Pearls of Discrete Mathematics (Discrete Mathematics and Its Applications)

丛 书 名：Discrete Mathematics and Its Applications

版本说明：1

作     者：Martin Erickson 

I S B N：(纸本) 1439816166 

出 版 社：CRC Press  Inc. 

出 版 年：2009年

主 题 词：Computers amp the Internet Operating Systems 

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

摘      要：Methods Used to Solve Discrete Math ProblemsInteresting examples highlight the interdisciplinary nature of this area 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 Pascals triangle, a recurrence relation for powers of Fibonacci numbers, ways to make change for a million dollars, integer triangles, the period of Alcuins sequence, and Rook and Queen paths and the equivalent Nim and Wythoffs Nim games. He also examines the probability of a perfect bridge hand, random tournaments, a Fibonacci-like sequence of composite numbers, Shannons theorems of information theory, higher-dimensional tic-tac-toe, 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. With over twenty-five years of teaching experience, the author takes an organic approach that explores concrete problems, introduces theory, and adds generalizations as needed. He delivers an absorbing treatment of the basic principles of discrete mathematics.