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Upon doing background research and looking at faculty in my department, it seems that it is easy to move from studying physics to studying applied mathematics. However, I have seen few, if any cases of the reverse, where someone started studying applied math and moved to study physics.

To this end, I am currently an applied math major applying for graduate schools, and although I will be applying to applied math graduate programs, I would like to move into the direction of physics, particularly applied physics. I am wondering if anyone here can describe how one can successfully transition from applied math to applied physics? In particular, what kind of background in physics should you have to be taken seriously? Would it be sufficient to get this background knowledge through reading textbooks on my own, or is there a bias toward learning from classes?

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  • What country is this for? What degree(s) will you have when you begin doctoral study?
    – Buffy
    Sep 29 at 23:49
  • @Buffy for the united states, and I will have a degree in applied mathematics from a "top ranked" applied math program (very complete and rigorous curriculum).
    – GEG
    Sep 29 at 23:53
  • What degree? BS? MS?
    – Buffy
    Sep 29 at 23:55
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    @Buffy A BS, but this year I am taking only graduate level courses in pure and applied math.
    – GEG
    Sep 30 at 0:02
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    Have a look at the graduate level syllabi for the various tracks in physics. It’s a bit optimistic, maybe a bit presumptuous, to think a jump from applied mathematics to applied physics could be done easily. Thought processes and intuition peculiar to each need to be built. The capacity lies in some folks for sure, but it’s not common. Sep 30 at 0:45
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A bare minimum is that you should be able to score well on the Physics GRE. Take a look at past exams and see if you can pass them. Probably you will find it challenging (most physics majors find it challenging). Go through the list of topics and see where you have gaps in your knowledge you need to fill. While the GRE itself is undoubtedly an artificial exam (research-level physics bears little resemblance to answering 100 multiple choice questions in a timed setting), you will absolutely be expected to know the content covered on the exam and you will probably have to take qualifying exams within a year or two of entering grad school where you show mastery of these topics, based on grad-level courses.

That's the minimum though. The real meat of grad school is about research. I would challenge you to be a bit more specific. What research problems are you interested in? Even if the problems involve physics, it may be that you can work on this type of problem in an applied math program. If the kind of research you want to do is mostly done in physics departments, then start finding out what physics departments do that type of research. Target your applications to those schools. In your application, explain why you are interested in switching and explain as precisely as possible the ways in which your background prepares you to study the kind of problem you want to study. Talk with your letter writers about the transition you want to make. If there are physics professors at your university that do something similar, reach out to them and ask them for advice. If you have a year or more, spend the time to do an independent study or take some physics courses. If you are applying this semester, then do your best to demonstrate that you have a serious interest, relevant background, and an ability to learn quickly.

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  • Let me note that in the US, an undergraduate physics degree has a quite deep prerequisite structure. This makes it more complex than some other majors that rely on fewer "basics" to reach the advanced courses. The advice in this answer to talk to physics professors at your own university for advice is especially valid.
    – Buffy
    Sep 30 at 14:05

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