A History of Algebraic and Differential Topology, 1900 - 1960

A History of Algebraic and Differential Topology, 1900 - 1960 PDF

Author: Jean Dieudonné

Publisher: Springer Science & Business Media

Published: 2009-09-01

Total Pages: 648

ISBN-13: 0817649077

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This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet

A History of Algebraic and Differential Topology, 1900 - 1960

A History of Algebraic and Differential Topology, 1900 - 1960 PDF

Author: Jean Dieudonné

Publisher: Birkhäuser

Published: 2009-06-09

Total Pages: 648

ISBN-13: 9780817649067

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This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet

History of Topology

History of Topology PDF

Author: I.M. James

Publisher: Elsevier

Published: 1999-08-24

Total Pages: 1067

ISBN-13: 0080534074

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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.

Algebraic and Differential Topology of Robust Stability

Algebraic and Differential Topology of Robust Stability PDF

Author: Edmond A. Jonckheere

Publisher: Oxford University Press, USA

Published: 1997

Total Pages: 625

ISBN-13: 0195093011

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In this book, two seemingly unrelated fields - algebraic topology and robust control - are brought together. The book develops algebraic/differential topology proceeding from an easily motivated control engineering problem, showing the relevance of advanced topological concepts and reconstructing the fundamental concepts of algebraic/differential topology from an application-oriented point of view. It is suitable for graduate students in engineering and/or applied mathematics, and academic researchers.

Basic Algebraic Topology and its Applications

Basic Algebraic Topology and its Applications PDF

Author: Mahima Ranjan Adhikari

Publisher: Springer

Published: 2016-09-16

Total Pages: 615

ISBN-13: 813222843X

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This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.

Handbook of the History of General Topology

Handbook of the History of General Topology PDF

Author: C.E. Aull

Publisher: Springer Science & Business Media

Published: 2013-04-18

Total Pages: 418

ISBN-13: 9401704708

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This book is the first one of a work in several volumes, treating the history of the development of topology. The work contains papers which can be classified into 4 main areas. Thus there are contributions dealing with the life and work of individual topologists, with specific schools of topology, with research in topology in various countries, and with the development of topology in different periods. The work is not restricted to topology in the strictest sense but also deals with applications and generalisations in a broad sense. Thus it also treats, e.g., categorical topology, interactions with functional analysis, convergence spaces, and uniform spaces. Written by specialists in the field, it contains a wealth of information which is not available anywhere else.

Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry

Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry PDF

Author: Jean H Gallier

Publisher: World Scientific

Published: 2022-01-19

Total Pages: 799

ISBN-13: 9811245045

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For more than thirty years the senior author has been trying to learn algebraic geometry. In the process he discovered that many of the classic textbooks in algebraic geometry require substantial knowledge of cohomology, homological algebra, and sheaf theory. In an attempt to demystify these abstract concepts and facilitate understanding for a new generation of mathematicians, he along with co-author wrote this book for an audience who is familiar with basic concepts of linear and abstract algebra, but who never has had any exposure to the algebraic geometry or homological algebra. As such this book consists of two parts. The first part gives a crash-course on the homological and cohomological aspects of algebraic topology, with a bias in favor of cohomology. The second part is devoted to presheaves, sheaves, Cech cohomology, derived functors, sheaf cohomology, and spectral sequences. All important concepts are intuitively motivated and the associated proofs of the quintessential theorems are presented in detail rarely found in the standard texts.

The Emergence of the American Mathematical Research Community, 1876-1900

The Emergence of the American Mathematical Research Community, 1876-1900 PDF

Author: Karen Hunger Parshall

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 532

ISBN-13: 9780821809075

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Cover -- Title page -- Contents -- Preface -- Acknowledgments -- Photograph and Figure Credits -- Chapter 1. An overview of American mathematics: 1776-1876 -- Chapter 2. A new departmental prototype: J.J. Sylvester and the Johns Hopkins University -- Chapter 3. Mathematics at Sylvester's Hopkins -- Chapter 4. German mathematics and the early mathematical career of Felix Klein -- Chapter 5. America's wanderlust generation -- Chapter 6. Changes on the horizon -- Chapter 7. The World's Columbian exposition of 1893 and the Chicago mathematical congress -- Chapter 8. Surveying mathematical landscapes: The Evanston colloquium lectures -- Chapter 9. Meeting the challenge: The University of Chicago and the American mathematical research community -- Chapter 10. Epilogue: Beyond the threshold: The American mathematical research community, 1900-1933 -- Bibliography -- Subject Index -- Back Cover

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