How should I choose which graduate programs to apply to for the PhD?

Question

This fall I will be an senior mathematics major at a small public liberal arts university. I'm trying to finalize the list of schools to which I will apply (to PhD programs in pure math), but I am finding it somewhat difficult. I know that I am not a candidate for admission at top-tier universities. My school is relatively unknown outside of its state, and the professors who will write my recommendation letters aren't very well-known either (although they do publish somewhat frequently in their respective fields). I have taken two semesters of abstract algebra, one semester of real analysis, and two semesters of topology, and received an A in all. By the time I graduate I'll have taken another semester in real analysis and a course in complex analysis, plus several other applied and discrete math classes. I haven't taken any graduate courses since my school doesn't offer them, but I have completed a research project with one of my professors in the area of math which I hope to study in grad school. My GPA is around 3.85.

I think (and please correct me if I am wrong) that I should focus on applying to "mid-tier" programs, but I find it very difficult to determine which programs are at this level. I know that one student from my school was accepted at a program ranked in the 40's by the U.S. News math grad school rankings.

Essentially, my question is this: Do the U.S. News rankings accurately reflect the selectivity of programs, and if so, is there some point in the rankings at which schools become "mid-tier" or at which I would be competitive for admission?

Answer 1

Yes, the rankings (roughly) reflect the selectivity of the program, as far as I know. Your choice to focus on mid-tier programs makes sense. (I think defining mid-tier as starting in the 40s is plausible, though I suspect you'll get conflicting answers from different people.) However

1. Don't confuse the quality of the program overall with the quality of their specialty that you hope to study. Their specialty program could be much better or worse than the program overall. In math departments (as opposed to, say, some computer science departments), students are typically admitted to the department, rather than to a professor's research group or a specialty area. Taking advantage of this could get you into a specialty program that's rated higher than you "deserve".

2. Don't exclude a school just because it's too highly rated. It's good to apply to a wide range of schools, some "reach" schools that you think it unlikely you'll be admitted to, and some "safety" schools that you would be quite surprised not to be admitted to. All sorts of factors influence how likely it is you'll be admitted to a given school in a given year, many of them completely unknowable to you. For example, maybe a new faculty member will be coming and looking for students (or maybe one will be leaving). Maybe the program has all their TA positions tied up with current students who haven't finished yet, or maybe not. Maybe a dean wants to grow the program, etc. Many of these things you just can't know. Most likely, you won't get into MIT, Harvard, Princeton, or Stanford. But once you get into the 20s, 30s and below, the outlook is less clear.

3. Focus on fit, rather than solely on ranking. Think about where the school is located. If you plan to live there for 5 or 6 years, you don't want to hate the place. This can include proximity to your family or friends, climate, scenery, nightlife, etc. If you know what specialty you want to study, the school should have at least 1, but hopefully 2 or 3 folks that you would potentially like as an adviser.

4. Focus on aspects of your application that you can still change. With a transcript no stronger than yours, I got into a top-25 school. The cool part is that for the specialty I chose, they were top-10. At this point, most of your transcript (and much of your application in total) is fixed. But you didn't mention your GRE scores. (The surprising thing about the GRE is that you can do pretty well if you're just really good at Calculus (through multivariable), Dif. Eq., and Linear Algebra.) I think my subject test was something like 65th percentile. That's not terribly good, but I think it was enough to convince the admissions committee that even though I was coming from a small LAC that no one had heard of, I did know something. The other thing I did, which I highly recommend you try, is get a letter of recommendation from a faculty member at that school (where I was admitted). I wrote code for him for 3 or 4 weeks (about 30 hours/week, I think) during Christmas break of my senior year. In exchange, he wrote a recommendation for me. I'm sure it didn't say that I was a math wunderkind, but whatever it said added just enough to my application to get me in.

Answer 2

Dan C's answer is great, and I just want to echo some points and add a few things to it.

First, I'm not sure why you've decided you're not a candidate for a "top-teir" school. It sounds like you've been successful in your coursework, and you can likely get strong letters of recommendation. If you don't bomb the GRE, you can certainly get into a "highly-ranked" school! I went to a college just like the one you describe, and my friends and I all did fine when it came to grad school admissions -- one of my friends got into a "top ten" department, and we all got accepted by schools in the top twenty or thirty. So don't count yourself out simply because your school is small and relatively unknown. And, most importantly, if you do get into a prestigious program, be sure to base your decision to enroll on more than the US News rankings!

(I've used the quotation marks above because the rankings are all a bit questionable, and one should really consider the strength of a department in your field of interest, like Dan C said.)

Regarding the professors who will be writing your letters of recommendation: They may not be heavyweights in their fields, but chances are they know some people of influence. Take a look at some departments, get a feel for what you'd like to study, and possibly with whom, and then talk to your letter writers. It may happen, when you mention your interest in working with Professor X, that your letter writer was roommates with Professor X in grad school. These little personal connections won't get you admitted, but they will help ensure that your application gets a fair evaluation despite your school's relative obscurity.

Good luck! Aim high.

Answer 3

I'll just note that my credentials weren't so different from yours when I graduated from college (obscure liberal arts college with little track record, etc.) and I got in to Berkeley, Michigan and Northwestern. Of course, I can't actually compare our cases (and this was a decade ago), but I don't think you should hesitate to apply to, say, Wisconsin, or UT Austin or Rutgers (depending on your regional preferences). If you doubt it, you can always contact the graduate coordinator and ask if they think you're a plausible candidate.

As Dan says, a good range is the best approach; apply at least one place you can't quite believe you'll get in, and at least one place where you feel absolutely confident, and a few in between. This stuff is indeed incredibly unpredictable, but there are a lot of slots in reasonable graduate programs, and fewer good candidates than you might think.

Answer 4

I'll only address the question of deciding what "mid-tier" means. There's one coarse classification that could be helpful to you.

There are 48 math departments considered as Group I under the AMS classification (the older one, deprecated as of last year but the most useful one in my opinion). There's obviously a lot of variation within this group, but I think it's safe to assume that the programs at these 48 schools are stronger than the 56 math departments in Group II. (The bottom of Group I is probably not separated from the top of Group II by too much, however, so don't stress too much about the cutoff.) However I have a lot less confidence in the division between the bottom of Group II and the top of Group III; in this region the AMS's case for switching to the new groupings seems quite strong to me.