2014/15 Undergraduate Module Catalogue
MATH3193 Algebras and Representations
15 creditsClass Size: 40
Module manager: Dr P Schuster
Email: P.Schuster@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2014/15
Pre-requisite qualifications
MATH2025 or (MATH2033 and MATH2080) or (MATH2033 and MATH2200), or equivalent.This module is mutually exclusive with
MATH5193M | Advanced Algebras and Representations |
This module is not approved as a discovery module
Module summary
Multiplication by a complex number of absolute value one gives a rotation of the complex plane. In the 19th Century, Hamilton tried to find an algebra which would represent rotations of three-dimensional space. After much thought he realized that he had to give up commutativity and needed a four-dimensional algebra, his quaternions. Soon a beautiful theory had developed, with Grassmann and Clifford providing other examples of algebras (now used in quantum mechanics and relativity) and Wedderburn determining the structure of all 'semisimple' algebras.As well as being of interest in its own right, this module should extend and consolidate the students' understanding of linear algebra.Objectives
On completion of this module, students should be able to:a) define some of the main concepts about associative algebras and representations.
b) state and prove some of the basic results about associative algebras and representations.
c) compute in various examples of algebras.
d) compute bases for some examples of algebras given by generators and relations.
e) use the isomorphism theorems to construct isomorphisms between modules
f) determine whether or not an algebra is semisimple.
Syllabus
- Associative algebras and examples
- Division algebras
- Algebras given by generators and relations
- Modules and the Isomorphism Theorems
- Simple and semisimple modules
- Semisimple algebras
Teaching methods
Delivery type | Number | Length hours | Student hours |
Lecture | 33 | 1.00 | 33.00 |
Private study hours | 117.00 | ||
Total Contact hours | 33.00 | ||
Total hours (100hr per 10 credits) | 150.00 |
Private study
Studying and revising of course material.Completing of assignments and assessments.
Opportunities for Formative Feedback
Regular example sheets.Methods of assessment
Exams
Exam type | Exam duration | % of formal assessment |
Standard exam (closed essays, MCQs etc) | 2 hr 30 mins | 100.00 |
Total percentage (Assessment Exams) | 100.00 |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Reading list
The reading list is available from the Library websiteLast updated: 05/02/2015
Browse Other Catalogues
- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue
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