## Training structure

Faculty of Science

## Presentation

## Program

### Select a program

### L1 - CUPGE Math

The Cycle Universitaire Préparatoire aux Grandes Écoles (CUPGE) Mathematics-Physics program is a reinforced mathematics-based program.

## General Physics

6 credits54h## Algebra I linear systems

5 credits## Electronics

6 credits## Calculus CUPGE & math

3 credits## Written Compositions CUPGE S1

2 credits18h## Reasoning and Set Theory

2 credits## English S1

1 credits## Geometry in the plane, space and complex plane

4 credits## Analysis I functions of one variable and sequences

5 credits

## Written compositions CUPGE S2

2 credits18h## Arithmetic and enumeration

6 credits## Thermodynamics 1

5 credits54h## Python for Science

4 credits36h## Algebra II, vector spaces and linear applications

6 credits## Kinematics and statics of the solid

5 credits45h## English S2

2 credits## Analysis II Suites, series, limited developments

6 credits

### L1 - Double Bachelor's Degree in Computer Science and Mathematics

## Algebra I linear systems

5 credits## Use of computer systems

4 credits## Let's play deterministic automata

3 credits## Calculus CUPGE & math

3 credits## Algorithmics 1

5 credits## Reasoning and Set Theory

2 credits## Functional programming

5 credits## English S1

1 credits## Geometry in the plane, space and complex plane

4 credits## Analysis I functions of one variable and sequences

5 credits

## Algorithmics 2

5 credits## C Programming

5 credits## Arithmetic and enumeration

6 credits## General Culture - To be chosen from the list below +.

2 credits## Your choice: 1 of 12

## Introduction to Oceanography

2 credits## Pleasures and addictions

2 credits## The place of man in the universe

2 credits## Creative writing

2 credits## Education for the ecological transition

2 credits## Sport

## Basic computer tools and concepts (PIX)

2 credits## Science and Music

2 credits## Sc. and Scent Culture

2 credits## Additive manufacturing

2 credits## The quantum computer, between physics and mathematics

2 credits## The questioning of the movement

2 credits

## Event and web programming

4 credits## Algebra II, vector spaces and linear applications

6 credits## English S2

2 credits## Analysis II Suites, series, limited developments

6 credits

### L1- Mathematics and its applications

## General Physics

## Level of study

BAC +1

## ECTS

6 credits

## Component

Faculty of Science

## Hourly volume

54h

The main objective of this course is to teach you to pose and solve simple physics problems. The areas of application are material point mechanics and geometric optics.

*Mechanics of the material point :*

- Static of forces: studies of mechanical systems in equilibrium.
- Kinematics: study of the movement of bodies independently of the causes that generate them.
- Dynamics: links between the causes of movement and the movement itself.
- Work and energy: work of forces (conservative and non-conservative), kinetic energy theorem, mechanical energy theorem and their applications.

*Geometric optics:*

- Propagation of light (Fermat's principle, Snell-Descartes laws, index of refraction),
- Image formation and optical systems (stigmatism, Gaussian approximation, mirrors, thin lenses, dispersive systems, centered systems, optical instruments)

## Algebra I linear systems

## ECTS

5 credits

## Component

Faculty of Science

This course is an introduction to linear algebra (formalized in S2) based on intuition from plane and space geometry. It includes an introduction to matrix calculus.

The EU also introduces the basic language of polynomials.

## Calculus CUPGE & math

## ECTS

3 credits

## Component

Faculty of Science

The aim of this course is to rework certain concepts of analysis from high school, by deepening them, and by developing the practice of calculation and the interpretation of calculations.

## Written Compositions CUPGE S1

## Level of study

BAC +1

## ECTS

2 credits

## Component

Faculty of Science

## Hourly volume

18h

4 knowledge control sessions during the semester in Mathematics and Physics.

## Reasoning and Set Theory

## ECTS

2 credits

## Component

Faculty of Science

## Geometry in the plane, space and complex plane

## ECTS

4 credits

## Component

Faculty of Science

This UE aims at working on the geometry of the plane, its objects but also the demonstrations. The UE also aims at introducing complex numbers. The parts geometry and complex numbers represent each half of the UE.

- objects of plane geometry: points, lines, vectors, angles, circles, triangles, etc.

- geometric transformations of the plane: symmetries, homotheties, rotations, translations.

- work on mathematical demonstration

- introduction of complex numbers, geometric interpretation, calculation with complex numbers

## Analysis I functions of one variable and sequences

## ECTS

5 credits

## Component

Faculty of Science

The aim of this course is to clarify the notions of limits of sequences and functions, to deepen the study of sequences and functions, and to study the notions of continuity and derivability of functions, as well as to introduce the main "usual" functions.

## Written compositions CUPGE S2

## Level of study

BAC +1

## ECTS

2 credits

## Component

Faculty of Science

## Hourly volume

18h

4 knowledge control sessions during the semester in Mathematics and Physics/Mechanics.

## Arithmetic and enumeration

## ECTS

6 credits

## Component

Faculty of Science

This UE aims to introduce the elementary concepts of arithmetic and enumeration useful for the beginning of the degree in mathematics.

## Thermodynamics 1

## Level of study

BAC +1

## ECTS

5 credits

## Component

Faculty of Science

## Hourly volume

54h

After some reminders of classical mechanics we will approach the fundamental quantities of thermodynamics: elementary work, macroscopic...

The distinction heat/temperature will be exposed at length.

The notion of pressure will be exposed macroscopically while giving however the microscopic interpretation.

Then with a historical approach we will show how the principles 1 and 2 could have been stated

From there applications will be seen: cycles, perfect/real gas....

Thanks to the introduction of changes of state, examples (critical point) will be exposed.

We will finish with thermics: essentially diﬀusion. Depending on the remaining time notions about radiation will be exposed.

## Python for Science

## Level of study

BAC +1

## ECTS

4 credits

## Component

Faculty of Science

## Hourly volume

36h

This module is an introduction to the use of Python for students in the sciences. It will cover notions of algorithmics and the Python language, but the approach is primarily oriented towards a usefulness in Science. The examples will be based on problems related to the other first year subjects.

## Algebra II, vector spaces and linear applications

## ECTS

6 credits

## Component

Faculty of Science

This course is a continuation of the S1 course (Algebra I) where linear algebra in R², R³ and ^{Rn}, matrix calculus and polynomials with real coefficients were introduced.

The objective is to introduce some elementary concepts of algebraic structure, and to deepen the work on vector spaces and linear applications, as well as polynomials.

## Kinematics and statics of the solid

## Level of study

BAC +1

## ECTS

5 credits

## Component

Faculty of Science

## Hourly volume

45h

This course in Solid Mechanics studies articulated systems made up of rigid solids through their movements and equilibrium positions. The concepts covered are velocity fields in solids, the classification of links and forces. Methods of kinematics and statics are also used.

## Analysis II Suites, series, limited developments

## ECTS

6 credits

## Component

Faculty of Science

This course follows the S1 course (Analysis I) where continuity and derivability of real functions, usual functions, and the study of real sequences were introduced.

The objective is to continue and deepen the work on sequences and functions, and to introduce the study of numerical series.

## Algebra I linear systems

## ECTS

5 credits

## Component

Faculty of Science

This course is an introduction to linear algebra (formalized in S2) based on intuition from plane and space geometry. It includes an introduction to matrix calculus.

The EU also introduces the basic language of polynomials.

## Use of computer systems

## ECTS

4 credits

## Component

Faculty of Science

Introduction of the main concepts of computer systems

## Let's play deterministic automata

## ECTS

3 credits

## Component

Faculty of Science

The theory of languages and automata belongs to the fundamental branch of computer science. In this course we will study languages and their representation, in particular rational languages and their representation by finite state automata.

## Calculus CUPGE & math

## ECTS

3 credits

## Component

Faculty of Science

The aim of this course is to rework certain concepts of analysis from high school, by deepening them, and by developing the practice of calculation and the interpretation of calculations.

## Algorithmics 1

## ECTS

5 credits

## Component

Faculty of Science

In this module we present the basic concepts in algorithms (notion of problem, problem instance, instance size, notion of complexity, termination, proof of validity).

The algorithms presented will focus on problems related to sorting, stacks, queues, arrays....

## Reasoning and Set Theory

## ECTS

2 credits

## Component

Faculty of Science

## Functional programming

## ECTS

5 credits

## Component

Faculty of Science

This course aims at introducing the functional programming paradigm. First, we will talk about lambda-calculus, which is the computational model on which functional languages are based. Then, we will teach a real functional programming language, namely OCaml.

The presentation of OCaml will mainly follow the following plan:

1. Basic types, definitions.

2. Function declarations.

3. Basic data structures (tuples, lists).

4. Advanced data structures (sum types, records).

5. Exceptions.

6. Higher order functions, iterators on lists.

If time permits, we will also look at the module system of OCaml, one of the main motivations of which is to group related definitions, but which also allows to introduce reusability through the system of parameterized modules (functors).

## Geometry in the plane, space and complex plane

## ECTS

4 credits

## Component

Faculty of Science

This UE aims at working on the geometry of the plane, its objects but also the demonstrations. The UE also aims at introducing complex numbers. The parts geometry and complex numbers represent each half of the UE.

- objects of plane geometry: points, lines, vectors, angles, circles, triangles, etc.

- geometric transformations of the plane: symmetries, homotheties, rotations, translations.

- work on mathematical demonstration

- introduction of complex numbers, geometric interpretation, calculation with complex numbers

## Analysis I functions of one variable and sequences

## ECTS

5 credits

## Component

Faculty of Science

The aim of this course is to clarify the notions of limits of sequences and functions, to deepen the study of sequences and functions, and to study the notions of continuity and derivability of functions, as well as to introduce the main "usual" functions.

## Algorithmics 2

## ECTS

5 credits

## Component

Faculty of Science

Continuation of HAI101I, Algorithms 1

## C Programming

## ECTS

5 credits

## Component

Faculty of Science

Mastery of the basics of C programming; Understanding how algorithms and abstract data structures are implemented in the machine.

## Arithmetic and enumeration

## ECTS

6 credits

## Component

Faculty of Science

This UE aims to introduce the elementary concepts of arithmetic and enumeration useful for the beginning of the degree in mathematics.

## General Culture - To be chosen from the list below +.

## ECTS

2 credits

## Component

Faculty of Science

## Introduction to Oceanography

## ECTS

2 credits

## Component

Faculty of Science

## Pleasures and addictions

## ECTS

2 credits

## Component

Faculty of Science

## The place of man in the universe

## ECTS

2 credits

## Component

Faculty of Science

## Education for the ecological transition

## ECTS

2 credits

## Component

Faculty of Science

## Basic computer tools and concepts (PIX)

## ECTS

2 credits

## Component

Faculty of Science

## The quantum computer, between physics and mathematics

## ECTS

2 credits

## Component

Faculty of Science

## The questioning of the movement

## ECTS

2 credits

## Component

Faculty of Science

## Event and web programming

## ECTS

4 credits

## Component

Faculty of Science

Introduction to web application programming

## Algebra II, vector spaces and linear applications

## ECTS

6 credits

## Component

Faculty of Science

This course is a continuation of the S1 course (Algebra I) where linear algebra in R², R³ and ^{Rn}, matrix calculus and polynomials with real coefficients were introduced.

The objective is to introduce some elementary concepts of algebraic structure, and to deepen the work on vector spaces and linear applications, as well as polynomials.

## Analysis II Suites, series, limited developments

## ECTS

6 credits

## Component

Faculty of Science

This course follows the S1 course (Analysis I) where continuity and derivability of real functions, usual functions, and the study of real sequences were introduced.

The objective is to continue and deepen the work on sequences and functions, and to introduce the study of numerical series.

## L1 Porfil Minor Info choice 1

## ECTS

30 credits

## Component

Faculty of Science

## Algebra I linear systems

## ECTS

5 credits

## Component

Faculty of Science

This course is an introduction to linear algebra (formalized in S2) based on intuition from plane and space geometry. It includes an introduction to matrix calculus.

The EU also introduces the basic language of polynomials.

## Algorithmics 1

## ECTS

5 credits

## Component

Faculty of Science

In this module we present the basic concepts in algorithms (notion of problem, problem instance, instance size, notion of complexity, termination, proof of validity).

The algorithms presented will focus on problems related to sorting, stacks, queues, arrays....

## Reasoning and Set Theory

## ECTS

2 credits

## Component

Faculty of Science

## Remediation in mathematics

## ECTS

3 credits

## Component

Faculty of Science

## Functional programming

## ECTS

5 credits

## Component

Faculty of Science

This course aims at introducing the functional programming paradigm. First, we will talk about lambda-calculus, which is the computational model on which functional languages are based. Then, we will teach a real functional programming language, namely OCaml.

The presentation of OCaml will mainly follow the following plan:

1. Basic types, definitions.

2. Function declarations.

3. Basic data structures (tuples, lists).

4. Advanced data structures (sum types, records).

5. Exceptions.

6. Higher order functions, iterators on lists.

If time permits, we will also look at the module system of OCaml, one of the main motivations of which is to group related definitions, but which also allows to introduce reusability through the system of parameterized modules (functors).

## Geometry in the plane, space and complex plane

## ECTS

4 credits

## Component

Faculty of Science

This UE aims at working on the geometry of the plane, its objects but also the demonstrations. The UE also aims at introducing complex numbers. The parts geometry and complex numbers represent each half of the UE.

- objects of plane geometry: points, lines, vectors, angles, circles, triangles, etc.

- geometric transformations of the plane: symmetries, homotheties, rotations, translations.

- work on mathematical demonstration

- introduction of complex numbers, geometric interpretation, calculation with complex numbers

## Analysis I functions of one variable and sequences

## ECTS

5 credits

## Component

Faculty of Science

The aim of this course is to clarify the notions of limits of sequences and functions, to deepen the study of sequences and functions, and to study the notions of continuity and derivability of functions, as well as to introduce the main "usual" functions.

## L1 Profile Info Minor choice 2

## ECTS

30 credits

## Component

Faculty of Science

## Algebra I linear systems

## ECTS

5 credits

## Component

Faculty of Science

The EU also introduces the basic language of polynomials.

## Calculus CUPGE & math

## ECTS

3 credits

## Component

Faculty of Science

The aim of this course is to rework certain concepts of analysis from high school, by deepening them, and by developing the practice of calculation and the interpretation of calculations.

## Algorithmics 1

## ECTS

5 credits

## Component

Faculty of Science

In this module we present the basic concepts in algorithms (notion of problem, problem instance, instance size, notion of complexity, termination, proof of validity).

The algorithms presented will focus on problems related to sorting, stacks, queues, arrays....

## Reasoning and Set Theory

## ECTS

2 credits

## Component

Faculty of Science

## Functional programming

## ECTS

5 credits

## Component

Faculty of Science

This course aims at introducing the functional programming paradigm. First, we will talk about lambda-calculus, which is the computational model on which functional languages are based. Then, we will teach a real functional programming language, namely OCaml.

The presentation of OCaml will mainly follow the following plan:

1. Basic types, definitions.

2. Function declarations.

3. Basic data structures (tuples, lists).

4. Advanced data structures (sum types, records).

5. Exceptions.

6. Higher order functions, iterators on lists.

If time permits, we will also look at the module system of OCaml, one of the main motivations of which is to group related definitions, but which also allows to introduce reusability through the system of parameterized modules (functors).

## Geometry in the plane, space and complex plane

## ECTS

4 credits

## Component

Faculty of Science

- objects of plane geometry: points, lines, vectors, angles, circles, triangles, etc.

- geometric transformations of the plane: symmetries, homotheties, rotations, translations.

- work on mathematical demonstration

- introduction of complex numbers, geometric interpretation, calculation with complex numbers

## Analysis I functions of one variable and sequences

## ECTS

5 credits

## Component

Faculty of Science

## Algorithmics 2

## ECTS

5 credits

## Component

Faculty of Science

Continuation of HAI101I, Algorithms 1

## C Programming

## ECTS

5 credits

## Component

Faculty of Science

Mastery of the basics of C programming; Understanding how algorithms and abstract data structures are implemented in the machine.

## Arithmetic and enumeration

## ECTS

6 credits

## Component

Faculty of Science

This UE aims to introduce the elementary concepts of arithmetic and enumeration useful for the beginning of the degree in mathematics.

## Algebra II, vector spaces and linear applications

## ECTS

6 credits

## Component

Faculty of Science

This course is a continuation of the S1 course (Algebra I) where linear algebra in R², R³ and ^{Rn}, matrix calculus and polynomials with real coefficients were introduced.

The objective is to introduce some elementary concepts of algebraic structure, and to deepen the work on vector spaces and linear applications, as well as polynomials.

## Analysis II Suites, series, limited developments

## ECTS

6 credits

## Component

Faculty of Science

This course follows the S1 course (Analysis I) where continuity and derivability of real functions, usual functions, and the study of real sequences were introduced.

The objective is to continue and deepen the work on sequences and functions, and to introduce the study of numerical series.

## General Physics

## Level of study

BAC +1

## ECTS

6 credits

## Component

Faculty of Science

## Hourly volume

54h

The main objective of this course is to teach you to pose and solve simple physics problems. The areas of application are material point mechanics and geometric optics.

*Mechanics of the material point :*

- Static of forces: studies of mechanical systems in equilibrium.
- Kinematics: study of the movement of bodies independently of the causes that generate them.
- Dynamics: links between the causes of movement and the movement itself.
- Work and energy: work of forces (conservative and non-conservative), kinetic energy theorem, mechanical energy theorem and their applications.

*Geometric optics:*

- Propagation of light (Fermat's principle, Snell-Descartes laws, index of refraction),
- Image formation and optical systems (stigmatism, Gaussian approximation, mirrors, thin lenses, dispersive systems, centered systems, optical instruments)

## Algebra I linear systems

## ECTS

5 credits

## Component

Faculty of Science

The EU also introduces the basic language of polynomials.

## Reasoning and Set Theory

## ECTS

2 credits

## Component

Faculty of Science

## Remediation in mathematics

## ECTS

3 credits

## Component

Faculty of Science

## Geometry in the plane, space and complex plane

## ECTS

4 credits

## Component

Faculty of Science

- objects of plane geometry: points, lines, vectors, angles, circles, triangles, etc.

- geometric transformations of the plane: symmetries, homotheties, rotations, translations.

- work on mathematical demonstration

- introduction of complex numbers, geometric interpretation, calculation with complex numbers

## Analysis I functions of one variable and sequences

## ECTS

5 credits

## Component

Faculty of Science

## List Minor Phy choice 2

## ECTS

30 credits

## Component

Faculty of Science

## General Physics

## Level of study

BAC +1

## ECTS

6 credits

## Component

Faculty of Science

## Hourly volume

54h

The main objective of this course is to teach you to pose and solve simple physics problems. The areas of application are material point mechanics and geometric optics.

*Mechanics of the material point :*

- Static of forces: studies of mechanical systems in equilibrium.
- Kinematics: study of the movement of bodies independently of the causes that generate them.
- Dynamics: links between the causes of movement and the movement itself.
- Work and energy: work of forces (conservative and non-conservative), kinetic energy theorem, mechanical energy theorem and their applications.

*Geometric optics:*

- Propagation of light (Fermat's principle, Snell-Descartes laws, index of refraction),
- Image formation and optical systems (stigmatism, Gaussian approximation, mirrors, thin lenses, dispersive systems, centered systems, optical instruments)

## Algebra I linear systems

## ECTS

5 credits

## Component

Faculty of Science

The EU also introduces the basic language of polynomials.

## Calculus CUPGE & math

## ECTS

3 credits

## Component

Faculty of Science

## Reasoning and Set Theory

## ECTS

2 credits

## Component

Faculty of Science

## Geometry in the plane, space and complex plane

## ECTS

4 credits

## Component

Faculty of Science

- objects of plane geometry: points, lines, vectors, angles, circles, triangles, etc.

- geometric transformations of the plane: symmetries, homotheties, rotations, translations.

- work on mathematical demonstration

- introduction of complex numbers, geometric interpretation, calculation with complex numbers

## Analysis I functions of one variable and sequences

## ECTS

5 credits

## Component

Faculty of Science

## Arithmetic and enumeration

## ECTS

6 credits

## Component

Faculty of Science

## Thermodynamics 1

## Level of study

BAC +1

## ECTS

5 credits

## Component

Faculty of Science

## Hourly volume

54h

After some reminders of classical mechanics we will approach the fundamental quantities of thermodynamics: elementary work, macroscopic...

The distinction heat/temperature will be exposed at length.

The notion of pressure will be exposed macroscopically while giving however the microscopic interpretation.

Then with a historical approach we will show how the principles 1 and 2 could have been stated

From there applications will be seen: cycles, perfect/real gas....

Thanks to the introduction of changes of state, examples (critical point) will be exposed.

We will finish with thermics: essentially diﬀusion. Depending on the remaining time notions about radiation will be exposed.

## Algebra II, vector spaces and linear applications

## ECTS

6 credits

## Component

Faculty of Science

^{Rn}, matrix calculus and polynomials with real coefficients were introduced.

## Kinematics and statics of the solid

## Level of study

BAC +1

## ECTS

5 credits

## Component

Faculty of Science

## Hourly volume

45h

This course in Solid Mechanics studies articulated systems made up of rigid solids through their movements and equilibrium positions. The concepts covered are velocity fields in solids, the classification of links and forces. Methods of kinematics and statics are also used.

## Analysis II Suites, series, limited developments

## ECTS

6 credits

## Component

Faculty of Science