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
