Complex Analysis: a Self-Study Guide

Description

This is not a college textbook. With a college textbook and course, you are expected to develop the skills to independently prove a medium-difficult complex analysis theorem. Our goal here is more modest. After studying this book, you should have the skills to read, follow, and understand someone else's proof of a complex analysis theorem.Motivation for This Book:My first published book is A Study of Bernhard Riemann’s 1859 Paper. In Riemann’s famous paper, he makes several important advances in mathematics and speculates (the "Riemann Hypothesis") about the location of the zeros of the Zeta function. My Riemann book is intended to bring an understanding of Riemann's paper to a wider audience by bridging the gap between John Derbyshire’s excellent but less technical book, Prime Obsession, and Harold Edward's excellent but highly technical book, Riemann’s Zeta Function.To advance your knowledge beyond Derbyshire’s book, you must have a good understanding of complex analysis (call it knowledge at the "hobbyist" level). Several people have said they want to get to the "hobbyist" level so they can better understand my Riemann book. However, when they look at Ahlfors and other well-known (400+ page) textbooks on complex analysis, it feels like a mountain just a little too high to climb. This book is intended to help you advance to the "hobbyist" level.