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I go to a small liberal arts college most people haven't heard of, but I really want to get a PhD in math from a decent (top 20-ish) school. From what I can tell, many serious PhD applicants have a wealth of graduate courses under their belt. My school only offers the standard undergraduate real analysis and abstract algebra sequence, both of which I've completed. Since I ran out of higher-level math classes to take, I've resorted to doing a few reading courses with some of my professors next semester, which will be the semester I'll be applying to graduate school.

I'll be studying algebraic topology, algebraic number theory, and category theory. How will an admissions committee view this?

I also have other things of note in my applications, like a semester abroad in the Math in Moscow program, and two REUs, one of which was at an ivy league school. At the ivy league REU, I was able to secure a rather strong letter of recommendation.

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Admissions committees in math departments know that a "small liberal arts college most people haven't heard of" might not offer the sort of advanced math courses that are available elsewhere. If your REUs and Math in Moscow lead to strong letters of recommendation, you should be OK. I'd suggest that you also get a letter from one (or maybe more) of the professors who are supervising your reading courses. Even if (s)he has to write before the reading course ends, it would be good for the admissions committee to have some idea of the level of the course (e.g., what book(s) are you reading) and how well you're doing.

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