discipline 
Pure
Mathematics

subject 
Combinatorial Number Theory

lecturers 
András Sárközy 
credits 
2 
period 

curriculum 
“Simple” or “pure” version of Brun’s sieve. Convergence of the sum of reciprocals of
twin primes. Schnirelmann
density, Schnirelmann’s theorem. The primes form a
basis. Mann’s theorem (without proof).
The CauchyDavenport theorem. Kneser’s
theorem (without proof). Subset sums. Gallagher’s larger sieve, with
application. Primitive sequences. The theorems of Erdős and Behrend. Finite and infinite Sidonsequences,
greedy algorithm. Multiplicative Sidonsequences.
The theorems of Van der Waerden
and Szemerédi (without
proof), with application to a problem
of Roth. Hilbert’s cube. 
literature 

form of tuition 
Lecture 
mode of assessment 
written/oral
exam 