Algebra
Description
An introduction to a range of important topics in algebra.
The course is split into three chapters, as follows:
- Chapter 1: Group Theory: (6 lectures) Basic concepts in group theory, including definitions and examples; constructions of groups; generators and relations;simple groups; the Jordan-Holder theorem; soluble groups; group actions; conjugation; Sylow theorems and applications.
- Chapter 2: Rings and Modules: (8 lectures) The definitions and basic properties of rings and modules; chain conditions; Hilbert Basis theorem; PIDs, Euclidean domains and UFDs; some elementary background on algebraic numbers and algebraic integers; finitely generated modules over a PID; Jordan canonical form of a matrix; the Artin-Wedderburn theorem; modules over semisimple Artinian rings.
- Chapter 3: Ordinary representation theory of finite groups: (6 lectures) Maschke''s theorem; characters and character tables; tensor products; applications to groups such as Burnside''s p^a q^b-theorem.
Teaching staff for 2011-2012
| Name | Department | University |
|---|---|---|
| Professor Meinolf Geck | Mathematics | University of Aberdeen |
| Dr Jean-Baptiste Gramain | Mathematics | University of Aberdeen |
| Radha Kessar | Mathematics | University of Aberdeen |
| Uli Kraehmer | Mathematics and Statistics | University of Glasgow |
| Max Neunhoeffer | Mathematics and Statistics | University of St Andrews |
| Yann Peresse | Mathematics and Statistics | University of St Andrews |
| Dr Guillaume Pouchin | Mathematics | University of Edinburgh |
| William Turner | Mathematics | University of Aberdeen |