Course details

Seminar of Discrete Mathematics and Logics

SDL Acad. year 2021/2022 Winter semester 1 credits

Current academic year

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

Holík Lukáš, doc. Mgr., Ph.D. (DITS)

Course coordinator

Vojnar Tomáš, prof. Ing., Ph.D. (DITS)

Language of instruction

Czech

Completion

Credit

Time span

  • 13 hrs seminar

Department

Department of Intelligent Systems (UITS)

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

  • Hliněný, P., Úvod do informatiky. Elportál, Brno, 2010.
  • Kovár, M.,  Diskrétní matematika, FEKT VUT, Brno, 2013
  • Anderson I., A First Course in Discrete Mathematics, Springer-Verlag, London 2001.
  • Grimaldi R. P., Discrete and Combinatorial Mathematics, Pearson Addison Valley, Boston 2004.
  • Grossman P., Discrete mathematics for computing, Palgrave Macmillan, New York 2002.
  • Kolibiar, M. a kol., Algebra a príbuzné disciplíny, Alfa, Bratislava, 1992.
  • Kolman B., Busby R. C., Ross S. C., Discrete Mathematical Structures, Pearson Education, Hong-Kong 2001.
  • Klazar M., Kratochvíl J, Loebl M., Matoušek J. Thomas R., Valtr P., Topics in Discrete Mathematics, Springer-Verlag, Berlin 2006.
  • Matoušek J., Nešetřil J., Kapitoly z diskrétní matematiky, Karolinum, Praha 2007.
  • Matoušek J., Nešetřil J., Invitation to Discrete Mathematics, Oxford University Press, Oxford 2008.
  • O'Donnell, J., Hall C., Page R., Discrete Mathematics Using a Computer, Springer-Verlag, London 2006.
  • 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 7 weeks of the semester)

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

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