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`

Continuation of Probability Theory I. Elements of stochastic processes, including Brownian motion, continuous time martingales, and Markov processes.

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.

Examines categories, functors, abelian catqegories, limits and colimits, chain complexes, homology and cohomology, homological dimension, derived functors, Tor and Ext, group homology, Lie algebra homology, spectral sequences, and calculations. Prerequisite: MATH 5770.

`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`

`MATH 8360`

`MATH 8380`

`MATH 8410`

`MATH 8450`

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

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

`MATH 8620`

`MATH 8630`

`MATH 8700`

Studies basic structure theory of Lie algebras.

`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`

`MATH 8852`

`MATH 8853`

`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

`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`

Studies the development of mathematics from classical antiquity to the end of the 19th century, focusing on critical periods in the evolution of geometry, number theory, algebra, probability, and set theory. Emphasizes primary source materials. Prerequisite: MATH 2310 and 3351, or instructor permission.

`MATH 5250`

`MATH 5305`

`MATH 5559`

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`