PDF Geometry of Complex Numbers (Dover Books on Mathematics)
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Published on: 2012-05-23
Released on: 2012-05-23
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"This book should be in every library, and every expert in classical function theory should be familiar with this material. The author has performed a distinct service by making this material so conveniently accessible in a single book." — Mathematical ReviewSince its initial publication in 1962, Professor Schwerdtfeger's illuminating book has been widely praised for generating a deeper understanding of the geometrical theory of analytic functions as well as of the connections between different branches of geometry. Its focus lies in the intersection of geometry, analysis, and algebra, with the exposition generally taking place on a moderately advanced level. Much emphasis, however, has been given to the careful exposition of details and to the development of an adequate algebraic technique.In three broad chapters, the author clearly and elegantly approaches his subject. The first chapter, Analytic Geometry of Circles, treats such topics as representation of circles by Hermitian matrices, inversion, stereographic projection, and the cross ratio. The second chapter considers in depth the Moebius transformation: its elementary properties, real one-dimensional projectivities, similarity and classification of various kinds, anti-homographies, iteration, and geometrical characterization. The final chapter, Two-Dimensional Non-Euclidean Geometries, discusses subgroups of Moebius transformations, the geometry of a transformation group, hyperbolic geometry, and spherical and elliptic geometry. For this Dover edition, Professor Schwerdtfeger has added four new appendices and a supplementary bibliography.Advanced undergraduates who possess a working knowledge of the algebra of complex numbers and of the elements of analytical geometry and linear algebra will greatly profit from reading this book. It will also prove a stimulating and thought-provoking book to mathematics professors and teachers. Fundamental Theorem of Algebra - Interactive Mathematics ... Fundamental Theorem of Algebra. Complex numbers are in a sense perfect while there is little doubt that perfect numbers are complex. Starting from the tail perfect ... TSM Resources - Mathematics Links Compiled by the iCT Training Centre Oundle School Peterborough. Foundations and Fundamental Concepts of Mathematics - Dover Third edition of popular undergraduate-level text offers overview of historical roots and evolution of several areas of mathematics. Topics include mathematics before ... Geometry - Wikipedia The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia and Egypt in the 2nd millennium BC. Early geometry was a collection of empirically ... Complex Analysis - Free E-Books Complex Analysis - list of freely downloadable books at E-Books Directory Books in the Mathematical Sciences This site is intended as a resource for university students in the mathematical sciences. Books are recommended on the basis of readability and other pedagogical value. Complex Number -- from Wolfram MathWorld Complex Number. The complex numbers are the field of numbers of the form where and are real numbers and i is the imaginary unit equal to the square root of Pi -- from Wolfram MathWorld The constant pi denoted pi is a real number defined as the ratio of a circle's circumference C to its diameter d=2r pi = C/d (1) = C/(2r) (2) pi has decimal ... Mathematics Books Math Books - Dover Publications Dover is most recognized for our magnificent math books list. Dover books on mathematics include authors Paul J. Cohen ( Set Theory and the Continuum ... Non-Euclidean geometry - Wikipedia In mathematics non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry. As Euclidean geometry lies ...
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