Geometries
 Author/Creator
 Sosinskiĭ, A. B. (Alekseĭ Bronislavovich)
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2012.
 Physical description
 xvi, 301 p. : ill ; 22 cm.
 Series
 Student mathematical library ; v. 64.
Access
Available online

Stacks

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QA445 .S593 2012

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QA445 .S593 2012
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Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Publisher's Summary
 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 equalalthough 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 firstyear 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 nonEuclidean 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Geometry > Textbooks.
 Geometry  Instructional exposition (textbooks, tutorial papers, etc.)
 Geometry  Research exposition (monographs, survey articles)
 History and biography  History of mathematics and mathematicians  Greek, Roman.
 History and biography  History of mathematics and mathematicians  19th century.
 Category theory; homological algebra  Instructional exposition (textbooks, tutorial papers, etc.)
Bibliographic information
 Publication date
 2012
 Responsibility
 A.B. Sossinsky.
 Series
 Student mathematical library ; v. 64
 ISBN
 082187571X (alk. paper)
 9780821875711 (alk. paper)