Training structure
Faculty of Science
Program
Select a program
L2 - General Maths
The second year of the mathematics bachelor's degree (L2 General Mathematics) is a stage in the acquisition of fundamental elements and orientation. A first group of teaching units provides a foundation of knowledge and skills that are essential for all students of mathematics, whatever their future function or sector of activity. These teaching units are based on the following fundamental pillars: algebra and polynomials, differential and integral calculus, sequences and series.
A second group of teaching units is designed to support students throughout their training. These include more numerical methodological elements, with the use of computer tools linked to numerical analysis, elements of reasoning in the theory of probabilities, elements of in-depth study of modern languages and future orientation (PPE).
English S3
2 creditsAnalysis III integration and differential equations element
6 creditsProbabilities
5 creditsAlgebra III Reduction of endomorphisms
6 creditsPolynomial arithmetic
3 creditsCHOICE 1
5 creditsYour choice: 1 of 2
Modeling and object programming 1
5 creditsCHOICE 2
5 creditsChoice: 2 of 2
Oral Mathematics
1 creditsThermodynamics 2
36h
Elementary numerical analysis
3 credits
English S4
2 creditsAnalysis IV Function sequences, integer series, Fourier
8 creditsTopology of R^n and functions of several variables
5 creditsAlgebra IV Euclidean spaces
6 creditsStatistics
3 creditsNumerical linear algebra
4 creditsPPE in mathematics
2 credits
L2 - CUPGE Maths
The Cycle Universitaire Préparatoire aux Grandes Ecoles (CUPGE) Mathematics-Physics course is a reinforced mathematics-based training program.
English S3
2 creditsAnalysis III integration and differential equations element
6 creditsProbabilities
5 creditsAlgebra III Reduction of endomorphisms
6 creditsRigid Solid Dynamics
Electrostatics & Magnetostatics
4 credits36hPolynomial arithmetic
3 creditsThermodynamics 2
36h
English S4
2 creditsAnalysis IV Function sequences, integer series, Fourier
8 creditsTopology of R^n and functions of several variables
5 creditsAlgebra IV Euclidean spaces
6 creditsStatistics
3 creditsNumerical linear algebra
4 creditsElectromagnetism
6 credits54hPPE in mathematics
2 credits
L2 - Double Computer Mathematics
Modeling and object programming 1
5 creditsInformation Systems and Databases
5 creditsEnglish S3
2 creditsAnalysis III integration and differential equations element
6 creditsProbabilities
5 creditsAlgebra III Reduction of endomorphisms
6 creditsPropositional logic
5 creditsSystems
5 creditsElementary numerical analysis
3 credits
Analysis IV Function sequences, integer series, Fourier
8 creditsAlgorithms 3
5 creditsTopology of R^n and functions of several variables
5 creditsModeling and Object Programming 2
5 creditsEnglish S4
2 creditsCalculation models
5 creditsStatistics
3 creditsNumerical linear algebra
4 creditsPPE in mathematics
2 credits
Analysis III integration and differential equations element
ECTS
6 credits
Component
Faculty of Science
Following on from the analysis course in S2, this course deals with the notion of series with terms of any sign. The Riemann integral will be defined and applied to linear and other differential equations. The integration section will be extended to generalized integrals.
Probabilities
ECTS
5 credits
Component
Faculty of Science
This course introduces probability spaces, the concepts of probability and independence, and defines discrete and density random variables, with an emphasis on modeling.
Algebra III Reduction of endomorphisms
ECTS
6 credits
Component
Faculty of Science
This course will cover the notions of symmetric group, determinants and will deal with the reduction of endomorphisms in finite dimension (up to Jordan form) and its applications. This is a first step towards spectral analysis.
Polynomial arithmetic
ECTS
3 credits
Component
Faculty of Science
In this course, we introduce an overview of algebraic structures (ring, ideal, body) before tackling K[X] algebra and defining arithmetic on polynomials, drawing parallels with integer arithmetic seen in L1. Calculations on polynomial functions and rational fractions will be covered (explicit factorizations/decompositions).
Modeling and object programming 1
ECTS
5 credits
Component
Faculty of Science
This course introduces the basic principles of object-oriented modeling and programming. The supporting languages are UML and Java, with possible elements of Python at the end of the semester.
From a modeling point of view, this course focuses on static view modeling, using class and instance diagrams. These diagrams cover the notions of classes, instances, attributes, operations, associations, interfaces and specialization. Their parallel implementation in Java will give them a concrete application, and show in particular the translation of associations in a programming language that doesn't have them. In Java, particular emphasis will be placed on the notions of class, instance, inheritance, instance variable, class variable and method, visibility and package organization, and static and dynamic binding. Data collections widely used in Java will be presented to translate some of the associations (associative lists and dictionaries). These collections will introduce students to the use of generic classes. Implementation of object-oriented programming concepts with Python may be tackled at the end of the semester, depending on progress.
Thermodynamics 2
Study level
BAC +2
Component
Faculty of Science
Hourly volume
36h
This module completes and formalizes the notions of thermodynamics introduced in EU Thermodynamics 1, by exploring several aspects in greater depth: thermodynamic potentials defined on the basis of Legendre transformations, thermodynamics of open systems, pure-body phase transitions and irreversible processes, with incursions at the microscopic level to provide an insight into the physical foundations of the theory.
Elementary numerical analysis
ECTS
3 credits
Component
Faculty of Science
In this course, we'll look at the particularities of floating-point calculus and then go into detail on the most common elementary numerical methods for solving non-linear equations, interpolating a function and approximating an integral. Students will learn how to implement an algorithm to solve a numerical analysis problem.
English S4
Study level
BAC +2
ECTS
2 credits
Component
Faculty of Science
The first-semester course reviews the grammar essential for oral and written communication(tenses and aspect, asking questions, comparisons and superlatives, passive voice) as well as essential general vocabulary(numbers, measurements, shapes); it also includes an introduction to technical vocabulary(basic building materials, plane engine, bike parts, electronic device) through themed lessons and videos in the field of mechanical engineering.
Finally, numerous activities are offered to promote oral expression skills (presentation vocabulary, simulations, role-playing and board games), so that students are able to describe the specific features, functions and uses of a piece of technical equipment of their choice in an oral presentation by groups of two.
S4
Grammatical aspects are limited to a review of modal auxiliaries.
The vocabulary is much more focused on the various elements involved in the design and operation of different types of heat engines, and on emerging technologies(drones, driverless vehicles, 3D-printing).
Students are also expected to produce a CV in English and practice writing emails in a formal style, so as to be prepared for internship or job-seeking situations where fluency in English will either be necessary or an additional skill.
The practice of expression is always the main objective, with an individual oral presentation at the end of the semester of their second-year project in mechanics.
Analysis IV Function sequences, integer series, Fourier
ECTS
8 credits
Component
Faculty of Science
This course covers the notions of function sequences and series, and the various convergences. Integer and Fourier series will also be developed.
Topology of R^n and functions of several variables
ECTS
5 credits
Component
Faculty of Science
This course covers an introduction to the topology of R^n, the basics of differential calculus for R^n functions in R and optimization. Parametric curves will also be covered.
Algebra IV Euclidean spaces
ECTS
6 credits
Component
Faculty of Science
This course is an introduction to bilinear algebra, covering Euclidean and Hermitian spaces. It covers isometries, duality, quadratic forms and endomorphisms.
Statistics
ECTS
3 credits
Component
Faculty of Science
This course introduces the main statistical concepts (graphical representation of data, indicators of central tendency and dispersion, relationships between two variables, confidence intervals).
Numerical linear algebra
ECTS
4 credits
Component
Faculty of Science
This course deals with numerical methods applied to linear algebra, and more specifically to matrices. The notions of conditioning, matrix decompositions and iterative methods, and the calculation of eigenvalues will be introduced.
PPE in mathematics
ECTS
2 credits
Component
Faculty of Science
This course includes presentations on career opportunities, themed lectures and round-table discussions on the various mathematical professions.
For students with a pre-professionalization AED contract, the UE accompanies their activity in the establishment, providing a few elements to enrich their observation and give them perspective. It also prepares them for the written work they will be required to submit.
Analysis III integration and differential equations element
ECTS
6 credits
Component
Faculty of Science
Following on from the analysis course in S2, this course deals with the notion of series with terms of any sign. The Riemann integral will be defined and applied to linear and other differential equations. The integration section will be extended to generalized integrals.
Probabilities
ECTS
5 credits
Component
Faculty of Science
This course introduces probability spaces, the concepts of probability and independence, and defines discrete and density random variables, with an emphasis on modeling.
Algebra III Reduction of endomorphisms
ECTS
6 credits
Component
Faculty of Science
This course will cover the notions of symmetric group, determinants and will deal with the reduction of endomorphisms in finite dimension (up to Jordan form) and its applications. This is a first step towards spectral analysis.
Rigid Solid Dynamics
Study level
BAC +2
Component
Faculty of Science
This unit deals with the study of the mechanics of rigid solids. It is the natural continuation of the unit devoted to the kinematics and statics of rigid solids in L1. In this unit, we'll take a dynamic approach and apply the Fundamental Principle of Dynamics. Writing this principle requires knowledge of the external action torsor, studied in L1, as well as knowledge of the dynamic torsor. The latter can be calculated using the kinetic torsor, which for a rigid solid involves the notion of moment of inertia. The main applications studied in this unit concern rigid solids or simple cases of articulated systems of rigid solids. In addition, we will study the special case of contact and friction actions (Coulomb friction) and the Kinetic Energy Theorem.
Electrostatics & Magnetostatics
Study level
BAC +2
ECTS
4 credits
Component
Faculty of Science
Hourly volume
36h
This course is the first step in teaching electromagnetism at university. It covers electrostatics, stationary currents and magnetostatics.
See the syllabus in the "+ info" tab.
Polynomial arithmetic
ECTS
3 credits
Component
Faculty of Science
In this course, we introduce an overview of algebraic structures (ring, ideal, body) before tackling K[X] algebra and defining arithmetic on polynomials, drawing parallels with integer arithmetic seen in L1. Calculations on polynomial functions and rational fractions will be covered (explicit factorizations/decompositions).
Thermodynamics 2
Study level
BAC +2
Component
Faculty of Science
Hourly volume
36h
This module completes and formalizes the notions of thermodynamics introduced in EU Thermodynamics 1, by exploring several aspects in greater depth: thermodynamic potentials defined on the basis of Legendre transformations, thermodynamics of open systems, pure-body phase transitions and irreversible processes, with incursions at the microscopic level to provide an insight into the physical foundations of the theory.
English S4
Study level
BAC +2
ECTS
2 credits
Component
Faculty of Science
The first-semester course reviews the grammar essential for oral and written communication(tenses and aspect, asking questions, comparisons and superlatives, passive voice) as well as essential general vocabulary(numbers, measurements, shapes); it also includes an introduction to technical vocabulary(basic building materials, plane engine, bike parts, electronic device) through themed lessons and videos in the field of mechanical engineering.
Finally, numerous activities are offered to promote oral expression skills (presentation vocabulary, simulations, role-playing and board games), so that students are able to describe the specific features, functions and uses of a piece of technical equipment of their choice in an oral presentation by groups of two.
S4
Grammatical aspects are limited to a review of modal auxiliaries.
The vocabulary is much more focused on the various elements involved in the design and operation of different types of heat engines, and on emerging technologies(drones, driverless vehicles, 3D-printing).
Students are also expected to produce a CV in English and practice writing emails in a formal style, so as to be prepared for internship or job-seeking situations where fluency in English will either be necessary or an additional skill.
The practice of expression is always the main objective, with an individual oral presentation at the end of the semester of their second-year project in mechanics.
Analysis IV Function sequences, integer series, Fourier
ECTS
8 credits
Component
Faculty of Science
This course covers the notions of function sequences and series, and the various convergences. Integer and Fourier series will also be developed.
Topology of R^n and functions of several variables
ECTS
5 credits
Component
Faculty of Science
This course covers an introduction to the topology of R^n, the basics of differential calculus for R^n functions in R and optimization. Parametric curves will also be covered.
Algebra IV Euclidean spaces
ECTS
6 credits
Component
Faculty of Science
This course is an introduction to bilinear algebra, covering Euclidean and Hermitian spaces. It covers isometries, duality, quadratic forms and endomorphisms.
Statistics
ECTS
3 credits
Component
Faculty of Science
This course introduces the main statistical concepts (graphical representation of data, indicators of central tendency and dispersion, relationships between two variables, confidence intervals).
Numerical linear algebra
ECTS
4 credits
Component
Faculty of Science
This course deals with numerical methods applied to linear algebra, and more specifically to matrices. The notions of conditioning, matrix decompositions and iterative methods, and the calculation of eigenvalues will be introduced.
Electromagnetism
Study level
BAC +2
ECTS
6 credits
Component
Faculty of Science
Hourly volume
54h
The first part of this course is designed to consolidate the concepts of magnetostatics and establish the relations between the electromagnetic field at the interface of a plane of charges or currents. We also introduce the expression of Laplace forces (force and moment) acting on volumetric or filiform circuits. The second part is devoted to the properties of fields and potentials in the variable regime. After introducing Faraday's law describing induction phenomena, we establish Maxwell's time-dependent equations. An energetic treatment allows us to define the electric and magnetic energies, as well as the Poynting vector. We apply these concepts to various examples, such as electromechanical conversion or induction heating via eddy currents. A final chapter is devoted to the equations of field and potential propagation, and their application in vacuum-like systems, as well as in perfect conductors and insulators. The notion of skin depth is also introduced.
PPE in mathematics
ECTS
2 credits
Component
Faculty of Science
This course includes presentations on career opportunities, themed lectures and round-table discussions on the various mathematical professions.
For students with a pre-professionalization AED contract, the UE accompanies their activity in the establishment, providing a few elements to enrich their observation and give them perspective. It also prepares them for the written work they will be required to submit.
Modeling and object programming 1
ECTS
5 credits
Component
Faculty of Science
This course introduces the basic principles of object-oriented modeling and programming. The supporting languages are UML and Java, with possible elements of Python at the end of the semester.
From a modeling point of view, this course focuses on static view modeling, using class and instance diagrams. These diagrams cover the notions of classes, instances, attributes, operations, associations, interfaces and specialization. Their parallel implementation in Java will give them a concrete application, and show in particular the translation of associations in a programming language that doesn't have them. In Java, particular emphasis will be placed on the notions of class, instance, inheritance, instance variable, class variable and method, visibility and package organization, and static and dynamic binding. Data collections widely used in Java will be presented to translate some of the associations (associative lists and dictionaries). These collections will introduce students to the use of generic classes. Implementation of object-oriented programming concepts with Python may be tackled at the end of the semester, depending on progress.
Information Systems and Databases
ECTS
5 credits
Component
Faculty of Science
This teaching unit introduces the design of processing in an information system and the management of relational databases. We will cover the following points:
(1) Information systems: Introduction of the entity/association model, Relational model, Processing modeling (Conceptual processing model, Organizational processing model),
(2) Databases: creating, manipulating and querying relational databases.
Analysis III integration and differential equations element
ECTS
6 credits
Component
Faculty of Science
Following on from the analysis course in S2, this course deals with the notion of series with terms of any sign. The Riemann integral will be defined and applied to linear and other differential equations. The integration section will be extended to generalized integrals.
Probabilities
ECTS
5 credits
Component
Faculty of Science
This course introduces probability spaces, the concepts of probability and independence, and defines discrete and density random variables, with an emphasis on modeling.
Algebra III Reduction of endomorphisms
ECTS
6 credits
Component
Faculty of Science
This course will cover the notions of symmetric group, determinants and will deal with the reduction of endomorphisms in finite dimension (up to Jordan form) and its applications. This is a first step towards spectral analysis.
Propositional logic
ECTS
5 credits
Component
Faculty of Science
- Formal syntax of propositional logic: symbols, connectors, well-formed formulas, syntactic trees, normal and clausal forms
- Semantics of propositional logic: interpretation, model, truth tables, satisfiability, validity, semantic equivalence, logical consequence
- Modeling: formalizing problems in propositional logic, expressiveness limits of propositional logic
- Formal proof: sequences, inference rules, axioms, theorems, LK system, solution method
- Correctness and completeness of a system with respect to semantics: proof of correctness and completeness of LK and resolution method (reduced to propositional case)
- Curry-Howard correspondence
- Introduction to first-order logic (predicate calculus) without function symbol
Systems
ECTS
5 credits
Component
Faculty of Science
The aim of this course is to describe the main concepts of operating systems, particularly Unix.
Elementary numerical analysis
ECTS
3 credits
Component
Faculty of Science
In this course, we'll look at the particularities of floating-point calculus and then go into detail on the most common elementary numerical methods for solving non-linear equations, interpolating a function and approximating an integral. Students will learn how to implement an algorithm to solve a numerical analysis problem.
Analysis IV Function sequences, integer series, Fourier
ECTS
8 credits
Component
Faculty of Science
This course covers the notions of function sequences and series, and the various convergences. Integer and Fourier series will also be developed.
Topology of R^n and functions of several variables
ECTS
5 credits
Component
Faculty of Science
This course covers an introduction to the topology of R^n, the basics of differential calculus for R^n functions in R and optimization. Parametric curves will also be covered.
Modeling and Object Programming 2
ECTS
5 credits
Component
Faculty of Science
Students will be able to model and develop using advanced aspects of object-oriented programming, and will have acquired good programming practices. They will be able to draw UML diagrams expressing the dynamics of interactions in a system, and will consolidate their knowledge of structural modeling.
Statistics
ECTS
3 credits
Component
Faculty of Science
This course introduces the main statistical concepts (graphical representation of data, indicators of central tendency and dispersion, relationships between two variables, confidence intervals).
Numerical linear algebra
ECTS
4 credits
Component
Faculty of Science
This course deals with numerical methods applied to linear algebra, and more specifically to matrices. The notions of conditioning, matrix decompositions and iterative methods, and the calculation of eigenvalues will be introduced.
PPE in mathematics
ECTS
2 credits
Component
Faculty of Science
This course includes presentations on career opportunities, themed lectures and round-table discussions on the various mathematical professions.
For students with a pre-professionalization AED contract, the UE accompanies their activity in the establishment, providing a few elements to enrich their observation and give them perspective. It also prepares them for the written work they will be required to submit.