Teaching

Future lectures/courses (tentative list)

Bachelor/Master Theses

I am offering Bachelor and Master theses from the area of applied and numerical analysis. Currently, they are mainly concerned with one of the following topics:

• Multivariate and high-dimensional approximation theory; particularly kernel-based methods and neural networks.
• Meshfree methods for the solution of partial differential equations; particularly radial basis functions and particle methods.
• Application of the methods mentioned above to problems from uncertainty quantification.

Some of the topics mentioned above are described in more detail on our research web page. In general, I am also open for own suggestions, as long as they are interesting and thematically not too far away from my own the research interests.

Required or suggested courses for a Bachelor thesis:

• Einführung in die numerische Mathematik
• Einführung in die höhere Analysis
• Einführung in die iterativen Verfahren
• Constructive approximation methods
• Applied functional analysis

Required or suggested courses for a Master thesis:

• Constructive approximation theory
• Applied functional analysis
• Numerics of partial differential equations
• Meshfree methods
• High-dimensional approximation
• Uncertainty quantification

Examples of previous theses:

• Operatortheortische Untersuchung kernbasierter Approximationsräume (Master)
• Fehlerabschätzungen für regelarisierte, kernbasierte Approximationsverfahren in höhendimensionalen Räumen (Master)
• Vergleich von Neuronalen Netzen und kernbasierten Verfahren zum Einfärben von Bildern (Bachelor)
• Über kernbasierte Lernverfahren und neuronale Netze (Bachelor)
• Ein gitterfreies Verfahren zur numerischen Lösung von Problemen der optimalen Steuerung partieller Differentialgleichungen (Master)
• Kernel-based reconstruction for parametric partial differential equations (Master)
• Approximative Berechnung der Helmholtz-Hodge Zerlegung mittels radialer Basisfunktionen (Bachelor)
• Konvergenz und Stabilität adaptiver Multilevelverfahren (Master)