








Pearls of Discrete Mathematics












Publisher:  CRC Press (Boca Raton, FL) 
  






Subsets of a Set  Pascal's Triangle  Binomial Coefficient Identities  Counting: Intermediate  Finding a Polynomial  The UpwardExtended 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 CoinTossing Game  Shannon's Theorems  Games  A Little Graph Theory Background  The Ramsey Game  TicTacToe and Animal Games  Algorithms  Counters  Listing Permutations and Combinations  Sudoku Solving and Polycube Packing






Pearls of Discrete Mathematics presents methods for solving counting problems and other types of problems that involve discrete structures. Through intriguing examples, problems, theorems, and proofs, the book illustrates the relationship of these structures to algebra, geometry, number theory, and combinatorics.
Each chapter begins with a mathematical teaser to engage readers and includes a particularly surprising, stunning, elegant, or unusual result. The author covers the upward extension of Pascal’s triangle, a recurrence relation for powers of Fibonacci numbers, ways to make change for a million dollars, integer triangles, the period of Alcuin’s sequence, and Rook and Queen paths and the equivalent Nim and Wythoff’s Nim games. He also examines the probability of a perfect bridge hand, random tournaments, a Fibonaccilike sequence of composite numbers, Shannon’s theorems of information theory, higherdimensional tictactoe, animal achievement and avoidance games, and an algorithm for solving Sudoku puzzles and polycube packing problems. Exercises ranging from easy to challenging are found in each chapter while hints and solutions are provided in an appendix.












Alcuin’s sequence, Nim and Wythoff’s Nim, integer triangles







   
 
