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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.

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Hello, Kurome: Welcome to Academia.SE. There are a couple of issues here that will likely prevent you from getting useful answers here. (1) You're asking two questions here, and should preferably asked separately. (2) The first question is too specific—questions asking for guidance on individual research projects are off-topic. The question "Can I do research in a field I haven't taken a course on?", however, would be on-topic here. –  aeismail May 24 at 15:36
    
I have deleted the second question part, and I believe I'm effectively asking only the "Can I do research in a field I haven't taken a course on?" question now. –  Kurome May 24 at 15:44
    
Like I said, you can ask the second question on its own. Also, I've edited the title to make it more reflective of the question now. –  aeismail May 24 at 16:15
    
I started my research project before taking any classes on the topic. If necessary, you could always take any relevant coursework after you begin the project. That's what I did. –  Mad Jack May 24 at 18:59
    
Rather than being under the impression that somebody's going to talk to you about something, and panicking that they dont -- open the conversation yourself! Professors are pretty smart but they're not psychic. –  David Richerby May 24 at 20:32
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To answer your question: it depends on the department and if you can find a supervisor.

It being a graduate level course or topic just means it may involve more work and the same is true for not having taken a formal course in it. If you do not mind the extra work (you shouldn't imho) it is no problem at all. However, there are two questions left: Is someone willing and able to be the advisor for that topic? Is the research question suitable for your undergrad thesis?

So, talk to your (potential) supervisor about it.

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Well, turns out I was just thinking too much by myself. The professor is willing to advice me as much as he can, and I confirmed it by actually initiating to open the topic to him. –  Kurome May 28 at 15:10
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Of course you can! (I did. My advisor did. Most of my students did.)

Someone will have to agree to supervise your research, but that's true even if you have taken a course in your proposed research area.

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