Introduction to Algebraic Number Theory

2024/2025

Academic Year

ENG

Instruction in English

6

ECTS credits

Delivered at:

Faculty of Mathematics

Course type:

Optional course (faculty)

When:

1, 2 module

Instructor

Zhgoon, Vladimir

Course Syllabus

Abstract

Many classical and modern problems in number theory can be interpreted in terms of properties of algebraic objects such as algebraic number fields, their rings of integers and orders in these rings, ideal class groups and unit groups. In this course, we will explore the main notions of algebraic number theory and connect them to some of the most classical problems and theorems, for example, the Dirichlet theorem on primes in arithmetic progressions, Gauss class number problem and Fermat’s last theorem. We will also learn about the properties of analytic and topological objects corresponding to number fields, such as the Dedekind zeta-function and the ring of adeles.