Finding the Right Math Graduate School for GM

[Geomancer]

Hi all.
I posted this inquiry on sci.math, but I only got one response. I'm hoping the good folks here can be a bit more helpful. I apologize in advance for the length of this post; I saw no other way of explaining things.

I'm having some trouble thinning the herd of graduate schools, and wonder if I can avail myself of the experience present here. I have no preference as to geography, though I'm a US citizen and English is my only fluent language. My issues come in two forms: where can I get in,
and where can I do interesting math. To wit:

Where can I get in:
My background is somewhat nontraditional, thus limiting the choices. I briefly attended a high ranking school but had to leave (for reasons that shouldn't be relevant). I completed my BS at a local state university (not well known for math). I have also taken a few graduate courses at another local state school (also a small department). All this has taken many years. My grades have been good, though not uniformly excellent. In spite of this, I have confidence in my abilities, and in my grasp of the undergraduate curriculum. I can do the problems in the UCB book at a reasonable rate. I'm hoping for GRE scores in the mid 90'th percentile, (judging by practice tests). Unfortunately, when I sat for he exam this month the test center shorted me 10 minutes. I'm in contact with ETS to resolve this, but I don't expect to have scores for another few months. Recommendations are likely to be good but not stellar.

Where can I do interesting math:
My interests are broad, so I'm looking for a school strong in a variety of areas. As far as core competency goes, my approach to problems has always had a somewhat "geometric" flavor to it. The first thing I tend to do to an object is try to apply an algebraic structure to it. When I do topology, I tend to use set based arguments rather than ones based on limit points (in spaces where both approaches work). The *problems* I've worked on, though, usually have a combinatorial nature,
so I want to be somewhere that recognizes that first class mathematics can occur in a discrete setting.


Does anyone have advice?
Thanks,
GM.

 

[kodiakghost]

It really depends on your life focus as to what would be best. What are the most important things to you? Do you want career recognition? High salary? More mental stimulation? Or is math something that for you to do that you find sort of interesting, but just one interest among many?

If you enjoy putting most or all of your time into your studies, then of course go for a more reputable school. There are plenty up north and only a couple in the south. If you have any sort of geographic preference, that can help. I know you said you have none, but I don't believe it =)

One good thing to do is go to various math department websites and see if they have pictures of their faculty and graduate students. If most of the people in the pictures are smiling, that is a good sign. If they all look doleful and defeated, then beware.

If math is just a casual interest of yours and you want time for lots of other things: rock climbing, cycling, writing, rec sports, music, etc, then you might consider a less reputable and more laid back graduate school.

Math grad programs take up a lot of time and the more competitive ones will take even more time. Making a wise decision here will involve figuring out what's most important to you in life and then planning accordingly.

 

[Moonbear]

One good thing to do is go to various math department websites and see if they have pictures of their faculty and graduate students. If most of the people in the pictures are smiling, that is a good sign. If they all look doleful and defeated, then beware.

I've never heard advice like that before. I'm not sure it really works that way. Usually the person taking photos for websites tells you to smile for the picture, unless they're just taking people's ID photos and sticking them up for their websites, in which case, I still don't think that means anything other than it's a bad ID photo.

I don't know anything about math graduate programs, so can't really help much. Though, compared to what I've seen in other posts here, it seems the OP has a good handle on how s/he likes to approach problems and the types of problems s/he likes to solve. That by itself is a plus for searching for grad schools, because you actually have a more mature outlook on what type of research you want to do, so can do a better job finding the right fit.

 

[Geomancer]

Thanks for the replies,

One of the things I worry about is ending up in a place where I get practically no outside mental stimulation. This was the case, for example, at my second undergrad institution, and I tend to perform badly under such conditions. Simultaneously, the suggestion to consider a more laid back environment is a good one, since I lack the single minded determination needed to be a great mathematician (i.e., I do other things as well). Do there exist schools with a decent talent pool yet relaxed culture? I have no need to be surrounded by mini-Gausses (indeed, it's nice to be near the front of the pack), but I need people I can talk to.

All this leads back to the question: how does one estimate competitiveness? Data are available, for instance, for undergrad selectivity, but these don't seem to always correlate with my other perceptions. Obviously, the most prestigious schools will be viciously competitive, but what about beyond the "top 5" (where I don't have a chance anyway)?

kodiakghost: I was only partly lying about geography. It is true that I'd go almost anywhere for the right program. All things being equal, though, the closer I am to the equator, the happier I get. Which is a bit disconcerting, seeing as US mathematicians have a tendency to congregate at the Canadian border. Perhaps I need to find a new profession, join a mariachi band? There's always Australia. I don't know anything about their university system, but I hear they're looking for a new crocodile hunter.

Regards,
GM