M2 - Preparation for the External Aggregation in Mathematics (Prépa Agreg)

This UE is devoted to the revision of the algebra notions included in the competition program. It is composed of 36 hours of lectures and 36 hours of tutorials. A large part of the tutorials will be reserved for interventions of the students of the preparation to present or corrections of exercises or important demonstrations of the course.

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The competition for the external agrégation in mathematics includes two oral exams for eligible candidates. These tests take place in June or July. The first test is entitled "Algebra and Geometry" and the second "Analysis and Probability". In order to prepare these tests, this UE first presents their specificity and then proposes to prepare the different themes announced by the jury of the competition.

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This UE is devoted to the revision of the notions of analysis included in the competition program. It is composed of 36 hours of lectures and 36 hours of tutorials. A large part of the tutorials will be reserved for interventions by the students of the preparation course to present either corrections of exercises or important demonstrations of the course.

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

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The oral exams in algebra/geometry and in analysis/probability of the agrégation competition include a "development" part where the candidate has to present for about fifteen minutes a point of the plan particularly interesting to him/her. In this UE, we propose to write a document that will compile the different developments prepared for these oral exams.

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This UE prepares students for the modelling test of the option C of the external agrégation of mathematics. This test, based on the study of texts, is centered on the links between algebra and formal calculation. The formal calculation software SageMaths is used for this preparation.

The problems addressed are those of the option C program: representation and algorithmic manipulation of mathematical objects usual 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 (fast exponentiation, extended Euclid, Hörner scheme, Gauss, modular methods, primality tests, etc.) are presented in class, and are then discussed on the computer with the help of SageMath software. It is also an opportunity to become familiar with this software.

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

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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 competitive examination for the external agrégation in mathematics contains two 6-hour written tests held in the spring. The first test is entitled "General Mathematics" and the second "Analysis and Probability". In order to prepare for these exams, this UE consists first of all of evaluations and corrections based on subjects at the level of the written exams of the agrégation. Supplements on the notions of the program are also proposed in parallel with the written tests.

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The competition for the external agrégation in mathematics includes two oral exams for eligible candidates. These tests 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 exams, this UE first presents their specificity and then proposes to prepare the different themes announced by the jury of the competition. This UE continues the work started in the UE " Preparation to the oral 1 ". 

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