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Beginning Topology
 
Sue E. Goodman :  University of North Carolina, Chapel Hill, NC
Beginning Topology
Hardcover ISBN:  978-0-8218-4796-1
Product Code:  AMSTEXT/10
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-6621-3
Product Code:  AMSTEXT/10.S
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $63.20
eBook ISBN:  978-1-4704-1123-7
Product Code:  AMSTEXT/10.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $60.00
Hardcover ISBN:  978-0-8218-4796-1
eBook: ISBN:  978-1-4704-1123-7
Product Code:  AMSTEXT/10.B
List Price: $160.00 $122.50
MAA Member Price: $144.00 $110.25
AMS Member Price: $128.00 $98.00
Softcover ISBN:  978-1-4704-6621-3
eBook: ISBN:  978-1-4704-1123-7
Product Code:  AMSTEXT/10.S.B
List Price: $154.00 $116.50
MAA Member Price: $138.60 $104.85
AMS Member Price: $123.20 $93.20
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Beginning Topology
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Beginning Topology
Sue E. Goodman :  University of North Carolina, Chapel Hill, NC
Hardcover ISBN:  978-0-8218-4796-1
Product Code:  AMSTEXT/10
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-6621-3
Product Code:  AMSTEXT/10.S
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $63.20
eBook ISBN:  978-1-4704-1123-7
Product Code:  AMSTEXT/10.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $60.00
Hardcover ISBN:  978-0-8218-4796-1
eBook ISBN:  978-1-4704-1123-7
Product Code:  AMSTEXT/10.B
List Price: $160.00 $122.50
MAA Member Price: $144.00 $110.25
AMS Member Price: $128.00 $98.00
Softcover ISBN:  978-1-4704-6621-3
eBook ISBN:  978-1-4704-1123-7
Product Code:  AMSTEXT/10.S.B
List Price: $154.00 $116.50
MAA Member Price: $138.60 $104.85
AMS Member Price: $123.20 $93.20
Add to cart
  • Book Details
     
     
    Pure and Applied Undergraduate Texts
    Volume: 10; 2005; 236 pp
    MSC: Primary 55; 57

    Beginning Topology is designed to give undergraduate students a broad notion of the scope of topology in areas of point-set, geometric, combinatorial, differential, and algebraic topology, including an introduction to knot theory. A primary goal is to expose students to some recent research and to get them actively involved in learning. Exercises and open-ended projects are placed throughout the text, making it adaptable to seminar-style classes.

    The book starts with a chapter introducing the basic concepts of point-set topology, with examples chosen to captivate students' imaginations while illustrating the need for rigor. Most of the material in this and the next two chapters is essential for the remainder of the book. One can then choose from chapters on map coloring, vector fields on surfaces, the fundamental group, and knot theory.

    A solid foundation in calculus is necessary, with some differential equations and basic group theory helpful in a couple of chapters. Topics are chosen to appeal to a wide variety of students: primarily upper-level math majors, but also a few freshmen and sophomores as well as graduate students from physics, economics, and computer science. All students will benefit from seeing the interaction of topology with other fields of mathematics and science; some will be motivated to continue with a more in-depth, rigorous study of topology.
    Readership

    Undergraduate students interested in topology.
  • Table of Contents
     
     
    • Front Cover
    • CONTENTS
    • PREFACE
    • AN OVERVIEW
    • CHAPTER1: INTRODUCTION TO POINT SET TOPOLOGY
    • 1.1 OPEN AND CLOSED SETS
    • 1.2 CONTINUOUS FUNCTIONS
    • 1.3 SOME TOPOLOGICAL PROPERTIES
    • 1.4 A BRIEF INTRODUCTION TO DIMENSION (OPTIONAL)
    • CHAPTER 2 SURFACES
    • 2.1 DEFINITION OF A SURFACE
    • 2.2 CONNECTED SUM CONSTRUCTION
    • 2.3 PLANE MODELS OF SURFACES
    • 2.4 ORIENTABILITY
    • 2.5 PLANE MODELS OF NONORIENTABLE SURFACES
    • 2.6 CLASSIFICATION OF SURFACES
    • 2.7 PROOF OF THE CLASSIFICATION THEOREM FOR SURFACES (OPTIONAL)
    • CHAPTER 3: THE EULER CHARACTERISTIC
    • 3.1 CELL COMPLEXES AND THE EULER CHARACTERISTIC
    • 3.2 TRIANGULATIONS
    • 3.3 GENUS
    • 3.4 REGULAR COMPLEXES
    • 3.5 b-VALENT COMPLEXES
    • CHAPTER: 4 MAPS AND GRAPHS
    • 4.1 MAPS AND MAP COLORING
    • 4.2 THE FIVE-COLOR THEOREM FOR S^2
    • 4.3 INTRODUCTION TO GRAPHS
    • 4.4 GRAPHS IN SURFACES
    • 4.5 EMBEDDING THE COMPLETE GRAPHS AND GRAPH COLORING
    • CHAPTER 5: VECTOR FIELDS ON SURFACES
    • 5.1 VECTOR FIELDS IN THE PLANE
    • 5.2 INDEX OF A CRITICAL POINT
    • 5.3 LIMIT SETS IN THE PLANE
    • 5.4 A LOCAL DESCRIPTION OF A CRITICAL POINT
    • 5.5 VECTOR FIELDS ON SURF ACES
    • CHAPTER 6: THE FUNDAMENTAL GROUP
    • 6.1 PATH HOMOTOPY AND THE FUNDAMENTAL GROUP
    • 6.2 THE FUNDAMENTAL GROUP OF THE CIRCLE
    • 6.3 DEFORMATION RETRACTS
    • 6.4 FURTHER CALCULATIONS
    • 6.5 PRESENTATIONS OF GROUPS
    • 6.6 THE SEIFERT-VAN KAMPEN THEOREM AND THE FUNDAMENTAL GROUPS OF SURFACES
    • 6.7 PROOF OF THE SEIFERT-VAN KAMPEN THEOREM
    • CHAPTER 7: INTRODUCTION TO KNOTS
    • 7.1 KNOTS: WHAT THEY ARE AND HOW TO DRAW THEM
    • 7 .2 PRIME KNOTS
    • 7.3 ALTERNATING KNOTS
    • 7.4 REIDEMEISTER MOVES
    • 7.5 SOME SIMPLE KNOT INVARIANTS
    • 7.6 SURFACES WITH BOUNDARY
    • 7.7 KNOTS AND SURFACES
    • 7.8 KNOT POLYNOMIALS
    • BIBLIOGRAPHY AND READING LIST
    • INDEX
    • Back Cover
  • Additional Material
     
     
  • Reviews
     
     

    • This text is an interesting introduction to some of the various aspects of topology . . . [A] very attractive way to learn more and discover new things in topology.
      Corina Mohorianu, Zentralblatt MATH
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    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
Pure and Applied Undergraduate Texts
Volume: 10; 2005; 236 pp
MSC: Primary 55; 57

Beginning Topology is designed to give undergraduate students a broad notion of the scope of topology in areas of point-set, geometric, combinatorial, differential, and algebraic topology, including an introduction to knot theory. A primary goal is to expose students to some recent research and to get them actively involved in learning. Exercises and open-ended projects are placed throughout the text, making it adaptable to seminar-style classes.

The book starts with a chapter introducing the basic concepts of point-set topology, with examples chosen to captivate students' imaginations while illustrating the need for rigor. Most of the material in this and the next two chapters is essential for the remainder of the book. One can then choose from chapters on map coloring, vector fields on surfaces, the fundamental group, and knot theory.

A solid foundation in calculus is necessary, with some differential equations and basic group theory helpful in a couple of chapters. Topics are chosen to appeal to a wide variety of students: primarily upper-level math majors, but also a few freshmen and sophomores as well as graduate students from physics, economics, and computer science. All students will benefit from seeing the interaction of topology with other fields of mathematics and science; some will be motivated to continue with a more in-depth, rigorous study of topology.
Readership

Undergraduate students interested in topology.
  • Front Cover
  • CONTENTS
  • PREFACE
  • AN OVERVIEW
  • CHAPTER1: INTRODUCTION TO POINT SET TOPOLOGY
  • 1.1 OPEN AND CLOSED SETS
  • 1.2 CONTINUOUS FUNCTIONS
  • 1.3 SOME TOPOLOGICAL PROPERTIES
  • 1.4 A BRIEF INTRODUCTION TO DIMENSION (OPTIONAL)
  • CHAPTER 2 SURFACES
  • 2.1 DEFINITION OF A SURFACE
  • 2.2 CONNECTED SUM CONSTRUCTION
  • 2.3 PLANE MODELS OF SURFACES
  • 2.4 ORIENTABILITY
  • 2.5 PLANE MODELS OF NONORIENTABLE SURFACES
  • 2.6 CLASSIFICATION OF SURFACES
  • 2.7 PROOF OF THE CLASSIFICATION THEOREM FOR SURFACES (OPTIONAL)
  • CHAPTER 3: THE EULER CHARACTERISTIC
  • 3.1 CELL COMPLEXES AND THE EULER CHARACTERISTIC
  • 3.2 TRIANGULATIONS
  • 3.3 GENUS
  • 3.4 REGULAR COMPLEXES
  • 3.5 b-VALENT COMPLEXES
  • CHAPTER: 4 MAPS AND GRAPHS
  • 4.1 MAPS AND MAP COLORING
  • 4.2 THE FIVE-COLOR THEOREM FOR S^2
  • 4.3 INTRODUCTION TO GRAPHS
  • 4.4 GRAPHS IN SURFACES
  • 4.5 EMBEDDING THE COMPLETE GRAPHS AND GRAPH COLORING
  • CHAPTER 5: VECTOR FIELDS ON SURFACES
  • 5.1 VECTOR FIELDS IN THE PLANE
  • 5.2 INDEX OF A CRITICAL POINT
  • 5.3 LIMIT SETS IN THE PLANE
  • 5.4 A LOCAL DESCRIPTION OF A CRITICAL POINT
  • 5.5 VECTOR FIELDS ON SURF ACES
  • CHAPTER 6: THE FUNDAMENTAL GROUP
  • 6.1 PATH HOMOTOPY AND THE FUNDAMENTAL GROUP
  • 6.2 THE FUNDAMENTAL GROUP OF THE CIRCLE
  • 6.3 DEFORMATION RETRACTS
  • 6.4 FURTHER CALCULATIONS
  • 6.5 PRESENTATIONS OF GROUPS
  • 6.6 THE SEIFERT-VAN KAMPEN THEOREM AND THE FUNDAMENTAL GROUPS OF SURFACES
  • 6.7 PROOF OF THE SEIFERT-VAN KAMPEN THEOREM
  • CHAPTER 7: INTRODUCTION TO KNOTS
  • 7.1 KNOTS: WHAT THEY ARE AND HOW TO DRAW THEM
  • 7 .2 PRIME KNOTS
  • 7.3 ALTERNATING KNOTS
  • 7.4 REIDEMEISTER MOVES
  • 7.5 SOME SIMPLE KNOT INVARIANTS
  • 7.6 SURFACES WITH BOUNDARY
  • 7.7 KNOTS AND SURFACES
  • 7.8 KNOT POLYNOMIALS
  • BIBLIOGRAPHY AND READING LIST
  • INDEX
  • Back Cover

  • This text is an interesting introduction to some of the various aspects of topology . . . [A] very attractive way to learn more and discover new things in topology.
    Corina Mohorianu, Zentralblatt MATH
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
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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