Compact Textbooks in Mathematics

Geometry

Authors: Izmestiev, Ivan

  • This Book deals with classical geometry on the basis of the Erlangen program.
  • Summarizes what every geometer should know.
  • Provides a basis for the study of more advanced subjects and gives an outlook into some of these areas.
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Buy this book

eBook  
  • ISBN 978-3-319-50370-7
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Softcover ca. 46,79 €
price for Spain (gross)
  • Due: March 4, 2019
  • ISBN 978-3-319-50369-1
  • Free shipping for individuals worldwide
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

Affine, projective, spherical, Möbius, and hyperbolic geometries are covered by this textbook. Special emphasis is given on the groups of transformations in the spirit of the Erlangen program of Felix Klein as transformation groups not only provide a theoretical basis for the geometries, but also allow to solve concrete problems, which are an organic part of the book.

By establishing direct connections and by looking at the same notion or problem from different points of view the author gives a harmonic overview of the geometry. Starting with classical topics such as conics and quadrics, duality and polarity, cross-ratio, spherical and hyperbolic trigonometry he leads to less classical ones like compositions of reflections, volumes of spherical and hyperbolic tetrahedra, billiards, de Sitter geometry.

As only the knowledge of linear algebra, complex numbers and basic group theory is required this book is accessible to second year undergraduate students. However, graduate students in algebraic geometry, differential geometry, or geometric topology will also find this basic inventory of what every geometer should know a helpful hand.

About the authors

Ivan Izmestiev is a professor at University of Fribourg

Buy this book

eBook  
  • ISBN 978-3-319-50370-7
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Softcover ca. 46,79 €
price for Spain (gross)
  • Due: March 4, 2019
  • ISBN 978-3-319-50369-1
  • Free shipping for individuals worldwide
  • The final prices may differ from the prices shown due to specifics of VAT rules

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Bibliographic Information

Bibliographic Information
Book Title
Geometry
Authors
Series Title
Compact Textbooks in Mathematics
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-319-50370-7
Softcover ISBN
978-3-319-50369-1
Series ISSN
2296-4568
Edition Number
1
Topics