Mathematics of the 19th Century: Geometry, Analytic Function Theory / Edition 1

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Overview

This book is the second volume of a study of the history of mathematics in the nineteenth century. The first part of the book describes the development of geometry. The many varieties of geometry are considered and three main themes are traced: the development of a theory of invariants and forms that determine certain geometric structures such as curves or surfaces; the enlargement of conceptions of space which led to non-Euclidean geometry; and the penetration of algebraic methods into geometry in connection with algebraic geometry and the geometry of transformation groups. The second part, on analytic function theory, shows how the work of mathematicians like Cauchy, Riemann and Weierstrass led to new ways of understanding functions. Drawing much of their inspiration from the study of algebraic functions and their integral, these mathematicians and others created a unified, yet comprehensive theory in which the original algebraic problems were subsumed in special areas devoted to elliptic, algebraic, Abelian and automorphic functions. The use of power series expansions made it possible to include completely general transcendental functions in the same theory and opened up the study of the very fertile subject of entire functions. This book will be a valuable source of information for the general reader, as well as historians of science. It provides the reader with a good understanding of the overall picture of these two areas in the nineteenth century and their significance today.
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Editorial Reviews

Booknews
The second volume of a study of the history of mathematics in the 19th century. The section on geometry revolves around the development of a theory of invariants and forms that determine certain geometric structures, the enlargement of conceptions of space beyond Euclid's wildest dreams, and the penetration of algebraic methods. The section on analytic function theory shows how mathematicians like Cauchy, Riemann, and Weierstrass created a unified, comprehensive theory in which originally algebraic problems were subsumed in special areas devoted to elliptic, algebraic, Abelian, and automorphic functions. Translated from Matematika XIX veka: geometriya, teoriya analiticheskikh funktsii published in 1981 by Nauka in Moscow. No subject index. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9783764350482
  • Publisher: Birkhauser Basel
  • Publication date: 4/30/1996
  • Edition description: 1996
  • Edition number: 1
  • Pages: 291
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.75 (d)

Table of Contents

Preface
Ch. 1 Geometry 1
1 Analytic and Differential Geometry 3
2 Projective Geometry 27
3 Algebraic Geometry and Geometric Algebra 44
4 Non-Euclidean Geometry 53
5 Multi-Dimensional Geometry 75
6 Topology 97
7 Geometric Transformations 106
Ch. 2 Analytic function 119
Literature 273
Index of Names 283
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