Description

Book Synopsis
Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry.

Trade Review
Despite the beauty of the subject and the many applications to other areas of mathematics and physics, the geometry of group actions is not a common part of an undergraduate mathematics curriculum. The book under review attempts to fill that gap...The text is well written in a conversational style with many nice figures. It is a pleasure to read, for the instructor." — Cristopher H. Cashen, Mathematical Reviews

"The clarity of the exposition and the richness of the topics make this a valuable addition to undergraduate math libraries." — J. McCleary, CHOICE

Table of Contents
  • Elements of group theory
  • Symmetry in the Euclidean world: Groups of isometries of planar and spatial objects
  • Groups of matrices: Linear algebra and symmetry in various geometries
  • Fundamental group: A different kind of group associated to geometric objects
  • From groups to geometric objects and back
  • Groups at large scale
  • Hints to selected exercises
  • Suggestions for projects and further reading
  • Bibliography
  • Index

From Groups to Geometry and Back

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    A Paperback by Vaughn Climenhaga, Anatole Katok

    £46.80

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    RRP £52.00 – you save £5.20 (10%)

    Order before 4pm today for delivery by Thu 26 Nov 2026.

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      Book details

      Publisher American Mathematical Society
      Published 3/30/2017 12:00:00 AM
      ISBN-13 9781470434793
      978-1470434793
      ISBN-10 1470434792
      Also in:
      Geometry

      Description

      Book Synopsis
      Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry.

      Trade Review
      Despite the beauty of the subject and the many applications to other areas of mathematics and physics, the geometry of group actions is not a common part of an undergraduate mathematics curriculum. The book under review attempts to fill that gap...The text is well written in a conversational style with many nice figures. It is a pleasure to read, for the instructor." — Cristopher H. Cashen, Mathematical Reviews

      "The clarity of the exposition and the richness of the topics make this a valuable addition to undergraduate math libraries." — J. McCleary, CHOICE

      Table of Contents
      • Elements of group theory
      • Symmetry in the Euclidean world: Groups of isometries of planar and spatial objects
      • Groups of matrices: Linear algebra and symmetry in various geometries
      • Fundamental group: A different kind of group associated to geometric objects
      • From groups to geometric objects and back
      • Groups at large scale
      • Hints to selected exercises
      • Suggestions for projects and further reading
      • Bibliography
      • Index

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