A Course in Combinatorics [Paperback]

J. H. van Lint (Author), R. M. Wilson (Author)

Book Description

ISBN-10: 0521006015 | ISBN-13: 978-0521006019 | Publication Date: December 3, 2001 | Edition: 2

Combinatorics, a subject dealing with ways of arranging and distributing objects, involves ideas from geometry, algebra, and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become an essential tool in many scientific fields. In this second edition the authors have made the text as comprehensive as possible, dealing in a unified manner with such topics as graph theory, extremal problems, designs, colorings, and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. It is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level, and working mathematicians and scientists will also find it a valuable introduction and reference.

Editorial Reviews

Review

"...their choice of subject matter is superb...would indeed make an excellent text for a full-year introduction to combinatorics." Mathematical Reviews

"...this is a valuable book both for the professional with a passing interest in combinatorics and for the students for whom it is primarily intended." Times Higher Education Supplement

Book Description

This is the second edition of a popular text on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. There are also many applications, so workers in many scientific fields need some familiarity with the subject. The extensive depth and breadth of the coverage make the book a unique guide to the whole of the subject, so that it is ideal for courses at the advanced undergraduate or beginning graduate level and also for working mathematicians and scientists.

Product Details

• Paperback: 620 pages
• Publisher: Cambridge University Press; 2 edition (December 3, 2001)
• Language: English
• ISBN-10: 0521006015
• ISBN-13: 978-0521006019
• Product Dimensions: 9.4 x 6.7 x 1.6 inches
• Shipping Weight: 2.5 pounds (View shipping rates and policies)
• Average Customer Review: 4.6 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #376,158 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

37 of 41 people found the following review helpful:

4.0 out of 5 stars A gentle introduction to combinatorics, July 22, 2000

By A Customer

This review is from: A Course in Combinatorics (Paperback)

This book was the text for a graduate-level course I took. The presentation is very laid-back, much like the lecturing style of one of the authors (Wilson), and so it was quite readable (unlike many other math books which you have to stop every few pages and pick apart everything before it sinks in).

Combinatorics is a relatively recent development in mathematics, one which is generally easy to explain, but with many difficult open questions. Van Lint and Wilson do an excellent job explaining, but there are a few places where the reader needs to know some background to place the particular problem in the appropriate mathematical context. Understandably, if the authors were to include all the mathematical machinery needed, the book would be huge! Instead, they have chosen to describe as many facets of the field as possible, and therefore have written a broad, well-balanced book which approaches the topic in a non-threatening way.

My one criticism, then, is that there is a lack of depth in several areas of the book, with further discussion of advanced topics or open problems. But even so, I can appreciate the omission for the sake of accessibility.

To fully appreciate the subject, the authors are correct in mentioning that the book is written with the graduate student in mind. But by no means does the reader require such a background to appreciate the remarkable concepts and the exciting questions revealed in this book.

12 of 12 people found the following review helpful:

4.0 out of 5 stars Excellent book, but organized in a unorthodox and inconvenient manner, June 11, 2006

By 

Alexander C. Zorach "Alex Zorach" (Lancaster, PA) - See all my reviews
(REAL NAME)   

This review is from: A Course in Combinatorics (Hardcover)

I think this is an excellent book but I have a few concerns about its organization.

The writing is very clear and there is a lot of explanation. Exercises are mixed in with the text, which I like very much; it makes them seem more natural, and it makes the book well-suited for self-study. I would say the difficulty level of this book is a bit inconsistent--but this is more a function of the material than of the writing style. The authors make everything as clear as possible, but they choose to include some difficult topics which require more thought.

My main criticism of this book is about the order of topics, which is not only unorthodox but can be inconvenient as well. Many concepts which are often presented earlier in combinatorics texts, such as binomial coefficients and stirling numbers, are relegated to later chapters, where their presentation depends on results from earlier chapters. I find it difficult to skip around in this book--if you do not read it from the beginning, in order, it will be hard to follow the arguments in some of the chapters. This sort of dependency is something I can accept in a more advanced text but I think is inappropriate for a text at this level.

I think this is an excellent book to add to your collection, but if you're going to grab only one or two books in combinatorics I would recommend other books. The organization issues I mentioned could make this book hard to use as a standalone text for a course if you did not wish to follow the same course of development chosen by the authors. Cameron's book is written at a similar level and covers a similar amount of material (although it has a very different style of presentation), and it is much easier to skip around in. Stanley's "Enumerative Combinatorics" is a denser, more advanced text that most will find more difficult to follow than this book, but it is still easier to skip around in as well.

13 of 14 people found the following review helpful:

5.0 out of 5 stars A nice tour of combinatorics, November 18, 2003

By A Customer

This review is from: A Course in Combinatorics (Paperback)

The first word that comes to my mind when I think of this text is "encyclopedic". It contains around 40 chapters, hitting most of the high points of combinatorics that a graduate student should see. The exposition is generally good with nice examples. The one thing that I fault it for is the number of statements that the authors claim are "obvious". In a way, this is good, because it makes you pay attention and understand the material, but sometimes the statement isn't obvious until you've thought about it for an hour and written out a lengthy proof. At that point, it does become completely obvious and you can't believe that you ever thought it wasn't, so I can understand why van Lint and Wilson fell into the trap so often. (In fact, I've heard that Wilson even stumbles over some of those points in lectures.) This is a great book to have on your shelf if you need somewhere to look up combinatorial ideas.