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Geometries (Paperback)
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Geometries (Paperback)
Series: Student Mathematical Library
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The book is an innovative modern exposition of geometry, or rather,
of geometries; it is the first textbook in which Felix Klein's
Erlangen Program (the action of transformation groups) is
systematically used as the basis for defining various geometries.
The course of study presented is dedicated to the proposition that
all geometries are created equal--although some, of course, remain
more equal than others. The author concentrates on several of the
more distinguished and beautiful ones, which include what he terms
``toy geometries'', the geometries of Platonic bodies, discrete
geometries, and classical continuous geometries. The text is based
on first-year semester course lectures delivered at the Independent
University of Moscow in 2003 and 2006. It is by no means a formal
algebraic or analytic treatment of geometric topics, but rather, a
highly visual exposition containing upwards of 200 illustrations.
The reader is expected to possess a familiarity with elementary
Euclidean geometry, albeit those lacking this knowledge may refer
to a compendium in Chapter 0. Per the author's predilection, the
book contains very little regarding the axiomatic approach to
geometry (save for a single chapter on the history of non-Euclidean
geometry), but two Appendices provide a detailed treatment of
Euclid's and Hilbert's axiomatics. Perhaps the most important
aspect of this course is the problems, which appear at the end of
each chapter and are supplemented with answers at the conclusion of
the text. By analyzing and solving these problems, the reader will
become capable of thinking and working geometrically, much more so
than by simply learning the theory. Ultimately, the author makes
the distinction between concrete mathematical objects called
``geometries'' and the singular ``geometry'', which he understands
as a way of thinking about mathematics. Although the book does not
address branches of mathematics and mathematical physics such as
Riemannian and Kahler manifolds or, say, differentiable manifolds
and conformal field theories, the ideology of category language and
transformation groups on which the book is based prepares the
reader for the study of, and eventually, research in these
important and rapidly developing areas of contemporary mathematics.
General
Imprint: |
American Mathematical Society
|
Country of origin: |
United States |
Series: |
Student Mathematical Library |
Release date: |
August 2012 |
Authors: |
A.B. Sossinsky
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Dimensions: |
218 x 140 x 16mm (L x W x T) |
Format: |
Paperback
|
Pages: |
301 |
ISBN-13: |
978-0-8218-7571-1 |
Categories: |
Books
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LSN: |
0-8218-7571-X |
Barcode: |
9780821875711 |
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