Recommended Advanced Math Courses For Undergraduate Leading to Physics Grad School

nicholls

Hey guys, this is my first thread here, and I have a question about courses to take during my undergraduate.

I am currently in Engineering Science at the University of Toronto, in the physics option (so basically eng phys). I am going into my third year and I have a large degree of flexibility now in choosing my courses. I am currently planning on going to graduate school in Physics (or a very closely related field) at a fairly prestigious school if I can. I am unsure of the particular field of physics I want to go into right now, but it is most likely in a more "modern physicsy" field.

Anyways, I have the option of choosing some advanced math courses for third and fourth year such as:
Groups and Symmetries
Real Analysis
Complex Analysis
Polynomials and Fields etc.
PDEs (this is a core course so I'm 100% taking this)
etc.

Basically I have two questions:
1) should I consider taking these advanced math courses over more practical and applied physics/engineering courses?
2) if I do take these courses, which ones would be most useful to learn during my undergrad (rather than having to pick up later)? ie. are there any math courses that are almost a necessity for any sort of physics
*the courses I listed aboved are just examples, you can elaborate on topics I didn't mention

The reason I am asking this question is that I don't want to take all applied courses in my upper years, get into grad school, and all of a sudden be lacking in the mathematical tools. At the same time, I don't want to spend my undergraduate learning advanced math, as that does not really help me decide what I want to do once I go to grad school. A mixture is probably key, but I need to prioritize in this case.

Your help is appreciated.

Kevin_Axion

If you want to go to graduate school in physics why didn't you just get a physics specialist or math & physics specialist degree. Engineering science makes it a lot more difficult.

EDIT: Lol, I didn't even answer your question. PDEs and complex analysis (Groups and symmetries is good for gauge theory) should be good but what is it that you want to study exactly?

nicholls

Because when I was applying for my undergraduate I had no idea whether I wanted to be an engineer and work in industry or pursue physics or math and work in academia/research. I chose one of the hardest if not the hardest programs I could find in Canada, which also offered me both an engineering degree and the option to take what interested me most. This program has opened a lot of doors for me, and for me at least, is a hundred times better than a physics specialist would have been. I am at the top of my class and in no way concerned about getting into an at least decent graduate school. But this isn't about what decisions I've made in the past, so please stay on topic.

Not entirely sure right now. I've read books on string theory, quantum gravity, looked a papers on quantum computing etc. etc. Everything looks interesting, but I need to take courses similar to these types of things for me to really know what I like. Hence, the reason I posed the original question. I want to maximize the number of courses I can take which will help me make my decision while at the same time not losing out on the benefits of taking math courses in my undergraduate.

In terms of complex analysis, what is it used a lot in? I talked to a physics professor on the idea of taking complex and he said it really isn't used a whole lot. He said there was really only one important idea (I think it was contour integration but I'm not sure) and that I could teach this myself easily. This may have only really applied to his line of work however, it would be nice to hear other peoples opinions.