M1120 Discrete mathematics

Faculty of Science
Autumn 2016
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jiří Rosický, DrSc. (lecturer)
Mgr. David Kruml, Ph.D. (seminar tutor)
Mgr. Radka Penčevová (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 19. 9. to Sun 18. 12. Thu 10:00–11:50 M1,01017
  • Timetable of Seminar Groups:
M1120/01: Mon 19. 9. to Sun 18. 12. Mon 16:00–17:50 M5,01013, R. Penčevová
M1120/02: Mon 19. 9. to Sun 18. 12. Mon 10:00–11:50 M2,01021, 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, combinatorics and graph theory. After passing the course, the student will be able to understand and explain basic mathematical notions and techniques and their mutual connections.
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, skeletons, 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.
Assessment methods
Students are examined in 2 tests during the term (10 pts per each) and in the final written test (80 pts). The mark is calculated as follows: A 90-100, B 80-89, C 70-79, D 60-69, E 50-59, F 0-49.
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
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 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2016, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2016/M1120