IB000 Mathematical Foundations of Computer Science

Faculty of Informatics
Autumn 2022
Extent and Intensity
2/2/1. 4 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Taught in person.
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Bc. Jakub Balabán (seminar tutor)
RNDr. Nikola Beneš, Ph.D. (seminar tutor)
Mgr. Tomáš Foltýnek, Ph.D. (seminar tutor)
Bc. Jan Jedelský (seminar tutor)
Tomáš Jusko (seminar tutor)
RNDr. David Klaška (seminar tutor)
Bc. Martin Kurečka (seminar tutor)
doc. RNDr. Martin Maška, Ph.D. (seminar tutor)
doc. RNDr. Pavel Matula, Ph.D. (seminar tutor)
RNDr. Petr Novotný, Ph.D. (seminar tutor)
doc. Mgr. Jan Obdržálek, PhD. (seminar tutor)
Mgr. Kristýna Pekárková (seminar tutor)
RNDr. Filip Pokrývka (seminar tutor)
Jindřich Sedláček (seminar tutor)
Bc. et Bc. Roman Solař (seminar tutor)
doc. RNDr. David Svoboda, Ph.D. (seminar tutor)
Adéla Štěpková (seminar tutor)
Dávid Šutor (seminar tutor)
Lukáš Bátora (assistant)
Roman Dvořák (assistant)
Martin Krebs (assistant)
Kateřina Matulová (assistant)
Bc. et Bc. Matěj Pavlík (assistant)
Adam Štafa (assistant)
Anna Vítová (assistant)
Guaranteed by
prof. RNDr. Petr Hliněný, Ph.D.
Department of Computer Science - Faculty of Informatics
Supplier department: Department of Computer Science - Faculty of Informatics
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 59 fields of study the course is directly associated with, display
Course objectives
This course is focused on understanding basic mathematical concepts necessary for study of computer science. This is essential for building up a set of basic concepts and formalisms needed for other theoretical courses in computer science. At the end of this course the successful students should: know the basic mathematical notions; understand the logical structure of mathematical statements and mathematical proofs, specially mathematical induction; know discrete mathematical structures such as finite sets, relations, functions, and graph; be able to precisely formulate their claims, algorithms, and relevant proofs; and apply acquired knowledge in other CS courses as well as in practice later on.
Learning outcomes
After finishing the course the student will be able to: understand the logical structure of mathematical statements and mathematical proofs, deal with and explain basic structures of discrete mathematics, precisely formulate their claims, algorithms, and relevant proofs.
  • The course focuses on understanding basic mathematical tools:
  • Basic formalisms - statements, proofs, and propositional logic.
  • Sets, relations, and functions.
  • Proof techniques, mathematical induction.
  • Recursion, structural induction.
  • Binary relations, closure, transitivity.
  • Equivalence and partial orders.
  • Composition of relations and functions.
  • Basics of graphs, isomorphism, connectivity, trees.
  • Graph distance, spanning trees. Directed graphs.
  • Proof techniques for algorithms.
  • Infinite sets and the halting problem.
    recommended literature
  • HLINĚNÝ, Petr. Úvod do informatiky. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. URL info
  • MATOUŠEK, Jiří and Jaroslav NEŠETŘIL. Kapitoly z diskrétní matematiky. 3., upr. a dopl. vyd. V Praze: Karolinum, 2007. 423 s. ISBN 9788024614113. info
Teaching methods
This subject has regular weekly lectures and compulsory tutorials. Moreover, the students are expected to practice at home using online questionnaires, via IS MU. All the study materials and study agenda are presented through the online IS syllabus.
Assessment methods
Students' evaluation in this course consists of (the sum of) three parts which have rougly equal weights: through term evaluation (minimal score is required), "computer" written exam, and optional classical written exam.
The semester evaluation is computed as the sum of a certain number of the best out of all term tests, plus possible bonus points for solving voluntary assignments. Details can be found in the IS course syllabus. Then the "computer" exam follows, and its sum with the semester evaluation determines student's success in the course. Optional written exam at the end gives students the opportunity to get higher grades.
Language of instruction
Further comments (probably available only in Czech)
Information on completion of the course: Pozor, ukončení zápočtem lze volit pouze ve výjimečných případech, kdy to umožňuje váš studijní program.
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
Teacher's information
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Spring 2006, Autumn 2006, Autumn 2007, Spring 2008, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2022/IB000