| |
| |
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 | |