As a Computer Science undergrad, I've taken Calculus I, II, III, Linear algebra and Differential equations. This exposure to higher mathematics encouraged me to pursue a PhD in mathematics. How feasible will this change be? How will the transition be from computer science to mathematics?
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2Some branches of computer science are very closely related to mathematics, whereas others are not. What branch of mathematics are you considering? And what branches of computer science have you studied?– user2768Commented May 15, 2017 at 14:07
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1This exposure to higher mathematics ... -- While the courses you have taken might be considered higher mathematics to you, there are other topics you should get exposed to before considering to seriously pursue graduate studies in math. At the very least, you would want to take a real analysis course, and then branch out from there, depending on whether you have pure or applied interests.– Mad JackCommented May 15, 2017 at 14:07
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1Just a general FYI, the listed math courses are standard for Engineering and Physics majors in the US, so I'd characterize them as a good background for math-heavy fields, though perhaps not quite enough for someone who specializes in Math specifically.– NatCommented May 15, 2017 at 14:13
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3@ZihanI. I'd have difficulty seeing you being competitive for a Math grad program with the stated background alone, primarily just because there's more coursework you'd probably want to do before starting the grad-level classes. That said, I think that some of the formal mathematical proof stuff is similar to what theoretical computer scientists do, so I dunno if you might have some exposure there, which might be a point in your favor.– NatCommented May 15, 2017 at 14:20
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3You might consider a master's degree in mathematics before starting your PhD.– user2768Commented May 15, 2017 at 14:34
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1 Answer
Any mathematics PhD program will require math coursework in abstract mathematics, which you likely have none of.
You will need enough real analysis to cover all of baby rudin, and a full year-long course in algebra. That's the bare basics for surviving first year graduate level courses for the first year exams.
It is completely feasible if you take another year or two and get a mathematics degree. You might want to consider getting courses in real analysis/algebra/complex analysis/logic and maybe a course in probability and then applying to masters programs for mathematics. There you could take graduate courses, do a math thesis, and then assuming your grades/prestige aren't already tanked, there's nothing in your current history that will prevent you from getting a good Mathematics PhD.
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1"You will need enough real analysis to cover all of baby rudin, and a full year-long course in algebra. " Is this for PhD courses or for Masters? Is this for a top school, or just average?– OviCommented May 15, 2017 at 18:28
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1In the U.S. one takes Ph.D. exams within roughly the first two years of beginning graduate school, and those exams are based on certain courses that students are expected to take during this time. (A few will have taken one or more of these courses as an undergraduate.) Antecedent is saying that you need baby Rudin and a year of abstract algebra to have the background to BEGIN those courses the Ph.D. exams are based on. For what it's worth, when I was in school typical texts for the exams were Royden for real analysis and Hungerford for algebra. Commented May 15, 2017 at 21:16
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2@Ovi: the OP hasn't seen enough mathematics to know whether he really wants to or is able to pursue a PhD in mathematics. Any school that takes him on as a PhD student is taking an enormous risk. But he has enough background to enroll in a Masters program at some schools (including some good schools). Commented May 15, 2017 at 21:24