Visual Group Theory

Front Cover
American Mathematical Soc., Dec 31, 2009 - Mathematics - 295 pages
Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring 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.
 

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Contents

Overview
1
What is a group?
3
What do groups look like?
11
Why study groups?
25
Algebra at last
41
Five families
63
Subgroups
97
Products and quotients
117
Sylow theory
193
Galois theory
221
Answers to selected Exercises
261
Bibliography
285
Index of Symbols Used
287
Index
288
About the Author
297
Back cover
298

The power of homomorphisms
157

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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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