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Course info
KMA / MSR
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Course description
Department/Unit / Abbreviation
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KMA
/
MSR
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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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Mathematical Structures
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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,
5
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]
Seminar
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
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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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0 / -
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0 / -
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0 / -
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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 + Summer
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Semester taught
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Winter + Summer
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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
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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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KMA/TGD1 and KMA/UFA
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Courses depending on this Course
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KMA/DIM, KMA/DMI
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Histogram of students' grades over the years:
Graphic PNG
,
XLS
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Course objectives:
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The course gives an overview of axiomatic foundations of some parts of Mathematics.
Continuous structures: metric spaces, topological spaces, uniformity, uniform spaces, metrizability.
Discrete structures: algebraic structures, algebraic methods of graph theory, matroids, duality.
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Requirements on student
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Active individual work with assigned texts (the course is taught as controlled self-study).
Examination consists of three parts (in this order):
- Metric spaces (Drábek)
- General Topology (Tesková)
- Matroid Theory (Ryjáček)
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Content
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Continuous structures: metric spaces, topological spaces, uniformity, uniform spaces, metrizability.
Discrete structures: algebraic structures, algebraic methods of graph theory, matroids, duality.
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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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-
Recommended:
Kučera, Luděk; Nešetřil, Jaroslav. Algebraické metody diskrétní matematiky : Velmi rychlé násobení, obvody vysoké koncentrace, charakteristické věty, matroidy - netradiční moderní lineární algebra. Praha : SNTL, 1989. ISBN 80-03-00107-2.
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Recommended:
Základy funkcionální analýzy, 1. kap.
(Kubr, Milan)
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Recommended:
Adámek, Jiří; Koubek, Václav; Reiterman, Jan. Základy obecné topologie. 1. vyd. Praha : SNTL, 1977.
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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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Preparation for an examination (30-60)
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33
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Contact hours
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52
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Presentation preparation (report) (1-10)
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15
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Individual project (40)
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30
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Total
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130
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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: |
Student are supposed to have knowledge in Graph Theory and Computational Complexity corresponding to the contents of the courses KMA/TGD1 and KMA/TGD2 and knowledge in Functional Analysis corresponding to the contents of the course KMA/UFA. |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
The student will have an overview of deeper connections between some seemingly unrelated parts of Mathematics. |
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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 |
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: |
Task-based study method |
Self-study of literature |
Individual study |
One-to-One tutorial |
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