Mathematical modelling of systems constituted by many agents using kinetic theory is a new tool that has proved effective in predicting the emergence of collective behaviours and self-organization. This idea has been applied by the authors to various problems which range from sociology to economics and life sciences.

• PART I: KINETIC MODELLING AND SIMULATION


• 1: A short introduction to kinetic equations


• 2: Mathematical tools


• 3: Monte Carlo strategies


• 4: Monte Carlo methods for kinetic equations


• PART II: MULTIAGENT KINETIC EQUATIONS


• 5: Models for wealth distribution


• 6: Opinion modelling and consensus formation


• 7: A further insight into economy and social sciences


• 8: Modelling in life sciences


• Appendix A: Basic arguments on Fourier transforms


• Appendix B: Important probability distributions

Lorenzo Pareschi is full professor of numerical analysis at the University of Ferrara. He holds a PhD in mathematics from Bologna University (1996). He is a leading expert in computational methods and modelling for nonlinear partial differential equations. His research interests include kinetic equations, hyperbolic conservation laws and relaxation systems, stiff systems and Monte Carlo methods. He has co-written three books and more than one hundred peer-reviewed articles. He serves as an associate editor for the SIAM Journal of Scientific Computing (SISC), Multiscale Modelling and Simulation (MMS), Kinetic and Related Models (KRM) and Communications in Mathematical Sciences (CMS). He held visiting professor positions at the University of Wisconsin, Madison (USA), the Georgia Institute of Technology, Atlanta, (USA), the University of Orleans (France) and the University of Toulouse (France).
Giuseppe Toscani is full professor of mathematical physics at the University of Pavia. His recent scientific interests are concerned with theoretical and numerical problems connected to the kinetic theory of rarefied gases, asymptotic behaviour of nonlinear diffusion equations by entropy methods, and kinetic modelling of socio-economic multi-agents systems. He has authored around 200 papers, written both individually or jointly with national and international experts, as well as two monographs on the mathematical aspects of Boltzmann equation and of Enskog equation in kinetic theory of rarefied gases. He held visiting professor positions at the Georgia Institute of Technology, Atlanta, (USA), and at the Universities of Paris VI, Paris Dauphine, Nice and Toulouse (France).