# Specialization "Applied Mathematics and Scientific Computing"

Here we present the area of specialization "Applied Mathematics and Scientific Computing", which covers the major part of the offered courses on applied mathematics. We also include hints on possible topics for Bachelor's and Master's theses for all students of mathematics: nearly all of these topics are directly linked to an application in the real wold and usually cover several areas of mathematics. Often computer programs are used for solving these problems and are created by the students in the course of their theses. This makes graduates of this area of specialization particularly attractive for industry. The information is sorted by study program.

## Master's program

In the Master's program, "Applied Mathematics and Scientific Computing" 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 "Applied Mathematics and Scientific Computing" consist of four compulsory modules:

- In the module "Numerical mathematics" the methods from the bachelor program are expanded and supplemented. Here the focus is on the solution of large systems of linear equations, eigenvalue problems, multiple integrals, Monte Carlo methods, and the foundations of the numerical solution of partial differential equations. Special attention is paid to the practical implementation of algorithms on computer systems.
- The compulsory module "Applied analysis" provides an introduction to one or two important branches of analysis (like differential equations, Fourier analysis, asymptotic analysis etc.) with special reference to their application to problems from the natural sciences.
- In the module "Optimization and variational calculus" the theoretical and practical foundations of the solution of finite- and infinite-dimensional optimization problems are developed. One aspect is the application of the methods to the solution of problems from economy and natural sciences.
- In the module "Seminars: Applied mathematics and scientific computing" you have to complete one seminar and one project seminar from the branches applied mathematics, image and signal processing, mathematical modelling, numerical mathematics or optimization. Usually the seminar is theoretically oriented, but the project seminar includes the development of computer programs.

The offer of advanced courses for the Master's program is closely linked to the research interests of the faculty members working in this area. It comprises courses on the branches ordinary and partial differential equations, dynamical systems, mathematical modelling, harmonic analysis, optimization, variational calculus, image and signal processing, numerical mathematics, scientific computing etc.

## 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 specialization "Applied Mathematics and Scientific Computing". An abundance of advanced lecture courses and seminars from this area is offered. The recognition of courses for the doctoral program will be specified individually in an 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 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 applied mathematics and scientific computing 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.