Courses

May include the theory of automorphic forms, elliptic curves, or any of a variety of advanced topics in analytic and algebraic number theory. Prereq., MATH 6110. Undergraduates must have approval of the instructor. Prerequisites: Restricted to graduate students only.

Focuses on Maxwell equations, Lorentz force, Minkowski space-time, Lorentz, Poincare, and conformal groups,metric manifolds, covariant differentiation, Einstein space-time, cosmologies, and unified field theories. Prereq., instructor consent. Undergraduates must have approval of the instructor.

Introduces such topics as Banach spaces (Hahn-Banach theorem, open mapping theorem, etc.), operator theory (compact operators and integral equations, and spectral theorem for bounded self-adjoint operators), and Banach algebras (the Gelfand theory). See also MATH 8340. Prereqs., MATH 6310 and 6320. Undergraduates must have approval of the instructor. Prerequisites: Restricted to graduate students only.

Examines trigonometric series, periodic functions, diophantine approximation, and Fourier series. Also covers Bohr and Stepanoff almost periodic functions, positive definite functions, and the L1 and L2 theory of the Fourier integral. Applications to group theory and differential equations. See also MATH 8380. Prereq., MATH 5150 and 6320. Undergraduates must have approval of the instructor.

May be repeated up to 3 total credit hours. Prerequisites: Restricted to graduate students only.

All doctoral students must register for not fewer than 30 hours of dissertation credit as part of the requirements for the degree. For a detailed discussion of doctoral dissertation credit, refer to the Graduate School portion of the catalog.