Course: Discrete Mathematics

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Course title Discrete Mathematics
Course code KMA/DMA
Organizational form of instruction Lecture + Tutorial
Level of course Bachelor
Year of study 1
Semester Summer
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory, Compulsory-optional, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Teska Jakub, RNDr. Mgr. Ph.D.
  • Šebková Milena, RNDr.
  • Kabela Adam, Mgr.
  • Ryjáček Zdeněk, Prof. RNDr. DrSc.
  • Holub Přemysl, Doc. RNDr. Ph.D.
  • Čada Roman, Doc. Ing. Ph.D.
  • Mockovčiaková Martina, RNDr. PhD.
  • Tomiczková Světlana, RNDr. Ph.D.
Course content
Week 1: Basic set theory notations, binary relations Week 2: mappings, basic algebraic structures Week 3: tolerances, equivalences, modulo p arithmetics Week 4: orderings and partial orderings, Hasse diagram Week 5: suprema and infima, distributive lattices Week 6: complementary lattices, Boolean algebras, Boolean calculus, Stone theorem on representation Week 7: direct sum of Boolean algebras, Boolean functions, Boolean polynomials Week 8: Basic graph theory notations, directed and undirected graphs, paths and circuits in graphs, vertex degree, Eulerian graphs, trees. Week 9: Directed graphs, strong connectedness and strong components, cycles, acyclic graphs, condensation. Week 10: Matrix representation of a graph: adjacency matrix, incidence matrix and their algebraic properties. Week 11: Adjacency matrix, number of walks, weighted graphs, distance in graphs, Dijkstra`s algorithm, distance matrix, Floyd's algorithm. Week 12: Applications: distance and minimum path - Dijkstra algorithm, minimum spanning tree, critical path. Week 13: Course summary, exercises, final notes

Learning activities and teaching methods
Collaborative instruction, Lecture
  • Contact hours - 52 hours per semester
  • Preparation for formative assessments (2-20) - 18 hours per semester
  • Preparation for an examination (30-60) - 58 hours per semester
prerequisite
professional knowledge
formulovat s porozuměním podstatě věci základní pojmy lineární algebry a maticového počtu v rozsahu předmětu KMA/LA nebo KMA/ME2 a vysvětlit jejich základní vlastnosti
professional skills
aplikovat s porozuměním podstatě věci základní metody a techniky lineární algebry a maticového počtu v rozsahu předmětu KMA/LA nebo KMA/ME2
general eligibility
N/A
learning outcomes
professional knowledge
vysvětlit algoritmické aspekty řešení základních grafových úloh
vysvětlit základní pojmy z teorie relačních struktur: binární relace, ekvivalence (včetně aplikace na aritmetiku modulo 2), uspořádání a částečného uspořádání, Booleovy algebry a Booleovské polynomy a funkce
formulovat základní pojmy z teorie grafů a vysvětlit jejich základní vlastnosti, včetně porozumění souvislostem
popsat maticový popis grafu a vysvětlit vztahy mezi vlastnostmi grafu a algebraickými vlastnostmi příslušné matice
professional skills
navrhnout a formulovat algoritmy řešení základních grafových úloh, analyzovat jejich teoretické a algoritmické vlastnosti, a navržené algoritmy prakticky použít
popsat grafovou strukturu pomocí matice včetně porozumění vztahům mezi vlastnostmi grafu a algebraickými vlastnostmi příslušné matice
řešit jednoduché úlohy v aritmetikách modulo k, a speciálně v aritmetice modulo 2
aktivně ovládat pojmy ekvivalence a rozkladu množiny na třídy ekvivalence
prakticky použít základy teorie Booleových algeber, včetně vyjádření Booleovského polynomu v konjunktivní a disjunktivní normální formě
general eligibility
aktivně využívá získané znalosti a dovednosti při řešení praktických problémů
teaching methods
professional knowledge
Practicum
Lecture
professional skills
Practicum
Lecture
general eligibility
Lecture
Practicum
assessment methods
professional knowledge
Combined exam
Test
Skills demonstration during practicum
professional skills
Skills demonstration during practicum
Combined exam
Test
general eligibility
Skills demonstration during practicum
Test
Combined exam
Recommended literature
  • Čada, Roman; Kaiser, Tomáš; Ryjáček, Zdeněk. Diskrétní matematika. Plzeň : Západočeská univerzita, 2004. ISBN 80-7082-939-7.
  • Holenda, Jiří; Ryjáček, Zdeněk. Lineární algebra II : úvod do diskrétní matematiky : 1. část. 1. vyd. Plzeň : Západočeská univerzita, 1992. ISBN 80-7082-060-8.
  • Holenda, Jiří; Ryjáček, Zdeněk. Lineární algebra II : úvod do diskrétní matematiky. 1. vyd. Plzeň : ZČU, 1992. ISBN 80-7082-060-8.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Education Geography in Education (15) Pedagogy, teacher training and social care 2 Summer
Faculty of Applied Sciences Information Systems (2016) Informatics courses 1 Summer
Faculty of Applied Sciences Information Systems (2015) Informatics courses 1 Summer
Faculty of Applied Sciences Information Technologies (2016) Informatics courses 1 Summer
Faculty of Applied Sciences Computer Systems (2013) Electrical engineering, telecommunication and IT 1 Summer
Faculty of Applied Sciences Geomatics (2014) Construction industry, geodesy and cartography 1 Summer
Faculty of Applied Sciences Geomatics (2012) Construction industry, geodesy and cartography 1 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2017) Mathematics courses 1 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2017) Mathematics courses 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 1 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2017) Economy 1 Summer
Faculty of Education Biology in Education (16) Biology courses 2 Summer
Faculty of Education Physics in Education (16) Physics courses 2 Summer
Faculty of Education Biology in Education (15) Biology courses 2 Summer
Faculty of Education Information Technologies in Education (13) Informatics courses 2 Summer
Faculty of Education Geography in Education (13) Pedagogy, teacher training and social care 2 Summer
Faculty of Education Physical Education in Education (1) Physical education and sport 2 Summer
Faculty of Education Studies in Mathematics (13) Mathematics courses 2 Summer
Faculty of Applied Sciences Cybernetics and Control Engineering (2016) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (1) Economy 1 Summer
Faculty of Education Chemistry in Education (17) Chemistry courses 2 Summer
Faculty of Education - (17) Pedagogy, teacher training and social care 2 Summer
Faculty of Applied Sciences Information Systems (2014) Informatics courses 1 Summer
Faculty of Applied Sciences Geomatics (2015) Construction industry, geodesy and cartography 1 Summer
Faculty of Applied Sciences Geomatics (2014) Construction industry, geodesy and cartography 1 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2011) Mathematics courses 1 Summer
Faculty of Applied Sciences Scientific Computing and Modelling (2011) Mathematics courses 1 Summer
Faculty of Applied Sciences Computer Systems (2017) Electrical engineering, telecommunication and IT 1 Summer
Faculty of Education Physics in Education (14) Physics courses 2 Summer
Faculty of Education Information Technologies in Education (15) Informatics courses 2 Summer
Faculty of Education Physics in Education (13) Physics courses 2 Summer
Faculty of Education Studies in Mathematics (15) Mathematics courses 2 Summer
Faculty of Applied Sciences Computer Modelling (2016) Special and interdisciplinary fields 3 Summer
Faculty of Applied Sciences Computer Systems (2016) Electrical engineering, telecommunication and IT 1 Summer
Faculty of Applied Sciences Geomatics (2017) Construction industry, geodesy and cartography 1 Summer
Faculty of Applied Sciences Computer Modelling (2017) Special and interdisciplinary fields 3 Summer
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 1 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2017) Economy 1 Summer
Faculty of Education Chemistry in Education (16) Chemistry courses 2 Summer
Faculty of Education - (16) Pedagogy, teacher training and social care 2 Summer
Faculty of Education Chemistry in Education (15) Chemistry courses 2 Summer
Faculty of Education Chemistry in Education (14) Chemistry courses 2 Summer
Faculty of Education Physics in Education (17) Physics courses 2 Summer
Faculty of Applied Sciences Computer Modelling (2014) Special and interdisciplinary fields 3 Summer
Faculty of Education Studies in Mathematics (17) Mathematics courses 2 Summer
Faculty of Applied Sciences Geomatics (2016) Construction industry, geodesy and cartography 1 Summer
Faculty of Education Information Technologies in Education (16) Informatics courses 2 Summer
Faculty of Education Geography in Education (16) Pedagogy, teacher training and social care 2 Summer
Faculty of Applied Sciences Applied and Engineering Physics (2012) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Information Technologies (2016) Informatics courses 1 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2016) Mathematics courses 1 Summer
Faculty of Applied Sciences Cybernetics and Control Engineering (2016) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2007) Economy 1 Summer
Faculty of Applied Sciences Computer Systems (2016) Electrical engineering, telecommunication and IT 1 Summer
Faculty of Applied Sciences Geomatics (2017) Construction industry, geodesy and cartography 1 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2016) Mathematics courses 1 Summer
Faculty of Applied Sciences Cybernetics and Control Engineering (2017) Special and interdisciplinary fields 1 Summer
Faculty of Education Chemistry in Education (13) Chemistry courses 2 Summer
Faculty of Education Biology in Education (13) Biology courses 2 Summer
Faculty of Education Studies in Mathematics (14) Mathematics courses 2 Summer
Faculty of Education Information Technologies in Education (17) Informatics courses 2 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2016) Economy 1 Summer
Faculty of Applied Sciences Information Systems (2017) Informatics courses 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 1 Summer
Faculty of Applied Sciences Cybernetics and Control Engineering (2017) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Computer Systems (2017) Electrical engineering, telecommunication and IT 1 Summer
Faculty of Education Physics in Education (15) Physics courses 2 Summer
Faculty of Education Biology in Education (14) Biology courses 2 Summer
Faculty of Education Information Technologies in Education (14) Informatics courses 2 Summer
Faculty of Education Studies in Mathematics (1) Mathematics courses 2 Summer
Faculty of Education Studies in Mathematics (16) Mathematics courses 2 Summer
Faculty of Applied Sciences Applied and Engineering Physics (2017) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Cybernetics and Control Engineering (2013) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2016) Economy 1 Summer
Faculty of Education Geography in Education (17) Pedagogy, teacher training and social care 2 Summer
Faculty of Applied Sciences Information Systems (2012) Informatics courses 1 Summer
Faculty of Applied Sciences Information Technologies (2015) Informatics courses 1 Summer
Faculty of Applied Sciences Information Technologies (2012) Informatics courses 1 Summer
Faculty of Applied Sciences Information Technologies (2017) Informatics courses 1 Summer
Faculty of Applied Sciences Information Technologies (2013) Informatics courses 1 Summer
Faculty of Applied Sciences Geomatics (2016) Construction industry, geodesy and cartography 1 Summer
Faculty of Applied Sciences Mathematics and Management (2011) Mathematics courses 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 1 Summer
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 1 Summer
Faculty of Applied Sciences Information Technologies (2017) Informatics courses 1 Summer
Faculty of Education Geography in Education (14) Pedagogy, teacher training and social care 2 Summer
Faculty of Education Geography in Education (1) Pedagogy, teacher training and social care 2 Summer
Faculty of Applied Sciences Applied and Engineering Physics (2016) Special and interdisciplinary fields 1 Summer
Faculty of Education Biology in Education (17) Biology courses 2 Summer
Faculty of Education Physical Education in Education (17) Physical education and sport 2 Summer
Faculty of Applied Sciences Information Systems (1) Informatics courses 1 Summer
Faculty of Applied Sciences Computer Systems (2012) Electrical engineering, telecommunication and IT 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 1 Summer
Faculty of Applied Sciences Cybernetics and Control Engineering (2012) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 1 Summer
Faculty of Applied Sciences Mathematics for Science (2012) Mathematics courses 1 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2015) Mathematics courses 1 Summer