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English
CRC Press Inc
16 September 2009
Methods Used to Solve Discrete Math Problems Interesting 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 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 Fibonacci-like sequence of composite numbers, Shannon's 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.

By:  
Imprint:   CRC Press Inc
Country of Publication:   United States
Volume:   v. 57
Dimensions:   Height: 234mm,  Width: 156mm,  Spine: 18mm
Weight:   385g
ISBN:   9781439816165
ISBN 10:   1439816166
Series:   Discrete Mathematics and Its Applications
Pages:   280
Publication Date:  
Audience:   College/higher education ,  General/trade ,  Primary ,  ELT Advanced
Format:   Paperback
Publisher's Status:   Active
Counting: Basic. Counting: Intermediate. Counting: Advanced. Discrete Probability. Number Theory. Information Theory. Games. Algorithms. Appendices. Bibliography. Index.

Martin Erickson is a professor of mathematics at Truman State University.

Reviews for Pearls of Discrete Mathematics

The book will be beneficial to many undergraduates in mathematics. In fact, many sections are within reach of some advanced high school students who would like to explore interesting topics in mathematics. ! Summing Up: Recommended. --CHOICE, April 2010, Vol. 47, No. 08 The book under review is a friendly volume in discrete mathematics, which covers various classical topics, such as counting, probability and number theory, and more recent topics, such as information theory, game theory and algorithms. As far as I know, this book is one of only a few at this level that covers such recent topics. Because it covers algorithms, ! the book may be interesting for students interested in computer programming. ! This is essentially a textbook for undergraduates, and perhaps it can be useful for high school students as well. ! because of the variety of topics, teachers will have many choices of what to cover for students in applied fields. ! --Mehdi Hassani, MAA Reviews, December 2009


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