To pursue a masters degree in theoretical physics

[Chri]

Hello, I'm about to start my last year of bachelor degree in physics, and in a few months I would like to have a clear idea of where I want to go for my master degree.

My dream since I started university is to pursue theoretical physics, in which specific field, that remains for me to definitely decide. I know it's a vast field and maybe not much can be said about it in general, but my problem is more specific: after two years I've taken two semesters of linear algebra, four of analysis, some numerical analysis, an introduction to probabilities and statistics and that's about it for the pure math courses. Looking at my third year I see nothing but physics courses (which, one could say, is normal for a physics degree).
My question is: where is all the math? Where is the all important differential geometry and tensor calculus for GR? And group theory and Lie algebras for QM? My university doesn't offer any more pure math courses during the masters degree in physics, despite offering GR and things such as relativistic QFT, courses that I feel I'm nowhere near being mathematically ready to follow.

I feel like I'm stuck on a track that will bring me towards something I wasn't really aiming for. We got lots and lots of lab hours and handwavy general physics which didn't really thrill me.

I'm starting to think that maybe I'd have been better off with a mathematics bachelor degree to have a serious shot at theoretical physics, back when I started I was way too afraid to try a double major, and I didn't really know if I had any mathematical ability, which I now think I have.

What should I do? I should point out that my uni is a relatively good one even worldwide, I would be surprised if it were to let me down that bad, maybe I misunderstood something? How do these things work usually? Should I hurry and sign up for additional math courses right now or trust the academic organization that it'll somehow work?
Thanks for your help.

 

[protonsarecool]

I'm in the second year of my masters in theoretical physics myself, and will follow it up with a PhD in the same institute (i'm in Germany, so M.Sc. is required for a PhD).

Anyway, the professors for these advanced courses will include the math needed for their intended rigor in the course, but this level of rigor varies a lot with each prof. For example, the GR sequence at my institute is always being hold by the same guy, and he constructed the sequence in a rigorous, but still introductory style. In the first semester, it starts with the typical coordinate-based style, ie. index battles and "tensors transform as ..." stuff, whereas in the second semester he does it all again, but in the modern mathematical viewpoint, ie. (co-)tangent bundles, differential forms etc...

On the other hand, some other professors completely ignore all the math of the last century and replace it with handwavy calculations. They won't tell you about complex line bundles and connections when talking about gauge theory, and they will talk about "infinitesimal generators" instead of Lie algebras. This is not necessarily bad, since they can get through a lot more physics during the course this way. But it can be extremely frustrating to the more mathematically inclined students.

There is, of course, always the possibility to take more pure math courses directly from the math department, and bring them in as electives. There are also regularly advanced math courses for physicists from the more math heavy physics profs, like "Lie groups for physicists" or "differential topology in physics".

To summarize, the advanced physics courses will include the math to the level it is needed in them. How much math that is depends on the prof., which can sometimes be frustrating if their mathematical sophistication does not match up with yours. In that case, you will have to do the extra work, eg. by self studying or by taking electives from the math department.

 

[Chri]

Thank you for your answer

I'm in the second year of my masters in theoretical physics myself, and will follow it up with a PhD in the same institute (i'm in Germany, so M.Sc. is required for a PhD).

Congratulations! I'm in Switzerland, so the same applies (don't try to reply in German though, I don't know the first thing about that).

Anyway, the professors for these advanced courses will include the math needed for their intended rigor in the course, but this level of rigor varies a lot with each prof. For example, the GR sequence at my institute is always being hold by the same guy, and he constructed the sequence in a rigorous, but still introductory style. In the first semester, it starts with the typical coordinate-based style, ie. index battles and "tensors transform as ..." stuff, whereas in the second semester he does it all again, but in the modern mathematical viewpoint, ie. (co-)tangent bundles, differential forms etc...

On the other hand, some other professors completely ignore all the math of the last century and replace it with handwavy calculations. They won't tell you about complex line bundles and connections when talking about gauge theory, and they will talk about "infinitesimal generators" instead of Lie algebras. This is not necessarily bad, since they can get through a lot more physics during the course this way. But it can be extremely frustrating to the more mathematically inclined students.

There is, of course, always the possibility to take more pure math courses directly from the math department, and bring them in as electives. There are also regularly advanced math courses for physicists from the more math heavy physics profs, like "Lie groups for physicists" or "differential topology in physics".

My doubts really started to worry me when I spoke to a mathematician I know, he told me that this math integrated in physics courses is mostly non rigorous quackery and his physicists friends don't know the first thing about serious differential geometry and other advanced topics in mathematics. This view was supported by a physics PhD student who has done a double math/physics bachelor. I suspect they were just being, pardon my French, a little cocky, and probably with all the rights to be, but I can't help but wonder if that's true, and real theoretical physicists have a math degree.

There is, of course, always the possibility to take more pure math courses directly from the math department, and bring them in as electives. There are also regularly advanced math courses for physicists from the more math heavy physics profs, like "Lie groups for physicists" or "differential topology in physics".
To summarize, the advanced physics courses will include the math to the level it is needed in them. How much math that is depends on the prof., which can sometimes be frustrating if their mathematical sophistication does not match up with yours. In that case, you will have to do the extra work, eg. by self studying or by taking electives from the math department.

I never saw such courses in the list for my universities or others I looked at, maybe I wasn't looking in the right place.
Self studying is a possibility I considered, but it's very resource consuming and you don't get awarded any credits, and your work isn't acknowledged by a grade that proves you followed that class, is that important?

 

[protonsarecool]

My doubts really started to worry me when I spoke to a mathematician I know, he told me that this math integrated in physics courses is mostly non rigorous quackery and his physicists friends don't know the first thing about serious differential geometry and other advanced topics in mathematics. This view was supported by a physics PhD student who has done a double math/physics bachelor. I suspect they were just being, pardon my French, a little cocky, and probably with all the rights to be, but I can't help but wonder if that's true, and real theoretical physicists have a math degree.

I think that's partially true. A lot of times, the math in physics classes is more on the handwaving side, and many students don't care about exploring the rigorous theorems and proofs behind the theory. And that's ok, there are many successful theorists who work mainly with "physical intuition" and handwavy reasoning about their non-rigorous calculation techniques. After all, they are still doing physics, and it is a valid viewpoint to care more about results and experimental validation than mathematical consistency.

On the other hand, there are also many areas within theoretical physics, which do require serious math and rigor. If you are more interested in that direction (i am as well), you will need more math background than provided in the bare physics education, either by self study or advanced math courses. I don't think it has to be a full degree though. I have taken almost enough courses from the math department during my bachelor and masters to get a B.Sc. in math, but i don't care at all about the remaining mandatory courses and seminars i would have to take to actually get it, so i probably won't.

I never saw such courses in the list for my universities or others I looked at, maybe I wasn't looking in the right place.
Self studying is a possibility I considered, but it's very resource consuming and you don't get awarded any credits, and your work isn't acknowledged by a grade that proves you followed that class, is that important?

I think it might be important if you plan to switch universities for your master or PhD. If you aim for a thesis advisor who is more on the mathematical side of theoretical physics, it won't hurt if you have a transcript of records to show your math background. Personally, i stayed where i also did my BSc. I'm currently about two months into my masters thesis, and my advisor never asked about my course background. I just told him my interests, and we looked together for a suitable topic.

To summarize, it will certainly be helpful to take additional pure math courses, but i don't think it has to be to the extend of a full degree.