Preparation for the option

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.

Prepare students for Option C of the agrégation, which requires:

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

The main prerequisites are the concepts and techniques covered in the algebra program for the third year of a bachelor's degree in mathematics: common algebraic structures (groups, rings, fields, vector spaces, modules over principal rings, algebras); elementary arithmetic and Euclid's algorithm (extended); polynomials with one and several indeterminates; finite fields and field extension theory; matrices and Gauss's algorithm.

Recommended prerequisites: Strong knowledge of algebra and formal calculation is an asset, but mastery of these subjects is not required beyond the prerequisites mentioned above.

Continuous assessment

See description of the EU and detailed program for the modeling exam for option C of the external mathematics aggregation.

Hourly volumes:

            CM: 22

            TD: 22

            TP: 0

            Land: 0