"Groups and Geometry" contains the Oxford Mathematical Institute notes for undergraduates and first-year postgraduates. The content, although guided by the Oxford syllabus, covers other material, some introductory and some that, because of limited time, had to be excluded from or curtailed in the syllabus. This book is about the measurement of symmetry, which is what groups are for. Symmetry is visable in all parts of mathematics and in many other areas, and geometrical symmetry is the most visable of all. For this reason, groups and geometry are close neighbours. The first half of the book (chapters 1-9) covers groups and the second half (chapters 10-18) covers geometry, with the symbiotic relationship between the two more than justifying the union. Both parts contain a number of exercises that should be helpful to the reader wishing to gain a fuller understanding of this area of mathematics.
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Illustrationen
ISBN-13
978-0-19-853452-5 (9780198534525)
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Schweitzer Klassifikation
A survey of some group theory; a menagerie of groups; actions of groups; a garden of G-spaces; transitivity and orbits; the classification of transitive G-spaces; G-morphisms; group actions in group theory; actions count; geometry - an introduction; the axiomatization of geometry; affine geometry; projective geometry; Euclidean geometry; finite groups of isometries; complex numbers and quaternions; inversive geometry; topological considerations; the group theory of Rubik's magic cube.
