1. Set Theory: Using Mathematics to Classify Objects. Problem Solving.Estimation.The Language of Sets.Comparing Sets.Set Operations.Survey Problems.Of Further Interest: Infinite Sets.
2. Logic: The Study of What's True or False or Somewhere in Between. Inductive and Deductive Reasoning.Statements, Connectives, and Quantifiers.Truth Tables.The Conditional and Biconditional.Verifying Arguments.Using Euler Diagrams to Verify Syllogisms.Of Further Interest: Fuzzy Logic.
3. Graph Theory: The Mathematics of Relationships. Graphs, Puzzles, and Map Coloring.The Traveling Salesperson Problem.Directed Graphs.Of Further Interest: Scheduling Projects Using PERT.
4. Numeration Systems: Does It Matter How We Name Numbers? The Evolution of Numeration Systems.Place Value Systems.Calculating in Other Bases.Of Further Interest: Modular Systems.
5. Number Theory and the Real Number System: Understanding the Numbers All Around Us. Number Theory.The Integers.The Rational Numbers.The Real Number System.Exponents and Scientific Notation.Of Further Interest: Sequences.
6. Algebraic Models: How Do We Approximate Reality? Linear Equations.Modeling With Linear Equations.Modeling with Quadratic Equations.Exponential Equations and Growth.Proportions and Variation.Functions.Of Further Interest: Dynamical Systems.
7. Modeling with Systems of Linear Equations and Inequalities: What's the Best Way to Do It? Systems of Linear Equations.Systems of Linear Inequalities.Of Further Interest: Linear Programming.
8. Geometry: Ancient and Modern Mathematics Embrace. Lines, Angles, and Circles.Polygons.Perimeter and Area.Volume and Surface Area.The Metric System and Dimensional Analysis.Geometric Symmetry and Tessellations.Of Further Interest: Fractals.
9. Apportionment: How Do We Measure Fairness? Understanding Apportionment.The Huntington-Hill Apportionment Principle.Applications of the Apportionment Principle.Other Paradoxes and Apportionment Methods.Of Further Interest: Fair Division.
10. Voting: Using Mathematics to Make Choices. Voting Methods.Defects in Voting Methods.Weighted Voting Systems.Of Further Interest: The Shapley-Shubik Index.
11. Consumer Mathematics: The Mathematics of Everyday Life. Percent.Interest.Consumer Loans.Annuities.Amortization.Of Further Interest: The Annual Percentage Rate.
12. Counting: Just How Many Are There? Introduction to Counting Methods.The Fundamental Counting Principle.Permutations and Combinations.Of Further Interest: Counting and Gambling.
13. Probability: What Are the Chances? The Basics of Probability Theory.Complements and Unions of Events.Conditional Probability and Intersections of Events.Expected Value.Of Further Interest: Binomial Experiments.
14. Descriptive Statistics: What Does a Data Set Tell Us? Organizing and Visualizing Data.Measures of Central Tendency.Measures of Dispersion.The Normal Distribution.Of Further Interest: Linear Correlation.
