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Elementary Applied Topology by Robert Ghrist
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Elementary Applied Topology written by
This text gives a brisk and engaging introduction to the mathematics behind the recently established field of Applied Topology. Over a century of development of principles and techniques in algebraic topology has of late crossed over to a variety of application domains. This text gives a completely novel introduction to these methods in the context of the applications. "Elementary Applied Topology" is short (250 pp. plus bibliography and index) and richly illustrated, with 268 figures. It is perfect for both self-study, and as the basis for a course in applied topology. This book is also well-suited for use as a supplementary text in a more traditional algebraic topology course, providing both context and motivation for the tools to be learned. The progression of mathematical techniques is a fresh approach. The book begins with a quick trip through manifolds and cell complexes. The segue to algebraic topology comes in the form of the Euler characteristic and the Euler calculus born from it.
Passing from this to homology, exact sequences, and cohomology sets the stage for the innovative content to come. This is comprised of modern Morse theory (including discrete Morse theory, Conley index, and stratified Morse theory), sheaf theory (with an emphasis on cellular sheaves and cosheaves), and, finally, category theory and categorification. Every tool and topic is paired with an application. These range in scope across the biological, economic, engineering, material, physical, and statistical sciences. Of particular note are the applications to topological data analysis, including persistent homology and barcodes. "Elementary Applied Topology" is the first comprehensive text on applied algebraic topology for students of all mathematical sciences.
Book Detail :-
Title: Elementary Applied Topology
Author(s): Robert W Ghrist
Publisher: CreateSpace Independent Publishing Platform
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About Author :-
Author Robert W Ghrist (born 1969) is an American mathematician, known for his work on topological methods in applied mathematics.
Ghrist received his bachelor's degree in mechanical engineering from the University of Toledo in 1991 and his master's degree and in 1995 his PhD from Cornell University in 1994 under Philip Holmes with thesis The link of periodic orbits of a flow.
He start his career as visiting scientist at the Isaac Newton Institute in Cambridge in 1995 and at the Isaac Newton Institute in Cambridge in 2000. From 1996 to 1998 he was R. H. Bing Instructor at the University of Texas and from 1998 an assistant professor and then from 2002 an associate professor at the Georgia Institute of Technology. In 2002 he became an associate professor and in 2004 a professor at the University of Illinois at Urbana-Champaign. From 2007 he was at the Information Trust Institute. In 2008, he was appointed Andrea Mitchell Penn Integrating Knowledge University Professor in Mathematics and Electrical/Systems Engineering at the University of Pennsylvania.Ghrist received a Presidential Early Career Award in 2002. He received the Chauvenet Prize for Barcodes: The Persistent Topology of Data in 2013 and the Gauss Lectureship of the German Mathematical Society in 2014.
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Book Contents :-
Elementary Applied Topology written by
cover the following topics.
3. Euler Characteristic
7. Morse Theory
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