Customer Reviews

Classical Complex Analysis (Jones and Bartlett Books in Mathematics and Computer Science)

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For me this text is a joy and a delight. In the preface the authors remark that to acquire a thorough grasp of the subject requires hard work They assert the virtues of this book to be clarity of presentation, selection of topics, and interesting exercises. They express their hope that the book will help the student to become as enthusiastic about the subject as the authors are. In my case they achieve their goals.

Very many years ago I took complex analysis in grad school using the then-recent text by Ahlfors, and with a 100% Teutonic professor; I then found the subject boring. This book, however makes me enthusiastic. It is one of the few math texts I own that I like for bedtime reading, opening it to something of interest, or just to a random section or some exercises, and relaxing while reading as if it were an adventure novel. When I put it down, consequences trickle through my mind as I go to sleep. No, it's not an easy subject, but the authors make it an enthralling one, at least for me.

This is not the easiest book on complex analysis to read, but nevertheless I really like it. If I had to use one word to describe it, it would be thorough. I have not read much beyond the first half of it, so my comments do not apply to the more advanced chapters.

The prose is sometimes clear, but at times you have to think very hard to get through it. Although there are a number of diagrams, I do not find them particularly helpful. The book does not move too fast, it actually moves quite slowly, but it explores a lot--it is very thorough.

This book has a ton of exercises, and some of them are very hard and very deep. I think the exercises are the best part of this book. This book makes me realize that a lot of other complex analysis textbooks do not have enough exercises, especially challenging ones. My favourite part are the exercises that explore counterexamples to converses of theorems. There are also a lot of great exercises involving infinite series.

I think this book would be most appropriate to someone who had already taken an undergraduate course in complex analysis and was taking a more advanced graduate course, or wanted to enrich their understanding on their own. This is a study text, not a reference text; it is ideal for learning and challenging a student. It is not concise, and it is harder to follow than the books by Lang, Newman & Bak, or Gamelin. However, I am convinced that someone reading this book would reach a deeper understanding of the subject than someone reading any of those other books.