Mathematics

# MATH 3275: Advanced Group Theory

Lecture - 4 credits

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- Serves as an accelerated introduction to the theory of groups, intended for students who wish to take a more advanced version of MATH 3175.
- Prior knowledge of group theory is not assumed.
- Introduces homomorphisms, subgroups, normal subgroups, quotient groups, and group actions, illustrated with a variety of examples.
- Subsequent topics include the class equation, simple groups, the Sylow theorems, and their applications to the classification of finite simple groups.
- Discusses classical matrix groups, with an emphasis on SU(2) and SO(3) as fundamental examples, and introduces the notion of a Lie algebra.
- Develops representation theory of finite groups and its correspondence to the representation theory of compact Lie groups sketched, again using SU(2) as an example.
- Students not meeting course prerequisites may seek permission of instructor.

Serves as an accelerated introduction to the theory of groups, intended for students who wish to take a more advanced version of MATH 3175.

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