Subjects(version: 849)
Course, academic year 2019/2020
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Projective Geometry II - NDGE008
Title in English: Projektivní geometrie II Department of Mathematics Education (32-KDM) Faculty of Mathematics and Physics from 2016 summer 6 summer s.:2/2 C+Ex [hours/week] unlimited unlimited cancelled Czech full-time
Guarantor: Mgr. Lukáš Krump, Ph.D.prof. RNDr. Adolf Karger, DrSc. M Bc. DGZVM Bc. DGZV > Povinné Mathematics > Geometry NMUG303 NMUG303 NMUG303 NMUG303
 Annotation - ---CzechEnglish
Last update: G_M (09.10.2001)
Projective extension of affine space, projective space, homogeneous coordinates. Colineations. Quadrics, their properties and classification.
 Aim of the course - ---CzechEnglish
Last update: T_KDM (19.05.2008)

This course helps to obtain theoretical background for teaching mathematics at high school.

 Literature - ---CzechEnglish
Last update: T_KDM (13.05.2008)

M. Sekanina a kol., Geometrie I, II, Státní pedagogické nakladatelství Praha 1986, 1988.

J. Janyška, A. Sekaninová; Analytická teorie kuželoseček a kvadrik, Masarykova univerzita v Brně, 2001

M. Lávička:Geometrie 2; pomocný učební text - ZČU Plzeň, 2004, http://home.zcu.cz/~lavicka/subjects/G2/texty/G2_text.pdf

 Teaching methods - ---CzechEnglish
Last update: T_KDM (20.05.2008)

Lectures and exercises.

 Syllabus - ---CzechEnglish
Last update: T_KDM (13.05.2008)

1. Basic properties of projective space. Definition of a projective space over R and C, linear objects, duality, corelation.

2. Classifications of quadrics in a projective space. Definition of a quadric in projective space, inertia theorem, nullity space of a quadric, classification of quadrics especially for n = 2, 3.

3. Desargues, Pappos and Pascal theorem.

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