## Table of Contents

**1. Problem Solving: Strategies and Principles**

1.1 Problem Solving

1.2 Inductive and Deductive Reasoning

1.3 Estimation

**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

**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

**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

**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

**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

**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 Functions

7.7 Looking Deeper: Dynamical Systems

**8. Modeling with Systems of Linear Equations and Inequalities: What's the Best Way to Do It?**

8.1 Systems of Linear Equations

8.2 Systems of Linear Inequalities

8.3 Looking Deeper: Linear Programming

**9. Consumer Mathematics: The Mathematics of Everyday Life**

9.1 Percent

9.2 Interest

9.3 Consumer Loans

9.4 Annuities

9.5 Amortization

9.6 Personal Finance

9.7 Looking Deeper: The Annual Percentage Rate

**10. Geometry: Ancient and Modern Mathematics Embrace**

10.1 Lines, Angles, and Circles

10.2 Polygons

10.3 Perimeter and Area

10.4 Volume and Surface Area

10.5 The Metric System and Dimensional Analysis

10.6 Geometric Symmetry and Tessellations

10.7 Looking Deeper: Fractals

**11. Apportionment: How Do We Measure Fairness?**

11.1 Understanding Apportionment

11.2 The Huntington-Hill Apportionment Principle

11.3 Applications of the Apportionment Principle

11.4 Other Paradoxes and Apportionment Methods

11.5 Looking Deeper: Fair Division

**12. Voting: Using Mathematics to Make Choices**

12.1 Voting Methods

12.2 Defects in Voting Methods

12.3 Weighted Voting Systems

12.4 Looking Deeper: The Shapley-Shubik Index

**13. Counting: Just How Many Are There?**

13.1 Introduction to Counting Methods

13.2 The Fundamental Counting Principle

13.3 Permutations and Combinations

13.4 Looking Deeper: Counting and Gambling

**14. Probability: What Are the Chances?**

14.1 The Basics of Probability Theory

14.2 Complements and Unions of Events

14.3 Conditional Probability and Intersections of Events

14.4 Expected Value

14.5 Looking Deeper: Binomial Experiments

**15. Descriptive Statistics: What a Data Set Tells Us**

15.1 Organizing and Visualizing Data

15.2 Measures of Central Tendency

15.3 Measures of Dispersion

15.4 The Normal Distribution

15.5 Looking Deeper: Linear Correlation

Appendix A Basic Mathematics Review

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