Functions of Complex Variables Analytic functions, Cauchy's theorem, Laurent series, calculus of residues, conformal mappings, Moebius transformations, infinite products, entire functions, Riemann mapping theorem, Picard's theorem. Mathematics 301 or permission of the instructor. Chaotic Dynamical Systems Topics chosen from among Cantor set, periodic points of a map, chaotic maps on the interval, period doubling, symbolic dynamics, maps on a circle and torus, Mandelbrot set, fractals and Julia sets. Number Theory Algebraic number fields and rings of integers, quadratic and cyclotomic fields, norm and trace, ideal theory, factorization and prime decomposition, lattices and the geometry of algebraic integers, class numbers and ideal class groups, computational methods, Dirichlet's unit theorem. Senior Conference A seminar for seniors majoring in mathematics.
Topics vary from year to year.
Introduction to Probability and Statistics 113a. Calculus I 114. Calculus II 120a. Accelerated Calculus 121. Calculus III 204b.