Description: The book provides an introduction to complex analysis for readers with some very basic familiarity with complex numbers. The sixteen chapters begin with the fundamentals at the undergraduate level, finishing with material designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics covered include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces. The three geometries, spherical, Euclidean, and hyperbolic, are stressed. Exercises range from the very simple to the quite challenging, in all chapters.

Please Wait