L1- Mathematics and its applications

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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.

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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.... 

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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).

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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

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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.

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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.

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

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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.... 

See full page

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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).

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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

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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.

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HAI101I Suite, Algorithms 1

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

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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.

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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.

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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.

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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).

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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.

See full page

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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

See full page

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.

See full page

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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).

See full page

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.

See full page

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

See full page

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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

See full page

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.

See full page

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.

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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.

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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.

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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.

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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.

See full page