Is it possible to switch from physics to maths after undergrad?

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I'm currently a few months into my second year of a physics undergraduate degree, I enjoy it but I've found myself becoming increasingly interested in maths and unsatisfied with the maths we do in my degree, which doesn't involve any proof and isn't very in depth. I think I want to go into theoretical or mathematical physics as a career so obviously this is a problem. Additionally, I feel like I'm missing out on some incredibly interesting topics and it seems a lot harder to self teach that sort of maths than it would be to study maths and self teach physics (Im in the uk so there isn't an option to dual major).

I think its too late in the year to switch degrees (and I think i do still want to study some physics, just in a more mathematically rigorous way) and its probably very unlikely i'd be allowed to take any modules from the maths department in place of some optional physics ones. This leaves me at a bit of a loss as to what I should do, especially since a lot of the masters courses I've looked at for mathematical/theoretical physics require maths undergrad or physics with 'a substantial maths component'. There's also the concern that if I did manage to get accepted onto one of these masters courses i'd be significantly behind mathematically compared to others. I suppose I could self teach some maths such as real analysis, but I'm not sure how realistic this is to do alongside my current studies, plus id have no proof that I had successfully learnt such things since I wouldn't have sat exams related to it.

Does anyone have any advice?
 
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(1) Your icon is very similar to that of another member; you may wish to change it to avoid confusion.

(2) Whether this is possible is something institution-dependent. You can find out better than us.

(3) Of course changing your degree focus will cost you time. How could it possibly be otherwise?

(4) Suppose you switch and get your PhD. How many permanent positions open up per year in the part of the world in which you want to live? If you shoot for such a narrow target, what happens if you miss? If five positions open up per year and you're the sixth best student, then what?
 
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There are many hidden questions in your report. My personal opinion is, that mathematics and physics are primarily different languages. Since you already learned the physical language and a double major isn't an option, you could either move to the continent or finish your study of physics in the UK. Oops, I forgot that you left the EU. That makes it harder to simply change to a university on the continent. However, I would recommend to finish your study where you are anyway.

Mathematics. I know there are dozens of exams inclusive solutions of various standard courses in mathematics on university servers throughout Europe. So having feedback per exam is a matter of the right search key and self-discipline, rather than a matter of opportunity. Those servers also host lecture notes as many as you have time to read. So even money or expensive textbooks aren't an issue, although I prefer good textbooks over pdf. In that case, it is important to figure out whom you can trust for recommendations. I like the GTM series.

Mathematics. You mentioned "real analysis". However, there are a few very different approaches to analysis. They vary from standard calculus courses to perspectives based on measure theory and sigma algebras. Since all of it will be outside of your major field of study, it is completely up to you - and probably up to the amount of available time - which approach you prefer.

In any case, you should answer yourself a few questions before you take any action:
  • What do you want to learn in mathematics?
  • Why do you want to learn more in mathematics than you already did?
  • How much time and money do you have to pursue this goal?
  • Will it have to pay out in terms of your career choices?
These are important questions because you always have the alternative to study mathematics as a hobby.
 
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