I teach at the Mathematics department of the University Denis Diderot Paris 7 . You'll find some courses and courses' notes (all in French).

- An algebra course taught at the Ecole Normale Supérieure de Cachan, corresponding to a third or fourth year course : Groups (Sylow theorems, semi-direct product, etc.), rings (principal, UFD rings, Nullstellensatz, etc.), fields, modules, with complements on classical groups and group representations (PDF File,  around 90 pages)

- A course on Arithmetic, fourth year level (Master course) : congruences and finite fields, quadratic reciprocity law, cryptography and primality test (including the recent Agrawal-Kayal-Saxena test), error correcting codes: Diophantine equations, sums of squares, Pell-Fermat, Fermat (for n=3,4), algebraic integers ring; Riemann's zeta and Dirichlet's "L" functions, theorem of arithmetic progression and prime number theorem ( PDF File, around 70 pages)

NEW!  This cours has been published in February (2008) chez Calvage & Mounet under the title "Arithmétique" .

The book contains as supplement many exercices and two chapters (elliptic curves; developments and open problems) as well as three appendices (Factorisation, Introduction to projective geometry, Galois Theory). See "Arithmétique (préface et couverture)" for further informations and the table of contents.

- A first year course (two semesters) " Elementary Algebra and Analysis". Mathematical language, sets, groups, the ring Z, the fields R and C, polynomials, matrices, vector spaces, linear maps, determinants, geometry (in dimension 2 and 3), sequences, continuous functions, derivatives and Taylor formula, integrals, classical functions,  primitives, indefinite integrals, series expansions and parametrised curves, differential equations, functions of several variables.(PDF File, around 200 pages) [The drawings and some fonts are unfortunately absent from the file I'm hoping to soon sort this out......]

For the academic year 2007-2008, I teach four courses

- An algebra course (M1, cursus "math. & computer science", first semester)
- Two graduate courses (M2) common to the  second year of master of  Paris 7  and  Paris 6) first semester "Elliptic Curves",   second semester "Abelian Varieties".
- A course "algorithmic number theory" (in the Ecole Normale Supérieure d'Ulm, second semester)

The notes of my Algebra course "math. & computer science" are available ( PDF File , around 40 pages).

The mid-semester  exam  (format PDF) and final exams  (final exam, format PDF) are available (with solutions)

Caution: These notes are in four parts : Groups (group action, Sylow theorems, solvable and abelian groups, permutation groups), Modules (essentially of finite type over a principal ring), fields (algebraic extensions, finite fields) and Galois theory; the last part is, at the moment, only a summary of results.