Course details

# Seminar of Discrete Mathematics and Logics

SDL Acad. year 2022/2023 Winter semester 1 credits

Set, relation, map, function, equivalence, ordering, lattice. Algebraical structures with one and two operations. Homomorphisms and congruences. Lattices and Boolean algebras. Propositional and predicate logic: syntax, semantics, normal forms of formulae, proofs, theories, correctness and completeness.

Guarantor

Course coordinator

Language of instruction

Czech

Completion

Credit

Time span

• 13 hrs seminar

Assessment points

• 100 pts written tests (written part)

Department

Instructor

Learning objectives

The goal is to refresh and possibly complete knowledge of notions from discrete mathematics and logic that are essential for computer science, and also practice usage of the mathematical apparatus and language.

Why is the course taught

Computer science is built on discrete mathematics and logic. Awareness of their basic notions and concepts is important in all areas of computer science, especially on a more advanced level, for orientation in literature, in discussions, to precisely and understandably express complex ideas and concepts, and to specify systems and their properties.

Prerequisite knowledge and skills

The course is designed as a recapitulation of basic concepts, hence a prior exposure to discrete mathematics and logic on a university level is desirable but not necessary.

Study literature

• Grossman P., Discrete mathematics for computing, Palgrave Macmillan, New York 2002.
• Kolibiar, M. a kol., Algebra a príbuzné disciplíny, Alfa, Bratislava, 1992.
• Matoušek J., Nešetřil J., Invitation to Discrete Mathematics, Oxford University Press, Oxford 2008.
• Sochor, A., Klasická matematická logika, Karolinum, Praha 2001.

Syllabus of seminars

1. Sets, relations, functions.
2. Sets, relations, functions, excercises.
3. Propositional and predicate logic.
4. Propositional and predicate logic, excercises.
5. Logical proof and logical systems.
6. Algebraic structures with one and two operations.
7. Logical systems and algebra, excercises.

(the seminar runs in the first 11 weeks of the semester, with four holes for the test from MSP, TIN, and for a state holiday)

Progress assessment

Final test, required is 55 points from 100.

Controlled instruction

• A written final test, with the maximum gain of 100 points. There will two terms of the test, hence a student has at most two attempts to pass the course (if he/she attends both terms).
• If a student can substantiate serious reasons for an absence from both tests, (s)he will be examined individually.
• Voluntary homeworks may be posted during the semester. They are scored according to their difficulty (solving the homeworks is not necessary to pass the course).

Exam prerequisites

Obtaining at least 50 points from the final test (and possibly also voluntary homeworks).

Course inclusion in study plans