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| Mathematical Ways of Thinking | |
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| The Path of the Billiard Ball | |
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| More Billiard-Ball Mathematics | |
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| Inductive Reasoning: Finding and Extending Patterns | |
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| The Limitations of Inductive Reasoning | |
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| Deductive Reasoning: Mathematical Proof | |
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| Number Tricks and Deductive Reasoning | |
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| Number Sequences | |
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| Arithmetic Sequences | |
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| Geometric Sequences | |
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| The Binary Sequence | |
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| The Sequence of Squares | |
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| The Sequence of Cubes | |
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| Fibonacci Sequence | |
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| Functions and Their Graphs | |
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| The Idea of a Function | |
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| Descartes and the Coordinate Graph | |
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| Functions with Line Graphs | |
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| Functions with Parabolic Graphs | |
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| More Functions with Curved Graphs | |
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| Interpolation and Extrapolation: Guessing Between and Beyond | |
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| Large Numbers and Logarithms | |
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| Large Numbers | |
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| Scientific Notation | |
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| An Introduction to Logarithms | |
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| Decimal Logarithms | |
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| Logarithms and Scientific Notation | |
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| Exponential Functions | |
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| Symmetry and Regular Figures | |
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| Symmetry | |
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| Regular Polygons | |
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| Mathematical Mosaics | |
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| Regular Polyhedra | |
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| Pyramids and Prisms | |
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| Mathematical Curves | |
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| The Circle and the Ellipse | |
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| The Parabola | |
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| The Hyperbola | |
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| The Sine Curve | |
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| Spirals | |
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| The Cycloid | |
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| Methods of Counting | |
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| The Fundamental Counting Principle | |
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| Permutations | |
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| More on Permutations | |
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| Combinations | |
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| The Mathematics of Chance | |
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| Probability: The Measure of Chance | |
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| Dice Games and Probability | |
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| Probabilities of Successive Events | |
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| Binomial Probability | |
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| Pascal's Triangle | |
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| Independent and Dependent Events | |
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| The Birthday Problem: Complimentary Events | |
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| An Introduction to Statistics | |
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| Organizing Data: Frequency | |
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| Distributions | |
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| The Breaking of Ciphers and Codes: An Application of Statistics | |
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| Measures of Central Tendency | |
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| Measures of Variability | |
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| Displaying Data: Statistical Graphs | |
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| Collecting Data: Sampling | |
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| Topics in Topology | |
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| The Mathematics of Distortion | |
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| The Seven Bridges of Konigsberg: An Introduction to Networks | |
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| Euler Paths | |
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| Trees | |
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| The Moebius Strip and Other Surfaces | |
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| Appendix: Basic Ideas and Operations | |
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| Angles and Their Measurement | |
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| The Distributive Rule | |
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| Signed Numbers | |
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| Percent | |
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| Answers to Selected Exercises | |
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| Index | |