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A Course in Modern Geometries

  • Textbook
  • © 1989

Overview

Authors:
  1. Judith N. Cederberg

    1. Department of Mathematics, St. Olaf College, Northfield, USA

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

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xii
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  2. Axiomatic Systems and Finite Geometries

    • Judith N. Cederberg
    Pages 1-24

  3. Non-Euclidean Geometry

    • Judith N. Cederberg
    Pages 25-73

  4. Geometric Transformations of the Euclidean Plane

    • Judith N. Cederberg
    Pages 74-126

  5. Projective Geometry

    • Judith N. Cederberg
    Pages 127-200

  6. Back Matter

    Pages 201-233
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Keywords

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.

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, St. Olaf College, Northfield, USA

    Judith N. Cederberg

Bibliographic Information

  • Book Title: A Course in Modern Geometries

  • Authors: Judith N. Cederberg

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-3831-5

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1989

  • eBook ISBN: 978-1-4757-3831-5Published: 09 March 2013

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XII, 233

  • Number of Illustrations: 77 b/w illustrations

  • Topics: Geometry

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