Algebraic Number Theory (MATH542) Course Details

Course Name: Algebraic Number Theory
Code: MATH542
Pre-requisite Course(s): Consent of the Department
Objective: This course is designed to give the essential elements of algebraic number theory.
Content: Integers, norm, trace, discriminant, algebraic integers, quadratic integers, Dedekind domains, valuations, ramification in an extension of Dedekind domains, different, ramification in Galois extensions, ramification and arithmetic in quadratic fields, the quadratic reciprocity law, ramification and integers in cyclotomic fields, Kronecker-Weber theorem on abelian extensions, Dirichlet’s theorem on the finiteness of the class group, Dirichlet’s theorem on units, Hermite-Minkowski theorem, Fermat’s last theorem.
Term: Spring
Theory: 3
Application: 0
Laboratory: 0
Credit: 3
ECTS Course File: Course File
Course File: