L1 - Mathematics and Its Applications - OuiSi

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

The EU is also introducing the basic language of polynomials.

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In this module, we introduce the basic concepts of algorithms (the concept of a problem, a problem instance, instance size, the concept of complexity, termination, and proof of correctness).

The algorithms presented will address problems related to sorting, stacks, queues, arrays, and more. 

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This course aims to introduce the functional programming paradigm. First, we will discuss lambda calculus, which is the computational model on which functional languages are based. Then, we will move on to teaching a real functional programming language, namely OCaml.

The OCaml presentation will mainly follow this 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, list iterators.

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

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This unit aims to explore plane geometry, its objects, and proofs. The unit also aims to introduce complex numbers. The sections on geometry and complex numbers each make up half of the unit.

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

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

- work on mathematical proofs

- Introduction to complex numbers, geometric interpretation, calculations with complex numbers

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The purpose of this unit is to clarify the concepts of limits of sequences and functions, to explore sequences and functions in greater depth, to examine the concepts of continuity and differentiability of functions, and to introduce the main “common” functions.

View the full page

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

The EU is also introducing the basic language of polynomials.

View the full page

The purpose of this unit is to revisit certain analytical concepts covered in high school, explore them in greater depth, and develop students’ computational skills and their ability to interpret calculations.

View the full page

In this module, we introduce the basic concepts of algorithms (the concept of a problem, a problem instance, instance size, the concept of complexity, termination, and proof of correctness).

The algorithms presented will address problems related to sorting, stacks, queues, arrays, and more. 

View the full page

View the full page

This course aims to introduce the functional programming paradigm. First, we will discuss lambda calculus, which is the computational model on which functional languages are based. Then, we will move on to teaching a real functional programming language, namely OCaml.

The OCaml presentation will mainly follow this 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, list iterators.

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

View the full page

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This unit aims to explore plane geometry, its objects, and proofs. The unit also aims to introduce complex numbers. The sections on geometry and complex numbers each make up half of the unit.

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

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

- work on mathematical proofs

- Introduction to complex numbers, geometric interpretation, calculations with complex numbers

View the full page

The purpose of this unit is to clarify the concepts of limits of sequences and functions, to explore sequences and functions in greater depth, to examine the concepts of continuity and differentiability of functions, and to introduce the main “common” functions.

View the full page

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The main objective of this course is to teach you how to formulate and solve simple physics problems. The areas of application are the mechanics of a point particle and geometric optics.

Mechanics of the Material Point:

• Statics: Analysis of Mechanical Systems in Equilibrium.
• Kinematics: the study of the motion of bodies, independent of the causes that produce it.
• Dynamics: the relationships between the causes of motion and motion itself.
• Work and Energy: Work Done by Forces (Conservative and Non-Conservative), the Kinetic Energy Theorem, the Mechanical Energy Theorem, and Their Applications.

Geometric Optics:

• Light Propagation (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).

View the full page

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

The EU is also introducing the basic language of polynomials.

View the full page

View the full page

View the full page

View the full page

View the full page

This unit aims to explore plane geometry, its objects, and proofs. The unit also aims to introduce complex numbers. The sections on geometry and complex numbers each make up half of the unit.

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

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

- work on mathematical proofs

- Introduction to complex numbers, geometric interpretation, calculations with complex numbers

View the full page

The purpose of this unit is to clarify the concepts of limits of sequences and functions, to explore sequences and functions in greater depth, to examine the concepts of continuity and differentiability of functions, and to introduce the main “common” functions.

View the full page

View the full page

The main objective of this course is to teach you how to formulate and solve simple physics problems. The areas of application are the mechanics of a point particle and geometric optics.

Mechanics of the Material Point:

• Statics: Analysis of Mechanical Systems in Equilibrium.
• Kinematics: the study of the motion of bodies, independent of the causes that produce it.
• Dynamics: the relationships between the causes of motion and motion itself.
• Work and Energy: Work Done by Forces (Conservative and Non-Conservative), the Kinetic Energy Theorem, the Mechanical Energy Theorem, and Their Applications.

Geometric Optics:

• Light Propagation (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).

View the full page

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

The EU is also introducing the basic language of polynomials.

View the full page

View the full page

The purpose of this unit is to revisit certain analytical concepts covered in high school, explore them in greater depth, and develop students’ computational skills and their ability to interpret calculations.

View the full page

View the full page

View the full page

This unit aims to explore plane geometry, its objects, and proofs. The unit also aims to introduce complex numbers. The sections on geometry and complex numbers each make up half of the unit.

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

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

- work on mathematical proofs

- Introduction to complex numbers, geometric interpretation, calculations with complex numbers

View the full page

The purpose of this unit is to clarify the concepts of limits of sequences and functions, to explore sequences and functions in greater depth, to examine the concepts of continuity and differentiability of functions, and to introduce the main “common” functions.

View the full page

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Sequel to HAI101I, Algorithms 1

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

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This course unit aims to introduce the basic concepts of arithmetic and counting that are useful for the beginning of the bachelor’s degree in mathematics.

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This course follows S1 (Algebra I), in which linear algebra in R², R³, and^{R^n}, matrix algebra, and polynomials with real coefficients were introduced.

The goal is to introduce some basic concepts of algebraic structure and to delve deeper into vector spaces and linear mappings, as well as polynomials.

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This course follows on from the S1 course (Analysis I), in which we were introduced to the continuity and differentiability of real-valued functions, common functions, and the study of real sequences.

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

View the full page

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Sequel to HAI101I, Algorithms 1

View the full page

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

View the full page

This course unit aims to introduce the basic concepts of arithmetic and counting that are useful for the beginning of the bachelor’s degree in mathematics.

View the full page

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This course unit aims to introduce the basic concepts of arithmetic and counting that are useful for the beginning of the bachelor’s degree in mathematics.

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After reviewing classical mechanics, we will discuss the fundamental quantities of thermodynamics: elementary work, macroscopic work...
The distinction between heat and temperature will be explained in detail.
The concept of pressure will be explained from a macroscopic perspective, while also providing its microscopic interpretation.
Next, using a historical approach, we will show how the first and second laws of thermodynamics came to be formulated.

From there, we will look at various applications: cycles, ideal and real gases, etc.

With the introduction of phase changes, examples (critical point) will be discussed.
We will conclude with thermal phenomena: primarily diffusion. Depending on the time remaining, concepts related to radiation will be discussed.

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The purpose of this Solid Mechanics course is to study articulated systems composed of rigid solids by examining their motions and equilibrium positions. Topics covered include velocity fields in solids, the classification of joints, and internal forces. Graphical methods of kinematics and statics are also used.

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This course unit aims to introduce the basic concepts of arithmetic and counting that are useful for the beginning of the bachelor’s degree in mathematics.

View the full page

After reviewing classical mechanics, we will discuss the fundamental quantities of thermodynamics: elementary work, macroscopic work...
The distinction between heat and temperature will be explained in detail.
The concept of pressure will be explained from a macroscopic perspective, while also providing its microscopic interpretation.
Next, using a historical approach, we will show how the first and second laws of thermodynamics came to be formulated.

From there, we will look at various applications: cycles, ideal and real gases, etc.

With the introduction of phase changes, examples (critical point) will be discussed.
We will conclude with thermal phenomena: primarily diffusion. Depending on the time remaining, concepts related to radiation will be discussed.

View the full page

This course follows S1 (Algebra I), in which linear algebra in R², R³, and^{R^n}, matrix algebra, and polynomials with real coefficients were introduced.

The goal is to introduce some basic concepts of algebraic structure and to delve deeper into vector spaces and linear mappings, as well as polynomials.

View the full page

The purpose of this Solid Mechanics course is to study articulated systems composed of rigid solids by examining their motions and equilibrium positions. Topics covered include velocity fields in solids, the classification of joints, and internal forces. Graphical methods of kinematics and statics are also used.

View the full page

View the full page

This course follows on from the S1 course (Analysis I), in which we were introduced to the continuity and differentiability of real-valued functions, common functions, and the study of real sequences.

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

View the full page