Secretariat for Master of Mathematics
- Mzia Goguadze
- office D200
- 01 49 40 28 10
Formation | M1 Fundamental and applied mathematics |
Semester | 2 |
Teaching staff | Lecturer : Pascal Boyer, Cédric Pépin, TA : Mohamed Zitouni |
Credits | 6 ECTS |
Teaching hours | 30h of lectures + 30h of TA sessions |
Validation scheme | Final exam |
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.