MU20007 Geometry

Mathematical Institute in Opava
Summer 2021
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Petr Vojčák, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava
Timetable
Mon 10:35–12:10 R1
  • Timetable of Seminar Groups:
MU20007/01: Thu 11:25–13:00 R1, P. Vojčák
Prerequisites (in Czech)
MU20001 Mathematical Analysis I && MU20005 Algebra I && TYP_STUDIA ( B )
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 course introduces basic concepts, methods, and applications of affine and Euclidean geometry.
Syllabus
  • Affine and Euclidean spaces and subspaces, affine maps and isometries, affine and Cartesian coordinates.
    Distance and inclination of subspaces in Euclidean space, the volume of a parallelepiped.
    Applications in planimetry, stereometry, and coding theory.
    Quaternions and their geometric applications.
    Polygons and polyhedra, applications in geometric modelling.
Literature
    required literature
  • M. Marvan. Geometrie lineárních útvarů. 2010. URL info
  • I. Kaplansky. Linear algebra and geometry : a second course. Boston, 1969. info
    recommended literature
  • W.F. Osgood, W.C. Graustein. Plane and solid analytic geometry. New York. info
  • R.G. Stanton, K.D. Fryer. Algebra and vector geometry. 1972. info
  • C.W. Dodge. Euclidean geometry and transformations. Reading, 1972. info
  • C.H. Lehmann. Analytic geometry. London, 1956. info
  • P.K. Rees. Analytic geometry. 1956. info
  • J.H. Kindle. Theory and Problems of Plane and Solid Analytic Geometry. New York, 1950. info
  • J.M.H. Olmsted. Solid analytic geometry. New York, 1947. info
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
Teacher's information
The course comprises lectures and tutorials. To pass the course, the first step is to earn credit for tutorials (by earning 70% on a written test). The final exam, which consists of a written and on oral part, tests theoretical knowledge and understanding of the subject, including proofs.

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