Learning outcomes of the course unit
Deepen the theory of finite fields, with particular regard to the problem of decomposition of polynomials over them and finding the roots of a polynomial, symbolic irreducibility, minimal q-polynomial.
Course contents summary
The course deals the following main topics: Berlekamp algorithm's, the cyclotomic polynomials, traces and norms, orders of polynomials over finite fields, linearized polynomial, symbolic irreducibility, minimal q-polynomial and the fundamental theorem about him.
Mario Girardi, Giorgio Israel “Teoria dei campi” Editrice Feltrinelli
The preferred teaching tool for the development of such knowledge are the lectures. The note taking is seen as part of the learning process.
Assessment methods and criteria
The assessment of learning is done in classic way, through the evaluation of an oral interview. In the colloquium, the student must be able to independently conduct demonstrations related to the intrinsic properties of the studied structures using an appropriate algebraic language and a proper mathematical formalism.