Computational topology : an introduction
著者
書誌事項
Computational topology : an introduction
（Applied mathematics）
American Mathematical Society, c2010
- : pbk.
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注記
Description based on a reprint in 2022
2010 Mathematics subject classification: primary 00-01, 52-XX, 55-XX, 57-XX, 68-XX
Includes bibliographical references (p. 227-233) and index
内容説明・目次
内容説明
Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering.
The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.
目次
Computational geometric topology: Graphs
Surfaces
Complexes
Computational algebraic topology: Homology
Duality
Morse functions
Computational persistent topology: Persistence
Stability
Applications
References
Index
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