Autumn School Mathematical Modeling – a cooperation between ZFM and TUDa

Since 2000 the Zentrum f¨ur Mathematik in Bensheim (ZFM) and the Technical University Darmstadt (TUDa) have organized an annual autumn school for mathematically highly talented pupils in their last year of school. For one week, the participants work in groups on application problems, which first need to be transformed into mathematics and then be solved by mathematical analyzation and numerical approximation and implementation on a computer. Finally, the results are presented. The problems are very realistic. Only minor details may be skipped, to make the problem easier to handle and to focus on the main issue at hand, but only if they do not affect the basic result. For some of the problems there exist similar, but much simpler, counterparts that can be solved in a shorter time period even in a usual school setting. Solving those simple problems opens the outlook to the hard problems if they are mentioned before. This paper examines two applications that led to mathematical problems from analysis and geometry.