MU20007 Geometry

Mathematical Institute in Opava
Summer 2024
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Petr Vojčák, Ph.D. (lecturer)
RNDr. Adam Hlaváč, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Petr Vojčák, Ph.D.
Mathematical Institute in Opava
Timetable
Mon 9:45–11:20 R1
  • Timetable of Seminar Groups:
MU20007/01: Wed 15:35–17:10 R2, A. Hlaváč
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 spaces and subspaces - affine coordinates, intersection and sum of subspaces, relative position of subspaces, transversals of skew subspaces, pencils and bundles of hyperplanes. Euclidean spaces and subspaces - scalar product, perpendicularity of subspaces, outer and vector product, parallelepipeds and their volumes, distance of subspaces, deviations of subspaces. Affine mappings - analytical expression of the affine mapping, invariant elements of the affine mapping, basic affine mappings, classification of affinities in the plane.
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)
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.
The course is also listed under the following terms Summer 2021, Summer 2022, Summer 2023.
  • Enrolment Statistics (recent)
  • Permalink: https://is.slu.cz/course/sumu/summer2024/MU20007