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
 

Chapter 2. Numerical Exploration

2.1 Discovering limits
2.2 Confirming Conjectures
2.3 The Floating Point Terrain
2.4 Interactive Frameworks
 

Chapter 3. Elementary Graphics

3.1 Grids
3.2 Rectangles and Ovals
3.3 Granularity
 

Chapter 4. Sequences

4.1 Summation
4.2 Recursions
 

Chapter 5. Random Simulations

5.1 Generating Random Reals and Integers
5.2 Estimating Probabilities and Averages
5.3 Monte Carlo
 

Chapter 6. Fast, Faster, Fastest

6.1 Benchmarking
6.2 Efficiency
 

Chapter 7. Exponential Growth

7.1 Powers
7.2 Binomial Coefficients
 

Chapter 8. Patterns

8.1 Encapsulation
8.2 Hierarchy
 

Chapter 9. Proximity

9.1 Distance
9.2 Inclusion
9.3 Collinearity
 

Chapter 10. Roots

10.1 Quadratic Equations
10.2 The Method of Bisection
10.3 The Method of Newton
 

Chapter 11. Area

11.1 Triangulation
11.2 Tiling
11.3 Integration
 

Chapter 12. Encoding Information

12.1 Notation and Representation
12.2 Place Value
 

Chapter 13. Visualization

13.1 Exploratory Environments
13.2 Coordinate Systems
 

Chapter 14. Points in the Plane

14.1 Centroids
14.2 Max's and Min's
 

Chapter 15. Tables

15.1 Set-Up
15.2 Plotting
15.3 Efficiency Issues
15.4 Look-Up
 

Chapter 16. Divisors

16.1 The Prime Numbers
16.2 The Apportionment Problem
 

Chapter 17. The Second Dimension

17.1 ij Thinking
17.2 Operations
17.3 Tables In Two Dimensions
17.4 Bit Maps
 

Chapter 18. Polygons

18.1 Points
18.2 Line Segments
18.3 Triangles and Rectangles
18.4 N-gons
 

Chapter 19. Special Arithmetics

19.1 The Extra Long Integer
19.2 The Rational
19.3 The Complex
 

Chapter 20. Polynomials

20.1 Representation and Operations
20.2 Evaluation
20.3 Quotients
 

Chapter 21. Permutations

21.1 Shifts and Shuffles
21.2 Sorting
21.3 Representation
 

Chapter 22. Optimization

22.1 Shortest Path
22.2 Best Design
22.3 Smallest Ellipse
 

Chapter 23. Divide and Conquer

23.1 Recursion vs. Iteration
23.2 Repeated Halving
23.2 Mesh Refinement
 

Chapter 24. Models and Simulation

24.1 Prediction and Intuition
24.2 The Effect of Dimension
24.3 Building Models from Data