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I am writing on behalf of someone else. But the question will be easier to pose if I put myself in his shoes and speak in the first person.

I will soon graduate with a Bachelor's in economics and mathematics in a Third World country. I have, however, also studied physics. I actually have more physics than mathematics courses on my transcript. I want to study for a PhD in mathematical physics in the U.S. I would need support (e.g. TAship).

Where I live, subject GREs are only offered once a year, and one is not permitted to take two different ones on the same day. It is too far and expensive for me to travel to another country to take a second subject GRE.

Suppose, for the purpose of this question:

  • I decide to take the Physics GRE, and apply to physics departments

  • I get admission to a physics department, and a TAship

  • I take a combination of both math and physics courses and do well

  • After several semesters I realize I'd rather that my home department were math, instead of physics

How hard would it be to apply to switch over to a math department (either in the same university, or a different one), assuming I had taken sufficient math courses, and done very well in them?

Note: The similar question is somewhat helpful, but I would like to see a specific focus on the math/physics interface; also, please consider the specific option of pausing at completion of a masters, with a switch of department at that point.

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It seems like "you" should do a lot more research into existing graduate programs, since you haven't mentioned maybe the most obvious thing you should do: apply to an applied math Ph.D. program. You should look carefully at what different programs expect, since "applied math" is a slippery concept; however, as such, applied math programs don't have an uniform an expectation of student background as pure math or physics programs. Interdisciplinary programs are hot at the moment, but unlike a usual math or physics degree, what's on offer will vary dramatically from university to university. In my new hometown of Waterloo alone, there are (I think usually funded)

That's a bit out of the norm, but there are many other programs out there.

  • Do applied math departments typically require a subject GRE? If so, which one? – aparente001 Apr 24 '17 at 14:13
  • @aparente001 I have no idea. Besides, what's typical doesn't matter; research the programs that interest "you." – Ben Webster Apr 24 '17 at 15:39
  • We certainly will, thank you for the suggestion. // Your answer would be strengthened with this information, since the problem of the GRE subject tests only being offered once a year was key to the question. – aparente001 Apr 24 '17 at 18:32
  • @aparente001 I understand your point, but I think you're missing mine. In pure math, there is a rough consensus about the basic background required for a graduate program (in the US; it can be quite different in other countries) and how that background is evaluated. As far I can tell this is just not the case with applied math. Sometimes applied math students go through the same application process as pure math students and thus require the same exams. – Ben Webster Apr 25 '17 at 1:14
  • Sometimes it's a completely separate department, and thus the students are evaluated differently. It would be very dangerous to generalize (and I'm far from the best qualified to do so). "You" need to research programs, and decide on the basis of the programs "you" want to get in to which GRE makes the most sense; it's not helpful for me to just guess which ones those are. – Ben Webster Apr 25 '17 at 1:18

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