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Intermediate Algebra
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12-month access
$125.00
Access to a complete online package that includes everything you need.
- Equivalent to 8th- or 9th-grade Algebra 1
- More than 230 video tutorials and 40 available contact hours.
- 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 Intermediate 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 Intermediate 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 An Introduction to Algebra
1.1.2 The Top Ten List of Mistakes
1.2 Properties of Real Numbers
1.2.1 Properties, Identities, & Inverses
1.3 Inequalities
1.3.1 Concepts of Inequality
1.3.2 Inequalities and Interval Notation
1.4 Absolute Value
1.4.1 Properties of Absolute Value
1.4.2 Evaluating Absolute Value Expressions
1.5 Operations on Real Numbers
1.5.1 Operations Considering Signs
1.5.2 Prime and Composite Numbers and Their Roots
1.5.3 Order of Operations
1.6 Conditional Statements
1.6.1 Forms of Conditional Statements
1.6.2 Inductive Reasoning
2.1 Equations in One Variable
2.1.1 An Introduction to Solving Equations
2.1.2 Equality or Identity?
2.1.3 Equivalent Equations and Equations with No Solution
2.1.4 Solving Linear Equations
2.2 Applications of Equations Using Formulas
2.2.1 An Introduction to Solving Word Problems
2.2.2 Finding Perimeter
2.2.3 Solving a Linear Geometry Problem
2.2.4 Solving for Constant Velocity
2.3 More Applications
2.3.1 Solving a Business Problem
2.3.2 Solving a Mixture Problem
2.3.3 Solving an Investment Problem
2.3.4 Solving for Consecutive Numbers
2.3.5 Finding an Average
2.4 Inequalities in One Variable
2.4.1 An Introduction to Solving Inequalities
2.4.2 Solving Inequalities
2.4.3 Solving Word Problems with Inequalities
2.5 Compound Inequalities
2.5.1 Sets, Intersections, and Unions
2.5.2 Solving Compound Inequalities
2.5.3 More on Compound Inequalities
2.6 Absolute Value Equations
2.6.1 Matching Number Lines with Absolute Value
2.6.2 Solving Absolute Value Equations
2.6.3 Solving Equations with Two Absolute Value Expressions
2.7 Absolute Value Inequalities
2.7.1 Solving Absolute Value Inequalities
2.7.2 Solving Absolute Value Inequalities: More Examples
3.1 Understanding Exponents
3.1.1 An Introduction to Exponents
3.1.2 Evaluating Exponential Expressions
3.1.3 Applying the Rules of Exponents
3.1.4 Evaluating Expressions with Negative Exponents
3.2 Scientific Notation
3.2.1 Converting between Decimal and Scientific Notation
3.3 Polynomial Basics
3.3.1 Determining Components and Degree
3.3.2 Adding and Subtracting Polynomials
3.3.3 Multiplying Polynomials
3.4 Techniques for Multiplying Polynomials
3.4.1 The FOIL Method
3.4.2 Multiplying Big Products
3.4.3 Using Special Products
3.5 Techniques for Factoring
3.5.1 Factoring Using the Greatest Common Factor
3.5.2 Factoring by Grouping
3.5.3 Factoring Trinomials Completely
3.5.4 Factoring Trinomials: The Guess and Check Method
3.6 Special Factoring
3.6.1 Factoring Perfect Square Trinomials
3.6.2 Factoring the Difference of Two Squares
3.6.3 Factoring Sums and Differences of Cubes
3.6.4 Factoring by Any Method
3.7 Solving Equations by Factoring
3.7.1 The Zero Factor Property
3.8 Division of Polynomials
3.8.1 Using Long Division with Polynomials
3.8.2 Long Division: Another Example
3.9 Synthetic Division
3.9.1 Using Synthetic Division with Polynomials
3.9.2 More Synthetic Division
3.10 The Remainder Theorem
3.10.1 Using the Remainder Theorem
3.10.2 More on the Remainder Theorem
4.1 The Basics of Rational Expressions
4.1.1 An Introduction to Rational Expressions
4.1.2 Working with Fractions
4.1.3 Writing Rational Expressions in Lowest Terms
4.2 Operations with Rationals
4.2.1 Multiplying and Dividing Rational Expressions
4.2.2 Adding and Subtracting Rational Expressions
4.2.3 Rewriting Complex Fractions
4.3 Equations with Rationals
4.3.1 Solving a Linear Equation with Rationals
4.3.2 Solving a Linear Equation with Restrictions
4.4 Inequalities with Rationals
4.4.1 Solving Rational Inequalities
4.4.2 Solving Rational Inequalities: Another Example
4.4.3 Determining Domain
4.5 Applications
4.5.1 Solving a Problem About Work
4.5.2 Resistors in Parallel
4.6 Variation
4.6.1 An Introduction to Variation
4.6.2 Direct Proportion
4.6.3 Inverse Proportion
4.6.4 Joint and Combined Proportion
5.1 Rational Exponents and Radicals
5.1.1 Radical Notation and Properties of Roots
5.1.2 Variables and Negative Values under a Radical
5.1.3 Converting Rational Exponents and Radicals
5.2 Simplifying Radical Expressions
5.2.1 Simplifying Radicals
5.2.2 Simplifying Radical Expressions with Variables
5.3 Operations with Radical Expressions
5.3.1 Adding and Subtracting Radical Expressions
5.3.2 Rationalizing Denominators
5.4 Equations with Radicals
5.4.1 Solving an Equation Containing a Radical
5.4.2 Solving Equations with Two Radical Expressions
5.4.3 Extraneous Roots
5.4.4 Solving Equations with Rational Exponents
5.5 Complex Numbers
5.5.1 Introducing and Writing Complex Numbers
5.5.2 Rewriting Powers of i
5.5.3 Adding and Subtracting Complex Numbers
5.5.4 Multiplying Complex Numbers
5.5.5 Dividing Complex Numbers
5.6 Applications
5.6.1 Finding the Length of the Diagonal of a Cube
5.6.2 Finding the Distance and Midpoint between Two Points
5.6.3 Applications in Meteorology
6.1 The Rectangular Coordinate System
6.1.1 Using the Cartesian System
6.1.2 Thinking Visually
6.2 An Introduction to Functions
6.2.1 Introducing Relations and Functions
6.2.2 Functions and the Vertical Line Test
6.2.3 Function Notation and Values
6.3 Domain and Range
6.3.1 Finding Domain and Range
6.3.2 Domain and Range: An Explicit Example
6.3.3 Satisfying the Domain of a Function
6.3.4 Graphing Important Functions
6.4 The Algebra of Functions
6.4.1 Operations on Functions
6.4.2 Composite Functions
6.4.3 Components of Composite Functions
7.1 The Slope of a Line
7.1.1 An Introduction to Slope
7.1.2 Finding the Slope Given Two Points
7.2 Graphing Linear Equations
7.2.1 Using Intercepts to Graph Lines
7.2.2 Working with Specific Lines
7.2.3 Interpreting Slope from a Graph
7.2.4 Graphing with a Point and the Slope
7.3 Linear Equations
7.3.1 Writing an Equation in Slope-Intercept Form
7.3.2 Writing an Equation Given Two Points
7.3.3 Writing an Equation in Point-Slope Form
7.3.4 Matching a Slope-Intercept Equation with its Graph
7.3.5 Slope for Parallel and Perpendicular Lines
7.4 Applications of Linear Concepts
7.4.1 Constructing a Linear Model from a Set of Data
7.4.2 Scatterplots and Predictions
7.4.3 Interpreting Line Graphs
7.4.4 Linear Cost and Revenue
8.1 Linear Systems in Two Variables
8.1.1 An Introduction to Linear Systems
8.1.2 Solving a System by Graphing
8.1.3 Solving a System by Substitution
8.1.4 Solving a System by Elimination
8.2 Linear Systems in Three Variables
8.2.1 An Introduction to Systems in Three Variables
8.2.2 Solving Systems with Three Variables
8.2.3 Solving Inconsistent Systems
8.2.4 Solving Dependent Systems
8.2.5 Solving Systems with Two Equations
8.3 Applications of Linear Systems
8.3.1 Investments
8.3.2 Partial Fractions
8.4 Solutions by Matrix Methods
8.4.1 An Introduction to Matrices
8.4.2 Using the Gauss-Jordan Method
8.4.3 Using Gauss-Jordan: Another Example
8.5 Determinants
8.5.1 Evaluating 2x2 Determinants
8.5.2 Evaluating nxn Determinants
8.6 Cramer's Rule
8.6.1 Using Cramer's Rule
8.6.2 Using Cramer's Rule in a 3x3 Matrix
8.7 Working with Inequalities
8.7.1 An Introduction to Graphing Linear Inequalities
8.7.2 Graphing Linear and Nonlinear Inequalities
8.7.3 Graphing the Solution Set of a System of Inequalities
8.8 Systems of Nonlinear Equations
8.8.1 Solving a Nonlinear System by Elimination
8.8.2 Solving a Nonlinear System by Substitution
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 Solution 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 Parabolas
10.1.1 An Introduction to Conic Sections
10.1.2 An Introduction to Parabolas
10.2 Equations for Parabolas
10.2.1 Determining Information about a Parabola from the Equation
10.2.2 Writing an Equation for a Parabola
10.3 Graphing Parabolas
10.3.1 Shifting Curves along Axes
10.3.2 Shifting or Translating Curves along Axes
10.3.3 Stretching a Graph
10.3.4 Graphing Quadratics Using Patterns
10.4 Applications of Parabolas
10.4.1 Finding the Maximum or Minimum of a Quadratic
10.4.2 Maximum Height in the Real World: A Bridge
10.5 Circles
10.5.1 The Center-Radius Equation of a Circle
10.5.2 Finding the Center or Radius of a Circle
10.5.3 Decoding the Circle Formula
10.5.4 Solving Circle Problems
10.6 Ellipses
10.6.1 An Introduction to Ellipses
10.6.2 Finding the Equation for an Ellipse
10.6.3 Applying Ellipses: Satellites
10.7 Hyperbolas
10.7.1 An Introduction to Hyperbolas
10.7.2 Finding the Equation for a Hyperbola
10.7.3 Applying Hyperbolas: Navigation
10.8 Identifying Conic Sections
10.8.1 Identifying a Conic
10.8.2 Name That Conic
10.9 Square Root Functions
10.9.1 Conic Halves
11.1 Inverse Functions
11.1.1 Understanding Inverse Functions
11.1.2 The Horizontal Line Test
11.1.3 Are Two Functions Inverses of Each Other?
11.1.4 Graphing the Inverse
11.1.5 Finding the Inverse of a Function
11.2 Exponential Functions
11.2.1 An Introduction to Exponential Functions
11.2.2 Graphing Exponential Functions: Patterns
11.2.3 Graphing Exponential Functions: More Patterns
11.2.4 The Number e
11.3 Using Exponential Functions
11.3.1 Using Properties of Exponents to Solve Exponential Functions
11.3.2 Finding Present and Future Value
11.3.3 Finding an Interest Rate to Match Goals
11.4 Logarithmic Functions
11.4.1 An Introduction to Logarithmic Functions
11.4.2 Converting between Exponential and Logarithmic Functions
11.4.3 Graphing Logarithmic Functions
11.4.4 Matching Logarithmic Functions with Their Graphs
11.5 Properties of Logarithms
11.5.1 Properties of Logarithms
11.5.2 Expanding a Logarithmic Expression with Properties
11.5.3 Combining Logarithmic Expressions
11.6 Evaluating Logarithms
11.6.1 Finding the Value of a Logarithmic Function
11.6.2 Solving for x in Logarithmic Equations
11.6.3 Using the Logarithmic Change of Base Formula
11.6.4 Evaluating Logarithmic Functions with a Calculator
11.7 Exponential and Logarithmic Equations
11.7.1 Solving Exponential Equations
11.7.2 Solving Logarithmic Equations
11.7.3 Solving Equations with Logarithmic Exponents
11.8 Applications of Exponential and Log Functions
11.8.1 Compound Interest
11.8.2 Predicting Change
11.9 Exponential Growth and Decay
11.9.1 An Introduction to Exponential Growth and Decay
11.9.2 Half Life
11.9.3 Newton's Law of Cooling
11.9.4 Continuously Compounded Interest
12.1 Sequences and Series
12.1.1 General and Specific Terms
12.1.2 Understanding Sequence Problems
12.1.3 Series Notation, Definitions and Evaluating
12.2 Arithmetic Sequences
12.2.1 Finding Terms in Arithmetic Sequences
12.2.2 Finding the Sum of an Arithmetic Sequence
12.3 Geometric Sequences
12.3.1 Finding Terms in Geometric Sequences
12.3.2 Finding the Sum of a Geometric Sequence
12.4 The Binomial Theorem
12.4.1 Using the Binomial Theorem
12.4.2 Binomial Coefficients
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.
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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.
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