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Workbook Notes, sample problems, exercises, and practice problems

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.

Foundations of Mathematics Details

Thinkwell's Foundations of Mathematics 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 Foundations of Mathematics 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

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1. Integers

  • 1.1 Introduction to Integers
    • 1.1.1 Integers and the Number Line
  • 1.2 Operations with Integers
    • 1.2.1 Addition of Integers
    • 1.2.2 Subtraction of Integers
    • 1.2.3 Multiplication and Division of Integers
    • 1.2.4 Introduction to Exponents
    • 1.2.5 Using the Order of Operations

2. Fractions

  • 2.1 Introduction to Fractions
    • 2.1.1 Factors, Multiples, and Equivalent Fractions
  • 2.2 Operations with Fractions
    • 2.2.1 Multiplying Fractions and Mixed Numbers
    • 2.2.2 Dividing Fractions and Mixed Numbers
    • 2.2.3 Adding and Subtracting Fractions and Mixed Numbers

3. Decimals

  • 3.1 Introduction to Decimals
    • 3.1.1 Representing, Comparing, and Ordering Decimals
    • 3.1.2 Rounding and Estimating Decimals
  • 3.2 Operations with Decimals
    • 3.2.1 Adding and Subtracting Decimals
    • 3.2.2 Multiplying Decimals
    • 3.2.3 Dividing Decimals
  • 3.3 Fractions and Decimals
    • 3.3.1 Converting between Fractions and Decimals
    • 3.3.2 The Order of Operations with Fractions and Decimals

4. Ratios, Proportions, and Percents

  • 4.1 Ratios and Proportions
    • 4.1.1 Ratios and Rates
    • 4.1.2 Proportions
    • 4.1.3 Finding an Unknown Value in a Proportion
    • 4.1.4 Applications of Proportions
  • 4.2 Percents
    • 4.2.1 Introduction to Percents
    • 4.2.2 Percents
    • 4.2.3 Relating Percents, Decimals, and Fractions
    • 4.2.4 Estimating with Percents
    • 4.2.5 Finding and Using Percents

5. Variables, Expressions, and Equations

  • 5.1 Introduction to Equations
    • 5.1.1 Variables and Expressions
    • 5.1.2 Translating Between Words and Math
    • 5.1.3 Simplifying Algebraic Expressions
    • 5.1.4 Translating Between Tables and Expressions
    • 5.1.5 Equations and Their Solutions
  • 5.2 Introduction to Solving Equations
    • 5.2.1 Solving Addition Equations
    • 5.2.2 Solving Subtraction Equations
    • 5.2.3 Solving Multiplication Equations
    • 5.2.4 Solving Division Equations
  • 5.3 Solving Equations
    • 5.3.1 Solving Equations Containing Integers
    • 5.3.2 Writing and Solving Two-Step Equations
    • 5.3.3 Writing and Solving Multi-Step Equations
    • 5.3.4 Solving Equations with Variables on Both Sides
    • 5.3.5 Solving Literal Equations

6. Measurement

  • 6.1 Measurement
    • 6.1.1 Understanding Customary Units of Measurement
    • 6.1.2 Understanding Metric Units of Measurement
    • 6.1.3 Converting Customary Units
    • 6.1.4 Converting Metric Units
    • 6.1.5 Converting between Customary and Metric Units
    • 6.1.6 Time and Temperature

7. Geometry

  • 7.1 Polygons
    • 7.1.1 Triangles
    • 7.1.2 Quadrilaterals
    • 7.1.3 Finding Angles in Polygons
  • 7.2 Area, Perimeter, and Circumference
    • 7.2.1 Perimeter
    • 7.2.2 Area of Rectangles and Parallelograms
    • 7.2.3 Circles and Circumference
    • 7.2.4 Area of Circles
  • 7.3 Solids
    • 7.3.1 Introduction to Three-Dimensional Figures
    • 7.3.2 Volume of Prisms and Cylinders

8. Statistics and Graphs

  • 8.1 Organizing, Displaying, and Interpreting Data
    • 8.1.1 Organizing Data
    • 8.1.2 Bar Graphs and Histograms
    • 8.1.3 Line Graphs
    • 8.1.4 Reading and Interpreting Circle Graphs
    • 8.1.5 Measures of Central Tendency

About the Author

Author BUR

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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