Complex Analysis

by Theodore W. Gamelin

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 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.

Genres: Mathematics, Textbooks, Nonfiction

498 pages, Paperback

First published May 18, 2001

Reviews

[Daniel Wright · Rating 4 out of 5]

Solid run-through of the basics of complex analysis. Very useful as a reference and as a text for a first serious introduction to the subject.

[Lucas · Rating 3 out of 5]

Good pacing and useful examples, but occasionally uses new concepts without introducing them at all, can be painfully dry, and could really use more figures

[Leon · Rating 4 out of 5]

A great balance between readability and depth. Topics are motivated well and organized sensibly. Good examples. Nice cover.

This is the kind of book you can start a few days before your exam after a semester of not going to class and still grasp enough to do well. Fantastic for an irresponsible undergraduate.

[Phillip Zhou · Rating 1 out of 5]

This is one of my least favorite math textbooks I have used in any class. It is not explicit enough, its notation is confusing and or inconsistent in some places, and it does not treat the subject with enough rigor. All of this combined to making this textbook very frustrating to use. Consider using Shakarchi and Stein's textbook instead.

[Olof · Rating 3 out of 5]

I feel like this book is more geared towards applications than theory and to its merit is therefore very compact.

Much of the matters concerning convergence and metric space theory is brushed over and not fully explained so a background in metric space theory enables a greater understanding.