L2-L3 BACHELOR'S DEGREE IN MATHEMATICS

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This course will build on the S2 analysis course by covering the concepts of series with terms of any sign. Riemann integrals will be defined and applied to solve differential equations, particularly linear ones. The integration section will be expanded to include generalized integrals.

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This course will introduce probability spaces, the concepts of probability and independence, and will define discrete and density random variables with an emphasis on modeling.

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This course will cover the concepts of symmetric groups and determinants, and will address the reduction of endomorphisms in finite dimensions (up to Jordan form) and its applications. It is a first step toward spectral analysis.

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In this course, we will introduce an overview of algebraic structures (rings, ideals, fields) before tackling the algebra K[X] and defining arithmetic on polynomials, drawing parallels with the arithmetic of integers seen in L1. Computational aspects of polynomial functions and rational fractions will be covered (explicit factorizations/decompositions).

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The teaching unit presents the basic principles of modeling and object-oriented programming. The supporting languages are UML and Java, with possible elements of Python at the end of the semester.

From a modeling perspective, the teaching unit focuses on modeling static views, using class and instance diagrams. These diagrams will be used to explore the concepts of classes, instances, attributes, operations, associations, interfaces, and specialization. Their parallel implementation in Java will provide a concrete application and demonstrate, in particular, how associations are translated into a programming language that does not have them. In Java, particular emphasis will be placed on the concepts of class, instance, inheritance, instance variable, class variable and method, visibility and organization into packages, and static and dynamic linking. 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. The implementation of object-oriented programming concepts with Python may be covered at the end of the semester, depending on progress.

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This module complements and formalizes the concepts of thermodynamics introduced in the Thermodynamics 1 course, exploring several aspects in greater depth: thermodynamic potentials defined using Legendre transformations, thermodynamics of open systems, phase transitions of pure substances and irreversible processes, with forays into the microscopic level to provide an overview of the physical foundations of the theory.

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This course will cover the particularities of floating-point arithmetic, then detail common elementary numerical methods for solving nonlinear equations, interpolating a function, and approximating an integral. Students will learn how to implement an algorithm for solving a numerical analysis problem.

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The first semester course reviews the grammar 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, bike parts, electronic devices) through lessons and videos on topics related to mechanical engineering.

Finally, numerous activities are offered to promote oral expression skills (presentation vocabulary, simulations, role-playing, and tabletop games) so that students are able to describe the specific features, functions, and uses of a technical device of their choice during an oral presentation in groups of two.

S4

Grammar 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 combustion engines and on emerging technologies (drones, driverless vehicles, 3D printing).

Students must also produce a CV in English and practice writing emails in a formal style, so that they are prepared for situations when looking for internships or jobs where English proficiency will either be necessary or an additional skill.

Practicing expression is always the main objective, with an individual oral presentation at the end of the semester on their second-year mechanics project.

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This course will cover the concepts of sequences and series of functions and various types of convergence. Entire series and Fourier series will also be discussed.

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This course will cover 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 discussed.

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This course is an introduction to bilinear algebra and will cover Euclidean and Hermitian spaces. It will cover everything related to isometries, duality, quadratic forms, and endomorphisms.

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Introduction to the main statistical concepts in this course (graphical representation of data, measures of central tendency and dispersion, relationship between two variables, confidence intervals).

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This course will cover numerical methods applied to linear algebra, with a particular focus on matrices. The concepts of conditioning, matrix decompositions and iterative methods, and eigenvalue computation will be introduced.

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This course will introduce students to the various careers available in mathematics through presentations on career opportunities, themed lectures, and roundtable discussions.

For students who have a pre-professional AED contract, the EU supports their activities at the institution by providing them with information designed to enrich their observations and give them perspective. This also involves preparing them to write the paper they will be required to submit.

See the full page

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This course will build on the S2 analysis course by covering the concepts of series with terms of any sign. Riemann integrals will be defined and applied to solve differential equations, particularly linear ones. The integration section will be expanded to include generalized integrals.

See the full page

This course will introduce probability spaces, the concepts of probability and independence, and will define discrete and density random variables with an emphasis on modeling.

See the full page

This course will cover the concepts of symmetric groups and determinants, and will address the reduction of endomorphisms in finite dimensions (up to Jordan form) and its applications. It is a first step toward spectral analysis.

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This course unit concerns the study of rigid body mechanics. It is the natural continuation of the course unit devoted to the kinematics and statics of rigid bodies in L1. In this course unit, we will place ourselves in a dynamic framework and apply the Fundamental Principle of Dynamics. Writing this principle requires knowledge of the tensor of external actions, studied in L1, as well as knowledge of the dynamic tensor. The latter can be calculated using the kinetic tensor, which involves the concept of moment of inertia for a rigid solid. The main applications studied in this course 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 we will discuss the kinetic energy theorem.

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This course is the first step in teaching electromagnetism at university. It covers electrostatics, steady currents, and magnetostatics.

See the syllabus in the "More info" tab.

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In this course, we will introduce an overview of algebraic structures (rings, ideals, fields) before tackling the algebra K[X] and defining arithmetic on polynomials, drawing parallels with the arithmetic of integers seen in L1. Computational aspects of polynomial functions and rational fractions will be covered (explicit factorizations/decompositions).

See the full page

This module complements and formalizes the concepts of thermodynamics introduced in the Thermodynamics 1 course, exploring several aspects in greater depth: thermodynamic potentials defined using Legendre transformations, thermodynamics of open systems, phase transitions of pure substances and irreversible processes, with forays into the microscopic level to provide an overview of the physical foundations of the theory.

See the full page

See the full page

The first semester course reviews the grammar 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, bike parts, electronic devices) through lessons and videos on topics related to mechanical engineering.

Finally, numerous activities are offered to promote oral expression skills (presentation vocabulary, simulations, role-playing, and tabletop games) so that students are able to describe the specific features, functions, and uses of a technical device of their choice during an oral presentation in groups of two.

S4

Grammar 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 combustion engines and on emerging technologies (drones, driverless vehicles, 3D printing).

Students must also produce a CV in English and practice writing emails in a formal style, so that they are prepared for situations when looking for internships or jobs where English proficiency will either be necessary or an additional skill.

Practicing expression is always the main objective, with an individual oral presentation at the end of the semester on their second-year mechanics project.

See the full page

This course will cover the concepts of sequences and series of functions and various types of convergence. Entire series and Fourier series will also be discussed.

See the full page

This course will cover 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 discussed.

See the full page

This course is an introduction to bilinear algebra and will cover Euclidean and Hermitian spaces. It will cover everything related to isometries, duality, quadratic forms, and endomorphisms.

See the full page

Introduction to the main statistical concepts in this course (graphical representation of data, measures of central tendency and dispersion, relationship between two variables, confidence intervals).

See the full page

This course will cover numerical methods applied to linear algebra, with a particular focus on matrices. The concepts of conditioning, matrix decompositions and iterative methods, and eigenvalue computation will be introduced.

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The first part of this course aims to consolidate the concepts of magnetostatics and establish the relationships between the electromagnetic field at the interface of a plane of charges or current. We also introduce the expression of Laplace forces (force and moment) acting on volume or wire circuits. The second part is devoted to the properties of fields and potentials in variable regimes. After introducing Faraday's law describing induction phenomena, we establish Maxwell's time-dependent equations. An energy treatment allows us to define electrical and magnetic energies, as well as the Poynting vector. We apply these concepts to various examples, such as electromechanical conversion and induction heating via eddy currents. The final chapter is devoted to the propagation equations of fields and potentials, and their application in systems assimilated to a vacuum, as well as in perfect conductors and insulators. The concept of skin depth is also introduced.

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This course will introduce students to the various careers available in mathematics through presentations on career opportunities, themed lectures, and roundtable discussions.

For students who have a pre-professional AED contract, the EU supports their activities at the institution by providing them with information designed to enrich their observations and give them perspective. This also involves preparing them to write the paper they will be required to submit.

See the full page

The teaching unit presents the basic principles of modeling and object-oriented programming. The supporting languages are UML and Java, with possible elements of Python at the end of the semester.

From a modeling perspective, the teaching unit focuses on modeling static views, using class and instance diagrams. These diagrams will be used to explore the concepts of classes, instances, attributes, operations, associations, interfaces, and specialization. Their parallel implementation in Java will provide a concrete application and demonstrate, in particular, how associations are translated into a programming language that does not have them. In Java, particular emphasis will be placed on the concepts of class, instance, inheritance, instance variable, class variable and method, visibility and organization into packages, and static and dynamic linking. 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. The implementation of object-oriented programming concepts with Python may be covered at the end of the semester, depending on progress.

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This teaching unit presents the design of processes in an information system and the management of relational databases. We will cover the following topics:
(1) Information systems: Introduction to the entity/association model, Relational model, Process modeling (Conceptual process model, Organizational process model),

(2) Databases: creation, manipulation, and querying of relational databases.

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This course will build on the S2 analysis course by covering the concepts of series with terms of any sign. Riemann integrals will be defined and applied to solve differential equations, particularly linear ones. The integration section will be expanded to include generalized integrals.

See the full page

This course will introduce probability spaces, the concepts of probability and independence, and will define discrete and density random variables with an emphasis on modeling.

See the full page

This course will cover the concepts of symmetric groups and determinants, and will address the reduction of endomorphisms in finite dimensions (up to Jordan form) and its applications. It is a first step toward spectral analysis.

See the full page

- 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: sequents, inference rules, axioms, theorems, LK system, resolution method

- Correctness and completeness of a system with respect to semantics: proof of correctness and completeness of LK and the resolution method (reduced to the propositional case)

- Curry-Howard correspondence

- Introduction to first-order logic (predicate calculus) without function symbols

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The objective of this course is to describe the main concepts of operating systems, particularly Unix.

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This course will cover the particularities of floating-point arithmetic, then detail common elementary numerical methods for solving nonlinear equations, interpolating a function, and approximating an integral. Students will learn how to implement an algorithm for solving a numerical analysis problem.

See the full page

See the full page

This course will cover the concepts of sequences and series of functions and various types of convergence. Entire series and Fourier series will also be discussed.

See the full page

See the full page

This course will cover 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 discussed.

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Students will learn how to model and develop using advanced aspects of object-oriented programming and will have acquired good programming practices. They will learn how to create UML diagrams expressing the dynamics of interactions in a system and will consolidate their knowledge of structural modeling.

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Introduction to the main statistical concepts in this course (graphical representation of data, measures of central tendency and dispersion, relationship between two variables, confidence intervals).

See the full page

This course will cover numerical methods applied to linear algebra, with a particular focus on matrices. The concepts of conditioning, matrix decompositions and iterative methods, and eigenvalue computation will be introduced.

See the full page

This course will introduce students to the various careers available in mathematics through presentations on career opportunities, themed lectures, and roundtable discussions.

For students who have a pre-professional AED contract, the EU supports their activities at the institution by providing them with information designed to enrich their observations and give them perspective. This also involves preparing them to write the paper they will be required to submit.

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This course introduces first-order logic, also known as predicate calculus.

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In the first part: deepen the basic concepts of differential calculus covered in L2.

In the second part: introduce the qualitative study of differential equations.

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The objective of this module is to understand the use of formal and numerical calculation both in mathematical experimentation and in helping to solve certain problems in computer science.

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Acquire the basic concepts of group and ring theory and illustrate them with examples.

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Acquire the fundamentals of measure theory and integration.

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Illustrate the concepts covered in the "Measurement - Integration - Fourier" course from a probabilistic perspective, and introduce the necessary tools to students who will be taking the Stochastic Modeling course in the second semester of their junior year. 

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This teaching unit aims to introduce students to the software environments necessary for modern development. Topics covered will include version control, modeling, test development, virtualization, continuous integration, and more.

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This module explores some advanced topics in algorithm design and analysis.

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Introduce the basic concepts of topology and their use in the study of functional spaces.

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Further explore the basic concepts of group and ring theory covered in the previous semester.

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Acquire basic concepts in mathematical optimization and its applications.

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In the first part: deepen the basic concepts of differential calculus covered in L2.

In the second part: introduce the qualitative study of differential equations.

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Acquire the basic concepts of group and ring theory and illustrate them with examples.

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Acquire the fundamentals of measure theory and integration, then use these fundamentals to introduce the spaces and tools of functional analysis.

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Illustrate the concepts covered in the "Measurement - Integration - Fourier" course from a probabilistic perspective, and introduce the necessary tools to students who will be taking the Stochastic Modeling course in the second semester of their junior year. 

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In the first part, we will explore the basic concepts of counting covered in L1 and L2.

In the second part, introduce the combinatorial study of graphs.

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• Enable students to discover the teaching profession and learn about mathematics education.
•  Address some major themes in mathematics education using practical examples.

• Begin to change your approach to teaching mathematics and learn to ask questions related to teaching.
• Adopting a reflective approach to issues related to secondary school mathematics education
• Taking a step back from the math content taught in secondary school

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This EU will address the following points:

     - Affine geometry: affine spaces, affine applications, barycenters. Affine geometry of the plane and space, classical theorems.

     - Euclidean affine geometry: Euclidean affine spaces, isometries. Euclidean affine geometry of the plane and space, classical theorems, use of complexes to describe objects in the Euclidean affine plane and isometries.

     - Isometries and groups.

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Revisit the mathematics content of the bachelor's degree in a cross-disciplinary manner.

Problem-solving activity: research and communication.

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Acquire basic knowledge of numerical methods for differential equations

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Introduce the basic concepts of topology and their use in the study of functional spaces.

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This EU will enable:

Manipulate the main results of probabilities from a practical perspective. Reinforce understanding of random phenomena with numerical illustrations. Introduce simulation methods using the Monte Carlo method for the numerical resolution of integration problems or the calculation of probabilities for complex events. Supplement knowledge of the main commonly used laws and their properties with a view to applications in inferential statistics and statistical tests covered in the Master's program.

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Further explore the basic concepts of group and ring theory covered in the previous semester.

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Acquire basic concepts in mathematical optimization and its applications.

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Acquire basic knowledge of numerical methods for differential equations

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Introduce the basic tools of complex analysis.

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