Pearls of Discrete Mathematics

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 Pascalâs triangle a recurrence relation for powers of Fibonacci numbers ways to make change for a million dollars integer triangles the period of Alcuinâs sequence and Rook and Queen paths and the equivalent Nim and Wythoffâs Nim games. He also examines the probability of a perfect bridge hand random tournaments a Fibonacci-like sequence of composite numbers Shannonâs 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. . Language: English