03428nam a22004935i 4500 978-3-031-51414-2 DE-He213 20251030112001.0 cr nn 008mamaa 240419s2024 sz | s |||| 0|eng d 9783031514142 978-3-031-51414-2 10.1007/978-3-031-51414-2 doi QA440-699 PBM bicssc MAT012000 bisacsh PBM thema Bădescu, Lucian. author. aut http://id.loc.gov/vocabulary/relators/aut 75431 Lectures on Geometry [electronic resource] / by Lucian Bădescu, Ettore Carletti. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XIII, 490 p. 50 illus., 23 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda La Matematica per il 3+2, 2038-5757 ; 158 1 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. This 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. Geometry. 68763 Geometry. 68763 Carletti, Ettore. author. aut http://id.loc.gov/vocabulary/relators/aut 75432 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031514135 Printed edition: 9783031514159 La Matematica per il 3+2, 2038-5757 ; 158 70145 https://doi.org/10.1007/978-3-031-51414-2 ZDB-2-SMA ZDB-2-SXMS 59235 59235