IB000ext Mathematical Foundations of Computer Science

Faculty of Informatics
Autumn 2025
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).
In-person direct teaching
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Mgr. Jakub Balabán (seminar tutor)
RNDr. Nikola Beneš, Ph.D. (seminar tutor)
Bc. Filip Blažek (seminar tutor)
Bc. Samuel Čepela (seminar tutor)
Mgr. Tomáš Foltýnek, Ph.D. (seminar tutor)
Mgr. Jan Jedelský (seminar tutor)
RNDr. Martin Jonáš, Ph.D. (seminar tutor)
Bc. Tomáš Jusko (seminar tutor)
Marek Lukášík (seminar tutor)
doc. RNDr. Martin Maška, Ph.D. (seminar tutor)
doc. RNDr. Pavel Matula, Ph.D. (seminar tutor)
RNDr. Vít Musil, Ph.D. (seminar tutor)
doc. RNDr. Petr Novotný, Ph.D. (seminar tutor)
doc. Mgr. Jan Obdržálek, PhD. (seminar tutor)
Mgr. Adam Straka (seminar tutor)
doc. RNDr. David Svoboda, Ph.D. (seminar tutor)
Bc. Adéla Štěpková (assistant)
Bc. Vojtěch Turland (seminar tutor)
Bc. Lukáš Bátora (assistant)
Bc. Matěj Pavlík (seminar tutor)
Bc. Jindřich Sedláček (assistant)
Pavol Trnavský (assistant)
Bc. Anna Vítová (assistant)
Mgr. Lukáš Másilko (seminar tutor)
Bc. Martin Michal Dyttert (seminar tutor)
Mgr. Marek Filakovský, Ph.D. (seminar tutor)
Mgr. Lukáš Málik (seminar tutor)
Bc. Kateřina Borošová (seminar tutor)
Iva Kasprzaková (seminar tutor)
Tomáš Kocián (seminar tutor)
Anna Hronová (seminar tutor)
Ondřej Švihnos (seminar tutor)
Andrea Večerková (seminar tutor)
Guaranteed by
prof. RNDr. Petr Hliněný, Ph.D.
Department of Computer Science – Faculty of Informatics
Supplier department: Department of Computer Science – Faculty of Informatics
Timetable
Wed 24. 9. to Wed 17. 12. Wed 18:00–19:50 P101; and Fri 19. 9. 7:50–9:30 P101
  • Timetable of Seminar Groups:
IB000ext/AA: Thu 25. 9. to Thu 18. 12. Thu 10:00–11:50 A220, J. Balabán
IB000ext/01: Mon 22. 9. to Mon 15. 12. Mon 8:00–9:50 C416, D. Svoboda
IB000ext/02: Mon 22. 9. to Mon 15. 12. Mon 8:00–9:50 A321, T. Foltýnek
IB000ext/03: Mon 22. 9. to Mon 15. 12. Mon 10:00–11:50 C408, P. Matula
IB000ext/04: Mon 22. 9. to Mon 15. 12. Mon 10:00–11:50 C416, L. Málik
IB000ext/05: Mon 22. 9. to Mon 15. 12. Mon 12:00–13:50 A220, M. Lukášík
IB000ext/06: Mon 22. 9. to Mon 15. 12. Mon 12:00–13:50 C416, A. Večerková
IB000ext/07: Mon 22. 9. to Mon 15. 12. Mon 14:00–15:50 A319, M. Lukášík
IB000ext/08: Mon 22. 9. to Mon 15. 12. Mon 18:00–19:50 C416, A. Straka
IB000ext/09: Tue 23. 9. to Tue 16. 12. Tue 8:00–9:50 A220, T. Kocián
IB000ext/10: Tue 23. 9. to Tue 16. 12. Tue 10:00–11:50 C416, O. Švihnos
IB000ext/11: Tue 23. 9. to Tue 16. 12. Tue 12:00–13:50 A220, J. Jedelský
IB000ext/12: Tue 23. 9. to Tue 16. 12. Tue 12:00–13:50 C416, S. Čepela
IB000ext/13: Tue 23. 9. to Tue 16. 12. Tue 14:00–15:50 C416, M. Dyttert
IB000ext/14: Tue 23. 9. to Tue 16. 12. Tue 16:00–17:50 A220, A. Hronová
IB000ext/15: Wed 24. 9. to Wed 17. 12. Wed 8:00–9:50 C416, J. Obdržálek
IB000ext/16: Wed 24. 9. to Wed 17. 12. Wed 10:00–11:50 C416, J. Obdržálek
IB000ext/17: Wed 24. 9. to Wed 17. 12. Wed 12:00–13:50 C416, V. Musil
IB000ext/18: Wed 24. 9. to Wed 17. 12. Wed 12:00–13:50 A218, P. Novotný
IB000ext/19: Thu 25. 9. to Thu 18. 12. Thu 8:00–9:50 C416, M. Maška
IB000ext/20: Thu 25. 9. to Thu 18. 12. Thu 10:00–11:50 C416, M. Maška
IB000ext/21: Thu 25. 9. to Thu 18. 12. Thu 12:00–13:50 A319, V. Musil
IB000ext/22: Thu 25. 9. to Thu 18. 12. Thu 12:00–13:50 A220, P. Hliněný
IB000ext/23: Thu 25. 9. to Thu 18. 12. Thu 14:00–15:50 C416, I. Kasprzaková
IB000ext/24: Thu 25. 9. to Thu 18. 12. Thu 14:00–15:50 A220, V. Turland
IB000ext/25: Thu 25. 9. to Thu 18. 12. Thu 16:00–17:50 C408, A. Straka
IB000ext/26: Fri 26. 9. to Fri 19. 12. Fri 8:00–9:50 A320, J. Balabán
IB000ext/27: Fri 26. 9. to Fri 19. 12. Fri 8:00–9:50 A220, K. Borošová
IB000ext/29: Fri 26. 9. to Fri 19. 12. Fri 10:00–11:50 A220, T. Jusko
IB000ext/30: Fri 26. 9. to Fri 19. 12. Fri 12:00–13:50 A220, M. Jonáš
IB000ext/31: Fri 26. 9. to Fri 19. 12. Fri 12:00–13:50 A321, M. Pavlík
Prerequisites
!( IB000 Math. Foundations of CS || NOW( IB000 Math. Foundations of CS ))
This course is primarily intended for students who have Informatics as a minor plan. Students in the Bachelor's degree programs of the Faculty of Informatics enroll in IB000. IB000 graduates can have IB000ext recognized.
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
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 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 and relevant proofs.
Syllabus
  • The course focuses on understanding basic mathematical tools:
  • Basic formalisms - statements, proofs, and propositional logic.
  • Introduction to predicate logic, quantifiers.
  • 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, subgraphs, directed graphs.
  • Graph connectivity and distance, trees, and spanning trees.
  • Infinite sets and the halting problem.
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 these parts: through term evaluation (minimal score is required), and "computer" written exam (again, minimal score is required).
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://is.muni.cz/el/1433/podzim2024/IB000ext/index.qwarp
The course is also listed under the following terms Autumn 2024.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2025/IB000ext