Advances in applied and computational topology American Mathematical Society Short Course on Computational Topology, January 4-5, 2011, New Orleans, Louisiana by American Mathematical Society. Short Course on Computational Topology

Cover of: Advances in applied and computational topology | American Mathematical Society. Short Course on Computational Topology

Published by American Mathematical Society in Providence, R.I .

Written in English

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Subjects:

  • Homology theory,
  • Computer science -- Artificial intelligence -- Robotics,
  • Homological Algebra,
  • Computer science -- Artificial intelligence -- Reasoning under uncertainty,
  • Ergodic theory,
  • Algebraic topology -- Applied homological algebra and category theory -- Abstract complexes,
  • Dynamical systems and ergodic theory -- Topological dynamics -- Index theory, Morse-Conley indices,
  • Algebraic topology -- Homology and cohomology theories -- Sheaf cohomology,
  • Computer science -- Algorithms -- Nonnumerical algorithms,
  • Dynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Strange attractors, chaotic dynamics,
  • Differential geometry -- Global differential geometry -- Integral geometry,
  • Algebraic topology -- Explicit machine computation and programs (not the theory of computation or programming),
  • Computer science -- Theory of computing -- Analysis of algorithms and problem complexity,
  • Congresses,
  • Algebraic topology -- Homology and cohomology theories -- Other homology theories,
  • Dynamical systems and ergodic theory -- Approximation methods and numerical treatment of dynamical systems -- None of the above, but in this section

Edition Notes

Includes bibliographical references and index.

Book details

StatementAfra Zomorodian, editor
SeriesProceedings of symposia in applied mathematics -- v. 70
ContributionsZomorodian, Afra J., 1974-
Classifications
LC ClassificationsQA169 .A475 2011
The Physical Object
Paginationp. cm.
ID Numbers
Open LibraryOL25276002M
ISBN 109780821853276
LC Control Number2012008031

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It turns out that topology is sufficiently tolerant to provide us with robust tools. This volume is based on lectures delivered at the AMS Short Course on Computational Topology, held Januaryin New Orleans, Louisiana. The aim of the volume is to provide a broad introduction to recent techniques from applied and computational Cited by: 3.

Advances in Applied and Computational Topology About this Title. Afra Zomorodian, The D. Shaw Group, New York, NY, Editor. Publication: Proceedings of Symposia in Applied Mathematics Publication Year: ; Volume 70 ISBNs: (print); (online).

This volume is based on lectures delivered at the AMS Short Course on Computational Topology, held January 4–5, in New Orleans, Louisiana.

The aim of the volume is to provide a broad introduction to recent techniques from applied and computational topology. Destination page number Search scope Search Text. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology.

The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic Cited by: parts of this book, like Chapter 5. Most of the computational techniques are introduced in Sect. Topological invariants, like Betti numbers and Euler characteristic, are introduced and methods for computing such invariants are presented.

Morse theory plays an important role in many recent advances in computational geometry and topology. The articles cover both fundamental and applied research, and provide the reader with state-of-the-art achievements in the development and application of new theories at the interfaces of applied mathematics, modeling, and computational science.

The book can serve as a reference on several important current topics in modern applied mathematics. The complete graph with five vertices, K5. It has ten edges which form five crossings if drawn as sides and diagonals of a convex pentagon.

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