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Discrete mathematics

General data

Course ID:	1000-134MAD
Erasmus code / ISCED:	11.114 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Discrete mathematics
Name in Polish:	Matematyka dyskretna
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	Elective courses for 1st degree studies in mathematics
ECTS credit allocation (and other scores):	6.00 Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	Polish
Type of course:	elective courses
Short description:	Selected topics in combinatorics and graph theory, in particular: counting principles, combinatorial proofs, recurrence relations, Burnside's lemma, Eulerian circuits and Hamiltonian cycles, trees, planarity, colorings, matchings.
Full description:	Combinatorics Basic counting principles. Binomial coefficients and combinatorial proofs. The principle of inclusion and exclusion. Recurrence relations and generating functions. Counting of orbits and Burnside's lemma. Graph theory Introductory concepts. Eulerian circuits and Hamiltonian cycles. Trees. Planarity. Colorings. Matchings.
Bibliography:	Victor Bryant, Aspects of combinatorics, Cambridge University Press 1993. Robin J. Wilson, Introduction to graph theory, Addison Wesley Lingman Ltd., London.
Learning outcomes:	Students: - know basic counting principles; - use binomial coefficients and combinatorial proofs; - are familiar with Stirling, Bell and Catalan numbers; - use the principle of inclusion and exclusion; - understand recurrence relations and use generating functions; - know how to count orbits and use Burnside's lemma; - are familiar with basic concepts of graph theory; - identify and use Eulerian circuits and Hamiltonian cycles in graphs; - know the basic properties of and theorems about trees; - are familiar with planar graphs and Euler's formula; - know basic theorems about colorings of graphs; - know and use Hall's Marriage Theorem.
Assessment methods and assessment criteria:	(in Polish) Egzamin pisemny, ewentualnie dodatkowo egzamin ustny.

Classes in period "Summer semester 2023/24" (in progress)

Time span:	2024-02-19 - 2024-06-16	Selected timetable range: weekly course term Navigate to timetable MO TU W CW WYK CW TH FR
Type of class:	Classes, 30 hours more information Lecture, 30 hours more information
Coordinators:	Piotr Zakrzewski
Group instructors:	Joanna Jaszuńska, Piotr Zakrzewski
Students list:	(inaccessible to you)
Examination:	Course - Examination Lecture - Examination

Classes in period "Summer semester 2024/25" (future)

Time span:	2025-02-17 - 2025-06-08	Selected timetable range: weekly course term Navigate to timetable
Type of class:	Classes, 30 hours more information Lecture, 30 hours more information
Coordinators:	Piotr Zakrzewski
Group instructors:	Joanna Jaszuńska, Piotr Zakrzewski
Students list:	(inaccessible to you)
Examination:	Course - Examination Lecture - Examination

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