Table of Contents

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