
Table of Contents 
Proceedings of Symposia in Applied Mathematics 2012; 232 pp; hardcover Volume: 70 ISBN10: 0821853279 ISBN13: 9780821853276 List Price: US$60 Member Price: US$48 Order Code: PSAPM/70 See also: Computational Topology: An Introduction  Herbert Edelsbrunner and John L Harer Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures  Janos Pach and Micha Sharir  What is the shape of data? How do we describe flows? Can we count by integrating? How do we plan with uncertainty? What is the most compact representation? These questions, while unrelated, become similar when recast into a computational setting. Our input is a set of finite, discrete, noisy samples that describes an abstract space. Our goal is to compute qualitative features of the unknown space. It turns out that topology is sufficiently tolerant to provide us with robust tools. This volume is based on lectures delivered at the 2011 AMS Short Course on Computational Topology, held January 45, 2011 in New Orleans, Louisiana. The aim of the volume is to provide a broad introduction to recent techniques from applied and computational topology. Afra Zomorodian focuses on topological data analysis via efficient construction of combinatorial structures and recent theories of persistence. Marian Mrozek analyzes asymptotic behavior of dynamical systems via efficient computation of cubical homology. Justin Curry, Robert Ghrist, and Michael Robinson present Euler Calculus, an integral calculus based on the Euler characteristic, and apply it to sensor and network data aggregation. Michael Erdmann explores the relationship of topology, planning, and probability with the strategy complex. Jeff Erickson surveys algorithms and hardness results for topological optimization problems. Readership Graduate students and research mathematicians interested in applied and computational topology. 


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