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lgli/K:\_add\2\kolxoz\78\78\M_Mathematics\MD_Geometry and topology\MDat_Algebraic and differential topology\Roe J. Winding around. The winding number in topology, geometry, and analysis (AMS, 2015)(ISBN 9781470421984)(600dpi)(K)(T)(O)(287s)_MDat_.djvu
Winding Around: The Winding Number in Topology, Geometry, and Analysis (Student Mathematical Library) 🔍
Roe, John American Mathematical Society [AMS] & Mathematics Advanced Study Semesters, The Student Mathematical Library, Student Mathematical Library, 2015
English [en] · Shona [sn] · DJVU · 2.5MB · 2015 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save
description
The winding number is one of the most basic invariants in topology. It measures the number of times a moving point $P$ goes around a fixed point $Q$, provided that $P$ travels on a path that never goes through $Q$ and that the final position of $P$ is the same as its starting position. This simple idea has far-reaching applications. The reader of this book will learn how the winding number can help us show that every polynomial equation has a root (the fundamental theorem of algebra), guarantee a fair division of three objects in space by a single planar cut (the ham sandwich theorem), explain why every simple closed curve has an inside and an outside (the Jordan curve theorem), relate calculus to curvature and the singularities of vector fields (the Hopf index theorem), allow one to subtract infinity from infinity and get a finite answer (Toeplitz operators), generalize to give a fundamental and beautiful insight into the topology of matrix groups (the Bott periodicity theorem). All these subjects and more are developed starting only from mathematics that is common in final-year undergraduate courses. This book is published in cooperation with Mathematics Advanced Study Semesters.
Alternative filename
lgrsnf/K:\_add\2\kolxoz\78\78\M_Mathematics\MD_Geometry and topology\MDat_Algebraic and differential topology\Roe J. Winding around. The winding number in topology, geometry, and analysis (AMS, 2015)(ISBN 9781470421984)(600dpi)(K)(T)(O)(287s)_MDat_.djvu
Alternative filename
lgli/M_Mathematics/MD_Geometry and topology/MDat_Algebraic and differential topology/Roe J. Winding around.. The winding number in topology, geometry, and analysis (STML076, AMS, 2015)(ISBN 9781470421984)(600dpi)(K)(T)(O)(287s)_MDat_.djvu
Alternative filename
nexusstc/Winding Around/aa7680aa057e09d9dba083601b88ca49.djvu
Alternative title
WINDING AROUND [Paperback] John Roe
Alternative author
John Roe
Alternative publisher
Education Development Center, Incorporated
Alternative publisher
ORIENT BLACKSWAN
Alternative edition
Student mathematical library -- volume 76, Providence, Rhode Island, Rhode Island, 2015
Alternative edition
Student mathematical library (Online), Providence (R.I.), 2015
Alternative edition
American Mathematical Society, Providence, Rhode Island, 2015
Alternative edition
Student Mathematical Library, 76, 1, 2015
Alternative edition
United States, United States of America
Alternative edition
1st, First Edition, PS, 2017
Alternative edition
FR, 2015
metadata comments
kolxoz -- 78
metadata comments
lg1505958
metadata comments
{"container_title":"The Student Mathematical Library","isbns":["1470421984","1470426250","9781470421984","9781470426255"],"issns":["1520-9121"],"last_page":269,"publisher":"American Mathematical Society","series":"Student Mathematical Library"}
metadata comments
Includes bibliographical references and index.
Alternative description
The winding number is one of the most basic invariants in topology. It measures the number of times a moving point PP goes around a fixed point QQ, provided that PP travels on a path that never goes through QQ and that the final position of PP is the same as its starting position. This simple idea has far-reaching applications. The reader of this book will learn how the winding number can help us show that every polynomial equation has a root (the fundamental theorem of algebra), guarantee a fair division of three objects in space by a single planar cut (the ham sandwich theorem), explain why every simple closed curve has an inside and an outside (the Jordan curve theorem), relate calculus to curvature and the singularities of vector fields (the Hopf index theorem), allow one to subtract infinity from infinity and get a finite answer (Toeplitz operators), generalize to give a fundamental and beautiful insight into the topology of matrix groups (the Bott periodicity theorem). All these subjects and more are developed starting only from mathematics that is common in final-year undergraduate courses
Alternative description
Prelude: Love, Hate, And Exponentials -- Paths And Homotopies -- The Winding Number -- Topology Of The Plane -- Integrals And The Winding Number -- Vector Fields And The Rotation Number -- The Winding Number In Functional Analysis -- Coverings And The Fundamental Group -- Coda: The Bott Periodicity Theorem -- Appendix A: Linear Algebra -- Appendix B: Metric Spaces -- Appendix C: Extension And Approximation Theorems -- Appendix D: Measure Zero -- Appendix E: Calculus On Normed Spaces -- Appendix F: Hilbert Space -- Appendix G: Groups And Graphs. John Roe. Includes Bibliographical References And Index.
Alternative description
Content: Prelude: Love, Hate, and Exponentials --
Paths and Homotopies --
The Winding Number --
Topology of the Plane --
Integrals and the Winding Number --
Vector Fields and the Rotation Number --
The Winding Number in Functional Analysis --
Coverings and the Fundamental Group --
Coda: The Bott Periodicity Theorem --
Appendix A: Linear Algebra --
Appendix B: Metric Spaces --
Appendix C: Extension and Approximation Theorems --
Appendix D: Measure Zero --
Appendix E: Calculus on Normed Spaces --
Appendix F: Hilbert Space --
Appendix G: Groups and Graphs.
Alternative description
Please Read Brand New, International Softcover Edition, Printed in black and white pages, minor self wear on the cover or pages, Sale restriction may be printed on the book, but Book name, contents, and author are exactly same as Hardcover Edition. Fast delivery through DHL/FedEx express.
date open sourced
2016-05-22
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