General Advice

The GRE math subject test examines a very specialized subset of an undergraduate mathematics curriculum in a very special way. Knowing this will allow you to effectively study for the exam.

For a detailed look at test content, see the test material section. In a nutshell, though: The exam primarily focuses upon high school material (polynomials, trig functions,...), calculus, and linear algebra. How does this affect your study plan? One consequence is as follows:

• You should take the exam as early as possible.

If you are a math, engineering, or hard science major, it is likely that you took calculus and linear algebra during your freshman or sophomore years. If you take the exam during your senior fall, then, it is likely that it's been a year or two since you took a course on the relevant material. The strategy here is similar to that for the SAT subject tests: If you take a chemistry course during your sophomore year (and do not plan to take another chemistry class while in high school), then the best time to take the subject test is during your sophomore year; waiting until your senior year will only increase your chances of forgetting important material.

Another reason for taking the exam early, of course, is that you will have the chance to retake the test if you are dissatisfied with your score.


I think that the most useful piece of advice to keep in mind while studying for the math subject test is the following:

• Do not brush off the nuts and bolts of actually solving problems to completion.

In my experience, it is all to easy to convince yourself that you remember something better than you actually do. When asked to integrate 1/(1+x^4) over the real line, I might vaguely remember that a nice way is to use a contour integral and then move on, convinced that I could work out the details if necessary. But this is a bad strategy on my part. On the exam, time is everything. If you are a math, engineering, or hard science major then sure, you could probably work out any problem on the test given enough time; but at 170 minutes for 66 questions, you must average around 2 minutes and 35 seconds on each problem. Would it take me more than that amount of time to remember how contour integrals work, to find the right contour, to count up the residues, and to add them together? Almost certainly. It is important to know the material cold so that you do not waste valuable time on the test; it is not enough to be able to work out the answer, given five minutes or so. 


My final piece of general advice is:

• Actually study for this exam.

I took the test in the Fall of 2010, and found it to be much harder than the previously administered tests. For comparison: When I practiced by taking the most recent past exam (the one on the official ETS website), I finished the test with about an hour to spare and only missed a couple of questions. But when I took the test this fall, I wasn't even able to make it to the end of the exam booklet. The discrepancy between the perceived difficulty of the two exams may be a personal failing of mine; however, I've talked with a number of people who also thought the 2010 test was much more difficult than earlier ones, and this sentiment also seems to be supported by discussion on the MathematicsGRE forum.

Perhaps the Fall 2010 test was an anomaly; perhaps I (and others) mistakenly perceived it as being more difficult. In that case, at least judging by previous exams (as listed in the web resources section), you may not need to study for this test too much. However, I think that it is better to be safe, especially if you only have one chance to take the exam (i.e. you're preparing for the second administration in the fall before applying to graduate school). So I recommend two things: First, keep tabs on what recent test takers have thought about the exam (so that you can get a rough idea of its difficulty in recent administrations). You can find this sort of information on the MathematicsGRE forum, for example. Second, don't brush off studying for this test. If you paid attention during your undergraduate classes, it shouldn't take you more than a month of concentrated study to regain the requisite familiarity with elementary calculus and linear algebra (along with a few other items; see the test material section). Studying will provide you with a valuable form of insurance, at a relatively small cost. (After all, if your Ph.D. program has an entrance/preliminary exam, you will need to study this material anyway.)