L1 - Mathematics and its applications

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

The EU is also introducing the basic language of polynomials.

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In this module, we present the basic concepts of algorithms (notion of a 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, etc. 

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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 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.

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

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This unit aims to cover plane geometry, its objects, and proofs. The unit also aims to introduce complex numbers. The geometry and complex numbers sections each represent half of the unit.

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

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

- work on mathematical proof

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

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The aim of this course is to clarify the concepts of limits of sequences and functions, to deepen the study of sequences and functions, to study the concepts of continuity and differentiability of functions, and to introduce the main "usual" functions.

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

The EU is also introducing the basic language of polynomials.

See the full page

The aim of this EU is to revisit certain concepts from high school analysis, exploring them in greater depth and developing calculation skills and the interpretation of calculations.

See the full page

In this module, we present the basic concepts of algorithms (notion of a 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, etc. 

See the full page

See 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 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.

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

See the full page

See the full page

This unit aims to cover plane geometry, its objects, and proofs. The unit also aims to introduce complex numbers. The geometry and complex numbers sections each represent half of the unit.

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

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

- work on mathematical proof

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

See the full page

The aim of this course is to clarify the concepts of limits of sequences and functions, to deepen the study of sequences and functions, to study the concepts of continuity and differentiability of functions, and to introduce the main "usual" functions.

See the full page

Continuation of HAI101I, Algorithms 1

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

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

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

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

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This follows on from S1 (Analysis I), where continuity and differentiability of real functions, common 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.

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

Mechanics of the material point:

• Statics: study of mechanical systems in equilibrium.
• Kinematics: the study of the motion of bodies independently of the causes that produce it.
• Dynamics: links between the causes of motion and motion itself.
• Work and energy: work done by 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, refractive index)
• Image formation and optical systems (stigmatism, Gaussian approximation, mirrors, thin lenses, dispersive systems, centered systems, optical instruments).

See the full page

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

The EU is also introducing the basic language of polynomials.

See the full page

See the full page

See the full page

See the full page

See the full page

This unit aims to cover plane geometry, its objects, and proofs. The unit also aims to introduce complex numbers. The geometry and complex numbers sections each represent half of the unit.

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

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

- work on mathematical proof

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

See the full page

The aim of this course is to clarify the concepts of limits of sequences and functions, to deepen the study of sequences and functions, to study the concepts of continuity and differentiability of functions, and to introduce the main "usual" functions.

See the full page

See the full page

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

Mechanics of the material point:

• Statics: study of mechanical systems in equilibrium.
• Kinematics: the study of the motion of bodies independently of the causes that produce it.
• Dynamics: links between the causes of motion and motion itself.
• Work and energy: work done by 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, refractive index)
• Image formation and optical systems (stigmatism, Gaussian approximation, mirrors, thin lenses, dispersive systems, centered systems, optical instruments).

See the full page

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

The EU is also introducing the basic language of polynomials.

See the full page

See the full page

The aim of this EU is to revisit certain concepts from high school analysis, exploring them in greater depth and developing calculation skills and the interpretation of calculations.

See the full page

See the full page

See the full page

This unit aims to cover plane geometry, its objects, and proofs. The unit also aims to introduce complex numbers. The geometry and complex numbers sections each represent half of the unit.

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

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

- work on mathematical proof

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

See the full page

The aim of this course is to clarify the concepts of limits of sequences and functions, to deepen the study of sequences and functions, to study the concepts of continuity and differentiability of functions, and to introduce the main "usual" functions.

See the full page

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

See the full page

After reviewing classical mechanics, we will discuss the fundamental quantities of thermodynamics: elementary work, macroscopic work, etc.
The distinction between heat and temperature will be explained in detail.
The concept of pressure will be explained macroscopically, while also providing a microscopic interpretation.
Next, using a historical approach, we will show how principles 1 and 2 were formulated.

From there, applications will be examined: cycles, ideal/real gas, etc.

Thanks to the introduction of state changes, examples (critical point) will be presented.
We will conclude with thermodynamics: mainly diffusion. Depending on the time remaining, concepts related to radiation will be presented.

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

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

See the full page

This Solid Mechanics course focuses on the study of articulated systems consisting of rigid solids through their movements and equilibrium positions. The concepts covered include velocity fields in solids, the classification of connections, and forces. Graphical kinematic and static methods are also used.

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This follows on from S1 (Analysis I), where continuity and differentiability of real functions, common 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.

See the full page