Preparation for the External Mathematics Agrégation Exam (Prépa Agreg)

This course unit is devoted to reviewing the algebra concepts included in the entrance exam curriculum. It consists of 36 hours of lectures and 36 hours of tutorials. A large portion of the tutorials will be devoted to presentations by students in the preparatory program, who will present either solutions to exercises or important proofs from the course.

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The external mathematics agrégation exam consists of two oral exams for eligible candidates. These exams take place in June or July. The first exam is titled “Algebra and Geometry,” and the second is titled “Analysis and Probability.” To help prepare for these exams, this course unit first outlines their specific characteristics and then provides guidance on preparing for the various topics announced by the exam committee.

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This course unit is devoted to reviewing the analytical concepts included in the competitive exam curriculum. It consists of 36 hours of lectures and 36 hours of tutorials. A large portion of the tutorials will be devoted to presentations by students in the preparatory program, who will present either corrections to exercises or key demonstrations from the course.

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The external agrégation exam in mathematics consists of two 6-hour written exams held in the spring. The first exam is titled “General Mathematics” and the second “Analysis and Probability.” To help students prepare for these exams, this course unit consists of assessments and answer keys based on questions at the level of the Agrégation written exams.

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The oral exams in algebra/geometry and analysis/probability for the Agrégation competition include a “presentation” section in which the candidate must spend about fifteen minutes discussing a topic from the syllabus that they find particularly interesting. In this course unit, we propose drafting a document that will compile the various presentations prepared in anticipation of these oral exams.

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This course prepares students for the modeling exam in Option C of the external mathematics certification exam. This exam, which is based on the analysis of texts, focuses on the connections between algebra and symbolic computation. The symbolic computation software SageMaths is used in this course.

The topics covered are those of Option C’s curriculum: representation and algorithmic manipulation of common mathematical objects in algebra and formal computation (integers, floating-point numbers, integers modulo n, polynomials, matrices); machine-imposed limitations (space and time optimization, the concept of algorithmic complexity), and application areas for these theories (error-correcting codes, cryptography, information processing and data compression, geometry, etc.).

Classical algorithms (fast exponentiation, extended Euclidean algorithm, Hörner's scheme, Gauss's algorithm, modular methods, primality tests, etc.) are introduced in class and then explored on the computer using SageMath software. This is also an opportunity to become familiar with this software.

Each student is required to present one or more oral lessons—depending on the requirements of the agrégation—based on texts from previous years.

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English tutorial course for students in the “M2 Preparation for the Mathematics Agrégation Exam” program who are aiming to achieve professional proficiency in English.

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The external Agrégation exam in mathematics consists of two 6-hour written exams held in the spring. The first exam is titled “General Mathematics” and the second “Analysis and Probability.” To help students prepare for these exams, this course unit begins with assessments and corrections based on exam questions at the level of the Agrégation written exams. Additional material covering concepts from the curriculum is also provided alongside the written exams.

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The external mathematics agrégation exam consists of two oral exams for eligible candidates. These exams take place in June or July. The first exam is titled “Algebra and Geometry,” and the second is titled “Analysis and Probability.” To help students prepare for these exams, this course unit first outlines their specific characteristics and then guides students through the various topics announced by the exam committee. This course unit builds on the work begun in the course unit “Preparation for Oral Exam 1.” 

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