书目名称 | Lectures on Geometry |
编辑 | Lucian Bădescu,Ettore Carletti |
视频video | |
概述 | A comparative presentation of affine, euclidean and projective geometries.An elementary but complete proof of the strong Bézout’s theorem for curves of P2 (K).A detailed exposition of Cayley-Klein pla |
丛书名称 | UNITEXT |
图书封面 |  |
描述 | .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 charact |
出版日期 | Textbook 2024 |
关键词 | Cross Product; ; Cross ratio; ; Cayley-Klein metrics; Intersection multiplicity; Barycentric coordinates |
版次 | 1 |
doi | https://doi.org/10.1007/978-3-031-51414-2 |
isbn_softcover | 978-3-031-51413-5 |
isbn_ebook | 978-3-031-51414-2Series ISSN 2038-5714 Series E-ISSN 2532-3318 |
issn_series | 2038-5714 |
copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |