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Mathematics of the 19th century : geometry, analytic function theory

Autore: A N Kolmogorov; A P I︠U︡shkevich
Editore: Basel ; Boston : Birkhäuser Verlag, ©1996.
Edizione/Formato:   Libro : EnglishVedi tutte le edizioni e i formati
Banca dati:WorldCat
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Presents a study of the history of mathematics in the nineteenth century. This book describes the development of geometry. It discusses analytic function theory, and shows how the work of  Per saperne di più…

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Genere/forma: History
Tipo documento: Book
Tutti gli autori / Collaboratori: A N Kolmogorov; A P I︠U︡shkevich
ISBN: 0817650482 9780817650483 3764350482 9783764350482
Numero OCLC: 33970112
Descrizione: x, 291 p. : ill. ; 24 cm.
Contenuti: 1. Geometry.- 1. Analytic and Differential Geometry.- Analytic Geometry.- The Differential Geometry of Monge's Students.- Gauss' Disquisitiones generales circa superficies curvas.- Minding and the Formulation of the Problems of Intrinsic Geometry.- The French School of Differential Geometry.- Differential Geometry at Midcentury.- Differential Geometry in Russia.- The Theory of Linear Congruences.- 2. Projective Geometry.- The Rise of Projective Geometry.- Poncelet's Traite des proprietes projectives des figures.- The Analytic Projective Geometry of Mobius and Plucker.- The Synthetic Projective Geometry of Steiner and Chasles.- Staudt and the Foundation of Projective Geometry.- Cayley's Projective Geometry.- 3. Algebraic Geometry and Geometric Algebra.- Algebraic Curves.- Algebraic Surfaces.- Geometric Computations Connected with Algebraic Geometry.- Grassmann's Lineale Ausdehnungslehre.- Hamilton's Vectors.- 4. Non-Euclidean Geometry.- Nikola? Ivanovich Lobachevski? and the Discovery of Non-Euclidean Geometry.- Gauss' Research in Non-Euclidean Geometry.- Janos Bolyai.- Hyperbolic Geometry.- J. Boyai's "Absolute Geometry".- The Consistency of Hyperbolic Geometry.- Propagation of the Ideas of Hyperbolic Geometry.- Beltrami's Interpretation.- Cayley's Interpretation.- Klein's Interpretation.- Elliptic Geometry.- 5. Multi-Dimensional Geometry.- Jacobi's Formulas for Multi-dimensional Geometry.- Cayley's Analytic Geometry of n Dimensions.- Grassmann's Multi-dimensional Geometry.- Plucker's Neue. Geometrie des Raumes.- Schlafli's Theorie der vielfachen Kontinuilat.- The Multi-dimensional Geometry of Klein and Jordan.- Riemannian Geometry.- Riemann's Idea of Complex Parameters of Euclidean Motions.- Riemann's Ideas on Physical Space.- The Work of Christoffel, Lipschitz. and Suvorov on Riemannian Geometry.- The Multi-dimensional Theory of Curves.- Multi-dimensional Surface Theory.- Multi-dimensional Projective Geometry.- The Terminology of Multi-dimensional Geometry.- 6. Topology.- Gauss' Topology.- Generalizations of Euler's Theorem on Polyhedra in the Early Nineteenth Century.- Listing's Vorstudien zur Topologie.- Mobius' "Theorie der elementaren Verwandschaft".- The Topology of Surfaces in Riemann's "Theorie der Abel'schen Funktionen".- The Multi-dimensional Topology of Riemann and Betti.- Jordan's Topological Theorems.- The "Klein Bottle".- 7. Geometric Transformations.- Geometrie Transformations in the Work of Mobius.- Helmholtz' Paper "Uber die Thatsachen, die der Geometrie zu Grunde liegen".- Klein's "Erlanger Programm".- Transference Principles.- Cremona Transformations.- Conclusion.- 2. Analytic Function.- Results Achieved in Analytic Function Theory in the Eighteenth Century.- Development of the Concept of a Complex Number.- Complex Integration.- The Cauchy Integral Theorem. Residues.- Elliptic Functions in the Work of Gauss.- Hypergeometric Functions.- The First Approach to Modular Functions.- Power Series. The Method of Majorants.- Elliptic Functions in the Work of Abel.- C.G.J. Jacobi. Fundamenta nova functionum ellipticarum.- The Jacobi Theta Functions.- Elliptic Functions in the Work of Eisenstein and Liouville. The First Textbooks.- Abelian Integrals. Abel's Theorem.- Quadruply Periodic Functions.- Summary of the Development of Analytic Function Theory over the First Half of the Nineteenth Century.- V. Puiseux. Algebraic Functions.- Bernhard Riemann.- Riemann's Doctoral Dissertation. The Dirichlet Principle.- Conformal Mappings.- Karl Weierstrass.- Analytic Function Theory in Russia. Yu.V. Sokhotski? and the Sokhotski?-Casorati-Weierstrass Theorem.- Entire and Meromorphic Functions. Picard's Theorem.- Abelian Functions.- Abelian Functions (Continuation).- Automorphic Functions. Uniformization.- Sequences and Series of Analytic Functions.- Conclusion.- Literature.- (F. A. Medvedev).- General Works.- Collected Works and Other Original Sources.- Auxiliary Literature to Chapter 1.- Auxiliary Literature to Chapter 2.- Index of Names (A. F. Lapko).
Altri titoli: Matematika XIX veka.
Mathematics of the nineteenth century
Responsabilità: edited by A.N. Kolmogorov, A.P. Yushkevich ; translated from the Russian by Roger Cooke.
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