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