Sorbonne Université

Mathematical modelling and randomness

Course coordinator : A. Gloria

The Major degree Partial Differential Equations and randomness (AMM) is one of the Majors proposed by the speciality Mathematics of Modelling, second year of the Masters in Mathematics and Applications.

Probabilistic aspects are more and more important in mathematical modelling, which leads to interactions between analysis and probability.

The main degree AMM aims at educating:

• researchers in applied mathematics (nonlinear analysis and partial derivative equations, numerical analysis and scientific data processing) with a strong taste for probabilistic aspects, likely to pursue a career in higher education and research (Universities, CNRS, ECA, INRIA,…) or to take part in the program of high technology in industry,
• high level mathematical engineers understanding all the aspects of modern scientific calculation (from modelling and mathematical analysis to numerical resolution and effective computer implementation), with an emphasis on probabilistic methods, and who intend to work for industrial research departments and in scientific calculation service companies.

The AMM Major's key topic is the theoretical and numerical study of problems described by linear and nonlinear partial differential equations with randomness or uncertainties. The recent development of uncertainty quantification and of random inputs in PDEs make probability more and more important in the field of PDE analysis and simulation. The courses offered cover the following fields:

• The mathematical modelling (deterministic and probabilistic) of many application areas: solid mechanics, fluid mechanics, propagation phenomena (acoustic, seismic, electromagnetism), the treatment of signal and image, finance, chemistry and combustion.
• Mathematical analysis of linear and nonlinear (deterministic or stochastic) partial differential equations (existence, unicity and regularity of solutions).
• Methods of approximation, with an emphasis on probabilistic approaches

It is possible to follow courses offered by other master programs, in consultation with the professor in charge of this major, and in particular from the master program in probabilities and random models at Sorbonne Université : https://www.lpsm.paris/masters/modale/index