Mathematics

GUIDO PEZZINI

General objectives: to acquire basic knowledge in elementary theory of numbers and finite fields (useful when studying public key cryptography or code theory in other courses or contexts).   Specific objectives:   Knowledge and understanding: at the end of the course the student will have acquired the basic notions and results related to the elementary theory of numbers, the resolution of equations to the comparisons (with particular regard to polynomial equations), akke arithmetic functions, the theory of quadratic residues, to the problem of enlargements, extensions and the detailed structure of finite fields.   Apply knowledge and understanding: at the end of the course the student will be able to solve simple problems that require the use of techniques related to equations to congruences, to the most important arithmetic functions; will be able to describe in a concrete way a finite field and his group of Galois.   Critical and judgmental skills: the student will have the basics to use the tools that underlie public-key cryptography and the theory of error-correcting codes. The aim of the course, which is purely theoretical, is to allow students interested in the cryptographic applications to easily manipulate the mathematical objects of the course.   Communication skills: ability to expose the contents in the oral part of the verification and in any theoretical questions present in the written test.   Learning skills: the acquired knowledge will allow a study, individual or given in an LM course, related to standard aspects of number theory and finite fields.