Using and Understanding Mathematics: A Quantitative Reasoning Approach prepares students for the mathematics they will encounter in college courses, their future career, and life in general. Its quantitative reasoning approach helps students to build the skills needed to understand major issues in everyday life, and compels students to acquire the problem-solving tools that they will need to think critically about quantitative issues in contemporary society.
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Table of Contents
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
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