Basics of Discrete Mathematics (FSI-9MDM)

Academic year 2020/2021
Supervisor: prof. RNDr. Josef Šlapal, CSc.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech or English
Aims of the course unit:
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.
Learning outcomes and competences:
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 mathematics on bachelor level are required.
Course contents:
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.
Teaching methods and criteria:
The course is taught through lectures explaining the basic principles and methods of discrete mathematics.
Assesment methods and criteria linked to learning outcomes:
Students are to pass an exam consisting of the written and oral parts. During the exam, their knowledge of the concepts introduced and of the basic propertief of these concepts will be assessed. Also their ability to use theoretic results for solving concrete problems will be evaluated.
Controlled participation in lessons:
Since the subject is taught in the form of a lecture, which is not compulsory for student, the attendance will not be checked.
Type of course unit:
    Lecture  10 × 2 hrs. optionally                  
Course curriculum:
    Lecture 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
Literature - fundamental:
1. Norman l. Biggs: Discrete Mathematics. Oxford Science Publications 1999
2. Mike Piff: Discrete Mathematics. Cambridge University Press 1991
Literature - recommended:
1. F.P. Preparata, R.T. Yeh: Úvod do teórie diskrétnych matematických štruktúr. Alfa-Bratislava 1982
2. S.V. Jablonskij_: Úvod do diskrétnej matematiky. Alfa-Bratislava 1984
3. J. Nešetřil: Teorie grafů. SNTL, Praha 1979
6. D.R Hankerson & al.: Coding Theory and Cryptography. Marcel Dekker, Inc. 2000.
7. Steven Roman: Lattices and ordered sets, Springer 2008.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
D-IME-P full-time study --- no specialisation -- DrEx 0 Recommended course 3 1 W