Topics in Contemporary Mathematics : Expanded Version

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Note: Each chapter concludes with a Summary, Research Questions, a Practice Test, and Answers to Practice Test. 1. Problem Solving 1.1 Inductive Reasoning 1.2 Estimation: A Problem-Solving Tool 1.3 Graph Interpretation: A Problem-Solving Tool 2. Sets 2.1 Sets: A Problem-Solving Tool 2.2 Set Operations 2.3 Venn Diagrams 2.4 The Number of Elements in a Set: A Problem-Solving Tool 2.5 Infinite Sets 3. Logic 3.1 Statements 3.2 Truth Tables: A Problem-Solving Tool 3.3 The Conditional and the Biconditional 3.4 Variations of the Conditional and Implications 3.5 Euler Diagrams: A Problem-Solving Tool 3.6 Truth Tables and Validity of Arguments 3.7 Switching Networks: A Problem-Solving Tool 4. Numeration Systems 4.1 Egyptian, Babylonian, and Roman Numeration Systems 4.2 The Hindu-Arabic (Decimal) System 4.3 Number Systems with Bases Other Than 10 4.4 Binary Arithmetic 4.5 Octal and Hexadecimal Arithmetic 5. Number Theory and the Real Numbers 5.1 Number Theory: Primes and Composites 5.2 Whole Numbers, Integers, and Order of Operations 5.3 The Rational Numbers 5.4 Decimals, Scientific Notation, Significant Digits 5.5 Rationals as Decimals: Percents 5.6 Real Numbers, Square Roots, and Decimal Representation 5.7 Radicals 5.8 Number Sequences 6. Equations, Inequalities, and Problem Solving 6.1 Solutions of First-Degree Sentences 6.2 Graphs of Algebraic Sentences 6.3 Sentences Involving Absolute Values 6.4 Quadratic Equations 6.5 Modeling and Problem Solving 6.6 Ratio, Proportion, and Variation 7. Functions and Graphs 7.1 Graphing Relations and Functions 7.2 Linear Functions, Relations, and Applications 7.3 Slopes and Equations of a Line 7.4 Quadratic Functions and Their Graphs 7.5 Exponential and Logarithmic Functions 7.6 Two Linear Equations in Two Variables 7.7 Linear Inequalities 7.8 Linear Programming 8. Geometry 8.1 Points, Lines, Planes, and Angles 8.2 Triangles and Other Polygons 8.3 Perimeter and Circumference 8.4 Area Measure and the Pythagorean Theorem 8.5 Volume and Surface Area 8.6 Networks, Non-Euclidean Geometry, and Topology 8.7 Chaos and Fractals 9. Mathematical Systems and Matrices 9.1 Matrix Operations 9.2 Solving Systems of Linear Equations with Matrices 9.3 Clock and Modular Arithmetic 9.4 Abstract Mathematical Systems: Groups and Fields 9.5 Game Theory 10. Counting Techniques 10.1 The Sequential Counting Principle (SCP): A Problem-Solving Tool 10.2 Permutations 10.3 Combinations 10.4 Miscellaneous Counting Methods 11. Probability 11.1 Sample Spaces and Probability 11.2 Counting Techniques and Probability 11.3 Computation of Probabilities 11.4 Conditional Probability 11.5 Independent Events 11.6 Odds and Mathematical Expectation 12. Statistics 12.1 Sampling and Frequency Distributions 12.2 Measures of Central Tendency: The Mean, Median, and Mode 12.3 Measures of Dispersion: The Range and Standard Deviation 12.4 The Normal Distribution: A Problem-Solving Tool 12.5 Statistical Graphs: A Problem-Solving Tool 12.6 Making Predictions: Linear Regression 12.7 Scattergrams and Correlation 13. Your Money and Your Math 13.1 Interest, Taxes, and Discounts 13.2 Credit Cards and Consumer Credit 13.3 Annual Percentage Rate (APR) and the Rule of 78 13.4 Buying a House 14. Voting and Apportionment 14.1 Voting Systems 14.2 Voting Objections 14.3 Apportionment Methods 14.4 Apportionment Objections 15. Graph Theory 15.1 Introduction to Graph Theory 15.2 Euler Paths and Euler Circuits 15.3 Hamilton Paths and Hamilton Circuits 15.4 Trees Appendix: The Metric System Answers to Odd-Numbered Problems Research Bibliography Acknowledgments Photo Credits Index