Surprisingly, the university (a major tech school) I attended does not offer a mathematical physics class. Consequently, I often get asked by my physics friends what are some good math classes to take to help them in their studies. The problem is two fold. One, I haven't taken more than the minimum physics classes required for a degree...so I can't say I have been exposed to much. And secondly, a math class often covers significantly more than is required; consequently, I am hesitant to suggest taking a full course over self study.
So rather than telling me a generic course physics students should take (e.g. complex analysis), can you tell me what specific topics (e.g. of complex analysis) have utility in physics (of any level). Moreover, can you explain the utility of these topics in the context of physics? The more specific, the better. It would be cool if this could become a repository of information I could point said friends to.
It may be the case that one has to take a whole math class to understand the topics you suggest. However, I believe that a specific list of topics and corresponding uses in physics provides significant motivation to take such classes. Apologies if this is a repeat question.