I am in graduate school pursuing a PhD in applied math. I study high dimensional probability/statistics, but most of what I do is theoretical. I am almost finished with course work (so the next years will be all research), and I had a question I wanted some opinions on.

Is it useful to self-study topics that are outside my field, or would it be a waste of time and I should just focus on my research? For some reason, if I obtain a PhD in math, I almost feel obligated to know at least a little about topology or abstract algebra. I feel obligated to know a little about computer science or physics.

The most knowledge I have of these subjects is just an undergraduate course, to which I have forgotten the content of most of them by now.

Is it normal to feel like this?

  • 1
    An important consideration is to what extent, and at what level, do you believe you may be teaching when you're finished. If you think you might be teaching in a department that offers at most a Masters degree, then it's likely that you would be expected to teach most any undergraduate level course, which certainly could be algebra and might be topology, although usually for these fields there are enough people interested in teaching these two subjects. That said, I think your primary (and secondary, and third, ...) concern NOW should be your Ph.D. research. Other things can be learned later. May 10, 2021 at 6:16


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