IMA04 Fundamentals of combinatorics

Faculty of Education
Spring 2025
Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
In-person direct teaching
Teacher(s)
RNDr. Petra Antošová, Ph.D. (seminar tutor)
Mgr. Helena Durnová, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jaroslav Beránek, CSc.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
At the end of the course students should be able to understand and explain divisibility of integers, common divisor (multiple), prime numbers and diophantine equations.
Learning outcomes
At the end of the course students should be able to understand and explain divisibility of integers, common divisor (multiple), prime numbers and diophantine equations.
Syllabus
  • Introduction of terms in mathematics, types of definitions. Binary relations divisibility of natural and integral numbers, properties, application in primary school. Divisibility criteria in numerical systems. Solving problems. Numerical digits of natural numbers and their use. The use of the terms common divisor, the greatest common divisor, the common multiple, the least positive common multiple in the tasks of school mathematics. Indefinite equations, their types and ways to resolve, their use in tasks of school mathematics. Congruences: introduction and basic features.
Literature
    required literature
  • HERMAN, Jiří. Matematika : dělitelnost. 2. vyd. Praha: Prometheus, 2003, 100 s. ISBN 9788071962618. info
  • DRÁBEK, Jaroslav and Václav VIKTORA. Základy elementární aritmetiky : pro učitelství 1. stupně ZŠ a. 1. vyd. Praha: Státní pedagogické nakladatelství, 1985, 223 s. info
    recommended literature
  • VAŇUROVÁ, Milena. Aritmetika 2 (dělitelnost celých čísel) [online e-learningový kurz]. 2005. URL info
  • HEJNÝ, Milan and Naďa VONDROVÁ. Elementární matematika : (rovnice, teorie čísel, kombinatorika, planimetrie). Vyd. 2. Praha: Univerzita Karlova v Praze - Pedagogická fakulta, 2000, 79 s. ISBN 8072900145. info
  • VIKTORA, Václav. Matematika I pro studium učitelství v 1. až 4. ročníku ZŠ. čtvrté. Brno: Univerzita Jana Evangelisty Purkyně v Brně, 1983, 222 s. info
    not specified
  • HALAŠ, Radomír. Úvod do teorie čísel. 2., upravené vydání. Olomouc: Univerzita Palackého v Olomouci, 2014, 151 stran. ISBN 9788024440682. info
Teaching methods
Seminar.
Assessment methods
Credit. Seminar, written test. To successfully manage the need to reach at least 60% points from the maximum number of points.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: in blocks.
Information on the extent and intensity of the course: 8 konzultací (KS).
  • Permalink: https://is.muni.cz/course/ped/spring2025/IMA04