MUC26 Theory of conic sections and quadrics

Faculty of Science
autumn 2021
Extent and Intensity
2/2/0. 4 credit(s). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
prof. RNDr. Josef Janyška, DSc. (lecturer)
RNDr. Jakub Novák (seminar tutor)
Guaranteed by
prof. RNDr. Josef Janyška, DSc.
Department of Mathematics and Statistics - Departments - Faculty of Science
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
Timetable
Tue 16:00–17:50 M5,01013
  • Timetable of Seminar Groups:
MUC26/01: Wed 18:00–19:50 M6,01011, J. Novák
Prerequisites
MUC23 Analytical Geometry 2
Knowledge of Geometry II and M4522 Geometry III.
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
there are 11 fields of study the course is directly associated with, display
Course objectives
The goals of the course are:
- application of analytical methods to study of conic sections in the projective, affine and euclidean plane;
- application of analytical methods to study of quadrics in the projective, affine and euclidean space;
- support spatial imagination of students.
Learning outcomes
At the end of the course students should be able to:
- understand and explain complex extension of vector and affine spaces;
- work with bilinear and quadratic forms;
- understand the theory of conic sections and quadrics, especially projective and metric classification;
- interpret algebraic results in the geometrical sense.
Syllabus
  • Complex extension of vector and affine spaces.
  • Projective extension of affine and Euclidean spaces.
  • Bilinear and quadratic forms.
  • Conic sections:
  • - projective classification of conic sections;
  • - affine properties of conic sections;
  • - affine classification of conic sections;
  • - metric properties of conic sections;
  • - metric classification of conic sections.
  • Quadrics:
  • - projective classification of quadrics;
  • - affine properties of quadrics;
  • - affime classification of quadrics;
  • - metric properties of quadrics;
  • - metric classification of quadrics.
Literature
    recommended literature
  • SEKANINA, Milan. Geometrie. D. 2, Sv. 2. Praha: SPN, 1988. 307 s. info
  • JANYŠKA, Josef and Anna SEKANINOVÁ. Analytická teorie kuželoseček a kvadrik. Vyd. 1. Brno: Masarykova univerzita, 1996. iii, 178. ISBN 8021014350. info
    not specified
  • KENDIG, Keith. Conics. [Washington, D.C.]: Mathematical Association of America, 2005. xvi, 403. ISBN 0883853353. info
Teaching methods
Lecture with a seminar.
Assessment methods
Exam: written and oral. Current requirements: Written tests in exercises. Student's presence in exercises is obligatory.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.

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