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# Year 2 Courses

> Pure mathematics
> Computer science
> Economics
> Physics
> Biology
> Mechanics
> Chemistry
> Applied Mathematics

Pure mathematics
Dynamical Systems

This course provides basic training in geometry and dynamic systems. The module gives students the opportunity to master the mathematical tools used to teach applied mathematics, physics, mechanics and economics.It opens the way to the more advanced year three mathematics programs.
Lecturer: Raphaël Krikorian

Fourier Analysis and Spectral Theory
The first objective of this course is to give students a deeper understanding of certain mathematical notions that are useful in other sciences, specifically Fourier analysis and spectral analysis. The second objective is to introduce some of the basic techniques used to solve several partial differential equations.
Lecturer: Yvan Martel

Distributions
This course provides basic analysis training. The module gives students the opportunity to master the mathematical tools used to teach applied mathematics, physics, mechanics and economics. It opens the way to the more advanced year three pure mathematics programs.
Lecturer: 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.
Lecturer: David Hernandez

Introduction to Differential Geometry
This course introduces some of the fundamental notions of differential geometry: sub-varieties, tangent spaces, Riemannian metrics, curvature, covariant derivatives, geodesy, etc., illustrating them through the study of surfaces.
It is aimed at all students who want to acquire basic knowledge of this central field of pure mathematics, particularly those keen to specialize in mechanics, physics or, of course, pure mathematics.
Lecturer: David Renard

Computer Science
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.
Lecturer: 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.
Lecturer: 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.
Lecturer: Benjamin Doerr

Concurrent and Distributed Programing
There is no longer an application that is not intrinsically parallel: from a simple graphic interface to the robot controller, which manages concurrent events and programs, executing themselves simultaneously, and sharing common resources. This course aims to give students the tools to master effective parallel programing, avoiding the many pitfalls associated with using shared resources.
Lecturer: Éric Goubault

There are many large-scale software programs (size, number of writers, lifespan) which are only possible thanks to a modular architecture, which ideally should allow each component to be designed, created, tested, modified and reused, independently from the system's other components.
The main objective of this course it to present the fundamental concepts and mechanisms which, in a modern programing language, allow this modular organization.
Lecturer: François Pottier

Mass Data Processing
This course aims to familiarize students with C++ language for mass data processing. In the first part of the course, we will study object-oriented programing in C++, and will demonstrate how to profile, optimize and debug the programs. In the second part, we will describe some algorithmic methods for data-based learning and demonstrate their uses in practice on a variety of concrete applications. In the final part of the course, we will focus on learning with large data sets.
Lecturer: Frank Nielsen

Economics
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.
Lecturers: Marie-Laure Allain and Pierre Picard

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.
Lecturer: Édouard Challe

Introduction to Econometrics
Econometrics is a discipline that applies statistics methods to the estimation and validation of economic models. This course presents the everyday concepts and tools of this discipline (hypothesis tests, distributions, causality, linear regression, qualitative variable models, etc.).
Lecturers: Francis Kramarz and Julien Pouget

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.
Lecturers: Grégory Corcos and Isabelle Méjean

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.
Lecturer: Philippe Tibi

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.
Lecturer: 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.
Lecturers: Christoph Kopper and 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.
Lecturers: Fabien Bretenaker and Jean-Marcel Rax

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.
Lecturers: Jean-Philippe Bouchaud and Gilles Montambaux

Statistical Physics 2
Phase transitions, dynamics and equilibrium approach, Monte-Carlo method, information theory, application to condensed matter (Bose condensation, band theory, magnetism).
Lecturers: Silke Biermann and Rémi Monasson

Biology
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.
Lecturer: 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.
Lecturer: 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.
Lecturer: Tatiana Giraud

Human Biology and Pathology: from Symptom to Mechanism
This course invites students to discover the functioning anomalies behind human pathologies by showing how scientific reasoning has progressed, moving from the symptom to an understanding of the mechanisms and anomalies in question, on a cellular and molecular level.
Lecturer: Jean-Louis Martin

Mechanics
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.
Lecturer: 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.
Lecturer: 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.
Lecturer: Laurent Jacquin

Industrial Application in Mechanics
This course is an introduction to the mechanical analysis of solids using numerical simulation (calculation codes), in preparation for future studies on industrial parts. The scope is deliberately limited to quasi-static analyses: some of the concepts used will have been presented in continuum mechanics courses, while others will be introduced here in a simplified way.
Lecturers: Éric Charkaluk and Éric Lorentz

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.
Lecturer: Hervé Le Treut

Chemistry
Introduction to Molecular Chemistry
This course introduces the basic theoretical foundations used to describe the structure and reactivity of organic molecules. The theory of molecular orbitals explains the preferential geometry of molecules and the nature of the transformations they undergo when placed in the presence of different types of reagents.
Lecturer: Gilles Frison

Organic Chemistry
The objective of this course is to add to the basics of organic chemistry learned in the classes préparatoires and to apply this knowledge by introducing, in particular, the reactivity of nitrogen compounds, heteroelements, or even transition metal complex derivatives.
Lecturer: Laurence Grimaud

Foundations of Molecular Chemistry and Materials
The course sets out the fundamental notions used to rationalize the chemistry of transition metals. Based on the theory of molecular orbitals (the basics of which will be covered briefly so that no prior knowledge is necessary), the course is illustrated by the study of molecules that are fundamentally important to industrial chemistry and green chemistry.
Then, based on the notions of conjugation and aromaticity, the structure of molecular and one-dimensional materials is addressed in order to introduce the electronic properties of solids and the applications in the field of electronics or energy conversion.
Lecturers: Gilles Frison and Narcis Avarvari

Coordination Chemistry
The course presents the basic concepts and reactions of organometallic chemistry and their applications in different fields: fine chemistry, industrially relevant catalytic transformations, natural product synthesis, preparation of materials, natural resource recovery, activation of small molecules, etc.
Lecturers: Didier Bourissou and Nicolas Mézailles

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.
Lecturers: Thierry Gacoin and Laurent Bouteiller

Applied Mathematics
Statistics
This introductory course presents the notion of a statistical model and the basic principles and concepts of estimation and tests.
Lecturer: Alexandre Tsybakov

Numerical Approximation and Optimization
Numerical simulations are becoming indispensable in sciences, technologies and services. They mainly rely on mathematical models. This course will cover the mathematical modeling of concrete problems, in particular engineering issues. The applied mathematician's approach will be presented as well as an overview of the numerical methods used.
Lecturer: 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.
Lecturer: François Alouges

Dynamic Model Control
This course covers dynamic models (differential equations). Such models are found in numerous concrete situations: satellite orbits, navigation, but also in economics. They can incorporate deterministic or random tools. The course will cover the analysis, numerical approximation and control of such models.
Lecturer: Pierre-Louis Lions

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.
Lecturer: Thierry Bodineau