Advanced Algebra

The content of the combined undergraduate/graduate course consists mainly of the second part of Serge Lang's Algebra. It is suitable as a pre-course for Algebraic Geometry, Representation theory of p-adic groups and Algebraic number theory.  The syllabus can be found here. Topics: 

1. Galois Theory and field extensions
2. Algebraic sets and basic algebraic geometry
3. Noethernian rings and modules
4. Number fields and extensions of primes
5. Henselian fields. 

Literature: 

1. Algebra, Serge Lang
2. Algebraic number theory, Jürgen Neukirch
3. The red book of varieties and schemes, David Mumford

Time and place: Every Tuesday and Friday 13:00-14:40 at IMS S506

Weights for the course grade: homework 10% ; final exam 90% 

Problem sheets: Sheet1

Lecture notes: Chapter1