Lectures on Geometry [Paperback]

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 Einsteins 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; B?zouts theorem for curves of P^2 (K), where K is a fixed algebraically closed field of arbitrary characteristic; and Cayley-Klein geometries.

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

“The book is devoted to fundamental topics of the affine, Euclidean and projective geometries. ... Each chapter ends with carefully selected exercises with some of them used to complement the material.” (Martin Lukarevski, zbMATH 1558.51001, 2025)

Lucian Silvestru B<lҠ