Computational topology : an introduction

著者

書誌事項

Computational topology : an introduction

Herbert Edelsbrunner, John L. Harer

American Mathematical Society, c2010

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注記

Includes bibliographical references 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

Preface Part I. Computational geometric topology Graphs Surfaces Complexes Part II. Computational algebraic topology Homology Duality Morse functions Part III. Computational persistent topology Persistence Stability Applications References Index

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