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Tables of Contents for Student's Guide and Solutions Manual to Accompany Using and Understanding Mathematics

Chapter/Section Title

Page #

Page Count

Introduction

1

3

Principles of Reasoning

The Forces of Persuasion --- Overview of Common Fallacies

4

1

Propositions: Building Blocks of Logic

5

5

Logical Arguments: Deductive and Inductive

10

5

Analyzing Real Arguments

15

4

Statistical Reasoning

Fundamentals of Statistics

19

2

Should You Believe a Statistical Study?

21

2

Basic Statistical Graphs

23

3

Graphics in the Media

26

2

Causal Connections

28

3

Problems Solving Tools

Using Unit Analysis

31

5

Systems of Standardized Units

36

3

The Process of Problem Solving

39

3

Numbers in the Real World

Concepts of Number

42

3

Uses and Abuses of Percentages

45

4

Putting Numbers in Perspective

49

3

Dealing with Uncertainty

52

4

Financial Management

The Power of Compound Interest

56

5

Savings Plans (Annuities)

61

3

Loan Payments, Credit Cards, and Mortgages

64

4

Income Taxes

68

4

Investments

72

4

Modeling Our World

Functions: The Building Blocks of Mathematical Models

76

4

Linear Graphs and Modeling

80

7

Formulas as Models

87

6

Exponential Growth and Decay

Exponential Astonishment

93

2

Doubling Time and Half-Life

95

5

Exponential Modeling

100

6

Real Population Growth

106

3

Living with the Odds

Principles of Counting

109

6

Fundamentals of Probability

115

3

Combining Probabilities

118

5

The Law of Averages

123

3

Probability, Risk, and Coincidence

126

4

Putting Statistics to Work

Characterizing Data

130

5

Linear Regression Models

135

3

Statistical Inference

138

4

Sample Issues in Statistical Research

142

3

Mathematics and the Arts

Fundamentals of Geometry

145

3

Mathematics and Music

148

3

Perspective and Symmetry

151

2

Proportion and the Golden Ratio

153

3

Fractal Geometry

156

2

Discrete Mathematics in Business and Society

Network Analysis

158

4

The Traveling Salesman Problem

162

2

Project Design

164

3

Voting: Does the Majority Always Rule?

167

4

Theory of Voting

171

4

The Power of Numbers -- A Few More Topics

Balancing the Federal Budget

175

3

Energy: Our Future Depends on It

178

4

Density and Concentration

182

3

Logarithmic Scales: Earthquakes, Sounds, and Acids

185