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Elementary Applied Topology

Name: Elementary Applied Topology
Price: 19.99 USD
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Rating: 4.5 (45 reviews)

4.5 of 5 Stars: Science & Mathematics - Elementary Applied Topology

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Book Synopsis: 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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Looking for a comprehensive and engaging introduction to the exciting field of Applied Topology? Look no further than the "Elementary Applied Topology" book. With over a century of development in algebraic topology, this book bridges the gap between theory and application. Whether you're a self-learner or a student in need of a supplementary text, this book is perfect for you. Packed with 268 illustrations, this short yet richly illustrated text (250 pp. plus bibliography and index) guarantees an immersive learning experience.

What sets "Elementary Applied Topology" apart is its fresh approach to mathematical techniques. Starting with a quick trip through manifolds and cell complexes, the book seamlessly transitions to introduce essential concepts like homology, exact sequences, and cohomology. Building on this foundation, the book delves into modern Morse theory, sheaf theory, and category theory. Each topic is paired with practical applications across diverse fields, including biology, economics, engineering, materials science, physics, and statistics.

Notably, "Elementary Applied Topology" explores the fascinating realm of topological data analysis, including persistent homology and barcodes. These tools are essential in understanding complex datasets and finding patterns and connections that may not be apparent through traditional statistical analysis. By mastering the concepts in this book, you'll gain valuable skills that can be applied to real-world problems and research.

Don't miss out on this groundbreaking resource. Whether you're a student of mathematics, biology, engineering, or any other field that requires data analysis, "Elementary Applied Topology" is a must-have. Start your journey into the world of applied algebraic topology today!

Ready to take your understanding of Applied Topology to the next level? Explore the world of algebraic topology and its practical applications with "Elementary Applied Topology." Visit our website to learn more about this comprehensive text and secure your copy today.

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