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Birkhäuser

Introduction to Classical Geometries

  • Textbook
  • © 2007

Overview

Authors:
  1. Ana Irene Ramírez Galarza

    1. Departamento de Matemáticas Facultad de Ciencias, Universidad Nacional Autónoma de México, México, México

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  2. José Seade

    1. Instituto de Matemáticas Unidad Cuernavaca, Universidad Nacional Autónoma de México, Cuernavaca, Morelos, México

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  • Presents all the classical geometries in a unified way, with many illustrations, thus making their understanding easier
  • Though the proofs and arguments are in general absolutely rigorous, emphasis is put on the concepts and the ideas, not on the technical difficulties
  • Presentation of several advanced concepts of geometry in a very simple way, so that they become easily accessible: the only pre-requisites are calculus, linear algebra and basic analytic geometry
  • Many interesting problems given as exercises
  • Wide bibliography for further reading
  • Using elementary mathematics, more advanced concepts such as manifolds and Lie groups, group actions, curvature and foliations are introduced
  • Includes supplementary material: sn.pub/extras

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-x
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  2. Euclidean geometry

    Pages 1-73

  3. Affine geometry

    Pages 75-89

  4. Projective geometry

    Pages 91-147

  5. Hyperbolic geometry

    Pages 149-198

  6. Appendices

    Pages 199-210

  7. Back Matter

    Pages 211-219
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Keywords

About this book

Geometry is one of the oldest branches of mathematics, nearly as old as human culture.Itsbeautyhasalwaysfascinatedmathematicians,amongothers.Inwriting this book we had the purpose of sharing with readers the pleasure derived from studying geometry,as well as giving a tasteof its importance, its deep connections with other branches of mathematics and the highly diverse viewpoints that may be taken by someone entering this ?eld. We also want to propose a speci?c way to introduce concepts that have arisen from the heyday of the Greek school of geometry to the present day. We workwithcoordinatemodels,sincethis facilitatestheuseofalgebraicandanalytic results, and we follow the viewpoint proposed by Felix Klein in the 19th century, of studying geometry via groups of symmetries of the space in question. We intend this book to be both an introduction to the subject addressed to undergraduate students in mathematics and physics, and a useful text-book for mathematicians and scientists in general who want to learn the basics of classical geometry: Euclidean, a?ne, elliptic, hyperbolic and projective geometry. These are all presented in a uni?ed way and the essential content of this book may be covered in a single semester, though a longer period of study would allow the student to grasp and assimilate better the material in it.

Reviews

From the reviews:

“This book offers an introduction to classical geometry. … The book contains many figures, which help the reader to develop geometric intuition, and lots of exercises. To follow the presentation, only a basic background in analysis and linear algebra is required, some necessary facts are collected in an appendix.” (A. Cap, Monatshefte für Mathematik, Vol. 158 (2), October, 2009)

Authors and Affiliations

  • Departamento de Matemáticas Facultad de Ciencias, Universidad Nacional Autónoma de México, México, México

    Ana Irene Ramírez Galarza

  • Instituto de Matemáticas Unidad Cuernavaca, Universidad Nacional Autónoma de México, Cuernavaca, Morelos, México

    José Seade

Bibliographic Information

  • Book Title: Introduction to Classical Geometries

  • Authors: Ana Irene Ramírez Galarza, José Seade

  • DOI: https://doi.org/10.1007/978-3-7643-7518-8

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Birkhäuser Basel 2007

  • Softcover ISBN: 978-3-7643-7517-1Published: 20 March 2007

  • eBook ISBN: 978-3-7643-7518-8Published: 02 May 2007

  • Edition Number: 1

  • Number of Pages: X, 220

  • Additional Information: Original Spanish edition published by Las Prensas de Ciencia of the Universidad Nacional Autónoma de M'exico

  • Topics: Geometry, Mathematics, general

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