(Replaces MAT331 beginning AY 2012-13)

Study of functions of a complex variable, with emphasis on interrelations with other parts of mathematics.

Cauchy's theorems, singularities, contour integration, power series, infinite products. The gamma and zeta functions and the prime number theorem. Elliptic functions, theta functions, Jacobi's triple product and combinatorics. An overall view of Special Functions via the hypergeometric series.

This course is the second semester of a four-semester sequence, but may be taken independently of the other semesters.