This class introduces students to the mathematics used in pricing derivative securities. Topics include a review of the relevant probability theory of conditional expectation and martingales/the elements of financial markets …
A second course in ordinary differential equations, from the dynamical systems point of view. Topics include: existence and uniqueness theorems; linear systems; qualitative study of equilibria and attractors; bifurcation theory; …
Includes Taylor's theorem, solution of nonlinear equations, interpolation and approximation by polynomials, numerical quadrature. May also cover numerical solutions of ordinary differential equations, Fourier series, or least-square approximation. Prerequisite: MATH …
Differential and integral calculus in Euclidean spaces. Implicit and inverse function theorems, differential forms and Stokes' theorem. Prerequisites: multivariable calculus, basic real analysis, linear algebra and one of the following: …
Introduces algebraic techniques for communicating information in the presence of noise. Includes linear codes, bounds for codes, BCH codes and their decoding algorithms. May also include quadratic residue codes, Reed-Muller …
Review of topics from Math 3351: vector spaces, bases, dimension, matrices and linear transformations, diagonalization; however, the material is covered in greater depth and generality. The course continues with more …
Structural properties of basic algebraic systems such as groups, rings, and fields. A special emphasis is made on polynomials in one and several variables, including irreducible polynomials, unique factorization, and …
Examines the knotting and linking of curves in space. Studies equivalence of knots via knot diagrams and Reidemeister moves in order to define certain invariants for distinguishing among knots. Also …
This course will introduce students to the techniques and methods of mathematical research. Students will independently work with mathematical literature on a topic assigned by the instructor and present their …
This is the second semester of a two semester sequence for the purpose of the completion of a Distinguished Major Thesis. A faculty member guides the student through all phases …
Reading and study programs in areas of interest to individual students. For third- and fourth-years interested in topics not covered in regular courses. Students must obtain a faculty advisor to …
Topics selected from analytic, affine, projective, hyperbolic, and non-Euclidean geometry. Prerequisite: MATH 2310, 3351, or instructor permission.
A rigorous program of supervised study designed to expose the student to a particular area of mathematics. Prerequisite: Instructor permission and graduate standing.
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 …
Introduces measure and integration theory. Prerequisite: MATH 5310 or equivalent.
Continuation of Probability Theory I. Elements of stochastic processes, including Brownian motion, continuous time martingales, and Markov processes.
Studies groups, rings, fields, modules, tensor products, and multilinear functions. Prerequisite: MATH 5651, 5652, or equivalent.
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 …
Examines fiber bundles; induced bundles, principal bundles, classifying spaces, vector bundles, and characteristic classes, and introduces K-theory and Bott periodicity. Prerequisite: MATH 7800.
Topics in the theory of operators on a Hilbert space and related areas of function theory.