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| Module Availability |
| Semester 2 |
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| Assessment Pattern |
Assessment Pattern
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Unit(s) of Assessment
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Weighting Towards Module Mark( %)
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Class tests
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25
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Examination: two hours unseen
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75
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Qualifying Condition(s)
A weighted aggregate mark of 40% is required to pass this module.
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| Module Overview |
| This module extends the group theory and ring theory introduced at Level 2. |
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| Prerequisites/Co-requisites |
MAT1016 Linear Algebra
MAT2006 Groups and Symmetry or MAT2048 Groups & Rings or MAT3001 Galois Theory
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| 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. |
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| 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. |
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| 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.
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| 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.
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| 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
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| Last Updated |
| 3 May 2011 |
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