M2 - Preparing for the external agrégation in mathematics (Prépa Agreg)

This course is devoted to reviewing the algebra concepts included in the competitive examination program. It comprises 36 hours of lectures and 36 hours of tutorials. A large part of the tutorials will be reserved for students from the preparatory course to present either corrections to exercises or important demonstrations from the course.

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The agrégation extern de mathématiques competitive examination includes two oral tests for eligible candidates. These take place in June or July. The first test is entitled "Algebra and Geometry" and the second "Analysis and Probability". In preparation for these tests, this UE first presents their specific features, and then proposes preparation for the various themes announced by the competition jury.

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This course is devoted to reviewing the analysis concepts included in the competitive examination program. It comprises 36 hours of lectures and 36 hours of tutorials. A large proportion of the tutorials will be devoted to presentations by students of the preparatory course, either to correct exercises or to demonstrate key points of the course.

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The external agrégation mathematics competitive examination contains two 6-hour written tests, held in the spring. The first is entitled "General Mathematics", and the second "Analysis and Probability". In preparation for these exams, this UE consists of assessments and corrections based on subjects at the level of the agrégation written exams.

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The oral exams in algebra/geometry and analysis/probability for the agrégation competitive examination include a "development" section, in which the candidate is required to present for around 15 minutes a point in the plan of particular interest to him or her. In this UE, we propose to write a document compiling the various developments prepared for these oral exams.

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This UE prepares students for the modeling test in option C of the agrégation externe in mathematics. This exam, based on the study of texts, focuses on the links between algebra and formal calculus. SageMaths software is used for this preparation.

The issues addressed are those of the Option C program: representation and algorithmic manipulation of mathematical objects common in algebra and formal calculus (integers, floats, integers modulo n, polynomials, matrices); limitations posed by the machine (optimization in space and time, notion of algorithmic complexity), and fields of application of these theories (error-correcting codes, cryptography, information processing and data compression, geometry, etc.).

Classical algorithms (rapid exponentiation, extended Euclid, Hörner's scheme, Gauss, modular methods, primality tests, etc.) are introduced in class, and are then worked out on the computer using SageMath software. This is also an opportunity to familiarize yourself with this software.

Each student is required to present one or more oral lessons on texts from previous years, in accordance with the agrégation procedure.

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TD courses in English for students in the "M2 Préparation au concours de l'agrégation en mathématiques" program, who are aiming for professional autonomy in English.

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The external agrégation mathematics competitive examination contains two 6-hour written tests, held in the spring. The first is entitled "General Mathematics" and the second "Analysis and Probability". To prepare for these exams, this UE consists firstly of assessments and corrections based on subjects at the level of the agrégation written exams. Complementary work on program concepts is also offered in parallel with the written tests.

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The agrégation extern de mathématiques competitive examination includes two oral tests for eligible candidates. These take place in June or July. The first test is entitled "Algebra and Geometry" and the second "Analysis and Probability". In order to prepare for these tests, this UE first presents their specific features and then proposes preparation for the various themes announced by the competition jury. This UE continues the work begun in UE "Préparation à l'oral 1". 

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