thanks for the reply!
I was unaware about this issue of taking courses, I always thought that one could just come to the program and take the 'qualifying exams' (had they taken the courses in another university). But yeah, it makes total sense that courses cannot be counted twice.
[However, in the hypothetical case where somebody has done a master degree and has seen all the important graduate courses of their subject of interest... if they start the PhD in said subject and there are no other courses to be taken (because, e.g. (s)he is doing the PhD in the same institution of the master), the supervisors cannot expect the student to take random courses just to fulfill 'credits', right? - I guess not.. and maybe that's one of the reason in America a lot of people jump from bachelor to PhD.]
thanks for your reply!
My area of research is algebraic geometry, more concretely my thesis will be about Deligne conjecture in the setting of higher algebraic structures -e.g. monoidal categories. And I'm based in Bonn. That said, there is not that much derived algebraic geometry going on in Germany. Sure, there are mathematicians working on this stuff, but DAG is as huge as AG itself, and I would be more interested in working in some topic concerning deformation theory (hence Deligne conjecture). There are other countries in Europe where DAG has had more impact, so I'm also applying there.
I see your point on students having already seen the subject previously (as a way for schools to weight students' applications). Even though as you may know, in Europe, a bachelor takes normally 3 years; thus forcing students who want to do a PhD, to first take a masters to specialize. In which case, if someone wants to do algebraic geometry, they will have to work with hartshorne/qing liu to at least learn about sheaf cohomology and all that jazz. So that's where my confusion was coming from, as to why master students need to take more courses during their PhD. But MathCat already stressed this point, so that's okay.
At this moment though, I may be more inclined to just staying in Europe though. Hopefully I can land in some of the PhD positions I have applied and, if not, it is perhaps better to stay at my current university.
Because in any case, even if I were to go do the masters in Canada, admission to their PhD is not certain afaik, right? So after a year there, I could end up worse than now. Overall, I don't think it's worth the risk.
(At least that's how I personally see it now, but I wanted to ask here to make sure I wasn't just 'chickening out' of going into the unknown in Canada and then missing out on a good opportunity -I mean, the funding is very high compared to what I'm earning right now, but I still can pay for everything with it.)
Also, the deadline for answering their offer is coming up soon, but I will probably not have heard from the European unis by then.
Thanks again for your comments! (and sorry for my rant)