Algebraic Foundations for Applied Topology and Data Analysis

By: Hal Schenck

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Hardcover | 22 November 2022

At a Glance

Hardcover
238 Pages

Dimensions(cm)
24.2 x 16.5 x 14.3

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$129.00

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This book gives an intuitive and hands-on introduction to Topological Data Analysis (TDA). Covering a wide range of topics at levels of sophistication varying from elementary (matrix algebra) to esoteric (Grothendieck spectral sequence), it offers a mirror of data science aimed at a general mathematical audience.

The required algebraic background is developed in detail. The first third of the book reviews several core areas of mathematics, beginning with basic linear algebra and applications to data fitting and web search algorithms, followed by quick primers on algebra and topology. The middle third introduces algebraic topology, along with applications to sensor networks and voter ranking. The last third covers key contemporary tools in TDA: persistent and multiparameter persistent homology. Also included is a user''s guide to derived functors and spectral sequences (useful but somewhat technical tools which have recently found applications in TDA), and an appendix illustrating a number of software packages used in the field.

Based on a course given as part of a masters degree in statistics, the book is appropriate for graduate students.

Industry Reviews

"This text book is a great companion for graduate students interested in applied topology. ... the book will remain highly-relevant for years to come; an advantage that does not apply to many other publications in data science. I can highly recommend pairing this book with the equally delightful work by R. W. Ghrist ... . Together, these two books provide a sweeping overview of an exciting nascent field, and I am sure that readers will appreciate them." (Bastian Rieck, zbMATH 1521.55001, 2023)

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