Improving my PhD application for math programs

Question

This past year I was accepted into two mid range phd programs in mathematics without funding. Here's what my profile looked like:

Domestic White Male Unknown state school in the midwest Majors: Mathematics and Philosophy GPA: 3.93 GRE: Q: 168 (97) V: 167 (97) W: 5.0 (92) M: not taken

Interests: Analysis, Medical Imaging/Modeling, Mathematical Physics

Major Coursework: Complex Analysis, Discrete Structures, Applied Math (survey course mostly in Fourier methods and PDEs), Mathematical Statistics.

Recommendations: One from a top applied mathematician who was very late in sending them out, one from a professor from the previous year who is well regarded but has not had much contact with me and one from a young professor who was fresh out of post doc.

Other: I'm 30 years old. Some former work experience as a co-op student in engineering at a national lab, dean's list, normal stuff like that. I had only completed two semesters at my current school, though. About 6 years ago I was an engineering student at a different institution with poor grades and I did not finish my degree. Also mid to high level (lots of national, some international competition) as an athletic coach working with kids, teens and adults. Some international experience as an athlete as well. I also speak basic German.

Here's how my profile has changed:

Current GPA: 3.94 (.01 difference! However, this does mean 6 more As and 1 more A- to counterbalance my poor record from the early-mid 2000s.)

GRE Subject Score: 660 (52)

Additional Coursework: Formal Logic, Real Analysis, Advanced Linear Algebra, Intro to Abstract Algebra. This summer I am doing a course in number theory and an independent study in Galois theory.

Recommendations: I am going to give the late professor a much longer lead time this time around. He has said that he wants to help me but is always extremely busy. I will also be asking (and almost certainly receiving) a rec from the professor I am doing my independent study with.

Interests in pure math have shifted away from analysis, more into algebra. In applied, medical applications (organ/system modeling and imaging more than bioinformatics) have taken the lead over mathematical physics.

Other changes: Medalist in school's math competition, math tutor in our honors college and privately. Taking a Spanish immersion course so I can list basic spanish on there as well.

I'll be taking the GRE subject again in October and am using saylor.org and MIT's opencourseware to review older subjects. I graduate in August and will be working for a year. I'm thinking about applying to teach at a high school or community college for that time. I also plan on taking one or two graduate courses per semester.

I plan on applying all over the place (>15 apps) compared to the 8 from last time. I would prefer to go to the west coast. Can anyone let me know if the mid level UCs (Irvine, Santa Barbara, Davis) are reasonable with what I've got now, especially since when I worked at that national lab I was technically a UC employee? Any other recommendations on schools or anything I can do over the next year to boost this?

One other thing: I have no REUs, but is a good independent study with a strong recommendation from it a decent substitute?

Thanks for taking the time to read my post.

Answer 1

In reading through your comments, I couldn't help but get the feeling that you are "all over the map" when it comes to what you're looking to do in graduate school. If this is similar to the way that your personal statement read to the committee, it could help to explain some of the challenges you faced in applying to graduate schools.

For instance, after reading what you have written, I can't tell if you're looking to do algebra or bioinformatics—or if you're in an "I'm happy with either" situation. If it's the latter, this can make it harder for a committee to accept you: algebra readers might think they'll admit you, only to have you wander off into applied math, and vice versa. You may find it better to concentrate on one area—or, better yet, show how the different topics you're interested in are actually related to one another.

Another potential issue is the quality of your letters of recommendation. Is there anyone who can help you to evaluate your letters for you? Some colleges have career offices or academic counselors who can comment on the suitability of your letters for different kinds of programs (academic, industrial, etc.), although they probably won't "rank" them for you. If you had a very late letter, it's a good question as to how helpful it would have been, even if it was from a big name (or perhaps that should be "in spite of" it being from a big name). By this, I mean that the letter would only have value if it actually discusses your talents and skills in a meaningful way. A pro forma letter isn't all that helpful, particularly if you are from an "unknown" program. (This latter can also make your job tougher, since your school might not have a track record at many graduate schools).

Finally, it also sounds like you have a rather untraditional academic history. This needs to be explained clearly somewhere on your application, in a way that shows thattaking you into a graduate program now would not be a risk. (Not doing this could again feed into the notion that you're flittering around from one thing to the next—which is not a good impression for an admissions committee to have of you.)

Answer 2

Since this was too long to leave as a comment, I'll post it here in addition to an answer: Regarding the GRE Subject test for math: admissions wise, the scores are mandatory for pretty much every top 10 program in the nation (Princeton, Harvard, MIT, UChicago, Stanford, UC Berkeley, etc). Since most potential candidates admitted to these programs have a track record for some type of research-related activity, less emphasis is placed on the scores and more on their potential as research mathematicians (after all, that's what grad school is about: research). However, in less prestigious departments like Irvine, Santa, and Barbara, more emphasis is placed on the subject test relatively speaking to the top 10 programs because one of the likely reasons some students end up in "lower" departments is due of the lack of research experience. Thus, much emphasis (though not all, credible research-related letters of recommendation are probably more essential) is placed on the subject test. Of course I'm not implying that lower grad schools look more at test scores than publications. I'm saying that it's probably more expected that the students will depend on their scores than their publications precisely for the aforementioned reasons. Right from the words of the UC Berkeley website "Experience has shown that the score on the Mathematics Subject GRE is a partial indicator of preparation for Berkeley's PhD program."

As for a "good" GRE score, take a look at what top programs expect of their applicants, and shoot for that range (the higher the better, of course). Once again, in the words of the Berkeley site "A score below the 80th percentile suggests inadequate preparation and must be balanced by other evidence if a favorable admission decision is to be reached." So if I was you, I would shoot for the 80th percentile at minimum.

Now onto your question: First of all, +1 to aeismail's answer. I agree with that assessment: It seems to me that you're all over the place! The lack of coordination, I think, might turn off the admissions committee because A) it shows you're not very concentrated in one or two areas which might imply that you don't know what you're going to do and B) you're not very committed to a specific program. Unless your research is going to coincide with different areas, and the scattering departments are a reflection of departmental strengths in those areas, I think that'll be a red flag that you really just want in based on rankings. And if that was the case, you might rejected on the basis of lack of coordination. It won't be on their consciousness of course: there'll be at least 14 other schools that may admit you, so why would they care? Here's my advice to you:

Apply to less schools: 8 - 10 seems like a very reasonable range for me. Even if you don't explicitly state it, imply that you're not just going to grad school based on prestige or naming. Over 15 schools is too much. Show that you're looking at specific programs, with specific goals in mind (i.e Applying to schools X, Y, Z because of their strong research areas in 1, 2, 3 and your interest in 2 and 3). 2 safeties, 2 matches, 2 reaches, and 2 "dreams" (you never know :-). They're paying you to do research, not the other way around. Why should schools invest their time in you if you end up switching fields?

As for whether or not these are reasonable choices, that's pretty much subjective. It would depend on the field you're going into (I have no idea how strong these departments are in analysis/mathematical physics) and that's something you can google. You'd also do well to check the websites of each of these schools and look at the expectations for their applicants. Whatever bar they set, shoot for just higher than that.

REUs are just one way of getting research experience so don't worry too much about it. Senior thesis projects that culminate in publications are another. Working closely with a professor is one other way. I think ultimately (aside from research publications) the most important factor that goes into graduate admissions are your letters of recommendation. If it doesn't show on paper, a credible professor may assess your research potential since they know best what research is all about. Of course the tricky part here is getting letters of rec from the right person: If you're getting them, you're better off getting it from someone who coincides with your research interest. Since you're interested in analysis, it wouldn't make sense to get letters of rec. from a basket weaving instructor. Get it from your analysis professor (preferably, someone who knows you well and from upper undergrad/graduate-level course).

Final thoughts: If you want to improve your PhD application, try starting an independent project or ask to work with a professor. Research that results in journal publications is very rare even for exceptional undergraduates, so do not worry about that. It's helpful to be able to focus on one project for a whole year rather than jump from one to another every single month (the reason for that is obvious: it indicates perseverance and patience, which is very important for any potential PhD candidate). And refine your statement of purpose to show what you have learned from undertaking said project(s).