So, I am an incoming MS student interested in going into condensed matter theory. I have always been more comfortable running C++ or FORTRAN simulations or crunching contour integrals than doing math proofs. I only gained the interest in CMT relatively late in my undergraduate career when I discovered what a horrible experimentalist I'd make(I'm hellishly clumsy), I began coding, and I took graduate level SS physics, meaning I didn't really have the time to go for a second degree in math. Thus, I neglected proof-based math courses throughout my undergraduate period and tended to instead learn stuff on my own, including in graduate level physics courses. This means while I am not completely ignorant about certain parts of "higher" mathematics that can be applied to physics-basic group theory, for example-I lack a truly rigorous background in things like algebra. Due to the rather unique nature of my upcoming years for a US student seeking a physics Phd, I will have the opportunity, if I choose to do so, to take undergrad classes in things like algebra, topology, and real analysis. I'm wondering how useful that would be. On one hand, you can never have enough math and I really do want to improve my mathematics skills. But I'm also wondering if it would be better to simply pick up the useful parts as I go by myself or in physics courses-my graduate CM professor says that he will be teaching a fair amount of differential geometry in class, for example. Graduate QM this semester included some basic group theory as we went through Chapter 3 in Sakurai that helped cement a lot of my self study. A lot of courses in pure math are going to have a lot of things that are irrelevant to physics, and I've never been a very proof-anal guy. That being said, I tried that as an undergraduate, and while it did work to an extent, I always felt somewhat lacking compared to many. I will confess that I'd rather focus on doing well in graduate level physics courses and if I have spare time, sharpening my computational skills. My research interests are relatively well defined for a guy fresh out of undergrad(I'm pretty set on condensed matter theory/computation), but I'm far from decided on what I'm going to do an eventual Phd thesis on, assuming (God willing) I get the chance to. I tend to lean towards strongly correlated electrons and many-body physics, which is very computational in nature, so I'm theoretically good to go for that. However there are branches of condensed matter theory that are more analytical-topological phenomena, for instance-and I don't want to be unable to understand or choose to do a Phd thesis in that direction, should I decide to do so. So, anybody got advice?