## M1121 Discrete mathematics

Faculty of Science
Autumn 2015
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)
Mgr. David Kruml, Ph.D. (lecturer)
Bc. Jan Kvapil (assistant)
prof. RNDr. Jiří Rosický, DrSc. (alternate examiner)
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
Wed 8:00–9:50 M2,01021
• Timetable of Seminar Groups:
M1121/01: Fri 10:00–11:50 M2,01021, D. Kruml
M1121/02: Wed 10:00–11:50 M4,01024, D. Kruml
Prerequisites
! OBOR ( OM ) && ! OBOR ( STAT ) && ! 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 context.
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 2014, Autumn 2016, autumn 2017, Autumn 2018.
• Enrolment Statistics (Autumn 2015, recent)