In this second edition of a Carus Monograph Classic, Steven G. Krantz, a leading worker in complex analysis and a winner of the Chauvenet Prize for outstanding mathematical exposition, develops material on classical non-Euclidean geometry. He shows how it can be developed in a natural way from the invariant geometry of the complex disk. He also introduces the Bergmann kernel and metric and provides profound applications, some of which have never appeared in print before. In general, the new edition represents a considerable polishing and re-thinking of the original successful volume. A minimum of geometric formalism is used to gain a maximum of geometric and analytic insight. The climax of the book is an introduction to several complex variables from the geometric viewpoint. Poincaré's theorem, that the ball and bidisc are biholomorphically inequivalent, is discussed and proved.
FREE Two-Day Shipping for Students. Learn more |
| ||||||||||||
Book Description
Special Offers and Product Promotions
- Buy $50 in qualifying physical textbooks, get $5 in Amazon MP3 Credit. Here's how (restrictions apply)
Frequently Bought Together
Editorial Reviews
Review
'A first-rate book, which can be used either as a text or a reference.' Choice
'In five very nicely written chapters this book gives an introduction to the approach to function theory via Riemannian geometry. Very little function-theoretic background is needed and no knowledge whatsoever of differential geometry is assumed.' Mathematical Reviews
'In five very nicely written chapters this book gives an introduction to the approach to function theory via Riemannian geometry. Very little function-theoretic background is needed and no knowledge whatsoever of differential geometry is assumed.' Mathematical Reviews
Book Description
Krantz develops material on classical non-Euclidean geometry and provides profound applications, some of which have never appeared in print before. The new edition represents a considerable polishing and re-thinking of the original successful volume. A minimum of geometric formalism is used to gain a maximum of geometric and analytic insight.
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
|
Share your thoughts with other customers:
|
||||||||||||||||||||||
|
Most Helpful Customer Reviews
5 of 5 people found the following review helpful:
5.0 out of 5 stars
A significant contribution to the literature of complex variables,
By Charles Ashbacher (Marion, Iowa United States) - See all my reviews (TOP 500 REVIEWER) (VINE VOICE) (HALL OF FAME REVIEWER)
This review is from: Complex Analysis: The Geometric Viewpoint, Second Edition (Carus Mathematical Monographs) (Hardcover)
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.
2 of 2 people found the following review helpful:
5.0 out of 5 stars
fresh take on complex analysis,
By
This review is from: Complex Analysis: The Geometric Viewpoint, Second Edition (Carus Mathematical Monographs) (Hardcover)
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.
6 of 24 people found the following review helpful:
1.0 out of 5 stars
The title is misleading...,
By
This review is from: Complex Analysis: The Geometric Viewpoint, Second Edition (Carus Mathematical Monographs) (Hardcover)
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.
Share your thoughts with other customers: Create your own review
|
|
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Inside This Book
(learn more)
First Sentence:
The purpose of this book is to explain how various aspects of complex analysis can be understood both naturally and elegantly from the point of view of metric geometry. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
continuously differentiable curve, classical function theory, biholomorphic mapping, complex function theory, several complex variables, holomorphic functions, unit disc, mapping theorem, planar domains, removable singularity, conformal map, essential singularity, little theorem, orthonormal system New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
The purpose of this book is to explain how various aspects of complex analysis can be understood both naturally and elegantly from the point of view of metric geometry. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
continuously differentiable curve, classical function theory, biholomorphic mapping, complex function theory, several complex variables, holomorphic functions, unit disc, mapping theorem, planar domains, removable singularity, conformal map, essential singularity, little theorem, orthonormal system New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
This book cites 33
books:
See all 33 books this book cites
18
books
cite this book:
See all 18 books citing this book
- Complex Analysis (Lecture Notes in Mathematics) by Steven G. Krantz in Front Matter, and Back Matter
- Complex Variables: A Physical Approach with Applications and MATLAB (Textbooks in Mathematics) by Steven G. Krantz in Back Matter (1), and Back Matter (2)
- Projective geometry, by Oswald Veblen and John Wesley Young. (Michigan Historical Reprint) by Oswald Veblen in Front Matter
- Advanced Calculus, Revised Edition by Loomis in Back Matter
- History of Mathematics, Vol. I (Dover Books on Mathematics) by David E. Smith in Front Matter
See all 33 books this book cites
- Function Theory of One Complex Variable (Graduate Studies in Mathematics, 40) by Steven G. Krantz Robert E. Greene in Back Matter
- Berkeley Problems in Mathematics by Paulo Ney de Souza in Back Matter
- The Sensual (Quadratic) Form (Carus Mathematical Monographs) by John Horton Conway in Front Matter
- A Panorama of Harmonic Analysis (Carus Mathematical Monographs) by Steven Krantz in Front Matter
- Handbook of Writing for the Mathematical Sciences by Nicholas J. Higham on page 261
See all 18 books citing this book
Books on Related Topics
(learn more)
|
What Other Items Do Customers Buy After Viewing This Item?
Tags Customers Associate with This Product(What's this?)Click on a tag to find related items, discussions, and people.
|
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
