Visual Group Theory
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.
- Includes over 300 full-colour illustrations
- Moves from the basics of group theory to Sylow theory and Galois theory
- An applications chapter shows how group theory describes the symmetry in crystals, dancing, art, architecture, and more
Product details
April 2009Hardback
9780883857571
306 pages
262 × 182 × 24 mm
0.8kg
This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
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.