Visual group theory

Nathan C. Carter

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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[目次]

  • 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.

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この本の情報

書名 Visual group theory
著作者等 Carter Nathan
Carter Nathan C.
シリーズ名 Classroom resource materials
出版元 Mathematical Association of America
刊行年月 c2009
ページ数 xiii, 297 p.
大きさ 27 cm
ISBN 9780883857571
NCID BA90281385
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国
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