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Groups : A Path to Geometry - R. P. Burn


A Path to Geometry


Published: 2nd November 1987
RRP $81.95
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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

Permutations of a finite set
Groups of permutations of R and C
The M÷bius group
The regular solids
Abstract groups
Inversions of the M÷bius plane and stereographic projection
Equivalence relations
Direct product
Fields and vector spaces
Linear transformations
The general linear group GL(2, F)
The vector space V3 (F)
Eigenvectors and eigenvalues
Linear fractional groups
Quaternions and rotations
Affine groups
Orthogonal groups
Discrete groups fixing a line
Wallpaper groups
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521347938
ISBN-10: 0521347939
Series: Path to Geometry
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 256
Published: 2nd November 1987
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 1.7
Weight (kg): 0.31