2

Maybe this is a question that should be posted in Academia StackExchange, but since is a question about a Ph.D. in Pure Mathematics I think that people that work in mathematics will be able to give me a better answer, so I have decided to post it here. Let me know if this is not the correct spot, and if so I will remove it.

I am starting a Ph.D. this year and I am a bit concerned about how prepared I am and how much is expected from me.

I assume that during my Ph.D. I will have to prove new results in the topic that I am working on. I have already done this for my Master's Thesis but in that case, I felt that my supervisor was constantly helping me. In the sense that whenever I was stuck he told me what to prove and how to do it and I just needed to work out the details.

I suppose that in a Ph.D. the supervisor is there to give you the guidelines on what you should read and how to get to the final goal but you are alone on the way. Here some questions arise:

  1. What is expected from a Ph.D. student in his first year? There are obviously some clear things like working a certain amount of hours, publicizing a number of papers, and in some cases also teaching or being a teaching assistant. But I am talking about what is expected in regards to researching. I mean, are you supposed to do everything by yourself in your research. If not which parts are you supposed to do on your own?

  2. Is there any systematic way to approach a mathematical problem? I would think that this is similar to what you do on your bachelor's and master's degrees when you are given a problem set: you read and understand the bibliography about the problem that you have and hope that some idea comes to your mind. But is there a more systematic approach?

  3. When you are stuck in a problem, what type of help are you suppose to get from your supervisor?

Thanks in advance.

Gillyweeds
  • 471
  • 3
  • 9
  • 4
  • Depends entirely on the institution. You should consult the institution in question rather than the public at large. 2. You are already describing a "systematic way to approach a problem." 3. Depends on what type of problem (homework? Take home exam? Seminar presentation? Research?) and the expectations of the institution and the individual supervisor. Neither 1 nor 3 are appropriate for the public at large: they vary too much.
    • – Arturo Magidin Sep 28 '21 at 18:18
  • 4
    This is far too broad. Obviously, PhD work, and advisor relations, differ considerably from student to student, and from institution to institution. These are conversations you should have with your advisor, or with any candidate advisors. – lulu Sep 28 '21 at 18:19
  • 1
    Everlasting Fealty – Will Jagy Sep 28 '21 at 19:29
  • You seem to have a mild case of mathematical anxiety which can't be treated here. If you end up feeling that you are like a caged obedient serf, fed on the mathematical scraps from the high table, remember the invisible college. – James Arathoon Sep 28 '21 at 19:49
  • 1
    @Gillyweeds : When you are stuck on a problem leave it for a while and do something else. It has been discussed amply in similar posts that you will need most of all a high tolerance against frustration. If there were a systematic way of solving all math problems that field would turn into something totally boring. – Kurt G. Sep 29 '21 at 09:19