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Discrete Morse Theory
 
Nicholas A. Scoville Ursinus College, Collegeville, PA
Discrete Morse Theory
Softcover ISBN:  978-1-4704-5298-8
Product Code:  STML/90
List Price: $59.00
MAA Member Price: $47.20
AMS Member Price: $47.20
eBook ISBN:  978-1-4704-5379-4
Product Code:  STML/90.E
List Price: $49.00
MAA Member Price: $39.20
AMS Member Price: $39.20
Softcover ISBN:  978-1-4704-5298-8
eBook: ISBN:  978-1-4704-5379-4
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
Discrete Morse Theory
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Discrete Morse Theory
Nicholas A. Scoville Ursinus College, Collegeville, PA
Softcover ISBN:  978-1-4704-5298-8
Product Code:  STML/90
List Price: $59.00
MAA Member Price: $47.20
AMS Member Price: $47.20
eBook ISBN:  978-1-4704-5379-4
Product Code:  STML/90.E
List Price: $49.00
MAA Member Price: $39.20
AMS Member Price: $39.20
Softcover ISBN:  978-1-4704-5298-8
eBook ISBN:  978-1-4704-5379-4
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
  • Book Details
     
     
    Student Mathematical Library
    Volume: 902019; 273 pp
    MSC: 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:

    Readership

    Undergraduate 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 902019; 273 pp
MSC: 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:

Readership

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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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