Studies differential geometry in the large; connections; Riemannian geometry; Gauss-Bonnet formula; and differential forms.
Studies regular and critical values, gradient flow, handle decompositions, Morse theory, h-cobordism theorem, Dehn's lemma in dimension 3, and disk theorem in dimension 4. Prerequisite: Math 5770.
Selected advanced topics in algebraic topology.
Studies the basic structure theory of groups, especially finite groups.
Studies the foundations of representation and character theory of finite groups.
Covers methods of abstract algebra that can be applied to various combinatorial problems and combinatorial methods to approach problems in representation theory, algebraic geometry, and homological algebra.
Studies the basic structure theory of associative or nonassociative algebras.
Studies groups of transformations operating on a space; properties of fixed-point sets, orbit spaces; and local and global invariants.
For master's research, taken before a thesis director has been selected.
For master's thesis, taken under the supervision of a thesis director.