Topics to be chosen from the areas of algebra, analysis, topology, geometry, and logic. This course can be repeated at most 2 times for a maximum of 12 credits total.
4 hr./wk.
Topics to be chosen from applied mathematics and related fields. Typical subjects are: asymptotic methods, wave propagation, mathematical biology. This course can be repeated at most 2 times for maximum of 12 credits total.
4 hr./wk.;
Topics to be chosen from the areas of probability, statistics, game theory, combinatorial analysis, etc. This course can be repeated at most 2 times for a maximum of 12 credits total.
4 hr./wk.
A continuation of MATH A3200, including such topics as analytic continuation, conformal mapping, Dirichlet problem, meromorphic functions, entire functions, Picard's Theorem, elliptic functions.
4 hr./wk.
Abstract measure and integration theory, abstract Lebesgue measure and integral, signed measures, Radon-Nikodym derivative, Lp spaces, product spaces, Daniell integral. Special topics such as Stieltjes integrals, Denjoy integral, Haar measure, measure rings, applications to probability.
4 hr./wk.
First order quasi-linear and nonlinear equations, Cauchy-Kowalewsky Theorem, well-posed problems, Cauchy problem for hyperbolic systems, the wave equation in n-dimensions, boundary value problems for elliptic equations, Laplace's equation, parabolic equations, heat equation.
4 hr./wk.
Topics will be chosen from the areas of ergodic theory, topological dynamics, differentiable dynamics, complex dynamics and symbolic dynamics.
4 hr./wk.
Field extensions, Galois theory, vector spaces and modules, category theory, special topics.
4 hr./wk.
An introduction to algebraic topology. Homology: simplicial and singular, computations and applications; categories and functors; cohomology of groups, cup product, and Poincare duality; universal coefficients for homology; homotopy theory: homotopy groups, calculating them, connections with cohomology.
4 hr./wk.
Markov chains, limit theorems, renewal equations, random walks, Brownian motion, branching processes, queuing theory.
4 hr./wk.
The general decision problem, decision-making principles, application to hypothesis testing and estimation, minimax and Bayes solutions, utility theory, sequential procedures.
MATH A7800
4 hr./wk.;
A program of independent study under the direction of a member of the Department, with approval of the Graduate Advisor.
Independent Study. This course can be repeated at most 2 times for a maximum of 3 credits total.
1 hr./wk.
Independent Study. This course can be repeated at most 2 times for a maximum of 6 credits total.
2 hr./wk.
Independent Study. This course can be repeated at most 2 times for a maximum of 9 credits total.
3 hr./wk.
Independent Study. This course can be repeated at most 2 times for a maximum of 12 credits total.
4 hr./wk.