Course detail

Seminar of Discrete Mathematics and Logics

FIT-SDLAcad. year: 2023/2024

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.

Language of instruction

Czech

Number of ECTS credits

1

Guarantor

doc. Mgr. Lukáš Holík, Ph.D.

Department

Department of Intelligent Systems (UITS)

Entry knowledge

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.

Rules for evaluation and completion of the course

Final test, required is 55 points from 100.


  • 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).

Aims

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.


Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

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.

Type of course unit

 

Seminar

13 hours, optionally

Teacher / Lecturer

doc. RNDr. Milan Češka, Ph.D.
Ing. Vojtěch Havlena, Ph.D.
doc. Mgr. Lukáš Holík, Ph.D.
Ing. Ondřej Lengál, Ph.D.
doc. Mgr. Adam Rogalewicz, Ph.D.
Mgr. Juraj Síč

Syllabus

  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)