How Long to Read Winding Around: The Winding Number in Topology, Geometry, and Analysis

How Long Does it Take to Read Winding Around: The Winding Number in Topology, Geometry, and Analysis?

It takes the average reader 4 hours and 38 minutes to read Winding Around: The Winding Number in Topology, Geometry, and Analysis by John Roe

Assuming a reading speed of 250 words per minute. Learn more

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.

How long is Winding Around: The Winding Number in Topology, Geometry, and Analysis?

Winding Around: The Winding Number in Topology, Geometry, and Analysis by John Roe is 269 pages long, and a total of 69,671 words.

This makes it 91% the length of the average book. It also has 85% more words than the average book.

How Long Does it Take to Read Winding Around: The Winding Number in Topology, Geometry, and Analysis Aloud?

The average oral reading speed is 183 words per minute. This means it takes 6 hours and 20 minutes to read Winding Around: The Winding Number in Topology, Geometry, and Analysis aloud.

What Reading Level is Winding Around: The Winding Number in Topology, Geometry, and Analysis?

Winding Around: The Winding Number in Topology, Geometry, and Analysis is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Winding Around: The Winding Number in Topology, Geometry, and Analysis?

Winding Around: The Winding Number in Topology, Geometry, and Analysis by John Roe is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

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