Winding Around-The Winding Number in Topology, Geometry and Analysis Book Information:

"text-align: justify; the < span style="text-align: justify; winding Number< span style="text-align: justify; 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 hope index theorem), allow one to subtract infinity from infinity and get a finite answer (toeplitz operators), generalized 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.
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• Book Type/Genre :

Society & Social Sciences

• Book Binding :

Paperback

• Language :

English

• Number of Pages :

Page count varies on each edition/reprint

• ISBN - 10 :

• Winding Around-The Winding Number in Topology, Geometry and Analysis Published On :

2017

• Resource:

Society & Social Sciences, Society & Culture Book is recommended for Students, Teachers, Graduates, Professionals, and all bibliophiles

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