- Publisher: Mathematical Association of America
- Format: Hardback | 306 pages
- Dimensions: 173mm x 257mm x 25mm | 703g
- Publication date: 31 July 2009
- Publication City/Country: Washington
- ISBN 10: 088385757X
- ISBN 13: 9780883857571
- Edition: 1
- Illustrations note: Illustrations (some col.)
- Sales rank: 204,163
This text approaches the learning of group theory visually. It allows the student to see groups, experiment with groups and understand their significance. It brings groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory. Opening chapters anchor the reader's intuitions with puzzles and symmetrical objects, defining groups as collections of actions. This approach gives early access to Cayley diagrams, the visualization technique central to the book, due to its unique ability to make group structure visually evident. This book is ideal as a supplement for a first course in group theory or alternatively as recreational reading.
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Nathan Carter earned his PhD in mathematics at Indiana University in July 2004. He received the University of Scranton Excellence in Mathematics Award in 1999, an Indiana University Rothrock Teaching Award in 2003, and a Bentley College Innovation in Teaching Award in 2007. Visual Group Theory is his first book, based on lessons learned while writing the software Group Explorer. Like several of his research projects, it puts computers to work to improve mathematical understanding and education.
Table of contents
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.