**Pure and Applied Undergraduate Texts**

Volume: 10;
2005;
236 pp;
Hardcover

MSC: Primary 55; 57;

**Print ISBN: 978-0-8218-4796-1
Product Code: AMSTEXT/10**

List Price: $70.00

AMS Member Price: $56.00

MAA Member Price: $63.00

**Electronic ISBN: 978-1-4704-1123-7
Product Code: AMSTEXT/10.E**

List Price: $66.00

AMS Member Price: $52.80

MAA Member Price: $59.40

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#### Supplemental Materials

# Beginning Topology

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*Sue E. Goodman*

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.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## Beginning Topology

- Front Cover 11 free
- CONTENTS 66
- PREFACE 88
- AN OVERVIEW 1010
- CHAPTER1: INTRODUCTION TO POINT SET TOPOLOGY 1616
- CHAPTER 2 SURFACES 5151
- CHAPTER 3: THE EULER CHARACTERISTIC 8181
- CHAPTER: 4 MAPS AND GRAPHS 105105
- CHAPTER 5: VECTOR FIELDS ON SURFACES 133133
- CHAPTER 6: THE FUNDAMENTAL GROUP 167167
- 6.1 PATH HOMOTOPY AND THE FUNDAMENTAL GROUP 168168
- 6.2 THE FUNDAMENTAL GROUP OF THE CIRCLE 175175
- 6.3 DEFORMATION RETRACTS 179179
- 6.4 FURTHER CALCULATIONS 182182
- 6.5 PRESENTATIONS OF GROUPS 186186
- 6.6 THE SEIFERT-VAN KAMPEN THEOREM AND THE FUNDAMENTAL GROUPS OF SURFACES 188188
- 6.7 PROOF OF THE SEIFERT-VAN KAMPEN THEOREM 194194

- CHAPTER 7: INTRODUCTION TO KNOTS 197197
- BIBLIOGRAPHY AND READING LIST 245245
- INDEX 249249
- Back Cover 252252