Doctoral Studies (PhD)
Traditionally, PhD candidates in Germany are not trained in standardised programmes. Thus, various possibilities exist to obtain a PhD in mathematics at RWTH Aachen University, loosely tied together by the Promotionsordnung (doctoral degree regulations).
In particular, there is not a unified application procedure. Usually a professor has one or more assistant positions in her/his institute at his/her disposal. These offer the possibility to do research but usually come with the obligation to fulfil teaching or other duties. In addition to that there might be some open positions in research projects funded by the DFG (German Science Foundation), industry or other organizations. All of these positions are usually managed personally by the professor.
You should definitely check the section on Faculty where all professors are named including contact details with the professors’ individual homepages for job offers. Moreover, you may write to any professor at any time to see if you could join their group in the near future. Please make sure to include meaningful resumes etc.
There are also graduate schools funded by the DFG, like the Graduierten-Kolleg "Experimental and Constructive Algebra", the "Aachen Institute for Advanced Studies in Computational Engineering Sciences" (AICES), or the Aachen-Jülich "German Research School for Simulation Sciences" (GRS), the research training group "Energy, Entropy and Dissipative Dynamics" (EDDy). While these schools offer their own doctoral programs, there is a lot of exchange between these groups and the mathematics department. You should have a look on the web sites of the mentioned graduate schools for the research being done in these programs and the application procedure.
During the doctoral studies there are no strict regulations on the amount of coursework the candidate has to do. Usually the personal research is considered the main source of mathematical qualification to be obtained. In addition to the doctoral thesis the candidate will have to take an oral exam, the content of which should be agreed upon with four different professors and should cover four different subjects. Thus it is advisable to attend some of the Advanced Courses and Seminars offered in the Bachelor's and Master's programmes .
In addition to the mathematical qualifications every doctoral candidate has the opportunity to enhance his secondary skills in the Center for Doctoral Studies (CDS). This programme offers courses in project management, professional presentation, personal development, foreign languages and the like. The goal of this programme is to improve certain job orientated skills alongside the subject-specific ones. The achievements will be noted in a performance record presented to the candidate along with his doctoral certificate. Further information in English is available in a Leaflet about the CDS (PDF). There are also possibilities for Financial Aid.