Combinatorics: Topics, Techniques, Algorithms [Paperback]

Peter J. Cameron (Author)

Book Description

ISBN-10: 0521457610 | ISBN-13: 978-0521457613 | Publication Date: January 27, 1995 | Edition: First Edition

Combinatorics is a subject of increasing importance because of its links with computer science, statistics, and algebra. This textbook stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more valuable than an existence proof. The author emphasizes techniques as well as topics and includes many algorithms described in simple terms. The text should provide essential background for students in all parts of discrete mathematics.

Editorial Reviews

Review

"Cameron covers an impressive amount of material in a relatively small space...an outstanding supplement to other texts..." M. Henle, Choice

"...used as a text at the senior or graduate level and is an excellent reference....The range of topics is very good." The UMAP Journal

Book Description

Including many algorithms described in simple terms, this textbook stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more valuable than an existence proof.

Product Details

• Paperback: 368 pages
• Publisher: Cambridge University Press; First Edition edition (January 27, 1995)
• Language: English
• ISBN-10: 0521457610
• ISBN-13: 978-0521457613
• Product Dimensions: 9.2 x 7.3 x 0.8 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 4.7 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #735,406 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

13 of 15 people found the following review helpful:

5.0 out of 5 stars Very helpful, January 9, 2004

By 

wiredweird "wiredweird" (Earth, or somewhere nearby) - See all my reviews
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This review is from: Combinatorics: Topics, Techniques, Algorithms (Paperback)

Combinatorics is a bit of an oddity. Although a few principles (like pigeonholing) apply in many cases, every combinatorial problem has unique features. Attacking a new situation is almost like starting all over again, unless you can recognize an old problem in your new one.

This book gives a number brief case studies. Its 18 chapters (not counting intro and closing) span a variety of interesting topics. Cameron doesn't write down to the reader - it takes serious thought and some mathematical background to get full value from the reading. The examples are nowhere near as concrete as you'd expect in a popularized version. Still, the author avoids opaque references to specialist terms, and keeps the text approachable.

I have personal reason to like this book more than it's high quality warrants. I was thumbing through it in a store, and skimmed a page that described Kirkman's schoolgirls (a two-level problem in selecting subsets). Quite abruptly, I realized that those charming young ladies exactly represented a problem I had in connecting the parts of a multiprocessor. One or two references later, I had a practical way out of a potentially ugly quandry. This material is not just fun for its own intellectual challenge, it has application to real engineering, too.

12 of 14 people found the following review helpful:

5.0 out of 5 stars Best Single Book on Combinatorics, June 14, 2000

By 

James M. Cargal (Montgomery, AL USA) - See all my reviews
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This review is from: Combinatorics: Topics, Techniques, Algorithms (Paperback)

The book is divided into two parts corresponding roughly to undergraduate material and graduate. The selection of topics is robust; the writing is clear and consise. The level is senior and above. The reader should have some knowledge of advanced math such as group theory, and analysis of algorithms. Great book! One of the best ever!

5 of 5 people found the following review helpful:

5.0 out of 5 stars Sigmas all over the place, March 30, 2007

By 

Henry Lenzi (Porto Alegre, RS Brazil) - See all my reviews
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This review is from: Combinatorics: Topics, Techniques, Algorithms (Paperback)

This isn't your usual "urn-has-3-red-balls-and-5-white-balls" sort of combinatorics book. It's sigma notation all over the place, if you know what I mean.
The first part can be used for undergraduates and the second part is more advanced. The book is broad in scope because, as the author explains, so is the subject matter.
The chapters have "techniques" and "algorithms." It's not a book that has a slew of examples of combinatorial problems (like so many), but leans toward mathematical sophistication in formalizing the techniques. This is either a feature or a bug, depending on what you needs are. For instance, it's not very often that introductory books present derrangements next to Fibonacci numbers. Or explain how calculate the average number of comparisons that Hoare's Quicksort does with a differential equation for the recurrence relation in the context of finite fields. It sounds scary, I know, but if you look at the explanation, you'll see you should have been born a nephew to this author.
In case you like Knuth's Concrete Mathematics you will like this book too (there's some overlap, because both are concerned with the analysis of algorithms). Knuth's book works more on skill-building, and I think Cameron's book is better for theoretical explanation.
Disclaimer: I haven't worked with the whole book (because of a lack of time - "Ars long, vita brevis", as they say).