Applied and Theoretical Mathematics - Master’s Year 2

Program Year

Preliminary courses list

  • A review of functional analysis tools for PDEs
  • A review of numerical methods for PDEs
  • A review of probability theory foundations
  • A review of differential calculus for ODEs and PDEs

Fundamental courses list

  • Stochastic Calculus
  • Introduction to non linear PDEs
  • Introduction to evolution PDEs
  • Numerical methods for PDE and control
  • Differential dynamical systems in Mechanics and Physics
  • Introduction to statistical mechanics

Specialized courses analysis list

  • Mean field games theory
  • Equations de réaction-diffusion et dynamiques des populations biologiques
  • Théorie spectrale et méthodes variationnelles
  • Continuous optimization
  • Introduction to control theory
  • Variational and geodesic methods for Image Analysis
  • Chaire Sciences des données "Information et Complexité"
  • Chaire Equation aux dérivées partielles : "Sur les équations de transport"
  • Systèmes à diffusion croisée
  • Geometric control and boundaries in kinetic theory
  • Analyse des EDS non linéaires issues de la géométrie : des applications harmoniques à la théorie de Yang-Mills

Spécialized courses probability list

  • Jump processes
  • Large deviations and applications in Physics and Analysis
  • Mixing times of Markov chains
  • Stochastic Control
  • Monte-Carlo and Finite Differences Methods with Applications to Finance
  • Random geometric models
  • Convergence en temps long pour les processus de Markov
  • Products of random matrices and disordered systems in statistical mechanics
  • High dimensional probability
  • Opérateurs aléatoires
  • Chaire combinatoire "La combinatoire additive linéaire"

Specialized courses geometry and dynamical systems list

  • Gravitation classique et mécanique céleste
  • Fibrés de Higgs et représentations de groupes de surfaces
  • Propriétés génériques des systèmes Hamiltoniens
  • Dynamique des systèmes gravitationnels à grand nombre de particules

Specialized courses macroscopic physics list

  • Instabilities and nonlinear phenomena
  • Plasma Physics and advanced fluid dynamics
  • Systems out of equilibrium and nonlinear dynamics
  • Numerical methods for fluid dynamics
  • Soft solids

Academic Training Year 2022 - 2023 - subject to modification

Internships and Supervised Projects

During the second semester students will do a supervised research project (internship) of variable duration (minimum 3 months, average 4/5 months).

The subject of the internship will be freely chosen by the students according to their interest. If needed, tutors will orient in identifying a suitable research subject and/or project supervisor.

We warmly encourage our students to visit the research pages of the laboratories associated to the master ( Ceremade - PSLand DMA - PSL) as well as of other research laboratories to identify potential directors and contact them directly. Students who want to conduct their research internship outside the Paris region can apply for financial assistance from the Paris Mathematical Sciences Foundation ( more details here).

With prior written approval from the program director, the research internship may be replaced by an internship in a private company, as long as it has a sufficient research component.