I haven't started QFT yet, but will likely start using this book - https://www.amazon.com/dp/1107034736/?tag=pfamazon01-20 - sometime next week. I've read a little bit of it, and I like how he introduces tensors. Try checking out the local or school library and see one that has a mathematical...
While I'm not on any graduate selection committee, the man who wrote this is:
http://matt.might.net/articles/how-to-apply-and-get-in-to-graduate-school-in-science-mathematics-engineering-or-computer-science/
I found some of topology (but not the course itself) useful for some classical mechanics. Notions of open balls and compactness are nice. I took topology without real analysis, but I wouldn't recommend it; it was rougher on me than the other students who had seen a lot more proof-based math...
For context: I'm an undergraduate as well. A good way to get a decent CV is to find a sample (Google/Bing would be useful here, or ask a professor) then start basing yours from that. The Owl at Purdue website has some information regarding writing CVs as well.
As far as descriptions, it...
You should definitely take linear first. Fourier, Legendre, and Bessel functions are all cases of orthogonal functions. Understanding a basis at a more fundamental level will help you understand when you see infinite series of these functions when solving PDEs.
Looking at grad school shopper I found U Wisconsin has MS and PhD programs in engineering physics. http://www.engr.wisc.edu/ep/ep-academics-graduate-programs.html
If you are looking more along the lines of EE/Physics, I believe that electrophysics programs are designed to be somewhere between...
I found this website indispensable when learning analog circuits for guitar effects: http://sound.westhost.com/articles.htm I imagine it may be of some use for the non-audio nerd.
Edit: For books, try flipping through the library books (local and college) until you find something that suits how...
I feel like metric spaces might be a bit much for you since you're in calc II. They're awesome, and a great (and useful) property to have in a topological space, but probably a bit advanced for calculus II.
Applying calculus to probability theory will be cool, and you'll see it again in thermal...
If you have to take both, take discrete first. Linear is a little better when you're more "mathematically mature." Both will help give you a flavor of what you'll be doing as a math major. Although, the material of linear is more directly applicable to physics. Discrete is used to understand...
I would recommend at least a little bit of real analysis as suggested. I'm taking a point-set course (with the Moore method) now and I am the weakest student of 4 as it is my first pure math experience since the introduction to proofs class. The course from which this class was cloned had real...
How comfortable are you with exponential, logarithmic, and trig functions? Can you deal with logarithms and exponential in any basis? What about when the base is e? Can you shift a trig function? Can you shrink or dilate the period of a trig function? Those are the big ones from pre-calc that...
I have Frankel's text. I flipped through it to skim certain material; my general impression: if you can gain insight from just mathematical expressions , then it is great. I like a little more exposition myself. It is a better reference text once one has learned from a more accessible text.
I had a course with Anton and I really liked it. I know we didn't cover as many theoretical things in linear as I'd like. If your linear for physicists course covered everything you mentioned for linear, I would vote for the introduction to proofs class. If you didn't do all of those mentioned...