The Contents of *About Mathematics*

Preface

Introduction

Chapter 1. Getting Started (24 programs)

1. Calculator logistics

2. Calculator history

3. Some characteristics of your calculator

- Accuracy
- Speed

- Disorder
- Order
- A middle ground: Fractals

1. An unexpected algorithm

2. An old school algorithm

- How the square root algorithm works

- Functions and equations

- Logistics

6. Programs replace complex computations

- Determining a linear equation passing through two points
- Determining a quadratic equation passing through three points
- Finding the center and radius of a circle given three points

- Trial and error
- Feedback
- Matrices

Chapter 3. Dimensional Analysis (4 programs)

1. Using dimensions in converting units

2. Using dimensions in calculations

- The Drake equation
- Fermi problems
- The Gimli Glider

Chapter 4. Money Matters (23 programs)

1. Interesting interest

- Greedy gangsters
- Formulas and programs

3. A detour through series sums

- Summing an arithmetic series
- Summing a geometric series

5. Savings

6. Credit cards

7. At the casino

- Roulette strategies

- Using the Kelly criterion
- Portfolio rebalancing
- Math works for cheats as well

1. Secret communication

- Binary, octal and hexadecimal numeration
- Some additional coding examples

3. Edgar Allen Poe: an early cryptologist

4. The Vigeniere cipher

5. Modulo arithmetic

6. The RSA code

- Setting up the RSA coding procedure
- Sending an RSA coded message
- Receiving an RSA coded message

Chapter 6. Calculus The Smallest Pebble on the Beach (6 programs)

1. Calculus: a perfect title

2. Slope and velocity

3. The derivative

- Is that all there is to the differential calculus?

5. The definite integral and area

6. The remarkable connection

7. The indefinite integral

8. Tying up loose ends

- Numerical differentiation
- Numerical integration

Chapter 7. Mathematicsl Models (17 programs)

1. Random number functions

2. Do we really need calculator-chosen random numbers?

3. Probability

4. Expectation

5. The St. Petersburg paradox

6. Monte Carlo simulations

7. Dart throwing for π

8. A project

Chapter 8. Revisiting Arithmetic (19 programs)

1. Counting

2. Addition

- Adding more than ten digits
- Speedy addition

- An aside about binary representation

- Duplation and mediation

Chapter 9. Powers, logarithms and exponential change (30 programs)

1. Integer Powers

2. Square Root

3. Rational and real powers

4. Logarithms

- How logs were used from 1620 to 1980

6. Exponential Change

- Newton's Law of Cooling

- Banking

- Doubling time and its consequences

- Population growth and Thomas Malthus

Chapter 10. Alternative Geometries (13 programs)

1. Triangle area formulas

2. Euclid's

*Elements*

3. Problems with Euclid

4. Geometry on the Earth

5. Where am I?

- Local time vs. standard time
- Determining latitude and logitude

7. The other alternative to Postulate 5

Answers

Teaching

*About Mathematics*