Assessing the Strength of my Graduate School Application

Question

I will be putting together applications to apply to math PhD programs soon, and I've been struggling to select schools to apply to. I'm not sure how competitive of an applicant I actually am. I've talked to several of my professors and get very differing opinions every time. Some of them claim they haven't been on admissions committees in a very long time, and don't have any intuition as to what schools are looking for now days. One claimed my GPA (a 4.0) doesn't matter and schools won't care. A few others said it's a good asset. One claimed (the same one that said my 4.0 wouldn't matter) that without an REU, I need not apply to competitive schools. Several others claim that an REU would be an asset, but probably won't be the deciding factor whether I get into a school or not. Overall, I feel pretty lost and confused at what schools I should be looking at.

Some points to my application

• 4.0 GPA
• Many upper-division courses in algebra, analysis, and topology
• An "introduction to research" project, in which I completed a reading course with a professor (algebraic geometry) and presented my work at a symposium.
• One letter writer is a distinguished professor who knows me decently well.
• One letter writer is an associate professor who knows me extremely well. He both offered to do the research project with me and mentored me through it.
• A post-doc who, again, is extremely familiar with me and I know will offer very high praise. I received my department's most prestigious scholarship with him as my letter writer.
• Approx. 95 percentile for math subject test.
• I taught mathematics at a juvenile detention center for 4 years.
• I am currently founding the AMS chapter at my university.

Some points that I lack, which worry me:

• No REU. I only decided that I wanted to do a PhD this last year, but I'm getting married this summer, which didn't really make doing an REU particularly conducive. There is a chance that I may be able to get involved in research this fall, but it's not guaranteed.
• No graduate classes. I'll be taking a full graduate load this year, including real analysis, algebra, topology, and a semester of representation theory in the fall, and then complex analysis, number theory, and algebraic geometry in the spring. But none of these will appear on my transcript when I apply.

As I said before, my professors give me a very broad range of opinions on the strength of my application. One says that they never had the chance to do graduate classes as an undergrad and got into Michigan just fine. Another one says that without a strong list of graduate classes, I probably won't be given much of a second look. I could go on, but the point is that for any opinion one professor has given, I have the opinion of another professor that says something very, very different. And, of course, when I bring up that "Professor so-and-so said this," I get "Well, I haven't had to apply to grad school in a long time, so I don't really know," in response (or something like it). This trend is consistent even with the professors who know me best and will be writing my letters of recommendation.

Is there anyone out there that could vouch for the strengths/ weaknesses of my profile, who maybe knows a bit about PhD admissions? I'm wondering if part of the problem is that I simply have a weak profile, and my professors don't want to hurt my feelings? Please be honest--if I don't have a good application, I want to know it!

Answer 1

Your professors are right -- all of them. The problem seems to be that you are thinking of graduate school as an extension of college, as if it were just another level up the chain. The difference between graduate school and undergrad college is one of kind, not degree.

Admissions to graduate school can be managed by a committee with no input from professors, or solely by the individual professors who can be your advisors, and everything in between. At programs where there's an admissions committee, the process is more systematic with the committee preparing a spreadsheet with all candidates ranked by a combination of GPA, test scores, research experience, etc. Some even try a formulatic approach arriving at a single number that is then used to rank students. At places where the individual professors admit students directly to their own groups, to know what the professor wants is an exercise in mind reading.

You have to choose programs and potential advisors based on your own criteria and then apply. Some will reject you, and if the stars align, some will like you and reply with an offer.