M2 - Preparation for the external mathematics teaching certification exam (Prépa Agreg)

This course is devoted to reviewing the algebra concepts included in the exam syllabus. It consists of 36 hours of lectures and 36 hours of tutorials. A large part of the tutorials will be reserved for presentations by students preparing for the exam, or for corrections of exercises or important demonstrations from the course.

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The external mathematics aggregation exam consists of two oral exams for eligible candidates. These exams take place in June or July. The first exam is entitled "Algebra and Geometry" and the second "Analysis and Probability." In order to prepare for these exams, this course first presents their specific characteristics and then offers preparation for the various topics announced by the exam jury.

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This course is devoted to reviewing the analytical concepts included in the exam syllabus. It consists of 36 hours of lectures and 36 hours of tutorials. A large part of the tutorials will be reserved for presentations by students preparing for the exam, corrections of exercises, or important demonstrations from the course.

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The external mathematics aggregation exam consists of two six-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 tests, this course consists of assessments and corrections based on topics at the level of the written aggregation tests.

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The oral exams in algebra/geometry and analysis/probability for the agrégation competitive examination include an "essay" section in which candidates must present a topic of particular interest to them for approximately 15 minutes. In this course, students are asked to write a document compiling the various essays prepared in preparation for these oral exams.

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This course prepares students for the modeling exam in Option C of the external mathematics aggregation. This exam, based on the study of texts, focuses on the links between algebra and computer algebra. The SageMaths computer algebra software is used for this preparation.

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

Classic algorithms (fast exponentiation, extended Euclidean algorithm, Hörner's scheme, Gauss, modular methods, primality tests, etc.) are presented in class and then explored on a 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, in accordance with the terms of the competitive examination, based on texts from previous years.

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English tutorial course for students enrolled in the "M2 Preparation for the competitive examination for the agrégation in mathematics" program who wish to achieve professional autonomy in the English language.

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The external mathematics aggregation exam consists of two six-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 tests, this course consists primarily of assessments and corrections based on topics from the written tests of the aggregation. Additional information on the concepts covered in the program is also provided alongside the written tests.

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The external mathematics aggregation exam consists of two oral exams for eligible candidates. These exams take place in June or July. The first exam is entitled "Algebra and Geometry" and the second "Analysis and Probability." In order to prepare for these exams, this course first presents their specific characteristics and then offers preparation for the various topics announced by the exam jury. This course continues the work begun in the course "Preparation for Oral Exam 1." 

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