| Each chapter concludes with a chapter summary, a chapter review, and a chapter test. 1. PROBLEM SOLVING. Inductive and Deductive Reasoning. Problem Solving with Patterns. Problem-Solving Strategies. 2. SETS. Basic Properties of Sets. Complements, Subsets, and Venn Diagrams. Set Operations. Applications of Sets. Infinite Sets. 3. LOGIC. Logic Statements and Quantifiers. Truth Tables, Equivalent Statements, and Tautologies. The Conditional and the Biconditional. The Conditional and Related Statements. Arguments. Euler Diagrams. 4. NUMERATION SYSTEMS AND NUMBER THEORY. Early Numeration Systems. Place-Value Systems. Different Base Systems. Arithmetic in Different Bases. Prime Numbers. Topics from Number Theory. 5. APPLICATIONS OF EQUATIONS. First-Degree Equations and Formulas. Rate, Ratio, and Proportion. Percent. Second-Degree Equations. 6. APPLICATIONS OF FUNCTIONS. Rectangular Coordinates and Functions. Properties of Linear Functions. Finding Linear Models. Quadratic Functions. Exponential Functions. Logarithmic Functions. 7. MATHEMATICAL SYSTEMS. Modular Arithmetic. Applications of Modular Arithmetic. Introduction to Group Theory. 8. GEOMETRY. Basic Concepts of Euclidean Geometry. Perimeter and Area of Plane Figures. Properties of Triangles. Volume and Surface Area. Introduction to Trigonometry. Non-Euclidean Geometry. Fractals. 9. THE MATHEMATICS OF GRAPHS. Traveling Roads and Visiting Cities. Efficient Routes. Planarity and Euler's Formula. Map Coloring and Graphs. 10. THE MATHEMATICS OF FINANCE. Simple Interest. Compound Interest. Credit Cards and Consumer Loans. Stocks, Bonds, and Mutual Funds. Home Ownership. 11. COMBINATORICS AND PROBABILITY. The Counting Principle. Permutations and Combinations. Probability and Odds. Addition and Complement Rules. Conditional Probability. Expectation. 12. STATISTICS. Measures of Central Tendency. Measures of Dispersion. Measures of Relative Position. Normal Distributions. Linear Regression and Correlation. 13. APPORTIONMENT AND VOTING. Introduction to Apportionment. Introduction to Voting. Weighted Voting Systems. APPENDIX: THE METRIC SYSTEM OF MEASUREMENT. Web Appendix: Algebra Review. |
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