## EMMA

### Experimentation with mathematical algorithms

The aim of the project was to work out aspects of mathematical algorithms by means of two ongoing research projects with focus on algorithmic questions. This was to be done in close cooperation with students. The focus of this cooperation wias 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 enabled the students to participate directly in the research activities and to provide a valuable contribution. The experiments allowed the researchers to convey important aspects of mathematical algorithms to the students so that a productive exchange ws established for both sides via the experimentation.
The object of research was 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 were developed and analyzed, where mixed finite elements were applied for the discretization. In particular, semi-smooth Newton schemes and active set algorithms were studied with respect to their convergence properties. In the second research project elliptic curves with high rank and Diophantine tuples were considered, where new rank records were aimed to be established and elliptic curves with high rank with the prescribed torsion subgroup were constructed.

The cooperation with the students at the affiliated school HTL Braunau was organised on the basis of the elective course 'University Mathematics', which provides the basic theoretical knowledge and helped establish a concrete framework for the cooperation with the students.

This project has been completed.