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Groups and Symmetry: A Guide to Discovering Mathematics
David W. Farmer, Bucknell University, Lewisburg, PA
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Mathematical World
1996; 102 pp; softcover
Volume: 5
Reprint/Revision History:
fourth printing 1999
ISBN-10: 0-8218-0450-2
ISBN-13: 978-0-8218-0450-6
List Price: US$23
Member Price: US$18.40
Order Code: MAWRLD/5
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See also:

Knots and Surfaces: A Guide to Discovering Mathematics - David W Farmer and 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 Groups and Symmetry 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 Knots and Surfaces: A Guide to Discovering Mathematics.

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Readership

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

Reviews

"Nicely produced and concentrates on the informal analysis of geometrical patterns with the emphasis on informality ... could serve as a useful collection of activities to precede a formal course and would provide a range of intuitive experiences to which the more formal treatment could refer."

-- The Mathematical Gazette

"On the basis of this book it is possible to tailor a good course for high school students to really discover mathematics ... for anyone who is working with high school students in an advanced level the book is really recommended."

-- Zentralblatt MATH

"Written in a lively conversational style ... entertaining, and sometimes provoking, and will doubtlessly prove useful to its intended audience."

-- Mathematical Reviews

Table of Contents

  • Squares, hexagons, and triangles
  • The rigid motions of the plane
  • Finite figures
  • Strip patterns
  • Wallpatterns
  • Finite groups
  • Cayley diagrams
  • Symmetry in the real world
  • Bibliography
  • Index
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