1. Problem Solving

• 1.1 Problem Solving
• 1.2 Inductive and Deductive Reasoning
• 1.3 Estimation

2. Set Theory

• 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

• 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)

• 4.1 Graphs, Puzzles, and Map Coloring
• 4.2 The Traveling Salesperson Problem
• 4.3 Directed Graphs

5. Numeration Systems

• 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

• 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 and Linear Systems

• 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 Variations
• 7.6 Modeling with Systems of Linear Equations and Inequalities
• 7.7 Looking Deeper - Dynamical Systems

8. Consumer Mathematics

• 8.1 Percents, Taxes, and Inflation
• 8.2 Interest
• 8.3 Consumer Loans
• 8.4 Annuities
• 8.5 Amortization
• 8.6 Looking Deeper - Annual Percentage Rate

9. Geometry

• 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

10. Apportionment

• 10.1 Understanding Apportionment
• 10.2 The Huntington-Hill Apportionment Principle
• 10.3 Other Paradoxes and Apportionment Methods
• 10.4 Looking Deeper - Fair Division

11. Voting

• 11.1 Voting Methods
• 11.2 Defects in Voting Methods
• 11.3 Weighted Voting Systems
• 11.4 Looking Deeper - The Shapley-Shubik Index

12. Counting

• 12.1 Introduction to Counting Methods
• 12.2 The Fundamental Counting Principle
• 12.3 Permutations and Combinations
• 12.4 Looking Deeper - Counting and Gambling

13. Probability

• 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

14. Descriptive Statistics

• 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. Basic Mathematics Review