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Pearls of Discrete Mathematics

Martin Erickson
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2009
Number of Pages: 
270
Format: 
Paperback
Series: 
Discrete Mathematics and Its applications
Price: 
59.95
ISBN: 
9781439816165
Category: 
Textbook
[Reviewed by
Mehdi Hassani
, on
12/28/2009
]

Discrete mathematics is a standard topic for undergraduate students in areas such as mathematics, engineering, computer science, and information technology. What we expect to see in a course with title “Discrete Mathematics” can vary according to which of those areas our students are in, and this is the case for the goals of the course as well. Finding a textbook with an acceptable number of pages and covering suitable topics can become a problem.

The book under review is a friendly volume in discrete mathematics, which covers in some brief words 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 cover such recent topics. Because it covers algorithms, for example an algorithm for solving Sudoku puzzles, the book has may be interesting for students interested in computer programming.

The book has twenty four chapters arranged in eight parts. Each chapter starts with a question, or with an answer for a question, that motivates the reader and gives a picture of what kinds of questions can be answered after studying that chapter. The chapters are rather short and quick, and they contain both easy and hard exercises. As we cross from the first few chapters to the final ones, we feel that the topics become more delicate and newer.

This is essentially a textbook for undergraduates, and perhaps it can be useful for high school students as well. It will be difficult to teach all the chapters in a semester, but because of the variety of topics, teachers will have many choices of what to cover for students in applied fields. I am not sure that this book will satisfy pure mathematics students and teachers, because of its short chapters and lack of focus on the details of the theory.


Mehdi Hassani is a co-tutelle Ph.D. student in Mathematics, Analytic Number Theory in the Institute for Advanced Studies in Basic Science in Zanjan, Iran, and the Université de Bordeaux I, under supervision of the professors M.M. Shahshahani and J-M. Deshouillers.

Counting: Basic

Subsets of a Set

Pascal’s Triangle

Binomial Coefficient Identities

Counting: Intermediate

Finding a Polynomial

The Upward-Extended 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 Coin-Tossing Game

Shannon’s Theorems

Games

A Little Graph Theory Background

The Ramsey Game

Tic-Tac-Toe and Animal Games

Algorithms

Counters

Listing Permutations and Combinations

Sudoku Solving and Polycube Packing

Appendix A: Hints and Solutions to Exercises

Appendix B: Notation

Bibliography

Index

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