I'm going to apply for a PhD in Mathematics in Europe with my BSc and MSc in Mathematics and Applied Mathematics (respectively), from two top-tier (say, top 10-20) US universities with advanced courses, and good GPA. Neither of my BSc and MSc had a thesis component though, and a capstone project wasn't available to me.

I do have some research experience, but my research mostly involved computational programming and data analysis, not serious Mathematics. More importantly perhaps, none of my research experiences were independent research, meaning that I was working on a project defined by my supervisor and my work was pretty much directed by my supervisor.

I'm aware that the norm in Europe is that students write a substantial thesis for their Master's degree, and possibly for their undergrad too, and then they'll apply for PhD. I did want to do a 2-year Master with a substantial research project, but since funding was an issue, I went with the 1-year MSc program that would fund me, and that one didn't have any thesis.

Given this situation, I'm looking for a way to fill that gap in my resume to make myself competitive for a top-tier PhD in Mathematics (or Applied Mathematics) in Europe.

First - do you think I'd have any chance without doing some sort of independent research before applying to a PhD?

Second - do you have any suggestion on how I can fill that gap?! I thought of doing an MPhil or an MRes in the UK, but financing is an issue for those programs (I'll apply for scholarships, but chances are high that I won't get one). Is there any sort of program where I can just spend some time doing a self-directed, but supervised, research in Math and get paid for that?

Edit: As for the specific countries in Europe I'm looking for, my top choices are Germany, Switzerland, UK, and France, but I'm open to other options if I find a good opportunity.

  • Regarding the study in Europe, you cannot enter a PhD program without a thesis in your Masters in prominent universities. There are 1.5 years thesis based degrees also. One option seems to be to get into a tuition-fee free university. Another option is to get into a structured PhD program. But, that won't be good for your future career. – user84565 Aug 10 at 6:24
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    Europe is a big and diverse place. Do you have specific countries in mind? E.g., for Germany, you should first check if your master actually qualifies you for a PhD position. E.g., I just quickly checked for Heidelberg University (picked at random) and they require that you do courses from their Master's program during your PhD if you have a one-year master instead of a two-year master. I didn't see a hard (or any) requirement of a Master's thesis. – Roland Aug 10 at 6:25
  • @Roland, Heidelberg Uni doesn't have PhD in Math. – user84565 Aug 10 at 6:27
  • @yahoo.com Maybe not in pure maths, but mathinf.uni-heidelberg.de/promotion.html – Roland Aug 10 at 6:30
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    @yahoo.com I'm not even sure what you are talking about. A PhD in Germany is generally not a "course". I'm not aware of any university where speaking German is a hard requirement for becoming a PhD student (with the obvious exceptions such as German language studies). – Roland Aug 10 at 6:40

First - do you think I'd have any chance without doing some sort of independent research before applying to a PhD?

Possibly. However, it would likely involve you finding some "angle" on the basis of which you can strike up a relationship with a prospective supervisor, who could promote/sponsor your Ph.D. candidacy.

But there's a deeper issue here:

Why do you want to enter a Ph.D. program?

Hopefully, you have some subject you are interested in studying. If that is not the case, and your motivation is to simply get the title and the piece of paper - then you should seriously reconsider. Working on a PhD without focused motivation is not just exceedingly difficult, but also exasperating. You may well find yourself in the middle of it, two or three years from now, grabbing your head by your hands and asking "What was I thinking? Why in blazes am I even doing this?" - and not having a good answer.

So, do consider some independent research, or even going into industry doing something you are interested in, but with a mind to sketch out relevant mathematical challenges to study more deeply in academia. These are my suggestions for filling the gap.

I thought of doing an MPhil

No, no no. Academic experience isn't a collection of degree tokens, in which you can substitute with less-fitting tokens. You can very well go studying philosophy, but don't do that unless you're interested in philosophy per se. Also, it won't help you much in becoming a Math Ph.D. (unless you'll do research that has philosophical-ontological aspects, which is possible I suppose but pretty rare).

my top choices are Germany, Switzerland, UK, and France

Once you find something relevant to research, locate relevant research groups in that field (in those countries or elsewhere), and talk to them.

I can only speak for Germany, but maybe the answer is transferable to the other mentioned countries as well.

Usually, Bachelor and Master in Germany should sum up to 300 ECTS (10 Semester, 5 years) as a pre-requisite for a PhD (well, in fact "Dr." ;-) ). In most cases, universities are having specific rules if you don't have enough ECTS, and since you are not from the European Union, you will always have to ask how your specific case will be treated.

So I would suggest to

a) choose a research group which you would like to join (e.g. by looking for open positions)

b) If they are interested in you, ask the PI / supervisor about the regulations and for support

c) ask the administration about your specific case.

It will be much more important to convince the potential supervisor to believe in you even without a thesis (since they will pay you for your work in a project) then sorting out the formal stuff.

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