Course detail

Seminar of Discrete Mathematics and Logics

FIT-SDLAcad. year: 2021/2022

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

Mode of study

Not applicable.

Guarantor

doc. Mgr. Lukáš Holík, Ph.D.

Department

Department of Intelligent Systems (UITS)

Learning outcomes of the course unit

Not applicable.

Prerequisites

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.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

Not applicable.

Work placements

Not applicable.

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.

Specification of controlled education, way of implementation and compensation for absences

  • 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).

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

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.
Hliněný, P., Úvod do informatiky. Elportál, Brno, 2010.
Klazar M., Kratochvíl J, Loebl M., Matoušek J. Thomas R., Valtr P., Topics in Discrete Mathematics, Springer-Verlag, Berlin 2006.
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.
Kovár, M.,  Diskrétní matematika, FEKT VUT, Brno, 2013
Matoušek J., Nešetřil J., Invitation to Discrete Mathematics, Oxford University Press, Oxford 2008.
Matoušek J., Nešetřil J., Kapitoly z diskrétní matematiky, Karolinum, Praha 2007.
O'Donnell, J., Hall C., Page R., Discrete Mathematics Using a Computer, Springer-Verlag, London 2006.
Sochor, A., Klasická matematická logika, Karolinum, Praha 2001.

Classification of course in study plans

  • Programme MITAI Master's

    specialization NISY up to 2020/21 , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
    specialization NADE , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
    specialization NBIO , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
    specialization NCPS , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
    specialization NEMB , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
    specialization NGRI , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
    specialization NHPC , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
    specialization NIDE , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
    specialization NISD , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
    specialization NMAL , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
    specialization NMAT , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
    specialization NNET , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
    specialization NSEC , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
    specialization NSEN , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
    specialization NSPE , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
    specialization NVER , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
    specialization NVIZ , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
    specialization NISY , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core

Type of course unit

 

Seminar

13 hod., optionally

Teacher / Lecturer

doc. Mgr. Lukáš Holík, Ph.D.

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 7 weeks of the semester)