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