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Complex Functions: An Algebraic and Geometric Viewpoint (Softcover)

Complex Functions: An Algebraic and Geometric Viewpoint (Softcover)

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VERY GOOD: The book shows a minimum amount of use and wear and is in very good condition: the pages are clean and the binding is tight.

Product Details

From the back cover: "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. These include geometrical ideas such as hyperbolic and spherical geometry, the regular solids and Dirichlet tessellations, topological ideas such as the fundamental group, the Euler characteristic and the Riemann-Hurwitz formula, and group-theoretic ideas like linear fractional groups and free products. In this way many of the abstract topics a mathematics student meets as an undergraduate are given concrete applications."

BRIEF CONTENTS

  • Introduction
  • 1 - The Riemann sphere
  • 2 - Möbius transformations
  • 3 - Elliptic functions
  • 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
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AUTHOR: Jones;Gareth A. and David Singerman
PUBLISHER: Cambridge University Press
ISBN-13: 9780521313667
ISBN-10: 052131366X
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Complex Functions: An Algebraic and Geometric Viewpoint (Softcover)
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Complex Functions: An Algebraic and Geometric Viewpoint (Softcover)1825
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