SubjectsSubjects(version: 945)
Course, academic year 2023/2024
   Login via CAS
Projective geometry II - NMUG303
Title: Projektivní geometrie II
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Additional information: http://www.karlin.mff.cuni.cz/~krump/projektiv_2_2017.htm
Guarantor: Mgr. Lukáš Krump, Ph.D.
Class: M Bc. DGZV
M Bc. DGZV > Povinné
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Incompatibility : NDGE008, NMTD206
Interchangeability : NDGE008, NMTD206
Is incompatible with: NMTD206, NDGE008
Is interchangeable with: NMTD206, NDGE008
Annotation -
Last update: RNDr. Jakub Staněk, Ph.D. (16.06.2019)
Projective extension of the affine space, projective space, homogeneous coordinates. Collineations. Quadrics, their properties and classification.
Course completion requirements -
Last update: Mgr. Lukáš Krump, Ph.D. (29.10.2019)

The course credit (="zápočet") is obtained for activity during tutorials; in well-reasoned cases (longer justified absence), the course credit can be obtained for given homeworks.

The nature of this study control excludes repeating.

The course credit is a necessary condition for admission to the exam.

Literature -
Last update: T_KDM (14.04.2014)
  • 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

Requirements to the exam -
Last update: Mgr. Lukáš Krump, Ph.D. (29.10.2019)

The exam is oral, its contents corresponds to the syllabus in the extent taught.

Syllabus -
Last update: T_KDM (17.04.2014)

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.

4. Projective transformations and their real Jordan forms. Theorems on dimensions

and on maximal linear subspaces on a quadric, polar properties, vertex of a quadric, general projective and affine classification of quadrics with application to n=2,3. Tangent cone and base of a quadric.

 
Charles University | Information system of Charles University | http://www.cuni.cz/UKEN-329.html