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

Entry Requirements (not applicable to Visiting Students)
Pre-requisites	Students MUST have passed: Basic Algebra 1 (MATH11125)	Co-requisites
Prohibited Combinations		Other requirements	None

Course Delivery Information

Academic year 2015/16, Not available to visiting students (SS1)		Quota: None
Course Start	Semester 2
Timetable	Timetable
Learning and Teaching activities (Further Info)	Total Hours: 200 ( Lecture Hours 20, Seminar/Tutorial Hours 10, Summative Assessment Hours 3, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 163 )
Assessment (Further Info)	Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Additional Information (Assessment)	See 'Breakdown of Assessment Methods' and 'Additional Notes', above.
Feedback	Not entered
Exam Information
Exam Diet	Paper Name		Hours & Minutes
Main Exam Diet S2 (April/May)	Basic Algebra 2 (MATH11126)		3:00

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.