## Training structure

Faculty of Science

## Presentation

## Program

### Select a program

### L1 - CUPGE Maths

The Cycle Universitaire Préparatoire aux Grandes Écoles (CUPGE) Mathématiques-Physique (Mathematics-Physics University Preparatory Cycle for the Grandes Écoles) is an advanced course with a focus on mathematics.

## Written compositions CUPGE S2

2 credits18h## Arithmetic and counting

6 credits## Thermodynamics 1

5 credits54h## Python for science

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

6 credits## Solid kinematics and statics

5 credits45h## English S2

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

6 credits

## General physics

6 credits54h## Algebra I linear systems

5 credits## Electronics

6 credits## Calculus CUPGE & maths

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

### 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 with deterministic automata

3 credits## Calculus CUPGE & maths

3 credits## Algorithms 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

## Algorithms 2

5 credits## C programming

5 credits## Arithmetic and counting

6 credits## General culture - Choose from the list below +.

2 credits## Your choice: 1 of 12

## Introduction to Oceanography

2 credits## Pleasures and addictions

2 credits## Man's place in the Universe

2 credits## Creative writing

2 credits## Ecological transition education

2 credits## Sport

## Basic computer tools and concepts (PIX)

2 credits## Science and Music

2 credits## Sc. and Fragrance Culture

2 credits## Additive manufacturing

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

2 credits## Questioning 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

### L1- Mathematics and its applications- YesSi

## Your choice: 1 of 2

## Profile Maths Minor info

## Your choice: 1 of 2

## L1 Porfil Minor Info choice 1

30 credits## Algebra I linear systems

5 credits## Algorithms 1

5 credits## Reasoning and Set Theory

2 credits## Remediation in mathematics

3 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

## L1 Profile Info Minor choice 2

30 credits## Algebra I linear systems

5 credits## Calculus CUPGE & maths

3 credits## Algorithms 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

## Profile Maths minor Physics

## Your choice: 1 of 2

## L1 Phy minor choice 1

30 credits## General physics

6 credits54h## Algebra I linear systems

5 credits## Electronics 1

4 credits## Reasoning and Set Theory

2 credits## Remediation in mathematics

3 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

## List Minor Phy choice 2

30 credits## General physics

6 credits54h## Algebra I linear systems

5 credits## Electronics 1

4 credits## Calculus CUPGE & maths

3 credits## 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

## Your choice: 1 of 4

## Profile Minor info

## Algorithms 2

5 credits## C programming

5 credits## Arithmetic and counting

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

6 credits## English S2

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

6 credits

## Profil Mineure Info - OuiSi

## Algorithms 2

5 credits## C programming

5 credits## Arithmetic and counting

6 credits## Computer remediation

## PCSI Math tutoring

## English S2

2 credits

## Profile Minor Physics - OuiSi

## PCSI Physics Remediation

## Arithmetic and counting

6 credits## Thermodynamics 1

5 credits54h## Solid kinematics and statics

5 credits45h## PCSI Math tutoring

## English S2

2 credits

## Profile Minor Physics

## Arithmetic and counting

6 credits## Thermodynamics 1

5 credits54h## Algebra II, vector spaces and linear applications

6 credits## Solid kinematics and statics

5 credits45h## English S2

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

6 credits

## Written compositions CUPGE S2

## Study level

BAC +1

## ECTS

2 credits

## Component

Faculty of Science

## Hourly volume

18h

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

## Arithmetic and counting

## ECTS

6 credits

## Component

Faculty of Science

The aim of this course is to introduce the elementary concepts of arithmetic and enumeration that will be useful at the beginning of a bachelor's degree in mathematics.

## Thermodynamics 1

## Study level

BAC +1

## ECTS

5 credits

## Component

Faculty of Science

## Hourly volume

54h

After a reminder of classical mechanics, we'll look at the fundamental quantities of thermodynamics: elementary and macroscopic work...

The heat/temperature distinction will be explained at length.

The notion of pressure will be explained macroscopically, but with a microscopic interpretation.

Then, with a historical approach, we'll show how Principles 1 and 2 came to be formulated.

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

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

We will finish with thermics: essentially diﬀusion. Depending on the time available, we'll also cover radiation.

## Python for science

## Study level

BAC +1

## ECTS

4 credits

## Component

Faculty of Science

## Hourly volume

36h

This module is an introduction to the use of Python for science students. It covers the basics of algorithms and the Python language, but the approach is primarily geared towards use in the sciences. Examples are given of problems related to other first-year subjects.

## Algebra II, vector spaces and linear applications

## ECTS

6 credits

## Component

Faculty of Science

This follows on from S1 (Algebra I), which introduced linear algebra in R², R³ and ^{Rn}, matrix calculus and polynomials with real coefficients.

The aim is to introduce a few elementary concepts of algebraic structure, and deepen work on vector spaces and linear applications, as well as polynomials.

## Solid kinematics and statics

## Study level

BAC +1

## ECTS

5 credits

## Component

Faculty of Science

## Hourly volume

45h

This Solid Mechanics course studies articulated systems made up of rigid solids through their movements and equilibrium positions. Concepts covered include velocity fields in solids, link classification and forces. Graphical kinematics and statics are also used.

## Analysis II Suites, series, limited developments

## ECTS

6 credits

## Component

Faculty of Science

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

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

## General physics

## Study level

BAC +1

## ECTS

6 credits

## Component

Faculty of Science

## Hourly volume

54h

The main aim of this course is to teach you how to pose and solve simple physics problems. The fields of application are material point mechanics and geometrical optics.

*Mechanics of the material point :*

- Force statics: studies of mechanical systems in equilibrium.
- Kinematics: the 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.

*Geometrical optics :*

- Propagation of light (Fermat's principle, Snell-Descartes laws, refractive index),
- 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 UE 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 UE also introduces the basic language of polynomials.

## Calculus CUPGE & maths

## ECTS

3 credits

## Component

Faculty of Science

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

## Written Compositions CUPGE S1

## Study level

BAC +1

## ECTS

2 credits

## Component

Faculty of Science

## Hourly volume

18h

4 tests 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 to work on plane geometry and its objects, as well as demonstrations. It also introduces complex numbers. The geometry and complex numbers sections each account for half of the UE.

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

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

- work on mathematical demonstration

- introduction to complex numbers, geometric interpretation, calculating 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.

## Algebra I linear systems

## ECTS

5 credits

## Component

Faculty of Science

This UE 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 UE also introduces the basic language of polynomials.

## Use of computer systems

## ECTS

4 credits

## Component

Faculty of Science

Introduction to the main concepts of computer systems

## Let's play with 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 teaching unit, we will study languages and their representation, in particular rational languages and their representation by finite state automata.

## Calculus CUPGE & maths

## ECTS

3 credits

## Component

Faculty of Science

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

## Algorithms 1

## ECTS

5 credits

## Component

Faculty of Science

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

The algorithms presented will deal with 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 introduces the functional programming paradigm. First, we'll talk about lambda-calculus, the computational model on which functional languages are based. We then move on to teach a real functional programming language, namely OCaml.

The presentation of OCaml will mainly follow the following outline:

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.

Time permitting, we'll also take a look at OCaml's module system, one of whose main motivations is to group together related definitions, but which also introduces 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 to work on plane geometry and its objects, as well as demonstrations. It also introduces complex numbers. The geometry and complex numbers sections each account for half of the UE.

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

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

- work on mathematical demonstration

- introduction to complex numbers, geometric interpretation, calculating 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.

## Algorithms 2

## ECTS

5 credits

## Component

Faculty of Science

HAI101I Suite, Algorithms 1

## C programming

## ECTS

5 credits

## Component

Faculty of Science

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

## Arithmetic and counting

## ECTS

6 credits

## Component

Faculty of Science

The aim of this course is to introduce the elementary concepts of arithmetic and enumeration that will be useful at the beginning of a bachelor's degree in mathematics.

## General culture - Choose 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

## Man's place in the Universe

## ECTS

2 credits

## Component

Faculty of Science

## Ecological transition education

## ECTS

2 credits

## Component

Faculty of Science

## Basic computer tools and concepts (PIX)

## ECTS

2 credits

## Component

Faculty of Science

## Sc. and Fragrance Culture

## ECTS

2 credits

## Component

Faculty of Science

## The quantum computer, between physics and mathematics

## 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 follows on from S1 (Algebra I), which introduced linear algebra in R², R³ and ^{Rn}, matrix calculus and polynomials with real coefficients.

The aim is to introduce a few elementary concepts of algebraic structure, and deepen 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 on from S1 (Analysis I), which introduced continuity and derivability of real functions, usual functions and the study of real sequences.

The aim is to continue and deepen 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 UE 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 UE also introduces the basic language of polynomials.

## Algorithms 1

## ECTS

5 credits

## Component

Faculty of Science

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

The algorithms presented will deal with 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 introduces the functional programming paradigm. First, we'll talk about lambda-calculus, the computational model on which functional languages are based. We then move on to teach a real functional programming language, namely OCaml.

The presentation of OCaml will mainly follow the following outline:

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.

Time permitting, we'll also take a look at OCaml's module system, one of whose main motivations is to group together related definitions, but which also introduces 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 to work on plane geometry and its objects, as well as demonstrations. It also introduces complex numbers. The geometry and complex numbers sections each account for half of the UE.

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

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

- work on mathematical demonstration

- introduction to complex numbers, geometric interpretation, calculating 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 UE also introduces the basic language of polynomials.

## Calculus CUPGE & maths

## ECTS

3 credits

## Component

Faculty of Science

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

## Algorithms 1

## ECTS

5 credits

## Component

Faculty of Science

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

The algorithms presented will deal with 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 introduces the functional programming paradigm. First, we'll talk about lambda-calculus, the computational model on which functional languages are based. We then move on to teach a real functional programming language, namely OCaml.

The presentation of OCaml will mainly follow the following outline:

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.

Time permitting, we'll also take a look at OCaml's module system, one of whose main motivations is to group together related definitions, but which also introduces reusability through the system of parameterized modules (functors).

## Geometry in the plane, space and complex plane

## ECTS

4 credits

## Component

Faculty of Science

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

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

- work on mathematical demonstration

- introduction to complex numbers, geometric interpretation, calculating with complex numbers

## Analysis I functions of one variable and sequences

## ECTS

5 credits

## Component

Faculty of Science

## Algorithms 2

## ECTS

5 credits

## Component

Faculty of Science

HAI101I Suite, Algorithms 1

## C programming

## ECTS

5 credits

## Component

Faculty of Science

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

## Arithmetic and counting

## ECTS

6 credits

## Component

Faculty of Science

The aim of this course is to introduce the elementary concepts of arithmetic and enumeration that will be useful at the beginning of a bachelor's degree in mathematics.

## Algebra II, vector spaces and linear applications

## ECTS

6 credits

## Component

Faculty of Science

This follows on from S1 (Algebra I), which introduced linear algebra in R², R³ and ^{Rn}, matrix calculus and polynomials with real coefficients.

The aim is to introduce a few elementary concepts of algebraic structure, and deepen 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 on from S1 (Analysis I), which introduced continuity and derivability of real functions, usual functions and the study of real sequences.

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

## General physics

## Study level

BAC +1

## ECTS

6 credits

## Component

Faculty of Science

## Hourly volume

54h

The main aim of this course is to teach you how to pose and solve simple physics problems. The fields of application are material point mechanics and geometrical optics.

*Mechanics of the material point :*

- Force statics: studies of mechanical systems in equilibrium.
- Kinematics: the 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.

*Geometrical optics :*

- Propagation of light (Fermat's principle, Snell-Descartes laws, refractive index),
- 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 UE 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

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

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

- work on mathematical demonstration

- introduction to complex numbers, geometric interpretation, calculating 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

## Study level

BAC +1

## ECTS

6 credits

## Component

Faculty of Science

## Hourly volume

54h

The main aim of this course is to teach you how to pose and solve simple physics problems. The fields of application are material point mechanics and geometrical optics.

*Mechanics of the material point :*

- Force statics: studies of mechanical systems in equilibrium.
- Kinematics: the 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.

*Geometrical optics :*

- Propagation of light (Fermat's principle, Snell-Descartes laws, refractive index),
- 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 UE also introduces the basic language of polynomials.

## Calculus CUPGE & maths

## 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

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

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

- work on mathematical demonstration

- introduction to complex numbers, geometric interpretation, calculating with complex numbers

## Analysis I functions of one variable and sequences

## ECTS

5 credits

## Component

Faculty of Science

## Arithmetic and counting

## ECTS

6 credits

## Component

Faculty of Science

## Thermodynamics 1

## Study level

BAC +1

## ECTS

5 credits

## Component

Faculty of Science

## Hourly volume

54h

After a reminder of classical mechanics, we'll look at the fundamental quantities of thermodynamics: elementary and macroscopic work...

The heat/temperature distinction will be explained at length.

The notion of pressure will be explained macroscopically, but with a microscopic interpretation.

Then, with a historical approach, we'll show how Principles 1 and 2 came to be formulated.

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

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

We will finish with thermics: essentially diﬀusion. Depending on the time available, we'll also cover radiation.

## Algebra II, vector spaces and linear applications

## ECTS

6 credits

## Component

Faculty of Science

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

## Solid kinematics and statics

## Study level

BAC +1

## ECTS

5 credits

## Component

Faculty of Science

## Hourly volume

45h

This Solid Mechanics course studies articulated systems made up of rigid solids through their movements and equilibrium positions. Concepts covered include velocity fields in solids, link classification and forces. Graphical kinematics and statics are also used.

## Analysis II Suites, series, limited developments

## ECTS

6 credits

## Component

Faculty of Science

## L1 Porfil Minor Info choice 1

## ECTS

30 credits

## Component

Faculty of Science

## Algebra I linear systems

## ECTS

5 credits

## Component

Faculty of Science

The UE also introduces the basic language of polynomials.

## Algorithms 1

## ECTS

5 credits

## Component

Faculty of Science

The algorithms presented will deal with 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

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.

## Geometry in the plane, space and complex plane

## ECTS

4 credits

## Component

Faculty of Science

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

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

- work on mathematical demonstration

- introduction to complex numbers, geometric interpretation, calculating with complex numbers

## Analysis I functions of one variable and sequences

## ECTS

5 credits

## Component

Faculty of Science

## 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 UE also introduces the basic language of polynomials.

## Calculus CUPGE & maths

## ECTS

3 credits

## Component

Faculty of Science

## Algorithms 1

## ECTS

5 credits

## Component

Faculty of Science

The algorithms presented will deal with 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

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.

## Geometry in the plane, space and complex plane

## ECTS

4 credits

## Component

Faculty of Science

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

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

- work on mathematical demonstration

- introduction to complex numbers, geometric interpretation, calculating with complex numbers

## Analysis I functions of one variable and sequences

## ECTS

5 credits

## Component

Faculty of Science

## General physics

## Study level

BAC +1

## ECTS

6 credits

## Component

Faculty of Science

## Hourly volume

54h

*Mechanics of the material point :*

- Force statics: studies of mechanical systems in equilibrium.
- Kinematics: the study of the movement of bodies independently of the causes that generate them.
- Dynamics: links between the causes of movement and the movement itself.

*Geometrical optics :*

- Propagation of light (Fermat's principle, Snell-Descartes laws, refractive index),

## Algebra I linear systems

## ECTS

5 credits

## Component

Faculty of Science

The UE 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

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

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

- work on mathematical demonstration

- introduction to complex numbers, geometric interpretation, calculating 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

## Study level

BAC +1

## ECTS

6 credits

## Component

Faculty of Science

## Hourly volume

54h

*Mechanics of the material point :*

- Force statics: studies of mechanical systems in equilibrium.
- Kinematics: the study of the movement of bodies independently of the causes that generate them.
- Dynamics: links between the causes of movement and the movement itself.

*Geometrical optics :*

- Propagation of light (Fermat's principle, Snell-Descartes laws, refractive index),

## Algebra I linear systems

## ECTS

5 credits

## Component

Faculty of Science

The UE also introduces the basic language of polynomials.

## Calculus CUPGE & maths

## 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

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

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

- work on mathematical demonstration

- introduction to complex numbers, geometric interpretation, calculating with complex numbers

## Analysis I functions of one variable and sequences

## ECTS

5 credits

## Component

Faculty of Science

## Algorithms 2

## ECTS

5 credits

## Component

Faculty of Science

HAI101I Suite, Algorithms 1

## C programming

## ECTS

5 credits

## Component

Faculty of Science

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

## Arithmetic and counting

## ECTS

6 credits

## Component

Faculty of Science

## Algebra II, vector spaces and linear applications

## ECTS

6 credits

## Component

Faculty of Science

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

## Analysis II Suites, series, limited developments

## ECTS

6 credits

## Component

Faculty of Science

## Algorithms 2

## ECTS

5 credits

## Component

Faculty of Science

HAI101I Suite, Algorithms 1

## C programming

## ECTS

5 credits

## Component

Faculty of Science

## Arithmetic and counting

## ECTS

6 credits

## Component

Faculty of Science

## Arithmetic and counting

## ECTS

6 credits

## Component

Faculty of Science

## Thermodynamics 1

## Study level

BAC +1

## ECTS

5 credits

## Component

Faculty of Science

## Hourly volume

54h

After a reminder of classical mechanics, we'll look at the fundamental quantities of thermodynamics: elementary and macroscopic work...

The heat/temperature distinction will be explained at length.

The notion of pressure will be explained macroscopically, but with a microscopic interpretation.

Then, with a historical approach, we'll show how Principles 1 and 2 came to be formulated.

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

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

We will finish with thermics: essentially diﬀusion. Depending on the time available, we'll also cover radiation.

## Solid kinematics and statics

## Study level

BAC +1

## ECTS

5 credits

## Component

Faculty of Science

## Hourly volume

45h

This Solid Mechanics course studies articulated systems made up of rigid solids through their movements and equilibrium positions. Concepts covered include velocity fields in solids, link classification and forces. Graphical kinematics and statics are also used.

## Arithmetic and counting

## ECTS

6 credits

## Component

Faculty of Science

## Thermodynamics 1

## Study level

BAC +1

## ECTS

5 credits

## Component

Faculty of Science

## Hourly volume

54h

The heat/temperature distinction will be explained at length.

The notion of pressure will be explained macroscopically, but with a microscopic interpretation.

Then, with a historical approach, we'll show how Principles 1 and 2 came to be formulated.

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

We will finish with thermics: essentially diﬀusion. Depending on the time available, we'll also cover radiation.

## Algebra II, vector spaces and linear applications

## ECTS

6 credits

## Component

Faculty of Science

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

## Solid kinematics and statics

## Study level

BAC +1

## ECTS

5 credits

## Component

Faculty of Science

## Hourly volume

45h

## Analysis II Suites, series, limited developments

## ECTS

6 credits

## Component

Faculty of Science