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So, my background is that I have a bachelor's degree in electrical engineering, but I am doing my master's in engineering physics, theoretical track. (Both will be part of my "Civilingenjörsexamen", as it is called in Swedish, which I believe is usually translated as Master of Science in Engineering.)

When making my choice for master's track, the clear front-runners were applied mathematics and theoretical physics. I ended up choosing physics mostly because I was curious about relativity theory and quantum field theory, even though I am certainly stronger in mathematics than in physics. I also had some vague idea that I could transition into more general applied mathematics later on if I wanted to, while it might be more difficult to go the other way.

Now, a year and a half into my master's studies, I feel that, while there are many areas of physics that fascinate me, life as a physics researcher would likely be frustrating and unsatisfying for me. I am frequently annoyed with how loose and hand-wavy physical arguments can be, and I find some physical theories (say, the standard model) to be a bit too messy to be enjoyable. But more importantly I realize that, while I appreciate the applications, it is really the mathematics that I enjoy the most. I really empathized with Steven Strogatz in a recent interview when he said something to the effect that he found physics a wonderful source of problems, but that he could not care less about specific results.

So this leads me to the obvious question: is it feasible that I could get into pure or applied mathematics PhD programs with my background? I guess I could just apply and find out, but that takes significant work, so I would prefer to know if I am wasting my efforts. I am interested in both Swedish and international PhD programs.

I should probably mention that I have taken a few extra mathematics courses, specifically real analysis, abstract algebra (groups and rings), and discrete mathematics, in addition to the standard courses in calculus, linear algebra, differential equations, statistics, numerical methods etc. Also a couple of "mathematical methods for physics" courses, with a mix of topics like partial differential equations, tensor calculus, variational calculus, analytical mechanics, representation theory, differential geometry etc., though not to the depth of a dedicated mathematics course. Moreover, I have a little bit of research experience, with two summer research internships under my belt; though these were both related to my bachelor's subject of electrical engineering rather than math/physics. I am also under the impression that my institution, KTH, is pretty well regarded in Sweden. At least the physics program.

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  • We get a lot of questions along the lines of this one: I've done my bachelors/MS in X, can I do my PhD in Y. Math seems like a particularly common destination for these questions, and "mathy-field but less pure" is often the source field. Have you searched the site for other Q&A about this? What have you learned from those and what specifically seems unanswered with respect to your particular circumstances?
    – Bryan Krause
    Jan 5 at 19:02
  • @BryanKrause I mostly found questions about going the other way, i.e. physics after mathematics. Those that I did find about going from physics to mathematics were about master's programs rather than PhD programs, or things like taking an additional master's. I don't think they addressed going directly from a master's in theoretical physics to a PhD program in pure or applied mathematics. I might be using the wrong key words in my searches though.
    – ummg
    Jan 5 at 19:34
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    I'd guess you'd be welcome in many doctoral programs in math in the US. You'd have to take a few advanced courses, perhaps, in order to pass qualifying exams.
    – Buffy
    Jan 5 at 20:04

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