Syllabus
- Natural numbers, construction, Peano axioms, adding, multiplying, order.
- Divisibility, prime numbers, perfect numbers, Fermat theorem, Euler theorem, Gauss theorem, Tchebysew theorem - the number of prime numbers.
- Integers, construction, operations and order.
- Rational numbers, construction, operations and order, enumerability.
- Real numbers, construction by means of fundamental sequences - Cantor method, supremum and infimum theorem, mention of other ways of construction - Dedekind, Kolmogorov, Conway.
- Algebraic and transcendental numbers.
- Euler number (e) a Ludolf number (pí), Euler constant (a), properties, relationship to sequences and series, relationship to probability.
Annotation
The subject deals with the basic concepts of number theory. The particular types of numbers, the ways of their construction and their most important properties are concerned there.