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 Cauchy-Davenport 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 Sidon-sequences, greedy algorithm. Multiplicative Sidon-sequences. 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