MAk026 Number Theory

Faculty of Education
autumn 2020
Extent and Intensity
0/0/1.3. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Chvalina, DrSc. (lecturer)
Mgr. Jitka Panáčová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jan Chvalina, DrSc.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
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
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
  • 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 exam (60 %), credit
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Information on the extent and intensity of the course: 16 hodin.
The course is also listed under the following terms Autumn 2021.
  • Enrolment Statistics (autumn 2020, recent)
  • Permalink: https://is.muni.cz/course/ped/autumn2020/MAk026