A Course in Combinatorics

Rating:
Summary: Proof that you can't judge a book by its cover
Review: 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.

Rating:
Summary: A nice tour of combinatorics
Review: 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.

Rating:
Summary: A gentle introduction to combinatorics
Review: 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.