Complex Functions: An Algebraic and Geometric Viewpoint

✍ Scribed by Gareth A. Jones

• Publisher: Cambridge University Press
• Year: 2010
• Tongue: English
• Leaves: 356
• Edition: 1
• Category: Library

✦ 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.

✦ Table of Contents

Frontmatter
Contents
Introduction
1 - The Riemann Sphere
2 - Möebius Transformations
4 - Meromorphic continuation and Riemann surfaces
5 - PSL(2,R) and its discrete subgroups
6 - The modular group
Appendix 1 - A review of complex variable theory
Appendix 2 - Presentations of groups
Appendix 3 - Resultants
Appendix 4 - Modern developments
References
Index of symbols
Index of names and definitions