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

O. P. Agrawal (Author), T. Elsner (Author), GMI Engineering (Author), J. Robertson (Author), J. T. Wilson (Author)

Book Description

Publication Date: March 30, 1989 | ISBN-10: 0878916377 | ISBN-13: 978-0878916375

This test preparation book includes six full-length exams with detailed explanations based on official exams released by the administrator of the GRE in Mathematics. Knowledge of algebra, calculus, and introductory real variable theory is tested. Includes a comprehensive review of mathematics topics found on the exam. For mathematics students bound for graduate school.

Editorial Reviews

Excerpt. © Reprinted by permission. All rights reserved.

ABOUT THIS BOOK
This book provides an accurate and complete representation of the GRE Mathematics Subject Test. Inside you'll find six full-length REA practice tests based on the format of the most recently administered GRE test. Like the GRE test itself, each of our model tests lasts two hours and 50 minutes. Each one includes every type of question that you can expect to encounter on the actual exam. We also give you an answer key complete with detailed explanations that spell out how the correct answers are arrived at. By completing all six practice exams and studying the explanations that follow, you can discover your strengths and weaknesses and thereby become well prepared for the actual exam.

To help you brush up on the subject matter, the book also features 281 pages of topical reviews, summarizing the essentials of the various topics covered on the GRE Mathematics Test. Our reviews are designed to work as an at-a-glance overview of the many topics that the test covers--each of which could fill a book of its own. Should you require more detail, a textbook whose contents parallel the topical coverage of the GRE should be consulted.

ABOUT THE TEST
The GRE Mathematics Test is offered three times a year by Educational Testing Service, under the direction of the Graduate Record Examinations Board. Applicants for graduate school submit GRE test results together with other undergraduate records as part of a highly competitive admission process.

The questions on the test are composed by a committee of specialists who are selected from various undergraduate and graduate faculties across the U.S. This test consists of 66 multiple-choice questions. Some questions are grouped together under a particular diagram and/or graph. Emphasis is placed on these areas:

I. Calculus (50%)
Material learned in the usual sequence of elementary calculus courses--differential and integral calculus of one and of several variables--includes calculus-based applications and connections with coordinate geometry, trigonometry, differential equations, and other branches of mathematics.
II. Algebra (25%)
A. Elementary algebra: basic algebraic techniques and manipulations acquired in high school and used throughout mathematics
B. Linear algebra: matrix algebra, systems of linear equations, vector spaces, linear transformations, characteristic polynomials, eigenvalues and eigenvectors
C. Abstract algebra and number theory: elementary topics from group theory; the theory of rings and modules, field theory, and number theory

III. Additional Topics (25%)
A. Introductory real analysis: sequences and series of numbers and functions, continuity, differentiability and intergrability, elementary topology of r and rn
B. Discrete mathematics: logic, set theory, combinatorics, graph theory, and algorithms
C. Other topics: general topology, geometry, complex variables, probability and statistics, and numerical analysis

This list is by no means all-embracing. (You may, for example, face questions asking you to find the correct mathematical model to represent a "real-life" situation.) The test requires more than simple recall: It gauges both your understanding of fundamental concepts and your ability to apply these concepts in specific situations. Because of the wide gamut of coursework in undergraduate mathematics, not all the material that you may have studied will be presented on the exam. Rather, the questions are based on the courses of study most commonly offered in an undergraduate mathematics curriculum.

Product Details

• Paperback: 640 pages
• Publisher: Research & Education Association (March 30, 1989)
• Language: English
• ISBN-10: 0878916377
• ISBN-13: 978-0878916375
• Product Dimensions: 10 x 6.7 x 1.8 inches
• Shipping Weight: 1.8 pounds
• Average Customer Review: 2.6 out of 5 stars  See all reviews (20 customer reviews)
• Amazon Best Sellers Rank: #186,885 in Books (See Top 100 in Books)
  • #83 in Books > Education & Reference > Education > Test Guides - Graduate & Professional > GRE

Customer Reviews

Most Helpful Customer Reviews

48 of 48 people found the following review helpful:

1.0 out of 5 stars For the most part, a complete waste of time., September 22, 2005

By 

Sean Raleigh (Sandy, UT) - See all my reviews
(REAL NAME)   

This review is from: GRE Mathematics (REA) - The Best Test Prep for the GRE (GRE Test Preparation) (Paperback)

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.

33 of 35 people found the following review helpful:

4.0 out of 5 stars BIG book that may help you prepare your GRE Math test., March 20, 2002

By 

F. Cueto "fcueto" (Houston, TX United States) - See all my reviews
(REAL NAME)   

Amazon Verified Purchase

This review is from: GRE Mathematics (REA) - The Best Test Prep for the GRE (GRE Test Preparation) (Paperback)

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.

21 of 22 people found the following review helpful:

4.0 out of 5 stars An excellent math review, with a serious and annoying flaw., April 15, 1999

By A Customer

This review is from: GRE Mathematics (REA) - The Best Test Prep for the GRE (GRE Test Preparation) (Paperback)

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.