## M1120 Discrete mathematics

Faculty of Science
Autumn 2022
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
Mgr. David Kruml, Ph.D. (lecturer)
Mgr. Miloslav Štěpán (seminar tutor)
Guaranteed by
prof. RNDr. Jiří Rosický, DrSc.
Department of Mathematics and Statistics - Departments - Faculty of Science
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
Timetable
Mon 12:00–13:50 M1,01017
• Timetable of Seminar Groups:
M1120/01: Mon 14:00–15:50 M2,01021, M. Štěpán
M1120/02: Mon 18:00–19:50 M4,01024, D. Kruml
M1120/03: Mon 16:00–17:50 M4,01024, D. Kruml
Prerequisites
! OBOR ( AMV ) && ! OBOR ( FINPOJ ) && ! OBOR ( UM )
Knowledge of high-school mathematics is supposeed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course links up high school knowledge with basic concepts of discrete mathematics. It mainly deals with fundaments of mathematical logic, set theory, notions of mappings and relations, combinatorics and graph theory. After passing the course, a student will be able to understand and explain basic mathematical notions and techniques and their mutual context. A student knows about practical applications of the methods and notions of discrete mathematics (function as a mapping, relations in databases, problems treated by graph theory).
Learning outcomes
After passing the course, a student will be able to understand and explain basic mathematical notions and techniques and their mutual context. A student knows about practical applications of the methods and notions of discrete mathematics (function as a mapping, relations in databases, problems treated by graph theory).
Syllabus
• Basic logical concepts (formulae, notation for mathematical statements, proofs)
• Basics of set theory (set operations, including the Cartesian product).
• Mappings (types of mappings, composition).
• Cardinality of a set (finite, countable and uncountable sets).
• Relations (types and properties of relations, composition).
• Equivalences and partitions (kernel of a mapping, constructions of selected number domains).
• Ordered sets (order relations, Hasse diagrams, complete lattices, isotone mappings).
• Combinatorics (permutation, combination, inclusion and exclusion principle).
• Graph theory (oriented and non-oriented graphs, conectedness, spanning trees, Euler graphs, basic alghorithms).
Literature
• Horák, Pavel. Základy matematiky. Učební text. Podzimní semestr 2010.
• MATOUŠEK, Jiří and Jaroslav NEŠETŘIL. Kapitoly z diskrétní matematiky. Vyd. 2., opr. Praha: Univerzita Karlova v Praze, nakladatelství Karolinum, 2000. 377 s. ISBN 8024600846. info
Teaching methods
The subject consists of talks and obligatory seminars. The talk presents key notions, their properties and methods of use. Problems are collectively solved in seminars to develop student's insight. Student's advances are checked by automatized testing.
Assessment methods
The examination consists of written and oral part. The written part is typically of more importance. The oral part tests student's ability to react and to discuss his/her work during the term.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
The course is a neccessary background for following subjects of the programs Mathematics and Applied mathematics.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.
• Enrolment Statistics (recent)