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FI:IB000 Math. Foundations of CS - Course Information

## IB000 Mathematical Foundations of Computer Science

**Faculty of Informatics**

Autumn 2021

**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 online. **Teacher(s)**- prof. RNDr. Petr Hliněný, Ph.D. (lecturer)

RNDr. Nikola Beneš, Ph.D. (seminar tutor)

RNDr. Jaroslav Čechák (seminar tutor)

RNDr. David Klaška (seminar tutor)

RNDr. Martin Maška, Ph.D. (seminar tutor)

doc. RNDr. Pavel Matula, Ph.D. (seminar tutor)

Bc. Markéta Naušová (seminar tutor)

RNDr. Petr Novotný, Ph.D. (seminar tutor)

doc. Mgr. Jan Obdržálek, PhD. (seminar tutor)

Matěj Pavlík (seminar tutor)

Bc. Kristýna Pekárková (seminar tutor)

Mgr. Filip Pokrývka (seminar tutor)

Roman Solař (seminar tutor)

doc. RNDr. David Svoboda, Ph.D. (seminar tutor)

Adéla Štěpková (seminar tutor)

Bc. Matouš Trnka (seminar tutor)

Jakub Balabán (assistant)

Bc. Ondřej Darmovzal (assistant)

Martin Krebs (assistant)

Mgr. Vojtěch Suchánek (assistant)

Adam Štafa (assistant)

Bc. Anh Minh Tran (assistant)

Anna Vítová (assistant)

Robert Zvara (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.
**Syllabus**- 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.

**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

*recommended literature*- HLINĚNÝ, Petr. Úvod do informatiky.
**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**- Czech
**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**- http://is.muni.cz/el/1433/podzim2017/IB000/index.qwarp

- Enrolment Statistics (recent)

- Permalink: https://is.muni.cz/course/fi/autumn2021/IB000