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I'm a rising senior majoring in math, and my coursework almost exclusively consists of grad-level pure math courses. However, I'm getting more and more interested in Machine Learning. I've studied applied math and machine learning by myself, and now that I've graduated from a college, I'm going to do research in machine learning full-time with a professor in another institution until the next summer. Nevertheless, I suppose I have better chance for math PhD programs due to my coursework (note that I may not publish before the admission), and there are some non-top-tier (though strong in some areas) math PhD programs whose university has a top-tier group of ML researchers in the CS department. A good example would be CMU. Of course, it would be better if one can go to the universities which are both top-level at math and ML, but math programs of such universities (e.g Berkeley, MIT and Stanford) are harder to get into.

My guess is that I just should go to the math PhD program of CMU if it has a ML researcher of my interest, and everything that decides my career afterward is the quality of my publications. But are there some obvious cons for this option?

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  • It's not just the advisor that you work with but also the course requirements, qualifying exams, etc. that will have a huge effect on your PhD experience. You might not be happy (and will certainly not be well prepared by) taking years of course work in areas unrelated to your research interest.
    – Brian Borchers
    May 12, 2017 at 18:50
  • I enjoy taking pure math courses as well as physics, CS and applied math all at graduate level. For pure math, I'm primarily interested in symplectic geometry, algebraic topology and rep theory, and I've taken all the courses for oral exams (or called quals) covering these. I've read transcripts of typical oral exams in Princeton and Berkeley, and I'm certain I will not have problem with them. Of course, CMU and others have different quals, but I don't think I will have problem with quals or courses.
    – Math.StackExchange
    May 12, 2017 at 18:58
  • This strikes me as an extremely odd plan. Assuming you've done well in your grad-level math classes, and that your boast that you would have no problem with Princeton's math orals is not idle, you might be competitive if you simply applied to the (CS) programs you are actually interested in. I would certainly recommend doing so. You might acquire at least some formal CS background while you have the chance. But most importantly, seek out the advice of individual professors working in the area of your interest. Good luck to you!
    – Anonymous
    May 13, 2017 at 2:58
  • Thanks for your answer. As I'm no longer in an university and I'm in another country, it is difficult for me to take some CS courses CS admission committee of, say, CMU would like to see on my transcript. However, if I will find any such course, I will definitely take it and ask the instructor, as well as my professor who will guide my research, to write a LOR for me.
    – Math.StackExchange
    May 13, 2017 at 23:32

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