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- Author: Robert Ghrist
- Pages: 276
- Language: English
- ISBN/ASIN: 1502880857
- ISBN13: 9781502880857
- Upload date: 28-12-2016, 17:17
- Category: Mathematics

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.

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Topology: An Introduction Topology Pearson New International Edition Topology (2nd Edition) Sheaf Theory (Graduate Texts in Mathematics) Mod Two Homology and Cohomology (Universitext) Lectures on the Topology of 3-Manifolds: An Introduction to the Casson Invariant 2E Lecture Notes in Algebraic Topology (Graduate Studies in Mathematics, 35) Introduction to Topology:Theory and Applications Introduction to Topology: Second Edition (Dover Books on Mathematics) Introduction to Topology and Geometry Fundamentals of Algebraic Topology (Graduate Texts in Mathematics) Elements of Topology Elementary Topology and Applications Directed Algebraic Topology and Concurrency Computational Topology: An Introduction Basic Modern Algebra with Applications Basic Algebraic Topology An Introduction to Hopf Algebras Algebraic Geometry for Associative Algebras (Chapman & Hall/CRC Pure and Applied Mathematics) Algebraic and Geometric Surgery (Oxford Mathematical Monographs) A User's Guide to Algebraic Topology (Mathematics and Its Applications) A First Course in Algebraic Topology Mathematical Tools for Shape Analysis and Description (Synthesis Lectures on Computer Graphics and Animation) Topology and Geometry for Physics (Lecture Notes in Physics, Vol. 822)

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