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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.