The **Institute of Mathematical Modelling, Analysis and Computational Mathematics (IMACM)** combines the expertise of different mathematical groups at the Bergische Universität Wuppertal for solving real-life problems in industry and services, with applications in natural and social sciences, economics and engineering. It is our belief that all mathematical fields in the widest sense can be important for the solution of problems posed by applications. These problems are a continuous source of challenges to the fundamental research on structure and methods of mathematics because it has often to deal with completely new mathematical problems. Hence the IMACM does not play *"pure"* mathematics off against *"applied"* mathematics, but combines both as necessary sources for solving the posed problems.

The programme in our collaborations at IMACM follows the following paradigm, recently summerized in the final report of the Forward Look Mathematics and Industry: "first, identify the problem of concern; then, build a quantitative mathematical model, analyse and solve it, apply the results, and potentially create appropriate mathematical software that can be commercialised. The emphasis is in pointing out which are the important and relevant variables controlling the problem, which are the constraints and what is the goal. This is done through the understanding of the underlying mechanisms involved in combination with the analysis of the respective observations and data. The next steps concern the analysis of the created mathematical model, its numerical simulation in different scenarios, and the validation the model in comparison with experimental data. In addition it is important to investigate the robustness and sensitivity of the model. Note that this is typically an iterative procedure, since if the results do not explain or fit the observations, one has to modify and adapt the model, and repeat the cycle, until the model describes – as accurately as needed – the situation to be studied or simulated. Typically after the iteration of validating and adapting the model then, when the model is finally accepted, it would be used to improve, optimise or control the process that it describes. Model based control and optimisation is a crucial element of automation in all areas of industry, often reducing the cost and time of product, process and service innovation."

See The European Science Foundation: Forward Look Mathematics and Industry, Final Report, 2011, p.8

**Institute of Mathematical Modelling, Analysis and Computational Mathematics**

Bergische Universität Wuppertal

Gaußstrasse 20

D-42119 Wuppertal

Germany

**Phone**: +49 202 439 5296

**E-Mail** imacm{at}math.uni-wuppertal.de