Topologie G N Rale Et Espaces Norm S 2e D
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Introduction To Knot Theory
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Author : R. H. Crowell
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Knot Theory written by R. H. Crowell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Knot theory is a kind of geometry, and one whose appeal is very direct because the objects studied are perceivable and tangible in everyday physical space. It is a meeting ground of such diverse branches of mathematics as group theory, matrix theory, number theory, algebraic geometry, and differential geometry, to name some of the more prominent ones. It had its origins in the mathematical theory of electricity and in primitive atomic physics, and there are hints today of new applications in certain branches of chemistryJ The outlines of the modern topological theory were worked out by Dehn, Alexander, Reidemeister, and Seifert almost thirty years ago. As a subfield of topology, knot theory forms the core of a wide range of problems dealing with the position of one manifold imbedded within another. This book, which is an elaboration of a series of lectures given by Fox at Haverford College while a Philips Visitor there in the spring of 1956, is an attempt to make the subject accessible to everyone. Primarily it is a text book for a course at the junior-senior level, but we believe that it can be used with profit also by graduate students. Because the algebra required is not the familiar commutative algebra, a disproportionate amount of the book is given over to necessary algebraic preliminaries.
The Homology Of Iterated Loop Spaces
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Author : F. R. Cohen
language : en
Publisher: Springer
Release Date : 2007-01-05
The Homology Of Iterated Loop Spaces written by F. R. Cohen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-05 with Mathematics categories.
Architecture For The Dead Cairo S Medieval Necropolis
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Author : Galila El Kadi
language : en
Publisher: American Univ in Cairo Press
Release Date : 2007
Architecture For The Dead Cairo S Medieval Necropolis written by Galila El Kadi and has been published by American Univ in Cairo Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Architecture categories.
The great medieval necropolis of Cairo, comprising two main areas that together stretch twelve kilometers from north to south, constitutes a major feature of the city's urban landscape. With monumental and smaller-scale mausolea dating from all eras since early medieval times, and boasting some of the finest examples of Mamluk architecture not just in the city but in the region, the necropolis is an unparalleled--and until now largely undocumented--architectural treasure trove. In Architecture for the Dead, architect Galila El Kadi and photographer Alain Bonnamy have produced a comprehensive and visually stunning survey of all areas of the necropolis. Through detailed and painstaking research and remarkable photography, in text, maps, plans, and pictures, they describe and illustrate the astonishing variety of architectural styles in the necropolis: from Mamluk to neo-Mamluk via baroque and neo-pharaonic, from the grandest stone buildings with their decorative domes and minarets to the humblest--but elaborately decorated--wooden structures. The book also documents the modern settlement of the necropolis by families creating a space for the living in and among the tombs and architecture for the dead.
An Introduction To Knot Theory
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Author : W.B.Raymond Lickorish
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
An Introduction To Knot Theory written by W.B.Raymond Lickorish and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A selection of topics which graduate students have found to be a successful introduction to the field, employing three distinct techniques: geometric topology manoeuvres, combinatorics, and algebraic topology. Each topic is developed until significant results are achieved and each chapter ends with exercises and brief accounts of the latest research. What may reasonably be referred to as knot theory has expanded enormously over the last decade and, while the author describes important discoveries throughout the twentieth century, the latest discoveries such as quantum invariants of 3-manifolds as well as generalisations and applications of the Jones polynomial are also included, presented in an easily intelligible style. Readers are assumed to have knowledge of the basic ideas of the fundamental group and simple homology theory, although explanations throughout the text are numerous and well-done. Written by an internationally known expert in the field, this will appeal to graduate students, mathematicians and physicists with a mathematical background wishing to gain new insights in this area.
The Topological Classification Of Stratified Spaces
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Author : Shmuel Weinberger
language : en
Publisher: University of Chicago Press
Release Date : 1994
The Topological Classification Of Stratified Spaces written by Shmuel Weinberger and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This book provides the theory for stratified spaces, along with important examples and applications, that is analogous to the surgery theory for manifolds. In the first expository account of this field, Weinberger provides topologists with a new way of looking at the classification theory of singular spaces with his original results. Divided into three parts, the book begins with an overview of modern high-dimensional manifold theory. Rather than including complete proofs of all theorems, Weinberger demonstrates key constructions, gives convenient formulations, and shows the usefulness of the technology. Part II offers the parallel theory for stratified spaces. Here, the topological category is most completely developed using the methods of "controlled topology." Many examples illustrating the topological invariance and noninvariance of obstructions and characteristic classes are provided. Applications for embeddings and immersions of manifolds, for the geometry of group actions, for algebraic varieties, and for rigidity theorems are found in Part III. This volume will be of interest to topologists, as well as mathematicians in other fields such as differential geometry, operator theory, and algebraic geometry.
Emerging Applications Of Algebraic Geometry
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Author : Mihai Putinar
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-10
Emerging Applications Of Algebraic Geometry written by Mihai Putinar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-10 with Mathematics categories.
Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research. The articles in this volume highlight a range of these applications and provide introductory material for topics covered in the IMA workshops on "Optimization and Control" and "Applications in Biology, Dynamics, and Statistics" held during the IMA year on Applications of Algebraic Geometry. The articles related to optimization and control focus on burgeoning use of semidefinite programming and moment matrix techniques in computational real algebraic geometry. The new direction towards a systematic study of non-commutative real algebraic geometry is well represented in the volume. Other articles provide an overview of the way computational algebra is useful for analysis of contingency tables, reconstruction of phylogenetic trees, and in systems biology. The contributions collected in this volume are accessible to non-experts, self-contained and informative; they quickly move towards cutting edge research in these areas, and provide a wealth of open problems for future research.
Handbook Of The History Of General Topology
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Author : C.E. Aull
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
Handbook Of The History Of General Topology written by C.E. Aull and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.
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.
Physics On Manifolds
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Author : M. Flato
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Physics On Manifolds written by M. Flato and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume contains the proceedings of the Colloquium "Analysis, Manifolds and Physics" organized in honour of Yvonne Choquet-Bruhat by her friends, collaborators and former students, on June 3, 4 and 5, 1992 in Paris. Its title accurately reflects the domains to which Yvonne Choquet-Bruhat has made essential contributions. Since the rise of General Relativity, the geometry of Manifolds has become a non-trivial part of space-time physics. At the same time, Functional Analysis has been of enormous importance in Quantum Mechanics, and Quantum Field Theory. Its role becomes decisive when one considers the global behaviour of solutions of differential systems on manifolds. In this sense, General Relativity is an exceptional theory in which the solutions of a highly non-linear system of partial differential equations define by themselves the very manifold on which they are supposed to exist. This is why a solution of Einstein's equations cannot be physically interpreted before its global behaviour is known, taking into account the entire hypothetical underlying manifold. In her youth, Yvonne Choquet-Bruhat contributed in a spectacular way to this domain stretching between physics and mathematics, when she gave the proof of the existence of solutions to Einstein's equations on differential manifolds of a quite general type. The methods she created have been worked out by the French school of mathematics, principally by Jean Leray. Her first proof of the local existence and uniqueness of solutions of Einstein's equations inspired Jean Leray's theory of general hyperbolic systems.
Nondifferentiable Optimization
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Author : V.F. Dem'yanov
language : en
Publisher: Springer
Release Date : 1985-12-12
Nondifferentiable Optimization written by V.F. Dem'yanov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-12-12 with Science categories.
Of recent coinage, the term "nondifferentiable optimization" (NDO) covers a spectrum of problems related to finding extremal values of nondifferentiable functions. Problems of minimizing nonsmooth functions arise in engineering applications as well as in mathematics proper. The Chebyshev approximation problem is an ample illustration of this. Without loss of generality, we shall consider only minimization problems. Among nonsmooth minimization problems, minimax problems and convex problems have been studied extensively ([31], [36], [57], [110], [120]). Interest in NDO has been constantly growing in recent years (monographs: [30], [81], [127] and articles and papers: [14], [20], [87]-[89], [98], [130], [135], [140]-[142], [152], [153], [160], all dealing with various aspects of non smooth optimization). For solving an arbitrary minimization problem, it is neces sary to: 1. Study properties of the objective function, in particular, its differentiability and directional differentiability. 2. Establish necessary (and, if possible, sufficient) condi tions for a global or local minimum. 3. Find the direction of descent (steepest or, simply, feasible--in appropriate sense). 4. Construct methods of successive approximation. In this book, the minimization problems for nonsmooth func tions of a finite number of variables are considered. Of fun damental importance are necessary conditions for an extremum (for example, [24], [45], [57], [73], [74], [103], [159], [163], [167], [168].
Mathematics And Technology
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Author : Christiane Rousseau
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-29
Mathematics And Technology written by Christiane Rousseau and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-29 with Mathematics categories.
This book introduces the student to numerous modern applications of mathematics in technology. The authors write with clarity and present the mathematics in a clear and straightforward way making it an interesting and easy book to read. Numerous exercises at the end of every section provide practice and reinforce the material in the chapter. An engaging quality of this book is that the authors also present the mathematical material in a historical context and not just the practical one. Mathematics and Technology is intended for undergraduate students in mathematics, instructors and high school teachers. Additionally, its lack of calculus centricity as well as a clear indication of the more difficult topics and relatively advanced references make it suitable for any curious individual with a decent command of high school math.