Note: Each chapter concludes with a Summary, Research Questions, a Practice Test, and Answers to Practice Test | |
Problem Solving | |
Inductive Reasoning | |
Estimation: A Problem-Solving Tool | |
Graph Interpretation: A Problem-Solving Tool | |
Sets | |
Sets: A Problem-Solving Tool | |
Set Operations | |
Venn Diagrams | |
The Number of Elements in a Set: A Problem-Solving Tool | |
Infinite Sets | |
Logic | |
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 | |
Switching Networks: A Problem-Solving Tool | |
Numeration Systems | |
Egyptian, Babylonian, and Roman Numeration Systems | |
The Hindu-Arabic (Decimal) System | |
Number Systems with Bases Other Than 10 | |
Binary Arithmetic | |
Octal and Hexadecimal Arithmetic | |
Number Theory and the Real Numbers | |
Number Theory: Primes and Composites | |
Whole Numbers, Integers, and Order of Operations | |
The Rational Numbers | |
Decimals, Scientific Notation, Significant Digits | |
Rationals as Decimals: Percents | |
Real Numbers, Square Roots, and Decimal Representation | |
Radicals | |
Number Sequences | |
Equations, Inequalities, and Problem Solving | |
Solutions of First-Degree Sentences | |
Graphs of Algebraic Sentences | |
Sentences Involving Absolute Values | |
Quadratic Equations | |
Modeling and Problem Solving | |
Ratio, Proportion, and Variation | |
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 | |
Geometry | |
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 | |
Chaos and Fractals | |
Mathematical Systems and Matrices | |
Matrix Operations | |
Solving Systems of Linear Equations with Matrices | |
Clock and Modular Arithmetic | |
Abstract Mathematical Systems: Groups and Fields | |
Game Theory | |
Counting Techniques | |
The Sequential Counting Principle (SCP): A Problem-Solving Tool | |
Permutations | |
Combinations | |
Miscellaneous Counting Methods | |
Probability | |
Sample Spaces and Probability | |
Counting Techniques and Probability | |
Computation of Probabilities | |
Conditional Probability | |
Independent Events | |
Odds and Mathematical Expectation | |
Statistics | |
Sampling and Frequency Distributions | |
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 | |
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 | |
Voting and Apportionment | |
Voting Systems | |
Voting Objections | |
Apportionment Methods | |
Apportionment Objections | |
Graph Theory | |
Introduction to Graph Theory | |
Euler Paths and Euler Circuits | |
Hamilton Paths and Hamilton Circuits | |
Trees Appendix: The Metric System | |
Answers to Odd-Numbered Problems | |
Research Bibliography | |
Acknowledgments | |
Photo Credits | |
Index | |
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