TEACHER: Prof. Jüri Engelbrecht (Tallinn University of Technology and Estonian Academy of Sciences)

Lectures are organized by the Scuola di Studi Superiori dell'Università di Torino within the "Modelli Matematici I" course. Admission free. For informations: web www.ssst.unito.it - email ssst@unito.it - tel. 0116702225.

27/04 h. 16:00-18:00 / Lecture 1 / Methodology of Mathematical Modelling

The main principles of mathematical modelling are briefly explained together with a short historical sketch. The main stages of modelling  are described focusing on validation of results and improvement of a  model. For modelling of physical processes, the importance of conservation laws is stressed and explained as well as the need for  using thermodynamical considerations. This forms a solid basis for many well-known and also for newly developed models. For modelling of processes in biology or social life, the situation is much more complicated and the emphasis is more on interpreting the observation data. Several arguments used for modelling such processes is discussed and examples given.

Motto: Everything must be made as simple as possible. But not simpler. (A. Einstein)

28/04 h. 10:00-12:00 / Lecture 2 / Complexity in Mathematical Modelling

Contemporary understanding of the world is based on the concept of complexity. Complexity research is a holistic process and takes many constituents of a whole into account while the outcome is strongly dependent on interaction between the constituents. That is why the systems out of equilibrium, adaptive and self-organising systems, networks, nonlinear dynamical systems, etc are of importance. The main properties of complex systems are explained and several examples given
which demonstrate simple models of complex behaviour in physics, biology, mathematics, economics and so on.

Motto:  The whole is more than the sum of its parts.  (Aristotle)