# Course syllabus B-DIM - Discrete Mathematics (FEEIT - SS 2019/2020)

**Information sheet**ECTS Syllabus

Slovak

**English**

University: | Slovak University of Technology in Bratislava | ||||||||||||

Faculty: | Faculty of Electrical Engineering and Information Technology | ||||||||||||

Course unit code: | B-DIM | ||||||||||||

Course unit title: | Discrete Mathematics | ||||||||||||

Mode of delivery, planned learning activities and teaching methods: | |||||||||||||

| |||||||||||||

Credits allocated: | 6 | ||||||||||||

Recommended semester/trimester: | Applied Informatics - bachelor (compulsory), 2. semester | ||||||||||||

Level of study: | 1. | ||||||||||||

Prerequisites for registration: | none | ||||||||||||

Assesment methods: | |||||||||||||

During the semester, ther will be two tests each for 15 points. During the examination period, there will be examination test for 70 points. To get the credit it is sufficient to get 15 points from semester. To pass the examination, it is sufficient to get at least 56 points together (from the semester and the examination test). | |||||||||||||

Learning outcomes of the course unit: | |||||||||||||

The students will gain knowledge in foundations of discrete mathematics. They will get acquainted
with various methods of proofs with emphasize on mathematical induction. They will have knowledge in the foundations of the set theory, graph theory and combinatorics. They will be able to solve some basic types of problems in these areas. They will unserstand the notion of algorithm and its relation to Turing machines. | |||||||||||||

Course contents: | |||||||||||||

The ways of logical reasoning. Induction. The notion of a set. Binary relations between sets. Relations of tolerance, equivalence and partial order. Graphs. Directed graphs. Reachability and strong connectivity. Undirected graphs. Travelling in graphs. Planar graphs and colouring.
Trees and spanning trees. Algorithms for finding spanning trees and minimum spanning trees of graphs. Illustration of combinatorics. Permutations and combinations. Recurrent relations. The cardinality of union of sets (the inclusion - exclusion principle). The notion of algorithm. Representation of algorithm by a flowchart. Requirements demanded on formal definition of algorithm. Turing machines. Universal Turing machine and the halting problem. | |||||||||||||

Recommended or required reading: | |||||||||||||

| |||||||||||||

Language of instruction: | slovak or english | ||||||||||||

Notes: | |||||||||||||

Courses evaluation: | |||||||||||||

Assessed students in total: 750
| |||||||||||||

Name of lecturer(s): | Mgr. Jozef Kollár, PhD. (examiner, instructor) doc. Mgr. Marcel Polakovič, PhD. (examiner, instructor, lecturer, person responsible for course) - slovak, english | ||||||||||||

Last modification: | 6. 5. 2019 | ||||||||||||

Supervisor: | doc. Mgr. Marcel Polakovič, PhD. and programme supervisor |

*Last modification made by RNDr. Marian Puškár on 05/06/2019.*