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Complex Analysis: The Argument Principle in Analysis and Topology

Alan Beardon

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Dover Publications Inc.
18 December 2019
Mathematics & Sciences; Mathematics
With its emphasis on the argument principle in analysis and topology, this book represents a different approach to the teaching of complex analysis. The three-part treatment provides geometrical insights by covering angles, basic complex analysis, and interactions with plane topology while focusing on the concepts of angle and winding numbers. Part I takes a critical look at the concept of an angle, illustrating that because a nonzero complex number varies continuously, one may select a continuously changing value of its argument. Part II builds upon this material, using the argument and its continuous variation as a tool in further studies and clarifying the complementary aspects of complex analysis and plane topology. Part III explores the link between the two subjects to their mutual benefit. The first two sections are intended for advanced undergraduates and graduate students in mathematics and contain sufficient material for a single course. The final section is geared toward the complex analyst and is intended to provide a foundation for further study. AUTHOR: Alan F. Beardon received his PhD from the University of London in 1964 and was Professor of Mathematics at the University of Cambridge from 1970 until he became Emeritus in 2007. His many books include A Primer on Riemann Surfaces, The Geometry of Discrete Groups, and Limits: A New Approach to Real Analysis.
By:   Alan Beardon
Imprint:   Dover Publications Inc.
Country of Publication:   United States
Dimensions:   Height: 229mm,  Width: 152mm, 
ISBN:   9780486837185
ISBN 10:   0486837181
Pages:   256
Publication Date:   18 December 2019
Audience:   General/trade ,  ELT Advanced
Format:   Paperback
Publisher's Status:   Active

Alan F. Beardon received his PhD from the University of London in 1964 and was Professor of Mathematics at the University of Cambridge from 1970 until he became Emeritus in 2007. His many books include A Primer on Riemann Surfaces, The Geometry of Discrete Groups, and Limits: A New Approach to Real Analysis.

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