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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.
Book Synopsis Winding Around by : John Roe
Download or read book Winding Around written by John Roe and published by American Mathematical Soc.. This book was released on 2015-09-03 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
The American Journal of Mathematics publishes research papers and articles of broad appeal covering the major areas of contemporary mathematics.
Book Synopsis American Journal of Mathematics by :
Download or read book American Journal of Mathematics written by and published by . This book was released on 1899 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The American Journal of Mathematics publishes research papers and articles of broad appeal covering the major areas of contemporary mathematics.
Reproduction of the original: Hawkins Electrical Guide Number Two, Questions, Answers and Illustrations by Hawkins and Staff
Book Synopsis Hawkins Electrical Guide Number Two, Questions, Answers and Illustrations by : Hawkins and Staff
Download or read book Hawkins Electrical Guide Number Two, Questions, Answers and Illustrations written by Hawkins and Staff and published by BoD – Books on Demand. This book was released on 2020-08-03 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reproduction of the original: Hawkins Electrical Guide Number Two, Questions, Answers and Illustrations by Hawkins and Staff
Download or read book The Overland Monthly written by and published by . This book was released on 1899 with total page 1172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pedestrian and general guide to the Lake district by : Herman Ludolph Prior
Download or read book Pedestrian and general guide to the Lake district written by Herman Ludolph Prior and published by . This book was released on 1881 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Individual Production Rating by : John Clifford Shover
Download or read book Individual Production Rating written by John Clifford Shover and published by . This book was released on 1926 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific Canadian Mechanics' Magazine and Patent Office Record by : Canada. Patent Office
Download or read book Scientific Canadian Mechanics' Magazine and Patent Office Record written by Canada. Patent Office and published by . This book was released on 1893 with total page 1324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Power written by and published by . This book was released on 1917 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Official Gazette of the United States Patent and Trademark Office by : United States. Patent and Trademark Office
Download or read book Official Gazette of the United States Patent and Trademark Office written by United States. Patent and Trademark Office and published by . This book was released on 2002 with total page 1404 pages. Available in PDF, EPUB and Kindle. Book excerpt:
This book is a collection of lecture notes from the Symposium on Quantum Computing, Thermodynamics, and Statistical Physics, held at Kinki University in March 2012. Quantum information theory has a deep connection with statistical physics and thermodynamics. This volume introduces some of the topics on interface among the mentioned fields. Subjects included in the lecture notes include quantum annealing method, nonequilibrium thermodynamics and spin glass theory, among others. These subjects were presented with much emphasis put in its relevance in quantum information theory. These lecture notes are prepared in a self-contained manner so that a reader with modest background may understand the subjects.
Book Synopsis Lectures On Quantum Computing, Thermodynamics And Statistical Physics by : Shu Tanaka
Download or read book Lectures On Quantum Computing, Thermodynamics And Statistical Physics written by Shu Tanaka and published by World Scientific. This book was released on 2012-09-17 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of lecture notes from the Symposium on Quantum Computing, Thermodynamics, and Statistical Physics, held at Kinki University in March 2012. Quantum information theory has a deep connection with statistical physics and thermodynamics. This volume introduces some of the topics on interface among the mentioned fields. Subjects included in the lecture notes include quantum annealing method, nonequilibrium thermodynamics and spin glass theory, among others. These subjects were presented with much emphasis put in its relevance in quantum information theory. These lecture notes are prepared in a self-contained manner so that a reader with modest background may understand the subjects.
