Math PhD application process I expect to be graduating with a maths BSc (with an honours year, in Australia) in the not-too-distant future. I’d like to pursue a PhD in pure maths, with the view of becoming a research mathematician. I’ve found it quite difficult to find information on what exactly the application process entails, and when I need to start worrying about it. I have some specific questions, but what I’m really interested in is if there’s a compiled source of advice and information for math PhD applicants internationally.


It seems that many universities have a specific (December in the USA) deadline, does this mean PhDs have to start at a particular time of year?
I see that occasionally people advertise a particular PhD position they’d like to fill, on some particular research topic. Is this kind of PhD different from the “generic” kind and have a different application process?
There are two main models of organizing doctoral programs:


The American system: graduate students proceed through a combined master's and doctoral program, usually starting with coursework, then taking some sort of "qualifying exam" to become doctoral candidates within the department. Admissions are handled at the department level.
The "German" system: doctoral candidates are employees rather than students. Candidates for a position must apply directly to the group of the professor who is sponsoring the project. There is no coursework phase, as applicants are expected to have already completed their master's degree. (However, they can "audit" courses if needed.)


I would suspect that these represent the "poles" of the spectrum; most other systems I'm aware of fall somewhere in between. [Note that even the German system is adopting some features of the American system, and is thus starting to become a hybrid.]