Visual Group Theory

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MAA, Apr 9, 2009 - Mathematics - 297 pages
1 Review
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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Review: Visual Group Theory (MAA Classroom Resource Materials) (MAA Problem Book Series)

User Review  - Will - Goodreads

"By now the reader is certainly convinced that group theory shows up in diverse situations. But it would be a great disservice to the history of mathematics if I did not mention one more application ... Read full review

Contents

Overview
1
What do groups look like?
11
Why study groups?
25
Algebra at last
41
Five families
63
Subgroups
97
Products and quotients
117
The power of homomorphisms
157
Sylow theory
193
Galois theory
221
A Answers to selected Exercises
261
Bibliography
285
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About the author (2009)

Nathan Carter grew up in Northeastern Pennsylvania, earning a bachelor's in mathematics and computer science from the University of Scranton in 1999. He earned masters degrees in mathematics and computer science and a Ph.D. in mathematics from Indiana University. Nathan received the University of Scranton Excellence in Mathematics award in 1999, an Indian University Rothrock Teaching Award in 2003, and a Bentley College Innovation in Teaching award in 2007.

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