Post
by **benjiemoe** » Wed May 14, 2008 10:45 am

1) I didn't major in mathematics as an undergrad, and was not sufficiently familiar with some of the material on the exam. I retook the exam in april of my first year in graduate school, and improved significantly.

2) As Undergrad: ~ 50th-75th percentile

As Grad: ~ 75+

(If you really want to know the scores, send me a message).

3) From most valuable to least valuable, I recommend the following resources:

Real practice GRE tests:

I could find 3 real tests somewhere or another. By far the most important (and most representative) was the one available for free online. The other two were given before the test was rescaled, and I feel the problems are not nearly as similar to the current test. Nonetheless, all three tests are very useful. One nice thing about these is that ETS includes real data about how students scored on each question, i.e. what percentage of students answered each problem successfully.

Cracking the GRE (Princeton Review):

This book has a very good review of the material overall, although it is notably lacking in some of the more special topics. The GRE however is 50% calculus and this book is excellent for reviewing that. The practice test comes with complete solutions and is very well done. This book is most useful for someone who wants to score at least average, but not sufficient for one who wants to score very high.

All the Mathematics You Missed (But need to know for graduate school), by Thomas Garrity:

This book fills in where princeton review lacks. It has a brief review of a HUGE number of topics and includes references for those who want to go further. A warning however, this book contains many topics that are not at all on the GRE and I advise the reader to carefully examine the syllabus. (This book is also very useful in graduate school for quick reminders).

REA book:

Review is not very useful, but there are six practice tests with complete solutions. The tests are too hard, but it's always helpful to work problems. Also the book has a bunch of errors

Advanced Mathematics Test by Morris Bramson (ARCO):

This book is out of print, but really fun. It contains a whole bunch of problems and solutions that were clearly intended for an older test format (some of the problems have 10 possible choices). These problems are really good for reviewing some of the basic stuff and contain the exact tricks the actual test is likely to have. (really hard to find. try buying a used copy somewhere or taking it out of a library).

4) Despite the rave reviews I've given of the books above, there is no substitute for taking the classes that cover the necessary undergraduate material. This is for a number of reasons: Firstly, you need to know the stuff; the gre tests only a fraction of what you need to know for grad school and certainly you should be able to write proofs in a subject like topology, which is of course absent from the test. Another reason is that taking shortcuts with studying will usually lead to disappointment. There were a whole bunch of subjects I didn't know well when taking the exam at first, and thought it sufficient to simply know what the review books cover, but failed to answer many of the questions on the actual test. So take the classes, and review your textbooks until you are thoroughly convinced you know stuff. Then use the review books simply to brush up and test your proficiency.

Finally, the test is 170 minutes long and there are 66 questions. This means that you need to work pretty fast to finish all the questions (and finish you should). This means you should focus when studying on solving problems quickly, and learning to move on if a particular problem is taking too long (I distinctly recall wasting a HUGE amount of time on a couple of problems). If you know your stuff well at least 50% of the problems require simply knowing simple things (e.g. rank+nullity theorem) and can be answered in a matter of seconds. The rest of the time can be used to solve the more tricky problems and review your answers.