This course is for students preparing for the no-thesis option for a master's degree. The content is set by the students' advisors. Requisites: Restricted to graduate students only.
May include the theory of automorphic forms, elliptic curves, or any of a variety of advanced topics in analytic and algebraic number theory. Department enforced prereq., MATH 6110. Instructor consent required for undergraduates. Requisites: Restricted to graduate students only.
Department enforced prereqs., MATH 6130 and MATH 6140. Instructor consent required for undergraduates. Requisites: 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. Department enforced restriction: instructor consent required. Instructor consent required for undergraduates. Requisites: Restricted to graduate students only.
Presents advanced topics in analysis including Lie groups, Banach algebras, operator theory, ergodic theory, representation theory, etc. Department enforced prereqs., MATH 8330 and MATH 8340. Instructor consent required for undergraduates. Requisites: Restricted to graduate students only.
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). Department enforced prereqs., MATH 6310 and MATH 6320. Instructor consent required for undergraduates. See also MATH 8340. Requisites: Restricted to graduate students only.
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). Department enforced prereq., MATH 8330. Instructor consent required for undergraduates. See also MATH 8330. Requisites: 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 L^1 and L^2 theory of the Fourier integral. Applications to group theory and differential equations. Department enforced prereq., MATH 5150 and MATH 6320. Instructor consent required for undergraduates. Requisites: 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. Requisites: Restricted to graduate students only.
