Course detail

Methods of Discrete Mathematics

FSI-SDMAcad. year: 2011/2012

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.

Language of instruction

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

prof. RNDr. Josef Šlapal, CSc.

Department

Institute of Mathematics (ÚM)

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.

Prerequisites

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

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

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.

Course curriculum

Not applicable.

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.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

A.D.Polimeni and H.J.Straight, Foundations of Discrete Mathematics, Brooks/Cole Publ. Comp., Pacific Grove, California, 1990. (EN)
D.R.Hankerson at al.: Coding Theory and Cryptography, Marcel Dekker, Inc., New York -Basel, 2000. (EN)
M.Piff, Discrete Mathematics, Cambridge Univ. Press, 1991. (EN)
N.L.Biggs, Discrete Mathematics, Oxford Univ. Press, 1999. (EN)

Type of course unit

Lecture

26 hod., optionally

Teacher / Lecturer

prof. RNDr. Ladislav Skula, DrSc.

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

Exercise

13 hod., compulsory

Teacher / Lecturer

prof. RNDr. Ladislav Skula, DrSc.

Syllabus

VUT

Faculties

University Institutes

Parts

Methods of Discrete Mathematics

Type of course unit