© 2001

A Course in Modern Geometries


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

Table of contents

  1. Front Matter
    Pages i-xix
  2. Judith N. Cederberg
    Pages 1-32
  3. Judith N. Cederberg
    Pages 33-97
  4. Judith N. Cederberg
    Pages 99-211
  5. Judith N. Cederberg
    Pages 213-313
  6. Judith N. Cederberg
    Pages 315-387
  7. Back Matter
    Pages 389-444

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.


Area Fractal Self-similarity algebra geometry similarity

Authors and affiliations

  1. 1.Department of MathematicsNorthfieldUSA

Bibliographic information

  • Book Title A Course in Modern Geometries
  • Authors Judith N. Cederberg
  • Series Title Undergraduate Texts in Mathematics
  • DOI
  • Copyright Information Springer-Verlag New York 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-98972-3
  • Softcover ISBN 978-1-4419-3193-1
  • eBook ISBN 978-1-4757-3490-4
  • Series ISSN 0172-6056
  • Edition Number 2
  • Number of Pages XIX, 441
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Geometry
  • Buy this book on publisher's site


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."