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I'm currently doing my bachelor's degree in mathematics in Germany (Heidelberg to be precise) and I'll soon be applying for master programs / grad school. I basically consider two options:

I) First do a master's degree and then a PhD in Europe and try to get a postdoc position in the US afterwards

II) Go to grad school in the US now and then look for a postdoc position in the US

Concerning I) I really like how math programs at universities in Germany (and other European countries) are structured and if I decide to stay in Europe for now, I will probably do my master's degree at Bonn. However, I am afraid that I'll have a hard time finding a postdoc position in the US having done my PhD in Europe, both because my experience (for instance regarding teaching) might not be what US universities are looking for and because European universities might not have as good of a reputation as universities in the US. I suspect, at least a PhD from Oxford or Cambridge might have some prestige in the US, however, I really don't like the 9 month master system there, as I feel like the material is rushed through and as I've heard, in order to get admitted to a PhD there, it is strongly advised to also do your master's there.

Concerning II) Since I prefer the European master/PhD system, for me to be happy with moving to the US now, it would be helpful to get a position at a top university. I already (successfully) did the TOEFL test but I would have to do the GRE (both general and math) test. Together with application fees this would probably add up to about 1000$ which is a hell of lot of money.

So I guess my questions are:

1) Are my concerns regarding I) justified? How hard is it for someone who just completed their PhD in Europe to find a job at a university in the US?

2) What is the reputation of places like Heidelberg, Bonn, ETH Zürich,... in the US? Is a PhD from Oxbridge prestigious enough for it to be worth it to overcome my aversion towards their program?

3) Do I even stand a chance of getting admitted to a top US program? I took a lot of courses and managed to score between 1.0 and 1.3 (if I looked it up correctly, this should be between 3.7 and 4.0 GPA?) almost everywhere. However I haven't participated in any REUs and don't have anything to offer besides the courses I took. Having read what people that got admitted to Harvard, Princeton, Berkely... have done prior to grad school, I don't think I can keep up with them.

4) Having said that, do you think it is even worth applying and spending such a huge amount of money in the application process?

5) Do you have any other piece of advice or experience to share?

Thank you so much for your help!

I think you should choose this based on personal preferences only. I see no career advantage either way. Bonn is a top level university by any standard as is ETH Zurich. You will find no feeling here that they are inferior in any way. Bonn, has, for example, several Nobel Prize and Fields Medal winners.

Whenever you do it, you will have to deal with visa issues in moving to the US, but you should have no academic problems with a good European doctorate. Language is unlikely to be an issue for any educated German today.

Not all postdocs require teaching, of course, or not a lot of it. Ability to advise grad students is a plus.

In comparison with someone who is completing a PhD in the US, a candidate who is completing a PhD in Europe will have a few issues to contend with in trying to get a job in the US.

1. Bringing you to campus for an interview will be much more expensive. Many institutions simply won't pay the travel expenses of interview candidates who are outside the US.




2. You won't have direct experience of the US higher education system, which can be quite different from systems in other countries. Teaching experience is generally expected of new Ph.D.'s in math and any teaching experience that you might have outside of the US is likely to be discounted as "not the same."




3. Someone who has completed a PhD in the US on an F1 student visa can work for one year (any discipline) or longer (Science, Engineering, Math) in the US under "Optional Practical Training" before having to get an employer-sponsored H-1B or J1 visa.

I got my PhD in Germany (Heidelberg) and then did a postdoc in the US. I think that was the right choice: In the US, you will have to spend a couple of years taking classes, satisfying your breadth requirement, and you will likely have to teach alongside your research. There is much to be said about this system -- including that it teaches you to teach, and that you get a broader overview of what mathematics is -- but it all gets in your way of doing research. On the other hand, in the German system, you will most likely have relatively light teaching duties (if any) and have time to specialize. This will help you find a research area, and it will likely mean that you are better qualified than many American applicants once you apply for postdoc positions.

What is going to be important is that you form the personal connections on the other side of the pond to get a postdoc position there. Postdoc positions are not just awarded by accomplishments alone -- much as we would like that to be the case -- but also based on who you know, who your adviser knows, etc. This is so because when you apply for postdoc positions, your resume is still relatively thin: A couple of papers, a couple of conference presentations. In essence, every applicant on paper looks equally good, and so things like what university you come from, who your adviser was, and what the letters of recommendation say all have influence. The biggest influencer is if you know someone at the university you apply to. In other words, build these connections: go to conferences in the US if you can, contact people there to see whether they want to collaborate with you, see if your adviser knows people there and can support you for a 4-week stay. All of these things are going to matter.

Second, see that you can teach a course for a semester. Almost all US graduate students teach courses, and postdocs generally have to do the same. As a consequence, having taught (and having letters of recommendation that speak to your abilities as a teacher) is a criterion that is often considered when evaluating postdoc candidates. Try to make the selection committees job easier by providing them something in this area.

Finally, make yourself knowledgeable about the application deadlines in the US. These days, they are often at the end of October or November, for appointments that start in August or September of next year, at the beginning of the next academic year. (One can think that that is crazy, but that's how it is.) Most applicants will not yet have graduated at the time they apply, hoping to graduate at the end of the spring (May) or even summer semester (August). In other words, don't wait until you have your PhD to apply for a postdoc position -- you might have a gap of nearly a year if you do!