A Taste Of Topology
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A Taste Of Topology
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Author : Volker Runde
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-07
A Taste Of Topology written by Volker Runde 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 2007-12-07 with Mathematics categories.
This should be a revelation for mathematics undergraduates. Having evolved from Runde’s notes for an introductory topology course at the University of Alberta, this essential text provides a concise introduction to set-theoretic topology, as well as some algebraic topology. It is accessible to undergraduates from the second year on, and even beginning graduate students can benefit from some sections. The well-chosen selection of examples is accessible to students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis. In places, Runde’s text treats its material differently to other books on the subject, providing a fresh perspective.
Experiments In Topology
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Author : Stephen Barr
language : en
Publisher: Courier Corporation
Release Date : 2012-12-04
Experiments In Topology written by Stephen Barr and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-04 with Mathematics categories.
Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.
Elementary Topology
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Author : O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
language : en
Publisher: American Mathematical Soc.
Release Date :
Elementary Topology written by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
This text contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment. Proofs of theorems are separated from their formulations and are gathered at the end of each chapter, making this book appear like a problem book and also giving it appeal to the expert as a handbook. The book includes about 1,000 exercises.
A Topological Aperitif
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Author : Stephen Huggett
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
A Topological Aperitif written by Stephen Huggett 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 2013-03-09 with Mathematics categories.
This book takes a new look at the subject, choosing a geometric approach rather than the usual algebraic or combinatorial approach. It starts with a wealth of examples of how to be mathematically certain whether two objects are the same from the point of view of topology. After introducing surfaces, the book explores the properties of polyhedra drawn on these surfaces. More refined tools are developed in a chapter on winding number.
Real Mathematical Analysis
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Author : Charles Chapman Pugh
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-19
Real Mathematical Analysis written by Charles Chapman Pugh 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 2013-03-19 with Mathematics categories.
Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.
Topology And The Language Of Mathematics
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Author : Chris Cunliffe
language : en
Publisher: Bobo Strategy
Release Date : 2008-07
Topology And The Language Of Mathematics written by Chris Cunliffe and has been published by Bobo Strategy this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07 with Mathematics categories.
An introduction to topology and the language of mathematics that works. Ideal for the undergraduate student with little to no background in the subject. Excellent for the advanced high school mathematics student, interested in a taste of next steps. Also useful to graduate students looking for a refresher or fresh take on their foundation in the topics.
Selected Applications Of Geometry To Low Dimensional Topology
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Author : Michael H. Freedman
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Selected Applications Of Geometry To Low Dimensional Topology written by Michael H. Freedman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
The inaugural volume in the popular AMS softcover series designed to make more widely available some of the outstanding lectures presented by various faculty in North America.
Classical Topology And Combinatorial Group Theory
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Author : John Stillwell
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Classical Topology And Combinatorial Group Theory written by John Stillwell 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.
In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l'isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec tions to other parts of mathematics which make topology an important as well as a beautiful subject.
Virtual Topology And Functor Geometry
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Author : Fred Van Oystaeyen
language : en
Publisher: CRC Press
Release Date : 2007-11-15
Virtual Topology And Functor Geometry written by Fred Van Oystaeyen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-15 with Mathematics categories.
Intrinsically noncommutative spaces today are considered from the perspective of several branches of modern physics, including quantum gravity, string theory, and statistical physics. From this point of view, it is ideal to devise a concept of space and its geometry that is fundamentally noncommutative. Providing a clear introduction to noncommutative topology, Virtual Topology and Functor Geometry explores new aspects of these areas as well as more established facets of noncommutative algebra. Presenting the material in an easy, colloquial style to facilitate understanding, the book begins with an introduction to category theory, followed by a chapter on noncommutative spaces. This chapter examines noncommutative lattices, noncommutative opens, sheaf theory, the generalized Stone space, and Grothendieck topology. The author then studies Grothendieck categorical representations to formulate an abstract notion of "affine open". The final chapter proposes a dynamical version of topology and sheaf theory, providing at least one solution of the problem of sheafification independent of generalizations of topos theory. By presenting new ideas for the development of an intrinsically noncommutative geometry, this book fosters the further unification of different kinds of noncommutative geometry and the expression of observations that involve natural phenomena.
Algebraic Topology
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Author : Edwin H. Spanier
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic Topology written by Edwin H. Spanier 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 book surveys the fundamental ideas of algebraic topology. The first part covers the fundamental group, its definition and application in the study of covering spaces. The second part turns to homology theory including cohomology, cup products, cohomology operations and topological manifolds. The final part is devoted to Homotropy theory, including basic facts about homotropy groups and applications to obstruction theory.