Topology for Computing Hardback (inbunden)
Format
Inbunden (Hardback)
Språk
Engelska
Antal sidor
243
Utgivningsdatum
2009-12-01
Upplaga
New
Förlag
CAMBRIDGE U.P.
Medarbetare
Ablowitz, M.J. (red.)/Ablowitz, M.J. (red.)
Illustratör/Fotograf
2 colour pl 118 diagrams
Illustrationer
118d.2col.pl.
Volymtitel
Series Number 16 Topology for Computing
Dimensioner
235 x 155 x 20 mm
Vikt
480 g
Antal komponenter
1
Komponenter
1314:Standard Color 6 x 9 in or 229 x 152 mm Case Laminate on White w/Gloss Lam
ISBN
9780521836661
Topology for Computing Hardback (inbunden)

Topology for Computing Hardback

Inbunden Engelska, 2009-12-01
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The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. 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 topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.
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  • Topology for Computing

    Afra J Zomorodian

    The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of w...

  • Advances in Applied and Computational Topology

    Afra J Zomorodian

    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. ...

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'In my knowledge, it is the first book covering these topics.' Numerical Algorithms

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Övrig information

Afra J. Zomorodian is an assistant professor in the Department of Computer Science at Dartmouth College. He is a former Post-Doctoral Fellow in Bio-X and the Department of Computer Science at Stanford University and has been a researcher at the Max-Planck-Institut fr Informatik in Saarbrcken, Germany. Using the material contained in this book, he has organized classes on computational topology at Stanford University, the MPI, and Dartmouth College.

Innehållsförteckning

1. Introduction; Part I. Mathematics: 2. Spaces and filtrations; 3. Group theory; 4. Homology; 5. Morse theory; 6. New results; Part II. Algorithms: 7. The persistence algorithms; 8. Topological simplification; 9. The Morse-Smale algorithm; 10. The linking number algorithm; Part III. Applications: 11. Software; 12. Experiments; 13. Applications.