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Cover: 9780521347938 | Groups | A Path to Geometry | R. P. Burn | Taschenbuch | Paperback
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Groups
A Path to Geometry
Taschenbuch von R. P. Burn
Sprache: Englisch

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Beschreibung
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 Möbius 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.
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 Möbius 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.
Inhaltsverzeichnis
Preface; Acknowledgements; 1. Functions; 2. Permutations of a finite set; 3. Groups of permutations of R and C; 4. The Möbius group; 5. The regular solids; 6. Abstract groups; 7. Inversions of the Möbius plane and stereographic projection; 8. Equivalence relations; 9. Cosets; 10. Direct product; 11. Fields and vector spaces; 12. Linear transformations; 13. The general linear group GL(2, F); 14. The vector space V3 (F); 15. Eigenvectors and eigenvalues; 16. Homomorphisms; 17. Conjugacy; 18. Linear fractional groups; 19. Quaternions and rotations; 20. Affine groups; 21. Orthogonal groups; 22. Discrete groups fixing a line; 23. Wallpaper groups; Bibliography; Index.
Details
Erscheinungsjahr: 1987
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 256
ISBN-13: 9780521347938
ISBN-10: 0521347939
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Burn, R. P.
Hersteller: Cambridge University Press
Maße: 229 x 152 x 16 mm
Von/Mit: R. P. Burn
Erscheinungsdatum: 01.10.1987
Gewicht: 0,421 kg
preigu-id: 101150047
Inhaltsverzeichnis
Preface; Acknowledgements; 1. Functions; 2. Permutations of a finite set; 3. Groups of permutations of R and C; 4. The Möbius group; 5. The regular solids; 6. Abstract groups; 7. Inversions of the Möbius plane and stereographic projection; 8. Equivalence relations; 9. Cosets; 10. Direct product; 11. Fields and vector spaces; 12. Linear transformations; 13. The general linear group GL(2, F); 14. The vector space V3 (F); 15. Eigenvectors and eigenvalues; 16. Homomorphisms; 17. Conjugacy; 18. Linear fractional groups; 19. Quaternions and rotations; 20. Affine groups; 21. Orthogonal groups; 22. Discrete groups fixing a line; 23. Wallpaper groups; Bibliography; Index.
Details
Erscheinungsjahr: 1987
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 256
ISBN-13: 9780521347938
ISBN-10: 0521347939
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Burn, R. P.
Hersteller: Cambridge University Press
Maße: 229 x 152 x 16 mm
Von/Mit: R. P. Burn
Erscheinungsdatum: 01.10.1987
Gewicht: 0,421 kg
preigu-id: 101150047
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