I want to retrain as a mathematician, I already have a masters in computer science, what's the best way forward?
February 4, 2010 6:34 PM   Subscribe

I want to retrain as a mathematician, I already have a masters in computer science, what's the best way forward?

After a lot of soul-searching, I've finally admitted artificial intelligence isn't for me for a bunch of philosophical and practical reasons. But I love the maths elements of it, still, and would love to retrain from comp. sci to more maths-oriented pursuits. Naturally I'd like to capitalise on anything I've already done, but I'm not sure of the best course forward. Any suggestions?
posted by Ultrahuman to Science & Nature (6 answers total) 9 users marked this as a favorite
Hmm.. if you are not sure how to go about it, perhaps you can enter a Master's in Math in order to take some courses and decide on a more concrete direction? Is that something you can afford? You could also try and set up your own self-study program, read some papers in order to get an idea of the research currently done in areas you might be interest in, and then apply to a PhD program directly. If these are too obvious, perhaps you can give us some more information about what your concerns are, and give more detail in general?
posted by albatross84 at 7:21 PM on February 4, 2010

Well, complete at least two upper division math courses, and/or have substantial exposure to math in other courses. Take a GRE subject test in computer science (in addition to the GRE math subject test). If possible, gain other experience working with mathematics (for instance, summer research positions.) Get letters of recommendation. Then, apply to an Applied Math grad program.

Depending on your situation, this might require getting a night job near a university or taking out a loan, for about three or four years.
posted by water bear at 7:40 PM on February 4, 2010

If you're still registered as a student, and you meet the prereqs, you can take the basic intro courses for mathematics graduate students. Real Analysis, Abstract Algebra, and Topology are the main courses for new math grad students. I'll also throw in a vote for Graph Theory, which is my own area, and very popular among pencil-and-paper computer scientists. I chose my PhD program based on the Graph Theory group, but you should be able to take at least an undergrad course at any medium-sized school. Take a look at Doug West's book "Introduction to Graph Theory", with or without a course, for a good, well, intro.
posted by monkeymadness at 8:19 PM on February 4, 2010

What do you think you maybe want to do as a mathematician? I know a number of (academic) computer scientists who basically are mathematicians at least some of the time---they write mathematical articles about mathematical topics published in mathematics journals.

So, if what you want to do is math, it's possible to do so as a computer scientist; just do research in mathematical-type areas. (The CS mathematician types I know do work in discrete geometry (polytopes, for example), but that's because that's the field I work in, too.) There are interesting questions in computational complexity, integer programming stuff, oriented matroids, ...

If you want an academic job in math and were willing to also teach computer science courses, it would likely be very, very easy for you to get a job at a liberal arts college if you had a PhD in math. In my experience, many math/cs departments would really love to have someone who could teach the odd programming course (or theory of computation) in addition to calculus. It would be hard to get an academic job without a PhD.

Your ease of getting into a math PhD program would depend on how much math you had in your previous educational experiences. There are some CS undergrad programs which require a lot of math and some that require very little. Like monkeymadness said, Algebra and Real Analysis, plus calculus and stuff, would go a long way; you probably know a lot of graph theory already, but a graph theory/discrete math/combinatorics course would probably speak to your CS background if you've not taken one.

If you want industry, as a mathematician, you might spend some time poking at the careers page from the Mathematical Association of America (MAA). The corresponding careers website from the Society of Industrial and Applied Mathematics (SIAM) looks like it might really have some good stuff for you.

(I am a mathematician, but not with much CS background. feel free to MeMail me if you think it would be helpful.)
posted by leahwrenn at 10:00 PM on February 4, 2010 [2 favorites]

What type of mathematics interests you? Theoretical computer science has a large overlap with mathematics: e.g. formal language theory, algorithmic information theory, NP completeness.
posted by Obscure Reference at 4:36 AM on February 5, 2010

Agreeing with everyone else, I wouldn't commit (even in your head) to a degree program until you've taken an intro. to real analysis course. The second semester, in particular, is the rock which has turned many B.S.s into B.A.s. Even if you plan on a different area of study, most-bordering-on-all graduate programs will require undergrad real analysis, it's one of the things people are regularly sent back to take after being accepted, and it's an area of math that you probably haven't been exposed to as a computer scientist.

(For comparison, an analysis of algorithms class would be a similar stumbling point for many CS undergrads, and similarly something that most math undergrads aren't seriously exposed to.)
posted by anaelith at 6:04 PM on February 5, 2010

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