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Cours scientifiques - FMA_3F003_EP : Algebra and Galois Theory

Domaine > Mathématiques.

Descriptif

Prerequisites: MAA101, MAA103, MAA201, MAA206

MAA303 focuses on groups, rings and fields.

The first part of the course will be dedicated to group theory, and we will cover all the basic notions and tools that one uses to study groups: normal subgroups, quotient groups, simple groups, group actions...

The second part of the course will focus on rings. We will introduce the basic notions related to them, such as ideals, principal ideal domains, prime and maximal ideals, ring quotients..., with a particular emphasis on polynomial rings.

In the last part of the course, we will focus on fields. We will introduce field extensions and study their basic properties. At the very end of the course, we will see how groups, rings and fields are deeply related through the study of algebraic equations and Galois theory.

Pour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique

Vous devez avoir validé l'équation suivante : UE FMA_2S006_EP

Règle d'exclusion : UE APM_3F007_EP

Format des notes

Numérique sur 20

Littérale/grade américain

Pour les étudiants du diplôme Programmes d'échange internationaux

Pour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique

Vos modalités d'acquisition :

The assessment will consist of two parts:
- A continuous assessment (coursework) based on short tests (quizzes and a midterm)
- A 2 hours long written final exam (closed book exam).

The final numerical grade will be the maximum between the grade of the final exam and a combination of the grades of the coursework and that of the final exam. The final mark will be on a scale from 0 to 20.

It will be then converted to the official final letter grade according to a table published by the instructor at the beginning of the course.

Le rattrapage est autorisé (Note de rattrapage conservée écrêtée à une note seuil de 10)
    L'UE est acquise si Note finale >= 9
    • Crédits ECTS acquis : 5 ECTS

    La note obtenue rentre dans le calcul de votre GPA.

    Mots clés

    Groups, rings, fields, Galois theory

    Méthodes pédagogiques

    Lectures and problem sessions
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