Discrete and Combinatorial Mathematics: An Applied Introduction

I bought this book as a supplement to a summer course in Discrete Math, and since this was my first ever exposure to mathematical proof and dialog, I first thought this book mostly alien, with occaisional sections of brevity; it did help me fill in some gaps left behind in Rosen's book, especially on some basic proofs dealing with integers and with combinatorial reasoning--something this book is REALLY good at... I'm in my first course of Combinatorics with a teacher that assumes we know alot more calculus than we do. We use Tucker's Applied combinatorics 5th, and I was cruising along just fine until we hit Generating Functions. Brick wall. Rosen's book didn't cover it (well; there's a great page of known identities, but not an intro-level version), neither did Epp, so I dusted this tome off my shelf and cracked it open... section 9.1 presents Generating functions on such an easy to use language and analytic explanation that I went from getting every problem wrong in Tucker's book to getting them all right; all due to the clarity of exposition. I've also found that as my 'mathematical maturity' has grown in the last year, so has the comprehensibility of this text. It may be too deep for a beginner--I would agree that it would be too much for all but your brightest minus an excellent teacher--but this book teaches 'real math' and does so *very* well. In conclusion, if you have the available student loan $$ and want a very good supplementary book that you really can take with you to higher classes, put this at the top of your list. I also own Epp and Rosen's discrete math texts, and have to say that for me ultimately I needed all three as a beginner; plus a few extra books from the library for special topics. But what I learned stayed with me and all three have their positives and negatives, but if I were to choose only one to stay on my shelf, THIS would be the one.

Excellent book, carefully chosen examples, ideal for self study. I like it very much. My advice is not to skip any section or solved examples or you might be lost.

The book is very well-written, clear and precise. I have read a couple of other books for discrete math courses, but found nothing exciting there; mostly frustrating errors, bad examples and confusion. Grimaldi's book covers pretty much everything you need to understand and apply in Discrete Mathematics. The exercises are well designed, in increasing difficulty. For most of the exercises, one can find similar examples in the text. Parts 1 and 2 of the book are by far the best read in Fundamentals and Enumeration I have ever encountered. Section 11 of Part 3 is a very nice introduction to Graph Theory. My only suggestion for improvement is some revision of sections 12 and 13 on graph algorithms - these can be simplified in terms of notation and description. Part 4 is for more advanced readers; it is usually used in a second course in Discrete mathematics. However, without being as exhaustive as the first three parts, the fourth part is presented with the same clarity and detail as the other three. I would strongly recommend this book not only to anyone who teaches Discrete mathematics, but also to any student who studies Discrete mathematics from a different book. If you are frustrated about the material; Grimaldi's book would give you the understanding and clarity you need. Definitely a five star product!

Grimaldi has produced a wonderful book. All the important topics in discrete math are explored, with many applications to computer science, the main client field of discrete math. The text is well balanced between theory and application. Especially nice is the introduction to modern algebra, with applications to coding theory. I highly recommend this text to anyone wishing to explore discrete mathematics. A good understanding of the concepts presented by Grimaldi will prepare the reader for more advanced work in discrete math (Aigner), computer science (Knuth), or theory of computation (Sipser).

Plenty of excercises and answers. Very well explained; this book is a must for those who want to learn combinatorics, elementary graph theory, and many other extremely useful topics.