Notes on Geometry

1. Front Matter

   Pages I-VIII

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2. Introduction

   • Elmer G. Rees

   Pages 1-1

3. Euclidean Geometry

   • Elmer G. Rees

   Pages 3-49

4. Projective Geometry

   • Elmer G. Rees

   Pages 51-78

5. Hyperbolic Geometry

   • Elmer G. Rees

   Pages 79-104

6. Back Matter

   Pages 105-114

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In recent years, geometry has played a lesser role in undergraduate courses than it has ever done. Nevertheless, it still plays a leading role in mathematics at a higher level. Its central role in the history of mathematics has never been disputed. It is important, therefore, to introduce some geometry into university syllabuses. There are several ways of doing this, it can be incorporated into existing courses that are primarily devoted to other topics, it can be taught at a first year level or it can be taught in higher level courses devoted to differential geometry or to more classical topics. These notes are intended to fill a rather obvious gap in the literature. It treats the classical topics of Euclidean, projective and hyperbolic geometry but uses the material commonly taught to undergraduates: linear algebra, group theory, metric spaces and complex analysis. The notes are based on a course whose aim was two fold, firstly, to introduce the students to some geometry and secondly to deepen their understanding of topics that they have already met. What is required from the earlier material is a familiarity with the main ideas, specific topics that are used are usually redone.

• Area
• Geometrie
• Microsoft Access
• Symmetry group
• algebra
• finite group
• geometry
• group theory
• hyperbolic geometry
• linear algebra
• metric space
• projective geometry
• quadratic form
• symmetry
• topology

From the Reviews: "This book is meant to fill a certain gap in the literature. Namely, it treats the classical topics of Euclidean, projective and hyperbolic geometry using the modern language of linear algebra, group theory, metric spaces and elementary complex analysis. In each of those geometries the main constructions are fully explained and the reader can check his understanding with the sets of problems included. The mixture of classical and modern material which is so difficult to find in the textbooks nowadays makes of this nice little book an enjoyable and profitable reading."
A. Dimca, Revue Roumaine de Mathématiques Pures et Appliquées (No. 5/1985)

• School of Mathematics, The University of Edinburgh, Edinburgh, Scotland

  Elmer G. Rees

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