Customer Reviews

Combinatorics and Graph Theory (Undergraduate Texts in Mathematics)

5 star:		(9)
4 star:		(1)
3 star:		(1)
2 star:		(0)
1 star:		(1)

 

 

I am a math student with Indiana University working out of this book for independent study credit. When my adviser and I sat down to discuss books, we sifted through 10 to 12 books, and it was clear from the start that this book was the best. And I haven't changed my mind since. The book is clear, concise, and easy to read. Excellent for anyone who is teaching themselves, which of course means it's great for a full course with actual instructors.

Unlike its competitors, this book states simple concepts simply. It gives an excellent selection of the most important techniques and examples, without endlessly repeated "real-world" applications. In 80 pages, it covers the most interesting topics in graph theory, including: Cayley's tree-counting theorem, vertex coloring (with proof of the 5-Color Theorem), Hall matching theorem, Ramsey numbers, and stable marriage. Another 80 pages contains the main concepts of enumeration: elementary combinations (poker hands), inclusion-exclusion, generating functions for Fibonacci and Catalan numbers, Polya counting of symmetry classes, Stirling numbers. There is final section on infinite sets and graphs.

The book covers quite as much as similar ones of twice the length. Finally, a textbook which is not afraid to be brief!

Little did I expect of a book that has seemingly not garnered that much attention among professors and students (at least the lack of reviews in Amazon.com might serve as a confirming instance of that speculation), but come exam time, the book proved that such prejudice is outright foolish.

The authors must really love both the field and writing about it, for their overflowing exuberance readily transfers to the pages. Pictures and humor are never a scarcity here: the authors took no shame providing both; a curious but pleasurably fresh anomaly in the often dry and coldly serious world that is mathematics writing.

I would exercise some caution before purchasing or adopting this text. While many reviewers find the style exuberant and humorous, I find it a bit breezy and even flip, at the expense of clarity. Here's an example, the definition of an SDR:

Given some family of sets X, a system of distinct representatives, or SDR, for
the sets in X can be thought of as a "representative" collection of distinct
elements from the sets of X. For instance, .... [What follows is a collection
of 5 sets and an SDR for them, along with a subcollection of 4 sets that doesn't
have an SDR.]

"Can be thought of"? Such tentative language is not helpful, and I'm not sure that the example would nail it down for the uninitiated.

The third chapter of the book (there are just three), "Infinite combinatorics and graphs", is what initially caught my attention, but the primary emphasis here is symbolic logic and abstract set theory. Very interesting topics, but the connection to combinatorics is a bit thin.

This is by far the best math book I have ever read. The authors present the material in a clear but also incredibly engaging way. The problems are interesting and spot-on in terms of difficulty for the sophomore to junior level introductory course. Those looking for a more classical definition-theorem-proof style textbook should look elsewhere. This is not to say that the textbook lacks rigor (the proofs are very precise), but that it reads more like a narrative, so that it might not serve as the best reference. For the student, however, there really isn't much more you could ask for in a math book.

My background: I am an MIS major that discovered too late that he had an intense love for the mathematics behind the magic of computer science. I had previously only taken business calc(!) and Discrete Math (for CS majors). The book assigned was Tucker's book which does a great job on generating functions, but loses brevity completely when entering the field of recursive relations.

This book's explanations dealing with poker hands did what Tucker's and Grimaldi's books left me hanging on. Treatment on the binomial theorem and its related applications was also very thorough and at an acceptable level. The beauty of this book however is that the exercises rapidly increase in punch, and I still return to it from time to time to tease out new relationships.

It's introduction to graph theory is also very stellar... and it decides to introduce it before the combinatorial arguments, which if I'd had a little stronger comp sci background before taking the class, I would have found a much more gradual introduction to the general theories.

I'm still raising in mathematical ability, and I plan on tackling this book when I've gotten a little more maturity under my belt.

Excellent book. Hands down.

I find the book to explain exactly what it intends to, providing pertinent examples where useful. I wish there were more examples, actually, but there is something to be said for being concise. The problems are well-organized and good problems. Also, it is a nice, sturdy hardcover version with non-glossy pages, which makes it easy to carry around without getting it beat up and easy on the eyes under fluorescent lights.

I haven't gone through the whole book yet but the portion on graph theory that I have read is brilliantly written. The authors inject humor and beauty in the subject. If you are a self learner then this book is ideal for you. The only negative point is the total lack of answers/hints to the problems in the exercises.

The authors of this book have managed to teach, in a complete and thorough manner, enough material to fill a book more than twice the size of this one. Do not mistake its brevity for a Rudin-esque lack of explanation, or for a lack of substance. Explanations are provided, a good deal of material is covered, and the book remains so concise and to the point that I have no complaints whatsoever.

Very few math books lend themselves well to being read cover-to-cover, but the unassuming nature of this book makes it perfect for a leisurely and fun read, or for a classroom.

Fans of the writing style of Joseph Gallian's "Contemporary Abstract Algebra" will enjoy this book's ability to present material in a friendly way without oversimplifying.

Buy this book.

Great book, it is in great condition. Very quick shipment. Thanks, and looking forward to doing doing business again in the future.