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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.
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 Fariness?
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.