Analysis - Master programme and Doctoral programme

In the Master's program, "Analysis" is one of 7 main areas of specialization. If this is the chosen main area of specialization, there is a compulsory module group of foundational courses. (The further modules of the Master's program can be divided between courses from the chosen area of specialization and courses from other areas of specialization.) The basic courses in the area of specialization "Analysis" consists of the following compulsory modules:

• The module advanced functional analysis deals with the theory of locally convex vector spaces. Moreover a deeper representation of bounded and unbounded operators on Hilbert spaces is conveyed. Another lecture course in this module is devoted to Lebesgue integration theory and the foundations of Fourier analysis. 
• The compulsory module advanced complex analysis deals with advanced topics of complex analysis of a single variables, culminating in Runge's approximation theorem and  the Riemann mapping theorem.
• In the theory of partial differential equations methods of functional analysis are taught for the approach of different aspects of differential equations.
• On the one hand, in the module "Seminars: Analysis" you have to complete the introductory seminar on one of the lecture courses advanced functional analysis, advanced complex analysis or theory of partial differential equations (further introductory seminars can be chosen as advanced courses, their attendance is in any case highly advisable). On the other hand, you have to complete two seminars. The offer of seminars in the area of analysis is various, a coordination of the seminars with the area of the Master's thesis is advisable.

The offer of deepening courses for the Master's program is closely linked to the research interests of the faculty members in this research area. It comprises lecture courses from the areas differential equations, functional analysis, complex analysis, distribution theory and generalized functions, harmonic analysis, global analysis, stochastic calculus, and variational calculus.

There are research groups pertaining to each compulsory module and they offer a solid basis for supervising Master's theses. It is advisable to think about a possible topics and appropriate supervisors of your Master's thesis at an early stage of the Master's program. (The standard study period of 4 semesters is short.) When looking for a topic and supervisors, you should also take into account whether you intend to continue onto the doctoral program. In this case, more consideration should given so that the topic has a strong connection to contemporary research. Otherwise a broader range of topics is possible.

Doctoral program

As usual at the Faculty of Mathematics, there is no real difference between advanced courses for the Master's program and courses for the doctoral program in the area of specialization "Analysis". An abundance of advanced lecture courses and seminars from the area of analysis is offered. The recognition of courses for the doctoral program will be specified individually in the "dissertation agreement" (Dissertationsvereinbarung). In particular, it is irrelevant for the recognition of a course whether the course  is announced with a course number for the Master's in mathematics (25XXXX) or for the doctoral (51XXXX) program. You can find general information on the doctoral program on the web pages of the SSC Mathematics and the Center of Doctoral Studies of the University of Vienna.

The research interests of the individual faculty members play a much larger role in the choice of a topic and supervisor for a doctoral dissertation than for a Master's thesis: dissertation topics are usually adjacent to the research area and interests of the supervisor. Therefore, it does not make sense to give general information regarding these questions. It is worth mentioning that many research groups are devoted to analysis at our faculty and various research grants for doctoral students are offered.

It is extremely important that you contact a potential supervisor before starting the doctoral program and talk about a possible supervision. It does not make sense to enroll for the doctoral program first and then look for a supervisor.