M1 - Fundamental Mathematics (MF)

In this UE we study classical groups (linear, unitary, orthogonal, symplectic), in their algebraic (reduction, conjugation classes...), geometric (actions, exponential application) and topological aspects.

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This UE develops the classical theory of modules over a principal ring, and the basics of group representation theory, focusing on finite groups.

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Description : Partial differential equations (PDEs) are nowadays an essential mathematical tool for studying and understanding physical and biological phenomena. Their great complexity often makes them impossible to solve analytically; hence the need to use numerical solution methods.

This course is dedicated to the introduction of PDEs, then to their resolution using well-known numerical schemes such as finite difference and finite volume methods. A more analytical part, necessary for the introduction of finite volume methods, will be devoted to the analytical resolution of scalar conservation laws. Four programming practical exercises will illustrate the scientific computing tools seen in class with simple examples.

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The construction of solutions to partial differential equations (PDEs) and the theoretical study of their qualitative behavior is essentially based on the use of analytical results, and in particular functional analysis. This course introduces the first important tools for solving PDEs from analytical or geometrical points of view. These tools will be put to use in the study of a few examples of PDEs representative of major classes of equations.

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This course develops the classical theory of Banach spaces and provides an introduction to spectral analysis.

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English TD course, for students in the M1 Fundamental Maths program who are aiming for professional autonomy in English.

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Introductory course on the theory of bodies, with Galois correspondence theorem as the main result.

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This course develops Cauchy's theory for functions of one complex variable, and introduces the notions of conformal representation, fundamental group and coverings.

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This course develops various aspects of effective calculus in algebra (linear algebra over Euclidean rings, resultants, etc.) and introduces the first elements of algebraic geometry.

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Introductory course in differential geometry, focusing on the notions of subvarieties of ^Rn, vector fields and flows.

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This course complements the differential geometry course in M1 Fundamental Mathematics. It applies the concepts of this course to the study of classical Lie groups.

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Each student works on a project supervised by a researcher or teacher-researcher. Students write a dissertation of around 30 pages, which they defend orally before a jury. Students may work in pairs.

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