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The simple version:

I've been out of college for 7 years and want to pursue graduate studies in a field unrelated to my undergraduate degree but am not sure how.

The detailed version:

My college career began as a Physics major. I made what I now consider the mistake of changing to a technically driven humanities major (Electronic Media, Arts and Communications) although I completed a great deal of my pure sciences coursework.

Years later I have a very solid job in a field that I hate and want desperately to get back to school to work towards higher degrees in mathematics. I've spent the last five years as a systems engineer with a focus on network distributed video and have a very solid resume in my field, but my academic credentials are poor. A 2.8 GPA (albeit from a strong school) and an unrelated B.S.

I've made it a point to keep up studies in math, participing in a great many MOOCs to try to backfill my mathematical education and keep my skills sharp.

What I don't know is how to re-approach academics. Would I need to earn some additional undergraduate credits before applying for a graduate program? I expect GREs will be required, but that's not a major issue as I've been scoring quite well on practice exams.

I know that I lack educational recommendations and undergraduate research, and I have absolutely no idea how to supplement this lack...

  • Given you were pursuing a Physics degree to start with, you most likely have a lot of undergraduate Mathematics coursework behind you, probably enough for a minor. Most graduate programs only require either a minor in the field or a major in a related field. It couldn't hurt to ask a few departments what you'd need to do in order to be a successful candidate for their department. – Jonathan Landrum Oct 1 '13 at 15:33
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    Is it reasonable to simply reach out to departments directly? Wasn't really sure of the etiquette there. – Robare Pruyn Oct 1 '13 at 15:34
  • I have. I've even made the trip to visit the campus and meet with a professor I liked, just so I could get to know him better and get a feel for what the department was like. That also gives him a face when they are going over which applicants to accept. – Jonathan Landrum Oct 1 '13 at 15:41
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    My suggestion would be to go for MS Math first. It is far more easy to get into a math MS program than math phd program. After your MS, you can apply for phd at top schools. – user774025 Oct 2 '13 at 1:40
  • Yes, it's very reasonable to email a director of graduate studies (not a general graduate admissions department; they won't be able to tell you anything), lay out your situation and ask if you are a plausible candidate, or what you would have to do to become one. I'll second @user774025's suggestion that a getting a masters at a localish school, maybe while still working, is probably the way to get into a respectable Ph.D. program. – Ben Webster Oct 6 '14 at 16:52
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As mentioned in the comments, visit the Universities, meet with the professors of the fields that interest you the most (of course, make an appointment to see them). I would suggest emailing professors (not to the point of pestering) - asking them about research papers they've had published - show an interest in and knowledge about their work.

Going further, you have Physics and you have been taking a lot of courses to keep your skill set up to date, so these would work in your favour. On top of that, your work experience provides a solid work-ethic and some more applied skills and knowledge (which, depending on what you are going for, may of a huge benefit to you).

Talk to the admissions people of the faculties in the universities that you are interested in.

Most of all, in all interactions, be truthful about everything including your grades, academic history, work experience and motivations. But speak of the skills that you have gained from each thing you have done.

  • I felt a little bad about downvoting, so I just want to say that I just thought Paul's answer had more helpful detail. The things you suggest aren't bad, but they won't help much. The OP needs good letters from research mathematicians, and a few short conversations is not sufficient to get them. – Ben Webster Oct 6 '14 at 16:48
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To get admitted to a graduate program in math, although work experience may suggest greater maturity, etc., the issues will be letters of recommendation and documentable standard-material background (whether in conventional courses or somehow-verifiable self-study...), and possibly a GRE subject test score if only to show that one is aware that the thing exists and is widely believed to be relevant (even while many, including myself, do not consider it a good predictor of anything much beyond multiple-choice-test-taking abilities).

Unless you've self-studied into a quite unusual state of expertise, you'll most likely not have much success in getting an idea of what contemporary research in mathematics is about, and it might be awkward to attempt a conversation with faculty about their current work. Perhaps such a thing would be feasible in other fields (I have no idea...) it is not typical in mathematics. That is, people going to grad school usually have only a general idea of the direction of their interests, even with a solid coursework background. In particular, funding for graduate work is rarely dependent upon connecting with any particular faculty more than tentatively. (Again, this is evidently unlike other fields.)

Helpful letters of recommendations would be from professional mathematicians actively involved in research, acquainted with graduate programs in mathematics, who can speak from direct personal experience both about what such programs will demand of you, and about your qualifications to meet those challenges in terms of prior preparation and in terms of interest.

Probably the way to put yourself in a position to have such letter writers is to take upper-division or beginning-graduate courses at a solid university, as a "non-degree student", do well, and thereby be able to ask the instructor for such letters. It's not the credits themselves, but the information and the certification by faculty (beyond "getting a good grade"). That is, you'll want people to attest to your future potential, beyond accomplishments to date, in the sense that (hopefully) "you've only just begun", rather than having peaked-out.

If you are an outstanding multiple-choice test-taker, getting a stellar score on the math subject test GRE will catch the eye of many! :)

Other routes for certifying that your self-study has made progress are difficult. E.g., certificates from on-line courses are not worth much, and, most often, those courses are too elementary to be relevant to graduate study in mathematics.

If you are not geographically flexible, going to the nearby universities mathematics departments and asking "what it would take" for admission, _with_funding_ (don't go without funding), and try to do it. The whole process might take long enough that it'd be wise to keep the job you have, even if you don't like it, to support yourself (and others?) through the preliminary stages of gaining entry into a graduate mathematics program.

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    I agree that taking some graduate level courses as a non-degree seeking student would help demonstrate the OP's abilities, in order to get recommendations though he would need to go much further, asking pertinent (but not attention seeking) questions in class. Conversing with the professor, and maybe looking for opportunities outside of the class to engage in research the professor is interested in. In fact the OP may want to talk to the professor first and then decide what class to take based off of that. – kleineg Oct 9 '14 at 14:30
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    @kleineg, yes, indeed, a very dynamic participation in such courses is necessary! However, I fear it is not so plausible that at the level in question a student could meaningfully engage in contemporary mathematics research immediately, especially prior to getting oriented in the milieu. – paul garrett Oct 9 '14 at 14:43

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