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I'm planning on taking the math GRE Subject Exam in April (~11 months from today). I want to start preparing now in the hopes of scoring in the 95+ percentile. I have already taken a number of graduate courses and really need to refresh on some of the lower level stuff so here's my plan:

May 14 - Stein & Shakarchi, Complex Analysis [for REU]

Jun 14 - Need to read through papers for REU. I'll probably read another complex analysis text.

Jul 14 - Axler, Linear Algebra Done Right (Ch 1-5)

Aug 14 - Axler, Linear Algebra Done Right (Ch 6-10); Lang, Calculus of Several Variables

Sep 14 - Spivak, Calculus (Ch 9-15)

Oct 14 - Spivak, Calculus (Ch 17-23)

Nov 14 - Munkres, Analysis on Manifolds (Ch 1-3)

Dec 14 - Munkres, Analysis on Manifolds (Ch 4-7); Apostol, Mathematical Analysis; Insel, Linear Algebra

Jan 15 - Stewart, Calculus; UCLA Bootcamp

Feb 15 - Artin, Algebra; Stewart, Calculus [agian]

Mar 15 - Saracino, Algebra; Schaums: Calculus, ODEs, Lin Alg, Complex, Discrete, Prob & Stats

Apl 15 - Princeton Review, Cracking the GRE; Practice Exams; Stewart, Calculus [for the third time]; Fritz, Calculus and Advanced Calculus Demystified.

I have never taken a course in multivariable calculus or multivariable analysis (but I have picked some up in complex analysis and measure theory courses). As I have heard it is very important for the exam, I've put a good bit of emphasis on it.

I have a particularly strong background in number theory and combinatorics. Also, during the semester of the exam, I will be taking a course in Algebra using Lang's Algebra and an intro topology course using Munkres along side an algebraic topology course using Massey's Algebraic Topology. As such, I probably don't need to study as hard for these subjects.

During my preparation, I hope to do every problem in each book with only few exceptions. By the end of this preparation, I hope to know all the topics on the exam like the back of my hand.

  • Does this seem reasonable?
  • What modifications would you make?
  • Am I focusing my time on the appropriate subjects?
  • Given nearly a year, how would you prepare?
YuiTo Cheng
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user149459
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  • You don't really plan on doing every problem in Stewart, do you? – RghtHndSd May 12 '14 at 03:24
  • Stewart's Calculus, unless the 7th edition is very different from the edition I used, is pretty week in the multivariable section. I'm unfamiliar with Spivak, but I wouldn't count on Stewart for a good multivariable foundation. – grantfgates May 12 '14 at 03:32
  • @rghthndsd It sounds terribly boring but everyone I know who has taken the exam says I should. I really want to get into a good grad school and this seems like a good way to give my application a small boost. – user149459 May 12 '14 at 03:40
  • @grantfgates That's whereLang's Calculus of Several Variables and Munkres Multivraible Analysis come in. – user149459 May 12 '14 at 03:41
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    I would suggest you start with a GRE prep book and some practice exams. That will give you a sense of what you need to study and what you don't. For example, for the GRE as I recall it, Munkres's Analysis on Manifolds is a waste of time, because the GRE has no questions on that subject. Furthermore, that much GRE studying would no doubt help your score and give you a "small boost", but all that time would be much more productively spent succeeding in challenging courses or research, which would give you a much larger boost. – Nate Eldredge May 12 '14 at 04:15

1 Answers1

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Preparing for the GRE really is something most math majors don't take as seriously as they should as a lot of top graduate schools are now using it as a filter to cut down on the number of applicants they have to deal with. Also, for students with relatively weak grades,a high Math Subject GRE score can be the difference between thier application being seriously considered and it being laughed at before being thrown in the shredder.

I don't claim to be an expert,but my own experiences with the GRE indicate that a big chunk of the test is "serious calculus"-i.e. epsilon-delta proofs with limits combined with complicated plug and chug computational problems in either geometry or physics. There's also a considerable number of problems on linear algebra, both theory and applications. As far as your general background goes,I'd focus on strengthening my skills in these 2 areas. There are other areas covered, of course-but most students get thrown by the calculus and linear algebra sections because they didn't really master them and the GRE really puts a lot of weight on testing not so much how much calculus the student knows, but how much they've mastered the subject.

Stewart-which sadly I learned calculus from-is a good choice for this prep simply because of the ENORMOUS number and diversity of exercises it has. Of course,you can't rely on it-you'll need much more serious calculus training in mathematics for the test. I'd get Arthur Mattuck's An Introduction To Analysis and Kenneth Ross' Elementary Analysis: The Theory of Calculus to work through to beef up your mastery of single variable calculus. Spivak is a classic,but it may be a bit too difficult given your limited time preparation. For multivariable calculus, Hubbard and Hubbard's Vector Calculus, Linear Algebra amd Differential Forms:A Unified Approach will probably give you more then you need on the subject. For linear algebra, besides Hubbard and Hubbard, you have lots of choices, but my favorite is Charles Curtis' Linear Algebra: An Introductory Approach. There's also plenty of free online resources for mathematics. (I personally know a major website that will attempt to collect all currently available free materials-lecture notes,online texts,etc.-in links for students-but it's not live yet.It should be within a month.)

As for other subjects,I'd stick to the test prep materials. I think trying to relearn an entire undergraduate degree's worth of mathematics purely for this test would be an enormous waste of precious time and energy. You can't make this test your life,you have other priorities. I'd begin talking to graduate students who have been through the test-see what they'd recommend.

Good luck!

Mathemagician1234
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