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Algebra 1 Details
Thinkwell's Algebra 1 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 Algebra 1 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.
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.
Table of Contents
(Expand All - Close All)1. Foundations for Algebra
- 1.1 The Language of Algebra
- 1.1.1 Variables and Expressions
- 1.1.2 Adding and Subtracting Real Numbers
- 1.1.3 Multiplying and Dividing Real Numbers
- 1.1.4 Powers and Exponents
- 1.1.5 Square Roots and Real Numbers
- 1.2 Tools of Algebra
- 1.2.1 Set Theory
- 1.2.2 Order of Operations
- 1.2.3 Simplifying Expressions
- 1.2.4 Introduction to Functions
2. Equations, Proportions, and Percent
- 2.1 Solving Equations
- 2.1.1 Addition and Subtraction Equations
- 2.1.2 Multiplication and Division Equations
- 2.1.3 Solving Two-Step Equations
- 2.1.4 Solving Multi-Step Equations
- 2.1.5 Solving Equations with Variables on Both Sides
- 2.1.6 Solving Literal Equations
- 2.1.7 Solving Absolute-Value Equations
- 2.2 Proportion and Percent
- 2.2.1 Rates, Ratios, and Proportions
- 2.2.2 Applications of Proportion
- 2.2.3 Percents
- 2.2.4 Applications of Percent
- 2.2.5 Percent Increase and Decrease
3. Inequalities
- 3.1 Introduction to Inequalities
- 3.1.1 Graphing and Writing Inequalities
- 3.1.2 Solving Inequalities by Adding or Subtracting
- 3.1.3 Solving Inequalities by Multiplying or Dividing
- 3.2 Multi-Step and Compound Inequalities
- 3.2.1 Solving Two-Step and Multi-Step Inequalities
- 3.2.2 Solving Inequalities with Variables on Both Sides
- 3.2.3 Solving Compound Inequalities
- 3.2.4 Solving Absolute-Value Inequalities
4. Functions
- 4.1 Introduction to Functions
- 4.1.1 Graphing Relationships
- 4.1.2 Relations and Functions
- 4.1.3 Writing Function Rules
- 4.2 Applying Functions
- 4.2.1 Graphing Functions
- 4.2.2 Scatter Plots and Trend Lines
- 4.2.3 Arithmetic Sequences
5. Linear Functions
- 5.1 Characteristics of Linear Functions
- 5.1.1 Identifying Linear Functions
- 5.1.2 Using Intercepts
- 5.1.3 Rate of Change and Slope
- 5.1.4 The Slope Formula
- 5.1.5 The Midpoint and Distance Formulas
- 5.1.6 Direct Variation
- 5.2 Using Linear Functions
- 5.2.1 Slope-Intercept Form
- 5.2.2 Point-Slope Form
- 5.2.3 Slopes of Parallel and Perpendicular Lines
- 5.2.4 Transforming Linear Functions
6. Systems of Equations and Inequalities
- 6.1 Systems of Linear Equations
- 6.1.1 Solving Systems by Graphing
- 6.1.2 Solving Systems by Substitution
- 6.1.3 Solving Systems by Elimination
- 6.1.4 Solving Special Systems
- 6.1.5 Applying Systems
- 6.2 Linear Inequalities
- 6.2.1 Graphing Linear Inequalities
- 6.2.2 Solving Systems of Linear Inequalities
7. Exponents and Polynomials
- 7.1 Exponents
- 7.1.1 Product and Power Properties of Exponents
- 7.1.2 Integer Exponents
- 7.1.3 Quotient Properties of Exponents
- 7.1.4 An Application of Exponents: Scientific Notation
- 7.1.5 Fractional Exponents
- 7.2 Polynomials
- 7.2.1 Polynomials
- 7.2.2 Adding and Subtracting Polynomials
- 7.2.3 Multiplying Polynomials by Monomials
- 7.2.4 Multiplying Binomials
8. Factoring Polynomials
- 8.1 Factoring Methods
- 8.1.1 Factors and Greatest Common Factors
- 8.1.2 Factoring by GCF
- 8.1.3 Factoring x2 + bx + c
- 8.1.4 Factoring ax2 + bx + c
- 8.2 Applying Factoring Methods
- 8.2.1 Factoring Special Products
- 8.2.2 Choosing a Factoring Method
9. Quadratic Functions and Equations
- 9.1 Quadratic Functions
- 9.1.1 Identifying Quadratic Functions
- 9.1.2 Characteristics of Quadratic Functions
- 9.1.3 Graphing Quadratic Functions
- 9.1.4 Transforming Quadratic Functions
- 9.2 Solving Quadratic Equations
- 9.2.1 Solving Quadratic Equations by Graphing
- 9.2.2 Solving Quadratic Equations by Factoring
- 9.2.3 Solving Quadratic Equations by Using Square Roots
- 9.2.4 Completing the Square
- 9.2.5 The Quadratic Formula
- 9.2.6 The Discriminant
10. Data Analysis and Probability
- 10.1 Probability
- 10.1.1 Experimental Probability
- 10.1.2 Theoretical Probability
- 10.1.3 Independent and Dependent Events
- 10.1.4 Combinations and Permutations
- 10.2 Data Analysis
- 10.2.1 Bar, Circle, and Line Graphs
- 10.2.2 Stem-and-Leaf Plots and Histograms
- 10.2.3 Mean, Median, Mode, and Range
- 10.2.4 Box-and-Whisker Plots
- 10.2.5 Expected Value
- 10.2.6 Normal Distribution
- 10.2.7 Misleading Graphs and Statistics
11. Exponential and Radical Functions
- 11.1 Exponential Functions
- 11.1.1 Geometric Sequences
- 11.1.2 Exponential Functions
- 11.1.3 Exponential Growth and Decay
- 11.1.4 Linear, Quadratic, and Exponential Models
- 11.2 Radical Functions, Expressions, and Equations
- 11.2.1 Square-Root Functions
- 11.2.2 Radical Expressions
- 11.2.3 Adding and Subtracting Radical Expressions
- 11.2.4 Multiplying and Dividing Radical Expressions
- 11.2.5 Solving Radical Equations
12. Rational Functions and Equations
- 12.1 Rational Functions and Expressions
- 12.1.1 Inverse Variation
- 12.1.2 Rational Functions
- 12.1.3 Simplifying Rational Expressions
- 12.2 Operations with Rational Expressions
- 12.2.1 Multiplying and Dividing Rational Expressions
- 12.2.2 Adding and Subtracting Rational Expressions
- 12.2.3 Dividing Polynomials
- 12.2.4 Solving Rational Equations
About the Author
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 listed him in the "100 Best of America". After completing his tenure as Gaudino Scholar at Williams, he was named Lissack Professor for Social Responsibility and Personal Ethics.
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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