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Beginning Algebra
Online Subscription
12-month access
$125.00
Access to a complete online package that includes everything you need.
- Dynamic videos explain all of the topics and concepts to make you successful.
- Interactive exercises with immediate feedback allow you to track your progress.
- Practice tests and final tests for each chapter (only available in the home school version).
- Illustrated notes help you review what you've learned in the videos.
There is no easier way to learn!
Thinkwell's Beginning Algebra with Edward Burger lays the foundation for success because, unlike a traditional textbook, students actually like using it. Thinkwell works with the learning styles of students who have found that traditional textbooks are not effective. Watch one Thinkwell video lecture and you'll understand why Thinkwell works better.
Comprehensive Video Tutorials
We've built Beginning Algebra around hundreds of multimedia tutorials that provide dozens of hours of instructional material. Thinkwell offers a more engaging, more effective way for you to learn.
Instead of reading dense chunks of text from a printed book, you can watch video lectures filled with illustrations, examples, and even humor. Students report learning more easily with Thinkwell than with traditional textbooks.
Interactive Exercises with Feedback
There are hundreds of exercise items with fully worked-out solutions and explanations. Each video topic has corresponding exercises to test your understanding.
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Test your understanding with hundreds of exercises that are automatically graded. Your results are available immediately, including fully worked-out solutions and explanations for each exercise. You can work on the exercises at the computer or print them out to work on later. Access your cumulative results anytime.
Review Notes and More
While the video lectures are the heart of Thinkwell products, we also offer concise, illustrated review notes, a glossary, transcripts of the video lectures, and links to relevant websites. All of these materials may be viewed online, and the notes and transcripts may be printed and kept for reference.
1.1 Introduction
1.1.1 Beginning Algebra
1.1.2 Review of Arithmetic: Addition and Subtraction
1.1.3 Review of Arithmetic: Multiplication and Division
1.1.4 Top Ten List of Mistakes
1.2 Factors and Fractions
1.2.1 Factors and Primes
1.2.2 Greatest Common Factor and Least Common Multiples
1.2.3 Introduction to Fractions
1.2.4 Multiplying Fractions
1.2.5 Dividing Fractions
1.2.6 Adding Fractions
1.2.7 Subtracting Fractions
1.2.8 Mixed Numbers
1.2.9 Adding and Subtracting Mixed Numbers
1.2.10 Multiplying and Dividing Mixed Numbers
1.3 Decimals
1.3.1 Decimal Numbers
1.3.2 Multiplying and Dividing Decimals
1.3.3 Percent
1.3.4 Conversion between Fractions, Percents, and Decimals
2.1 The Real Number System
2.1.1 Real Numbers
2.1.2 Ordering Real Numbers
2.1.3 Arithmetic on the Number Line
2.1.4 Multiplying Real Numbers
2.1.5 Multiplying a Negative by a Negative: The Why
2.1.6 Dividing Real Numbers
2.1.7 Order of Operations
2.1.8 Properties of Real Numbers
2.2 Exponents, Exponential Notation, and Scientific Notation
2.2.1 Introduction to Exponents
2.2.2 Evaluating Exponential Expressions
2.2.3 Applying the Rules of Exponents
2.2.4 Evaluating Expressions with Negative Exponents
2.2.5 Converting between Decimal and Scientific Notation
2.3 Algebraic Expressions and the Language of Algebra
2.3.1 Algebraic Expressions
2.3.2 Introduction to Word Problems
3.1 Introduction to Solving Equations
3.1.1 Equations
3.1.2 Addition Property of Equality
3.1.3 Multiplication Property of Equality
3.2 Further Techniques for Solving Equations
3.2.1 Solving Equations with the Variable on One Side
3.2.2 Solving Equations with the Variable on Both Sides
3.2.3 Equality or Identity?
3.2.4 Equivalent Equations and Equations with No Solution
4.1 Formulas and Word Problems
4.1.1 Formulas
4.1.2 Formulas: Temperature Conversion and Rate
4.1.3 Ratios and Proportions
4.1.4 More Ratios and Proportions
4.1.5 Finding a Perimeter
4.1.6 Solving a Linear Geometry Problem
4.1.7 Solving for Constant Velocity
4.1.8 Solving a Business Problem
4.1.9 Solving a Mixture Problem
4.1.10 Solving an Investment Problem
4.1.11 Solving for Consecutive Numbers
4.1.12 Finding an Average
4.2 Inequalities in One Variable
4.2.1 Introduction to Inequalities
4.2.2 Solving Inequalities
4.2.3 Solving Word Problems with Inequalities
4.3 Compound Inequalities
4.3.1 Sets, Intersections, and Unions
4.3.2 Solving Compound Inequalities
4.3.3 More On Compound Inequalities
4.4 Absolute-Value Equations
4.4.1 Matching Number Lines with Absolute Value
4.4.2 Solving Absolute-Value Equations
4.4.3 Solving Equations with Two Absolute-Value Expressions
4.5 Absolute-Value Inequalities
4.5.1 Solving Absolute-Value Inequalities
4.5.2 Solving Absolute-Value Inequalities: More Examples
5.1 Polynomial Basics
5.1.1 Determining Components and Degree
5.1.2 Adding and Subtracting Polynomials
5.1.3 Multiplying Polynomials
5.2 Techniques for Multiplying Polynomials
5.2.1 The FOIL Method
5.2.2 Multiplying Big Products
5.2.3 Using Special Products
5.3 Techniques for Factoring
5.3.1 Factoring Using the Greatest Common Factor
5.3.2 Factoring by Grouping
5.3.3 Factoring Trinomials Completely
5.3.4 Factoring Trinomials: The Guess and Check Method
5.4 Special Factoring
5.4.1 Factoring Perfect-Square Trinomials
5.4.2 Factoring the Difference of Two Squares
5.4.3 Factoring the Sums and Differences of Cubes
5.4.4 Factoring by Any Method
5.5 Solving Equations by Factoring
5.5.1 The Zero-Factor Property
5.6 Division of Polynomials
5.6.1 Using Long Division with Polynomials
5.6.2 Long Division: Another Example
5.7 Synthetic Division
5.7.1 Using Synthetic Division with Polynomials
5.7.2 More Synthetic Division
5.8 The Remainder Theorem
5.8.1 Using the Remainder Theorem
5.8.2 More on the Remainder Theorem
6.1 The Basics of Rational Expressions
6.1.1 An Introduction to Rational Expressions
6.1.2 Working with Fractions
6.1.3 Writing Rational Expressions in Lowest Terms
6.2 Operations with Rationals
6.2.1 Multiplying and Dividing Rational Expressions
6.2.2 Adding and Subtracting Rational Expressions
6.2.3 Rewriting Complex Fractions
6.3 Equations with Rationals
6.3.1 Solving a Linear Equation with Rationals
6.3.2 Solving a Linear Equation with Restrictions
6.4 Inequalities with Rationals
6.4.1 Solving Rational Inequalities
6.4.2 Solving Rational Inequalities: Another Example
6.4.3 Determining Domain
6.5 Applications
6.5.1 Solving a Problem about Work
6.5.2 Resistors in Parallel
6.6 Variation
6.6.1 An Introduction to Variation
6.6.2 Direct Proportion
6.6.3 Inverse Proportion
6.6.4 Joint and Combined Proportion
7.1 The Rectangular Coordinate System
7.1.1 Using the Cartesian System
7.1.2 Thinking Visually
7.2 An Introduction to Functions
7.2.1 Introducing Relations and Functions
7.2.2 Functions and the Vertical-Line Test
7.2.3 Function Notation and Values
7.3 Domain and Range
7.3.1 Finding Domain and Range
7.3.2 Domain and Range: An Explicit Example
7.3.3 Satisfying the Domain of a Function
7.3.4 Graphing Important Functions
7.4 The Algebra of Functions
7.4.1 Operations on Functions
7.4.2 Composite Functions
7.4.3 Components of Composite Functions
7.5 The Slope of a Line
7.5.1 An Introduction to Slope
7.5.2 Finding the Slope Given Two Points
7.6 Graphing Linear Equations
7.6.1 Using Intercepts to Graph Lines
7.6.2 Working with Specific Lines
7.6.3 Interpreting Slope from a Graph
7.6.4 Graphing with a Point and the Slope
7.7 Linear Equations
7.7.1 Writing an Equation in Slope-Intercept Form
7.7.2 Writing an Equation Given Two Points
7.7.3 Writing an Equation in Point-Slope Form
7.7.4 Matching a Slope-Intercept Equation with Its Graph
7.7.5 Slope for Parallel and Perpendicular Lines
7.8 Applications of Linear Concepts
7.8.1 Constructing a Linear Model from a Set of Data
7.8.2 Scatterplots and Predictions
7.8.3 Interpreting Line Graphs
7.8.4 Linear Cost and Revenue
8.1 Rational Exponents and Radicals
8.1.1 Converting Rational Exponents and Radicals
8.1.2 Radical Notation and Properties of Roots
8.1.3 Variables and Negative Values under a Radical
8.2 Simplifying Radical Expressions
8.2.1 Simplifying Radicals
8.2.2 Simplifying Radical Expressions with Variables
8.3 Operations with Radical Expressions
8.3.1 Adding and Subtracting Radical Expressions
8.3.2 Rationalizing Denominators
8.4 Equations with Radicals
8.4.1 Extraneous Roots
8.4.2 Solving an Equation Containing a Radical
8.4.3 Solving Equations with Two Radical Expressions
8.4.4 Solving Equations with Rational Exponents
8.5 Complex Numbers
8.5.1 Introducing and Writing Complex Numbers
8.5.2 Rewriting Powers of i
8.5.3 Adding and Subtracting Complex Numbers
8.5.4 Multiplying Complex Numbers
8.5.5 Dividing Complex Numbers
8.6 Applications
8.6.1 Finding the Length of the Diagonal of a Cube
8.6.2 Finding the Distance and the Midpoint between Two Points
8.6.3 Applications in Meteorology
9.1 The Basics of Quadratics
9.1.1 An Introduction to Quadratics
9.1.2 Solving Quadratics by Factoring
9.2 Graphs of Quadratics
9.2.1 Finding x- and y-intercepts
9.2.2 Nice-Looking Parabolas
9.2.3 Graphing Parabolas
9.3 Solving by Completing the Square
9.3.1 Solving by Completing the Square
9.3.2 Completing the Square: Another Example
9.3.3 Finding the Vertex by Completing the Square
9.4 Writing Quadratic Equations
9.4.1 Using the Vertex to Write the Equation
9.4.2 Building a Polynomial Equation from Its Solutions
9.5 Solving with the Quadratic Formula
9.5.1 Proving the Quadratic Formula
9.5.2 Using the Quadratic Formula
9.5.3 Predicting Types of Solutions From the Discriminant
9.5.4 Using the Discriminant to Graph Parabolas
9.6 Equations Quadratic in Form
9.6.1 Solving for a Squared Variable
9.6.2 Finding Real-Number Restrictions
9.6.3 Solving Fancy Quadratics
9.6.4 Horizontal Parabolas
9.7 Formulas and Applications
9.7.1 Solving a Quadratic Geometry Problem
9.7.2 Solving with the Pythagorean Theorem
9.7.3 Solving a Motion Problem
9.7.4 Solving a Projectile Problem
9.7.5 Solving Other Problems
9.8 Nonlinear Inequalities
9.8.1 Solving Quadratic Inequalities
9.8.2 Solving Quadratic Inequalities: Another Example
10.1 Linear Systems in Two Variables
10.1.1 An Introduction to Linear Systems
10.1.2 Solving a System by Graphing
10.1.3 Solving a System by Substitution
10.1.4 Solving a System by Elimination
10.2 Linear Systems in Three Variables
10.2.1 An Introduction to Systems in Three Variables
10.2.2 Solving Systems with Three Variables
10.2.3 Solving Inconsistent Systems
10.2.4 Solving Dependent Systems
10.2.5 Solving Systems with Two Equations
10.3 Applications of Linear Systems
10.3.1 Investments
10.3.2 Partial Fractions
10.4 Solutions by Matrix Methods
10.4.1 An Introduction to Matrices
10.4.2 Using the Gauss-Jordan Method
10.4.3 Using Gauss-Jordan: Another Example
10.5 Determinants
10.5.1 Evaluating 2x2 Determinants
10.5.2 Evaluating nxn Determinants
10.6 Cramer's Rule
10.6.1 Using Cramer's Rule
10.6.2 Using Cramer's Rule in a 3x3 Matrix
10.7 Working with Inequalities
10.7.1 An Introduction to Graphing Linear Inequalities
10.7.2 Graphing Linear and Nonlinear Inequalities
10.7.3 Graphing the Solution Set of a System of Inequalities
10.8 Systems of Nonlinear Equations
10.8.1 Solving a Nonlinear System by Elimination
10.8.2 Solving a Nonlinear System by Substitution
Edward Burger
Williams College
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
Workbook
Notes, sample problems, exercises, and practice problems$29.00
Study without a computer. Our workbook companion contains the same lecture notes and sample problems that are delivered online, as well as some additional exercises, all in a convenient print format. Answers to the odd-numbered exercises are in the back of the book. Online Subscription is required; workbook not sold separately.
CD Set
Video Lectures on CD-ROM$25.00
This optional CD-ROM set delivers the exact same video lectures delivered online, but without an internet connection. Online Subscription is required; CDs not sold separately. The CDs only contain the videos.
Video lessons
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Illustrated Notes
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