<p>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?</p>
<p>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).</p>
<p>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). </p>
<p>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. </p>
<p>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?</p>
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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.</p>
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<p>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. </p>
<p>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.</p>