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Main menu for Browse IS/STAG
Courses found, count: 1
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Abbreviation unit / Course abbreviation |
Title |
Variant |
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KMA
/
7GEOM
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Geometry
Show course
Geometry
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2023/2024
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Course info
KMA / 7GEOM
:
Course description
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Department/Unit / Abbreviation
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KMA
/
7GEOM
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Geometry
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
6
Cred.
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Type of completion
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Written
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Type of completion
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Written
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Time requirements
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lecture
2
[Hours/Week]
practical class
2
[Hours/Week]
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Course credit prior to examination
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No
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Course credit prior to examination
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No
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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Czech, English
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Occ/max
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Automatic acceptance of credit before examination
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No
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Summer semester
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0 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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9 / -
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0 / -
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3 / 3
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Winter semester
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Semester taught
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Winter semester
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Minimum (B + C) students
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not determined
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech, English
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Internship duration
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0
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| No. of hours of on-premise lessons |
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Evaluation scale |
A|B|C|D|E|F |
| Periodicity |
every year
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| Specification periodicity |
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Fundamental theoretical course |
Yes
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| Fundamental course |
No
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| Fundamental theoretical course |
Yes
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| Evaluation scale |
A|B|C|D|E|F |
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Substituted course
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None
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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N/A
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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Euclidean spaces and geometry of curves.
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Requirements on student
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The course is finished by an examination - which consists of a written part and an oral interview which relates to the problems in the written test.
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Content
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1. Euclidean space, its definition and properties, Cartesian coordinate system. Distances and metric properties.
2. Euclidean subspaces, perpendicularity of Euclidean subspaces, projections and distances of points from the subspace.
3. Distances and angles of subspaces of Euclidean spaces.
4. Identical representations and isometries of Euclidean spaces.
5. Use of constructions problems.
6. Analytic geometry of conics.
7. Methods of construction of conics.
8.-9. Curves in Euclidean space and their basic properties.
10. Reparametrization of curves, tangent properties, normal, binormal, planes corresponding to the curve at a given point.
11. Curve arc, natural parametrization, plane curve in polar coordinates.
12. Flexure and torsion, Frenet's formulae.
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Activities
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Fields of study
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Guarantors and lecturers
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Guarantors:
doc. Baruch Schneider, PhD. (100%),
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Lecturer:
Mgr. Věra Ferdiánová, Ph.D. (50%),
doc. Baruch Schneider, PhD. (50%),
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Tutorial lecturer:
Doktorand Doktorand (50%),
Mgr. Věra Ferdiánová, Ph.D. (50%),
Mgr. Jakub Poruba (100%),
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Literature
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Basic:
A. Vondra. Diferenciální geometrie křivek a ploch. VAAZ Brno.
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Basic:
Pressley, A. Elementary diffrential geometry, Springer 2001. ISBN 9781852331528.
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Basic:
Burian, K. Kapitoly z geometrie II. PřF OU Ostrava, 1996. ISBN 80-7042-732-9.
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Extending:
W. Kühnel. Differential Geometry: Curves-Surfaces-Manifolds. AMS, US, 2005. ISBN 9781470423209.
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Recommended:
Kolář, I., Pospíšilová, L. Diferenciální geometrie křivek a ploch - elektronické skriptum.. Masarykova univerzita Brno, 2008.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Consultation of work with the teacher/tutor (incl. electronic)
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5
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Preparation for an exam
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38
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Being present in classes
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52
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Scientific text studying in the Czech language
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20
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Self-tutoring
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20
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Continuous tasks completion (incl. correspondence tasks)
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20
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Unaided e-learning tasks completion
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20
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Total
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175
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Prerequisites
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Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
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| Elements of linear algebra, analysis and geometry at undergraduate (bachelor) level. |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
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| Student knows elements of the geometry of curves in the plane. Student knows elements of the geometry of curves and surfaces in the space. He/she knows elements of the inner and external geometry of surfaces. He/she knows the terminology of geometry. He/she knows basic definitions and theorems. |
Skills - skills resulting from the course: |
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| Student acquires the ability to apply known concepts, properties and methods to solve different problems concerning the topics of the course. |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
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| IC6 - Oral examiantion |
| IC7 - Written examination |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
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| A1 - Lecture |
| A2 - Expert report |
| B1 - Discussion |
| G2 - Self-study, controlled study |
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