Red flag to have pure and applied interests?

Forum for the GRE subject test in mathematics.
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Red flag to have pure and applied interests?

Post by pde_manifold » Fri Jan 13, 2023 12:54 pm

Is it a red flag to state on our app, e.g. SOP, that we have interests in both pure and applied math? I've gotten mixed answers to this question

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Re: Red flag to have pure and applied interests?

Post by FieldsMedalist » Fri Jan 13, 2023 5:22 pm

If they are put in one program, applicants are usually seperated into two groups: pure and applied. So I think generally it is not good to state interests in both. Take for example Tufts University, they "alternate recruiting in-coming classes that are focused on either applied or pure mathematics". That is, one year they admit only applied math students, and the next one they admit only pure math ones.

However, if they are in two distinct programs, then you can apply to each one seperately, with no harm.

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Re: Red flag to have pure and applied interests?

Post by gzero » Fri Jan 13, 2023 5:47 pm

I guess it depends how natural the overlap is. In analysis say, there's not really a hard line between "pure" and "applied". For example PDEs or spectral theory, despite being possibly very "pure" in flavour, are largely motivated by physics and most of the famous operators & PDEs arise from there, and you might also be interested in the physical theory that gives rise to these objects. Similarly if you were interested in differential geometry it could be that you become interested in mathematical aspects of general relativity. I think this would all make sense to an admissions committee, provided their department could support both.

What might not make sense would be if you declared an interest in two completely unrelated areas, say both algebraic number theory and convex optimisation. You may look undecided and like you've just listed your two strongest grades from undergrad.

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Re: Red flag to have pure and applied interests?

Post by Scathrules » Fri Jan 13, 2023 6:01 pm

I would be careful in listing research interests from widely different fields unless you can somehow connect in a nontrivial way. As others have said, it might make you look undecided which is not a good sign for grad school. I have heard that if you do have the background in two or more different fields to the point that you can actually write about it at length in your SOP, then it might be fine but even then, it's still kind of a risk

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