A Course in Modern Geometries

Judith N. Cederberg

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English

Springer-Verlag New York Inc.
01 December 2010

Mathematics & Sciences; Geometry

Series: Undergraduate Texts in Mathematics

"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. In 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 Poincaré model, isometries, projectivities, conics and fractals. Parallel versions of these explorations are available for ""Cabri Geometry"" and ""Geometer's Sketchpad"".

Judith N. Cederberg is an associate professor of mathematics at St. Olaf College in Minnesota."

By: Judith N. Cederberg
Imprint: Springer-Verlag New York Inc.
Country of Publication: United States
Edition: Softcover reprint of hardcover 2nd ed. 2001
Dimensions: Height: 235mm, Width: 155mm, Spine: 23mm
Weight: 712g
ISBN: 9781441931931
ISBN 10: 1441931937
Series: Undergraduate Texts in Mathematics
Pages: 441
Publication Date: 01 December 2010
Audience: College/higher education , A / AS level
Format: Paperback
Publisher's Status: Active

1 Axiomatic Systems and Finite Geometries.- 2 Non-Euclidean Geometry.- 3 Geometric Transformations of the Euclidean Plane.- 4 Projective Geometry.- 5 Chaos to Symmetry: An Introduction to Fractal Geometry.- Appendices.- B Hilbert’s Axioms for Plane Geometry.- C Birkhoff’s Postulates for Euclidean Plane Geometry.- D The SMSG Postulates for Euclidean Geometry.- E Some SMSG Definitions for Euclidean Geometry.- F The ASA Theorem.- References.

Reviews for A Course in Modern Geometries

Second Edition J. N. Cederberg A Course in Modern Geometries Cederberg,s book has the virtue of exceptionally clear exposition and at the same time, it is brief enough not to exhaust one,s patience ... I have seen hundreds of college-level texts on geometry and this is one of the handful I like the most. -THE UMAP JOURNAL