Due to the philosophy of this research training group, the perfect environment for a PhD student in mathematics needs to provide a stimulating scientific environment and plenty of time to work independently on his or her thesis.

The first one is realised naturally by research teams that are embedded into the scientific activities in the respective areas on an international level. This ensures contacts with the leading scientists visiting the RTG, communication and presentations at conferences, and short or long-term mutual research stays at partner institutes abroad. These are starting points for scientific networks built up by each PhD student.

The second characteristic, however, needs to be matched with the competences of PhD students coming from diverse mathematical backgrounds and the RTG's endeavour to make an impact in applications. To this end, a structured study programme is implemented, which equips the PhD students with the necessary mathematical knowledge and sufficient insight into the application areas.

In addition, the soft skills programme aims at enhancing scientific independence and the capability of working in interdisciplinary teams. Moreover, the students of this RTG will be prepared for their careers after their PhD, where most of them are expected to reach leading positions in science or industry. Building up leadership qualities is a notible part of the soft skills programme.

The study groups are connecting these ingredients of the qualification concept: interaction and cooperation within a study group upgrades individual research, enhances communication and soft skills (team building), and, last but not least, help to develop leadership abilities.