I'm a physics graduate coming out of a physics program that was so poorly structured and disorganized. In the last year and a half of undergraduate school, I developed a very keen interest in the applications of abstract algebra and geometry in constructing physical theories. I don't have a good background in mathematics, I've only taken calculus differential equations, and complex variables, but I'm studying more algebra and geometry on my own at the moment. My problem is that I don't know where to start and what roadmap I should follow to organize my efforts to make up for the lost time in undergrad school. What fundamental mathematics should I start with as a foundation? I studied linear algebra and some group theory and topology, but it all feels so disorganized. Should I have a strong background in real or functional analysis? What would I use that for? What other fields should I be familiar with?

I asked the question in Academia SE but it was closed and I was told that here would be a more appropriate place to ask.

  • $\begingroup$ This question was closed as opinion-based, because there surely is no clearly acceptable answer to it. Mathematical physics is more of a style of research than a topic of research, so it might be better to specify some topic you are interested in (e.g. Statistical Mechanics, or General Relativity, or some topic in Quantum Field Theory, etc) and then ask which sort of mathematics occurs in this topic of interest. This is way more objective to answer and has a better chance of being on-topic (although I'm not fully sure it would be). $\endgroup$ Dec 27, 2022 at 9:43


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