## Table of Contents

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