Topics that may be covered include graph theory, Ramsey theory, finite geometries, combinatorial enumeration, combinatorial games. May not receive credit for both MATH 382 and MATH 427 . Presentation of one lecture and attendance at all sessions required. Includes an introduction to the concept of curvature and thorough treatment of the Gauss-Bonnet theorem. Content varies from year to year.
Content varies from year to year.
May include Fourier series, harmonic analysis, probability theory, advanced topics in measure theory, ergodic theory, and elliptic integrals. May include the Riemann mapping theorem, uniformization, Runge's theorem, elliptic function theory, the prime number theorem, and Riemann surfaces. Includes a treatment of cardinality and well ordering, as well as metrization. MATH 321 or permission of instructor recommended. Includes elementary homotopy theory and covering spaces.