Preparation for the option

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.

Prepare students for Option C of the Associate's degree, which requires:

• apply the mathematical concepts and tools in the program with precision and rigor;
• distinguish between exact and approximate representations of mathematical objects ;
• estimate the cost and limitations of simple algorithms: complexity, accuracy ;
• analyze the relevance of the models.
• know how to implement a formal calculation algorithm.

The main prerequisites are the concepts and techniques of the algebra program of the Licence 3 of mathematics: usual algebraic structures (group, ring, body, vector space, module on a main ring, algebra); elementary arithmetic and Euclid's algorithm (extended); polynomials with one or more indeterminates; finite bodies and theory of extensions of bodies; matrices and Gauss' algorithm

Recommended prerequisites: Strong knowledge of algebra and formal calculus is an asset, but is not required beyond the necessary prerequisites mentioned above.

Continuous control

See the description of the UE and the detailed program of the modelling test of the option C of the external agrégation of mathematics

Hourly volumes:

            CM : 22

            TD : 22

            TP : 0

            Land : 0