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Main menu for Browse IS/STAG
Course info
KMA / VKG
:
Course description
Department/Unit / Abbreviation
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KMA
/
VKG
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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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Selected Topics in 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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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
3
[Hours/Week]
Tutorial
1
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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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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1 / -
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0 / -
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0 / -
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Repeated registration
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YES
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Repeated registration
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YES
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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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1
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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 |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
No
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Fundamental course |
No
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Fundamental theoretical course |
No
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
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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The course is focused on selected current topics of geometry and geometric modelling that are important from a theoretical point of view but from time and content limitations are not discussed in the compulsory courses. The main aim of this course is to explain the fundamental principles and methods of higher geometry. The topicality, practical aspects of applications and usage in solving particular non-trivial problems will be emphasized.
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Requirements on student
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During semester, students have to write several homework assignments which will demonstrate knowledge of theory, constructions, applications, and proofs. In addition, students elaborate a non-trivial individual assigned project.
The final examination is in the form of a written exam (70% of the grade) which is supplemented by an oral examination (30% of the grade). All assessment tasks will assess the learning outcomes, especially, the ability to provide logical and coherent proofs of chosen theoretical results and to use the methods from the course on solving given non-trivial problems.
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Content
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Major topics of this course include which are not scheduled in standard geometric courses.: projective algebraic geometry, finite geometry, geometric algebra, spherical and line geometries, higher differential geometry, up-to-date topics of computer aided geometric design etc. Considerable attention is given to the modern alliance of geometry with linear and abstract algebra and topology.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Basic:
Smith, Karen E. An invitation to algebraic geometry. New York : Springer, 2000. ISBN 0-387-98980-3.
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Basic:
Pottmann, Helmut; Wallner, Johannes. Computational line geometry. Berlin : Springer-Verlag, 2001. ISBN 3-540-42058-4.
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Basic:
Toth, Gabor. Glimpses of algebra and geometry. [1st ed.]. New York : Springer, 1998. ISBN 0-387-98213-2.
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Basic:
Farin, Gerald; Kim, Myung-Soo; Hoschek, Josef. Handbook of computer aided geometric design. 1st ed. Amsterdam : Elsevier, 2002. ISBN 0-444-51104-0.
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Recommended:
Sommer, Gerald. Geometric computing with Clifford algebras : theoretical foundations and applications in computer vision and robotics : with 89 figures and 16 tables. Berlin : Springer, 2001. ISBN 3-540-41198-4.
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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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Contact hours
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52
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Presentation preparation (report) (1-10)
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10
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Preparation for an examination (30-60)
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50
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Graduate study programme term essay (40-50)
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50
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Total
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162
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
to understand the basic principles of linear algebra, projective affine and Euclidean geometry |
to understand the basic principles of differential geometry |
to understand the basic principles of the theory of algebraic structures |
to learn the basics of geometric object representation and geometric modelling |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
to apply the learned procedures to selected geometric problems in n-dimensional projective, affine and Euclidean spaces |
to solve problems using knowledge of differential geometry |
to use the apparatus of algebraic structures |
to formulate and solve basic geometric modelling problems |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
to orient in selected parts of higher geometry and geometric modelling |
to understand the proofs of important theorems of the theory under study |
to understand and describe the tools and methods of selected geometric disciplines |
Skills - skills resulting from the course: |
to use appropriate geometric models, tools and methods
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to carry out proofs of selected important theorems of the theory under study |
to demonstrate the basic propositions of an abstract theory using an appropriate combination of examples and counterexamples, look for analogies and make generalisations |
to algorithmise basic methods, use appropriate numerical-symbolic computer software |
Competences - competences resulting from the course: |
N/A |
N/A |
to actively specialise more in the field of geometry and geometric modelling, especially in relation to the topic of the thesis |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Seminar work |
Individual presentation at a seminar |
Skills - skills achieved by taking this course are verified by the following means: |
Combined exam |
Seminar work |
Skills demonstration during practicum |
Competences - competence achieved by taking this course are verified by the following means: |
Combined exam |
Seminar work |
Individual presentation at a seminar |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Lecture supplemented with a discussion |
Interactive lecture |
Task-based study method |
Self-study of literature |
Skills - the following training methods are used to achieve the required skills: |
Lecture |
Lecture with visual aids |
Interactive lecture |
Task-based study method |
Self-study of literature |
Competences - the following training methods are used to achieve the required competences: |
Lecture |
Lecture supplemented with a discussion |
Interactive lecture |
Task-based study method |
Self-study of literature |
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