Algebraic Foundations for Applied Topology and Data Analysis by Hal Schenck (Eng

Description: Algebraic Foundations for Applied Topology and Data Analysis by Hal Schenck This book gives an intuitive and hands-on introduction to Topological Data Analysis (TDA). 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. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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 users 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. Back Cover Aimed at a general mathematical audience, this book introduces the key structures and algebraic tools used in topological data analysis (TDA). 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 of the book introduces algebraic topology, along with applications to sensor networks and voter ranking. The last third of the book covers key contemporary tools in TDA: persistent and multiparameter persistent homology. The book concludes with a users 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 the software packages used in the field. The book is based on a course taught to masters degree students in statistics, and is appropriate for graduate students. Author Biography Hal Schenck received a BS in Applied Math and Computer Science from Carnegie-Mellon University in 1986. From 1986 to 1990 he served as an Army officer in Georgia and Germany, then returned to graduate school at Cornell, earning his Ph.D. in 1997. After an NSF postdoc at Harvard and Northeastern, he was a professor at Texas A&M (2001–2007), at the University of Illinois (2007–2017), and Chair at Iowa State (2017–2019). Since 2019 he has been the Rosemary Kopel Brown Eminent Scholars Chair at Auburn University. He has earned teaching awards from Cornell and Illinois, and awards for departmental leadership and outreach to student veterans from Iowa State. He was elected as a fellow of the AMS in 2020, and as a fellow of the AAAS in 2023; recent academic visits include a Leverhulme Professorship at Oxford, and a Clare Hall Fellowship at Cambridge. His research is at the interface of algebra, geometry, and computation. Table of Contents Preface.- 1. Linear Algebra Tools for Data Analysis.- 2. Basics of Algebra: Groups, Rings, Modules.- 3. Basics of Topology: Spaces and Sheaves.- 4. Homology I: Simplicial Complexes to Sensor Networks.- 5. Homology II: Cohomology to Ranking Problems.- 6. Persistent Algebra: Modules over a PID.- 7. Persistent Homology.- 8. Multiparameter Persistent Homology.- 9. Derived Functors and Spectral Sequences.- Appendix A. Examples of Software Packages.- Bibliography. Review "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) Feature A well-written and original take on the interaction between pure math and the applications of data science The first book on TDA to focus on developing in detail the requisite algebraic background Defines and provides examples of the algebraic structures and techniques used in topological data analysis Details ISBN3031066634 Author Hal Schenck Publisher Springer International Publishing AG Series Mathematics of Data Language English Year 2022 ISBN-10 3031066634 ISBN-13 9783031066634 Format Hardcover Series Number 1 Imprint Springer International Publishing AG Place of Publication Cham Country of Publication Switzerland Edition 1st Pages 224 Illustrations 1 Illustrations, black and white; XII, 224 p. 1 illus. Publication Date 2022-11-22 UK Release Date 2022-12-09 Edition Description 1st ed. 2022 Alternative 9783031066665 DEWEY 514.2 Audience Tertiary & Higher Education We've got this At The Nile, if you're looking for it, we've got it. 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