000			01958cam a22001818i 4500
999			_c223241 _d223241
020			_a9781107103405 (hardback)
082	0	0	_a516 _bJOH. G
100	1		_aJohnson, Norman W.,
245	1	0	_aGeometries and transformations / _cNorman W. Johnson, Wheaton College.
260			_aUK _bCambridge University Press _c2018
300			_apages cm
504			_aIncludes bibliographical references and index.
505	8		_aMachine generated contents note: Introduction; 1. Homogenous spaces; 2. Linear geometries; 3. Circular geometries; 4. Real collineation groups; 5. Equiareal collineations; 6. Real isometry groups; 7. Complex spaces; 8. Complex collineation groups; 9. Circularities and concatenations; 10. Unitary isometry groups; 11. Finite symmetry groups; 12. Euclidean symmetry groups; 13. Hyperbolic coxeter groups; 14. Modular transformations; 15. Quaternionic modular groups.
520			_a"Euclidean and other geometries are distinguished by the transformations that preserve their essential properties. Using linear algebra and transformation groups, this book provides a readable exposition of how these classical geometries are both differentiated and connected. Following Cayley and Klein, the book builds on projective and inversive geometry to construct 'linear' and 'circular' geometries, including classical real metric spaces like Euclidean, hyperbolic, elliptic, and spherical, as well as their unitary counterparts. The first part of the book deals with the foundations and general properties of the various kinds of geometries. The latter part studies discrete-geometric structures and their symmetries in various spaces. Written for graduate students, the book includes numerous exercises and covers both classical results and new research in the field. An understanding of analytic geometry, linear algebra, and elementary group theory is assumed"--
650		0	_aGeometry _vTextbooks.
650		7	_aMATHEMATICS / Topology.
942			_cBK