03218nam a22004455i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001600186072002300202072001500225100008700240245008900327250001800416264006900434300006600503336002600569337002600595338003600621347002400657490004800681505039300729520124301122650002102365650002102386700008602407710003402493773002602527776003602553776003602589830005502625856004602680912001402726912001502740999001702755978-3-031-51414-2DE-He21320251030112001.0cr nn 008mamaa240419s2024    sz |    s    |||| 0|eng d  a97830315141429978-3-031-51414-27 a10.1007/978-3-031-51414-22doi 4aQA440-699 7aPBM2bicssc 7aMAT0120002bisacsh 7aPBM2thema1 aBădescu, Lucian.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97543110aLectures on Geometryh[electronic resource] /cby Lucian Bădescu, Ettore Carletti.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXIII, 490 p. 50 illus., 23 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aLa Matematica per il 3+2,x2038-5757 ;v1580 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.  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. 0aGeometry.96876314aGeometry.9687631 aCarletti, Ettore.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9754322 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303151413508iPrinted edition:z9783031514159 0aLa Matematica per il 3+2,x2038-5757 ;v15897014540uhttps://doi.org/10.1007/978-3-031-51414-2  aZDB-2-SMA  aZDB-2-SXMS  c59235d59235