Number Theory 1000-135TL1

1) student knows basic notions conserning the fundamental theorem of arithmetic, knows how to compute GCD of two or more numbers;
2) she/he recognizes the fundamental importance of prime nimbers in mathematics; knows the history of their investigations; is capable of proving Chebyshev's theorem and can formulate the Prime Number Theorem,
3) knows the notion of congruence in integers and can see it in the context of abstract algebra; can apply the basic theorems (little Fermats theorem, Eulers theorem, Wilsons theorem); understands the importance of congruences in contemporary cryptography.
4) can solve the simplest diophantine equations,
5) knows the quadratic reciprocity law (with elements of its history) and can apply it.
6) knows the most famous open problems in number theory; recognizes their importance in mathematics and culture.

the final score is the weighted average: 30% of the grade from classes and 70% of the result in final exam

K. Ireland, M. Rosen, A classical introduction in modern number theory, Springer 1990.
W.Narkiewicz, Number Theory, World Scientific, Singapore, 1983.
W.Sierpiński, Elementary theory of numbers, Warszawa-Amsterdam-New York-Oxford 1987.
Z.I. Borevich, I.R.Shafarevich, Number Theory, Academic Press 1966

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

• Description of 1000-135TL1 in USOSweb