MODELLING AND NUMERICAL SIMULATIONS

First of all, we will aim at introducing the basics of probability theory and statistics, with an emphasis on numerical techniques (probability functions generation, data analysis). Data analysis could give the chance to introduce modeling in the simple form of data fitting. A large fraction of the course will be devoted to applications of Markov processes theory. Modeling of queues will be the main application of the formalism. Simple examples of dynamic MonteCarlo will be proposed to Physics students (if any). An elementary introduction to stochastic differential equations will be proposed to Maths students (if any), in particular facing Langevin equation (brownian motion and tree-cutting problem). Basics of percolation theory will be introduced as an example of how a simple model can model a variety of phenomena.