Teaching
I teach applied mathematics as a connected process. We formulate a mathematical problem, study its structure, develop a numerical or algorithmic method, and turn it into a computation. Mathematics sets the questions and standards. The implementation makes the ideas concrete and shows their consequences.
Teaching philosophy
My teaching is organized around three central ideas.
Mathematics drives computation
Programming is taught through mathematical problems, not as syntax on its own. Number theory, algebra, numerics, geometry, graphs, PDEs, and linear algebra provide the questions from which representations and algorithms arise.
Analysis and experiment belong together
Proofs, invariants, pre- and postconditions, tests, benchmarks, and complexity estimates provide different evidence. Students learn to use them together and to state precisely what each can establish.
Abstractions should solve a problem
I introduce concepts through concrete mathematical or numerical problems. Students first encounter a limitation, then develop the data structure, interface, or abstraction that resolves it. This connects theory to design decisions and helps students apply the idea to new problems.
Teaching profile
My teaching covers a spectrum from mathematical foundations to the development of scientific software. Across these courses, assessment asks students to explain and justify as well as calculate and implement. I have also organized the institute seminar since 2018 and co-organized the seminar in applied mathematics from 2020 to 2024.
Current course pages, semester information, and enrollment links are maintained on my TU Dresden teaching page.
Numerical analysis · Master’s level
Mathematical and numerical methods
In Large Sparse Linear Systems, numerical linear algebra led to the implementation of parallel solvers and problem-dependent preconditioners. PDEs and Manifolds, taught with Hanne Hardering, developed mathematical and numerical methods for PDEs posed on surfaces and manifolds before considering their implementation.
My earlier teaching includes finite elements and numerical PDEs, basic numerical analysis, modeling and simulation, and mathematics for electrical engineers.
Mathematics · Bachelor’s level
Programming for mathematicians
My Bachelor’s-level teaching includes the sequence Programmieren – Grundlegende Konzepte and Programmieren – Weiterführende Konzepte. Julia serves as a medium for connecting mathematical objects with finite representations, algorithms, correctness, numerical reliability, and complexity.
The courses use problems from several areas of mathematics so that programming remains embedded in mathematical reasoning.
Scientific computing · Master’s level
Scientific programming and software design
In Scientific Programming – Advanced Concepts, numerical examples motivate modern C++, generic programming, data layout, testing, and performance analysis. Students work with the complete development process, including build systems, libraries, debugging, profiling, version control, and code review.
Further courses on object-oriented scientific programming and programming languages add to this part of my teaching.
Student supervision
I supervise Bachelor’s and Master’s theses in numerical analysis, geometric PDEs, finite-element methods, and scientific computing. The projects introduce students to independent research and connect analysis, numerical experiments, and software. Some are developed with external research or industry partners. My experience also includes diploma and doctoral projects.
Current topics, prerequisites, and project descriptions are maintained on the TU Dresden thesis page.
Research that continues
SL’s doctoral work on independently refined finite-element meshes led to joint publications. FR later transferred this approach to the new Dune and AMDiS software. The result still supports current master’s and doctoral projects.
A broad range of mathematics
Topics include surface PDEs, domain decomposition, active matter, finite-element software, machine learning, and scientific data fusion. Current projects study vector- and tensor-valued surface PDEs and surrogate models for computational fluid dynamics.
Work with external partners
Several master’s projects were developed with partners from science and industry. These include DLR, the German Weather Service, Bosch Semiconductor Manufacturing, and Continental. Students connect mathematical methods with real data, domain knowledge, and the requirements of a larger project.