Bilinear, quadratic and Hermitian forms. Examples are given, and the elementary theory of these structures is described. Geometry Possible topics include Euclidean geometry, non-Euclidean geometry, projective geometry, transformation geometry, complex geometry. Junior Seminar Seminars and discussions designed to integrate readings of mathematical literature with both oral and written presentations. I and II Topics chosen from among operations research, optimization, including an introduction to the calculus of variations, combinatorics, discrete mathematics, Fourier analysis, integral equations, partial differential equations.
Students acquire some experience at constructing mathematical models.
3 credits each. 2-3 credits each. Introduction to Complex Analysis Analytic functions, elementary functions and mappings, integrals, Cauchy's integral theorem and formula, power series, residues and poles. This course continues MATH 3815. Further properties of groups and fields, with a section on the applications of finite fields.