|
| Module Availability |
| Semester 1 |
|
|
| Assessment Pattern |
Assessment Pattern
|
Unit(s) of Assessment
|
Weighting Towards Module Mark( %)
|
|
Two 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 |
| The module provides an introduction to abstract algebra via elementary group and ring theory. |
|
|
| Prerequisites/Co-requisites |
| MAT1016 Linear Algebra |
|
|
| Module Aims |
| The course aims to introduce the axiomatic approach to group theory and ring theory. |
|
|
| Learning Outcomes |
| At the end of the module the student should be familiar with various aspects of group theory and ring theory, and understand the purpose of abstraction and generalisation. |
|
|
| Module Content |
• Revision of the group concept, permutations and the integers modulo n.
• Symmetries and the dihedral groups.
• Cyclic groups, direct products.
• Group homomorphisms. Cosets, normal subgroups, factor groups. Lagrange's theorem.
• Application to error-correcting codes.
• Introduction to rings and fields. Ideals, quotient rings.
• Rings of polynomials. Construction of finite fields.
|
|
|
| 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 |
| 21 April 2011 |
|
