Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics)

By Afra J. Zomorodian

Written by means of a working laptop or computer scientist for computing device scientists, this booklet teaches topology from a computational perspective, and exhibits the right way to clear up actual difficulties that experience topological elements concerning pcs. Such difficulties come up in lots of parts, akin to special effects, robotics, structural biology, and chemistry. the writer begins from the fundamentals of topology, assuming no earlier publicity to the topic, and strikes swiftly as much as contemporary advances within the sector, together with topological endurance and hierarchical Morse complexes. Algorithms and knowledge constructions are provided while applicable.

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For that reason, a few chapters, comparable to these partly 3, have a thesis consider to them. i've got additionally integrated notes from numerous graduate-level classes i've got equipped within the zone: creation to Computational Topology at Stanford college, California, in the course of Fall 2002 and iciness 2004; and Topology for Computing on the Max-Planck-Institut für Informatik, Saarbrücken, Germany, in the course of Fall 2003. The objective of this booklet is to make algorithmically minded members fluent within the language of topology. presently, so much researchers in computational topology have a arithmetic historical past. My wish is to recruit extra desktop scientists into this rising box. Stanford, California June 2004 A. J. Z. Acknowledgments i'm indebted to Persi Diaconis for the genesis of this booklet. He attended my first actual speak within the Stanford arithmetic division, requested for a duplicate of my thesis, and urged it for booklet. To have my paintings be well-known through this kind of fantastic and notable determine is a gigantic honor for me. i want to thank Lauren Cowles for venture this undertaking and training me through the modifying technique and Elise Oranges for copyediting the textual content. in the course of my time at Stanford, i've got collaborated essentially with Leonidas Guibas and Gunnar Carlsson. Leo has been greater than only a post-doctoral manager, yet a colleague, a mentor, and a pal. he's a profitable educational who balances study, educating, and the mentoring of scholars. He publications a wide lively examine staff that works on a manifold of vital difficulties. And his striking educational progeny testify to his deal with their good fortune. 11 years after being a freshman in his “honors calculus,” i'm lucky to have Gunnar as a colleague. Gunnar astounds me regularly together with his wisdom, humility, generosity, and kindness. I proceed to depend upon his estimation, recommendation, and help. i'd additionally wish to thank the contributors of Leo and Gunnar’s learn teams in addition to the Stanford photographs Laboratory, for encouraged talks and invigorating discussions. This e-book was once partly written in the course of a four-month remain on the Max-Planck-Institut. i want to thank Lutz Kettner and Kurt Mehlhorn for his or her sponsorship, in addition to for coaxing me into instructing a mini-course. eventually, i want to thank my examine collaborators, whose paintings seems during this e-book: Gunnar Carlsson, Anne Collins, Herbert Edelsbrunner, Leonidas Guibas, John Harer, and David Letscher. My examine used to be supported, partially, by way of ARO less than furnish DAAG55-98-1-0177, via NSF less than delivers CCR-00-86013 and DMS-0138456, and via NSF/DARPA below furnish shipment 0138456. xiii 1 advent the point of interest of this publication is shooting and figuring out the topological homes of areas. to take action, we use tools derived from exploring the connection among geometry and topology. during this bankruptcy, i'll inspire this method by way of explaining what areas are, how they come up in lots of fields of inquiry, and why we're drawn to their homes. i'll then introduce new theoretical equipment for conscientiously interpreting topologies of areas.

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