Table of Contents (Short Version)
Chapter 1. From Formula to Program
- 1.1 A Small Example
- 1.2 Sines and Cosines
- 1.3 Max's and Min's
- 1.4 Formulas that Involve Integers
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Chapter 2. Numerical Exploration
- 2.1 Discovering limits
- 2.2 Confirming Conjectures
- 2.3 The Floating Point Terrain
- 2.4 Interactive Frameworks
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Chapter 3. Elementary Graphics
- 3.1 Grids
- 3.2 Rectangles and Ovals
- 3.3 Granularity
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Chapter 4. Sequences
- 4.1 Summation
- 4.2 Recursions
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Chapter 5. Random Simulations
- 5.1 Generating Random Reals and Integers
- 5.2 Estimating Probabilities and Averages
- 5.3 Monte Carlo
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Chapter 6. Fast, Faster, Fastest
- 6.1 Benchmarking
- 6.2 Efficiency
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Chapter 7. Exponential Growth
- 7.1 Powers
- 7.2 Binomial Coefficients
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Chapter 8. Patterns
- 8.1 Encapsulation
- 8.2 Hierarchy
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Chapter 9. Proximity
- 9.1 Distance
- 9.2 Inclusion
- 9.3 Collinearity
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Chapter 10. Roots
- 10.1 Quadratic Equations
- 10.2 The Method of Bisection
- 10.3 The Method of Newton
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Chapter 11. Area
- 11.1 Triangulation
- 11.2 Tiling
- 11.3 Integration
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Chapter 12. Encoding Information
- 12.1 Notation and Representation
- 12.2 Place Value
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Chapter 13. Visualization
- 13.1 Exploratory Environments
- 13.2 Coordinate Systems
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Chapter 14. Points in the Plane
- 14.1 Centroids
- 14.2 Max's and Min's
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Chapter 15. Tables
- 15.1 Set-Up
- 15.2 Plotting
- 15.3 Efficiency Issues
- 15.4 Look-Up
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Chapter 16. Divisors
- 16.1 The Prime Numbers
- 16.2 The Apportionment Problem
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Chapter 17. The Second Dimension
- 17.1 ij Thinking
- 17.2 Operations
- 17.3 Tables In Two Dimensions
- 17.4 Bit Maps
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Chapter 18. Polygons
- 18.1 Points
- 18.2 Line Segments
- 18.3 Triangles and Rectangles
- 18.4 N-gons
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Chapter 19. Special Arithmetics
- 19.1 The Extra Long Integer
- 19.2 The Rational
- 19.3 The Complex
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Chapter 20. Polynomials
- 20.1 Representation and Operations
- 20.2 Evaluation
- 20.3 Quotients
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Chapter 21. Permutations
- 21.1 Shifts and Shuffles
- 21.2 Sorting
- 21.3 Representation
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Chapter 22. Optimization
- 22.1 Shortest Path
- 22.2 Best Design
- 22.3 Smallest Ellipse
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Chapter 23. Divide and Conquer
- 23.1 Recursion vs. Iteration
- 23.2 Repeated Halving
- 23.2 Mesh Refinement
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Chapter 24. Models and Simulation
- 24.1 Prediction and Intuition
- 24.2 The Effect of Dimension
- 24.3 Building Models from Data