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Search - A Course in Modern Geometries (Undergraduate Texts in Mathematics)

A Course in Modern Geometries - Undergraduate Texts in Mathematics
Author: 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 continues the synthetic approach as it introduces Euclid's geometry and ideas of non-Euclidean geometry. I... more »n Chapter 3, a new introduction to symmetry and hands-on explorations of isometries precedes the extensive analytic treatment of isometries, similarities and affinities. A new concluding section explores isometries of space. 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. The new Chapter 5 uses a descriptive and exploratory approach to introduce chaos theory and fractal geometry, stressing the self-similarity of fractals and their generation by transformations from Chapter 3. Each chapter includes a list of suggested resources for applications or related topics in areas such as art and history. The second edition also includes pointers to the web location of author-developed guides for dynamic software explorations of the Poincar\'{e} model, isometries, projectivities, conics and fractals. Parallel versions of these explorations are available for {\em Cabri Geometry} and {\em Geometer's Sketchpad}. Judith N. Cederberg is an associate professor of mathematics at St. Olaf College in Minnesota where she often teaches a modern geometry course. In the last decade, she has been one of the Principal Investigators for two St. Olaf-based NSF Teacher Enhancement projects designed to revitalize the teaching of geometry in secondary school. 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 or related topics in areas such as art and history.

ISBN-13: 9780387969220
ISBN-10: 0387969225
Publication Date: 11/3/1995
Pages: 232
Edition: Corrected
Rating:

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Publisher: Springer
Book Type: Hardcover
Members Wishing: 0
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