Preface

Acknowledgments

Prologue: Literacy for the Modern World

PART ONE: LOGIC AND PROBLEM SOLVING

1. Thinking Critically

1A Living in the Media Age

1B Propositions and Truth Values

1C Sets and Venn Diagrams

1D Analyzing Arguments

1E Critical Thinking in Everyday Life

2. Approaches to Problem Solving

2A Working with Units

2B Problem-Solving with Units

2C Problem-Solving Guidelines and Hints

PART TWO: QUANTITATIVE INFORMATION IN EVERYDAY LIFE

3. Numbers in the Real World

3A Uses and Abuses of Percentages

3B Putting Numbers in Perspective

3C Dealing with Uncertainty

3D Index Numbers: The CPI and Beyond

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

4. Managing Money

4A Taking Control of Your Finances

4B The Power of Compounding

4C Savings Plans and Investments

4D Loan Payments, Credit Cards, and Mortgages

4E Income Taxes

4F Understanding the Federal Budget

PART THREE: PROBABILITY AND STATISTICS

5. Statistical Reasoning

5A Fundamentals of Statistics

5B Should You Believe a Statistical Study?

5C Statistical Tables and Graphs

5D Graphics in the Media

5E Correlation and Causality

6. Putting Statistics to Work

6A Characterizing Data

6B Measures of Variation

6C The Normal Distribution

6D Statistical Inference

7. Probability: Living with the Odds

7A Fundamentals of Probability

7B Combining Probabilities

7C The Law of Large Numbers

7D Assessing Risk

7E Counting and Probability

PART FOUR: MODELING

8. Exponential Astonishment

8A Growth: Linear versus Exponential

8B Doubling Time and Half-Life

8C Real Population Growth

8D Logarithmic Scales: Earthquakes, Sounds, and Acids

9. Modeling Our World

9A Functions: The Building Blocks of Mathematical Models

9B Linear Modeling

9C Exponential Modeling

10. Modeling with Geometry

10A Fundamentals of Geometry

10B Problem Solving with Geometry

10C Fractal Geometry

PART FIVE: FURTHER APPLICATIONS

11. Mathematics and the Arts

11A Mathematics and Music

11B Perspective and Symmetry

11C Proportion and the Golden Ratio

12. Mathematics and Politics

12A Voting: Does the Majority Always Rule?

12B Theory of Voting

12C Apportionment: The House of Representatives and Beyond

12D Dividing the Political Pie

Credits

Answers

Index