Course detail

# Methods of Discrete Mathematics

FSI-SDMCompulsoryBachelor's (1st cycle)Acad. year: 2016/2017Winter semester2. year of study6  credits

The subject Methods of discrete mathematics gets students acquainted with three basic areas of applied algebra. The first of them is the theory of ordered sets and lattices with the main stress focussed on the theory of Bolean algebras. The next area is the algebraic theory of automata and formal languages. The last one is an introduction to the coding theory. Thus, all the three areas represent theoretical fundamentals of informatics. With respect to the expansion of using computers in all branches of engineering, the acquired knowledge is necessary for graduates in mathematical engineering.

Learning outcomes of the course unit

The students will learn about the fundamentals of applied algebra. This will privide them with basic knowledge of the theory of ordered sets and lattices with an emphasis on Boolean algebras, the algebraic theory of automata and formal languages, and the coding theory.

Mode of delivery

90 % face-to-face, 10 % distance learning

Prerequisites

Only the basic knowledge of the set theory is supposed that students acquired in high schools.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

N.L.Biggs, Discrete Mathematics, Oxford Univ. Press, 1999.
F. Preparata, R. Yeh: Úvod do teórie diskrétnych matematických štruktúr, Alfa, Bratislava, 1982.
M. Demlová, V. Koubek: Algebraická teorie automatů, SNTL, Praha, 1990.
M.Piff, Discrete Mathematics, Cambridge Univ. Press, 1991.
A.D.Polimeni and H.J.Straight, Foundations of Discrete Mathematics, Brooks/Cole Publ. Comp., Pacific Grove, California, 1990.
J. Kopka: Svazy a Booleovy algebry, Univerzita J.E.Purkyně v Ústí nad Labem, 1991.
M.Novotný, S algebrou od jazyka ke gramatice a zpět, Academia, Praha, 1988.
D.R.Hankerson at al.: Coding Theory and Cryptography, Marcel Dekker, Inc., New York -Basel, 2000.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

To receive a positive credit assessment from the teacher supervising the seminar classes, students will have to attend them taking an active part in solving the problems discussed and pass a written test. In the written part of an exam, a student will have to prove that he or she is able to deal with various problems using the knowledge and skills acquired in the course. In the oral part, it must be proved that he or she has mastered the related theory.

Language of instruction

Czech

Work placements

Not applicable.

Aims

The course aims to acquaint the students with some usual methods of discrete mathematics used in various applications, especially in computer science.

Specification of controlled education, way of implementation and compensation for absences

As the attendance at seminars is required, it will be checked regularly by the teacher supervising a seminar. If a student misses a seminar due to excused absence, he or she will receive problems to work on at home and catch up with the lessons missed.

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

1. Relations between sets
2. Mappings
3. Relations on a set
4. Tolerances and equivalences
5. Ordered sets
6. Lattices
7. Boolean lattices
8. Boolean functions
9. Applications of Boolean lattices
10.Formal languages
11.Finite automata
12.Grammars
13.Selfcorrecting codes

seminars

26 hours, compulsory

Teacher / Lecturer

Syllabus

1. Relations between sets
2. Mappings
3. Relations on a set
4. Tolerances and equivalences
5. Ordered sets
6. Lattices
7. Boolean lattices
8. Boolean functions
9. Applications of Boolean lattices
10.Formal languages
11.Finite automata
12.Grammars
13.Selfcorrecting codes