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020 _a9783031514142
_9978-3-031-51414-2
024 7 _a10.1007/978-3-031-51414-2
_2doi
050 4 _aQA440-699
072 7 _aPBM
_2bicssc
072 7 _aMAT012000
_2bisacsh
072 7 _aPBM
_2thema
100 1 _aBădescu, Lucian.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_975431
245 1 0 _aLectures on Geometry
_h[electronic resource] /
_cby Lucian Bădescu, Ettore Carletti.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXIII, 490 p. 50 illus., 23 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLa Matematica per il 3+2,
_x2038-5757 ;
_v158
505 0 _a1 Linear Algebra -- 2 Bilinear and quadratic forms -- 3 Affine Spaces -- 4 Euclidean Spaces -- 5 Affine hyperquadrics -- 6 Projective Spaces -- 7 Desargues' Axiom -- 8 General Linear Projective Automorphisms -- 9 Affine Geometry and Projective Geometry -- 10 Projective hyperquadrics -- 11 Bezout's Theorem for Curves of P^2(K) -- 12 Absolute plane geometry -- 13 Cayley-Klein Geometries.
520 _aThis is an introductory textbook on geometry (affine, Euclidean and projective) suitable for any undergraduate or first-year graduate course in mathematics and physics. In particular, several parts of the first ten chapters can be used in a course of linear algebra, affine and Euclidean geometry by students of some branches of engineering and computer science. Chapter 11 may be useful as an elementary introduction to algebraic geometry for advanced undergraduate and graduate students of mathematics. Chapters 12 and 13 may be a part of a course on non-Euclidean geometry for mathematics students. Chapter 13 may be of some interest for students of theoretical physics (Galilean and Einstein’s general relativity). It provides full proofs and includes many examples and exercises. The covered topics include vector spaces and quadratic forms, affine and projective spaces over an arbitrary field; Euclidean spaces; some synthetic affine, Euclidean and projective geometry; affine and projective hyperquadrics with coefficients in an arbitrary field of characteristic different from 2; Bézout’s theorem for curves of P^2 (K), where K is a fixed algebraically closed field of arbitrary characteristic; and Cayley-Klein geometries.
650 0 _aGeometry.
_968763
650 1 4 _aGeometry.
_968763
700 1 _aCarletti, Ettore.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_975432
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031514135
776 0 8 _iPrinted edition:
_z9783031514159
830 0 _aLa Matematica per il 3+2,
_x2038-5757 ;
_v158
_970145
856 4 0 _uhttps://doi.org/10.1007/978-3-031-51414-2
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c59235
_d59235