Course detail

Basics of Discrete Mathematics

FSI-9MDMAcad. year: 2016/2017

The subject makes students acquainted with some basic methods of discrete mathematics employed in (not only technical) practice. The content can be divided into four areas. The first of them is logic, especially the propositional and predicate logic, and its applications in computer science. The second area is formed by the graph theory with an emphasis on the graph algorithms utilized for solving optimization problems of different kinds. The next area is algebra and its applications in the theory of formal languages and automata. The last area is represented by the fundamentals of coding theory, especially the linear codes are discussed.

Language of instruction

Czech

Number of ECTS credits

1

Guarantor

prof. RNDr. Josef Šlapal, CSc.

Department

Institute of Mathematics (ÚM)

Learning outcomes of the course unit

Students will learn basic facts about logic, graph theory, automata theory, formal languages and coding theory. This will be useful for research in their specializations and for affective use of computers because they will better understand the principles computers work on.

Prerequisites

Basic knowledge of set theory and algebra are required.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline.

Assesment methods and criteria linked to learning outcomes

Students are to pass an exam. During the exam their knowledge of the concepts introduced and of the basic propertief of these comcepts will be assessed. Also their ability to use theoretic results for solving concrete problems will be evaluated.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The goal of the subject is to make students acquainted with principal methods of discrete mathematics employed in technical applications. The knowledge of these methods will help students to understand their specializations more deeply and to utilize computers and programming when solving given problems.

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

Since the subject is taught in the form of a lecture, which is not compulsory for student, the attendance will not be checked.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Norman l. Biggs: Discrete Mathematics. Oxford Science Publications 1999 (EN)
Mike Piff: Discrete Mathematics. Cambridge University Press 1991 (EN)

Recommended reading

F.P. Preparata, R.T. Yeh: Úvod do teórie diskrétnych matematických štruktúr. Alfa-Bratislava 1982 (CS)
S.V. Jablonskij_: Úvod do diskrétnej matematiky. Alfa-Bratislava 1984 (CS)
J. Nešetřil: Teorie grafů. SNTL, Praha 1979 (CS)

Type of course unit

 

Lecture

20 hours, optionally

Teacher / Lecturer

prof. RNDr. Josef Šlapal, CSc.

Syllabus

1. Propositional logic
2. Axiomatization of propositional logic
3. Predicate logic
4. Axiomatization of predicate logic
5. Directed and non-directed graphs
6. Graph algorithms
6. Nets and their applications
8. Groupoids and groups
9. Rings and fields
10.Formal languages
11.Automata
12.Introduction to coding theory
13.Linear codes