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Course, academic year 2024/2025
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Linear Algebra and Geometry II - OKBM3M054A
Title: Lineární algebra a geometrie II
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2023
Semester: winter
E-Credits: 6
Examination process: winter s.:
Hours per week, examination: winter s.:0/0, C+Ex [HT]
Extent per academic year: 18 [hours]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: combined
Note: course can be enrolled in outside the study plan
enabled for web enrollment
priority enrollment if the course is part of the study plan
Guarantor: Mgr. Michal Zamboj, Ph.D.
prof. RNDr. Jarmila Novotná, CSc.
Pre-requisite : OKBM3M023A
Annotation -
This follow-up course to Linear Algebra and Geometry is focused on the classification of geometric spaces based on the invariants of linear representations. Extended are parts of algebra and the theory of matrices. Knowledge is used to classify quadrics according to their projective, affine, and metric properties. The acquired knowledge and skills belong to the parts needed for other mathematics courses and are needed for teaching high school analytic geometry.
Last update: Zamboj Michal, Mgr., Ph.D. (29.04.2024)
Aim of the course -

Students acquire the skill to use the methods of linear algebra and geometry to become familiar with the theoretical knowledge that is the basic equipment of a mathematics teacher and is necessary for further study.

Students acquire the ability to use the methods of linear algebra and geometry independently and in their common relation.

Last update: Zamboj Michal, Mgr., Ph.D. (20.09.2024)
Descriptors -

The materials are located in the LMS Moodle course Lineární Algebra a Geometrie II (https://dl1.cuni.cz/course/view.php?id=7754).

Students' tasks will be available in the LMS Moodle. 

In the case of suspension of in-person meetings, the course will be conducted online. The link for online meetings will be available in the LMS Moodle.

Preparation for lessons:

  • Preparation for  lessons 1 hour (60 min) in the distant stadium,  self-study and reading: 120 minutes (32h per semester)

Preparation for subject requirements :

  • Homework: 50h
  • Preparation for exam: 50h
Last update: Zamboj Michal, Mgr., Ph.D. (29.04.2024)
Course completion requirements -

Present 

Credit conditions: active attendance at exercise classes of at least 80%

Exam: The exam consists of a written and an oral part; there are two correction attempts.

The grade consists of 50% of the points obtained from the written part and 50% from the oral part.

  • 90 - 100% excellent
  • 75 - 89% very good
  • 60 - 74% good

Combined

Credit conditions: attendance at classes of at least 80%, submission of two sets of homework (to be assigned during the semester)

Exam: The exam consists of a written and an oral part; there are two correction attempts.

The grade consists of 50% of the points obtained from the written part and 50% from the oral part.

  • 90 - 100% excellent
  • 75 - 89% very good
  • 60 - 74% good
Last update: Zamboj Michal, Mgr., Ph.D. (10.09.2024)
Literature -

ZLATOŠ, P.: Lineárna algebra a geometria, Marenčin PT, Bratislava, 2011.
BARTO, L., TŮMA, J.: Lineární algebra, skripta k přednášce na MFF UK, aktuální verze.
SEKANINA, M., BOČEK, L., KOČANDRLE, M., ŠEDIVÝ. J.: Geometrie II, Praha: SPN 1988.
JANYŠKA, J., SEKANINOVÁ, A.: Analytická teorie kuželoseček a kvadrik, Brno 2017.
RICHTER-GEBERT, J.: Perspectives on Projective Geometry, Springer, 2011.
CASAS-ALVERO, E.: Analytic Projective Geometry, EMS, 2014.

Last update: Zamboj Michal, Mgr., Ph.D. (11.09.2023)
Syllabus -
  • Projective extension of an affine space; Projective space, projective transformation
  • Groups of linear mappings
  • Transition matrix and change of basis
  • Dot product
  • Orthogonalization
  • Euclidean vector space, isometry classification in E3, isometry representation in En
  • Similar transformation in En
  • Affine transformation in En
  • Real and complex matrices and their properties
  • Linear forms, Bilinear and quadratic forms
  • Conics
  • Projective classification of conics
  • Affine classification of conics
  • Metric classification of conics
Last update: Zamboj Michal, Mgr., Ph.D. (29.04.2024)
Learning resources -
https://dl1.cuni.cz/course/view.php?id=7754
Last update: Zamboj Michal, Mgr., Ph.D. (11.09.2023)
Learning outcomes - Czech
  • Studující definuje a aplikuje probíráné pojmy z oblasti geometrie a algebry ve vzájemných souvislostech.
  • Studující popíše konstrukci euklidovské, afinní a projektivní geometrie.
  • Studující řeší teoretické a aplikační úlohy metodami lineární algebry a analytické geometrie.
  • Studující formuluje a dokáže probírané věty z lineární algebry a geometrie.  
  • Studující klasifikuje kuželosečky na záladě jejich projektivních, afinních a metrických vlastností. 
Last update: Zamboj Michal, Mgr., Ph.D. (20.09.2024)
 
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