Author | Cederberg, Judith N. author |
---|---|

Title | A Course in Modern Geometries [electronic resource] / by Judith N. Cederberg |

Imprint | New York, NY : Springer New York : Imprint: Springer, 1989 |

Connect to | http://dx.doi.org/10.1007/978-1-4757-3831-5 |

Descript | XII, 233 p. online resource |

SUMMARY

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

CONTENT

1 Axiomatic Systems and Finite Geometries -- 2 Non-Euclidean Geometry -- 3 Geometric Transformations of the Euclidean Plane -- 4 Projective Geometry -- Appendixes -- A. Euclidโ{128}{153}s Definitions, Postulates, and the First 30 Propositions of Book I -- B. Hilbertโ{128}{153}s Axioms for Plane Geometry -- C. Birkhoffโ{128}{153}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

Mathematics
Geometry
Mathematics
Geometry