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Knots and Surfaces: A Guide to Discovering Mathematics
David W. Farmer, Bucknell University, Lewisburg, PA, and Theodore B. Stanford, University of Nevada, Reno, NV

Mathematical World
1996; 101 pp; softcover
Volume: 6
ISBN-10: 0-8218-0451-0
ISBN-13: 978-0-8218-0451-3
List Price: US$23
Member Price: US$18.40
Order Code: MAWRLD/6
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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 Knots and Surfaces is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; no procedures to follow. The book is a guide: its job is to start you in the right direction and to bring you back if you stray too far. Discovery is left to you.

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.

Request an examination or desk copy.


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


"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

  • Networks (Chapter 1)
  • Surfaces (Chapter 2)
  • Knots (Chapter 3)
  • Projects (Chapter 4)
  • Bibliography
  • Index
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