Customer Reviews

GRE Mathematics (REA) - The Best Test Prep for the GRE (GRE Test Preparation)

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

 

 

Let me first say that I have the 1997 printing. From what I can see, very little seems to change from printing to printing, so I'm assuming that most of my complaints from this printing still hold for a "newer" edition that you buy now.

Many reviewers have pointed out that the practice tests in this volume are harder than the actual GRE math subject test, which I found to be true. It's not that this is, a fortiori, a bad thing; sometimes training on harder tests makes the real thing seem much easier in contrast. However, the practice tests in this book are not just harder than the actual test, but quite different in terms of the skill set they seem to require. So if you practice from this book, you're really not practicing the types of questions you'll see on the GRE.

More specifically, there are plenty of questions in the REA book that require odd leaps of intuition that even the more seasoned mathematician is not likely to make, at least not without a lot of time to sit down and play with the problem. (Of course this is an impossibility given the tight schedule they give you on the real exam to answer 66 questions!)

As an example (and this is a bit rough since it's not easy typing up math expressions like this):

SUM (from 1 to m) arctan( 1 / ( n^2 + n + 1 ) )

I won't detail the contorted series of substitutions and simplifications the answer key suggests. Perhaps I'm being naive, but I'm in my fifth year of graduate study and I have never come across a problem like this on a timed test. This is more like the kind of brain-teaser you might find in one of the common math journals. (Think Putnam exam problem, but not really as difficult.) Needless to say, the real test does not require this kind of reasoning. Everything on the real test suggests to the well-prepared student a reasonably standard method of attack.

Unfortunately, there are a lot of these useless practice problems. They are a distraction, especially when you want to time yourself and take a full practice test. (It's easy enough to skip these when casually working problems.) It's also distracting to find questions covering relatively obscure topics. Like, what is Green's function for a 2nd order differential equation? (I guess the solution guide "explained" it to me.) I've taught differential equations from multiple books for years and I've never seen it. I'm sure somebody covers in it their curriculum, but can we really expect that everyone should know how to compute Green's function?

A lot has been said as well about typos. Again, perhaps I am wrong about the new edition, but I suspect many of these remain. Worse than the typos for me was the typesetting. In this, the modern age of technology, why, I ask, does this book still look like it was produced on a typewriter? We've had TeX for many years now, for crying out loud! A few of my favorite typographic blunders:

In a discussion of continuity, an appropriate looking epsilon symbol appears, and then in the very same line, the symbol for element inclusion in a set (which sort of looks like an e I guess) plays the role of the very same epsilon. Later in the book, the epsilon symbols reappears, but now used as element inclusion.

In another solution, the Greek letter alpha appears, and then suddenly turns into the symbol for "proportional to"--only vaguely resembling an alpha in the most superficial of characteristics--again in the very same line.

The most unforgivable offense is the following "computation" of the number non-isomorphic abelian groups of order 40:

The answer according to REA? Seven. Here's their explanation:

"Non-isomorphic abelian groups of the same order, n, are effectively the direct products Z_n1 X Z_n2 X ... X Z_nk where n_1 x n_2 x ... n_k = n and each n_i is a divisor of n. In this case, the products yielding 40 are 40, 10 x 4, 8 x 5, 20 x 2, 10 x 2 x 2, 5 x 4 x 2, and 5 x 2 x 2 x 2."

Huh!?! I'm pretty sure the answer is three. The very elementary theorem from your first abstract algebra course states:

Z_m = Z_m1 X Z_m2 iff m1 and m2 are relatively prime.

Hence,

Z_40 = Z_8 X Z_5

Z_10 X Z_4 = Z_5 X Z_2 X Z_4 = Z_20 X Z_2

Z_10 X Z_2 X Z_2 = Z_5 X Z_2 X Z_2 X Z_2

Yup. Three isomorphism classes, not seven. Heaven help the poor sap who uses this book to "remember" the facts long ago forgotten.

I admit, truly egregious errors like this are rare. But little slips, typos, errors, and miscalculations abound, all laid out in ugly, ugly typeface.

It's a shame. There are so few resources out there to help students practice for this test. The ETS book is great, but it has no detailed solutions; only the answer key.

Oh, yeah, and the math review that occupies the first half ot this tome? It sucks too.

Pros:
1. It has 6 full-length exams with "explanations" to every question.

Cons:
1. The included "Comprehensive Mathematics Review" which is supposed to cover all major topics, is pretty BAD. It is rarely useful, I didn't like it at all. I recommend much more the review that's included in "Cracking the GRE Math", which is much more detailed and explanatory, with plenty of exercises.
2. As someone has already noted, the exam does not have the same "feeling" as a real ETS test. The questions are generally more difficult, and the distribution of question types are very strange. It seems that they had never seen a real GRE Math test when they did this book.
3. The explanations to every question are very often quite unsatisfactory. The explanations given in "Cracking the GRE Math" are much more helpful.

Summarizing, it could have been a great book, because it has 6 full-length questions, which I think, it is the best way to prepare for this test. However, one notices right away that it has a completely different flavor from the actual GRE Math test.

Knowing this, I still bought it, because I needed more practice tests, but I'm not really sure if it did help me.

The book is divided into two parts of about 300 pages each. The first is a review of undergraduate math, from polynomials through calculus to higher undergrad topics like complex variables, statistics, topology, abstract algebra, etc. The second half is a set of 6 practice tests, which I found to be harder than the actual GRE subject test. (That makes for good reviewing, on the student's part.) After each test is an answer key and an explanation of each answer.

My main concern about this book -- and it's a big one -- is that whoever proofread the first half (the "review") apparently doesn't understand math. Some expressions are wrong; some are nonsense. (This was the 1997 printing.) If you know enough math to get past that sort of hazard, I highly recommend the book.

Under no circumstances should you buy this book. It has major flaws:

1) The material covered does not seem to match what is actually on the test.

2) The mathematics is full of typographical errors; as a result many of the problems are incomprehensible.

3) Some of the solutions are ridiculous, incoherent nonsense.

A much better book is "Cracking the GRE Math Test" by Leduc

This book contains a few hundred pages of math review, six practice exams, and explanations for all the exam answers. Although the content of the exams is close to the actual Math GRE, the "spirit" of the questions is quite different, and the way problems are worked in the explanations is often not the best way to solve problems from the actual GRE. The review section also has some problems--typos, too many elementary topics, and sketchy explanations of complex topics. Still, it makes an okay review, and could help greatly if you're rusty at math.

I bought this book because of the 6 practice exams. However, after trying the first practice exam, I found myself digging out all my college mathematics books. It was getting ridiculous, and I'm glad that several other reviewers agree that the practices exams in this book is harder than the actual exam. I suppose it would be good practice, so I will keep the book; but I will be purchasing Princeton Review's test prep to prepare for this exam.

First of all, the review section in this book is worthless. The real reason that you would buy this book would have to be the 6 practice tests.

Do not attempt to do the first four tests or the last (Test I - IV, VI) since you will almost certainly not be able to complete them. Instead, go through each question in these four tests and if you can't do one then mark the problem, look at the book's solution and learn how they did it. Try doing the marked problems again in a couple of days.

Some of these problems have solutions that are so complex that you know that they will not be on the GRE so just ignore them or try to think of simpler solutions (several of these very difficult problems do have simpler solutions than what the book shows, and this will help prepare you for the hard problems on the GRE).

The second to last test (Tests V) is, in my opinion, representative of the real GRE test. Take this tests like you would a regular practice GRE.

There are typos in the practice tests and some mistakes, but I did not find this to cause much trouble.

There are basically only two books on the GRE Math SUBJECT test, namely, this one ("The Best Test Preparation for the GRE Math Test" by REA) and "Cracking the GRE Math Test" by Princeton Review. When your grad school future is at stake, it never hurts to have "too much" practices. So, any rating of this (or the other) book probably won't help much because you are most likely going to get your hands on both books (and whatever else is available) regardless of the ratings anyway. However, I still think perhaps it is worthwhile to mention that this book has been largely unchanged since its first edition published in 1989. Currently it is in its fourth edition (2002) or what the publisher calls the "Year 2004 Printing". It seems that they have done little besides fixing old errors and removing those problems that are too wrong and too embarassing to be fixed. Even though the newer edition has a study guide and a new score-to-percentile conversion scale, I was still disappointed because I was looking for substantially new problems. One major weakness of this book, like its counterparts on the market, is that it is not realistic enough to adequately prepare the testers. After four editions, it still remains the case here. For that reason, I took one star off.

First, many of the types of questions in the 6 practice exams are pointless to study, since you won't encounter anything remotely resembling them on the real GRE. Second, the explanations of the solutions are rarely satisfactory. Third, the review section is a complete joke and, like the questions in the practice exams, many of the topics it covers are completely worthless with regards to the GRE (e.g. cubic spline interpolation, fourier series). I didn't read the review section very thoroughly (though I did glance over subtitles, so I know that a lot of time-wasting material was included), but what I did look at in some depth was poorly explained.
All of this said, the book isn't entirely useless. If you use it as a companion to a better GRE prep book (cracking the GRE) and have a discerning eye for what will and won't be necessary to study, it does offer some good review questions if you have time to weed through it.

The level of difficulty and depth of the questions in this book is generally much higher than the real exam. While studying questions that are modestly harder than the actual test is often a good way to score high, this book goes well beyond that level, to the point of being almost useless.

The proofreading of this book is remarkably poor. Several problems have incorrect solutions. Such inaccuracies (as well as many typos) leave a reader wondering whether any of the content can be trusted.

The typesetting is also very poor. While this is primarily a cosmetic issue, in some places it makes the content less comprehensible.