Undergraduate Texts in Mathematics

A Course in Modern Geometries

Authors: Cederberg, Judith

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  • ISBN 978-1-4757-3490-4
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Hardcover $64.95
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  • ISBN 978-0-387-98972-3
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Softcover $64.95
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  • ISBN 978-1-4419-3193-1
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About this Textbook

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.

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


Table of contents (5 chapters)

  • Axiomatic Systems and Finite Geometries

    Cederberg, Judith N.

    Pages 1-32

  • Non-Euclidean Geometry

    Cederberg, Judith N.

    Pages 33-97

  • Geometric Transformations of the Euclidean Plane

    Cederberg, Judith N.

    Pages 99-211

  • Projective Geometry

    Cederberg, Judith N.

    Pages 213-313

  • Chaos to Symmetry: An Introduction to Fractal Geometry

    Cederberg, Judith N.

    Pages 315-387

Buy this book

eBook $49.99
price for USA (gross)
  • ISBN 978-1-4757-3490-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $64.95
price for USA
  • ISBN 978-0-387-98972-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $64.95
price for USA
  • ISBN 978-1-4419-3193-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
A Course in Modern Geometries
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
2001
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-3490-4
DOI
10.1007/978-1-4757-3490-4
Hardcover ISBN
978-0-387-98972-3
Softcover ISBN
978-1-4419-3193-1
Series ISSN
0172-6056
Edition Number
2
Number of Pages
XIX, 441
Topics