Course detail
Methods of Discrete Mathematics
FSI-SDM Acad. year: 2018/2019 Winter semester
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
6
Supervisor
Department
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
None
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
The course unit credit is awarded on condition of having attended the seminars actively and passed a written test. The exam has a written and an oral part. The written part tests student's ability to deal with various problems using the knowledge and skills acquired in the course. In the oral part, the student has ro prove that he or she has mastered the related theory.
Work placements
None
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
The attendance at seminars is required and 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
None
The study programmes with the given course
Programme B3A-P: Applied Sciences in Engineering, Bachelor's
branch B-MAI: Mathematical Engineering, compulsory
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
Exercise
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