Customer Reviews

Complex Analysis: The Geometric Viewpoint, Second Edition (Carus Mathematical Monographs)

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The complex plane is a very valuable palette on which an enormous variety of problems can be placed. It allows for a melding of the ideas of analysis and geometry and makes it possible to solve problems in ways that are much simpler than using other techniques. Furthermore, as is always the case in mathematics, the use of the complex plane has revealed new and interesting results that were sometimes unanticipated.
In this volume, Krantz demonstrates some of the marriage between analysis and geometry and the interesting results. He starts with the assumption that the reader understands the basics of complex variables and some of the basic theorems of function theory. The subsequent topics are:

*) Basic notions of differential geometry
*) Curvature and applications
*) Some new invariant metrics
*) Introduction to the Bergman theory
*) A glimpse of several complex variables

Many theorems are presented and proofs of nearly all of them are given.
This book is a significant contribution to the literature of complex variables; it could be used as a textbook in a special topics course in complex analysis, self-study or simply review.

As one of the reviewers said this is not for the beginner in complex analysis but if you have been exposed to a standard course on complex analysis and have some knowledge of differential geometry, simple knowledge of tangent spaces should be more than sufficient, then this book is a delight. The introduction of a metric structure recasts old proofs in a new light and shifts the focus from counting zeroes and poles to understanding analytic maps as geometric objects that reveal a lot of their properties through their interaction with the metric structure. Highly recommended.

If you are a math nerd who can follow books like
Theorem
Proof
Corollary
Proposition
Proof
Corollary
Proposition
Lemma
Proof
Corollary
Theorem
Proof
Corollary
...
[Some Explanatory Text]
...
Theorem
Proof
Corollary
Proposition
Proof
Corollary
Proposition
Lemma
Proof
...
[Figure]
...

Then this is the book for you. If you know Complex analysis
already, you may enjoy this one. IT IS NOT INTENDED FOR SOMEONE
WHO WANT'S TO LEARN C.A. FROM SCRATCH.

I was personally looking for something more of the like of
"Visual Complex Analysis" by Tristan Needham. Lots of Fun Indeed.