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Books > Science & Mathematics > Mathematics > Topology
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Geometry and Topology (Paperback)
Loot Price: R1,124
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Geometry and Topology (Paperback)
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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 Moebius 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.
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