Hi everybody, I'd like to ask: besides your "calculus", "ordinary/partial differential equations", "complex numbers", "probability", and "linear algebra" that a physicist should be familiar with, what else should I study? My goal to studying this math is to understand my physics-graduate-course-core-material from as many perspectives as possible. For instance: - it seems in quantum mechanics, the wavefunction is part of the set of all functions that are square-integrable to 1, and that it is complex-valued. Would my understanding of QM therefore be furthered by...I think...a "real analysis" course? - Group theory also seems important. Therefore...should I study "abstract algebra"? - So-called "differential geometry" for general relativity, I think? - Are Lie groups/algebra/chickens important in physics? - ??? There are other examples I could give. Or, maybe I could study math on my own? Advantages to self-study: 1) My grad advisor doesn't want me to load up on courses, and I'm about 60% in agreement with him, knowing that I tend to bite off more than I can chew 2) I've discovered a few tricks and techniques to self-study that has made it easier (which I will be more than happy to share with askers) 3) in self-study, I won't be stuck considering "pathological" examples that are very far-removed from physical reality...like this Wierstrauss (sp?) function I just skimmed a Wikipedia article about 5 minutes ago that is supposedly everywhere continuous but nowhere differentiable. So yeah...my original question (to recapitulate): what specialized math is good for best-understanding the core-classes of physics that I will be crunching through in 1 month's time? For instance: I guess Arnold's "Mathematical Methods of Classical Mechanics" would be good for...classical mechanics. I think I just answered my own question (get math-books with corresponding titles!), but please feel free to make recommendations.