Complex Functions: An Algebraic and Geometric Viewpoint - Hardcover

Jones, Gareth A.; Singerman, David

Hardcover

ISBN 10: 0521308933 ISBN 13: 9780521308939

Publisher: Cambridge University Press, 1987

Synopsis

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 Möbius 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.

About this title

Book Description

An elementary account of many aspects of classical complex function theory, including Mobius transformations, elliptic functions, Riemann surfaces, Fuchsian groups and modular functions. The book is based on lectures given to advanced undergraduate students and is well suited as a textbook for a second course in complex function theory.

Review

"...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, Möbius 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

Edition details

• Publisher: Cambridge University Press
• Publication date: 1987
• ISBN 10: 0521308933
• ISBN 13: 9780521308939
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 356