Multidisciplinary Scientific Studies

For Year 2 of the Ingénieur Polytechnicien Program, each student must complete courses in at least 4 different subjects among the Year 2 courses offered by the Departments of Pure and Applied Mathematics, Physics, Chemistry, Biology, Mechanics, Economics, Computer Science, and Innovation Management and Entrepreneurship.

Each student is also required to select a practical Applied Laboratory Module (MODAL). A MODAL may only be chosen once and counts as an independent subject.

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Cycle Ingenieur in class

Calcul différentiel et fonctions holomorphes *
Ce cours est un enseignement de base en mathématiques permettant d’acquérir des outils utilisés dans les enseignements de mathématiques appliquées, physique, mécanique et économie. Il prépare aux autres cours de mathématiques plus avancés, en particulier ceux du programme d’approfondissement/M1.
Enseignant : Thomas Gauthier

Distribution, Analyse de Fourier et EDP *
Ce cours présente une formation de base en analyse. Ce module permet de dominer les outils mathématiques utilisés dans les enseignements de mathématiques appliquées, physique, mécanique et économie. Il ouvre la voie aux programmes d’approfondissement de mathématiques de troisième année.

Le cours présente le formalisme des distributions, introduites par Laurent Schwartz à la fin des années 1940, qui fournit un cadre naturel pour l’étude de la transformation de Fourier. Il se concentre ensuite sur l’étude des propriétés fondamentales des principales équations aux dérivées partielles de la physique mathématique.

Professor: François Golse

Algebra and Galois Theory
The goal of this course is to firstly introduce the basics and tools of general algebra (groups, rings, algebra, quotients, field extensions, etc.) which will then make it possible to later develop the
Galois theory and some of its more remarkable applications.
Professor: David HERNANDEZ

Analyse fonctionnelle *
Ce cours entend fournir les bases de l’analyse fonctionnelle aussi bien en amont des applications aux équations aux dérivées partielles, qu’en amont des applications aux algèbres d’opérateurs.
Des considérations de théories des groupes topologiques seront également prises en compte. Le cours reprend les propriétés analytiques et géométriques des espaces de Hilbert, de Banach et de leurs généralisations, avant de les mettre en action en théorie de la mesure, théorie spectrale, etc. Parmi la liste des sujets abordés, voici quelques notions importantes : convexité, points fixes, mesures de Haar, représentations des groupes compacts, opérateurs elliptiques, théorèmes de plongements entre espaces fonctionnels.
Professor: Bertrand RÉMY

Advanced Quantum Physics
A reminder of the basic principles; evolution operator; approximation methods (variations, stationary perturbation, time-dependent perturbation); nuclear magnetic resonance; identical particles and the Pauli principle; angular momentum; hydrogen atom; addition of angular momenta; atoms and molecules.
Professor: Manuel JOFFRE

Relativity and Variational Principles
Foundations of restricted relativity; Lorentz transformations and relativist optics; Minkowski space-time; Variational principles, Euler-Lagrange equations; Invariance and conservation laws, Relativistic Lagrangian theory, Relativistic mechanics; Relativity and electromagnetism; Hamiltonian mechanics and links with quantum mechanics; Introduction to general relativity.
Professor: Christoph KOPPER et Roland LEHOUCQ

Electromagnetism
Field-material interaction and application. Media, Materials and Structures; Energy, Power and Forces; Modes, Waves and Rays; Anisotropies and Nonlinearities; Antenna and oscillators; Metamaterials; Magnetism; Near fields.
Professor: Fabien BRETENAKER et Antoine BROWAEYS

Statistical Physics 1
Introductory course to the basic concepts of statistical physics. Basic principles of statistical physics; Boltzmann entropy and statistics; microcanonical, canonical and grand canonical ensembles; simple illustration: classical ideal gas. Quantum statistics: Bose-Einstein and Fermi-Dirac.
Professor: Gilles MONTAMBAUX

Molecular Biology and Genetic Information
This course allows students to discover a basic discipline and is recommended in order to pave the way to the other year 2 biology courses and the year 3 specialization programs offered by the department. It will reveal the logic of the workings of the living world and show how biology, a discipline which is currently growing rapidly, is developing more and more at the interface between physics, chemistry, computer science and engineering science.
Professor: Arnaud ECHARD

The Cell, A Living Unit
The cell is the structural and functional unit of all living organisms. The aim of this course is to describe the organization, functioning and dysfunctions of the cell. It introduces students to cellular biology, a central discipline of life sciences, at the interface between numerous other aspects of biology, but also between physics, chemistry, computer science and engineering science.
Professor: Sandrine ÉTIENNE-MANNEVILLE

Ecology and Biodiversity
The theories of biodiversity are at the interface between ecology and evolution. This course presents the processes involved in genesis and biodiversity maintenance. These processes are genetic, macroevolutionary and ecological. The concepts are addressed in the form of models which use the game theory, spatially structured models and population genetics and dynamics, but also using specific case studies.
Professor: Tatiana GIRAUD

Pathologie et stratégies thérapeutiques
Ce cours illustre quelques pathologies et les méthodes les plus actuelles pour les prendre en charge. Les pathologies choisies sont celles qui représentent les plus grands défis pour nos sociétés développées. Ce cours de biomédecine insiste sur le substrat biologique des pathologies et des traitements et fait une place à l’économie de la santé.
Professor:
Alexis Gautreau

Microeconomics
This course presents an introduction to the main notions and reasoning behind microeconomic analysis, i.e. analysis of the behavior of economic agents and their interactions on the markets and in organizations.
Professor: Marie-Laure ALLAIN et Pierre BOYER

Macroeconomics
This course covers a large number of traditional macroeconomics topics, while providing students with the basic tools to understand the world around them and to rigorously address the economic problems they may face.
Professor: Édouard CHALLE

International Economics
This course aims to provide students with a range of analytical tools for macroeconomics and international commerce. It presents fundamental theoretical models and pays specific attention to empirical analysis and the way in which the models reproduce data.
Professor: Enseignants: Grégory CORCOS et Isabelle MÉJEAN

Business Economics
Intended for students who want to familiarize themselves with economic issues and business problems, this business economics course aims, on the one hand, to provide the conceptual tools used to understand the macroeconomic trends that structure the world of business, and, on the other hand, business-related strategic analysis, financial and management operational tools.
Professor: Enseignant : Philippe TIBI

Statistics
This introductory course presents the notion of a statistical model and the basic principles and concepts of estimation and tests.
Enseignant : Eric MOULINES

Optimisation et Contrôle
Ce cours est une introduction à l'optimisation et au contrôle de modèles dynamiques qui sont des outils indispensables à la conception et au bon fonctionnement des systèmes issus des sciences, de la technologie ou de l'industrie et des services.

La première partie du cours portera sur l'optimisation, avec ou sans contraintes, en dimension finie ou infinie. Après quelques aspects théoriques sur les conditions d'optimalité et l'existence d'optima, l'accent sera mis sur les algorithmes numériques de type gradient. Une attention particulière sera portée à certaines grandes classes de problèmes comme la programmation linéaire et la programmation quadratique séquentielle.

La seconde partie du cours étudiera le contrôle d'équations différentielles modélisant des problèmes d'évolution en temps. Les notions de contrôlabilité, d'état adjoint et le principe du minimum de Pontryaguine seront introduits.

Par delà de ces aspects techniques, le cours se veut aussi une illustration de la démarche des mathématiques appliquées, mélant modélisation, analyse mathématique et simulation numérique, qu'il est nécessaire de maîtriser dans tout processus innovant.

Enseignant : Grégoire ALLAIRE

Variational Analysis of Partial Differential Equations
This course covers partial differential equation-based models. Such models are found in multiple scientific and industrial fields such as solid and fluid mechanics, electromagnetism, climatology, blood flows, etc. The focus will be on how to use variational principles for theoretical resolution and for developing numerical solution methods.
Enseignant : François ALOUGES

Random Phenomena Modeling
Randomness plays a decisive role in multiple aspects of engineering science (telecommunications, shape recognition, network administration, etc.) and more generally economics, medicine, biology and physics. The purpose of this course is to formalize the notion of random dynamics and illustrate it through a variety of applications. We will describe two fundamental notions in probability theory: Markov chains and Martingales.
Enseignant : Thierry Bodineau

Introduction à l’Analyse Numérique : des fondements mathématiques à l’expérimentation avec Jupyter
Ce cours propose une introduction à l’analyse numérique, partant des fondements mathématiques sur lesquels les méthodes numériques reposent et allant jusqu’à l’implémentation et l’emploi de ces méthodes sur la base de notebooks Jupyter en passant par la compréhension de leur efficacité numérique. Le lien est fait avec les applications afin de comprendre l’étendue de l’utilisation de ce type de méthode d’un point de vue pratique. Les implémentations de ces méthodes dans des bibliothèques numériques existantes sont aussi documentées.

Enseignant : Marc Massot

Réactivité et Synthèse Moléculaire
Le cours aborde la synthèse moléculaire en partant des concepts de base de réactivité. Tout au long de ce cours, différentes interventions, effectuées sous la forme de mini-conférences, donnent des éclairages sur divers aspects très actuels de la recherche et de l'industrie en chimie moléculaire.

Professor: Laurence GRIMAUD

Orbitales, molécules et matériaux
Le cours propose d’établir et de renforcer les bases fondamentales et rationnelles de cette discipline et de les illustrer par de nombreuses applications, notamment dans le domaine de l’énergie. Il est construit pour s’adresser à tous les élèves intéressés, sans prérequis. Les élèves qui envisagent de faire de la chimie en 3ème année, et par la suite, trouveront dans ce cours de nouvelles notions, fondamentales pour la poursuite de leur apprentissage en chimie moléculaire et en chimie des matériaux. Les autres élèves s’enrichiront d’une culture scientifique générale et rigoureuse qui pourra leur être d’une grande utilité pour d’autres disciplines comme la biologie ou la physique moléculaire.     
Professor: Gilles FRISON et Narcis AVARVARI

Materials Chemistry
The course presents an introduction to polymers (syntheses and properties), illustrated by concrete examples of industrial polymers. It continues with an introduction to solid chemistry, notably oxides and their structural characterization, thus addressing the relationships between structure and properties, which play an essential role in the concrete applications of functional materials.
Professor: Thierry GACOIN, Guilhem DEZANNEAU et Laurent BOUTEILLER

Continuum Mechanics I
This course presents the fundamental concepts of the mechanics of deformable continua within the simplified framework of slender structures. The objective is to introduce all of the concepts into this restricted geometric framework in order to quickly move on to applications and address numerous phenomena with a simplified mathematical formalism.
Enseignant : Jean-Jacques MARIGO

Continuum Mechanics 2
The course presents the fundamental concepts of continuum mechanics in a general three-dimensional framework. It applies them to simple examples in fluid mechanics and solid mechanics.
Enseignant : Patrick LE TALLEC

Fluid Mechanics
The goal of this course is to provide students with a general solid foundation on the subject. The course starts by going over the different fluids, with regards to physics, thermodynamics and mechanics, then covers the different principles of continuum mechanics and finishes off with the fundamental equations of fluid mechanics: Navier-Stokes equations.
Enseignant : Laurent JACQUIN

Dynamics of the Atmosphere and Oceans
This course is an introduction to "geophysical fluid mechanics", i.e. the mechanics of the rotating and vertically stratified fluids which constitute the ocean and the atmosphere. It is an opportunity to study a large number of generic methods and processes found in the study of all other fluids. However, the main focus is on the role of the Coriolis forces and invariants associated with rotation (vorticity, potential vorticity, angular momentum) which primarily structure atmospheric and oceanic flows.
Enseignant : Hervé LE TREUT

Programing and Algorithm Basics
This course aims to take students from "Introduction to Computer Science" level to the end of the "Principles of Programing Languages" course level, so that they can go on to complete the École Polytechnique's computer science program. Teaching will mainly cover data structures (graphs, lists, stacks, lines, trees), algorithmics and a minimum of complexity theory.
Professor: Jean-Christophe FILLIÂTRE

Foundations of Computer Science: Logic, Models and Calculations
This course presents the foundations of computer science as a science. While the idea of using machines to perform calculations is an old one, it was only in the 1930s that the work of Alan Turing, Alonzo Church, Kurt Goedel and others laid the foundations for what would become computer science as we know it today.
Professor: Olivier BOURNEZ

Algorithm Design and Analysis
Algorithms are at the heart of all calculations. This course, drawing on the algorithmic foundations laid during the first computer science course, provides students with solid training in modern algorithmics.
During this course, students will gain in-depth knowledge of the main algorithms, understand how and why they function and be capable of reducing other calculation problems to these fundamental basics.
Professor: Benjamin DOERR

Algorithmes pour l’analyse de données en C++ *
L'analyse de données moderne s'appuie sur des langages de haut niveau comme Python ou R pour la manipulation et le traitement des données. Toutefois, derrière les bibliothèques standard comme Scikit-Learn se cachent des implémentations dans des langages de bas niveau comme C ou C++ pour une exécution optimisée et une gestion efficace des ressources mémoire ou de calcul. D'où l'intérêt de ce cours, dont l'objectif est double : d'une part, se familiariser avec certaines des techniques standard d'analyse de donnéés et d'apprentissage machine ; d'autre part, acquérir une compétence en programmation C/C++ qui permette à terme aux élèves d'adapter les implémentations bas niveau existantes à leurs besoins spécifiques. A noter que les paradigmes de programmation abordés lors du cours sont quasi-exclusivement séquentiels, la programmation concurrente étant tout juste effleurée lors de la dernière séance et réservée pour d'autres cours.
Professor: Steve OUDOT

Informatique Graphique 3D *
Outre son importance pour le loisir numérique (jeux vidéos, effets spéciaux, films d'animation 3D), l'informatique graphique 3D est indispensable au prototypage virtuel industriel (design d'objets ou de mécanismes destinés à être fabriqués), aux simulateurs d'apprentissage et autres "serious games", ainsi qu'à la visualisation scientifique, par exemple pour l'exploration visuelle de données ou de résultats de simulation. Ce cours présente l'ensemble de l'informatique graphique, en se concentrant sur son volet interactif. Il couvre en particulier les techniques de modélisation géométrique, le rendu projectif, et les bases de l'animation 3D.

Professor: Marie-Paule Cani

Group Science Project

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Cycle Ingenieur project in group

The Group Science Project is carried out throughout Year 2. For half a day every week, all students of the Program, in groups of four or five, must identify and resolve a major problem, or work on designing and producing an innovative technology demonstrator. Students must independently apply, over a long period of time, one or more scientific disciplines and an appropriate method and organization.

The topics chosen by the students must present a relevant scientific and/or technological challenge. They may range from fundamental research to engineering, and relate to the in-depth study of a specific discipline, or to the implementation of knowledge derived from several disciplines. Subjects for the Group Science Project may be chosen in conjunction with one of the labs of École Polytechnique, a third-party research organization, a business or a state-owned company.

The Group Science Project involves people from École Polytechnique, as well as its close partners, in particular the École Polytechnique Foundation.

Every year, students are given prizes for their Group Science Projects, awarded by École Polytechnique or companies, or won in national or international competitions. A number of Group Science Projects per year also lead to the creation of start-ups.

The Group Science Project aims to:

  • Allow students to complete specialized scientific work on their chosen project, using an approach that must be both creative and collective.
  • Encourage group work and team spirit, over a long period, enabling students to gain fundamental organizational skills.
  • Give students their first experience in project management.
  • Promote collaboration between students and researchers.

Innovation, Humanities and Social Sciences

Innovation Management and Entrepreneurship
During year 2, students attend a series of modules dedicated to the "Fundamentals of Organizations", during which they discover how companies operate (strategy, finance, organization, power, innovation, etc.). Each session is based on a business case analysis. Learn more

Humanities and Social Sciences
During the 1st semester, students take classes in:

Law, Economics and Political Science
(examples: corporate law, communications and media).

Humanities
(examples: political philosophy, history of religion).

Art
(examples: art history, architecture, design).

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Cycle Ingénieur sculpture

During the 2nd semester, students take classes such as Art History and Business Process and Management, as well as seminars on various topics, including: Geopolitics and Strategy, Introduction to Psychoanalysis and Philosophies of the Far East.

In addition, students take courses in foreign languages and sports.

Internship

The Internship takes place at the end of Year 2, either in France or abroad, and lasts three months. It is mandatory and gives students the opportunity to observe operational and organizational procedures while acquiring valuable professional experience.

Workshops are also offered by the school's Career Assistance and Resource Center to help students with their internship choice, from filling out applications to career plan development.

Students also have the opportunity to complete their internship abroad with a foreign company for three months.

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Cycle Ingenieur pro