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I'm a third year Physics & Mathematics student, and I want to work with a specific advisor. I have read almost all the related questions in this site and this blog post. However, almost all of them suggest the student to make a research proposal, or - sort of - a problem that s/he is planning to work in his/her Phd.

But, the thing is, I haven't had a chance to neither doing a self-study, nor taking a course in the field that I want to work on, though I'm very familiar with the basic concepts; I can easily read papers on the level of undergraduate.

In that case, how am I supposed to make -sort of - a research proposal, or suggest a problem that I can work on ?

I mean, for example, this last semester I took a graduate level Algebra I course, if I were to work on Group/ Ring theory, I could almost find fifty interesting research problems top of my head, but I'm not familiar with the actual problems in the field that I want to work on; I'm only familiar with general problems and general methods, and I don't want to look like "I'm interested with the field and to work with you, but I don't know what I'm actual interested in" in my email, so what should I supposed to do in this case ?

closed as off-topic by Solar Mike, scaaahu, user3209815, user68958, iayork Feb 5 at 15:54

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  • May you precise the reasons why you want to work with this specific advisor? Do you know if they accept PhD students? You might want to contact them saying why you want to work with them (1st question), asking them the 2nd question, and, if yes, if they'd be interested with working with you/what they'd need from you to consider your application. – ebosi Feb 5 at 10:12
  • Speak to potential PhD advisors (ideally face-to-face) and discuss your questions with them. – user2768 Feb 5 at 10:22
  • I'm sorry but @user2768 have you even read the question ? – onurcanbektas Feb 5 at 10:23
  • @ebosi so you are saying that I shouldn't mention any potential research topic to work on ? – onurcanbektas Feb 5 at 10:23
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    Ah, I see below this person is not at your institution. It was unclear to me why you hadn't taken a course with this person and did not offer to work on their projects as an undergrad vs. waiting until grad school. Makes more sense now. – Dawn Feb 5 at 17:12
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You may be giving yourself an unnecessary task. While I don't know the academic traditions specific to Turkey, for mathematics in the US it isn't normally necessary to propose a specific problem to a professor. It may be different in the physical sciences, such as the blog post you cite implies, but in maths you need only suggest a fairly narrow sub-field in which you want to work. Algebra is too broad, Group Theory, still very broad. But non-Abelian groups is getting you closer to a field of interest.

Your question suggests that you may have some insight into algebra since you think you can propose interesting questions. That is what you want to stress in your communication with a potential advisor. "I'm interested in this tiny field and think I have some insight into the inner workings there."

Research problems in mathematics don't come out of the blue, they come out of study of other mathematical things and questions that arise there. They come from asking "what if". What if I drop an axiom? What if I change this definition?

Topology, for example, as a field suitable for deep study, came out of focusing on a particular aspect of Analysis (open sets), and then generalizing. But that came out of studying analysis, not just proposing something unrelated to other mathematics.

One great way to come up with research problems in mathematics is to attend research seminars led by the potential advisor. Take a lot of notes. Ask a lot of questions. What is known? What isn't known? What is related? What if we change something just a bit (generalizing or specializing).

But for the initial contact, it is likely enough (here anyway) to express that you have narrowed the field of study to one that is feasible to explore more deeply.

  • Thanks a lot for the answer; I wish I had an insight about the field that I actually want to work on as much as I have on Group/Ring Theory. The field is general Nonlinear dynamics and Chaos, and there are lots of interesting subfiles; such as quantum chaos, turbulence etc., and he is interested in all of those subfield, but I haven't narrowed myself down. I mean I'm like child in a candy shop; I want all of them :) – onurcanbektas Feb 5 at 13:38
  • By the way, the advisor that I'm referring is working in US. – onurcanbektas Feb 5 at 13:39
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Just try to open a conversation with the fellow. It is not an expected thing for every new grad student to have a research problem. For all you know, the fellow is looking for students or wants them to work on what he wants them to (this is very normal).

Sure, there is nothing wrong with developing your own research proposal and it is an act of independence. But I really wouldn't put it in your head as a requirement or the norm (whatever those blog posts say).

It would help if you would examine why you want to work with this fellow in particular. If you and him interested in same scientific subfield (fluid dynamics, star spectra, whatever) than surely that is a point to open the discussion between you two.

If it's for some other reason than I wonder if your motives are correct (there are a lot of professors that are nice, have funding, get people jobs, etc.) But really I don't know. But it sounds peculiar to be so fastened in on one guy already.

In any case, I would emphasize to look at more than one school or one professor (even if you want to study physics of crocodidle bites and this is the only guy publishing on it). Profs sometimes lack funding or don't like you or turn out to be jerks or what have you. You need to have options.

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