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Course detail

Methods of Discrete Mathematics

Course unit code: FSI-SDM
Academic year: 2016/2017
Type of course unit: compulsory
Level of course unit: Bachelor's (1st cycle)
Year of study: 2
Semester: winter
Number of ECTS credits:
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.
Course contents (annotation):
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.
Recommended or required reading:
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.
Course curriculum:
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: doc. RNDr. Petr Emanovský, Ph.D.
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: doc. RNDr. Petr Emanovský, Ph.D.
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

The study programmes with the given course