Master M1

Mathematics – Jacques Hadamard


The Master 1 Mathematics Jacques Hadamard at Polytechnique offers a very high level program in Applied and/or Fundamental Mathematics with possible combinations of courses in other disciplines.
It concerns mainly excellent Bachelor students in Mathematics.
It consists of two semesters and an internship. For each of the two semesters, the student must take 3 Regular Courses and 1 Deepening Teaching (EA) from the list of courses below.
The program is parallel to the third year of studies at Ecole polytechnique for students choosing Fundamental or Applied Mathematics.

Language of instruction: French. Some courses can be given in English.
ECTS: 60 Oriented: Industry or research
Duration: 1 year
Courses Location: Ecole polytechnique. It is also possible to take some courses in Partner Institutions, like Université Paris-Saclay or ENS Paris-Saclay.

Educational objectives

The aim of the Master 1 Mathematics Jacques Hadamard is to offer to students a wide range of courses in all fields of Fundamental and Applied Mathematics and an Research Internship.
In Applied Mathematics, the students will be able to specialize in topics as varied as data analysis, life sciences, optimization, energy, finance, etc., as well as to mix his/her training program with other courses in other disciplines like Fundamental Mathematics, Computer Science, Mechanics, Physics.
In Fundamental Mathematics, the students can follow courses in Algebra, Geometry and/or Analysis with possible combinations with some courses in other disciplines like: Physics, Computer Science and Applied Mathematics.

Program structure

Each course listed below corresponds to 5 ECTS (4 hours a week during 9 weeks). The evaluation is done either on the basis of an oral or written exam, either on the realization of a personal project.

MAP corresponds to courses offered by the Applied Mathematics Department at Polytechnique.
MAT corresponds to courses offered by the (Pure) Mathematics Department at Polytechnique.

Internship (April-July): 15 ECTS.
English and other courses : 5 ECTS.

Semester 1 :
MAP551 Systèmes dynamiques pour la modélisation et la simulation des « milieux réactifs » multi-échelles (M. Massot)
MAP552 Modèles stochastiques en Finance (N. Touzi)
MAP553 Regression (K. Lounici)
MAP555 Signal Processing (O. Rioul)
MAP556 Stochastic simulation and Monte-Carlo methods (E. Gobet)
MAP557 Recherche opérationnelle : aspects mathématiques et applications (S. Gaubert)
MAT551 Systèmes dynamiques (D. Burguet)
MAT552 Théorie algébrique des nombres (G. Chennevier)
MAT553 Variétés, fibrés vectoriels et formes différentielles (S. Bouksom)
MAT554 Équation d’évolution (Y. Martel)
MAT556 Groupes, anneaux, modules et représentations (D. Renard)
MAT557 Topologie algébrique (G. Ginot)

Semester 2
MAP560 Variational Methods for Coputional Fluid Dynamics (F. Alouges)
MAP561 Automatic Control with applications in Robotics and in Quantum Engineering (U. Boscain-M. Mirrahimi)
MAP562 Optimal Design of Structures (G. Allaire)
MAP563 Modèles aléatoires en écologie et évolution (S. Méléard)
MAP564 Communication Networks and Social Networks : probabilistic models and algorithms / réseaux sociaux et de communication : modèles et algorithmes probabilistes (L.Massoulié)
MAP565 Modélisation statistique (M. Rosenbaum)
MAP566 Statistics in Action (M. Lavielle)
MAP/MAT567 Transport et diffusion (G. Allaire & F. Golse)
MAP568 – Gestion des incertitudes et analyse de risque (J. Garnier)
MAP569 Machine Learning II (E. Le Pennec)
MAT561 Théorie spectrale et mécanique quantique (M. Lewin)
MAT562 Introduction à la géométrie algébrique et courbes elliptiques (Benjamin Schraen)
MAT563 Groupes compacts et groupes de Lie (B. Stroh)
MAT565 Surfaces de Riemann (C. Matheus Santos Silva)
MAT568 Équation des ondes et relativité générale (C. Huneau)

A Deepening Teaching can be proposed in relation with any of the MAT courses.
Additional Deepening Teaching in Theoretical Mathematics :
MAT/PHY575 Groupes de symétrie en physique subatomique
Deepening Teaching in Applied Mathematics :

Semester 1
MAP572 Mise en oeuvre de méthodes numériques
MAP573 R pour les statistiques
MAP575 Fondements des probabilités et applications

Semester 2 :
MAP583 Apprentissage profond
MAP584 Mise en oeuvre effective de la méthode des éléments finis
MAP585 Théories de l’apprentissage
MAT/MAP587 Transport et diffusion

IP Paris labs involved

Applied Mathematics Center (CMAP) : EP/CNRS
Laurent Schwartz Mathematics Center (CMLS) : EP/CNRS

Career prospects

It is highly recommanded to follow a Master 2 in fundamental or applied mathematics.
The wide variety of courses, seminars, projects and internships proposed during the master offers the
possibility, for every student, to build his/her own curriculum in mathematical sciences.
After M2 graduation, the student can apply for PhD funding in top research labs or apply for jobs with solid scientific content.

Institutional partners

The mention « Mathématiques et Applications » is co-accreditated with Université Paris-Saclay.
In remplacement of courses at Polytechnique, it is possible (submitted to approval of the pedagogical team) to take some courses from: Université Paris-Saclay, Université Paris-Descartes, Université Paris-Dauphine, Ecole Nationale des Ponts et Chaussées, Ecole des Mines, ENS Ulm.

Industrial partners

  • Aérospatiale,
  • Airbus
  • Air Liquide
  • CEA
  • Danone
  • Dassault
  • EADS
  • EDF
  • EuroDecision
  • GDF
  • General Electrics
  • Ingenico
  • Peugeot
  • Renault
  • RTE
  • Sanofi
  • Thalès
  • Véolia
  • Xerox


Application guidelines for a master’s program at IP Paris

Academic prerequisites

  • Bachelor of Science (or equivalent) in mathematics, mathematical sciences or related field.

Language prerequisites

  • French or English (for some courses)

Application timeline

Deadlines for the Master application sessions are as follows:
– First session: February 28, 2020
– Second session: April 30, 2020
– Third Session (optional): June 30, 2020 (only if there are availabilities remaining after the 2 first sessions)
Applications not finalized for a session will automatically be carried over to the next session.

You shall receive an answer 2 months after the application deadline of the session.

Tuition fees

National Master: Official tuition fees of the Ministry of Higher Education, Research and innovation (2019-2020, EU students: 243 euros / Non-EU students: 3770 euros)


Yvan Martel