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A Course in Modern Geometries

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概要 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 i...n 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.続きを見る
目次 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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登録日 2020.06.27
更新日 2020.06.28