Cambridge Monographs on Applied and Computational Mathematics: Topology for Computing (Softcover)
Cambridge Monographs on Applied and Computational Mathematics: Topology for Computing (Softcover)
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From the back cover: "A primary goal of this book is to present basic concepts from topology and Morse theory to enable a nonspecialist 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-Smale theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus in on computational challenges and on presenting algorithms and data structures when appropriate."BRIEF CONTENTS
- Preface
- Acknowledgments
- 1 - Introduction
- PART ONE: MATHEMATICS
- 2 - Spaces and Filtration
- 3 - Group Theory
- 4 - Homology
- 5 - Morse Theory
- 6 - New Results
- PART TWO: ALGORITHMS
- 7 - The Persistence Algorithms
- 8 - Topological Simplification
- 9 - The Morse-Smale Complex Algorithm
- 10 - The Linking Number Algorithm
- PART THREE: APPLICATION
- 11 - Software
- 12 - Experiments
- 13 - Applications
- Bibliography
- Index
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PUBLISHER: Cambridge University Press
ISBN-13: 9780521136099
ISBN-10: 0521136091