Customer Reviews

A Course in Combinatorics

5 star:		(3)
4 star:		(2)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

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.

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.

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.

The cover says, "...ideally suited for use as a text...at the advanced undergraduate or beginning graduate level." WRONG!! I'm a sixteen year old-- far from graduate school-- and I am reading, understanding, and LOVING this book. I cannot think of a greater introduction to combinatorics-- it has examples and problems to test your comprehension, and logical flow from one subject to another. This book is a rare find-- clear explanations and definitions at a fast pace that doesn't bore you. I would recommend this book unconditionally to ANYBODY interested in mathematics.

I am a lover of combinatorics, and I have read quite a few on the topic. This one is as good as any. Lucidly written, you can pretty much dive into any chapter, reading, scribbling, racking your brain, and come away with a deep sense of satisfaction and pride and vanity:). Price is so resonable with regard for its extensive content. You get a feel that the author really wants to share with readers his love and joy for the subject and not just to make some money. Thank you, my dear professors!