- can independently solve simple and more demanding exercises related to the theory from the corresponding lecture
- can independently formulate and prove simple theorems and results in the context of the theory from the lecture
- can independently develop and present more demanding proofs related to the lecture using suitable literature
- can independently generalize results from the lecture
- can independently work on related topics beyond the lecture course material using literature
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Arithmetic functions, Dirichlet series, multiplicativity, prime number counting function, distribution of prime numbers, prime number theorem, Bertrand's postulate, continued fraction algorithm and convergents, periodic continued fractions and quadratic irrationalities, approximation theorems of Dirichlet and Hurwitz, Pell's equation, algebraic and transcendental numbers, Diophantine approximation, best approximation, uniform distribution modulo 1, Weyl's criterion and numerical integration, discrepancy, Kronecker's theorem, normal numbers, structure of the prime residue class group, quadratic residues, elementary number theory in general integral domains
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