Mathematical Excursions
Each chapter concludes with a chapter summary, a chapter review, and a chapter test. 1. Problem Solving 1.1 Inductive and Deductive Reasoning 1.2 Problem Solving with Patterns 1.3 Problem-Solving Strategies 2. Sets 2.1 Basic Properties of Sets 2.2 Complements, Subsets, and Venn Diagrams 2.3 Set Operations 2.4 Applications of Sets 2.5 Infinite Sets 3. Logic 3.1 Logic Statements and Quantifiers 3.2 Truth Tables, Equivalent Statements, and Tautologies 3.3 The Conditional and the Biconditional 3.4 The Conditional and Related Statements 3.5 Arguments 3.6 Euler Diagrams 4. Numeration Systems and Number Theory 4.1 Early Numeration Systems 4.2 Place-Value Systems 4.3 Different Base Systems 4.4 Arithmetic in Different Bases 4.5 Prime Numbers 4.6 Topics from Number Theory 5. Applications of Equations 5.1 First-Degree Equations and Formulas 5.2 Rate, Ratio, and Proportion 5.3 Percent 5.4 Second-Degree Equations 6. Applications of Functions 6.1 Rectangular Coordinates and Functions 6.2 Properties of Linear Functions 6.3 Finding Linear Models 6.4 Quadratic Functions 6.5 Exponential Functions 6.6 Logarithmic Functions 7. Mathematical Systems 7.1 Modular Arithmetic 7.2 Applications of Modular Arithmetic 7.3 Introduction to Group Theory 8. Geometry 8.1 Basic Concepts of Euclidean Geometry 8.2 Perimeter and Area of Plane Figures 8.3 Properties of Triangles 8.4 Volume and Surface Area 8.5 Introduction to Trigonometry 8.6 Non-Euclidean Geometry 8.7 Fractals 9. The Mathematics of Graphs 9.1 Traveling Roads and Visiting Cities 9.2 Efficient Routes 9.3 Planarity and Euler's Formula 9.4 Map Coloring and Graphs 10. The Mathematics of Finance 10.1 Simple Interest 10.2 Compound Interest 10.3 Credit Cards and Consumer Loans 10.4 Stocks, Bonds, and Mutual Funds 10.5 Home Ownership 11. Combinatorics and Probability 11.1 The Counting Principle 11.2 Permutations and Combinations 11.3 Probability and Odds 11.4 Addition and Complement Rules 11.5 Conditional Probability 11.6 Expectation 12. Statistics 12.1 Measures of Central Tendency 12.2 Measures of Dispersion 12.3 Measures of Relative Position 12.4 Normal Distributions 12.5 Linear Regression and Correlation 13. Apportionment and Voting 13.1 Introduction to Apportionment 13.2 Introduction to Voting 13.3 Weighted Voting Systems Appendix: The Metric System of Measurement Web Appendix: Algebra Review