May 14, 2009
Visual Group Theory
Nathan C. Carter
310 pp., hardcover, 2009. Series: Classroom Resource Materials
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.Highlights:
Preface. Overview. 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. Bibliography. Index of symbols used. Index.
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.
Nathan Carter's website for this book features further info, including an image gallery, sample chapters, and links to podcasts.
Steven Strogatz's "Group Think" NYT Column
Order Visual Group Theory from the MAA Bookstore or call 1.800.331.1622.
MAA Member Price: $57.50