Table of Contents
1. PROBLEM SOLVING.
Inductive and Deductive Reasoning. Estimation: A Problem-Solving Tool. Graph Interpretation: A Problem-Solving Tool.
Sets: A Problem-Solving Tool. Set Operations. Venn Diagrams. The Number of Elements in a Set: A Problem-Solving Tool. Infinite Sets.
Statements. Truth Tables: A Problem-Solving Tool. The Conditional and the Biconditional. Variations of the Conditional and Implications. Euler Diagrams: A Problem-Solving Tool. Truth Tables and Validity of Arguments.
4. NUMERATION SYSTEMS.
Egyptian, Babylonian, and Roman Numeration Systems. The Hindu-Arabic (Decimal System). Number Systems with Bases Other Than 10. Binary Octal, and Hexadecimal Arithmetic.
5. NUMBER THEORY AND THE REAL NUMBERS.
Number Theory: Primes and Composites. Whole Numbers, Integers, and Order of Operations. Operations with Rational Numbers, Expanded and Scientific Notation. Rationals and Irrationals as Decimals: Percents. Radicals and Real Numbers. Number Sequences.
6. EQUATIONS, INEQUALITIES, AND PROBLEM SOLVING.
Solutions of First-Degree (linear) Sentences. Graphs of Algebraic Sentences. Sentences Involving Absolute Values. Quadratic Equations. Modeling and Problem Solving. Ratio, Proportion, and Variation.
7. FUNCTIONS AND GRAPHS.
Graphing Relations and Functions. Linear Functions, Relations, and Applications. Slopes and Equations of a Line. Quadratic Functions and Their Graphs. Exponential and Logarithmic Functions. Two Linear Equations in Two Variables. Linear Inequalities. Linear Programming.
Points, Lines, Planes, and Angles. Triangles and Other Polygons. Perimeter and Circumference. Area Measure and the Pythagorean Theorem. Volume and Surface Area. Networks, Non-Euclidean Geometry, and Topology. Right Triangle Trigonometry. Chaos and Fractals.
9. MATHEMATICAL SYSTEMS.
Clock and Modular Arithmetic. Abstract Mathematical Systems: Groups and Fields. Game Theory.
10. COUNTING TECHNIQUES. The Sequential Counting Principle (SCP): A Problem-Solving Tool. Permutations. Combinations. Miscellaneous Counting Methods.
Sample Spaces and Probability. Counting Techniques and Probability. Computations of Probabilities. Conditional Probability. Independent Events. Odds and Mathematical Expectation.
Sampling, Frequency Distributions, and Graphs. Measures of Central Tendency: The Mean, Median, and Mode. Measures of Dispersion: The Range and Standard Deviation. The Normal Distribution: A Problem-Solving Tool. Statistical Graphs: A Problem-Solving Tool. Making Predictions: Linear Regression. Scattergrams and Correlation.
13. YOUR MONEY AND YOUR MATH.
Interest, Taxes, and Discounts. Credit Cards and Consumer Credit. Annual Percentage Rate (APR) and the Rule of 78. Buying a House. Investing in Stocks, Bonds, and Mutual Funds.
14. VOTING AND APPORTIONMENT.
Voting Systems. Voting Objections. Apportionment Methods. Apportionment Objections.
15. GRAPH THEORY.
Introduction to Graph Theory. Euler Paths and Euler Circuits. Hamilton Paths and Hamilton Circuits. Trees.