© 1989

A Course in Modern Geometries


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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Judith N. Cederberg
    Pages 1-24
  3. Judith N. Cederberg
    Pages 25-73
  4. Judith N. Cederberg
    Pages 74-126
  5. Judith N. Cederberg
    Pages 127-200
  6. Back Matter
    Pages 201-233

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 introduces Euclid's geometry and the basic ideas of non-Euclidean geometry. The synthetic approach of Chapters 1 - 2 is followed by the analytic treatment of transformations of the Euclidean plane in Chapter 3. 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. Each chapter includes a list of suggested sources for applications and/or related topics.


Abstract algebra Excel Finite Matrix Non-Euclidean Geometry algebra design form framework geometry linear algebra mathematics presentation projective geometry transformation

Authors and affiliations

  1. 1.Department of MathematicsSt. Olaf CollegeNorthfieldUSA

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 1989
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-96922-0
  • Softcover ISBN 978-1-4757-3833-9
  • eBook ISBN 978-1-4757-3831-5
  • Series ISSN 0172-6056
  • Edition Number 1
  • Number of Pages XII, 233
  • Number of Illustrations 77 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."