 "Seems a little Stiff at first..." | 2008-12-28 |
| - Reviewed By xeno6696 |
Out of the three main discrete math texts, Rosen, Epp, and this one--Grimaldi--this text unites the best parts of both; Epp has some really great explanations, but suffers from not having enough solutions and lacks depth. Rosen's book manages to write hundreds of words per concept while completely confusing new students in dense mathematical jargon.
I used this book as a supplement to my discrete math class in summer and as a supplement for a combinatorics class this past fall.
My mathematical 'maturity' when approaching discrete math was business calculus. (Yeah, I know that sucks, and all you mathematicians and engineers can laugh your hind off about it. Don't remind me.) So basically, I was behind the class in both this and in the combinatorics class this fall.
This book is best approached if you take the explanations it uses *while trying to solve the problems.* It seemed pitched high to me because Epp is focused on giving you concepts and Rosen is concerned with making sure you learn theory.
Grimaldi is interested in teaching you to solve problems.
This book also has the one of the *best* sections on recurrence relations. I thought Chen's book was king here, but this book, when working through gobs of problems, helps you learn them inside and out. It has two charts detailing what happens in a non-homegeneous recurrence relation, one that states general solutions, another that gives you a relation, its homogeneous counterpart, and changes the NH part and shows you how the general form changes.
Brilliant, and blows Tucker's "Applied Combinatorics" out of the water in clarity when solving recurrence relations.
Best book in its class.
(Got an A- and a B in those classes, for the results-minded.)
This is where this book became the holy grail. |
| |
| "Beautifully Written and an Excellent Reference" | 2008-11-23 |
| - Reviewed By xeno6696 |
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. |
| |
 "More rigorous and lengthy than other discrete texts, too much for my purposes" | 2007-01-17 |
| - Reviewed By 71603522 |
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.
|
| |
| "ideal for self study" | 2006-01-26 |
| - Reviewed By comm@gameshop.sk |
| 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. |
| |
| "great book on discrete math" | 2005-03-21 |
| - Reviewed By quailster |
| 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 can't stand discrete!" | 2004-04-12 |
| - Reviewed By Anonymous |
| ...that shouldn't reflect badly on this book though. While I think discrete sucks, I think this book does a good job for the discrete courses I did. I think the examples are good & helpful with doing the problems, and the problems range from easy verifications of theorems or mechanical computations to trickier problems or proofs of theorems. This book was pretty good, IMO. (for a discrete text anyway) |
| |
International Available
