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Counting: The Art of Enumerative Combinatorics (Undergraduate Texts in Mathematics) (Englisch) Gebundene Ausgabe – 1. Juli 2001

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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)


Counting is hard. "Counting" is short for "Enumerative Combinatorics," which certainly doesn't sound easy. This book provides an introduction to discrete mathematics that addresses questions that begin, How many ways are there to...At the end of the book the reader should be able to answer such nontrivial counting questions 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? There are no prerequisites for this course beyond mathematical maturity. The book can be used for a semester course at the sophomore level as introduction to discrete mathematics for mathematics, computer science, and statistics students. The first five chapters can also serve as a basis for a graduate course for in-service teachers.

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Amazon.com: 4.7 von 5 Sternen 6 Rezensionen
2 von 2 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Solid but fun to read. 30. Juli 2014
Von Just a Guy - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe Verifizierter Kauf
This book uniquely combines comprehensiveness and rigor with conciseness and a friendly, accessible tone.

From the point of view of someone interested in computer science, all the key stuff is covered: perms/combs, pigeonhole, inclusion/exclusion, Stirling, Bell, Catalan, Fibonacci, recurrences, generating functions, induction, etc. There are lots of worked out examples and plenty of excellent, instructive problems with useful hints and solutions in the "back of the book" section (which comprises over 60 pages).

As the author explains in the preface, chapters 1-3 plus 6 (recurrences) form a good CS course, to which I would add chapter 7 on induction. The final chapter on graph theory is necessarily incomplete, but still worth reading.

Chapters 4 and 5 discuss symmetry groups and Polya theory, and are treated equally well for those who wish to delve into these subjects.

Top notch stuff.
4.0 von 5 Sternen A fun book to learn counting 4. Februar 2016
Von Dr S Muralidharan - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe Verifizierter Kauf
This is a fun book to read. Contains lots of exercises (with solutions). The best part of the book is the one in which the author explains Polya's pattern inventory without taxing the reader with too many definitions. He uses coloring a dodecahedron to illustrate the theorem and one can easily appreciate the power of the technique through this well chosen example. One glaring error is presenting the Lagranges theorem (order of a subgroup divides the order of the group) as Legendre's theorem. The answers at the end of the book are detailed and very helpful for the student.
5.0 von 5 Sternen The book was a wonderful introduction to combinatorics for me 12. Mai 2016
Von Pocket - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe Verifizierter Kauf
The book was a wonderful introduction to combinatorics for me. I taught myself combinatorics through this book. The book provided enough examples and answers for me to dive into combinatorics. I look forward to more combinatorics in the future thanks to this book!
9 von 11 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen Great Introduction on Counting 1. März 2004
Von Ein Kunde - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
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.
4 von 5 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Interesting book on combinatorics 8. Juli 2008
Von Chee Lim Cheung - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
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.
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