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

`MATH 7000`

This seminar discusses the issues related to research in Mathematics. There are speakers from the different areas of mathematics represented at the University of Virginia. Credit may not be used towards a Master's degree. Prerequisite: Graduate standing in mathematics.

`MATH 7250`

`MATH 7305`

Introduces measure and integration theory. Prerequisite: MATH 5310 or equivalent.

`MATH 7320`

`MATH 7340`

`MATH 7360`

`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`

This course provides the opportunity to offer a new topic in the subject of mathematics.

`MATH 7600`

`MATH 7705`

`MATH 7751`

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

`MATH 7753`

`MATH 7754`

`MATH 7755`

Topics include the fundamental group, covering spaces, covering transformations, the universal covering spaces, graphs and subgroups of free groups, and the fundamental groups of surfaces. Additional topics will be from homology, including chain complexes, simplicial and singular homology, exact sequences and excision, cellular homology, and classical applications. Prerequisite: MATH 5352, 5770, or equivalent.

`MATH 7810`

`MATH 7820`

Examines fiber bundles; induced bundles, principal bundles, classifying spaces, vector bundles, and characteristic classes, and introduces K-theory and Bott periodicity. Prerequisite: MATH 7800.

`MATH 7840`

`MATH 8250`

`MATH 8310`

`MATH 8320`

This course presents the basic theory of stochastic differential equations and provides examples of its applications. It is an essential topic for students preparing to do research in probability. Topics covered include a review of the relevant stochastic process and martingale theory; stochastic calculus including Ito's formula; existence and uniqueness for stochastic differential equations, strong Markov property; and applications. Prerequisite: MATH 7360 and 7370, or instructor permission.

`MATH 8380`

`MATH 8410`

`MATH 8450`

`MATH 8510`

`MATH 8559`

The foundations of commutative algebra, algebraic number theory, or algebraic geometry.

`MATH 8620`

Theory of number fields and local fields, ramification theory, further topics as chosen by instructor.

`MATH 8700`

`MATH 8710`

Studies differential geometry in the large; connections; Riemannian geometry; Gauss-Bonnet formula; and differential forms.

`MATH 8750`

Selected advanced topics in algebraic topology.

Studies the basic structure theory of groups, especially finite groups.

`MATH 8852`

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.

`MATH 8855`

`MATH 8880`

`MATH 8995`

`MATH 8998`

`MATH 8999`

`MATH 9010`

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

For doctoral research, taken before a dissertation director has been selected.

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 5250`

`MATH 5305`

`MATH 5559`

`MATH 5653`

`MATH 5657`

Topics selected from analytic, affine, projective, hyperbolic, and non-Euclidean geometry. Prerequisite: MATH 2310, 3351, or instructor permission.

`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`