Training Structure
College of Sciences
Overview
Mathematics Track: First Year (L1) in the Mathematics and Its Applications Portal
Program
Select a program
Second Year of the Bachelor's Degree Program
Junior Year
English S3
ECTS
2 credits
Training Structure
College of Sciences
Analysis III: Integration and Elementary Differential Equations
ECTS
6 credits
Training Structure
College of Sciences
Building on the analysis course from the second semester, this course will cover the concepts of series with terms of arbitrary sign. The Riemann integral will be defined and applied to solve differential equations, particularly linear ones. The section on integration will be expanded to include generalized integrals.
Probabilities
ECTS
5 credits
Training Structure
College of Sciences
This course will introduce probability spaces, the concepts of probability and independence, and will define discrete and continuous random variables, with an emphasis on modeling.
Algebra III: Reduction of Endomorphisms
ECTS
6 credits
Training Structure
College of Sciences
This course will cover the concepts of symmetric groups and determinants, and will address the reduction of endomorphisms to finite dimensions (up to Jordan form) and its applications. It serves as an introduction to spectral analysis.
Polynomial Arithmetic
ECTS
3 credits
Training Structure
College of Sciences
In this course, we will provide an overview of algebraic structures (rings, ideals, fields) before introducing the algebra K[X] and defining polynomial arithmetic, drawing parallels with the arithmetic of integers covered in L1. We will also cover computational aspects of polynomial functions and rational fractions (factorization and explicit expansions).
CHOICE 1
ECTS
5 credits
Training Structure
College of Sciences
Object-Oriented Modeling and Programming 1
ECTS
5 credits
Training Structure
College of Sciences
This course introduces the basic principles of object-oriented modeling and programming. The primary languages covered are UML and Java, with some Python concepts possibly introduced at the end of the semester.
From a modeling perspective, this course focuses on static modeling, including class and instance diagrams. Through these diagrams, students will explore the concepts of classes, instances, attributes, operations, associations, interfaces, and specialization. Implementing these concepts in parallel in Java will provide concrete applications and, in particular, demonstrate how associations are represented in a programming language that does not natively support them. In Java, particular emphasis will be placed on the concepts of classes, instances, inheritance, instance variables, class variables and methods, visibility, organization into packages, and static and dynamic binding. Commonly used data collections in Java will be presented to represent certain associations (lists and associative dictionaries). These collections will introduce students to the use of generic classes. The implementation of object-oriented programming concepts using Python may be covered at the end of the semester, depending on the class’s progress.
OPTION 2
ECTS
5 credits
Training Structure
College of Sciences
Oral Math Exam
ECTS
1 credit
Training Structure
College of Sciences
Thermodynamics 2
Level of Education
2 years of post-secondary education
Training Structure
College of Sciences
Number of hours
36h
This module supplements and formalizes the thermodynamic concepts introduced in the Thermodynamics 1 course unit, exploring several aspects in greater depth: thermodynamic potentials defined using Legendre transformations, the thermodynamics of open systems, phase transitions in pure substances, and irreversible processes, with forays into the microscopic level to provide an overview of the physical foundations of the theory.
Elementary Numerical Analysis
ECTS
3 credits
Training Structure
College of Sciences
In this course, we will cover the fundamentals of floating-point arithmetic and then discuss common basic numerical methods for solving nonlinear equations, interpolating functions, and approximating integrals. Students will learn how to implement an algorithm to solve a numerical analysis problem.
ASTRE's Scientific Approach to the Ecological Transition
ECTS
2 credits
Training Structure
College of Sciences
Time of year
Fall
English S4
Level of Education
2 years of post-secondary education
ECTS
2 credits
Training Structure
College of Sciences
Time of year
Spring
The first-semester course covers the grammatical concepts 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, airplane engines, bicycle parts, electronic devices) through themed lessons and videos in the field of mechanical engineering.
Finally, a wide range of activities are offered to develop oral communication skills (presentation vocabulary, simulations, role-playing, and board games) so that students will be able to describe—during an oral presentation in pairs—the specific features, functions, and uses of a piece of technical equipment of their choice.
S4
The grammatical aspects are limited to a review of modal auxiliaries.
The vocabulary focuses much more on the various components involved in the design and operation of different types of internal combustion engines and on emerging technologies (drones, driverless vehicles, 3D printing).
Students must also submit a resume in English and practice writing formal emails, so that they are prepared for situations involving internship or job searches where proficiency in English will be either required or considered an added asset.
The focus is always on practical application, culminating in an individual oral presentation at the end of the semester on their second-year mechanics project.
Analysis IV: Function Sequences, Power Series, Fourier Series
ECTS
8 credits
Training Structure
College of Sciences
Time of year
Spring
This course will cover the concepts of sequences and series of functions, as well as various types of convergence. Integral series and Fourier series will also be discussed.
Topology of R^n and Functions of Several Variables
ECTS
5 credits
Training Structure
College of Sciences
Time of year
Spring
This course will provide an introduction to the topology of R^n, the basic concepts of differential calculus of functions from R^n to R, and optimization. Parametric curves will also be covered.
Algebra IV: Euclidean Spaces
ECTS
6 credits
Training Structure
College of Sciences
Time of year
Spring
This course is an introduction to bilinear algebra and will cover Euclidean and Hermitian spaces. It will address topics such as isometries, duality, quadratic forms, and endomorphisms.
Statistics
ECTS
3 credits
Training Structure
College of Sciences
This course introduces the main statistical concepts (graphical representation of data, measures of central tendency and dispersion, the relationship between two variables, and confidence intervals).
Numerical Linear Algebra
ECTS
4 credits
Training Structure
College of Sciences
This course will cover numerical methods applied to linear algebra, with a particular focus on matrices. The concepts of conditioning, matrix decompositions, iterative methods, and eigenvalue calculation will be introduced.
Master's in Mathematics
ECTS
2 credits
Training Structure
College of Sciences
This course will introduce students to the various careers in mathematics through presentations on career opportunities, thematic lectures, and roundtable discussions.
For students with an AED contract as part of a pre-professional training program, the course unit supports their work at the school by providing resources designed to enrich their observations and help them gain perspective. It also aims to prepare them for the written assignment they will be required to submit.
English S3
ECTS
2 credits
Training Structure
College of Sciences
Analysis III: Integration and Elementary Differential Equations
ECTS
6 credits
Training Structure
College of Sciences
Building on the analysis course from the second semester, this course will cover the concepts of series with terms of arbitrary sign. The Riemann integral will be defined and applied to solve differential equations, particularly linear ones. The section on integration will be expanded to include generalized integrals.
Probabilities
ECTS
5 credits
Training Structure
College of Sciences
This course will introduce probability spaces, the concepts of probability and independence, and will define discrete and continuous random variables, with an emphasis on modeling.
Algebra III: Reduction of Endomorphisms
ECTS
6 credits
Training Structure
College of Sciences
This course will cover the concepts of symmetric groups and determinants, and will address the reduction of endomorphisms to finite dimensions (up to Jordan form) and its applications. It serves as an introduction to spectral analysis.
Rigid Body Dynamics
Level of Education
2 years of post-secondary education
Training Structure
College of Sciences
This unit focuses on the mechanics of rigid bodies. It is the natural continuation of the unit on the kinematics and statics of rigid bodies covered in the first year of undergraduate studies. In this unit, we will adopt a dynamic framework and apply the Fundamental Principle of Dynamics. Deriving this principle requires knowledge of the torque of external forces, which was studied in the first year, as well as knowledge of the dynamic torque. The latter can be calculated using the kinetic torque, which, for a rigid body, involves the concept of moment of inertia. The main applications studied in this unit concern rigid bodies or simple cases of articulated systems of rigid bodies. In addition, we will study the special case of contact and friction forces (Coulomb friction) and discuss the Kinetic Energy Theorem.
Electrostatics & Magnetostatics
Level of Education
2 years of post-secondary education
Training Structure
College of Sciences
Number of hours
36h
This course is the first step in university-level electromagnetism instruction. It covers electrostatics, steady-state currents, and magnetostatics.
See the syllabus in the “More Info” tab
Polynomial Arithmetic
ECTS
3 credits
Training Structure
College of Sciences
In this course, we will provide an overview of algebraic structures (rings, ideals, fields) before introducing the algebra K[X] and defining polynomial arithmetic, drawing parallels with the arithmetic of integers covered in L1. We will also cover computational aspects of polynomial functions and rational fractions (factorization and explicit expansions).
Thermodynamics 2
Level of Education
2 years of post-secondary education
Training Structure
College of Sciences
Number of hours
36h
This module supplements and formalizes the thermodynamic concepts introduced in the Thermodynamics 1 course unit, exploring several aspects in greater depth: thermodynamic potentials defined using Legendre transformations, the thermodynamics of open systems, phase transitions in pure substances, and irreversible processes, with forays into the microscopic level to provide an overview of the physical foundations of the theory.
ASTRE's Scientific Approach to the Ecological Transition
ECTS
2 credits
Training Structure
College of Sciences
Time of year
Fall
English S4
Level of Education
2 years of post-secondary education
ECTS
2 credits
Training Structure
College of Sciences
Time of year
Spring
The first-semester course covers the grammatical concepts 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, airplane engines, bicycle parts, electronic devices) through themed lessons and videos in the field of mechanical engineering.
Finally, a wide range of activities are offered to develop oral communication skills (presentation vocabulary, simulations, role-playing, and board games) so that students will be able to describe—during an oral presentation in pairs—the specific features, functions, and uses of a piece of technical equipment of their choice.
S4
The grammatical aspects are limited to a review of modal auxiliaries.
The vocabulary focuses much more on the various components involved in the design and operation of different types of internal combustion engines and on emerging technologies (drones, driverless vehicles, 3D printing).
Students must also submit a resume in English and practice writing formal emails, so that they are prepared for situations involving internship or job searches where proficiency in English will be either required or considered an added asset.
The focus is always on practical application, culminating in an individual oral presentation at the end of the semester on their second-year mechanics project.
Analysis IV: Function Sequences, Power Series, Fourier Series
ECTS
8 credits
Training Structure
College of Sciences
Time of year
Spring
This course will cover the concepts of sequences and series of functions, as well as various types of convergence. Integral series and Fourier series will also be discussed.
Topology of R^n and Functions of Several Variables
ECTS
5 credits
Training Structure
College of Sciences
Time of year
Spring
This course will provide an introduction to the topology of R^n, the basic concepts of differential calculus of functions from R^n to R, and optimization. Parametric curves will also be covered.
Algebra IV: Euclidean Spaces
ECTS
6 credits
Training Structure
College of Sciences
Time of year
Spring
This course is an introduction to bilinear algebra and will cover Euclidean and Hermitian spaces. It will address topics such as isometries, duality, quadratic forms, and endomorphisms.
Statistics
ECTS
3 credits
Training Structure
College of Sciences
This course introduces the main statistical concepts (graphical representation of data, measures of central tendency and dispersion, the relationship between two variables, and confidence intervals).
Numerical Linear Algebra
ECTS
4 credits
Training Structure
College of Sciences
This course will cover numerical methods applied to linear algebra, with a particular focus on matrices. The concepts of conditioning, matrix decompositions, iterative methods, and eigenvalue calculation will be introduced.
Electromagnetism
Level of Education
2 years of post-secondary education
ECTS
6 credits
Training Structure
College of Sciences
Number of hours
54h
The first part of this course aims to reinforce the concepts of magnetostatics and to establish the relationships governing the behavior of the electromagnetic field at the interface of a plane of charges or currents. We also introduce the expression for Laplace’s forces (force and torque) acting on volumetric or filiform circuits. The second part is devoted to the properties of fields and potentials in a time-varying regime. After introducing Faraday’s law, which describes induction phenomena, we derive the time-dependent Maxwell’s equations. An energy-based approach 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 propagation of fields and potentials, and their application in systems approximated as a vacuum, as well as in perfect conductors and insulators. The concept of skin depth is also introduced.
Master's in Mathematics
ECTS
2 credits
Training Structure
College of Sciences
This course will introduce students to the various careers in mathematics through presentations on career opportunities, thematic lectures, and roundtable discussions.
For students with an AED contract as part of a pre-professional training program, the course unit supports their work at the school by providing resources designed to enrich their observations and help them gain perspective. It also aims to prepare them for the written assignment they will be required to submit.
Object-Oriented Modeling and Programming 1
ECTS
5 credits
Training Structure
College of Sciences
This course introduces the basic principles of object-oriented modeling and programming. The primary languages covered are UML and Java, with some Python concepts possibly introduced at the end of the semester.
From a modeling perspective, this course focuses on static modeling, including class and instance diagrams. Through these diagrams, students will explore the concepts of classes, instances, attributes, operations, associations, interfaces, and specialization. Implementing these concepts in parallel in Java will provide concrete applications and, in particular, demonstrate how associations are represented in a programming language that does not natively support them. In Java, particular emphasis will be placed on the concepts of classes, instances, inheritance, instance variables, class variables and methods, visibility, organization into packages, and static and dynamic binding. Commonly used data collections in Java will be presented to represent certain associations (lists and associative dictionaries). These collections will introduce students to the use of generic classes. The implementation of object-oriented programming concepts using Python may be covered at the end of the semester, depending on the class’s progress.
Information Systems and Databases
ECTS
5 credits
Training Structure
College of Sciences
This course covers the design of business processes within an information system and the management of relational databases. We will cover the following topics:
(1) Information Systems: Introduction to the entity-relationship model, the relational model, and business process modeling (conceptual business process model, organizational business process model),
(2) Databases: Creating, Manipulating, and Querying Relational Databases.
English S3
ECTS
2 credits
Training Structure
College of Sciences
Analysis III: Integration and Elementary Differential Equations
ECTS
6 credits
Training Structure
College of Sciences
Building on the analysis course from the second semester, this course will cover the concepts of series with terms of arbitrary sign. The Riemann integral will be defined and applied to solve differential equations, particularly linear ones. The section on integration will be expanded to include generalized integrals.
Probabilities
ECTS
5 credits
Training Structure
College of Sciences
This course will introduce probability spaces, the concepts of probability and independence, and will define discrete and continuous random variables, with an emphasis on modeling.
Algebra III: Reduction of Endomorphisms
ECTS
6 credits
Training Structure
College of Sciences
This course will cover the concepts of symmetric groups and determinants, and will address the reduction of endomorphisms to finite dimensions (up to Jordan form) and its applications. It serves as an introduction to spectral analysis.
Propositional Logic
ECTS
5 credits
Training Structure
College of Sciences
- Formal syntax of propositional logic: symbols, connectives, well-formed formulas, syntactic trees, normal forms, and clause forms
- Semantics of propositional logic: interpretation, model, truth tables, satisfiability, validity, semantic equivalence, logical consequence
- Modeling: formalization of problems in propositional logic; expressive limits of propositional logic
- Formal proof: sequences, inference rules, axioms, theorems, the LK system, the resolution method
- Correctness and completeness of a system with respect to a semantics: proof of the correctness and completeness of the LK and the resolution method (reduced to the propositional case)
- Curry–Howard Correspondence
- Introduction to first-order logic (predicate calculus) without function symbols
Systems
ECTS
5 credits
Training Structure
College of Sciences
The objective of this learning unit is to describe the main concepts of operating systems, particularly Unix.
Elementary Numerical Analysis
ECTS
3 credits
Training Structure
College of Sciences
In this course, we will cover the fundamentals of floating-point arithmetic and then discuss common basic numerical methods for solving nonlinear equations, interpolating functions, and approximating integrals. Students will learn how to implement an algorithm to solve a numerical analysis problem.
ASTRE's Scientific Approach to the Ecological Transition
ECTS
2 credits
Training Structure
College of Sciences
Time of year
Fall
Analysis IV: Function Sequences, Power Series, Fourier Series
ECTS
8 credits
Training Structure
College of Sciences
Time of year
Spring
This course will cover the concepts of sequences and series of functions, as well as various types of convergence. Integral series and Fourier series will also be discussed.
Algorithms 3
ECTS
5 credits
Training Structure
College of Sciences
Topology of R^n and Functions of Several Variables
ECTS
5 credits
Training Structure
College of Sciences
Time of year
Spring
This course will provide an introduction to the topology of R^n, the basic concepts of differential calculus of functions from R^n to R, and optimization. Parametric curves will also be covered.
Object-Oriented Modeling and Programming 2
ECTS
5 credits
Training Structure
College of Sciences
Students will learn to model and develop using advanced aspects of object-oriented programming and will have acquired best programming practices. They will be able to create UML diagrams that illustrate the dynamics of interactions within a system and will strengthen their knowledge of structural modeling.
English S4
ECTS
2 credits
Training Structure
College of Sciences
Calculation Models
ECTS
5 credits
Training Structure
College of Sciences
Statistics
ECTS
3 credits
Training Structure
College of Sciences
This course introduces the main statistical concepts (graphical representation of data, measures of central tendency and dispersion, the relationship between two variables, and confidence intervals).
Numerical Linear Algebra
ECTS
4 credits
Training Structure
College of Sciences
This course will cover numerical methods applied to linear algebra, with a particular focus on matrices. The concepts of conditioning, matrix decompositions, iterative methods, and eigenvalue calculation will be introduced.
Master's in Mathematics
ECTS
2 credits
Training Structure
College of Sciences
This course will introduce students to the various careers in mathematics through presentations on career opportunities, thematic lectures, and roundtable discussions.
For students with an AED contract as part of a pre-professional training program, the course unit supports their work at the school by providing resources designed to enrich their observations and help them gain perspective. It also aims to prepare them for the written assignment they will be required to submit.
First-order logic
ECTS
5 credits
Training Structure
College of Sciences
This course aims to introduce first-order logic, also known as predicate calculus.
Differential Calculus and Differential Equations
ECTS
6 credits
Training Structure
College of Sciences
In the first part: a more in-depth look at the basic concepts of differential calculus covered in the second year.
In the second part: introduce the qualitative analysis of differential equations.
Formal and Scientific Computation
ECTS
4 credits
Training Structure
College of Sciences
The objective of this module is to gain an understanding of how to use symbolic and numerical computation both in mathematical experimentation and to aid in solving certain problems in computer science.
Groups and Rings 1
ECTS
6 credits
Training Structure
College of Sciences
Acquire a basic understanding of group and ring theory and illustrate these concepts with examples.
Measurement and Integration
ECTS
4 credits
Training Structure
College of Sciences
Acquire a basic understanding of the theory of measure and integration.
English S5
ECTS
2 credits
Training Structure
College of Sciences
Probability Theory
ECTS
4 credits
Training Structure
College of Sciences
To illustrate, from a probabilistic perspective, the concepts covered in the “Measure—Integration—Fourier” course unit, and to introduce the necessary tools for students who will take the Stochastic Modeling course unit in the second semester of their third year of undergraduate studies.
Software Engineering Workshops
ECTS
5 credits
Training Structure
College of Sciences
This course is designed to provide an introduction to the software environments necessary for modern software development. Topics covered will include version control, modeling, test development, virtualization, continuous integration, and more.
Algorithms 4
ECTS
5 credits
Training Structure
College of Sciences
This module explores some advanced topics in algorithm design and analysis.
Complexity, computability, decidability
ECTS
5 credits
Training Structure
College of Sciences
Topology of Metric Spaces
ECTS
7 credits
Training Structure
College of Sciences
Time of year
Spring
Introduce the basic concepts of topology and their application to the study of functional spaces.
Multimedia Data
ECTS
5 credits
Training Structure
College of Sciences
Groups and Rings 2
ECTS
5 credits
Training Structure
College of Sciences
Time of year
Spring
To build on the basic concepts of group and ring theory covered in the previous semester.
Convex Optimization
ECTS
5 credits
Training Structure
College of Sciences
Time of year
Spring
Acquire a basic understanding of mathematical optimization and its applications.
Syntax Analysis and Interpretation
ECTS
5 credits
Training Structure
College of Sciences
Programming Project
ECTS
5 credits
Training Structure
College of Sciences
Differential Calculus and Differential Equations
ECTS
6 credits
Training Structure
College of Sciences
In the first part: a more in-depth look at the basic concepts of differential calculus covered in the second year.
In the second part: introduce the qualitative analysis of differential equations.
Groups and Rings 1
ECTS
6 credits
Training Structure
College of Sciences
Acquire a basic understanding of group and ring theory and illustrate these concepts with examples.
Measure and Integration, Fourier
ECTS
8 credits
Training Structure
College of Sciences
To acquire a foundation in the theory of measure and integration, and then use that foundation to introduce the spaces and tools of functional analysis.
Probability Theory
ECTS
4 credits
Training Structure
College of Sciences
To illustrate, from a probabilistic perspective, the concepts covered in the “Measure—Integration—Fourier” course unit, and to introduce the necessary tools for students who will take the Stochastic Modeling course unit in the second semester of their third year of undergraduate studies.
English S5
ECTS
2 credits
Training Structure
College of Sciences
Enumerative Combinatorics
ECTS
4 credits
Training Structure
College of Sciences
In the first part, explore in greater depth the basic concepts of counting covered in L1 and L2.
In the second part, introduce the combinatorial study of graphs.