PřF:M3722 Non-Euclidean geometry - Course Information

M3722 Non-Euclidean geometry

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

• Mathematics (programme PřF, M-MA)
• Upper Secondary School Teacher Training in Descriptive Geometry (programme PřF, M-MA)
• Upper Secondary School Teacher Training in Descriptive Geometry (programme PřF, M-SS)
• Upper Secondary School Teacher Training in Mathematics (programme PřF, N-MA)
• Upper Secondary School Teacher Training in Mathematics (programme PřF, N-SS)

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.

• Enrolment Statistics (Spring 2011 - only for the accreditation, recent)
  
• Permalink: https://is.muni.cz/course/sci/spring2011-onlyfortheaccreditation/M3722