Preface
I Counting: Basic
1 Subsets of a Set
2 Pascal's Triangle
3 Binomial Coefficient Identities
II Counting: Intermediate
4 Finding a Polynomial
5 The Upward-Extended Pascal's Triangle
6 Recurrence Relations and Fibonacci Numbers
III Counting: Advanced
7 Generating Functions and Making Change
8 Integer Triangles
9 Rook Paths and Queen Paths
IV Discrete Probability
10 Probability Spaces and Distributions
11 Markov Chains
12 Random Tournaments
V Number Theory
13 Divisibility of Factorials and Binomial Coefficients
14 Covering Systems
15 Partitions of an Integer
VI Information Theory
16 What is Surprise?
17 A Coin-Tossing Game
18 Shannon's Theorems
VII Games
19 A Little Graph Theory Background
20 The Ramsey Game
21 Tic-Tac-Toe and Animal Games
VIII Algorithms
22 Counters
23 Listing Permutations and Combinations
24 Sudoku Solving and Polycube Packing
A Hints and Solutions to Exercises
B Notation
Bibliography
Index