Preparing for the option

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.

Prepare students for Option C of the agrégation, 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, precision ;
• analyze the relevance of models.
• know how to implement a formal calculation algorithm.

The main prerequisites are the concepts and techniques of the Licence 3 algebra program in mathematics: usual algebraic structures (group, ring, body, vector space, module on a principal 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's algorithm.

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

Full continuous assessment

See the description of the UE and the detailed program for the modeling test of option C of the agrégation externe in mathematics.

Hourly volumes :

            CM: 22

            TD : 22

            TP: 0

            Land: 0