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I'm currently a rising undergraduate senior pursuing a dual degree in both mathematics and quantitative finance. I am interested in pursuing a PhD with the dream of going into quantitative research. I haven't had too much exposure to research since my junior year and this upcoming fall I'll be doing two senior theses (one is a pure math topic and the other is more quantitative research orientated (applied math topic). I have done 3 other research projects (applied in financial mathematics), worked two summer internships, have several teaching experience in math and computer science courses (optimization, real analysis, introduction to python).

I have been studying for the GRE Mathematics Subject Test with the main goal of pursuing an applied mathematics PhD but lately I have been questioning if I want to do applied mathematics or statistics. From my school, we have a small mathematics department and most of the faculty come from pure mathematics backgrounds, so it is difficult to get their input on this. I have taken several statistics courses and applied mathematics courses, but my main goal is to go into mathematical modeling and do extensive research.

Should I stop studying for the GRE Mathematics Subject Test and take the General GRE Test for a statistics program or should I continue with the GRE Mathematics Subject Test, regardless if I choose statistics or applied mathematics? And would a statistics PhD equip me with the necessary tools for quantitative research or would an applied mathematics PhD be stronger? I also am interested in fields such as optimization, financial mathematics, and differential equations if it makes a difference.

I am more drawn toward applied mathematics programs at the moment, but I am not sure whether I'd be a better fit for applied math PhD or statistics PhD programs. I also have looked at what research faculty are doing at certain schools that I am applying to and both the applied mathematics and statistics research are something I would be interested in.

Any thoughts on this? Any input is greatly appreciated.

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    Is the mathematical modeling you’re interested in doing more related to statistics (e.g., regression, machine learning) or more related to differential equations? Something else? // As an aside, you might find yourself interested in two fields that are not especially well known: 1) Topological data analysis & 2) Information geometry. If you do not know these, I suggest checking them out!
    – Dave
    Commented Jul 26, 2023 at 2:20
  • To be completely honest, I really like both regression/machine learning and differential equations. At my internships, I had more exposure to machine learning and regression, so I do feel a bit more comfortable with those topics, but I feel like differential equations may be more useful in quantitative research (I could be wrong). I haven't looked at information geometry but I have at topological data analysis. Would information geometry fall under an applied math PhD or a statistics PhD?
    – Koshun
    Commented Jul 26, 2023 at 12:32
  • It could be either. The particular faculty interests would probably matter more.
    – Dave
    Commented Jan 1 at 23:56

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