Formation M1 Fundamental and applied mathematics
Semester2
Teaching staffLecturer : Pascal Boyer, Cédric Pépin, TA : Mohamed Zitouni
Credits 6 ECTS
Teaching hours 30h of lectures + 30h of TA sessions
Validation schemeFinal exam

Syllabus

The first half of the course is a core curriculum; we then offer two options.

Common core: Arithmetic. Quadratic reciprocity law, finite fields, rupture and decomposition fields, Galois theory.

Fundamental option: Commutative algebra. We present notions of commutative algebra, necessary to tackle a course in algebraic geometry (scheme theory): commutative rings, ideals (and artinian / noetherian conditions), modules (and tensor product), localization, completion, primary decomposition, entiere dependency relationships.

Applied option: Cryptography. Primality tests and factorization algorithm. RSA, AES cryptography. Discrete logarithm. Cyclic linear codes.

Prerequisites

Linear license algebra (including diagonalization and trigonalisation), basic programming skills for the applied option.