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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