> You can spend 2 years (not a joke) to get mathematics to prove Stokes theorem, in one of the more general versions. You're out of your mind. You don't need t

> You can spend 2 years (not a joke) to get mathematics to prove Stokes theorem, in one of the more general versions. You're out of your mind. You don't need to prove Gauss-Stokes in the general version to understand Maxwell's equations; you just need 3-d calculus, and you're done. Bike shedding the process further is silly: I could claim you don't really understand GR (or for that matter, E&M) without Hatcher-level understanding of Algebraic topology. All you need is the simple calculus theorem, such as is presented in Jackson. > For anything going into quantum field theory.... This is a rubbish argument: yes, you need more math to do quantum field theory. You also need basic quantum mechanics first, which is what I'm talking about for a self study program. If you want to go on to fiddle with QED, you can fool around with Itzykson and Zuber (and Griffiths book) later, when you actually know how non-relativistic QM works, and how relativity works. First learn basic Schroedinger stuff and something like S-matrix theory. Don't learn the shitty undergrad training wheels crapola; do the real thing. That's my advice in general. If you work your way through a differential equations book; there is no point in doing the intermediate stuff and a great argument (it's a waste of time; a make work program for physics professors, and a weeder for people with low dedication to the subject) for skipping it. FWIIW I was not a theorist, though I had some theory papers queued up on quantum dynamics. I think what everyone knows after first year of grad school is a pretty good basket of knowledge, which is why the 1st year grad school program is virtually identical everywhere in the world. It's like a gentleman learning Latin in the old days. There is a direct line from advanced calculus to completed first years of grad school physics; one which I outlined above. The imbecile make-work program of doing a bunch of intermediate problems in junior and senior year; it's really not worth it if you're an adult with a functioning cerebral cortex. Or if you're trying to pass prelims/GREs which test you on these subjects. Otherwise; skip it -do the important bits, and revisit the training wheels versions later when you need them. That's all.