**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: $66.00

Individual Member Price: $52.80

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

List Price: $66.00

Individual Member Price: $52.80

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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.

#### Table of Contents

# Table of Contents

## Beginning Topology

- Cover Cover11 free
- Title iii4
- Copyright iv5
- Contents v6
- 1 INTRODUCTION TO POINT SET TOPOLOGY 116
- 2 SURFACES 3651
- 3 THE EULER CHARACTERISTIC 6681
- 4 MAPS AND GRAPHS 90105
- 5 VECTOR FIELDS ON SURFACES 118133
- 6 THE FUNDAMENTAL GROUP 152167
- 6.1 Path Homotopy and the Fundamental Group 153168
- 6.2 The Fundamental Group of the Circle 160175
- 6.3 Deformation Retracts 164179
- 6.4 Further Calculations 167182
- 6.5 Presentations of Groups 171186
- 6.6 Seifert-van Kampen Theorem and the Fundamental Groups of Surfaces 173188
- 6.7 Proof of the Seifert-van Kampen Theorem 179194

- 7 INTRODUCTION TO KNOTS 182197
- Bibliography and Reading List 230245
- Index 234249
- Back Cover Back Cover1252

#### Readership

Undergraduate students interested in topology.

#### 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

- Introduction to point set topology
- Surfaces
- The Euler characteristic
- Maps and graphs
- Vector fields on surfaces
- The fundamental group
- Introduction to knots
- Bibliography and reading list
- Index