Math 675R: Special Topics in Algebra.
Special Topics in Algebra.
Advanced topics in algebra drawn from pure and applied mathematics. Possible topics include: representation theory, Lie groups and Lie algebras, geometric group theory, Galois theory, algebraic number theory, computational algebra, Category theory, Grobner bases, algebraic geometry, algebraic combinatorics, cryptanalysis, finite group theory, modular forms, commutative algebra, homological algebra, group cohomology, character theory of finite groups, mathematical physics, ring theory.
Desired Learning Outcomes
Minimal learning outcomes
These will depend on the topic chosen.
Possible textbooks for this course include (but are not limited to):
Past topics chosen include:
- Representations of algebras and finite groups, using the book by Curtis and Reiner.
- Modular forms using a book by Kilford "Modular forms: a classical and computational introduction."
- Lie algebras, using a book by J Humphreys.
- Lie groups, using the book "Lie groups, Lie algberas and representations", by Brian C. Hall.