Download or read book Seifert and Threlfall A Textbook of Topology written by and published by Academic Press. This book was released on 1980-07-04 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seifert and Threlfall, A Textbook of Topology

Download or read book History of Topology written by I.M. James and published by Elsevier. This book was released on 1999-08-24 with total page 1067 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book A Panorama of Pure Mathematics As Seen by N Bourbaki written by and published by Academic Press. This book was released on 1982-08-18 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Panorama of Pure Mathematics, As Seen by N. Bourbaki

Download or read book The Calculus of Variations in the Large written by Marston Morse and published by American Mathematical Soc.. This book was released on 1934-12-31 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Morse theory is a study of deep connections between analysis and topology. In its classical form, it provides a relationship between the critical points of certain smooth functions on a manifold and the topology of the manifold. It has been used by geometers, topologists, physicists, and others as a remarkably effective tool to study manifolds. In the 1980s and 1990s, Morse theory was extended to infinite dimensions with great success. This book is Morse's own exposition of his ideas. It has been called one of the most important and influential mathematical works of the twentieth century. Calculus of Variations in the Large is certainly one of the essential references on Morse theory.

Download or read book Algebraic Topology written by Smail Djebali and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-11-18 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the textbook is two-fold: first to serve as an introductory graduate course in Algebraic Topology and then to provide an application-oriented presentation of some fundamental concepts in Algebraic Topology to the fixed point theory. A simple approach based on point-set Topology is used throughout to introduce many standard constructions of fundamental and homological groups of surfaces and topological spaces. The approach does not rely on Homological Algebra. The constructions of some spaces using the quotient spaces such as the join, the suspension, and the adjunction spaces are developed in the setting of Topology only. The computations of the fundamental and homological groups of many surfaces and topological spaces occupy large parts of the book (sphere, torus, projective space, Mobius band, Klein bottle, manifolds, adjunctions spaces). Borsuk's theory of retracts which is intimately related to the problem of the extendability of continuous functions is developed in details. This theory together with the homotopy theory, the lifting and covering maps may serve as additional course material for students involved in General Topology. The book comprises 280 detailed worked examples, 320 exercises (with hints or references), 80 illustrative figures, and more than 80 commutative diagrams to make it more oriented towards applications (maps between spheres, Borsuk-Ulam Theory, Fixed Point Theorems, ...) As applications, the book offers some existence results on the solvability of some nonlinear differential equations subject to initial or boundary conditions. The book is suitable for students primarily enrolled in Algebraic Topology, General Topology, Homological Algebra, Differential Topology, Differential Geometry, and Topological Geometry. It is also useful for advanced undergraduate students who aspire to grasp easily some new concepts in Algebraic Topology and Applications. The textbook is practical both as a teaching and research document for Bachelor, Master students, and first-year PhD students since it is accessible to any reader with a modest understanding of topological spaces. The book aspires to fill a gap in the existing literature by providing a research and teaching document which investigates both the theory and the applications of Algebraic Topology in an accessible way without missing the main results of the topics covered.

Download or read book Topological Library written by Serge? Petrovich Novikov and published by World Scientific. This book was released on 2012 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: The final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in 1950-60s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950. That is, from Serre's celebrated "singular homologies of fiber spaces."

Download or read book The Poincare Conjecture written by James Carlson and published by American Mathematical Soc.. This book was released on 2014-10-16 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conference to celebrate the resolution of the Poincare conjecture, which is one of the Clay Mathematics Institute's seven Millennium Prize Problems, was held at the Institut Henri Poincare in Paris. Several leading mathematicians gave lectures providing an overview of the conjecture--its history, its influence on the development of mathematics, and, finally, its proof. This volume contains papers based on the lectures at that conference. Taken together, they form an extraordinary record of the work that went into the solution of one of the great problems of mathematics.

Download or read book Formal Power Series and Algebraic Combinatorics written by Daniel Krob and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 815 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the extended abstracts presented at the 12th International Conference on Power Series and Algebraic Combinatorics (FPSAC '00) that took place at Moscow State University, June 26-30, 2000. These proceedings cover the most recent trends in algebraic and bijective combinatorics, including classical combinatorics, combinatorial computer algebra, combinatorial identities, combinatorics of classical groups, Lie algebra and quantum groups, enumeration, symmetric functions, young tableaux etc...

Download or read book Topics in Geometric Group Theory written by Pierre de la Harpe and published by University of Chicago Press. This book was released on 2000-09-15 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.

Download or read book Topological Library Part 3 Spectral Sequences In Topology written by Serguei Petrovich Novikov and published by World Scientific. This book was released on 2012-07-25 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: The final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in the 1950s-1960s. The partition of these papers among the volumes is rather conditional. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950. That is, from Serre's celebrated “singular homologies of fiber spaces.”

Download or read book Advances in Topological Quantum Field Theory written by John M. Bryden and published by Springer Science & Business Media. This book was released on 2007-09-27 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the conference proceedings of the NATO ARW during August 2001 at Kananaskis Village, Canada on 'New Techniques in Topological Quantum Field Theory'. This conference brought together specialists from a number of different fields all related to Topological Quantum Field Theory. The theme of this conference was to attempt to find new methods in quantum topology from the interaction with specialists in these other fields. The featured articles include papers by V. Vassiliev on combinatorial formulas for cohomology of spaces of Knots, the computation of Ohtsuki series by N. Jacoby and R. Lawrence, and a paper by M. Asaeda and J. Przytycki on the torsion conjecture for Khovanov homology by Shumakovitch. Moreover, there are articles on more classical topics related to manifolds and braid groups by such well known authors as D. Rolfsen, H. Zieschang and F. Cohen.

Download or read book Mathematicians under the Nazis written by Sanford L. Segal and published by Princeton University Press. This book was released on 2014-11-23 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contrary to popular belief--and despite the expulsion, emigration, or death of many German mathematicians--substantial mathematics was produced in Germany during 1933-1945. In this landmark social history of the mathematics community in Nazi Germany, Sanford Segal examines how the Nazi years affected the personal and academic lives of those German mathematicians who continued to work in Germany. The effects of the Nazi regime on the lives of mathematicians ranged from limitations on foreign contact to power struggles that rattled entire institutions, from changed work patterns to military draft, deportation, and death. Based on extensive archival research, Mathematicians under the Nazis shows how these mathematicians, variously motivated, reacted to the period's intense political pressures. It details the consequences of their actions on their colleagues and on the practice and organs of German mathematics, including its curricula, institutions, and journals. Throughout, Segal's focus is on the biographies of individuals, including mathematicians who resisted the injection of ideology into their profession, some who worked in concentration camps, and others (such as Ludwig Bieberbach) who used the "Aryanization" of their profession to further their own agendas. Some of the figures are no longer well known; others still tower over the field. All lived lives complicated by Nazi power. Presenting a wealth of previously unavailable information, this book is a large contribution to the history of mathematics--as well as a unique view of what it was like to live and work in Nazi Germany.

Download or read book Introduction to Global Analysis written by and published by Academic Press. This book was released on 1980-09-19 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Global Analysis

Download or read book Smooth Dynamical Systems written by and published by Academic Press. This book was released on 1980-08-12 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Smooth Dynamical Systems

Download or read book An Introduction to Nonharmonic Fourier Series written by and published by Academic Press. This book was released on 1981-01-09 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Nonharmonic Fourier Series

Download or read book System Theory written by and published by Academic Press. This book was released on 1982-09-08 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: System Theory

Download or read book The Shape of Space written by Jeffrey R. Weeks and published by CRC Press. This book was released on 2020-01-14 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Shape of Space, Third Edition maintains the standard of excellence set by the previous editions. This lighthearted textbook covers the basic geometry and topology of two- and three-dimensional spaces—stretching students’ minds as they learn to visualize new possibilities for the shape of our universe. Written by a master expositor, leading researcher in the field, and MacArthur Fellow, its informal exposition and engaging exercises appeal to an exceptionally broad audience, from liberal arts students to math undergraduate and graduate students looking for a clear intuitive understanding to supplement more formal texts, and even to laypeople seeking an entertaining self-study book to expand their understanding of space. Features of the Third Edition: Full-color figures throughout "Picture proofs" have replaced algebraic proofs Simpler handles-and-crosscaps approach to surfaces Updated discussion of cosmological applications Intuitive examples missing from many college and graduate school curricula About the Author: Jeffrey R. Weeks is a freelance geometer living in Canton, New York. With support from the U.S. National Science Foundation, the MacArthur Foundation and several science museums, his work spans pure mathematics, applications in cosmology and—closest to his heart—exposition for the general public.