Graduate School Choices, etc.

Forum for the GRE subject test in mathematics.
asindex
Posts: 4
Joined: Mon May 21, 2012 8:16 pm

Graduate School Choices, etc.

Postby asindex » Sat May 26, 2012 7:58 pm

I am an undergraduate math major planning to apply for graduate programs in pure math this fall. I've been getting much help from reading many of the posts on this forum, and this time I was hoping to get some direct advice on graduate school selection. (...)
Last edited by asindex on Wed Jun 27, 2012 9:35 pm, edited 1 time in total.

kuz
Posts: 42
Joined: Wed Jan 18, 2012 3:32 am

Re: Graduate School Choices, etc.

Postby kuz » Sun May 27, 2012 1:25 am

A couple of things to consider:
Is your university well-known? In particular, are your letter of recommendation writers well-known in their fields? For top-notch universities, it's easier for them to assess the strength of the application if they know that your GPA and research experience actually mean something.
Are you from a non-English speaking country? Then your TOEFL score becomes very important.
How do your research interests mesh with the universities you're applying for? The elite universities want students who fit in well with the research groups at that university. Choose universities where you recognise names or research interests, and then mention these in detail in your statement of purpose when you apply. They want to know that you're applying to their university not just because of the prestige of the university, but because you can contribute research there that fits in well with the interests of the faculty. Of course, the more you can back up your interest with previous research experience the better, so if you're changing areas then you're going to have to do some work in convincing them that you will be a good student in the new area.
As for contacting the faculties, I'm not sure that's particularly necessary; unless you have something interesting to say to them research-wise, they're probably not going to be able to really vouch for you to the advisory committee.

All in all, you sound like you ought to be aiming reasonably high, but like I said, make sure you only apply for universities where you'd be a good fit (I applied for Stanford and Princeton because they're great at number theory, but not Harvard, MIT, or Chicago). Also, make sure you have a couple of back-up universities, where the university isn't quite as prestigious but where there's one or two professors who you think would be great PhD supervisors (my back-ups were Illinois-Urbana Champaign and Michigan, and both had some great faculty in number theory).

asindex
Posts: 4
Joined: Mon May 21, 2012 8:16 pm

Re: Graduate School Choices, etc.

Postby asindex » Sun May 27, 2012 3:57 pm

Thanks for the reply. I am from an English-speaking country, so fortunately I don't have to take TOEFL. My school is respectable, though not particularly renowned outside of the country. Professors who will be writing my reference letters are mostly well-known internationally in their fields. To be honest, I think I lack the confidence to apply strictly to programs which suit my research interest, but thanks otherwise for the sound advice. One of the research projects this summer will be related to my area, so I hope that will help in my application.

Anyway, it's comforting to hear that my aim is at least reasonably high, especially if it comes from a Princeton admittee. If you don't mind, could you tell me a little about your experience with reference letters? Again, I would be grateful for any kind of advice, and any further comments on my status.

kuz
Posts: 42
Joined: Wed Jan 18, 2012 3:32 am

Re: Graduate School Choices, etc.

Postby kuz » Tue May 29, 2012 9:48 am

I'm not sure what I can really add about my recommendation letters. One was from my honours supervisor, the second from my masters supervisor, and the third from my supervisor for a summer research project. I'm guessing they were very positive letters, but to be honest there's not much really more to say; I told them I was interested in applying for universities to study number theory, and so I guessed they discussed how qualified I was to be a good research student in that field. Perhaps some other applicants on here can say more about letters of recommendation. Otherwise there's probably more references for that kinda thing on thegradcafe forums.

asindex
Posts: 4
Joined: Mon May 21, 2012 8:16 pm

Re: Graduate School Choices, etc.

Postby asindex » Tue May 29, 2012 9:56 pm

I see! Thanks a lot for the input. Once again, I really appreciate your advice regarding research interests in the previous post. If there are any others who could judge the reasonableness of my list in a different light, I would be very grateful. I would especially be interested in getting advice from people who, like kuz, had application profiles far exceeding mine; I noticed several of them on this forum, though I don't know how many are active anymore.

gromov
Posts: 38
Joined: Sun Feb 13, 2011 6:49 pm

Re: Graduate School Choices, etc.

Postby gromov » Thu May 31, 2012 12:55 am

Minor comment: I seem to recall kuz was interested in analytic number theory. Some of the other strong schools (Harvard in particular) most definitely would be of interest to someone interested in arithmetic.

The key thing is whether your school has a good history sending people to strong programs. Sometimes, a program may or may not have very strong research faculty, but will be a known undergraduate institution and have a history of feeding successful students to very strong programs.

Some people say to ask reference writers if they are comfortable writing a strong reference. This isn't the ideal question, in my opinion. Strong for what program? And what is "strong" defined as?

Better is to ask them what sorts of schools you should be focusing on. If a professor seems to express concern as to your list, then perhaps either get a new letter writer or realize that the professor is right (one or the other) that you aren't likely getting into that school. This is especially helpful if you ask a professor with experience writing letters and/or conducting admissions in some significant way. I'd say to err slightly on the side of caution even after hearing what your professors have to say, but mostly if their assessment of your profile and your assessment seem to match, it's probably a safe bet to keep your list as is.

Usually, I think letter writers try to describe what the student's strong points are, and if there are any glaring weaknesses, perhaps those too. A useful letter might compare the student favorably to others. It might answer questions like ... Has the student demonstrated a knack for certain kinds of mathematical insight? Has the student done an outstanding project the professor can describe in some detail? What convinces them that the student will be able to conduct his/her own independent research with some coaxing and training?

asindex
Posts: 4
Joined: Mon May 21, 2012 8:16 pm

Re: Graduate School Choices, etc.

Postby asindex » Sun Jun 03, 2012 11:26 pm

gromov wrote:Some of the other strong schools (Harvard in particular) most definitely would be of interest to someone interested in arithmetic.

I see! Thanks for your point, and I will keep this in mind. At the moment, this brings me to wonder if I actually have sufficient knowledge in number theory to compete for challenging programs. Would there perhaps be some number-theoretic readers willing to give an assessment of my (rather scattered) background in the area? (...) Number theory is not my primary area of interest at the moment, but I would certainly be interested in studying it, provided that I am capable. Again, I would be grateful for any comments on my current background; also, in case anyone would be willing to share their knowledge, I would be very eager to hear about how the various graduate schools compare in number theory.
Last edited by asindex on Wed Jun 27, 2012 9:36 pm, edited 1 time in total.

kuz
Posts: 42
Joined: Wed Jan 18, 2012 3:32 am

Re: Graduate School Choices, etc.

Postby kuz » Mon Jun 04, 2012 5:42 am

I think your number theory background should be fine entering a decent program. It's hard to say though because programs have different expectations: Princeton's degree is only four years with a general exam after a year, so they expect you to have a very firm background (or be quick getting up to scratch) and that you're ready to start researching straight away. Some others are five year degrees with a general exam after two years, so they don't expect you to be quite as ready yet.

gromov
Posts: 38
Joined: Sun Feb 13, 2011 6:49 pm

Re: Graduate School Choices, etc.

Postby gromov » Sat Jun 09, 2012 3:47 am

That background does not seem to be expressly lacking, even for the most competitive programs for number theory. I think entering a program like Princeton (although you should ask someone who's actually doing that, since that option is there) for number theory means, beyond having that very solid foundation, having strong letters saying you'll fare well in that sort of program. Meaning, you'll benefit from a program that puts you through research almost immediately. Not everyone (not even some of the strongest students) needs to find that the right style for them at the time.

That is, I don't necessarily think background will be the deciding factor in what programs you get into at this point. It will be your luck and your letters mainly (particularly at a school like Princeton which rejects many of the best but ultimately has to take a few very qualified people).




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