Computational Homology
Seiten
2004
Springer-Verlag New York Inc.
978-0-387-40853-8 (ISBN)
Springer-Verlag New York Inc.
978-0-387-40853-8 (ISBN)
Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing.
Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.
Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.
Homology.- Preview.- Cubical Homology.- Computing Homology Groups.- Chain Maps and Reduction Algorithms.- Preview of Maps.- Homology of Maps.- Computing Homology of Maps.- Extensions.- Prospects in Digital Image Processing.- Homological Algebra.- Nonlinear Dynamics.- Homology of Topological Polyhedra.- Tools from Topology and Algebra.- Topology.- Algebra.- Syntax of Algorithms.
| Reihe/Serie | Applied Mathematical Sciences ; 157 |
|---|---|
| Zusatzinfo | XVIII, 482 p. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-387-40853-3 / 0387408533 |
| ISBN-13 | 978-0-387-40853-8 / 9780387408538 |
| Zustand | Neuware |
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