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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$25
Member Price: US$20
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.

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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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