snickers412

Hey,

I'm thinking about applying for a (pure) math phd program sometime in the next year or so. I was wondering how competitive the "top" programs are, generally speaking. I know that acceptance rates are typically low, but is anyone familiar with the level of competition for admission into these programs?

I've taken a decent set of classes as an undergrad -- the required calculus; set theory; linear algebra; abstract algebra; analysis I (the basic stuff) and II (measure theory, Lebesgue integration, etc); complex analysis; Fourier analysis; probability; and number theory (elementary and some algebraic).

I'll also be taking topology and ODEs in the Fall (strange that I haven't done the latter yet...), along with a year-long research project in analytic number theory. And then probably a more advanced linear/abstract algebra class in the spring. My grades in the above have all been A's, though I may end up with a B in probability (haven't found out yet). (I also spent a semester abroad at one of the top universities in the world for math, though I don't know if that helps at all).

So I have a good GPA and I'll be doing a research project with a somewhat-well-known professor. I'm assuming his recommendation and the others I get will be enthusiastic.

So if I score well on the GREs and keep up my grades in the fall, do you think I would be in competition at a school like NYU, Penn, Rutgers, or Columbia (given that they attract the smartest mathematics students in the world, though maybe not as much as Princeton/Harvard/MIT/Berkeley/etc)? If so, how many universities should I apply to to feel safe about getting into at least one program?

b@r!um

I am not familiar with NYU and Rutgers.

Penn and Columbia seem to admit different kinds of students. When I was an undergraduate at Penn, many of their graduate student were the proverbial "big fish in a small pond." Many graduated from liberal arts colleges, had exhausted the curriculum there and did extensive one-on-one work with their professors as an undergraduate.

Columbia, in contrast, seemed to admit students from larger universities who'd already received solid graduate-level training as an undergraduate. I think I still have the invitation to Columbia's Open House for admitted students. The email was addressed to students from: Northwestern, Stanford, Harvard, MIT, Princeton, Yale, Stanford, Stony Brook, Michigan, Waterloo, Florida State, Chicago, Yale, MIT.

Once the basic eligibility criteria (in terms of coursework, GPA, test scores) are met, graduate application outcomes seem to hinge crucially on a student's letters of recommendations. There are two considerations:
- How positive they are. Are you the most talented and hardworking student your professors have met in their career? A solid student but nothing exceptional? Struggling to keep up with your classmates?
- How credible they are. If your professor has a reputation for writing very inflated letters of recommendation, their letter won't be given much weight regardless of how positive it is. You'll have a huge advantage if the professors evaluating your application know and trust your references.

b@r!um

To add to my previous post: do discuss your application strategy with your professors. They know you and have probably guided other students with similar backgrounds through the application process. They'll be in a much better position to give you advice than anyone on this forum.

vienneselights

Lol barium I thought you went to bryn mawr for some reason

b@r!um

I graduated from Bryn Mawr, but I was also an undergraduate at Penn for 5 semesters. Took most of my math classes at Penn.

mathboy98

One good approach as far as I can tell is asking one of the above credible recommendation writers to assess one's list of programs, and then apply to around 3 programs that are definitely less competitive than the list of programs they say you have a very good shot at.

This could for a candidate who was assessed to have a very good shot at the most competitive schools mean applying only to programs in the top 25, or for another candidate, applying to mostly top 25 programs and a few others they'd be very happy at.

Sometimes, size can be an influencing factor. A small and quite competitive program can reject almost any applicant who is anywhere near mortal, from what I have seen.

The honest answer is these programs reject in large numbers students with very solid numerical credentials, hence the emphasis on a solid letter from a reputed source, as well as the emphasis on different features of the application - after all, even though it is very hard to get a very good letter of recommendation from a professor at a top school, it's hardly the case that having such a letter is a guarantee into some of the most competitive schools, whose only successful admits all probably have that credential.