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A Course in Modern Geometries

  • Judith N. Cederberg

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

Introduction

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.

Keywords

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

Authors and affiliations

  • Judith N. Cederberg
    • 1
  1. 1.Department of MathematicsSt. Olaf CollegeNorthfieldUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3831-5
  • Copyright Information Springer-Verlag New York 1989
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-3833-9
  • Online ISBN 978-1-4757-3831-5
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site