M3722 Non-Euclidean geometry

Faculty of Science
Spring 2011
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
Timetable
Mon 12:00–13:50 M6,01011
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 origins, basic notions, and models of non-Euclidean geometries.
Syllabus
  • Classification of geometries, elementary Euclidean and neutral geometry.
  • Introduction to hyperbolic geometry, angle of parallelism, spherical and hyperbolic trigonometry.
  • Models of elliptic and hyperbolic plane, transformations in geometry.
Literature
  • EUKLEIDÉS. Eukleidovy Základy : Elementa. V Praze: Nákladem Jednoty českých mathematiků, 1907, 314 s. info
  • GREENBERG, Marvin Jay. Euclidean and non-Euclidean geometries :development and history. 3rd ed. New York: W.H. Freeman, 1994, xvi, 483 s. ISBN 0-7167-2446-4. info
  • Geometry. II, Spaces of constant curvature. Edited by E. B. Vinberg. Berlin: Springer-Verlag, 1993, 254 s. ISBN 3-540-52000-7-. info
  • COXETER, H. S. M. Introduction to geometry. 2nd ed. [New York]: John Wiley & Sons, 1989, xvi, 469. ISBN 0471504580. info
  • KAGAN, Veniamin Fedorovič. Osnovanija geometrii : učenie ob obosnovanii geometrii v chode jego istoričeskogo razvitija. Moskva: Gosudarstvennoje izdatel'stvo techniko-teoretičeskoj literatury, 1949, 492 s. info
  • HLAVATÝ, Václav. Úvod do neeuklidovské geometrie. Vyd. 2. Praha: Jednota československých matematiků a fysiků, 1949, 227 s. URL info
Teaching methods
Lectures 2 hours a week, homeworks.
Assessment methods
Oral examination.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught once in two years.
Teacher's information
http://is.muni.cz/el/1431/jaro2011/M3722/op/index.html
The course is also listed under the following terms Spring 2011 - only for the accreditation, Spring 2001, Spring 2002, Spring 2003, Spring 2005, Spring 2007, Spring 2009.
  • Enrolment Statistics (recent)
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