TOPICS IN
MATHEMATICS
BY
SAUL STAHL
DEPARTMENT OF MATHEMATICS
UNIVERSITY OF KANSAS
LAWRENCE, KS 66045
Copyright 2000
8/18/00
The author is indebted to his colleagues James Church and Ben Cobb for several informative discussions regarding probability and statistics.
CONTENTS
CHAPTER 1 PROBABILITY
1.1 The Quantification of Likelihood
1.2 Galileo Galilei (A Historical Interlude)*
1.3 Binomial Processes
1.4 The Normal Approximation
1.5 Activities/Websites
CHAPTER 2 STATISTICS
2.1 Summarizing Data
2.2 Compiling Measurement Errors
2.3 Least Squares and Regression
2.4 Normally Distributed Data
2.5 Statistical Inference
2.6 The Central Limit Theorem
2.7 Activities/Websites
CHAPTER 3 GAME THEORY
3.1 Introduction to Games
3.2 Formal Zero-Sum Games
3.3 Pure Strategies for Nonzero-Sum Games
3.4 Mixed Strategies for Nonzero-Sum Games
3.5 The Solution of Zero-Sum Games
3.6 Activities/Websites
CHAPTER 4 LINEAR PROGRAMMING
4.1 Graphing Inequalities
4.2 Optimization
CHAPTER 5 PLANAR SYMMETRIES
5.1 Introduction
5.2 Rigid Motions of the Plane
5.3 Symmetries of Polygons
5.4 Frieze Patterns
5.5 Wallpaper Designs
5.6 Activities/Websites
CHAPTER 6 SPATIAL SYMMETRIES
6.1 Regular and Semiregular Solids
6.2 Symmetries of Regular Solids
6.3 Monstrous Moonshine
6.4 Activities/Websites
APPENDIX A
A Letter Written by Galileo Galilei
TABLE A
A Table of the Normal Distribution
TABLE B
A Table of Binomial Probabilities