MA0026 Number Theory

Faculty of Education
Autumn 2023
Extent and Intensity
2/2/1.3. 6 credit(s). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
Mgr. Helena Durnová, Ph.D. (lecturer)
prof. RNDr. Jan Chvalina, DrSc. (lecturer)
RNDr. Karel Lepka, Dr. (lecturer)
Guaranteed by
prof. RNDr. Jan Chvalina, DrSc.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Timetable
Mon 8:00–9:50 učebna 41
  • Timetable of Seminar Groups:
MA0026/Kombi01: Fri 29. 9. 8:00–11:50 učebna 20, Fri 6. 10. 8:00–11:50 učebna 51, Fri 10. 11. 8:00–11:50 učebna 72, Fri 1. 12. 12:00–15:50 učebna 24, K. Lepka
MA0026/Prez01: Mon 10:00–11:50 učebna 30, K. Lepka
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 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 be able to explain basic notions and theorems of number theory. Exploitations of number theory in teaching of mathematics.
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
  • VINOGRADOV, Ivan Matvejevič. Základy theorie čísel. Translated by I. M. Hrázský. 1. vyd. Praha: Československá akademie věd, 1953, 173 s. info
    recommended literature
  • Znám, Štefan. Theória čísel. 1. vyd. Bratislava: Alfa, 1986. 207 s.
  • KOWAL, Stanisław. Matematika pro volné chvíle : (zábavou k vědě). Edited 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
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 exam (60 %), credit
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 2024.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/ped/autumn2023/MA0026