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My dilemma: I'm interested in potentially going to graduate school to obtain my PhD in math with an ideal career as a professor at a research university. I entered undergrad as a computer engineer and didn't add a math major until the end of my third semester. In my school, you have to select electives to satisy an "elective focus area" (cohesive plans of study in fields such as data mining, signal processing, applied physics, etc). My field of study is currently software engineering, something that still interests me. I'm still early enough in my undergraduate career (going into my fifth semester) where I could alter my focus area to include many more upper-level and graduate math courses instead of continuing on the software track. However, I'm hesitant to do so because I know that software engineering is a lucrative field with significantly more job availability than math academia and I would likely enjoy my work as a software engineer.

My inclination: Given that software engineering is something that I'm interested in (although not as much as math) and the job market isn't quite as cutthroat, I'm inclined to continue on my path while trying to sneak in a couple upper-level math courses that have crossover -- large data analysis, numerical methods -- where I can. I could work in industry for a few years after graduating. Ideally, I would be able to take one or two courses a year throughout this period, most likely online, that would solidify my mathematical background and make me a more desirable student when applying for grad schools.

My question(s): Would taking a solid portion of my post-calculus mathematics coursework online have any adverse affect on my graduate admissions? Would it matter if the coursework came from my undergraduate university or from a variety of institutions? Are there other unconsidered obstacles in my inclined path?

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    For PhD admissions, you need strong reference letters. In online classes, there is often much less interaction with the instructor, so it might be hard for you to make the impression that you need to in order to get those strong reference letters. – ff524 Aug 3 '16 at 4:35
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    Small correction: In online classes, there is often no interaction with the instructor – JeffE Aug 3 '16 at 20:49
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    Are you working full-time while taking the coursework? Because you talk a lot about software engineering but don't indicate what you're currently doing. Realistically speaking, whether or not you can dedicate time to drive to campus while working full-time could potentially impact what you should do. – Compass Aug 3 '16 at 20:53
  • @Compass I'm currently a third year student but in this theoretical situation I would be working full-time in industry while taking one or two courses a semester (most likely online). – kanderson8 Aug 4 '16 at 5:21
  • I wouldn't recommend a part-time Master's program unless it was specifically for industry advancement, i.e. EMBA or MS Computer Science. – Compass Aug 4 '16 at 14:24
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Given your terminology (you wrote "research university"), I'm going to assume you're in the US.

This is a bad idea. Admissions committees will have no idea how to evaluate the online classes, and will probably not put very much weight on them. As @ff524 notes in his comment, you will not have any good letters of recommendation, which are essential for an application which is a bit outside the norm. You are incredibly unlikely to get a spot in a graduate program that is likely to result in a becoming a professor at a research university if you depend on online classes instead.

So, what should you do instead? Well, first reconsider if being a math professor is what you want. You're absolutely right that there's a real risk of it not working out, and a lot of competition. But if by trying to keep your options open, you do less to make yourself a qualified candidate (both on paper, and in actual point of fact), then you're just putting yourself at a disadvantage, and making your chances that much worse. You will be in very bad shape if you don't get a BA which includes a math major, and take a lot of advanced math courses (more than the bare minimum required for a math major!) in person with faculty at a well-respected research university. Note, that doesn't necessarily preclude getting another major.

On the other hand, there is good news. The people who get BAs in math, or start mathematics grad school and don't finish, or who finish but don't get an academic job (or one they want) do find other things to do. If you have complementary skills in computer programming, then you will be very well set up to do a lot of things. I don't suggest starting a math PhD as preparation for a job at Google, but I do know several math PhD's who do have such jobs. So, if getting a BA in math and then perhaps a PhD in math feels like what you want to be doing in the moment, then I think you can reasonably do it, and figure you will find a job if the academia thing doesn't work out.

  • I'd strongly second all of this answer. In particular, doing half of one thing and half of another, unless you're twice as able as all those very able people around you, will most likely lead to inadequate outcomes in both. Maybe not "failure", but almost surely substantially compromised outcomes. That is, yes, trying to hedge one's bets in the academic math game is mostly infeasible. Yet, as Ben Webster notes, people who have good PhD's in math, or even part of one, do not usually have much difficulty finding other opportunities, especially if they have computing chops. So... – paul garrett Aug 3 '16 at 22:42
  • ... figure out what you want to do, and don't do it half-way. – paul garrett Aug 3 '16 at 22:42

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