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M2 Mathematics, Vision, Learning

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The Master 2 MVA (Mathematics, Vision, Learning), created by the mathematics department of the ENS Paris-Saclay, is a unique master in France since its creation in 1996. In cooperation with several academic partners, it trains a large number of university and "grandes ecoles" students each year in Research, Development and Innovation for public and private organizations and companies in the field of mathematics applied to data, image and signal processing.
The huge growth in the use of digital data in all fields of science, technology and society requires the training of high-level mathematical researchers mastering the acquisition and processing of digital data on the one hand, and their automatic interpretation on the other. These two aspects are strictly complementary and are reflected in the three terms characterizing the MVA program.

Course Prerequisites

Admission: On a case-by-case basis, for holders of an M1 in mathematics, informatics or physics, or for 3rd-year engineering school students (potentially admitted for dual programmes, according to agreements).

  • Understand and proficiently use high-level mathematical tools and methods.

  • Understand and mathematically model a problem in order to resolve it.

  • Analyse data and implement digital simulations.

  • Analyse a research paper with a view to summarising it and using it.

  • Be proficient in the use of digital tools and major programming languages.

  • Explain and write, clearly and rigorously, a theory and mathematical results.

Post-graduate profile

Upon completing the MVA Master's degree, graduates have acquired a solid theoretical and practical grounding in the field of data analysis in the broad sense.

Career prospects

Career paths available include doctoral studies, R&D in large organisations and major groups, areas of innovation (start-ups), in almost all sectors of activity.
Students are prepared for these prospects through:
-the teaching modules (the contents of the teaching are illustrated via case studies of real applications)
-the lab-companies forum held each year in November, inviting students to meet potential employers (public or private) in a direct and informal setting.


Centre de mathématiques et de leurs applications.

Fédération de Mathématiques (CentraleSupélec),.


ECTS au choix à valider.

Subjects ECTS Lecture directed study practical class Lecture/directed study Lecture/practical class directed study/practical class distance-learning course Project Supervised studies
3D Computer Vision 5 18
Advanced Learning for Text and Graph 5 14 14
Algorithms for speech and natural language processing 5 20
Apprentissage Profond pour la Restauration et la Synthese d'Images 5 12 9
Approches géométriques en apprentissage statistique: l'exemple des données longitudinales 5 21
Audio signal Analysis, Indexing and Transformations 5 14 10
Traitement du signal sonore 5 21
Bayesian machine learning 5 16
Biostatistics 5 24
Computational optimal transport 5 18
Computational statistics 5 16 16
Convex optimization and applications in machine learning 5 21
Deep Learning 5 21 3
Deep Learning in Practice 5 12 12
Modèles déformables et méthodes geodesiques 5 21 9
Discrete inference and learning 5 24
Fondements Théoriques du deep learning 5 25 5
Foundations of distributed and large scale computing optimization 5 24
Géométrie et espaces de formes 5 27 9
Graphs in Machine Learning 5 16 6
Image denoising : the human machine competition 5 20 10 10
Imagerie fonctionnelle cérébrale et interface cerveau machine 5 24
Introduction à l'imagerie numérique 5 21 6
Medical Image Analysis based on generative, geometric and biophysical models 5 24
Introduction to statistical learning 5 16 6
Kernel Methods for machine learning 5 23
Introduction to Probabilistic Graphical Models and Deep Generative Models 5 27
Méthodes mathématiques pour les neurosciences 5 24 16
EDPs numériques pour l'analyse d'images 5 15 6
Modélisation en neurosciences et ailleurs 5 20
Nuages de points et modélisation 3D 5 12 12
Reconnaissance d’objets et vision artificielle 5 30
Information et Complexité 5 24
Apprentissage pour les séries temporelles 5 18 9
Deep learning for medical imaging 5 27
Problèmes inverses et imagerie : approches statistiques et stochastiques 5 24
Reinforcement Learning 5 17 4.5
Remote sensing data: from sensor to large-scale geospatial data exploitation 5 31.5
Sub-pixel Image Processing 5 20 16
Théorie des matrices aléatoires et apprentissage 5 24 6
Topological data analysis for imaging and machine learning 5 12 12
Responsible machine learning 5 22
Application de l’analyse de données, des statistiques descriptives et de l’apprentissage automatique dans l’industrie aéronautique. 5 12 18
Apprentissage profond et traitement du signal, introduction et applications industrielles 5 12 18
Fondamentaux de la recherche reproductible et du logiciel libre 5 12 4 8
Geometric Data analysis 5 21
Modèles génératifs pour l'image 5 18 9
Sequential learning 5 18
Théorie de la détection et ses applications industrielles 5 24
Deep reinforcement learning 5 24
Méthodes de séparation de sources pour l'analyse de données en astrophysique 5 24
Méthodes en télédétection : observer la Terre 5 12 18
Introduction à l'apprentissage statistique pour les géosciences 5 12 18
Algorithmes pour l’optimisation et la gestion des réseaux 5 12 18
The machine intelligence of images 5 12 18
Projet de recherche reprodutible 5 8 16
Université de Paris-Immersion en hôpital - collaboration en binôme avec un médecin 5

Stage obligatoire.

Subjects ECTS Lecture directed study practical class Lecture/directed study Lecture/practical class directed study/practical class distance-learning course Project Supervised studies
Stage 20
Modalités de candidatures
Application period
From 01/04/2024 to 01/07/2024
Compulsory supporting documents
  • Copy of identity document.

  • Motivation letter.

  • Letter of recommendation or internship evaluation.

  • All transcripts of the years / semesters validated since the high school diploma at the date of application.

  • Curriculum Vitae.

  • Detailed description and hourly volume of courses taken since the beginning of the university program.

Additional supporting documents
  • Copy of the last diploma.

  • Certificate of English level (compulsory for non-English speakers).

  • VAP file (obligatory for all persons requesting a valuation of the assets to enter the diploma).

  • The application procedure, which depends on your nationality and your situation is explained here :

  • Supporting documents :
    - Residence permit stating the country of residence of the first country
    - Or receipt of request stating the country of first asylum
    - Or document from the UNHCR granting refugee status
    - Or receipt of refugee status request delivered in France
    - Or residence permit stating the refugee status delivered in France
    - Or document stating subsidiary protection in France or abroad
    - Or document stating temporary protection in France or abroad.

Course manager(s)
Administrative office