Mathematics: PDEs, modelling and numerics Master (ANEDP)

The ANEDP Major's key topic is the theoretical and numerical study of modeled problems by linear and nonlinear partial differential equations from various fields such as physics, engineering, chemistry, biology,  economy, as well as methods of scientific computing aiming at the digital simulation of these problems. Scientific computing has become the key element of technological progress. It requires a deep understanding of mathematical modelling, numerical analysis, and computer science. The broad portfolio of courses of the Major allows students to explore and manage the various aspects of these disciplines. The various fields of mathematics concerned are diversified and developing quickly; their development involves an increasing need for mathematicians.

The Major degree Numerical Analysis & Partial Differential Equations (ANEDP) is one of five Majors proposed by the Mathematics of Modelling speciality , in the second year of the Masters in Mathematics and Applications and is jointly managed by Sorbonne University, École Polytechnique and École Nationale des Ponts et Chaussées.
The main degree ANEDP aims at educating:

  • researchers in applied mathematics (nonlinear analysis and partial derivative equations, numerical analysis and scientific data processing) 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) and who intend to work for industrial research departments and in scientific calculation service companies.

Programme structure

The courses offered cover the following fields:

  1. The mathematical modelling of many application areas: solid mechanics, fluid mechanics, propagation phenomena (acoustic, seismic, electromagnetism), the treatment of signal and image, finance, chemistry and combustion.
  2. Mathematical analysis of linear and nonlinear partial differential equations (existence, unicity and regularity of solutions).
  3. Methods of appoximation: finite elements, finite differences, spectral methods, particulate methods, wavelets.
  4. computer implementation of these methods and design of scientific computing software.

M1 in Mathematics or an equivalent




Semester 3  (S3)
First 6 weeks of the academic year

Basic courses (at least 4 to choose) (*):


-Partial derivative equations
-Functional analysis
-Numerical methods for the non stationary EDP: finite differences and finite volumes
-Approximation of functions and Sobolev spaces
-Stochastic calculus (other speciality)
-Discrete Markov Processes (other speciality)


Semester 3  (S3)
Eight-week period
(Mid-October to mid-December)

Fundamental courses (at least 3 to choose) (**):

3 each

-Continuous optimisation
-Control in finale and infinite dimension
-Discrete optimisation
-Elliptic equations
-From EDP to their resolution by finite elements
-Game theory and applications in finance and economics (Master MASEF Dauphine)
-High performance computing for numerical methods and data analysis
-Introduction to evolution PDE
-Introduction to stochastic PDEs
-Mathematical methods in Biology
-Multiscale modelling, simulations for data analysis: from molecular to system neuroscience
-Méthodes du premier ordre pour l'optimisation non convexe et non lisse
-Probalistic numerical methods
-Reject [CG] Theoretical and Numerical Aspects
-Some Mathematical Methods for the Neurosciences
-Statistics and learning
-Structured equations in biology
-Theoretical and numerical analysys of hyperbolic systems of conservation laws
-Variational approximations of PDEs

Semester 4 (S4)

Specialised courses (at least 2 to choose) (***):

6 each

--Analyse d’edp non-linéaires issues de la géométrie : des applications harmoniques à la théorie de Yang-Mills
-Cinetic models and hydrodynamic limits
-Discontinuous Galerkin methods and applications
-Fluid dynamics models in life sciences, mathematical and computational viewpoints
-Fonctionnement des réseaux de neurones: analyse mathématique
-Geometric control theory
-High performance computing, parallel computation algorithms in large-scale linear algebra, numerical stability
-Hyperbolic models for complex flow in the field of energy
-Lorentzian geometry and hyperbolic PDE
-Mathematical Epidemiology of Infectious Diseases
-Mathematical methods and numerical analysis for molecular simulation.
-Mean field games (Master MASEF Dauphine)
-Modelling of growth and regeneration processes in multi-cellular tissues involving agent-based models
Modern methods and algorithms for parallel computation
-Optimal Control of Partial Differential Equations
-Optimal transport : theory and applications
-Optimisation de formes: aspects géométriques et topologiques
-Probabilistic models in the neurosciences
-Problèmes variationnels et de transport en économie (Master MASEF Dauphine)
-Propagation of evidence in bayesian networks, application to medical science
-Randomised trees for evolutionary biology
-Reaction-diffusion equations and dynamics of biological populations
-Reaction-diffusion equations and the evolution of dispersal
-Spectral theory and variational methods
-Stochastic models of molecular biology
-Theoretical and numerical aspects of incompressible fluids
-Theoretical and numerical aspects of incompressible fluids

Internship (3 to 6 months)  

 (*) During this period, students must take at least four courses out of the five offered. Every course consists of a three-hour lecture, and a three-hour tutorial per week.  At the end of this six-week period, students will have to choose their Major. Students who make a definitive decision concerning the choice of the MBIO Major before the basic courses begin, can replace one or two of the proposed basic courses by the following courses (referred to as "other speciality" ) :

(**)During an eight-week period, from mid-October to mid-December, students must choose at least three courses, each accounting for 6 ECTS in the S3 semester. Each course consists of three hours per week, over eight weeks, for a total of twenty-four hours. Each course may be completed by one or two tutorial sessions of two or three hours.
The courses chosen by students should correspond to the recommendations for each Major, if not they will be chosen in conjunction with the course coordinator. Students are reminded that their Major will be chosen at the end of the "Basic Courses" period

(***)In this phase, students must choose between at least 2 specialised courses. Each of these is a 20-hour course, divided into 2-hour sessions over the course of 10 weeks. These courses are closely-related to research subjects. They must especially be consistent with the topics proposed for the internship project. There are no tutorials. Each course is worth 6 ECTS in the S4 semester.

Student mobility

The programme partners with the Shanghai Jiao Tong University.


Admission to the speciality is given after examining the student's application file, containing :

  1. CV with details of professional experiences and training periods
  2. Cover letter
  3. List of grades from baccalauréat (included) to the 5th semester of Licence (included) or to the highest year reached
  4. Any passed language certificates
  5. Planned choice of theme(s) among the 5 Majors which are part of this Masters degree
  6. For students from non-French universities: certified translations of the diplomas and a description of the courses taken with detailed marks or grades.

Employment prospects

This Masters degree opens up many opportunities, allowing students to apply for a thesis (whether academic or industrial) or job opportunities in the private sector. Many mathematical job profiles have recently become prominent, like data scientist or mathematical engineer, and are now recognized as strategic for small and large companies.
In the long term, our Masters degree leads to all the mathematical sciences-related jobs in university or industry, such as :

  • Academic professors, researchers (universities, engineering schools)
  • Research institutes (CNRS, INRIA, INRA, IFSSTAR,…)
  • Scientific engineering (ECA, CNES, IFPEN, ONERA,…)
  • R & D departments of large companies, such as Airbus, Alstom, Areva, Dassault, EDF, Google, Huawei, IBM, IFPEN, LVMH, Michelin, Microsoft, Orange, PSA, Renault, RTE, Safran, Thalès, Total,… or in start-ups and SME.

Students will receive advice and contact opportunities from the professors responsible for their Major and from all the members of the pedagogical team.


Didier Smets