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I'm an applied math and data science student currently doing undergrad research in statistics. I don't want to dox myself, but it falls under optimization research. It's a good mix between math and data science, but I want to understand my chances when applying to graduate school in a couple of years. I'm talking in reference to competitive math programs, such as HYPSM and CMU (I have specific schools in mind).

This isn't general grad school app advice, although I'd love to hear it out as well! I've also seen that similar questions have been asked elsewhere on here, but I'm not sure of the mathematics admissions climate in particular. Specifically, I'm wondering how important it is to do research directly within math, even if your research interests are an "indirect" branch of math.

Edits: Any added info based on feedback from y'all, I'll add here.

Geographically, I'm from the US. I go to a southern R1.

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    Where (geographically) are you? American and European schools, for example, have different expectations regarding what a students with a bachelors degree should know and be able to do, and what an incoming graduate student should know and be able to do. Without having more specifics, it is hard to answer the question.
    – Xander Henderson
    Commented Jul 11, 2023 at 3:57
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    @XanderHenderson, just updated the post with more information!
    – slo sud
    Commented Jul 11, 2023 at 21:23

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In the US, it is natural to switch fields when applying for a doctorate with only a bachelors. You will need to take some advanced math courses in the program, but so do others. Your background in analysis, is probably strong, but probably less in the other required areas.

Note that not all undergraduates have an opportunity to do research and even fewer to do serious research. That is unlikely to be a limiting factor.

OTOH, any positive thing you do is "relevant" in some sense, though applied stats and pure math are pretty far apart.

However, limiting applications to only the very top schools will be unlikely to result in success. You will be competing in a large pool with others better prepared to start. Perhaps there is something unique about you that will overcome that. And many in that pool will have some research experience.

I suggest that in addition to the schools you are considering you cast a much wider net among R1 universities. Perhaps you will be successful with a narrow search, but it your chances of finding a suitable place expand greatly if you open up to most of the R1s, down to at least #50. You will find strong programs in math at most of them. Not all highly qualified faculty wind up at the top four or so schools.

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    Thank you so much for the feedback! I described the schools as HPYSM misleadingly, because I don't want to apply to most of those schools anyways! I like the research at a couple of them, just didn't want to be overly specific. I feel the same way about R1 professors even if theyre not at the top four, particularly from experience with them as mentors/professors. I do have a couple more questions: 1. What required areas should I focus on? 2. What did you mean by "better prepared to start"? Would applied statistics research not be within the scope of an applied mathematics PhD program?
    – slo sud
    Commented Jul 12, 2023 at 3:43
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    Those others will have had the upper division math courses that you may not. Focus on those. Algebra and Topology, perhaps. Applied stats is closer to applied math than to pure math, of course.
    – Buffy
    Commented Jul 12, 2023 at 10:06
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To me, whether it's beneficial for your PHD applications depends on the level you're working at. To make an analogy, it would be a little like asking if your work as a first year dancer could get you into the Julliard School of Dance.

Maybe. Can you literally and metaphorically dance with the other applicants and not miss many steps? PHD programs worth your time will focus on RESEARCH. Grades and stuff matter, but RESEARCH, you need to show that you can do research at the graduate level that suggests you'll be successful in those programs at those schools.

In other words, if you could make whatever you're doing into a solo publication, then I'd say it helps you. It shows that you can compete with other me experienced applicants at a younger (I think) age.

Edit: my field is in econometrics and statistics (even though my major is public policy). Some might call me a data scientist. If you want more of my thoughts, email me. But, these are my general remarks. It's all about how competitive you are, and if the work you're doing right now is a good fit for these programs.

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In short, the answer is yes: your work in applied statistics is relevant.

First, applied statistics is, in a way, still a branch of mathematics.

Second, the people from Admissions will want to make sure that an applicant is mature and knows exactly what (s)he wants. You thus will get extra points by emphasising in your cover letter that you have some experience, and this experience has convinced you that your choice is right and you absolutely must become a mathematician.

Last, and by no means least, the Admissions people will be interested not so much in the particular area of your experience but in your ability to conduct research, to achieve results, to complete the projects you started. So, if your work in applied statistics leads to a publication -- that will look very good in the eyes of both the Admissions and your prospective advisor.

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