Course Task：The first objective is to learn about algebraic structures, to get a profound knowledge about groups, rings and modules and basics in Galois theory. It will be connected with number theoretical and geometric applications. Secondly we strengthen the ability to workout and write abstract proofs in a more academic way.
Course Contents：The algebraic behavior of real vector spaces carries over to a much wider class. Replacing the field of real numbers by a (more general) ring provides a theory with a much more diverse picture. Modules, the analogue for vector spaces, do not need to carry a basis anymore. Rings carry a beautiful set of ideals, which one could think about as a generalization of divisors of integers. Analyzing the behavior of ideals is very successful for proving difficult number theoretical problems. The theory of abstract algebra occurs in almost all mathematical directions. In this course we will learn about:
groups, rings, ideals, modules , number theoretical applications, Galois theory, localization, local-global principle
Teaching building 404
Tuesdays and Thursdays 8:15-9:55
Start 23rd of February 2021
Office hours: Tuesdays 10-11 IMS413