ビジュアル群論 Visual Group Theory (Classroom Resource Materials) （1ST）

Carter, Nathan

Mathematical Assn of Amer（2009/07発売）

• 製本 Hardcover:ハードカバー版／ページ数 340 p.
• 言語 ENG
• 商品コード 9780883857571
• DDC分類 512.2

Full Description

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.

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.