## 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

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

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

9.1 Distance
9.2 Inclusion
9.3 Collinearity

## Chapter 10. Roots

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