Linear Differential Equations And Group Theory From Riemann To Poincare

Author : Jeremy Gray
Publisher : Springer Science & Business Media
Page : 357 pages
File Size : 48,9 Mb
Release : 2010-01-07
Category : Mathematics
ISBN : 9780817647735

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Linear Differential Equations and Group Theory from Riemann to Poincare by Jeremy Gray Pdf

This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry. The text for this second edition has been greatly expanded and revised, and the existing appendices enriched. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.

Author : Jeremy J. Gray
Publisher : Unknown
Page : 460 pages
File Size : 44,9 Mb
Release : 1986
Category : Differential equations, Linear
ISBN : 3764333189

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Linear Differential Equations and Group Theory from Riemann to Poincaré by Jeremy J. Gray Pdf

Author : J. J. Gray
Publisher : Unknown
Page : 128 pages
File Size : 45,7 Mb
Release : 1981
Category : Electronic
ISBN : OCLC:53586958

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Differential Equations and Group Theory from Riemann to Poincare by J. J. Gray Pdf

Author : Michio Kuga
Publisher : Springer Science & Business Media
Page : 147 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461203292

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Galois’ Dream: Group Theory and Differential Equations by Michio Kuga Pdf

First year, undergraduate, mathematics students in Japan have for many years had the opportunity of a unique experience---an introduction, at an elementary level, to some very advanced ideas in mathematics from one of the leading mathematicians of the world. English reading students now have the opportunity to enjoy this lively presentation, from elementary ideas to cartoons to funny examples, and to follow the mind of an imaginative and creative mathematician into a world of enduring mathematical creations.

Author : John Ratcliffe
Publisher : Springer Science & Business Media
Page : 761 pages
File Size : 50,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475740134

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Foundations of Hyperbolic Manifolds by John Ratcliffe Pdf

This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. Particular emphasis has been placed on readability and completeness of ar gument. The treatment of the material is for the most part elementary and self-contained. The reader is assumed to have a basic knowledge of algebra and topology at the first-year graduate level of an American university. The book is divided into three parts. The first part, consisting of Chap ters 1-7, is concerned with hyperbolic geometry and basic properties of discrete groups of isometries of hyperbolic space. The main results are the existence theorem for discrete reflection groups, the Bieberbach theorems, and Selberg's lemma. The second part, consisting of Chapters 8-12, is de voted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the structure of geometrically finite hyperbolic manifolds. The third part, consisting of Chapter 13, in tegrates the first two parts in a development of the theory of hyperbolic orbifolds. The main results are the construction of the universal orbifold covering space and Poincare's fundamental polyhedron theorem.

Author : Henryk Zoladek
Publisher : Springer Science & Business Media
Page : 589 pages
File Size : 49,9 Mb
Release : 2006-08-10
Category : Mathematics
ISBN : 9783764375362

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The Monodromy Group by Henryk Zoladek Pdf

In singularity theory and algebraic geometry, the monodromy group is embodied in the Picard-Lefschetz formula and the Picard-Fuchs equations. It has applications in the weakened 16th Hilbert problem and in mixed Hodge structures. There is a deep connection of monodromy theory with Galois theory of differential equations and algebraic functions. In covering these and other topics, this book underlines the unifying role of the monogropy group.

Author : Michael Grinfeld
Publisher : John Wiley & Sons
Page : 634 pages
File Size : 41,7 Mb
Release : 2015-01-12
Category : Science
ISBN : 9783527411887

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Mathematical Tools for Physicists by Michael Grinfeld Pdf

The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

Author : Thomas Hawkins
Publisher : Springer Science & Business Media
Page : 578 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461212027

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Emergence of the Theory of Lie Groups by Thomas Hawkins Pdf

The great Norwegian mathematician Sophus Lie developed the general theory of transformations in the 1870s, and the first part of the book properly focuses on his work. In the second part the central figure is Wilhelm Killing, who developed structure and classification of semisimple Lie algebras. The third part focuses on the developments of the representation of Lie algebras, in particular the work of Elie Cartan. The book concludes with the work of Hermann Weyl and his contemporaries on the structure and representation of Lie groups which serves to bring together much of the earlier work into a coherent theory while at the same time opening up significant avenues for further work.

Author : Jeremy Gray
Publisher : Unknown
Page : 0 pages
File Size : 45,8 Mb
Release : 1986
Category : Differential equations, Linear
ISBN : OCLC:1345631292

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Linear Differential Equations and Group Theory from Riemann to Poincar{acute}e by Jeremy Gray Pdf

Author : Ivor Grattan-Guiness
Publisher : Routledge
Page : 571 pages
File Size : 42,5 Mb
Release : 2004-11-11
Category : History
ISBN : 9781134887552

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Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences by Ivor Grattan-Guiness Pdf

First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.

Author : Umberto Bottazzini,Jeremy Gray
Publisher : Springer Science & Business Media
Page : 848 pages
File Size : 52,6 Mb
Release : 2013-06-21
Category : Mathematics
ISBN : 9781461457251

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Hidden Harmony—Geometric Fantasies by Umberto Bottazzini,Jeremy Gray Pdf

​This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject – Cauchy, Riemann, and Weierstrass – it looks at the contributions of authors from d’Alembert to Hilbert, and Laplace to Weyl. Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory.​

Author : Jaume Navarro
Publisher : Oxford University Press
Page : 272 pages
File Size : 43,8 Mb
Release : 2018-08-30
Category : Science
ISBN : 9780192517791

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Ether and Modernity by Jaume Navarro Pdf

Ether and Modernity offers a snapshot of the status of an epistemic object, the "ether" (or "aether"), in the early twentieth century. The contributed papers show that the ether was often regarded as one of the objects of modernity, hand in hand with the electron, radioactivity or X-rays, and not simply as the stubborn residue of an old-fashioned, long-discarded science. The prestige and authority of scientists and popularisers like Oliver Lodge and Arthur Eddington in Britain, Phillip Lenard in Germany or Dayton C. Miller in the USA was instrumental in the preservation, defence or even re-emergence of the ether in the 1920s. Moreover, the consolidation of wireless communications and radio broadcasting, indeed a very modern technology, brought the ether into audiences that would otherwise never have heard about such an esoteric entity. The ether also played a pivotal role among some artists in the early twentieth century: the values of modernism found in the complexities and contradictions of modern physics, such as wireless action or wave-particle puzzles, a fertile ground for the development of new artistic languages; in literature as much as in the pictorial and performing arts. Essays on the intellectual foundations of Umberto Boccioni's art, the linguistic techniques of Lodge, and Ernst Mach's considerations on aesthetics and physics witness to the imbricate relationship between the ether and modernism. Last but not least, the ether played a fundamental part in the resurgence of modern spiritualism in the aftermath of the Great War. This book examines the complex array of meanings, strategies and milieus that enabled the ether to remain an active part in scientific and cultural debates well into the 1930s, but not beyond. This portrait may be easily regarded as the swan song of an epistemic object that was soon to fade away as shown by Paul Dirac's unsuccessful attempt to resuscitate some kind of aether in 1951, with which this book finishes.

Author : Albert Marden
Publisher : Cambridge University Press
Page : 535 pages
File Size : 51,6 Mb
Release : 2016-02
Category : Mathematics
ISBN : 9781107116740

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Hyperbolic Manifolds by Albert Marden Pdf

This study of hyperbolic geometry has both pedagogy and research in mind, and includes exercises and further reading for each chapter.

Author : I.M. James
Publisher : Elsevier
Page : 1067 pages
File Size : 45,9 Mb
Release : 1999-08-24
Category : Mathematics
ISBN : 9780080534077

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History of Topology by I.M. James Pdf

Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.

Author : A.N. Kolmogorov,A.P. Yushkevich
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 50,5 Mb
Release : 1998-03-24
Category : Mathematics
ISBN : 3764358459

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Mathematics of the 19th Century by A.N. Kolmogorov,A.P. Yushkevich Pdf

The editors of the present series had originally intended to publish an integrated work on the history of mathematics in the nineteenth century, passing systemati cally from one discipline to another in some natural order. Circumstances beyond their control, mainly difficulties in choosing authors, led to the abandonment of this plan by the time the second volume appeared. Instead of a unified mono graph we now present to the reader a series of books intended to encompass all the mathematics of the nineteenth century, but not in the order of the accepted classification of the component disciplines. In contrast to the first two books of The Mathematics of the Nineteenth Century, which were divided into chapters, this third volume consists of four parts, more in keeping with the nature of the publication. 1 We recall that the first book contained essays on the history of mathemati 2 cal logic, algebra, number theory, and probability, while the second covered the history of geometry and analytic function theory. In the present third volume the reader will find: 1. An essay on the development of Chebyshev's theory of approximation of functions, later called "constructive function theory" by S. N. Bernshtein. This highly original essay is due to the late N. I. Akhiezer (1901-1980), the author of fundamental discoveries in this area. Akhiezer's text will no doubt attract attention not only from historians of mathematics, but also from many specialists in constructive function theory.