Mathematics centres of competence develop mathematical models for applications in all sciences and engineering, including social sciences, and medicine. They analyse the models, develop and implement algorithms for the simulation of the models as well as for the optimization and control of the involved processes. They provide transversal competences which allow transferring concepts and methods from one specific science to another and they also provide consulting concerning the use of methods and their implementation for specific applications. When needed, they generate the basic mathematical theory that is needed to perform the described tasks. (Mathematical modelling; numerical and statistical simulation; control theory; optimization; mathematical algorithm repository).