After successful completion of the course, students are able to to give in an advanced manner well understandable, mathematically correct and clear lectures containing material from higher mathematics 

We trace the development of Schauderbases from pure functional analysis to applied numerical analysis. Schauderbases are objects of the theory of separable Banach spaces and generalize orthogonal bases in Hilbert spaces. They are extremely interesting from a mathematical point of view and questions regarding their existence and uniqueness often have suprising answers. Concrete examples of Schauderbases, so-called Wavelets, lead us to interessting applications in partial differential equations, image processing, and even machine learning. Often, they provide an efficient and way to discretize those problems, i.e., to make them computable.

Individual support and preparation

We grade the talk as well as the written thesis