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Complex Functions : An Algebraic and Geometric Viewpoint - Gareth A. Jones

Complex Functions

An Algebraic and Geometric Viewpoint

Paperback

Published: 18th May 1987
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Elliptic functions and Riemann surfaces played an important role in nineteenth-century mathematics. At the present time there is a great revival of interest in these topics not only for their own sake but also because of their applications to so many areas of mathematical research from group theory and number theory to topology and differential equations. In this book the authors give elementary accounts of many aspects of classical complex function theory including Moebius transformations, elliptic functions, Riemann surfaces, Fuchsian groups and modular functions. A distinctive feature of their presentation is the way in which they have incorporated into the text many interesting topics from other branches of mathematics. This book is based on lectures given to advanced undergraduates and is well-suited as a textbook for a second course in complex function theory. Professionals will also find it valuable as a straightforward introduction to a subject which is finding widespread application throughout mathematics.

"...a very nice treatment which emphasizes the unity of mathematics...Several years ago the reviewer wanted to teach an undergraduate course that gave an introduction to hyperbolic geometry, Mobius transformations and discrete groups. There was no suitable undergraduate text. This book fills that void," Mathematical Reviews "Well motivated with good selection of problems at the end of each chapter." American Mathematical Monthly "...clear and well written...Its message, admirably conveyed, is that mathematics is not a collection of neat parcels, the contents of one being blind to the contents of another." Times Higher Education Supplement "...clearly presented...a delightful book..." American Scientist

Introduction
The Riemann sphere
M+ bius transformations
Elliptic functions
Meromorphic continuation and Riemann surfaces
PSL(2,R) and its discrete subgroups
The modular group
Appendices
References
Index of symbols
Index of names and definitions
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521313667
ISBN-10: 052131366X
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 360
Published: 18th May 1987
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 1.91
Weight (kg): 0.43