 "Worst Math Text I Have Seen (My Opinion)" | 2009-09-14 |
| - Reviewed By Sanford Wilson from Atlanta, GA |
First, a little background. I'm not a mathematician or a teacher, but I do have an undergrad CS degree from Georgia Tech and I've seen my share of math books. My son is a college junior and is using this text and I have been helping him study. I think this is without doubt the worst math text I have ever seen. Some of the problems:
1. In solved examples, some CRUCIAL steps in the process are not explained at all. This is not just the usual algebraic manipulation that is left for the student to work through; these are major milestones in the solution that are used with no justification or explanation. For instance, one problem begins by trying to solve x1 + x2 + x3 + x4 = 18. Shortly thereafter, it's solving for x1 + x2 + x3 + x4 = 10. I finally determined why it happened, but at first I could come up only with the idea that it was somehow related to the fact that 1 + 2 + 3 + 4 = 10. This kind of "leap" occurs about every 2 or 3 pages and most of the time it would take only a brief sentence to explain the sudden change. It's unacceptable, especially in an undergraduate text.
2. Concepts and formulas are introduced in examples. At first, it may seem that this style is useful, but it is not. About 80% of the text is examples and the reader must slog through every one of them to avoid missing some important development.
3. Notation. The front and back inside covers purport to show the notation conventions used in the book. But when "Pi-notation is used on p.395 to discuss Euler's phi, you find that Pi-notation is not included in the notation conventions. If you skipped Chapter 4 on Mathematical Induction, as my son's class did, you would have missed the introduction of Pi-notation on p. 239. Also, the Pi-notation as used on p. 395 does not conform to the convention shown on p. 239; specifically, the upper limit of the index is omitted.
4. How about a 24-page, 3-column per page index???
As I said, I'm not a mathematician or a teacher, and I don't feel qualified to discuss the finer points of instruction on higher math. But in my opionion these are major omissions and stylistic errors that make this text clearly lacking in instructional value. Buy a different book (my son and I just ordered 2 more - God help us.) |
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 "Seems a little Stiff at first..." | 2008-12-28 |
| - Reviewed By xeno6696 from Omaha NE |
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. |
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| "Beautifully Written and an Excellent Reference" | 2008-11-23 |
| - Reviewed By xeno6696 from Omaha NE |
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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| "Do not buy this book." | 2007-05-20 |
| - Reviewed By Ricardo Auguste from Japan |
| This book is very poorly written and lacks any kind of order in which to study the chapters. The explanations of theorums and formulas are just not enough. Another thing that I do not like about this is that the section problems want you to work out precise mathematical concepts that were not explained in the relevant section, thus making you have to re-read the section several times over, and even then it is still not enough. I have completed Calculus II and that textbook was nowhere near as difficult to understand than this one. If you want to get a general idea of what Discret Mathematics is or want to do self study, then get this book. But in my opinion, avoid this book at all cost. Pun intended. |
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 "More rigorous and lengthy than other discrete texts, too much for my purposes" | 2007-01-17 |
| - Reviewed By (cashbacher@yahoo.com) from Marion, Iowa United States(cashbacher@yahoo.com) |
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.
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| "ideal for self study" | 2006-01-26 |
| - Reviewed By Tomas Selnekovic from Bratislava, SLOVAKIA |
| 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. |
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