Chapter 1 Problem Solving: Strategies and Principles

1.1 Problem Solving

1.2 Inductive and Deductive Reasoning

1.3 Estimation

Chapter 2 Set Theory: Using Mathematics to Classify Objects

2.1 The Language of Sets

2.2 Comparing Sets

2.3 Set Operations

2.4 Survey Problems

2.5 Looking Deeper: Infinite Sets

Chapter 3 Logic: The Study of What’s True or False or Somewhere in Between

3.1 Statements, Connectives, and Quantifiers

3.2 Truth Tables

3.3 The Conditional and Biconditional

3.4 Verifying Arguments

3.5 Using Euler Diagrams to Verify Syllogisms

3.6 Looking Deeper: Fuzzy Logic

Chapter 4 Graph Theory (Networks): The Mathematics of Relationships

4.1 Graphs, Puzzles, and Map Coloring

4.2 The Traveling Salesperson Problem

4.3 Directed Graphs

4.4 Looking Deeper: Scheduling Projects Using PERT

Chapter 5 Numeration Systems: Does It Matter How We Name Numbers?

5.1 The Evolution of Numeration Systems

5.2 Place Value Systems

5.3 Calculating in Other Bases

5.4 Looking Deeper: Modular Systems

Chapter 6 Number Theory and the Real Number System: Understanding the Numbers All Around Us

6.1 Number Theory

6.2 The Integers

6.3 The Rational Numbers

6.4 The Real Number System

6.5 Exponents and Scientific Notation

6.6 Looking Deeper: Sequences

Chapter 7 Algebraic Models: How Do We Approximate Reality?

7.1 Linear Equations

7.2 Modeling with Linear Equations

7.3 Modeling with Quadratic Equations

7.4 Exponential Equations and Growth

7.5 Proportions and Variation

7.6 Modeling with Systems of Linear Equations and Inequalities

7.7 Looking Deeper: Dynamical Systems

Chapter 8 Consumer Mathematics: The Mathematics of Everyday Life

8.1 Percents, Taxes, and Inflation

8.2 Interest

8.3 Consumer Loans

8.4 Annuities

8.5 Amortized Loans

8.6 Looking Deeper: Annual Percentage Rate

Chapter 9 Geometry: Ancient and Modern Mathematics Embrace

9.1 Lines, Angles, and Circles

9.2 Polygons

9.3 Perimeter and Area

9.4 Volume and Surface Area

9.5 The Metric System and Dimensional Analysis

9.6 Geometric Symmetry and Tessellations

9.7 Looking Deeper: Fractals

Chapter 10 Apportionment: How Do We Measure Fairness?

10.1 Understanding Apportionment

10.2 The Huntington-Hill Apportionment Principle

10.3 Other Paradoxes and Apportionment Methods

10.4 Looking Deeper: Fair Division

Chapter 11 Voting: using Mathematics to make Choices

11.1 Voting Methods

11.2 Defects in Voting Methods

11.3 Weighted Voting Systems

11.4 Looking Deeper: The Shapley-Shubik Index

Chapter 12 Counting: Just How many Are There?

12.1 Introduction to Counting Methods

12.2 The Fundamental Counting Principle

12.3 Permutations and Combinations

12.4 Looking Deeper: Counting and Gambling

Chapter 13 Probability: What Are the Chances?

13.1 The Basics of Probability Theory

13.2 Complements and Unions of Events

13.3 Conditional Probability and Intersections of Events

13.4 Expected Value

13.5 Looking Deeper: Binomial Experiments

Chapter 14 Descriptive Statistics: Making Sense of the Data

14.1 Organizing and Visualizing Data

14.2 Measures of Central Tendency

14.3 Measures of Dispersion

14.4 The Normal Distribution

14.5 Looking Deeper: Linear Correlation

Appendix A

Answers to Quiz Yourself Problems

Answers to Exercises

Credits

Index