Counting: The Art of Enumerative Combinatorics [Hardcover]

George E. Martin (Author)

Book Description

Publication Date: June 21, 2001 | ISBN-10: 038795225X | ISBN-13: 978-0387952253 | Edition: 1

This book provides an introduction to discrete mathematics. At the end of the book the reader should be able to answer counting questions such as: How many ways are there to stack n poker chips, each of which can be red, white, blue, or green, such that each red chip is adjacent to at least 1 green chip? The book can be used as a textbook for a semester course at the sophomore level. The first five chapters can also serve as a basis for a graduate course for in-service teachers.

Editorial Reviews

Review

From the reviews: "Much of Martin’s charming and accessible text could be used with bright school students. … The book is rounded off by a section called ‘The back of the book’ which includes solutions and discussion of many exercises. George E. Martin is a remarkable writer who brings combinatorics alive. He has written a splendid introduction that requires very few prerequisites, yet soon delivers the reader into some highly effective methods of counting. The book is highly recommended." (S. C. Russen, The Mathematical Gazette, Vol. 88 (551), 2004) "This truly is an undergraduate mathematics text; parts of it could be the text for a high school combinatorics course. The author has made a successful effort to illuminate and teach the elementary parts of combinatorics. He uses examples and problems to teach; there are 245 problems in Chapter 1! … If I were not retired and had been asked to teach an undergraduate course in combinatorics, I would have liked to use this book." (W. Moser, Mathematical Reviews, Issue 2002 g) "This book is a nice textbook on enumerative combinatorics to undergraduates. It introduces the most important ideas … . A lot of ‘easy’ applications are given and homework is listed (with hints). The book also touches some elementary graph enumeration problems. The text is clear and easy to follow. It is even suitable to learn it alone, which is also aided by nice exam problems." (Péter L. Erdös, Zentralblatt MATH, Vol. 968, 2001) "The teaching of topics in discrete mathematics is becoming increasingly popular and this text contains chapters on a number of pertinent areas for exposure at an elementary level. … The author uses non-worked discovery-type examples to lead into observations about the material. … There are many interesting exercises for the student to attempt. These are spread throughout the various chapters and are effective in developing interest in the topics. The book contains a ‘Back of the Book’ section rather than an Answers section." (M. J. Williams, The Australian Mathematical Society Gazette, Vol. 29 (1), 2002)

About the Author

From the reviews: "Much of Martin’s charming and accessible text could be used with bright school students. … The book is rounded off by a section called ‘The back of the book’ which includes solutions and discussion of many exercises. George E. Martin is a remarkable writer who brings combinatorics alive. He has written a splendid introduction that requires very few prerequisites, yet soon delivers the reader into some highly effective methods of counting. The book is highly recommended." (S. C. Russen, The Mathematical Gazette, Vol. 88 (551), 2004) "This truly is an undergraduate mathematics text; parts of it could be the text for a high school combinatorics course. The author has made a successful effort to illuminate and teach the elementary parts of combinatorics. He uses examples and problems to teach; there are 245 problems in Chapter 1! … If I were not retired and had been asked to teach an undergraduate course in combinatorics, I would have liked to use this book." (W. Moser, Mathematical Reviews, Issue 2002 g) "This book is a nice textbook on enumerative combinatorics to undergraduates. It introduces the most important ideas … . A lot of ‘easy’ applications are given and homework is listed (with hints). The book also touches some elementary graph enumeration problems. The text is clear and easy to follow. It is even suitable to learn it alone, which is also aided by nice exam problems." (Péter L. Erdös, Zentralblatt MATH, Vol. 968, 2001) "The teaching of topics in discrete mathematics is becoming increasingly popular and this text contains chapters on a number of pertinent areas for exposure at an elementary level. … The author uses non-worked discovery-type examples to lead into observations about the material. … There are many interesting exercises for the student to attempt. These are spread throughout the various chapters and are effective in developing interest in the topics. The book contains a ‘Back of the Book’ section rather than an Answers section." (M. J. Williams, The Australian Mathematical Society Gazette, Vol. 29 (1), 2002)

Product Details

• Hardcover: 264 pages
• Publisher: Springer; 1 edition (June 21, 2001)
• Language: English
• ISBN-10: 038795225X
• ISBN-13: 978-0387952253
• Product Dimensions: 9.3 x 6.4 x 1 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #659,580 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

8 of 10 people found the following review helpful:

4.0 out of 5 stars Great Introduction on Counting, March 1, 2004

By A Customer

This review is from: Counting: The Art of Enumerative Combinatorics (Hardcover)

This book is a good introduction to counting (combinatoric type counting). The book has answers to most of it's problems and recommends you try the problems before looking at the answers. Most of the problems are simple, and hit hard on the idea the section of the book is trying to get across.

It covers simple counting, groups, generating functions, recurrence relations and mathematical induction. The book concludes with graph theory. Some chapter sections get a little hard to understand, hence the 4 star and not 5 star rating (2 stars is what I'd give a decent book, so this one is a shining star). Most of the book is clear cut.

3 of 4 people found the following review helpful:

5.0 out of 5 stars Interesting book on combinatorics, July 8, 2008

By 

Chee Lim Cheung - See all my reviews
(REAL NAME)   

This review is from: Counting: The Art of Enumerative Combinatorics (Hardcover)

This is a charming text on elementary combinatorics. Counting, or enumerative combinatorics, is-as the writer says-hard, but after you have gone through this very readable book, it becomes less hard and more interesting-so much so that you will want more of it. The reader is very much helped by the Back of the Book section which provides answers and, in many cases, solutions as well.