Mathematics GRE Materials
Back when I was a mathematics graduate student at the University of Chicago, I helped out with the REU program in the summer. During this time, I was asked to help run sessions to prepare the undergraduate students for the GRE Mathematics subject test. I created a set of materials, along with Jon Dewitt, Nat Mayer, and Liam Mazurowski. It was generally agreed that I put in the most effort, so I was left in control of the materials.
I will make a couple of remarks here.
- These materials were created for undergraduate students at the University of Chicago REU. Thus, there is a base assumption that the students are advanced, with a strong background.
- Similarly, the materials are much more difficult than the average problem on the exam. Some of the more difficult problems may be more difficult than any problem that appears on the exam. The intent is to help students get top scores.
- The problems were created to approximately match the distribution of problems that appear on the actual exam (at least at the time that they were created). However, they were created by multiple different people, and each person had their own biases and obsessions. Thus the problems are necessarily skewed in weird ways.
- Some or many of the problems were created to emphasize particular lacks that my fellow graduate students and I believed might have existed in the undergraduate students at the University of Chicago. Although I would have to carefully review the materials to get a full list, one example is that such students were not trained in multiple choice math exams. Thus some of the created problems were not meant to be solved explicitly at all, with some extreme problems possibly intending students to guess without actually solving the problem.
- There are typos and/or small mistakes in the problems that I have found. I am in the process of improving and expanding the materials, which would then address these issues.
- There are short answers at the end of the below document. These are made to be extremely short: The goal was a single line. They were more there to remind the person talking about the problem how to solve it, rather than necessarily informing a student. If you have a question on how to solve it, you may contact me. Email may make the most sense for this: michael@neaton.org
- The problems are separated into six sets, since the sessions that were held spanned six weeks. The six sets each have 22 problems, which is a third of the length of the exam.
- There is an additional extra set. These were additional problems that were written, but were not included for various reasons (too difficult, too obscure, too stupid, who knows). However, either the problem was interesting enough that it was sad to remove it or the person who wrote it was attached to it for some reason, and thus we created an extra document that had these few problems. It only consists of 9 problems.
When I pointed a fellow mathematician to this new site, the only complaint was that I did not have the original advice document we wrote back then. Thus, I have retrieved this as well. I mostly stand by this document (except that it is old). There are three major notes:
- The relevant website where materials are hosted is, of course, this one, not what is referenced in the document.
- The relevant email is mine, michael@neaton.org.
- Gilad Pagi has significantly improved his materials since this was written. In fact, he was in the process of improving them when it was written, so this document's opinion was out-of-date in this regard basically when it was first published.
I should really re-write the document with these couple of corrections, so that there is no confusion.
The original version of these documents can be found here:
As I stated above, I am in the process of improving and expanding these materials. As this happens, the above documents and links may move around.
Links to other materials
The above advice document reference other study materials. Here are some links.
Officially released tests
ETS occasionally officially releases an exam in order to aid students who are studying. I must make it clear that these documents are not in any way owned by me. I asked my lawyer† if I could officially host these documents on a site that was arguably advertisement for paid tutoring services, and I was told that I should just make it absolutely clear that these documents are not mine, they are owned by ETS, and that ETS made them publicly available. Also, if at any time ETS requests me to take these documents down, I must comply.
Other materials
Other people have also prepared materials. Note this list was complied in 2018, so it is missing modern things.
- Charles Rambo has created at least one test (availble for free here with answers here, and for sale with full solutions on Amazon). He also has a book containing three officially released tests, and solutions to GR1768.
- The UCLA Math GRE bootcamp has a lot of materials. I believe they were originally hosted by Charlie Marshak, but now files seem to be hosted by Christian Parkinson and Ian Coley.
- UCSB also has some prepared materials. These were once hosted on Padraic Bartlett's site. I did not find a current host in a very brief search, so I will temporarily host these materials until either I find a proper site or one is pointed out to me. The materials are as follows:
- Gilad Pagi has a course, a couple tests, and (amusingly) a question-of-the-day. There are two practice tests available online. You may also purchase paper copies. He has a couple other handouts, including a six week study schedule. The course consists of eight modules. I initially had a very negative outlook on these materials; this was not really due to the quality of the materials but more the apparent consumerism. Since then Gilad Pagi has made plenty of improvements; I have not had a chance to look them over again, at no fault of Gilad Pagi (who even offered to let me see the materials for free so I could provide a proper evaluation). I hope to come back to review them properly.
- Princeton Review's Cracking the GRE Mathematics Subject Test (available on Amazon) is a well-known source. It is reasonably solid, until the end, but is not free.
- This is REA's (Research and Education Association) book, which was released in 1989. Entitled The Best Test Preparation for the GRE Mathematics (ISBN 0878916377). Again, not free, and also old.
- Morris Bramson's Mathematics Subject Test/Advanced (available on Amazon), containing five full tests mostly limited to calculus. Note this is not free, and the oldest (1983), so less relevant. It would still be good practice for calculus.
If you know of additional things to include in the above list, or updated links, feel free to email me at michael@neaton.org.
Mathematics GRE Materials