A Course in Modern Geometries [electronic resource] / by Judith N. Cederberg.
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-Euc...
Saved in:
| Online Access: |
Full Text (via Springer) |
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| Main Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY :
Springer New York,
1989.
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| Series: | Undergraduate texts in mathematics.
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| Subjects: |
MARC
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| 245 | 1 | 2 | |a A Course in Modern Geometries |h [electronic resource] / |c by Judith N. Cederberg. |
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| 520 | |a 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. | ||
| 505 | 0 | |a 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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