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A Course in Modern Geometries

A Course in Modern Geometries
Catalogue Information
Field name Details
Dewey Class 516
Title A Course in Modern Geometries ([EBook] /) / by Judith N. Cederberg.
Author Cederberg, Judith N.
Other name(s) SpringerLink (Online service)
Publication New York, NY : : Springer New York : : Imprint: Springer, , 1989.
Physical Details XII, 233 p. 77 illus. : online resource.
Series Undergraduate texts in mathematics 0172-6056
ISBN 9781475738315
Summary Note A Course in Modern Geometries is designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. Chapter 1 presents several finite geometries in an axiomatic framework. Chapter 2 introduces Euclid's geometry and the basic ideas of non-Euclidean geometry. The synthetic approach of Chapters 1 - 2 is followed by the analytic treatment of transformations of the Euclidean plane in Chapter 3. Chapter 4 presents plane projective geometry both synthetically and analytically. The extensive use of matrix representations of groups of transformations in Chapters 3 - 4 reinforces ideas from linear algebra and serves as excellent preparation for a course in abstract algebra. Each chapter includes a list of suggested sources for applications and/or related topics.:
Contents note 1 Axiomatic Systems and Finite Geometries -- 2 Non-Euclidean Geometry -- 3 Geometric Transformations of the Euclidean Plane -- 4 Projective Geometry -- Appendixes -- A. Euclid’s Definitions, Postulates, and the First 30 Propositions of Book I -- B. Hilbert’s Axioms for Plane Geometry -- C. Birkhoff’s Postulates for Euclidean Plane Geometry -- D. The S.M.S.G. Postulates for Euclidean Geometry -- E. Some S.M.S.G. Definitions for Euclidean Geometry -- F. The A.S.A. Theorem -- G. References.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1007/978-1-4757-3831-5
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