The Section of Mathematics supervises Fagprojekter, Bachelor theses, and Master theses broadly within theoretical and applied mathematics. Below, each group has described which kind of projects they supervise. See also Past student projects for concrete examples of completed projects. Completed theses are available (requires DTU logins) in DTU Findit, DTU's online library service.

**Algebra **

The Algebra group supervises projects broadly within our research area of discrete algebra and computer algebra: e.g. number theory, algebraic geometry, algorithms for solving many types of discrete equations, or applications in coding theory or cryptography.

A project with us will have emphasis on the mathematical essence. It will often be natural to include algorithms or implementations. It can span widely from being purely theoretical to very applied, as long as there is a strong mathematical content.

See our group web page for concrete project proposals. Contact persons: Peter Beelen, Johan Rosenkilde.

**Dynamical Systems**

A project in dynamical systems will typically consist of an analysis of a mathematical model from an applied field in engineering or natural sciences. Using mathematical tools, various types of solutions will be identified, their stability will be determined, and the robustness of the model when parameters are varied will be examined. Interpreting the mathematical results in terms of the original problem is an important aspect. Numerical computations will generally be a part of the analysis. We also offer projects where the mathematical modelling is in focus, or very theoretical projects, where the main purpose is to understand some mathematical technique in detail. Co-advisors from other departments at DTU or industry can be associated with the project.

We offer projects at all levels of the educations at DTU. Please contact one of the group members for further information. Contact persons: Morten Brøns, Christian Henriksen, and Kristian U. Kristiansen.

**Functional Analysis
**

The activities in the research group HATA (Harmonic Analysis - Theory and Applications) are centered around frame theory. Frames are generalizations of the well-known orthonormal bases, and yield efficient representations of signals in terms of convenient basic vectors. Frames provide considerably more flexibility than orthonormal bases, and often one can construct frames with properties that can not be obtained for orthonormal bases. In general one aims at constructions of frames having a convenient structure, e.g., wavelet frames and Gabor frames. The results from this particular branch of harmonic analysis are important in image processing, modern consumer electronics, and several areas of engineering.

Concrete projects:

- Frame theory and sampling theory
- Frame theory in finite-dimensional spaces
- Wavelet analysis and applications
- Gabor analysis and applications

Contact persons: Ole Christensen,Jakob Lemvig.

**Geometry**

Members of the geometry group are very happy to supervise student projects within the area of geometry, including differential geometry, topology, analysis, complex analysis and Lie group theory, as well as related applications in mechanics, architecture and design, relativity, biology and other relevant fields.

Some sample projects and also more information about our research can be found at our group web page. Contact persons: Steen Markvorsen, Jens Gravesen, David Brander