Mathematics for physicists

I was thinking of double majoring with mathematics to complement my bachelor's in physics, but this would end up extending my graduation by a year (two semesters), cost more tuition over my financial aid, and make me double up/ add another class onto my normal fall/spring credits. Would I just be better off studying more mathematics on my own time during the summer to be better prepared for graduate school? If anything I'd love to study both in graduate school but I don't really think I can juggle both at this point of academia. Again, just for my bachelor's.

Are you doing theory or experiment?  Experimentalists don't require that much crazy math.

I don't think you should delay graduation by a yr...

>>2
Either. I see myself in labs doing research and such, but if I can balance both in graduate school, probably theoretical. My university's highest required math for Physics is differential equations. I guess I can do a math minor and only have to take linear algebra and a higher upper level one.

I plan to just get names of the textbooks from the mathematics catalog and during the summer just go over some of it myself if I don't get REUs. I just want to be best prepared for graduate school.

>>3
An undergrad physics degree is your best preparation for grad school.  None of the upper level math classes I've taken have been crucial.  You've taken diff eqs (I assume with proofs and stuff), so you're probably already ahead of me.

real analysis - I understand limits/calculus better, but useless
complex analysis - supposedly useful in QFT, but I haven't had the need to do contour integrals yet
numerical analysis - vaguely enriching, but useless
linear algebra - how did I pass this class?
abstract algebra - some use in QM/QFT, but physicists are interested in representation theory, which mathematicians completely ignore

>>4
As an undergrad, I've been lectured by at least two eminent mathematicians whose area of interest has centred strongly on Representation Theory. Maybe the mathematical community as a whole has disdain for it, but there are plenty of competent guys doing work with it.

>>4
>representation theory, which mathematicians completely ignore

Modern number theory is all about representation theory.

http://en.wikipedia.org/wiki/Langlands_program

>>4
I'm doing a rep theory course as an undergrad.

Fucking thing seems so easy and so hard at the same time :(

>>5,6,7
I was a bit too hasty with my words.  Apparently, there is some mathematical research into rep theory (not surprisingly), but the physicists are incredibly close minded in that they only care about 1 representation.  ie groups -> matrices...