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