Mathematics: A Human Endeavor

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