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Course in Modern Geometries

Course in Modern Geometries - 2nd edition

ISBN13: 978-0387989723

Cover of Course in Modern Geometries 2ND 01 (ISBN 978-0387989723)
ISBN13: 978-0387989723
ISBN10: 0387989722

Cover type: Hardback
Edition: 2ND 01
Copyright: 2001
Publisher: Springer-Verlag New York
Published: 2001
International: No

List price: $64.95

Course in Modern Geometries - 2ND 01 edition

ISBN13: 978-0387989723

Judith N. Cederberg

ISBN13: 978-0387989723
ISBN10: 0387989722

Cover type: Hardback
Edition: 2ND 01
Copyright: 2001
Publisher: Springer-Verlag New York
Published: 2001
International: No
Summary

A Course in Modern Geometries, Second Edition, 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. In Chapter 3, a new introduction to symmetry and hands-on explorations of isometries precede 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 Poincaré model, isometries, projectivities, conics and fractals. Parallel versions of these explorations are available for Cabri Geometry and Geometer's Sketchpad.

Author Bio

Cederberg, Judith N. : St. Olaf College, Northfield MN


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.

Table of Contents

Axiomatic systems and finite geometries
Non-Euclidean geometry
Geometric transformations of the Euclidean plane
Projective geometry
Chaos to symmetry: an introduction to fractal geometry
Appendices
References
Index