Course teached as: B018797 - TEORIA DEI NUMERI Second Cycle Degree in MATHEMATICS Curriculum DIDATTICO
Teaching Language
Italian.
Course Content
The course is an introduction to algebraica number theory. Starting from the definition of algebraic number, we go on studying the basic properties of rings of integers in number fields (number rings). In the final part some applications are given
1) Marcus: Number fields
2) Stewart-Tall: Algebraic number theory and Fermat's last theorem
Learning Objectives
The goal of the course is to introduce the students to the basic tools needed to undertake the study of deeper subjects in number theory and Galois theory.
Prerequisites
Full programs of the courses of Algebra 1 and 2 of the first two years of Laurea Triennale in Matematica. It is also preferable that the student feels comfortable with the program of Algebra 3 of Laurea Triennale in Matematica.
Teaching Methods
Blackboard lectures.
Type of Assessment
Oral exam.
Course program
Algebraic integers and ring of integers in number fields. Ideal in number rings and their factorization. Class group. Minkowski's theorem. Dirichlet's units theorem. Cyclotomic extensions. Some cases of Fermat's last theorem.