MA0026 Number Theory

Faculty of Education
Autumn 2024
Extent and Intensity
2/2/1.3. 6 credit(s). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
Mgr. Helena Durnová, Ph.D. (lecturer)
RNDr. Jakub Novák (seminar tutor)
Guaranteed by
Mgr. Helena Durnová, Ph.D.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Timetable of Seminar Groups
MA0026/KombiSem01: Fri 25. 10. 9:00–12:50 učebna 39, Fri 15. 11. 12:00–15:50 učebna 42, Fri 22. 11. 15:00–18:50 učebna 39, Fri 13. 12. 8:00–11:50 učebna 37, H. Durnová
MA0026/PrezPred01: Mon 14:00–15:50 učebna 37, H. Durnová
MA0026/PrezSem01: Mon 16:00–17:50 učebna 37, H. Durnová
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
there are 8 fields of study the course is directly associated with, display
Course objectives
At the end of this course, students should be able to understand and explain notions and theorems of number theory, including its use in everyday life as well as the teaching practice
Learning outcomes
At the end of the course students should be able to understand and to solve ground tasks of number theory: Divisibility of natural numbers, proofs of chosen theorems. The greatest common divisor, the least common multiple, exercises. Prime numbers and some of their interesting properties. Congruence of a single variable and their solutions. Indefinite equations. Euler's function, Euler's theorem, arithmetic functions
Syllabus
  • Divisibility of natural numbers, proofs of chosen theorems. The greatest common divisor, the least common multiple, exercises. Prime numbers and some of their interesting properties. Congruence of a single variable and their solutions. Indefinite equations. Euler's function, Euler's theorem, arithmetic functions
Literature
    required literature
  • LEPKA, Karel. Základy elementární teorie čísel (Elements of elementary number theory). 1. vydání. Masarykova univerzita, 2023, 76 pp. ISBN 978-80-280-0423-1. info
    recommended literature
  • Znám, Štefan. Theória čísel. 1. vyd. Bratislava: Alfa, 1986. 207 s.
  • KOWAL, Stanisław. Matematika pro volné chvíle : (zábavou k vědě). Translated by Jiří Jarník. 2., upr. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 323 s. URL info
  • BIAŁAS, Aleksander. O dělitelnosti čísel. Translated by Pavel Vít. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1966, 97 s. info
  • VINOGRADOV, Ivan Matvejevič. Základy theorie čísel. Translated by I. M. Hrázský. 1. vyd. Praha: Československá akademie věd, 1953, 173 s. info
Teaching methods
Lecture providing to students an insight into the calculus of a structure of all inegers and natural numbers with aiming on mathematics of basic school.
Assessment methods
Written test, followed by a brief discussion.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Information on the extent and intensity of the course: 16 hodin (kombinovaná forma).
The course is also listed under the following terms autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/ped/autumn2024/MA0026