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" A Course in Modern Geometries "
by Judith N. Cederberg.
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BL
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574593
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b403812
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| Main Entry
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Cederberg, Judith N.
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| Title & Author
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A Course in Modern Geometries\ by Judith N. Cederberg.
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| Publication Statement
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New York, NY :: Springer New York :: Imprint: Springer,, 1989.
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| Series Statement
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Undergraduate Texts in Mathematics,
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| ISBN
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9781475738315
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: 9781475738339
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| Contents
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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.
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| Abstract
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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.
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Mathematics.
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Geometry.
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SpringerLink (Online service)
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