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