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

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