000			04078nam a22003377a 4500
003			OSt
005			20240627130213.0
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020			_a9781470425951
040			_aNISER LIBRARY _beng _cNISER LIBRARY
041			_aEnglish
082			_a514 _bSOS-G
100			_aSossinsky, A.B. _q(Alekseĭ Bronislavovich)
245			_aGeometries
260			_aProvidence : _bAmerican Mathematical Society, _c2012
300			_axvi, 301 p. : _bill. ; _c22 cm.
490			_aStudent mathematical library ; _vvolume 64
504			_aIncludes bibliographical references (p. 287-298) and index.
520			_aThe 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 Kähler 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.
521			_aUndergraduates interested in geometry.
650			_aGeometry
650			_aGeometry -- Instructional exposition (textbooks, tutorial papers, etc.).
650			_aGeometry -- Research exposition (monographs, survey articles).
650			_aHistory and biography -- History of mathematics and mathematicians -- Greek, Roman.
650			_aHistory and biography -- History of mathematics and mathematicians -- 19th century.
650			_aCategory theory; homological algebra -- Instructional exposition (textbooks, tutorial papers, etc.).
856			_3Table of Contents _uhttps://www.ams.org/bookstore/pspdf/stml-64-toc.pdf?_gl=1*1wkqjf9*_ga*OTY4OTA1OTY3LjE3MTc5OTU1MTY.*_ga_26G4XFTR63*MTcxOTQ2NDk2MC41LjEuMTcxOTQ3MzEyNC4wLjAuMA..
856			_3Index _uhttps://www.ams.org/bookstore/pspdf/stml-64-index.pdf?_gl=1*bipd3i*_ga*OTY4OTA1OTY3LjE3MTc5OTU1MTY.*_ga_26G4XFTR63*MTcxOTQ2NDk2MC41LjEuMTcxOTQ3MzQ0OC4wLjAuMA..
856			_3Reviews _uhttps://www.goodreads.com/book/show/14997000-geometries-student-mathematical-library?from_search=true&from_srp=true&qid=cEXDEH0i5s&rank=1#CommunityReviews
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