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Lecturer(s)
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Pařez Klaus, doc. RNDr. Ph.D.
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Course 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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Learning activities and teaching methods
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Interactive lecture, Lecture supplemented with a discussion, E-learning, Task-based study method, Students' self-study, Self-study of literature, Textual studies, Lecture
- Contact hours
- 52 hours per semester
- Graduate study programme term essay (40-50)
- 50 hours per semester
- Preparation for an examination (30-60)
- 50 hours per semester
- Presentation preparation (report) (1-10)
- 10 hours per semester
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| prerequisite |
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| Knowledge |
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| 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 |
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| 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 |
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| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| 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 |
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| to use appropriate geometric models, tools and methods |
| 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 |
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| 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 |
| teaching methods |
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| Knowledge |
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| Lecture |
| Lecture supplemented with a discussion |
| Interactive lecture |
| Task-based study method |
| Self-study of literature |
| Skills |
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| Lecture |
| Lecture with visual aids |
| Interactive lecture |
| Task-based study method |
| Self-study of literature |
| Competences |
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| Lecture |
| Lecture supplemented with a discussion |
| Interactive lecture |
| Task-based study method |
| Self-study of literature |
| assessment methods |
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| Knowledge |
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| Combined exam |
| Seminar work |
| Individual presentation at a seminar |
| Skills |
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| Combined exam |
| Seminar work |
| Skills demonstration during practicum |
| Competences |
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| Combined exam |
| Seminar work |
| Individual presentation at a seminar |
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Recommended literature
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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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Pottmann, Helmut; Wallner, Johannes. Computational line geometry. Berlin : Springer-Verlag, 2001. ISBN 3-540-42058-4.
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Smith, Karen E. An invitation to algebraic geometry. New York : Springer, 2000. ISBN 0-387-98980-3.
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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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Toth, Gabor. Glimpses of algebra and geometry. [1st ed.]. New York : Springer, 1998. ISBN 0-387-98213-2.
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