**Mathematical World**

Volume: 6;
1996;
101 pp;
Softcover

MSC: Primary 57;
Secondary 05

Print ISBN: 978-0-8218-0451-3

Product Code: MAWRLD/6

List Price: $25.00

AMS Member Price: $20.00

MAA member Price: $22.50

**Electronic ISBN: 978-1-4704-1191-6
Product Code: MAWRLD/6.E**

List Price: $25.00

AMS Member Price: $20.00

MAA member Price: $22.50

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# Knots and Surfaces: A Guide to Discovering Mathematics

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*David W. Farmer; Theodore B. Stanford*

In most mathematics textbooks, the most exciting part
of mathematics—the process of invention and
discovery—is completely hidden from the reader. The aim of

Suitable for a one-semester course at the beginning
undergraduate level, there are no prerequisites for understanding the
text. Any college student interested in discovering the beauty of
mathematics will enjoy a course taught from this book. The book has also
been used successfully with nonscience students who want to fulfill
a science requirement.

Also available from the AMS by David W. Farmer is
Groups and Symmetry: A Guide
to Discovering Mathematics.

#### Readership

Undergraduate students, graduate students, and research mathematicians interested in an introduction to modern areas of mathematics.

#### Reviews & Endorsements

The book is perfectly suited to a course for non-science majors in need of fulfilling a math requirement. All the sections have worked well at sparking student interest and convincing them that math is much more interesting than mere number-crunching and graphing.

-- Professor William Bloch, Wheaton College

Would serve well as the basis of an independent study course in which the student would work through the tasks in a journal subject to periodic review by the instructor … the writing is clear and engaging, and the tasks should be effective at setting a reasonable pace.

-- American Mathematical Monthly

#### Table of Contents

# Table of Contents

## Knots and Surfaces: A Guide to Discovering Mathematics

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Table of Contents v6 free
- Chapter 1 Networks 110 free
- 1.1 Countries of the insect world 110
- 1.2 Notation, and a catalog 413
- 1.3 Trees 615
- 1.4 Trees in graphs 817
- 1.5 Euler's formula 918
- 1.6 Planar graphs 1019
- 1.7 Paths in graphs 1322
- 1.8 Dual graphs 1625
- 1.9 A map of the United States 1827
- 1.10 Coloring graphs 2029
- 1.11 The six-color theorem 2332
- 1.12 Notes 2736

- Chapter 2 Surfaces 3140
- 2.1 The shape of the world 3140
- 2.2 The flat torus 3443
- 2.3 Graphs on the torus 3645
- 2.4 Euler's formula, again 3746
- 2.5 Regular graphs 3948
- 2.6 More surfaces: holes 4352
- 2,7 More surfaces: connected sums 4453
- 2.8 One–sided surfaces 4756
- 2.9 Identifying two–sided surfaces 4958
- 2.10 Cell complexes 5362
- 2.11 Notes 5564

- Chapter 3 Knots 5968
- Chapter 4 Projects 8796
- Bibliography 97106
- Index 99108
- Back Cover Back Cover1111