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I'm a non-EU resident and I want to pursue a PhD in pure math in Germany. I am currently in the process of writing to as many professors in my field of interest (functional analysis) as I can requesting that they take me as a doctoral student under their supervision.

I don't want to do research in the same area that I specialized in during my masters education (in fact, I want to switch from algebraic geometry to functional analysis). My question is how can I convince someone to take me on as their student if I'm making such a big leap and hardly have a clue as to what research in functional analysis entails? Professors naturally look for students that are already very familiar with their research area and don't need much training before they start working.

Usually when I email a professor requesting them to take me as a student, I attach a short CV (not that impressive either) and transcripts of my masters education. I don't have a research proposal for them and I feel that's hindering my likelyhood of getting an acceptance letter. I'm sure I'm not the first student with this problem and people in my situation do get admitted into a PhD program doing work unlike that which they did during their masters so I was wondering how do I become one of those people?

Thank you for your help.

@PaulGarrett: Since I can't comment below, I'll clarify here: I have some research experience in the area of fixed point theory (which is close enough) working as a research assistant for a professor in our department. I can get a reference letter if there is a need. I don't have a paper published, however, but I did learn a lot and so this is how I believe that that's what I want to work on. I of course realize that saying I've read a few articles and enjoy the work is one thing but convincing someone to pay me for 3/4 years to do some work in this area is something else, but that's all I can say and I can sense it doesn't really sound very convincing. I hope my situation isn't so hopeless that I either have to force myself to learn to enjoy algebraic geometry or start again with first getting another masters degree.

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    If you hardly have a clue what research in X entails, how are your confident at all that you want to do it? The people you're applying to will wonder the same thing. Just having the experience of studying Y and deciding you don't want to pursue it further is not an argument in favor of X... Clarify? – paul garrett Jul 31 '18 at 18:47
  • @paulgarrett The OP can't comment, but edited: "I have some research experience in the area of fixed point theory working as a research assistant for a professor in our department. I don't have a paper published, but I did learn a lot and so this is how I believe that that's what I want to work on." – aeismail Jul 31 '18 at 20:07
  • @aeismail, ah, ok. This should surely be edited into the question... is it pending approval, or something? – paul garrett Jul 31 '18 at 20:35
  • @paulgarrett Someone's tried to reply twice through suggested edits (1, 2). ...ohhh, I see, the OP's an unregistered account. OP, can't you just use your account to edit or comment your reply? – Nat Jul 31 '18 at 21:27
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    The professor you worked with seems like a great resource to ask exactly this sort of questions. That person might also be able to help you make contact, since they might know some relevant people. – Tobias Kildetoft Aug 1 '18 at 6:32
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I work in computer science, but I think it doesn't matter in this case.

Please don't think it's a stretch to say that, but how do you achieve attention of someone on an online dating site? That's right: by standing out. As a professor, I get occassional emails from prospective students. They differ a lot in terms of content, language and attitude, so they make very different impressions on me.

There is no, and there can be no universal rule: people are different, and it is not possible to give a recipe that works for everyone. Some professors are simply not interested in getting new students (it's a "load"), and thus won't reply positively regardless of the quality of your mail.

For me, "a request, a CV, and a transcript" looks like something that you send in bulk, to dozens of people. Why should I react? Basically, I treat any bulk mail as spam. Yes, I get it: as a student you might simply want to enter a certain resonable university and study a certain field you want to work in. But what should be my (professor's) motivation to support this endeavor of yours? It is a commitment both for you and for me.

What works for me is when people are genuinely interested in my research project, and they wish to support it, so they will be not just a burden, but my assistants. Fake interest ("I am very impressed by your work and want to be your student") is easy to spot, BTW. I have no interest in studying random people's CVs and transcripts; if I wished to do it, I would work in HR.

Bottom line: connect what you already studied with something that you want to study, think how to present your previous experience and obtained knowledge as a valuable asset for the prospective professor's lab. Find a person who does something that you genuinely like. Read his/her research papers (i.e., do your homework), try to propose a possible direction for your studies. Try to be a collaborator, not a burden.

I must also say that things become more complicated when you need more than just "an approval". If people just wish to come and join our lab, it's different from asking to fight together for their scholarship, for example.

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