Description
Book SynopsisGroups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry.
Trade ReviewDespite the beauty of the subject and the many applications to other areas of mathematics and physics, the geometry of group actions is not a common part of an undergraduate mathematics curriculum. The book under review attempts to fill that gap...The text is well written in a conversational style with many nice figures. It is a pleasure to read, for the instructor." — Cristopher H. Cashen,
Mathematical Reviews"The clarity of the exposition and the richness of the topics make this a valuable addition to undergraduate math libraries." — J. McCleary,
CHOICETable of Contents
- Elements of group theory
- Symmetry in the Euclidean world: Groups of isometries of planar and spatial objects
- Groups of matrices: Linear algebra and symmetry in various geometries
- Fundamental group: A different kind of group associated to geometric objects
- From groups to geometric objects and back
- Groups at large scale
- Hints to selected exercises
- Suggestions for projects and further reading
- Bibliography
- Index
