## Introduction to algebraic number theory

Algebraic number theory studies problems from number theory using algebraic methods. More precisely, one studies number fields, i.e. finite extensions of the field Q of rational numbers, and their rings of integers which are ring extensions of Z. Their algebraic properties, for example assertions on their sets of invertible elements or their ideals, one can deduce information on the set of integral solutions of polynomial equations.

In this lecture we will introduce the notions of number fields and their rings of integers, and we will study their basic properties. In addition we will apply the theory to explicit examples of number theoretic equations.

Time and venue

Lecture: Th, 10:20-11:50 am, 02.10.011

Tutor group: Th, 3-4 pm, 02.07.014

Exercise sheets

1, 2 ,3, 4 ,5, 6, 7, 8, 9, 10, 11, 12, 1314

Prerequisites

Linear Algebra 1,2, Algebra 1.

Previous attendance of "Commutative Algebra" is helpful but not mandatory. I will provide all necessary knowledge from commutative algebra within the lecture.

References

Neukirch: Algebraic Number Theory, Chapter 1.