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Softcover ISBN:  9781470452988 
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Softcover ISBN:  9781470452988 
Product Code:  STML/90 
List Price:  $59.00 
MAA Member Price:  $47.20 
AMS Member Price:  $47.20 
Sale Price:  $38.35 
eBook ISBN:  9781470453794 
Product Code:  STML/90.E 
List Price:  $49.00 
MAA Member Price:  $39.20 
AMS Member Price:  $39.20 
Sale Price:  $31.85 
Softcover ISBN:  9781470452988 
eBook ISBN:  9781470453794 
Product Code:  STML/90.B 
List Price:  $108.00 $83.50 
MAA Member Price:  $86.40 $66.80 
AMS Member Price:  $86.40 $66.80 
Sale Price:  $70.20 $54.28 

Book DetailsStudent Mathematical LibraryVolume: 90; 2019; 273 ppMSC: Primary 55; 58; 57
Discrete Morse theory is a powerful tool combining ideas in both topology and combinatorics. Invented by Robin Forman in the mid 1990s, discrete Morse theory is a combinatorial analogue of Marston Morse's classical Morse theory. Its applications are vast, including applications to topological data analysis, combinatorics, and computer science.
This book, the first one devoted solely to discrete Morse theory, serves as an introduction to the subject. Since the book restricts the study of discrete Morse theory to abstract simplicial complexes, a course in mathematical proof writing is the only prerequisite needed. Topics covered include simplicial complexes, simple homotopy, collapsibility, gradient vector fields, Hasse diagrams, simplicial homology, persistent homology, discrete Morse inequalities, the Morse complex, discrete Morse homology, and strong discrete Morse functions. Students of computer science will also find the book beneficial as it includes topics such as Boolean functions, evasiveness, and has a chapter devoted to some computational aspects of discrete Morse theory. The book is appropriate for a course in discrete Morse theory, a supplemental text to a course in algebraic topology or topological combinatorics, or an independent study.
Ancillaries:
ReadershipUndergraduate and graduate students interested in discrete Morse theory.

Table of Contents

Chapters

What is discrete Morse theory?

Simplicial complexes

Discrete Morse theory

Simplicial homology

Main theorems of discrete Morse theory

Discrete Morse theory and persistent homology

Boolean functions and evasiveness

The Morse complex

Morse homology

Computations with discrete Morse theory

Strong discrete Morse theory


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Discrete Morse theory is a powerful tool combining ideas in both topology and combinatorics. Invented by Robin Forman in the mid 1990s, discrete Morse theory is a combinatorial analogue of Marston Morse's classical Morse theory. Its applications are vast, including applications to topological data analysis, combinatorics, and computer science.
This book, the first one devoted solely to discrete Morse theory, serves as an introduction to the subject. Since the book restricts the study of discrete Morse theory to abstract simplicial complexes, a course in mathematical proof writing is the only prerequisite needed. Topics covered include simplicial complexes, simple homotopy, collapsibility, gradient vector fields, Hasse diagrams, simplicial homology, persistent homology, discrete Morse inequalities, the Morse complex, discrete Morse homology, and strong discrete Morse functions. Students of computer science will also find the book beneficial as it includes topics such as Boolean functions, evasiveness, and has a chapter devoted to some computational aspects of discrete Morse theory. The book is appropriate for a course in discrete Morse theory, a supplemental text to a course in algebraic topology or topological combinatorics, or an independent study.
Ancillaries:
Undergraduate and graduate students interested in discrete Morse theory.

Chapters

What is discrete Morse theory?

Simplicial complexes

Discrete Morse theory

Simplicial homology

Main theorems of discrete Morse theory

Discrete Morse theory and persistent homology

Boolean functions and evasiveness

The Morse complex

Morse homology

Computations with discrete Morse theory

Strong discrete Morse theory