A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.
NIE-GAK Graph theory and combinatorics Extent of teaching: 2P+2C Instructor: Valla T. Completion: Z,ZK Department: 18101 Credits: 5 Semester: L Annotation:
The goal of the class is to introduce the most important topics in graph theory, combinatorics, combinatorial structures, discrete models and algorithms. The emphasis will be not only on undestanding the basic principles but also on applications in problem solving and algorithm design. The topics include: generating functions, selected topics from graph and hypergraph coloring, Ramsey theory, introduction to probabilistic method, properties of various special classes of graphs and combinatorial structures. The theory will be also applied in the fields of combinatorics on words, formal languages and bioinformatics.
Lecture syllabus:
List of the topics
1. Generating functions 2. Graph coloring and perfect graphs 3. Introduction to Ramsey theory 4. Matching in general graphs 5. Counting spanning trees 6. Introduction to probabilistic method 7. Extremal combinatorics 8. Planar graphs and Kuratowski theorem 9. Coloring graphs on surfaces 10. List coloring and choosability 11. Edge coloring 12. Combinatorial games Seminar syllabus:
1. Generating functions 2. Graph coloring and perfect graphs 3. Introduction to Ramsey theory 4. Matching in general graphs 5. Counting spanning trees 6. Introduction to probabilistic method 7. Extremal combinatorics 8. Planar graphs and Kuratowski theorem 9. Coloring graphs on surfaces 10. List coloring and choosability 11. Edge coloring 12. Combinatorial games Literature:
1. B. Bollobas : Modern Graph Theory. Springer, 1998. ISBN 0-387-98488-7. 2. Graham, R. L. - Knuth, D. - Patashnik, O. : Concrete Mathematics. Addison-Wesley, 1994. ISBN 978-0-201-55802-9. 3. Diestel, R. : Graph Theory. Springer, 2016. ISBN 978-3-662-53621-6. Requirements:
We expect knowledge of topics from the courses Algorithms and graphs I. and II. (BI-AG1, BI-AG2).
Chybí metody akriteria hodnocení (CZ i EN), anglické překlady osnovy přednášek, osnovy cvičení, vstupních požadavků.Informace o předmětu a výukové materiály naleznete na https://courses.fit.cvut.cz/MI-GAK/ The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester NIE-TI.21 Computer Science 2021 PS 2 NIE-PSS.21 Computer Systems and Networks 2021 V 2 NIE-NPVS.21 Design and Programming of Embedded Systems 2021 V 2 NIE-PB.21 Computer Security 2021 V 2 NIE-SI.21 Software Engineering 2021 V 2
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