Groups: A Path to Geometry

Description

Following the same successful approach as Dr. Burn's previous book on number theory, this text consists of a carefully constructed sequence of questions that will enable the reader, through participation, to study all the group theory covered by a conventional first university course. An introduction to vector spaces, leading to the study of linear groups, and an introduction to complex numbers, leading to the study of Mobius transformations and stereographic projection, are also included. Quaternions and their relationships to 3-dimensional isometries are covered, and the climax of the book is a study of the crystallographic groups, with a complete analysis of these groups in two dimensions.

'There is much here of value both for students and for those who are seeking a refresher course in modern group theory.' Times Higher Education Supplement '... the author is encouraging throughout and patiently leads his audience to an understanding of the interplay between group theory and the classical geometry of two and three dimensions ... the author is a knowledgeable and considerate guide.' Mathematical Gazette