Postgraduate Course: Basic Algebra 2 (MATH11126)
Course Outline
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 |
SCQF Credits | 20 |
ECTS Credits | 10 |
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) |
Course description |
Not entered
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Entry Requirements (not applicable to Visiting Students)
Pre-requisites |
Students MUST have passed:
Basic Algebra 1 (MATH11125)
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Co-requisites | |
Prohibited Combinations | |
Other requirements | None |
Course Delivery Information
Not being delivered |
Learning Outcomes
A thorough understanding of 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, with the ability to apply the theory to problems concerning Jordan Canonical Form, finitely generated abelian groups and representation theory.
Ability to manipulate representations of groups, particularly through character tables.
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Additional Information
Graduate Attributes and Skills |
Not entered |
Special Arrangements |
Selection of this course requires the approval of your Programme Director. |
Keywords | BAlg2 |
Contacts
Course organiser | Dr Thomas Leinster
Tel: (0131 6)50 5057
Email: Tom.Leinster@ed.ac.uk |
Course secretary | Mrs Frances Reid
Tel: (0131 6)50 4883
Email: f.c.reid@ed.ac.uk |
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