Counting: Basic
Subsets of a Set
Pascal’s Triangle
Binomial Coefficient Identities
Counting: Intermediate
Finding a Polynomial
The Upward-Extended Pascal’s Triangle
Recurrence Relations and Fibonacci Numbers
Counting: Advanced
Generating Functions and Making Change
Integer Triangles
Rook Paths and Queen Paths
Discrete Probability
Probability Spaces and Distributions
Markov Chains
Random Tournaments
Number Theory
Divisibility of Factorials and Binomial Coefficients
Covering Systems
Partitions of an Integer
Information Theory
What Is Surprise?
A Coin-Tossing Game
Shannon’s Theorems
Games
A Little Graph Theory Background
The Ramsey Game
Tic-Tac-Toe and Animal Games
Algorithms
Counters
Listing Permutations and Combinations
Sudoku Solving and Polycube Packing
Appendix A: Hints and Solutions to Exercises
Appendix B: Notation
Bibliography
Index