To provide a background, I am currently a Physics major and along the way I ended up getting really interested in Mathematics, so much that I'm now planning to do pure math in graduate school. Now, the problem is that, we are required to do a senior's thesis before we graduate, and I still don't have a topic in mind.
I actually worked a little bit with a professor in Theoretical Physics, I did bits of grunt work under him. I got exposed in Asymptotic methods when I was in his lab, and I got the idea that maybe I could do an undergraduate thesis about/using asymptotics. During the time I was working there, I was under the impression that he'll eventually talk about my thesis topic but he never even mentioned it (to be fair though, I never talked about it to him either), so now I'm kinda panicking that I might end up going solo in my research.
Now, in the case that he'll not accept to advice me on this , my question is, is it naive to even think about doing an undergraduate research that mainly involves Asymptotic Analysis/Methods when I've never even taken a formal course in it? To make the odds worse, it seems it's a graduate level topic, I am willing self study it though.
I want to know just how far I can go with doing research in a topic I haven't formally studied in a classroom setting, it doesn't really need to be Asymptotics or anything, I just wanted to do something that's theoretical, and that's borderline math, just so I'd be forced to learn as much math as I can during my last year in undergrad. I figured doing research in applied math is the best area to do work on since I'm still a Physics major.
