Softcover ISBN:  9781470467692 
Product Code:  MBK/69.S 
List Price:  $66.00 
MAA Member Price:  $59.40 
AMS Member Price:  $52.80 
Electronic ISBN:  9781470412081 
Product Code:  MBK/69.E 
List Price:  $62.00 
MAA Member Price:  $55.80 
AMS Member Price:  $49.60 

Book Details2010; 241 ppMSC: Primary 00; 52; 55; 57; 68;
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.ReadershipGraduate students and research mathematicians interested in topology, algorithms, and applications to science and engineering.

Table of Contents

A. Computational geometric topology

I. Graphs

II. Surfaces

III. Complexes

B. Computational algebraic topology

IV. Homology

V. Duality

VI. Morse functions

C. Computational persistent topology

VII. Persistence

VIII. Stability

IX. Applications


Additional Material

Reviews

This book is a very welcome, untraditional, thorough and wellorganized introduction to a young and quickly developing discipline on the crossroads between mathematics, computer science, and engineering.
DMV Newsletter


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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.
Graduate students and research mathematicians interested in topology, algorithms, and applications to science and engineering.

A. Computational geometric topology

I. Graphs

II. Surfaces

III. Complexes

B. Computational algebraic topology

IV. Homology

V. Duality

VI. Morse functions

C. Computational persistent topology

VII. Persistence

VIII. Stability

IX. Applications

This book is a very welcome, untraditional, thorough and wellorganized introduction to a young and quickly developing discipline on the crossroads between mathematics, computer science, and engineering.
DMV Newsletter