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2011/2 Provisional Module Catalogue - UNDER CONSTRUCTION & SUBJECT TO CHANGE
 Module Code: MAT3033 Module Title: ADVANCED ALGEBRA (MMATH)
Module Provider: Mathematics Short Name: MAT3033
Level: HE3 Module Co-ordinator:
Number of credits: 15 Number of ECTS credits: 7.5
 
Module Availability
Semester 2
Assessment Pattern
Assessment Pattern
Unit(s) of Assessment
Weighting Towards Module Mark( %)
Class tests
25
Examination: two hours unseen
75
Qualifying Condition(s) 
A weighted aggregate mark of 40% is required to pass this module.
 
Module Overview
This module extends the group theory and ring theory introduced at Level 2.
Prerequisites/Co-requisites
MAT1016 Linear Algebra
MAT2006 Groups and Symmetry or MAT2048 Groups & Rings or MAT3001 Galois Theory
Module Aims
The module aims to extend students' knowledge of abstract algebra and their appreciation of the inter-connectedness of the different areas of the subject.
Learning Outcomes
Students should acquire a deeper knowledge of groups and rings. They will become familiar with some classical theorems in algebraic structure theory and will have an introduction to algebras and modules.
Module Content
Topics covered will include some or all of:
• Further group theory. Group actions, conjugacy. The class equation.
• Cauchy's theorem and the Sylow theorems.
• Further ring theory. Division rings. The quaternions.
• Maximal and prime ideals, principal ideal domain, euclidean domains.
• Representations of groups and rings.
• Algebras. Group algebras. Wedderburn's structure theorem.
• Introduction to modules over a commutative ring.
Methods of Teaching/Learning
Teaching is by lectures and tutorials, 3 hours per week for 11 weeks.
Learning takes place through lectures, tutorials, exercises and class tests.
Selected Texts/Journals
J. B. Fraleigh, A First Course in Abstract Algebra, Addison-Wesley (2003), ISBN 0321156080
M.A. Armstrong, Groups and Symmetry, Springer-Verlag, (1988), ISBN 0387966757
R. B. J. T. Allenby, Rings, Fields and Groups, Arnold (1991), ISBN. 0340544406
W. Gilbert and W. Nicholson : Modern Algebra with Applications, Wiley (2004), ISBN 0471414514
Last Updated
3 May 2011