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Course info
KMA / VPDM
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Course description
Department/Unit / Abbreviation
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KMA
/
VPDM
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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 Discrete Mathematics
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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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|
|
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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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3 / -
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0 / -
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1 / -
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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
|
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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KMA/TGD1
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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 at parts of Discrete Mathematics that, despite their theoretical relevance, are not included in the basic courses due to time constraints. The course aims to enable students interested in Discrete Mathematics to study one of its subfields in a deeper and more detailed way.
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Requirements on student
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This course involves several assignments of homework in which students are expected to demonstrate their active understanding of the theory, constructions, applications and proofs. The instruction methods include independent study under the direction of the teacher. Each student is assigned a related research project.
The examination is an oral one. The evaluation is based on the acquired competences, such as the ability to present known theoretical results, carry out correct logical proofs, and apply theory to the analysis and solution of specific problems.
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Content
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The course is focused on a selection from the following areas which exceed the scope of the standard courses in Discrete Mathematics: structural graph theory, Hamiltonian graph theory, connections of graph theory to algebra and topology, colouring properties of combinatorial structures, the probabilistic method.
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Activities
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Fields of study
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Text k přednášce na adrese http://home.zcu.cz/~kaisert/vpdm/VPDM_all.pdf .
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Guarantors and lecturers
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Literature
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-
Recommended:
Bondy, J. A.; Murty, U. S. R. Graph theory. New York : Springer, 2008. ISBN 978-1-84628-969-9.
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Recommended:
Diestel, Reinhard. Graph theory. 4th ed. Heidelberg : Springer, 2010. ISBN 978-3-642-14278-9.
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Recommended:
Cvetkovic Doob Sachs. Spectra of graphs. VEB Deutscher Verlag der Wissenschaften, Berlin, 1982.
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Recommended:
Nešetřil, Jaroslav. Teorie grafů. 1. vyd. Praha : SNTL - Nakladatelství technické literatury, 1979.
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Recommended:
Gross, Tucker. Topological Graph Theory. Wiley, 1987.
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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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Graduate study programme term essay (40-50)
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50
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Preparation for an examination (30-60)
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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: |
rozumět základním principům z oblasti teorie grafů |
rozumět základním principům z oblasti výpočetní složitosti |
rozumět základním principům z oblasti lineární algebry |
rozumět základním souvislostem nezi výše uvedenými oblastmi |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
formulovat základní úlohy teorie grafů a popsat jejich základní vlastnosti a typické aplikace |
pro základní úlohy teorie grafů navrhnout algoritmy řešení a vyhodnotit jejich výpočetní složitost |
ovládat vzájemné převody mezi vybranými úlohami |
umět klasifikovat základní úlohy diskrétní matematiky a teorie grafů z hlediska jejich výpočetní složitosti |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
orientovat se ve vybraných partiích z oblasti diskrétní matematiky |
být schopen hlubší orientace ve vybrané oblasti s předpokladem možnosti přípravy k samostatné vědecké práci |
Skills - skills resulting from the course: |
pracovat s matematickými modely |
používat nástroje a metody vybraných matematických disciplín |
vhodnou kombinací příkladů a protipříkladů demonstrovat základní tvrzení abstraktní teorie |
Competences - competences resulting from the course: |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Oral exam |
Seminar work |
Individual presentation at a seminar |
Skills - skills achieved by taking this course are verified by the following means: |
Oral exam |
Seminar work |
Individual presentation at a seminar |
Competences - competence achieved by taking this course are verified by the following means: |
Oral exam |
Seminar work |
Individual presentation at a seminar |
|
Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture supplemented with a discussion |
Task-based study method |
Self-study of literature |
Individual study |
One-to-One tutorial |
Skills - the following training methods are used to achieve the required skills: |
Lecture supplemented with a discussion |
Task-based study method |
Self-study of literature |
Individual study |
One-to-One tutorial |
Competences - the following training methods are used to achieve the required competences: |
Lecture supplemented with a discussion |
Task-based study method |
Self-study of literature |
Individual study |
One-to-One tutorial |
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