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Geometry and Topology

£51.99

textbook
  • Date Published: November 2005
  • availability: Available
  • format: Paperback
  • isbn: 9780521613255

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About the Authors
  • Geometry provides a whole range of views on the universe, serving as the inspiration, technical toolkit and ultimate goal for many branches of mathematics and physics. This book introduces the ideas of geometry, and includes a generous supply of simple explanations and examples. The treatment emphasises coordinate systems and the coordinate changes that generate symmetries. The discussion moves from Euclidean to non-Euclidean geometries, including spherical and hyperbolic geometry, and then on to affine and projective linear geometries. Group theory is introduced to treat geometric symmetries, leading to the unification of geometry and group theory in the Erlangen program. An introduction to basic topology follows, with the Möbius strip, the Klein bottle and the surface with g handles exemplifying quotient topologies and the homeomorphism problem. Topology combines with group theory to yield the geometry of transformation groups,having applications to relativity theory and quantum mechanics. A final chapter features historical discussions and indications for further reading. With minimal prerequisites, the book provides a first glimpse of many research topics in modern algebra, geometry and theoretical physics. The book is based on many years' teaching experience, and is thoroughly class-tested. There are copious illustrations, and each chapter ends with a wide supply of exercises. Further teaching material is available for teachers via the web, including assignable problem sheets with solutions.

    • Exercises and practical illustrations introduce topics across maths and its applications
    • Prerequisites are minimal: ideally suited to beginner courses and newcomers to the subject
    • Further teaching material is available for teachers, including assignable problem sheets with solutions
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    Product details

    • Date Published: November 2005
    • format: Paperback
    • isbn: 9780521613255
    • length: 216 pages
    • dimensions: 244 x 170 x 12 mm
    • weight: 0.443kg
    • contains: 93 b/w illus. 156 exercises
    • availability: Available
  • Table of Contents

    Introduction
    1. Euclidean geometry
    2. Composing maps
    3. Non-Euclidean
    4. Affine geometry
    5. Projective geometry
    6. Geometry and group theory
    7. Topology
    8. Geometry of transformation groups
    9. Concluding remarks
    A. Metrics
    B. Linear algebra
    References
    Index.

  • Instructors have used or reviewed this title for the following courses

    • Geometry in Action
    • Geometry ll
  • Authors

    Miles Reid, University of Warwick
    Miles Reid is a Professor of Mathematics at the Mathematics Institute, University of Warwick.

    Balazs Szendroi, University of Oxford
    Balàzs Szendröi is a Tutor and Martin Powell Fellow in Pure Mathematics at St Peter's College, and a Faculty Lecturer in the Mathematical Institute, University of Oxford.

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