M3722 Non-Euclidean geometry

Faculty of Science
Spring 2011 - only for the accreditation
Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Vojtěch Žádník, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Josef Janyška, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Linear algebra and elementary projective geometry.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of the course is to introduce the basic notions and models of non-Euclidean geometries.
Syllabus
  • 1. Classification of geometries. 2. Models of Euclidean and non-Euclidean geometries. 3. Elementary geometry of hyperbolic plane. 4. Hyperbolic and elliptic trigonometry. 5. Laguerre's formula with applications. 6. Transformations in non-Euclidean geometry.
Literature
  • EUKLEIDÉS. Eukleidovy Základy : Elementa. V Praze: Nákladem Jednoty českých mathematiků, 1907, 314 s. info
  • COXETER, H. S. M. Introduction to geometry. 2nd ed. [New York]: John Wiley & Sons, 1989, xvi, 469. ISBN 0471504580. info
  • KUTUZOV, Boris Veniaminovič. Lobačevského geometrie a elementy základů geometrie. Translated by Rudolf Zelinka - Vlastimil Macháček. 1. vyd. Praha: Československá akademie věd, 1953, 167 s. URL info
  • Geometry. II, Spaces of constant curvature. Edited by E. B. Vinberg. Berlin: Springer-Verlag, 1993, 254 s. ISBN 3-540-52000-7-. info
  • HLAVATÝ, Václav. Úvod do neeuklidovské geometrie. Vyd. 2. Praha: Jednota československých matematiků a fysiků, 1949, 227 s. URL info
  • VYŠÍN, Jan. Geometrie pre pedagogické fakulty. Vyd. 2. Bratislava: Slovenské pedagogické nakladatel'stvo, 1970, 360 s. info
Teaching methods
Lectures 2 hours a week, homeworks.
Assessment methods
Oral examination.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2001, Spring 2002, Spring 2003, Spring 2005, Spring 2007, Spring 2009, Spring 2011.