*For courses in Liberal Arts Mathematics and Quantitative Literacy.*

**The standard in quantitative reasoning instruction – by authorities in the field**

The **7th Edition** of ** ***Using & Understanding Mathematics* by Jeff Bennett and Bill Briggs aims to prepare students for the mathematics they will encounter in other college courses, future careers, and life.

The authors' goal is to develop students’ ability to reason with quantitative information in a way that will help achieve success in their careers, and to give students the critical-thinking and quantitative reasoning skills needed to understand major life issues. Through new resources in MyLab™ Math and updated content within the text, the Bennett/Briggs team continues to set the standard in quantitative reasoning instruction.

**Also available with MyLab Math**

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**0134679091 / 9780134679099 Using & Understanding Mathematics: A Quantitative Reasoning Approach Plus MyMathLab -- Access Card Package, 7/e**

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- 0134715853 / 9780134715858 MyLab Math with Pearson eText - Access Card - for Using & Understanding Mathematics: A Quantitative Reasoning Approach

**Jeffrey Bennett** specializes in mathematics and science education. He has taught at every level from pre-school through graduate school, including more than 50 college courses in mathematics, physics, astronomy, and education. His work on ** ***Using and Understanding Mathematics * began in 1987, when he helped create a new mathematics course for the University of Colorado’s core curriculum. Variations on this course, with its quantitative reasoning approach, are now taught at hundreds of colleges nationwide. In addition to his work in mathematics, Dr. Bennett (whose PhD is in astrophysics) has written leading college-level textbooks in astronomy, statistics, and the new science of astrobiology, as well as books for the general public. He also proposed and developed both the Colorado Scale Model Solar System on the University of Colorado at Boulder campus and the Voyage Scale Model Solar System, a permanent, outdoor exhibit on the National Mall in Washington, DC. He has recently begun writing science books for children, including the award-winning *Max Goes to the Moon and Max Goes to Mars*. When not working, he enjoys swimming as well as hiking the trails of Boulder, Colorado with his family.

**William L. Briggs** has been on the mathematics faculty at the University of Colorado at Denver for 22 years. He teaches numerous courses within the undergraduate and graduate curriculum, and has special interest in teaching calculus, differential equations, and mathematical modeling. He developed the quantitative reasoning course for liberal arts students at University of Colorado at Denver supported by his textbook ** ***Using & Understanding Mathematics*. He has written two other tutorial monographs, *The Multigrid Tutorial and The DFT: An Owner's Manual for the Discrete Fourier Transform*, as well as *Ants, Bikes, Clocks*, a mathematical problem-solving text for undergraduates. He is a University of Colorado President's Teaching Scholar, an Outstanding Teacher awardee of the Rocky Mountain Section of the MAA, and the recipient of a Fulbright Fellowship to Ireland. Bill lives with his wife, Julie, and their Gordon setter, Seamus, in Boulder, Colorado. He loves to bake bread, run trails, and rock climb in the mountains near his home.

Preface

Acknowledgments

Prologue: Literacy for the Modern World

**I. LOGIC AND PROBLEM SOLVING**

**1. Thinking Critically**

**Activity: Bursting Bubble **

1A. Living in the Media Age

*In Your World: Fact Checking on the Web*

1B. Propositions and Truth Values

1C. Sets and Venn Diagrams

*Brief Review: Sets of Numbers*

1D. Analyzing Arguments

*Mathematical Insight: Deductive Proof of the Pythagorean Theorem*

1E. Critical Thinking in Everyday Life

*In Your World: Beware of “Up to” Deals*

**2. Approaches to Problem Solving**

**Activity: Global Melting**

2A. Understand, Solve, and Explain

*Brief Review: Common Fractions *

*Brief Review: Decimal Fractions *

*Using Technology: Currency Exchange Rates*

*In Your World: Changing Money in Foreign Countries*

2B. Extending Unit Analysis

*In Your World: Gems and Gold Jewelry *

*Brief Review: Powers of 10 *

*Using Technology: Metric Conversions *

*In Your World: Save Money and Save the Earth*

2C. Problem-Solving Hints

*Mathematical Insight: Zeno’s Paradox*

**II. QUANTITATIVE INFORMATION IN EVERYDAY LIFE**

**3. Numbers in the Real World**

**Activity: Big Numbers**

3A. Uses and Abuses of Percentages

*Brief Review: Percentages *

*Brief Review: What Is a Ratio?*

3B. Putting Numbers in Perspective

*Brief Review: Working with Scientific Notation *

*Using Technology: Scientific Notation*

3C. Dealing with Uncertainty

*Brief Review: Rounding *

*Using Technology: Rounding in Excel*

3D. Index Numbers: The CPI and Beyond

*Using Technology: The Inflation Calculator *

*In Your World: The Chained CPI and the Federal Budget*

3E. How Numbers Can Deceive: Polygraphs, Mammograms, and More

**4. Managing Money**

**Activity: Student Loans**

4A. Taking Control of Your Finances

4B. The Power of Compounding

*Brief Review: Powers and Roots *

*Using Technology: Powers *

*Using Technology: The Compound Interest Formula *

*Using Technology: The Compound Interest Formula for Interest Paid More Than Once a Year *

*Using Technology: APY in Excel *

*Using Technology: Powers of e *

*Brief Review: Four Basic Rules of Algebra *

*In Your World: Effects of Low Interest Rates *

4C. Savings Plans and Investments

*Mathematical Insight: Derivation of the Savings Plan Formula *

*Using Technology: The Savings Plan Formula *

*Using Technology: Fractional Powers (Roots) *

*In Your World: Building a Portfolio*

4D. Loan Payments, Credit Cards, and Mortgages

*Using Technology: The Loan Payment Formula (Installment Loans) *

*Mathematical Insight: Derivation of the Loan Payment Formula *

*Using Technology: Principal and Interest Portions of Loan Payments *

*In Your World: Avoiding Credit Card Trouble *

*In Your World: Choosing or Refinancing a Loan*

4E. Income Taxes

4F. Understanding the Federal Budget

**III. PROBABILITY AND STATISTICS**

**5. Statistical Reasoning**

**Activity: Cell Phones and Driving**

5A. Fundamentals of Statistics

*Using Technology: Random Numbers*

5B. Should You Believe a Statistical Study?

*In Your World: The Gun Debate: Defensive Gun Use*

5C. Statistical Tables and Graphs

*Using Technology: Frequency Tables in Excel *

*Using Technology: Bar Graphs and Pie Charts in Excel *

*Using Technology: Line Charts in Excel*

5D. Graphics in the Media

*Using Technology: Graphs with Multiple Data Sets*

5E. Correlation and Causality

*Using Technology: Scatterplots in Excel*

**6. Putting Statistics to Work**

**Activity: Are We Smarter Than Our Parents?**

6A. Characterizing Data

*Using Technology: Mean, Median, and Mode in Excel*

6B. Measures of Variation

*Using Technology: Standard Deviation in Excel*

6C. The Normal Distribution

*Using Technology: Standard Scores and Percentiles in Excel*

6D. Statistical Inference

*In Your World: Is Polling Reliable?*

**7. Probability: Living With The Odds**

**Activity: Lotteries**

7A. Fundamentals of Probability

Brief Review: The Multiplication Principle

7B. Combining Probabilities

7C. The Law of Large Numbers

7D. Assessing Risk

In Your World: Terrorism, Risk, and Human Psychology

7E. Counting and Probability

*Using Technology: Factorials *

*Brief Review: Factorials *

*Using Technology: Permutations *

*Using Technology: Combinations*

**IV. MODELING**

**8. Exponential Astonishment**

**Activity: Towers of Hanoi**

8A. Growth: Linear vs. Exponential

8B. Doubling Time and Half-Life

*Using Technology: Logarithms *

*Brief Review: Logarithms*

8C. Real Population Growth

*In Your World: Choosing Our Fate*

8D. Logarithmic Scales: Earthquakes, Sounds, and Acids

*In Your World: Ocean Acidification*

**9. Modeling Our World**

**Activity: Climate Modeling**

9A. Functions: The Building Blocks of Mathematical Models

*Brief Review: The Coordinate Plane*

9B. Linear Modeling

*Using Technology: Graphing Functions *

*In Your World: Algebra’s Baghdad Connection*

9C. Exponential Modeling

*Brief Review: Algebra with Logarithms *

*Mathematical Insight: Doubling Time and Half-Life Formulas *

*In Your World: Changing Rates of Change *

**10. Modeling With Geometry**

**Activity: Eyes in the Sky**

10A. Fundamentals of Geometry

*Mathematical Insight: Archimedes and Pi *

*In Your World: Plato, Geometry, and Atlantis*

10B. Problem Solving with Geometry

10C. Fractal Geometry

**V. FURTHER APPLICATIONS**

**11. Mathematics and The Arts**

**Activity: Digital Music Files**

11A. Mathematics and Music

*In Your World: Music Just for You*

11B. Perspective and Symmetry

11C. Proportion and the Golden Ratio

**12. Mathematics and Politics**

**Activity: Partisan Redistricting**

12A. Voting: Does the Majority Always Rule?

*In Your World: Counting Votes–Not as Easy as It Sounds*

12B. Theory of Voting

In Your World: The Electoral College and the Presidency

12C. Apportionment: The House of Representatives and Beyond

12D. Dividing the Political Pie

Credits

Answers to Quick Quizzes and Odd-Numbered Exercises

Index