Courses

Numerical linear algebra, eigenvalue problems, optimization problems, and ordinary and partial differential equations. Prereq., APPM 5600 or MATH 5600. Prerequisites: Restricted to Graduate Students only.

Same as APPM 4720.

Continuation of APPM 5470. Advanced study of the properties and solutions of elliptic, parabolic, and hyperbolic partial differential equations. Topics include the study of Sobolev spaces and variational methods as they relate to PDEs, and other topics as time permits. Prereq., APPM 5470. Prerequisites: Restricted to Graduate Students only.

Emphasizes mathematical theory of statistics. Topics include distribution theory, estimation and testing of hypotheses, multivariate analysis, and nonparametric inference, all with emphasis on theory. Prereq., APPM 5520 or MATH 5520.

Systematic study of Markov chains and some of the simpler Markov processes including renewal theory, limit theorems for Markov chains, branching processes, queuing theory, birth and death processes, and Brownian motion. Applications to physical and biological sciences. Prereqs., MATH 4001, MATH 4510 or APPM 3570, or APPM 4560, or instructor consent. Same as MATH 6550.

Covers finite difference, finite element, finite volume, pseudo-spectral, and spectral methods for elliptic, parabolic, and hyperbolic partial differential equations. Prereq., APPM 5600. Recommended prereq., APPM 5610 or graduate numerical linear algebra. Prerequisites: Restricted to Graduate Students only.

Develops a fundamental understanding of the principles and techniques of the multigrid methodology, which is a widely used numerical approach for solving many problems in such diverse areas as aerodynamics, astrophysics, chemistry, electromagnetics, hydrology, medical imaging, meteorology/oceanography, quantum mechanics, and statistical physics.

Introduces graduate students to research foci of the Department of Applied Mathematics. Prereq., instructor consent. Prerequisites: Restricted to Graduate Students only.

May be repeated up to 6 total credit hours. Prerequisites: Restricted to Graduate Students only.

Covers dynamical systems defined by mappings and differential equations. Hamiltonian mechanics, action-angle variables, results from KAM and bifurcation theory, phase plane analysis, Melnikov theory, strange attractors, chaos, etc. Prereq., APPM 5460. Prerequisites: Restricted to Graduate Students only.

Includes basic results associated with linear dispersive wave systems, first-order nonlinear wave equations, nonlinear dispersive wave equations, solitons, and the methods of the inverse scattering transform. Prereqs., APPM 5470--5480, PHYS 5210, or instructor consent.

Provides a vehicle for the development and presentation of new topics with the potential of being incorporated into the core courses in applied mathematics. May be repeated up to 6 total credit hours. Prereq., instructor consent. Prerequisites: Restricted to Graduate Students only.

Introduces graduate students to research foci of the Department of Applied Mathematics. Prereq., instructor consent. Prerequisites: Restricted to Graduate Students only.

Introduces graduate students to the major research foci of the Department of Applied Mathematics. Prereq., instructor consent. Prerequisites: Restricted to Graduate Students only.

Introduces advanced topics and research in dynamical systems. Prereq., instructor consent. Prerequisites: Restricted to Graduate Students only.

Introduces the core methods in the analysis of nonlinear partial differential and integral equations or systems to graduate students. Provides a vehicle for the development, presentation, and corporative research of new topics in PDE and analysis. Prereq., APPM 5440. Prerequisites: Restricted to Graduate Students only.

Introduces advanced topics and research in computational mathematics. Prereq., instructor consent. Prerequisites: Restricted to Graduate Students only.

All doctoral students must register for no fewer than 30 hours of dissertation credit as part of the requirements for the degree. No more than 10 credit hours may be taken in any one semester. Prerequisites: Restricted to Graduate Students only.