Mathematical Excursions

Description

Cover Contents Preface AIM for Success Ch 1: Problem Solving 1.1 Inductive and Deductive Reasoning 1.2 Problem Solving with Patterns 1.3 Problem-Solving Strategies Chapter 1 Summary Chapter 1 Review Exercises Chapter 1 Test Ch 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 Chapter 2 Summary Chapter 2 Review Exercises Chapter 2 Test Ch 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 Symbolic Arguments 3.6 Arguments and Euler Diagrams Chapter 3 Summary Chapter 3 Review Exercises Chapter 3 Test Ch 4: Apportionment and Voting 4.1 Introduction to Apportionment 4.2 Introduction to Voting 4.3 Weighted Voting Systems Chapter 4 Summary Chapter 4 Review Exercises Chapter 4 Test Ch 5: The Mathematics of Graphs 5.1 Graphs and Euler Circuits 5.2 Weighted Graphs 5.3 Planarity and Euler's Formula 5.4 Graph Coloring Chapter 5 Summary Chapter 5 Review Exercises Chapter 5 Test Ch 6: Numeration Systems and Number Theory 6.1 Early Numeration Systems 6.2 Place-Value Systems 6.3 Different Base Systems 6.4 Arithmetic in Different Bases 6.5 Prime Numbers 6.6 Topics from Number Theory Chapter 6 Summary Chapter 6 Review Exercises Chapter 6 Test Ch 7: Measurement and Geometry 7.1 Measurement 7.2 Basic Concepts of Euclidean Geometry 7.3 Perimeter and Area of Plane Figures 7.4 Properties of Triangles 7.5 Volume and Surface Area 7.6 Right Triangle Trigonometry 7.7 Non-Euclidean Geometry 7.8 Fractals Chapter 7 Summary Chapter 7 Review Exercises Chapter 7 Test Ch 8: Mathematical Systems 8.1 Modular Arithmetic 8.2 Applications of Modular Arithmetic 8.3 Introduction to Group Theory Chapter 8 Summary Chapter 8 Review Exercises Chapter 8 Test Ch 9: Applications of Equations 9.1 First-Degree Equations and Formulas 9.2 Rate, Ratio, and Proportion 9.3 Percent 9.4 Second-Degree Equations Chapter 9 Summary Chapter 9 Review Exercises Chapter 9 Test Ch 10: Applications of Functions 10.1 Rectangular Coordinates and Functions 10.2 Properties of Linear Functions 10.3 Finding Linear Models 10.4 Quadratic Functions 10.5 Exponential Functions 10.6 Logarithmic Functions Chapter 10 Summary Chapter 10 Review Exercises Chapter 10 Test Ch 11: The Mathematics of Finance 11.1 Simple Interest 11.2 Compound Interest 11.3 Credit Cards and Consumer Loans 11.4 Stocks, Bonds, and Mutual Funds 11.5 Home Ownership Chapter 11 Summary Chapter 11 Review Exercises Chapter 11 Test Ch 12: Combinatorics and Probability 12.1 The Counting Principle 12.2 Permutations and Combinations 12.3 Probability and Odds 12.4 Addition and Complement Rules 12.5 Conditional Probability 12.6 Expectation Chapter 12 Summary Chapter 12 Review Exercises Chapter 12 Test Ch 13: Statistics 13.1 Measures of Central Tendency 13.2 Measures of Dispersion 13.3 Measures of Relative Position 13.4 Normal Distributions 13.5 Linear Regression and Correlation Chapter 13 Summary Chapter 13 Review Exercises Chapter 13 Test Solutions to Check Your Progress Problems Answers to Selected Exercises Index of Applications Index