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A Course in Modern Geometries

  • Textbook
  • © 2001
  • Latest edition

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Authors:
  1. Judith N. Cederberg

    1. Department of Mathematics, Northfield, USA

Part of the book series: Undergraduate Texts in Mathematics (UTM)

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About this book

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.

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xix
    Download chapter PDF

  2. Axiomatic Systems and Finite Geometries

    • Judith N. Cederberg
    Pages 1-32

  3. Non-Euclidean Geometry

    • Judith N. Cederberg
    Pages 33-97

  4. Geometric Transformations of the Euclidean Plane

    • Judith N. Cederberg
    Pages 99-211

  5. Projective Geometry

    • Judith N. Cederberg
    Pages 213-313

  6. Chaos to Symmetry: An Introduction to Fractal Geometry

    • Judith N. Cederberg
    Pages 315-387

  7. Back Matter

    Pages 389-444
    Download chapter PDF
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Reviews

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

Authors and Affiliations

  • Department of Mathematics, Northfield, USA

    Judith N. Cederberg

Accessibility Information

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Bibliographic Information

  • Book Title: A Course in Modern Geometries

  • Authors: Judith N. Cederberg

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-3490-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2001

  • Hardcover ISBN: 978-0-387-98972-3Published: 29 November 2000

  • Softcover ISBN: 978-1-4419-3193-1Published: 01 December 2010

  • eBook ISBN: 978-1-4757-3490-4Published: 09 March 2013

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 2

  • Number of Pages: XIX, 441

  • Topics: Geometry

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