Chapter 5: Programming in Sage and Python

5.1. Repetition without Boredom: The For Loop

• 5.1.4. Wasteful Loops
• 5.1.4
• 5.1.9. For Loops and Taylor Polynomials
• 5.1.9
• 5.1.10. Exploring Chaos Theory
• 5.1.10

5.2. Writing Subroutines

• 5.2.1. An Example: Working with Coinage
• 5.2.1
• 5.2.3. An Example: Designing Aquariums
• 5.2.3 (Figure 5.1)

5.3. Loops and Newton's Method

• 5.3.2. Newton's Method with a For Loop
• 5.3.2 (Figure 5.2)
• 5.3.6. Returning a Value and Nesting Subroutines
• 5.3.6.a (Figure 5.3)
• 5.3.6.b (Figure 5.4)
• 5.3.6.c (Figure 5.5)

5.4. An Introduction to Control Flow

• 5.4.1. Verbosity Control
• 5.4.1 (Figure 5.7)
• 5.4.3. Stopping Newton's Method Early
• 5.4.3 (Figure 5.8)

5.5. More Concepts in Flow Control

• 5.5.1. Raising an "Exception"
• 5.5.1 (Figure 5.9)
• 5.5.2. The If-Then-Else Construction
• 5.5.2.a
• 5.5.2.b
• 5.5.4. The elif Command
• 5.5.4 (Figure 5.10)

5.6. While Loops versus For Loops

• 5.6.1. A Question about Factorials
• 5.6.1
• 5.6.3. Newton's Method with a While Loop
• 5.6.3 (Figure 5.11)
• 5.6.5. Factorization by Trial Division
• 5.6.5.a
• 5.6.5.b

5.7. How Arrays and Lists Work

• 5.7.1 Lists of Points and Plotting
• 5.7.1 (Figure 5.12)
• 5.7.3 Operations on Lists
• 5.7.3
• 5.7.4 Looping through an Array
• 5.7.4

5.8. Simulations: the Monte-Carlo Method

• 5.8.1. Throwing Darts to Estimate Pi
• 5.8.1 (Figure 5.13)
• 5.8.2. Archimedes, the Cylinder, and the Sphere
• 5.8.2.a (Figure 5.14) (black-and-white)
• 5.8.2.b (color)
• 5.8.2. A Monte-Carlo Simulation
• 5.8.2
• 5.8.4 Rolling Dice in Sage
• 5.8.4
• 5.8.5. Estimation Error and Confidence Intervals
• 5.8.5
• 5.8.5. An Application to Political Science
• 5.8.5 (Figure 5.15)

5.9. Some Intermediate-Level Techniques

• 5.9.1. Using the assert Command
• 5.9.1
• 5.9.3 Averaging Some Numbers
  • 5.9.3.a
  • 5.9.3.b
  • 5.9.3.c
• 5.9.6. Useful Shortcut Commands for Lists
• 5.9.6
• 5.9.8. Understanding the try command
• 5.9.8