Acceptance into graduate math programs

Question

I have been hearing different views about my likelihood of getting accepted into a math graduate program.

Which of the following factors contribute most to the acceptance of a non-math undergraduate into a math graduate program (please order them)?

1. GPA
2. Recommendation letters
3. Publishing math papers

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Since I am an engineering student I only registered basic math courses (such as calculus, linear algebra, etc.). However, I studied a lot of other more advanced courses by myself. My GPA is about 3.5. A lot of people have told me that I need to raise my GPA in order to get accepted into a decent math graduate program and this is worrying me.

Courses that I self-studied: Undergraduate abstract algebra, real analysis (with an introduction to measure theory), first 4 chapters of Munkres' Topology, elementary number theory, graph theory

Courses that I am self studying: Hungerford's abstract algebra, algebraic topology

Courses that I plan to study: algebraic geometry, algebraic number theory, complex analysis.

I also managed to finish 2 math papers. So the question is:

Where do I stand now?

Answer 1

Since you are an engineering major who took only the standard math courses, I infer that your overall GPA is driven by your engineering coursework. I don't think that graduate admissions will learn much from your grades in engineering, good or bad. The GPA of 3.5 is not that bad in engineering, especially if (as it seems) your heart was not really in it.

Self-studying is great, but the knowledge acquired from it needs to be evaluated by someone. Acing GRE Math would send a signal that you indeed learned something. If during your studies you kept in touch with math professors in your school, and they know enough about you to write an informed letter full of specifics, that would be even better.

The opinions on undergraduate papers in math are divided: e.g., not everyone considers them a good way to spend time as an undergraduate. I would not expect the admission committees to seriously read papers sent with an application, though they will glance at them.

So, my order is: letters, GRE math, papers, GPA.

Answer 2

I don't see this question as being definitively answerable without a lot more information, both about your background and qualifications and about where you are applying. Grad schools differ enormously in their approach to admissions in unusual cases. Some lower-tier schools are eager to take a chance on smart but nontraditional applicants who will be rejected by more prestigious universities. Others have established rigid rules after having had bad experiences with admitted students who had inadequate backrounds or didn't understand what they were getting themselves into.

Regarding grades, keep in mind that the world has seen a lot of grade inflation, and there are startlingly large numbers of applicants with nearly perfect grades. You generally cannot impress an admissions committee by having excellent grades, although poor grades can hurt your chances. Math departments typically care a lot about grades in mathematics and heavily mathematical fields (e.g., theoretical physics or CS), a little about grades in other scientific or engineering fields, and not at all about other grades, except that exceptionally poor grades in any field suggest the applicant is not good at getting things they don't care about done (which is not a good omen for their career). I.e., math departments don't care if you get a B- in history, but getting an F in history could be a problem.

Recommendation letters are absolutely crucial. In my experience they are by far the most important factor: other aspects of the application could hurt your chances even if you get good letters, but those other aspects cannot get you admitted by themselves. If you can't arrange for enthusiastic letters that the admissions committee will trust, then you have no chance at all of being admitted at a higher-ranked school. It's possible that a lower-ranked school might take a chance on you, but as I understand it every graduate program cares a lot about letters.

As for math papers, it's unfortunately not hard to write a near-vacuous or unoriginal paper and get it published somewhere obscure, and carefully evaluating a paper can take a lot of time and effort (refereeing is hard). If you simply list a paper in your application, with no evidence of its quality, then it's unlikely anyone will have the time to investigate carefully. The important thing for graduate admissions is not the publication per se, but rather the research experience that led to it, and you need a letter of recommendation that talks about this research and vouches for it. (In fact, having such a letter can be very valuable even if the research did not lead to a published paper.) This means you need a letter from your supervisor or mentor, or at the very least from someone who has read the paper and knows something about how it came about (for example, someone who can single out your own contribution if you had coauthors). In principle, if you publish in an especially prestigious journal and without senior coauthors, then the journal's high standards might serve as enough of signal of quality by themselves. However, this very rarely happens with undergraduate research.

So in short:

1. Bad grades could hurt you but good grades won't serve as a strong argument for admission.

2. Recommendation letters are crucial.

3. Research experience could help you get great letters but is very difficult to judge except through the letters.

However, as I said in the beginning, there are a lot of graduate programs out there, with different approaches to admissions. If all goes well, you'll get strong letters from math faculty and will be admitted in more or less the usual way. Otherwise, you may have to find a school that is willing to take a chance (usually because they have trouble attracting strong students with conventional backgrounds).

Answer 3

The earlier answers make good points...

And I would say, in your situation, most likely the "papers" are of little consequence in admission-or-not, and a 3.5 GPA is fine. No one cares beyond that. Letters matter a great deal when I recommend-or-not admission. What I read first, however, is the personal statement. Do be aware that in many programs there is a dominating impulse to "mechanize" admissions, which obviously has difficulty making use of either letters of recommendation or personal statements. But, still, if you explain your interests, your self-study, this can have a huge, repeat huge, impact on admission chances. I suspect you've not had much contact with math faculty in the course of your self-study, so can't get letters from math faculty. (If this is not correct, so much the better!) Letters from engineering faculty about students' mathematical talent are typically nearly worthless, since there seems to be a general tendency for "engineers" to believe that "mathematics" is "just a tool", and that they've mastered it, etc. Nevermind.

But the point is that you should not expect even glowing letters from engineering faculty to have much impact on admission to math grad school, exactly because the prejudices of many engineers are very familiar to mathematicians.

The subject-test GRE may help your chances, and you must take it, because a low-ish score is vastly better than the cluelessness indicated by having no score at all.

But for a person approach mathematics with genuine enthusiasm, but "belatedly", the personal statement, explaining unapologetically how you came to your present course, is the most important thing. Very few people choose to self-study mathematics... (although quite a few seem to believe that they have special gifts that require no study...!)

Explain yourself in your personal statement. Get letters from the people who think well of you who have the best idea of what professional mathematics entails.

Edit/addition: very literally, it is best to have letters from people who have been to math grad school themselves, preferably at better places, so have an idea of what that entails. Many or most math grad programs have "breadth" requirements apart from the eventual goal of "original research"=thesis. So it's not so much a question of your letter writers' "peer-reviewed publications" so much as their first-hand experience with math grad school. (These days some people who've done PhD's in math do end up in engineering depts, and vice-versa, but this is still unusual.) Thus, a recommendation letter should perhaps literally say something like "From my first-hand experience in math grad school at X, and observations of math grad students at Y and Z, [student] will be a success." That's the kind of thing that leaps out at me when I read these letters. (No, don't have your letter writers send CVs or publication lists.)

Answer 4

3,1,2 . And high GRE (subject) score may help.The content and level of your papers is crucial. And your goal will determine your chance.By the way ,this math-gre website lists many applicant profiles and admission results. Definitely worth a look..