Customer Reviews

Discrete and Combinatorial Mathematics: An Applied Introduction (4th Edition)

5 star:		(13)
4 star:		(9)
3 star:		(1)
2 star:		(5)
1 star:		(6)

 

 

Finally! A math book which is acutally well written, has enough examples to illustrate key concepts, and has enough problems to keep the math student busy. Discrete mathematics is a fairly involved subject and books on the topic range from relatively basic to extremely difficult treatises which only a PhD or a math professor could understand. Discrete and Combinatorial Mathematics : An Applied Introduction by Ralph Grimaldi is a book which will appeal to both sides of the spectrum. The book is written so that most undergraduate students will have little difficulty understanding, but graduate students will also find it indispensable as a reference. The illustrated examples are actually relevant to the homework problems, which is often missing in mathematical texts. Finally, the book does not try to overwhelm the reader with lofty proofs or stilted language. Each chapter builds on the previous subjects learned. That's all I can ask for in a math text. I like the coverage of combinatorics in the first chapter, which does a better job than many probability textbooks. And be sure to understand Euclid's theroem and the examples given in the book. Quite a few high-tech companies will ask you about the problem Grimaldi gives as an example of Euclid's theorem in their job interviews.

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.
The coverage is split into four parts, the first of which consists of the seven chapters:

*) Fundamental principles of counting
*) Fundamentals of logic
*) Set theory
*) Properties of integers: mathematical induction
*) Relations and functions
*) Languages: finite state machines
*) Relations: second time around

In my opinion, the order of the topics should be:

*) Fundamentals of logic
*) Set theory
*) Relations and functions
*) Relations: second time around
*) Fundamental principles of counting
*) The principle of inclusion and exclusion (currently chapter 8)
*) Properties of integers: mathematical induction
*) Generating functions (currently chapter 9)
*) Recurrence relations (currently chapter 10)
*) Languages: finite state machines

The current chapters 8 through 10 make up part two of the book.
Part three is graph theory and applications and part four is modern applied algebra. I have no issues with the order here. The chapter headings for the fourth part are:
*) Rings and modular arithmetic
*) Boolean algebra and switching functions
*) Groups, coding theory and Polya's method of enumeration
*) Finite fields and combinatorial design

With this part being nearly two hundred pages in length, the coverage is extensive.
Grimaldi takes a more rigorous approach than many other authors of discrete texts, while I did not examine every single theorem, I did look at a lot of them and all were accompanied by a proof. The exposition is clear, there are many worked examples, a large number of exercises and solutions to the odd-numbered exercises are included. A summary and historical review of the topic follows each section.
If we offered a two course sequence in discrete mathematics, then I would consider adopting this book. Such a situation would allow me to present the material at a higher level of rigor, where this book excels. However, with a one semester course designed to teach computer science majors the mathematical fundamentals they need, this book is both too long and too deep.

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!

This book is perhaps the best reference for Discrete Math I have seen. The book is comprehensive. It gives an introduction to many topics every CS coding theory, number theory, partial orders, even automata. There are many examples and illustrations to understand the material. There are plenty of excercises. The text is well written; no errors or typos. It would be nice if the book had more proofs.

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).

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.

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.

This is an excellent book for self study. However, there are parts in this book that must be rearranged or deleted. For example, I think Catalan numbers should be deleted. This might be useful for the matrix chaining problem, but that's in the realms of algorithm design (specifically in dynamic programming). Also, I do not understand why Grimaldi sandwiched in a chapter on Finite State Machines between two chapters on Functions and Relations. Maybe he should make a section on languages for FSMs, but I recommend Sipser's Introduction to the Theory of Computation if you want to learn about FSMs.

I needed this book for my CPSC 2405 class. My class was warned at the beginning of the semestre, by the teacher, that a lot of the material will be confusing and the book probably won't assist you very much if you don't already have a basic idea of what to do. He was right. A lot of examples are provided. I am gratefull for this. But, his explanations are far too concise and compact for easy learning. This book would be much more usefull, if more time was spent explaining the theories and techniques and not just showing us how to apply them.