. If you don't, it will help you achieve things you may feel are out of your reach. Inside, each problem is clearly stated and diagrammed, and the fully detailed solutions are presented in easy-to-understand pseudocode. You also get the mathematics and geometry background needed to make optimal use of the solutions, as well as an abundance of reference material contained in a series of appendices.
Filled with robust, thoroughly tested solutions that will save you time and help you avoid costly errors. Covers problems relevant for both 2D and 3D graphics programming. Presents each problem and solution in stand-alone form allowing you the option of reading only those entries that matter to you. Provides the math and geometry background you need to understand the solutions and put them to work. Clearly diagrams each problem and presents solutions in easy-to-understand pseudocode. Resources associated with the book are available at the companion Web site |
Linear Algebra: Real World Uses
Engineering:
Linear algebra is the simplest way to look at functions of many variables, which usually arise in engineering by the discretization of a concept stated in terms of a continuum, e.g. the law governing the relation between stresses and strains in a structure.
Linear Algebra is used quite heavily in Structural Engineering. This is for a very simple reason. The analysis of a structure in equilibrium involves writing down many equations in many unknowns. Often these equations are linear, even when material deformation (i.e. bending) is considered. This is exactly the sort of situation for which linear algebra is the best technique. linear algebra and structural engineering
Going to Mars:
Most missions to mars are based on a Hohmann trajectory. This trajectory is the fastest trajectory possible that is minimum energy (based on the two body problem). Less energetic trajectories are available using the three body patched trajectories (Interplanetary super highway) but these can take a considerably longer length of time.
For basic mission planning the delta V of the two body problem is used to calculate the mass fraction for the trip between Earth and Mars. The mass fraction tells mission planers how much mass they need to deliver to LEO in order to get a given mass to Mars. For calculating other trajectories Numeric or algebraic techniques can be used. |
Index PrealgebraHaving the answer to one specific problem is not terribly useful, but having the skills to answer a whole class of problems is. One |
Math books |
CK-12 Geometry - Basic
Table of Contents
Teachers and parents can access additional teaching materials from the Resources Tab above.
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Description
CK-12's Basic Geometry FlexBook is designed to present students with geometric principles in a simpler, more graphics-oriented course. Students will explore geometry at a slower pace with an emphasis placed on visual aids and approachability.
very easy way to obtain textbook to aid in learning geometry for my 9th grader Great choice for his learning needs. like that textbooks offerred choice in matching book to students learning - Choice of books from slower paced to advanced paced were all on same site. |
Essential Math With Application - 8th edition
Summary: The latest book from Cengage Learning on Essential Mathematics As in previous editions, the focus in ESSENTIAL MATHEMATICS with APPLICATIONS remains on the Aufmann Interactive Method (AIM). Users are encouraged to be active participants in the classroom and in their own studies as they work through the How To examples and the paired Examples and You Try It problems. The role of ''active participant'' is crucial to success. Presenting students with worked examples, and then providing ...show morethem with the opportunity to immediately work similar problems, helps them build their confidence and eventually master the |
gebra II
College-level algebra can be challenging for both those new to it and those who want to revisit it for professional reasons. Express Review Guides: ...Show synopsisCollege-level algebra can be challenging for both those new to it and those who want to revisit it for professional reasons. Express Review Guides: Algebra II makes mastering advanced algebra simple and even fun. There are individual chapters on equations and inequalities, linear relations and functions, matrices, rational expressions, exponential and logarithmic functions, probability, and much more. Particularly beneficial are the book's practice exercise with detailed answer explanations and tips for preparing for standardized tests |
This course covers maximisation problems leading to game strategies, and some aspects of combinatorics. Topics include: Linear Programming and Game Theory - maximisation under linear constraints and applications to strategy in zero sum two person games; Combinatorics - the number of selections under various conditions, and the use here of recurrence relations and enumerator functions.
This course presents a variety of methods in the solution of ordinary and partial differential equations. Topics include: ODEs - classification and methods of solution of various types of first and second order ODEs, including the use of the Laplace transform; PDEs - classification and methods of solution of various types of first and second order PDEs, including the use of Fourier series.
The aim of this course is to introduce students to basic notions in analysis and set up the background for the subsequent course in complex methods. The course covers sequences, series and limits as well as the mean value and intermediate value theorems.
Many important problems in applied mathematics are modelled by systems of ordinary differential or difference equations. Even when one cannot solve these equations explicitly, it is important to know the qualitative properties of their solutions. Often these system depend on parameters and at critical values of the fundamental nature of the solution may change. Identifying such bifurcation points is vital to an understanding of the model. The topics covered in the course are: Equilibrium solutions, fixed points and limit cycles of a nonlinear system. Linearisation of the system about such solutions and study of their stability. Sketching a phase portrait for a two dimensional system. Bifurcations in the system as parameters change. Fixed points and periodic points for a nonlinear map and their stability. Bifurcations of nonlinear maps. |
Offerings by Semester
Mathematics for Teachers
Mathematics for Teachers
What mathematical knowledge should elementary and secondary teachers have in the 21st century? Participants in this course will strengthen and deepen their own mathematical understanding in a student-centered workshop setting. We will investigate the number system, operations, algebraic thinking, measurement, data, and functions, and consider the attributes of quantitative literacy. We will also study recent research that describes specialized mathematical content knowledge for teaching. (Not open to students who have taken MATH/EDST 1005. Students looking for a course in elementary school teaching methods should consider EDST 0315 instead.)Math Proof: Art and Argument
Mathematical Proof: Art and Argument
Mathematical proof is the language of mathematics. As preparation for upper-level coursework, this course will give students an opportunity to build a strong foundation in reading, writing, and analyzing mathematical argument. Course topics will include an introduction to mathematical logic, standard proof structures and methods, set theory, and elementary number theory. Additional topics will preview ideas and methods from more advanced courses. We will also explore important historical examples of proofs, both ancient and modern. The driving force behind this course will be mathematical expression with a primary focus on argumentation and the creative process. (MATH 0122 or MATH 0200) 3 hrs. lectGraph Theory
Graph Theory
A graph (or network) is a useful mathematical model when studying a set of discrete objects and the relationships among them. We often represent an object with a vertex (node) and a relation between a pair with an edge (line). With the graph in hand, we then ask questions, such as: Is it connected? Can one traverse each edge precisely once and return to a starting vertex? For a fixed k/, is it possible to "color" the vertices using /k colors so that no two vertices that share an edge receive the same color? More formally, we study the following topics: trees, distance, degree sequences, matchings, connectivity, coloring, and planarity. Proof writing is emphasized. (MATH 0122 or by waiver) 3 hrs. lect./disc.
History of Mathematics
History of Mathematics
This course studies the history of mathematics chronologically beginning with its ancient origins in Babylonian arithmetic and Egyptian geometry. The works of Euclid, Apollonius, and Archimedes and the development of ancient Greek deductive mathematics is covered. The mathematics from China, India, and the Arab world is analyzed and compared. Special emphasis is given to the role of mathematics in the growth and development of science, especially astronomy. European mathematics from the Renaissance through the 19th Century is studied in detail including the development of analytic geometry, calculus, probability, number theory, and modern algebra and analysis. (MATH 0122 or waiver)
Mathematical Logic
Mathematical Logic
Mathematicians confirm their answers to mathematical questions by writing proofs. But what, exactly, is a proof? This course begins with a precise definition specifying what counts as a mathematical proof. This definition makes it possible to carry out a mathematical study of what can be accomplished by means of deductive reasoning and, perhaps more interestingly, what cannot be accomplished. Topics will include the propositional and predicate calculi, completeness, compactness, and decidability. At the end of the course we will study Gödel's famous Incompleteness Theorem, which shows that there are statements about the positive integers that are true but impossible to prove. 3 hrs. lect. DED (D. Velleman)
Topics In Algebra
Topics in Algebra
A further study of topics from MATH 0302. These may include field theory, algebraic extension fields, Galois theory, solvability of polynomial equations by radicals, finite fields, elementary algebraic number theory, solution of the classic geometric construction problems, or the classical groups. (MATH 0302Senior Seminar
Senior Seminar
Each student will explore in depth a topic in pure or applied mathematics, under one-on-one supervision by a faculty advisor. The course culminates with a major written paper and presentation. This experience emphasizes independent study, library research, expository writing, and oral presentation. The goal is to demonstrate the ability to internalize and organize a substantial piece of mathematics. Class meetings include attendance at a series of lectures designed to introduce and integrate ideas of mathematics not covered in the previous three years. Registration is by permission: Each student must have identified a topic, an advisor, and at least one principal reference source. 3 hrs. lect./disc. |
Series
Lessons: 12
Total Time: 0h 59m
Use: Watch Online & Download
Access Period: Unlimited
Created At: 06/29/2011
Last Updated At: 06/29/2011
This 11-lesson video series will walk you through several applications of quadratic functions and equations. We'll look at some word problems, some quadratic geometry problems, some problems that ask us to find minimum and maximum points using quadratic functions, etc. To learn about these concepts, which are critical to Algebra, we'll cover the topic through a series of video lessons, each of which will cover pertinent ideas and related problems. The video content in this series will include a lesson on each of the following:
* Word Problems Involving Quadratics, Ex 1
* Word Problems Involving Quadratics, Ex 2
* Word Problems Involving Quadratics, Ex 3
* Maximum Values of Quadratic Functions
* Find Max & Min of a Quadratic Function
* Solving a Quadratic Geometry Problem, Ex 1
* Solving a Quadratic Geometry Problem, Ex 2
* Solving a Quadratic Geometry Problem, Ex 3
* The Pythagorean Theorem, Ex 1
* The Pythagorean Theorem, Ex 2
* The Pythagorean Theorem, Ex 3
These videos are available to be viewed online for free on PatrickJMT
About this Author
Many of the videos for sale are also available on my website: or you can also do a search and check out my popular 'math channel' on YouTube (PatrickJMT). You can watch all of them there for FREE!
Masters degree in Mathematics; former math instructor at a top 20 university! |
Discrete Math in the Classroom
This list contains some of the best discrete math
lesson plans. For a more exhaustive list, or to find
materials that fit your specific needs, search or browse
Discrete Math or Lesson
Plans in the Forum's Internet Mathematics Library. |
Abstract: This issue focuses on using technology and algebra to
investigate the number of solutions for a particular exponential function and
its inverse over a given interval. Also includes "The Angles between the
Sides of a Quadrilateral and Its Diagonals" by Steven Siegel.he aim of
Delving Deeper is for teachers to pose and solve novel math problems, expand on
mathematical connections, or offer new insights into familiar math concepts.
Delving Deeper focuses on mathematics content appealing to secondary school
teachers. It provides a forum that allows classroom teachers to share their
mathematics from their work with students, their classroom investigations and
products, and their other experiences. Delving Deeper is a regular department
of Mathematics Teacher.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research. |
This is the free version of "Function Plotter". Completely free and without advertisements.This app, is able to draw multiple function graphs, calculate function values and value tables. It's also possible to integrate functions numerically.The following mathematical functions are available:polynomials, rational functions, trigonometric functions, inverse trigonometric functions, hyperbolic functions, natural logarithm, exponential function and all the possible combinations |
More About
This Textbook
Overview
The theory of finite fields is a branch of modern algebra that has come to the fore in recent years because of its diverse applications in such areas as combinatorics, coding theory, cryptology and the mathematical study of switching circuits. The first part of this book presents an introduction to this theory, emphasizing those aspects that are relevant for application. The second part is devoted to a discussion of the most important applications of finite fields, especially to information theory, algebraic coding theory, and cryptology. There is also a chapter on applications within mathematics, such as finite geometries, combinatorics and pseudo-random sequences. The book is designed as a graduate level textbook; worked examples and copious exercises that range from the routine, to those giving alternative proofs of key theorems, to extensions of material covered in the text, are provided throughout.
Editorial Reviews
From the Publisher
"...this book will continue to serve its purpose as an introduction for students, since it is devoted mainly to those parts that have a certain quality of timelessness, namely the classical theory and the standard applications of finite fields |
Introduzione al Calcolo Scientifico Metodi e Applicazioni con MATLAB
Written in Italian, this text can be used as an introduction to numerical analysis and scientific computing for undergraduate students in mathematics, science, and engineering, yet is comprehensive enough for higher-level students. Topics covered include matrix computations, differential equations, linear algebra, interpolation, optimization, and Monte Carlo equations. Each chapter includes real-world application problems solved with MATLAB. In additon, the Symbolic Math Toolbox is briefly introduced and used to solve examples. |
Applied Mathematical and Physical Formulas Pocket Reference
Book Description: If formulas have always been your nemeses, this book is for you! Thoroughly practical and authoritative, this book brings together, in three parts, thousands of formulas, rules, and figures to simplify, review, or to refresh the user's memory of what he/she studied in school. This desktop reference shows how to solve every kind of math and physics problem you're likely to encounter in school and business, and it explains simply and easily how to find answers fast, learn key formulas and definitions, study quickly and learn more effectively--from fundamental mathematical rules to physical definitions and constants. Presents all formulas, rules, and definitions precisely, simply, and clearly.Covers metric units of measurement, U.S. units of measurement (USCS), tables of equivalents metrics and USCS units.Reviews the fundamentals of algebra, geometry, trigonometry, and analytical geometry.Presents the application of differential equations and integral calculus.Solves problems concerning simple interest, compound interest, effective rate, annuity, amortization of loans, and sinking fund payment.Shows the comparative advantages of binomial distribution, standard distribution, Poisson distribution, and normal distribution.Includes most used definitions and formulas of kinematics, dynamics, statics, mechanics of fluids, thermal variable of state, thermodynamics, electricity and magnetism, light, and basic definition of atomic and nuclear physics.Offers most used fundamentals of physical constants |
SmartGraph is a mathematical graph plotting and equation solving tool that helps you plot mathematical graph(s) based on single or multiple mathematical equation(s) and investigate some mathematical graph properties such as coordinates of interception points, slope of a straight line, etc. SmartGraph is suitable for use in the secondary school Mathematics curriculum, although part of it can also be used in the primary school Mathematics curriculum after some adaptation. |
The Way of Analysis, Revised Edition (Jones and Bartlett Books in Mathematics)
Book Description: The Way of Analysis gives a thorough account of real analysis in one or several variables, from the construction of the real number system to an introduction of the Lebesgue integral. The text provides proofs of all main results, as well as motivations, examples, applications, exercises, and formal chapter summaries. Additionally, there are three chapters on application of analysis, ordinary differential equations, Fourier series, and curves and surfaces to show how the techniques of analysis are used in concrete settings |
How to Count: An Introduction to Combinatorics, Second Edition (Discrete Mathematics and Its Applications)
9781420082609
ISBN:
1420082604
Edition: 2 Pub Date: 2010 Publisher: C R C Press LLC
Summary: Allenby, Regnaud B. J. T. is the author of How to Count: An Introduction to Combinatorics, Second Edition (Discrete Mathematics and Its Applications), published 2010 under ISBN 9781420082609 and 1420082604. Six hundred five How to Count: An Introduction to Combinatorics, Second Edition (Discrete Mathematics and Its Applications) textbooks are available for sale on ValoreBooks.com, one hundred one used from the cheape...st price of $72.31, or buy new starting at $65.291420082609
ISBN:1420082604
Edition:2nd
Pub Date:2010 Publisher:C R C Press LLC
ValoreBooks.com is the top book store for cheap How to Count: An Introduction to Combinatorics, Second Edition (Discrete Mathematics and Its Applications) rentals, or new and used condition books for purchase. |
Jo, like several of her 14- and 15-year-old peers, had some previous experience with algebra. But she disliked mathematics and had performed very poorly on the algebra test given at the beginning of the study. She viewed algebraic symbols as no more than letters of the alphabet whose numerical values corresponded to their position in the alphabet. During a four-month study (with one lesson per week), Jo learned how to use a spreadsheet to solve various kinds of word problems. At the end of the study, she was given the following problem to solve (with no computer available):
One hundred chocolates were distributed to three groups of children. The second group received four times as many chocolates as the first group. The third group received 10 chocolates more than the second group. How many chocolates did the first, second, and third groups receive?
Jo drew a spreadsheet on paper and showed in her written solution how the spreadsheet code was beginning to play a role in her thinking processes. Interviewed subsequently, she was asked,
"If we call this cell x, what could you write down for the number of chocolates in the other groups?"
She wrote the following, which shows that she was now able to represent the problem using the literal symbols of algebra (note that the syntax of many spreadsheets requires the entry of an equal sign before the algebraic expression):
=x
=x×4
=x×4+10
SOURCE: Sutherland, 1993, p. 22. Used by permission of Micromath.
values of the variable.44 For example, given the situation that a plumbing company charges $42 per hour plus $35 for the service call, students are asked to find the cost of a 3-hour service call and of a 4.5-hour service call. This inductive-support strategy has students provide an arithmetic representation for the problem before being asked to give the algebraic representation. Such an intelligent tutor has been made part of an experimental ninth-grade algebra curriculum that focuses on the mathematical analysis of realistic situations. |
9781571460462 Differential Geometry (Series in Undergraduate Texts)
The origins of differential geometry go back to the early days of the differential calculus, when one of the fundamental problems was the determination of the tangent to a curve. With the development of the calculus, additional geometric applications were obtained. The principal contributors in this early period were Leonhard Euler (1707- 1783), GaspardMonge(1746-1818), Joseph Louis Lagrange (1736-1813), and AugustinCauchy (1789-1857). A decisive step forward was taken by Karl FriedrichGauss (1777-1855) with his development of the intrinsic geometryon a surface. This idea of Gauss was generalized to n( > 3)-dimensional spaceby Bernhard Riemann (1826- 1866), thus giving rise to the geometry that bears his name. This book is designed to introduce differential geometry to beginning graduate students as well as advanced undergraduate students (this introduction in the latter case is important for remedying the weakness of geometry in the usual undergraduate curriculum). In the last couple of decades differential geometry, along with other branches of mathematics, has been highly developed. In this book we will study only the traditional topics, namely, curves and surfaces in a three-dimensional Euclidean space E3. Unlike most classical books on the subject, however, more attention is paid here to the relationships between local and global properties, as opposed to local properties only. Although we restrict our attention to curves and surfaces in E3, most global theorems for curves and surfaces in this book can be extended to either higher dimensional spaces or more general curves and surfaces or both. Moreover, geometric interpretations are given along with analytic expressions. This will enable students to make use of geometric intuition, which is a precious tool for studying geometry and related problems; such a tool is seldom encountered in other branches of mathematics |
Created by artist Cynthia Wilson at Spokane Falls Community College, this lesson combines art, geometry, and algebra to create two-dimensional models for abstract paintings. On this page, visitors will find a very...
Created by artist Melissa Tomlinson Newell and mathematician Deann Leoni, this page presents lecture-studio courses in both 2-dimensional and 3-dimensional design. These courses allow students to explore elements and...
This site, created by Maria Andersen of Muskegon Community College, has a great deal of information for math instructors. Its purpose is to create and support the community of teachers by provide a space for them to...
How much liquid can that glass hold? What are the dimensions of that package that's heading off to a friend overseas? Answers to both of those questions (and many more) can be found in this lovely interactive feature on...
This joint effort between architecture and mechanical engineering researchers at the University of Michigan applied geometrical and topological optimization techniques to building floorplan layout. In the course of... |
Posts Tagged '9th class IIT preparation'
Indian Institute of Technology. The name is enough to describe the intelligence, success and personality of the person. IIT is the dream of every Indian student who aspires to be an engineer one day. It is not only an institute but the dream destination of over 4,00,000 students appearing every year and amount is increasing.
But Joint Entrance Exam or JEE stands as a barrier between success and the student. This exam is one of the toughest exams in India. The reputation of the exam can be judged from the fact that not a single question has been repeated in past 30 years. So, not training but very tough and expert training, along with regular testing is required. You do not require knowledge but instead skilled knowledge is required.
Pioneer Mathematics is the only website in the country providing online IIT Foundation Course for classes 9th and 10th. Realizing the knowledge and the competition in this exam, we start preparing students right from 9th class onwards. The foundation course for IIT JEE is very important as it strengthen the basics roots of students.
9th class is the one in which most of the students realize what exactly is their goal in life. The explanation to this theory lies on the fact of the advice given by the exam toppers. Those students started preparing for the competition and their goal right from the ninth class since in ninth class students get a bit mature to understand the gravity of preparation of exam.
So, for such ambitious students who want to prepare for their future competitions Pioneer Mathematics is here with the right guidance and best quality study material.
IIT Foundation Course and Olympiad Foundation Course. These 2 courses help prepare the students for the competitions exams which everyone has to give.
IIT Foundation Course in most useful specially for IIT and engineering aspirants and even for Commerce and Medical students. Mathematics is base of every subject and physics is all mathematics. In Commerce, mathematics is used everywhere like accounts, economics etc. This course will lay a very strong foundation for Mathematics Competition exam which will be given by everyone eg. IIT-JEE, AIEEE, CAT, CLAT, GRE, TOEFL etc.
The Olympiad Foundation course will provide exposure to students at international level. In this course proper and right guidance for 9th class maths olympiad students. Also it will raise the mathematics standard of every child. Olympiad Foundation Program will lay the strong base for olympiad preparation for the students who will be trained on regional, national and international level.
With the introduction of CBSE CCE pattern, Pioneer Mathematics has come to the rescue of lakhs of students and teachers as well for providing them right guidance. Latest CBSE CCE pattern papers, model papers, sample papers, latest online tests, mock tests etc. are provided to all our members.
Students will also get NCERT solutions, RD Sharma solutions, RS Aggarwal solutions, ML Aggarwal Solutions, smart mathematics, vedic mathematics which included mathematics tricks and techniques making sure to make them human calculator. |
Beginning Algebra
9780495118077
ISBN:
0495118079
Edition: 8 Pub Date: 2007 Publisher: Thomson Learning
Summary: Easy to understand, filled with relevant applications, and focused on helping students develop problem-solving skills, BEGINNING ALGEBRA is unparalleled in its ability to engage students in mathematics and prepare them for higher-level courses. Gustafson and Frisk's accessible style combines with drill problems, detailed examples, and careful explanations to help students overcome any mathematics anxiety. Their prove...n five-step problem-solving strategy helps break each problem down into manageable segments: analyze the problem, form an equation, solve the equation, state the conclusion, and check the result. Examples and problems use real-life data to make the text more relevant to students and to show how mathematics is used in a wide variety of vocations. Plus, the text features plentiful real-world application problems that help build the strong mathematical foundation necessary for students to feel confident in applying their newly acquired skills in further mathematics courses, at home or on the job.
Gustafson, R. David is the author of Beginning Algebra, published 2007 under ISBN 9780495118077 and 0495118079. Eighty Beginning Algebra textbooks are available for sale on ValoreBooks.com, seventy two used from the cheapest price of $0.53, or buy new starting at $111.58.[read more heavy shelf & corner wear, but still a good reading copy. Does not include Online Resource We are a tested and proven company with over 900,000 satisfied customers si [more]
Has heavy shelf & corner wear, but still a good reading copy. Does not include Online Resource We are a tested and proven company with over 900,000 satisfied customers since 1997. Choose expedited shipping (if available) for much faster delivery. Delivery confirmation on all US orders Instructor's Edition. Like new hardcover 8th edition, NO ACCESS CARD. Identical to Student Edition only contains notes and solutions to all problems.Shipping from Ca [more]
ALTERNATE EDITION: Annotated Instructor's Edition. Like new hardcover 8th edition, NO ACCESS CARD. Identical to Student Edition only contains notes and solutions to all problems.Shipping from California.[less] |
Students will develop foundational math skills needed for higher education and practical life skills with ACE's Math curriculum. Algebra 1 PACE 1102 covers graphing numbers on a number line; graphing linear equations of one and two variables on a coordinate plane; solving for one unknown in in terms of the other unknown before substituting; solving a system of two simultaneous equations by addition when none of the coefficients of like terms are additive inverses.removed from the center) to measure understanding.
Customer Reviews for Algebra 1 PACE 1102
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With Checkpoint Maths Revision Guide for the Cambridge Secondary 1 test you can aim for the best grade with the help of relevant and accessible notes, examiner advice plus questions and answers on each key topic. - Clear explanations of every topic covered in the Cambridge Secondary 1 Checkpoint Maths syllabus. - Builds revision skills you need forLearn the basics of practical accounting easily and painlessly with Accounting For Dummies, 4th Edition , which features new information on accounting methods and standards to keep you up to date. With this guide, you can avoid accounting fraud, minimize confusion, maximize profits, and make sense of accounting basics with this plain-English guide... more... |
Handbook of Sinc Numerical Methods presents an ideal road map for handling general numeric problems. Reflecting the author?s advances with Sinc since 1995, the text most notably provides a detailed exposition of the Sinc separation of variables method for numerically solving the full range of partial differential equations (PDEs) of interest to... more...
Pappas has come up with yet another way to make math part of your life. MATH -A-DAY is not a calendar and not a reference book, but a compendium of mathematical information that will give you your math fix everyday. Each day - kick starts your brain with a problem or puzzle with detailed solutions included has a mathematical quote to inspire... more...
State-of-the-Art Approaches to Advance the Large-Scale Green Computing Movement
Edited by one of the founders and lead investigator of the Green500 list, The Green Computing Book: Tackling Energy Efficiency at Large Scale explores seminal research in large-scale green computing. It begins with low-level, hardware-based approaches and then
This book introduces numerical programming using Python and C/C++, emphasizing methods used in physics and engineering. Its helps readers develop the ability to navigate relevant algorithms, knowledge of coding design, and efficient scientific programming skills. It requires minimal background in mathematics, leading readers from elementary methods... more...
Designed for graduate students, this text provides a much-needed contemporary introduction to optimization. Emphasizing general problems and the underlying theory, it covers the fundamental problems of constrained and unconstrained optimization, linear and convex programming, fundamental iterative solution algorithms, gradient methods, the Newton-Raphson... more...
This book provides an introduction to numerical methods for students in chemical engineering. The book starts with a recap on linear algebra. It then presents methods for solving linear and nonlinear equations, with a special focus on Gaussian elimination and Newton?s method. It also discusses ordinary differential equations and partial differential... more... |
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more |
Written in a readable, yet mathematically mature manner appropriate for college algebra level students, Coburn's Precalculus uses narrative, extensive examples, and a range of exercises to connect seemingly disparate mathematical topics into a cohesive whole.
With the same design and feature sets as the market leading Precalculus, 8/e, this addition to the Larson Precalculus series provides both students and instructors with sound, consistently structured explanations of the mathematical concepts. Designed for a two-term course, this text contains the features that have made Precalculus a complete solution for both students and instructors: interesting applications, cutting-edge design, and innovative technology combined with an abundance of carefully written exercises. In addition to a brief algebra review and the core precalculus topics, PRECALCULUS WITH LIMITS covers analytic geometry in three dimensions and introduces concepts covered in calculus.
Mathematics Describing the Real World Precalculus and Trigonometry-Bruce H. Edwards AVI, XviD, 640x480, 29.97 fps | English, MP3@128 kbps , 2 Ch | ~36x30 mins | 10.82 GB The Teaching Company | 2011 | Course no. 1005 Trad... Filesonic, Fileserve, Uploading, Wupload, Uploadstation Links Engoy all members !!!...
TradClear explanations, an uncluttered and appealing layout, and examples and exercises featuring a variety of real-life applications have made this text like you. The book also provides calculator examples, including specific keystrokes that show you how to use various graphing calculators to solve problems more quickly. Perhaps most important-this book effectively prepares you for further courses in mathematics. |
CLE 3102.1.3 Develop inductive and deductive reasoning to independently make and evaluate mathematical arguments and construct appropriate proofs; include various types of reasoning, logic, and intuition.
CLE 3102.1.5 Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies. |
Books
Matrices
An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by doing, writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site,
codingthematrix.com
provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant xkcd comics.
Chapters: The Function, The Field, The Vector, The Vector Space, The Matrix, The Basis, Dimension, Gaussian Elimination, The Inner Product, Special Bases, The Singular Value Decomposition, The Eigenvector, The Linear Program
The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool.
This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms• parallel LU• discrete Poisson solvers• pseudospectra• structured linear equation problems• structured eigenvalue problems• large-scale SVD methods• polynomial eigenvalue problems
Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software.
"Comprehensive . . . an excellent introduction to the subject." — Electronic Engineer's Design Magazine. This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods. The first seven chapters, which require only a first course in calculus and analytic geometry, deal with matrices and linear systems, vector spaces, determinants, linear transformations, similarity, polynomials, and polynomial matrices. Chapters 8 and 9, parts of which require the student to have completed the normal course sequence in calculus and differential equations, provide introductions to matrix analysis and numerical linear algebra, respectively. Among the key features are coverage of spectral decomposition, the Jordan canonical form, the solution of the matrix equation AX = XB, and over 375 problems, many with answers.
Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: - New sections on the singular value and CS decompositions - New applications of the Jordan canonical form - A new section on the Weyr canonical form - Expanded treatments of inverse problems and of block matrices - A central role for the Von Neumann trace theorem - A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetric-skew symmetric pair - Expanded index with more than 3,500 entries for easy reference - More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finite-dimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid - A new appendix provides a collection of problem-solving hints.
Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth century--a feat he celebrated by carving the founding equations into a stone bridge--mathematicians and engineers have been fascinated by these mathematical objects. Today, they are used in applications as various as describing the geometry of spacetime, guiding the Space Shuttle, and developing computer applications in virtual reality. In this book, J. B. Kuipers introduces quaternions for scientists and engineers who have not encountered them before and shows how they can be used in a variety of practical situations.
The book is primarily an exposition of the quaternion, a 4-tuple, and its primary application in a rotation operator. But Kuipers also presents the more conventional and familiar 3 x 3 (9-element) matrix rotation operator. These parallel presentations allow the reader to judge which approaches are preferable for specific applications. The volume is divided into three main parts. The opening chapters present introductory material and establish the book's terminology and notation. The next part presents the mathematical properties of quaternions, including quaternion algebra and geometry. It includes more advanced special topics in spherical trigonometry, along with an introduction to quaternion calculus and perturbation theory, required in many situations involving dynamics and kinematics. In the final section, Kuipers discusses state-of-the-art applications. He presents a six degree-of-freedom electromagnetic position and orientation transducer and concludes by discussing the computer graphics necessary for the development of applications in virtual reality.
The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.
Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.
Lie groups, Lie algebras, and representation theory are the main focus of this text. In order to keep the prerequisites to a minimum, the author restricts attention to matrix Lie groups and Lie algebras. This approach keeps the discussion concrete, allows the reader to get to the heart of the subject quickly, and covers all of the most interesting examples. The book also introduces the often-intimidating machinery of roots and the Weyl group in a gradual way, using examples and representation theory as motivation. The text is divided into two parts. The first covers Lie groups and Lie algebras and the relationship between them, along with basic representation theory. The second part covers the theory of semisimple Lie groups and Lie algebras, beginning with a detailed analysis of the representations of SU(3). The author illustrates the general theory with numerous images pertaining to Lie algebras of rank two and rank three, including images of root systems, lattices of dominant integral weights, and weight diagrams. This book is sure to become a standard textbook for graduate students in mathematics and physics with little or no prior exposure to Lie theory. Brian Hall is an Associate Professor of Mathematics at the University of Notre Dame.
The of statisticians, mathematicians, and scientists.
"This book is intended to teach useful matrix algebra to 'students, teachers, consultants, researchers, and practitioners' in 'statistics and other quantitative methods'.The author concentrates on practical matters, and writes in a friendly and informal style . . . this is a useful and enjoyable book to have at hand." -Biometrics
This book is an easy-to-understand guide to matrix algebra and its uses in statistical analysis. The material is presented in an explanatory style rather than the formal theorem-proof format. This self-contained text includes numerous applied illustrations, numerical examples, and exercises.
When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices.
Each chapter describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly and rigorously with cross references, citations to the literature, and illuminating remarks. Beginning with preliminaries on sets, functions, and relations,Matrix Mathematics covers all of the major topics in matrix theory, including matrix transformations; polynomial matrices; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; vector and matrix norms; the matrix exponential and stability theory; and linear systems and control theory. Also included are a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. This significantly expanded edition of Matrix Mathematics features a wealth of new material on graphs, scalar identities and inequalities, alternative partial orderings, matrix pencils, finite groups, zeros of multivariable transfer functions, roots of polynomials, convex functions, and matrix norms.
Covers hundreds of important and useful results on matrix theory, many never before available in any book
Provides a list of symbols and a summary of conventions for easy use
Includes an extensive collection of scalar identities and inequalities
Features a detailed bibliography and author index with page references |
Emeryville Math these tests and the new common core standards. Algebra 1 consists of symbolic reasoning and calculations with symbols. Through
the study of algebra, a student develops an understanding of the symbolic language
of mathematics and the sciencesIn the conventional education system today memorization is stressed over comprehension, but for professionals to be successful in the increasingly competitive work world today, there needs to be more than just rote drilling and memorization--there needs to be a true appreciation and comprehension... |
The two-line display scientific calculator combines statistics and advanced scientific functions and is a durable and affordable calculator for the classroom. The two-line display helps students explore math and science concepts in the classroom.Color: Orange
The TI-84 Plus Silver Edition graphing calculator comes with a USB cable, plenty of storage and operating memory, and lots of pre-loaded software applications all to help you gain an academic edge from pre-algebra through calculus, as well as biology, chemistry and physics. You can use this TI graphing calculator on the PSAT, SAT, and ACT college entrance exams
This is the new 2013 plastic and paper packaging. These are not returns, or refurbished, and have not been opened. These will include the manufacturer 1 year warranty. (Additional extended warranty is available through ebay.) This is not the CAS Model. Package Includes: -Rechargeable Battery (These can be recharged through USB connection to computer are with wall adapter) -Wall Adapter ...
The two-line display scientific calculator combines statistics and advanced scientific functions and is a durable and affordable calculator for the classroom. The two-line display helps students explore math and science concepts in the classroom.Color: Lavender
DETAILS: Middle Grade Graphing Calculator The Texas Instruments TI73 graphing calculator is designed for middle-grade students. It has a large screen to help students see patterns and analyze data. It features stacked fractions and data analysis functions that allow students to easily view and edit numeric and alphanumeric data in the list editor. They will be able to plot data ...
From the kitchen table to the playground, children are intrigued by their world. The TI-15 is a pedagogically sound tool that helps students make connections between classroom learning and real-world situations.The TI-15 combines the fraction capabilities of the Math Explorer with a two-line display, problem solving, place value and more. When the TI-15 is combined with traditional learning ...
The two-line display scientific calculator combines statistics and advanced scientific functions and is a durable and affordable calculator for the classroom. The two-line display helps students explore math and science concepts in the classroom.Color: Pink. Color Class: Pink
Ideal for the algebra classroom. Lets students graph and compare functions, as well as perform data plotting and analysis. Horizontal and vertical split screen options. Advanced functions accessed through pull-down display menus. Includes tools for finance. I/O port for communication with other TI products.
Color: Blue
... |
Algebra 2 introduces independent and dependent variables and how their solution can be determined by for linear relationships for two or three variables. Algebra 2 also gives an overview of more complex mathematical functions like basic trigonometric functions, power functions, logarithms, and ... |
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