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Visual Group Theory

Visual Group Theory

By Nathan C. Carter

Print ISBN: 978-0-88385-757-1
Electronic ISBN: 978-1-61444-102-1
310 pp., Hardbound, 2009
List Price: $75.00
Member Price: $56.25
Series: Classroom Resource Materials

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Nathan Carter's colorful text, Visual Group Theory, approaches the learning of group theory visually. Its topics and theorems are accompanied by visual demonstrations of the meaning and importance of groups, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory. It allows students to see groups, to experiment with groups’and to understand the significance of groups, subgroups, homomorphisms, products, and quotients.

Defining groups as collections of actions, the opening chapters anchor readers' intuitions with puzzles and symmetrical objects. This approach leads to Cayley diagrams, which embody the visualization technique central to the book because of their unique ability to make group structure visually apparent.

  • Includes more than 300 full-color illustrations
  • Moves from the basics of group theory to Sylow theory and Galois theory
  • An applications chapter shows how group theory describes the symmetry of crystals, dancing, art, architecture, and much more
  • The book is an ideal supplement to a first course in group theory

Table of Contents

1. What is a group?
2. What do groups look like?
3. Why study groups?
4. Algebra at last
5. Five families
6. Subgroups
7. Products and quotients
8. The power of homomorphisms
9. Sylow theory
10. Galois theory
Answers to selected exercises
Index of symbols used

About the Author

Now at Bentley University, Nathan Carter earned a Ph.D. in mathematics from Indiana University, Bloomington. He received the University of Scranton Excellence in Mathematics award in 1999, an Indiana University Rothrock Teaching award in 2003, and a Bentley University Innovation in Teaching award in 2007. This is his first book, based on lessons learned while writing the software Group Explorer.

Additional Links

Nathan Carter's website for this book features further info, including an image gallery, sample chapters, and links to podcasts.

Steven Strogatz Lauds MAA Book Visual Group Theory in NYT Column (May 2, 2010)