Goals: An introduction to complex variables, including a study of the topology of the plane required. Content: Properties of complex numbers and analytic functions of one complex variable. Power series. Cauchy's theorem, and applications to integration. Applications. While not a prerequisite for MATH 5910, this course is the first in a two semester sequence, along with MATH 5910, in modern analysis. Taught: Spring term. Prerequisite: MATH 1180.