Algebraic Foundations for Applied Topology and Data Analysis

Häftad, Engelska, 2023

AvHal Schenck

889 kr

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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.

Produktinformation

Utgivningsdatum2023-11-22
Mått155 x 235 x 13 mm
Vikt365 g
FormatHäftad
SpråkEngelska
SerieMathematics of Data
Antal sidor224
FörlagSpringer International Publishing AG
ISBN9783031066665

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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.

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.

“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)