An introduction to complex analysis for students with some knowledge of
complex numbers from high school. It contains sixteen chapters, the
first eleven of which are aimed at an upper division undergraduate
audience. The remaining five chapters are designed to complete the
coverage of all background necessary for passing PhD qualifying exams in
complex analysis. Topics studied include Julia sets and the Mandelbrot
set, Dirichlet series and the prime number theorem, and the
uniformization theorem for Riemann surfaces, with emphasis placed on the
three geometries: spherical, euclidean, and hyperbolic. Throughout,
exercises range from the very simple to the challenging. The book is
based on lectures given by the author at several universities, including
UCLA, Brown University, La Plata, Buenos Aires, and the Universidad
Autonomo de Valencia, Spain.Download
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