A Course in Modern Geometries

1. Front Matter

   Pages i-xii

   PDF

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

   PDF

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

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

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

  Judith N. Cederberg

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