Mathematics 751: Further Group Theory (Honours)

Semester 1, 2008

Lecturer: Professor J Moori (Office: F9) moori@ukzn.ac.za

Mondays: 10:00 - 11:30 (F26);  Wednesdays: 10:00 - 11:30 (F26)

Young men should prove theorems, old men should write books. Godfrey H. Hardy, (1877 - 1947)

Quoted by Freeman Dyson in Freeman Dyson: Mathematician, Physicist, and Writer. Interview with Donald J. Albers, The College Mathematics Journal, vol. 25, No. 1, January 1994.

Content: This is a further course in GroupTheory which covers topics on: 

• Groups of Small Order
• Permutation Groups and Simplicity of An
• Permutation Representations
• p-Groups and Sylow Theorems
• Normal Series and  Soluble  Groups
• Fundamental Theorem of Abelian Groups
• Some Examples of Simple Groups
• Representation Theory (Basic Concepts and Characters of Finite Groups)

Assessment:  33% [Class mark based on theoretical and computational assignments] , 67% [3 hour final examination]

References:

1. An Introduction to the Theory of Groups, J J Rotman, 4th  Edition, Graduate texts in Mathematics, Springer-Verlag 1994.
2. An Introduction to the Theory of Groups, J J Rotman, 3rd Edition, Wm C Brown Publishers, 1984.
3. Representations and Characters of Groups, G James and M Liebeck, 2nd Edition, Camb. Univ. Press, 2001
4. Character Theory of Finite Groups, I M Isaacs, Dover Publications, 1994.
5. A Course in the Theory of Groups, DJS Robinson,. Springer-Verlag, 1982.
6. A Course on Group Theory, J S Rose, Dover Publications, INC, 1978.
7. Introduction to the Theory of Finite Groups, W Ledermann, Oliver & Boyd, 1973.
8. Group Theory, WR Scott, Prentice-Hall, 1964.
9. The Theory of Groups, M Hall, Macmillan, 1959.

Links:

    The development of group theory        Group Pub Forum Home Page

    GAP at Aachen, Germany   GAP at St-Andrews

    What can you do with a Mathematics Major?    MathWorld     Applications

Last updated: 02/20/08