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.
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