714-0441 – Geometry (G)

Gurantor departmentDepartment of Mathematics and Descriptive Geometry
Subject guarantorRNDr. Jana Volná, Ph.D.
Study levelundergraduate or graduate
Subject version
Version codeYear of introductionYear of cancellationCredits
714-0441/01 2003/2004 2019/2020 6
714-0441/02 2016/2017 2019/2020 6
714-0441/03 2019/2020 2019/2020 4
714-0441/04 2019/2020 2019/2020 4

Subject aims expressed by acquired skills and competences

In this course the students can acquaint with properties of affine and euclidean spaces, with affine, isometric and similar tranformations in this spaces.

Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

Summary

Vector spaces. Orientation, spaces with scalar multiplication. Vector multiplication, orthogonal transformations. Affine spaces. Affine coordinates, relations between linear subspaces. Linear systems of hyperplanes. Affine transformations, classification of affine transformations in spaces of dimension 2 and 3. Euclidean spaces. Cartesian coordinates, Euclidean metrics, orthogonality. Isometric transformations. Classification of isometries in spaces of dimension 1 and 2. Similarities.

Compulsory literature:

Holme, A.: Geometry. Springer – Verlag, Berlin, Heidelberg, New York, 2002, ISBN 3-540-41949-7.

Recommended literature:

Jennings, G.A.: Modern Geometry with Applications, Springer-Verlag, New York, 1994, ISBN 0-387-94222-X.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.