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.

I think the book is good, hoever, I do not finish reading it, that's why I did not rate it "5".

By the way, I think your worker in China do not take his job seriously. When I was not at home, he simply put the book on the floor leaning the door. It was easily picked by others, and I could have no chance to get it back.

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.

The first half of this book gives as so called "review", but it's not review, it's a joke. There are lots of problems to work on, but they are not representative of the problems that will be on the GRE subject test in mathematics. There are far too many errors to be considered even "fairly" written. If I was studying for the GRE test, I would not study this text. There are many other much more valuable sources out there.

I just completed test #3 of 6 that are in the book and once again I feel like I don't know a thing about math after studying for the past 2 and a half months for an hour or two a day. There are questions that are asked on the test based on material that you usually don't see until grad school.

A total waste of time and negative emotion.