Training structure
Faculty of Science
Program
Mathematics S3 (Joffre)
2 creditsPhysics of Oscillators
36hComplements to general mathematics CPES S3
2 creditsAdvanced CPES Mathematics S3
2 creditsThermodynamics 2
36hCPES chemistry modeling
2 creditsComputing S3 (Joffre)
2 creditsPhysics-Chemistry S3 (Joffre)
6 creditsCPES Computer Science S3
2 creditsAdvanced CPES Sc subject S3
4 creditsEnglish CPES S3
1 creditsGeneral Culture S3 (Joffre)
1 credits
General Culture S4 (Joffre)
1 creditsCPES Computer Science S4
2 creditsMathematics S4 (Joffre)
2 creditsPhysics-Chemistry S4 (Joffre)
6 creditsAtomistics & reactivity
Advanced CPES Mathematics S4
2 creditsProject CPES Sc matter S4
1 creditsComputer Physics
36hConservation, dissemination and propagation CPES S4
2 creditsIT S4 (Joffre)
2 creditsAdvanced CPES Sc subject S4
3 creditsEnglish CPES S4
1 credits
Mathematics S3 (Joffre)
Level of study
BAC +2
ECTS
2 credits
Component
Faculty of Science
Second year mathematics program, part taught at Lycée Joffre :
# Reminders of linear algebra and complements of Euclidean geometry
# Advanced probability
# Analysis of functions of one variable
# Functions of several variables
Physics of Oscillators
Level of study
BAC +2
Component
Faculty of Science
Hourly volume
36h
The oscillator is an essential concept in physics: matter is often modeled by a collection of oscillators (harmonic or not) interacting with each other and with the external environment. The latter acts on the matter through a wave, such as an acoustic or electromagnetic wave. This makes it possible to lay the theoretical foundations of the problems of radiation-matter interaction and thus to build one of the fundamental tools for the study of matter (in the broad sense): spectroscopy.
Spectroscopy is indeed the basic tool for the study of the physical properties of objects that surround us, such as a molecule, a crystal, a star, a galaxy. These properties are deduced either from their spontaneous emission or from their response to an external excitation. For example we measure the properties of absorption, reflection, transmission of an applied electromagnetic radiation (visible, infra-red, X, neutrons, ...). The response to this radiation is then a way to discover which are the various types of oscillators constituting the studied medium.
In short, the study of the physical media that surround us requires the use of two fundamental theoretical tools: oscillators and waves, which are the subject of this course.
The principle adopted here is a step-by-step progression from the harmonic oscillator, then from coupled oscillators, to waves treated in the framework of discrete systems: infinite and then finite coupled oscillators with different edge conditions.
Complements to general mathematics CPES S3
Level of study
BAC +2
ECTS
2 credits
Component
Faculty of Science
Complements to linear algebra, reduction theory and applications
# Complements to linear algebra, notion of direct sum
# Determinants
# Reduction: diagonalization and applications to the study of discrete and continuous dynamic systems in physics, chemistry, biology or economics.
Advanced CPES Mathematics S3
Level of study
BAC +2
ECTS
2 credits
Component
Faculty of Science
This course continues the training of students in applied mathematics, with a focus on numerical methods.
Program (subject to change depending on the year and time available) :
# numerical matrix analysis
# digital integration
# numerical resolution of diferential equations
# introduction to the qualitative study of nonlinear differential equations
.
Thermodynamics 2
Level of study
BAC +2
Component
Faculty of Science
Hourly volume
36h
This module completes and formalizes the notions of thermodynamics introduced by the EU Thermodynamics 1, by deepening several aspects: thermodynamic potentials defined from Legendre transformations, thermodynamics of open systems, phase transitions of the pure body and irreversible processes, with incursions at the microscopic level in order to give an overview of the physical foundations of the theory.
CPES chemistry modeling
Level of study
BAC +2
ECTS
2 credits
Component
Faculty of Science
This course is only open to students in the Matter Sciences stream of the CPES. It includes a mathematical part and a chemical part, focusing on the notion of symmetry group (of a chemical molecule) and its application to the determination of molecular orbitals by linear combination of atomic orbitals.
Indicative program :
# introduction to group theory, finite groups, symmetry groups of molecules
# linear group representations, character theory and applications to molecular orbitals or vibrational modes of a molecule
Computing S3 (Joffre)
Level of study
BAC +2
ECTS
2 credits
Component
Faculty of Science
The 2nd year computer science course at the Lycée focuses on advanced concepts in algorithms and programming:
# Tree-like data structures: binary trees, heaps, ABR, priority queues
# Heap sorting, lower limit on sorting
# Graph structure: representations (adjacency matrices, edge lists, neighbor lists)
# Basic algorithms (connectivity, depth and width traversal, topological sorting)
# Distance calculation (Dijkstra, heap implementation)
# Introduction to object programming (encapsulation, late linking, classes, methods, etc.)
# Programming in Python
Physics-Chemistry S3 (Joffre)
Level of study
BAC +2
ECTS
6 credits
Component
Faculty of Science
Program taught at Lycée Joffre in 2nd year
# Solid mechanics (statics, dynamics, not torsors)
# Electromagnetism in a vacuum
# Diffraction optics, Fourier optics
# Waves and radiation, wave scattering.
# Kinetics and thermochemistry, intro to electrochemistry
# Organic chemistry: some reaction mechanisms that lend themselves well to quantum modeling with frontier orbitals
CPES Computer Science S3
Level of study
BAC +2
ECTS
2 credits
Component
Faculty of Science
This UE completes the computer science training by opening up to the study of information systems and databases (design of processing in an information system and management of relational databases):
# Information systems: introduction of the entity/association model, relational model, processing modeling (conceptual processing model, organizational processing model).
# Databases: create, manipulate and query relational databases.
Advanced CPES Sc subject S3
Level of study
BAC +2
ECTS
4 credits
Component
Faculty of Science
As in the first year, this course is based on tutored projects involving data acquisition, processing and interpretation: the approach combines numerical methods, mathematical ideas and modeling.
Study topics may evolve from year to year, in order to renew students' interests.
English CPES S3
Level of study
BAC +2
ECTS
1 credits
Component
Faculty of Science
This modern language course focuses on written and spoken English, with particular emphasis on oral expression.
General Culture S3 (Joffre)
Level of study
BAC +2
ECTS
1 credits
Component
Faculty of Science
General culture (epistemology and philosophy) :
# history of ideas
# epistemology of science and digital technology
#argumentatition et communicatition
General Culture S4 (Joffre)
Level of study
BAC +2
ECTS
1 credits
Component
Faculty of Science
General culture (epistemology and philosophy) :
# history of ideas
# epistemology of science and digital technology
#argumentatition et communicatition
CPES Computer Science S4
Level of study
BAC +2
ECTS
2 credits
Component
Faculty of Science
Introduction to the use of data mining methods :
# Motivations, fields of application
# Data mining tasks (classification, estimation, prediction, etc.)
# Data processing (pre/post-processing)
# Supervised learning (Bayes method, k nearest neighbors, neural networks, etc.)
# Unsupervised learning (k-means)
# Method evaluation
# Data mining software (R, Scikit, Weka, etc.)
Mathematics S4 (Joffre)
Level of study
BAC +2
ECTS
2 credits
Component
Faculty of Science
Second year mathematics program, part taught at Lycée Joffre :
# Reminders of linear algebra and complements of Euclidean geometry
# Advanced probability
# Analysis of functions of one variable
# Functions of several variables
Physics-Chemistry S4 (Joffre)
Level of study
BAC +2
ECTS
6 credits
Component
Faculty of Science
Program taught at Lycée Joffre in 2nd year
# Solid mechanics (statics, dynamics, not torsors)
# Electromagnetism in a vacuum
# Diffraction optics, Fourier optics
# Waves and radiation, wave scattering.
# Kinetics and thermochemistry, intro to electrochemistry
# Organic chemistry: some reaction mechanisms that lend themselves well to quantum modeling with frontier orbitals
Atomistics & reactivity
Component
Faculty of Science
The first part of this course presents the basics of quantum chemistry for chemists and physical chemists. It begins by reviewing the principles of quantum mechanics and its master equation, the Schrödinger equation. The resolution of the Schrödinger equation in simple cases and the notions of wave functions and quantization are presented and illustrated in simple cases. The hydrogen atom is then studied.
The teaching also focuses on approximation methods to determine the properties of complex systems where the Schrödinger equation cannot be solved directly. The effect of spin on the electronic properties of atoms and molecules will also be discussed.
The second part of this teaching focuses on the quantum description of molecular properties and reactivity. The qualitative construction of molecular orbitals using symmetry properties will be introduced and the link between molecular orbital diagram and chemical bonding is made. The link between molecular geometry and electronic structure will be discussed. This teaching will then focus on Huckel's method of obtaining molecular orbital diagrams of π systems. The classical notions of conjugation, delocalization, donor or acceptor character and aromaticity will be studied in this approach. The theory of boundary orbitals is used to rationalize molecular reactivity (cycloadditions, electrocyclisation) and molecular geometries.
Advanced CPES Mathematics S4
Level of study
BAC +2
ECTS
2 credits
Component
Faculty of Science
This course continues the training of students in applied mathematics, in particular the use of statistical tools:
# Notions of populations and random samples.
# Estimators.
#Mean square error and bias-variance decomposition.
# Empirical estimators of mean and variance. Construction of estimators using the method of moments. Maximum likelihood.
Interval estimation.
# Hypothesis testing: null hypothesis, alternative hypothesis. First and second errors. Power of a test. Test statistics, rejection region. Examples of classical tests.
Project CPES Sc matter S4
Level of study
BAC +2
ECTS
1 credits
Component
Faculty of Science
This course, similar in spirit to the first-year project, is an introduction to the research approach, more advanced than in the first year: it includes immersion in a research laboratory, a bibliographical study, and the completion of a project involving the study of a physical or chemical context, the acquisition of experimental or observational data, and the implementation of a modeling and/or digital simulation approach.
Computer Physics
Level of study
BAC +2
Component
Faculty of Science
Hourly volume
36h
This module constitutes an introduction to the approach of using computer tools in Physics: it is a question of analyzing a phenomenon, of idealizing/modeling it, then of studying it on computer. The critical interpretation of the results is also part of it. The examples are chosen in relation with the other current subjects in the training.
Conservation, dissemination and propagation CPES S4
Level of study
BAC +2
ECTS
2 credits
Component
Faculty of Science
This course covers the theoretical tools for describing distributed and conserved quantities, such as density, energy or charge density.
The first introductory chapter presents the general conservation equation, and the vector analysis tools needed to understand it, as well as the various fields in which this equation is used (practically all physics, but also chemistry, economics, etc.).
The following chapters are mainly devoted to the case with one dimension of space and one of time (1+1 D). Chapter 2 deals with convective transport, and presents the characteristic method for solving the corresponding quasi-linear first-order partial differential equation. Diffusive transport is then studied in Chapter 3, with the heat equation and the Fourier solution method. Finally, Chapter 4, devoted to reaction-diffusion equations, considers the case of convective and diffusive transport with the Smoluchowsky equation, and the derivation of the famous Einstein equation for diffusion.
The course is accompanied by theoretical and numerical tutorials, covering road traffic and queue modeling, for example.
IT S4 (Joffre)
Level of study
BAC +2
ECTS
2 credits
Component
Faculty of Science
The 2nd year computer science course at the Lycée focuses on advanced concepts in algorithms and programming:
# Tree-like data structures: binary trees, heaps, ABR, priority queues
# Heap sorting, lower limit on sorting
# Graph structure: representations (adjacency matrices, edge lists, neighbor lists)
# Basic algorithms (connectivity, depth and width traversal, topological sorting)
# Distance calculation (Dijkstra, heap implementation)
# Introduction to object programming (encapsulation, late linking, classes, methods, etc.)
# Programming in Python
Advanced CPES Sc subject S4
Level of study
BAC +2
ECTS
3 credits
Component
Faculty of Science
As in the first year, this course is based on tutored projects involving data acquisition, processing and interpretation: the approach combines numerical methods, mathematical ideas and modeling.
Study topics may evolve from year to year, in order to renew students' interests.
English CPES S4
Level of study
BAC +2
ECTS
1 credits
Component
Faculty of Science
This modern language course focuses on written and spoken English, with particular emphasis on oral expression.