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I just graduated from a regional university in the US with a minor in mathematics. There is a masters program overseas, for economics, that I want to attend but they require applicants to take the Math subject GRE. I have never had a formal introduction to abstract algebra or to topology. I have some time to take the GRE next year, I understand it is only administered three times a year.

My question is, would the following be a good selection of textbooks to self-study intensively for say, six months?

  • Apostol Volume 1,2

  • Dummit Foote Abstract Algebra

  • Munkres Topology, just up to chapter 3

  • Rudin Analysis

I did take an Advanced Calculus course, but dropped it. I really wanted an A in the course and was headed for a B-.

I have found some lecture notes online, plus videos such as Harvard's algebra course online. Also, I planned on asking questions here if I got stumped or confused in the more abstract material.

Would going through these books be sufficient? It seems like the entire undergrad in math, except for things like number theory...should I even care about that?

Thank you.

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    $\begingroup$ Looks like several people have good advice. I'd particularly recommend you don't spend much time on Rudin. The analysis material is all about being able to apply the mean value theorem etc, at a somewhat lower level. $\endgroup$ – Kevin Carlson Aug 13 '12 at 12:26
  • $\begingroup$ Edgar, is the topology part of the GRE subject really only up to Chapter 3 in Munkres Topology? I read it's up to Chapter 6. Asked here and here $\endgroup$ – BCLC Sep 14 '18 at 8:39
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The Math Subject GRE is 50% Calc 1, 2, 3, and Differential Equations. High school algebra and linear algebra are another 15-20% probably. If you do well on just those questions, you will be in the 70th or 80th percentile. Note, this is compared to students wanting to study math at graduate school, so this is very good. Learning several entirely new subject will take months, probably more time than you have, and will end up adding just a few points to your score. Mastering the subjects you have already had will help your score much more.

Here is a link to a previous test, including the breakdown of subjects.

http://www.ets.org/Media/Tests/GRE/pdf/Math.pdf

Note 25% is "Additional Topics". You'd need to learn several semester courses worth of material to get this stuff. Don't worry about that.

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    $\begingroup$ Here are 3 additional, previously published exams: math.ucsb.edu/mathclub/GRE. Also check the advice on this page: physicsgre.com/mathematics-gre.shtml $\endgroup$ – dls Dec 13 '11 at 17:47
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    $\begingroup$ @Graphth I am planning to take GRE subject test in September. I have not studied Real Analysis, Field theory, group theory, ring theory and topology. I would have to self study them. Would I be better of doing the calculus and other areas that I know of or should I start working on the subjects that I haven't previously studied? $\endgroup$ – sam_rox Mar 14 '16 at 4:21
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    $\begingroup$ @sam_rox "Learning several entirely new subjects will take months, probably more time than you have, and will end up adding just a few points to your score. Mastering the subjects you have already had will help your score much more." This is my opinion. $\endgroup$ – Graphth Mar 16 '16 at 17:13
  • $\begingroup$ Graphth and @sam_rox, what's the coverage for Munkres Topology? Asked here and here. I read that it's up to Chapter 6. Just wanna make sure. Others say Chapter 3. $\endgroup$ – BCLC Sep 14 '18 at 8:41
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I took it last year. Make sure you are an expert at calculus. The higher level questions are very easy. For example one question on mine was which of these sets is not a group under multiplication, the one that failed didn't have inverses... I tried to study a little of everything and wished I just studied tons of calculus and linear algebra.

Good luck. Oh also, when you take the test keep in mind that you do not need to answer every question to get a very good score. Check out past scores and the rules for scoring before you take the test. So you don't feel overwhelmed during it.

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  • $\begingroup$ john w., what's the coverage for Munkres Topology? Asked here and here. I read that it's up to Chapter 6. Just wanna make sure. Others say Chapter 3. $\endgroup$ – BCLC Sep 14 '18 at 8:40

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