Please refer to SIS or Lou’s list for details about current instructors and current enrollment numbers.

Discussion of issues related to the practice of teaching, pedagogical concerns in college level mathematics, and aspects of the responsibilities of a professional mathematician. Credits may not be used towards a Master's degree. Prerequisite: Graduate standing in mathematics.

`MATH 7010`

`MATH 7250`

`MATH 7305`

`MATH 7310`

`MATH 7320`

Studies the fundamental theorems of analytic function theory.

Rigorous introduction to probability, using techniques of measure theory. Includes limit theorems, martingales, and stochastic processes. Prerequisite: 7310 or equivalent.

`MATH 7370`

Studies the basic principles of linear analysis, including spectral theory of compact and selfadjoint operators. Prerequisite: MATH 7340 and 7310, or equivalent.

`MATH 7420`

`MATH 7450`

`MATH 7559`

`MATH 7600`

`MATH 7705`

Studies groups, rings, fields, modules, tensor products, and multilinear functions. Prerequisite: MATH 5651, 5652, or equivalent.

`MATH 7752`

Studies the Wedderburn theory, commutative algebra, and topics in advanced algebra. Prerequisite: MATH 7751, 7752, or equivalent.

`MATH 7754`

`MATH 7755`

`MATH 7800`

Devoted to chomology theory: cohomology groups, the universal coefficient theorem, the Kunneth formula, cup products, the cohomology ring of manifolds, Poincare duality, and other topics if time permits. Prerequisite: MATH 7800.

Topics include smooth manifolds and functions, tangent bundles and vector fields, embeddings, immersions, transversality, regular values, critical points, degree of maps, differential forms, de Rham cohomology, and connections. Prerequisite: MATH 5310, 5770, or equivalent.

`MATH 7830`

`MATH 7840`

Theory of distributions. Sobolev spaces and their properties (trace and embedding theorems). Theory of elliptic equations. Time-dependent partial differential equations: parabolic and hyperbolic equations. Topics in nonlinear partial differential equations. Prerequisites: MATH 7410 and 7250.

`MATH 8310`

`MATH 8320`

`MATH 8360`

`MATH 8380`

`MATH 8410`

`MATH 8450`

`MATH 8559`

`MATH 8600`

Studies the foundations of algebraic geometry.

`MATH 8630`

`MATH 8700`

`MATH 8710`

`MATH 8720`

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.

`MATH 8851`

Studies the foundations of representation and character theory of finite groups.

`MATH 8853`

`MATH 8855`

`MATH 8880`

`MATH 8995`

For master's research, taken before a thesis director has been selected.

For master's thesis, taken under the supervision of a thesis director.

`MATH 9000`

`MATH 9010`

`MATH 9020`

Harmonic Analysis and PDEs seminar

Operator Theory Seminar

Probability Seminar

Galois-Grothendieck Seminar

`MATH 9450`

`MATH 9559`

Topology Seminar

Discusses subjects from geometry.

Algebra Seminar

Independent Research

`MATH 9998`

The Mathematics Colloquium is held weekly, the sessions being devoted to research activities of students and faculty members, and to reports by visiting mathematicians on current work of interest. For doctoral dissertation, taken under the supervision of a dissertation director.

`MATH 5010`

`MATH 5030`

`MATH 5100`

`MATH 5250`

`MATH 5305`

`MATH 5330`

`MATH 5559`

`MATH 5700`

`MATH 5720`

`MATH 5770`

`MATH 5855`

`MATH 5896`

`MATH 6060`

`MATH 6120`

`MATH 6452`

`MATH 6453`

`MATH 6454`

`MATH 6559`

`MATH 6600`

`MATH 6630`

`MATH 6650`

`MATH 6660`

`MATH 6670`

`MATH 6700`

`MATH 6760`

`MATH 6800`