Postgraduate Course: Basic Algebra 2 (MATH11126)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 11 (Postgraduate)
||Availability||Not available to visiting students
|Summary||*Only Postgraduate Taught students on Mathematics Degree Programmes and Undergraduate MMath Year 5 students may take this course, and selection requires the approval of the Programme Director.*
Basic module theory, including such categorical notions as simple and projective modules.
Module theory for principal ideal domains, with examples such as Jordan Canonical Form and finitely generated abelian groups.
Artin-Wedderburn theory, in the context of finite dimensional algebras over fields. (8 hours)
Ordinary representation theory of finite groups: Maschke's theorem; characters and character tables; tensor products; applications to groups such as Burnside's Theorem. (12 hours)
Entry Requirements (not applicable to Visiting Students)
|| Students MUST have passed:
Basic Algebra 1 (MATH11125)
||Other requirements|| None
Course Delivery Information
|Not being delivered|
On completion of this course, the student will be able to:
- Thoroughly understand the basics of module theory including the fundamental theorem for finitely generated modules over principal ideal domains in the commutative setting and the decomposition theory for finitely generated modules over finite dimensional semisimple algebras.
- Apply the theory to problems concerning Jordan Canonical Form, finitely generated abelian groups and representation theory.
- Manipulate representations of groups, particularly through character tables.
|Graduate Attributes and Skills
||Selection of this course requires the approval of your Programme Director.
|Course organiser||Dr Thomas Leinster
Tel: (0131 6)50 5057
|Course secretary||Mrs Frances Reid
Tel: (0131 6)50 4883