I will once again be teaching discrete mathematics this summer, so I am searching through the mathematical publishing pathways looking for a suitable textbook. Therefore, that is the context within which I examined this book.
It certainly is the largest discrete book that I have encountered; including the appendices and problem solutions, there are over one thousand pages. Grimaldi has tried to include every topic that falls under the discrete mathematics tent. Therefore, this is a book that could be used for a two semester sequence in discrete mathematics.
When examining discrete books for possible adoption I start with the simple premise that logic, set theory and functions and relations must be covered very early. In my ideal world, they are the first three chapters. Set theory and relations are so fundamental a part of other areas that I am surprised when authors don't cover them first. The first chapter in this book covers basic counting principles. While this doesn't break too much from my ideal sequence, I see no overpowering reason why fundamental counting should be before set theory. Given that the rules of counting for sums and products can easily be related to sets, there is a strong justification for putting set theory first.Read more ›
This is a bad book if you are not already familiar with the basic concepts of the material. The author was more interested in showing worked examples than explaining concepts, and the more difficult problems in the exercise sections do not have solutions in the back of the book, so even 'self-learning' is extremely hard.
Unless you have a very good teacher, you will not benefit from the way the material is presented inside this book. 'Solutions' and 'examples' are presented 'as is' without explanations. One of my friends into math did mention it's not a bad reference guide for proofs, but he was as unimpressed with this book as a learning tool as I was. The level of rigor is very high, but the simple explanations to go with it are not present. I advise finding a good source on the subject instead of this unfriendly text, which has a target audience of math professionals.
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.
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It is common to feel you need someone to explain what you are reading while studying from a book and even more if the subject is mathematics. That is what surprises readers while starting to explore this interesting book.
At the beginning it is hard to believe how simple it becomes to understand the different topics. That is a consequence of the easy way readers assimilate what is learnt by analyzing general and particular examples. That is the way in which the book presents the different units: the usual incomprehensible explanations are replaced by a lot of short examples which are easily understandable. Students not only feel they understand what they read but also enjoy and are attracted by a subject that is nice when comprehended.
Even if it seems to be too long, its more than eight-hundred pages do not reflect the period of time which takes to learn each unit. They are considerably short and are also divided in sections that reduce the difficulty of continuous reading, especially after having stopped for a wile, leaving aside the need to go over the last pages.
I consider this is a recommendable book for those students who are studying all the mathematic points which are analyzed in the volume. I believe it is the best complement for daily classes or a good option to study on your own.
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