Experimentation with mathematical algorithms
The aim of the project is to work out aspects of mathematical algorithms by means of two ongoing research projects with focus on algorithmic questions. This is to be done in close cooperation with students. The focus of this cooperation will be on computer experimentations to be carried out in large part by the students thus forming an important bridge between the students and the involved researchers. This will enable the students to participate directly in the research activities and to provide a valuable contribution. The experiments will allow the researchers to convey important aspects of mathematical algorithms to the students so that a productive exchange can be established for both sides via the experimentation.
The object of research will be provided by two ongoing research projects in numerical mathematics and in discrete mathematics, which meet modern standards of mathematical sciences.
In the first research project numerical solution schemes for variational inequalities are developed and analyzed, where mixed finite elements are applied for the discretization. In particular, semi-smooth Newton schemes and active set algorithms are studied with respect to their convergence properties. In the second research project elliptic curves with high rank and Diophantine tuples are considered, where new rank records are aimed to be established and elliptic curves with high rank with the prescribed torsion subgroup are constructed.
The cooperation with the students at the affiliated school HTL Braunau will be organised on the basis of the elective course 'University Mathematics', which provides the basic theoretical knowledge and will help establish a concrete framework for the cooperation with the students.