FI:IB000 Math. Foundations of CS

IB000 Mathematical Foundations of Computer Science

Faculty of Informatics
Autumn 2026

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)

Guaranteed by

prof. RNDr. Petr Hliněný, Ph.D.
Department of Computer Science – Faculty of Informatics
Supplier department: Department of Computer Science – Faculty of Informatics

Prerequisites

!( IB000ext Math. Foundations of CS || NOW( IB000ext Math. Foundations of CS ))
The course is intended primarily for students of Bachelor's degree programs at the Faculty of Informatics. Students with a minor plan in Informatics enroll in IB000ext.

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 39 fields of study the course is directly associated with, display

Abstract

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.

Key topics

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.

Study resources and 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

Approaches, practices, and methods used in teaching

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.

Method of verifying learning outcomes and course completion requirements

Students' evaluation in this course consists of these three parts: through term evaluation (minimal score is required), "computer" written exam (again, minimal score is required), and an optional classical written exam.

Language of instruction

Czech

Further comments (probably available only in Czech)

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/podzim2026/IB000/index.qwarp

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, Autumn 2022, Autumn 2023, Autumn 2024, Autumn 2025.

Enrolment Statistics (recent)
Permalink: https://is.muni.cz/course/fi/autumn2026/IB000

FI:IB000 Math. Foundations of CS - Course Information

IB000 Mathematical Foundations of Computer Science

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