Asymptotic distribution of the number of monochromatic arithmetic progressions in random colourings of the integers

In this thesis we research arithmetic progressions in random colourings of the integers. We ask ourselves how many arithmetic progressions are contained in zero density subsets of the integers? And what is the asymptotic distribution of the number of arithmetic progressions? Key motivation for this research are the famous results of Van der...

Implementation and Analysis of an Algorithm on Positive Integer Addition for Quantum Computing

In this project, an positive integer addition algorithm for quantum computing is analyzed which does not makes use of carry bits. The paper shows a general parallelization method. Using this method, the circuit runs in O(n) time instead of O(n^2). The algorithm is executed with different input sizes and error rates such that usable values are...

Using the slice rank for finding upper bounds on the size of cap sets

The cap set problem consists of finding the maximum size cap sets, i.e. sets without a 3-term arithmetic progression in F₃. In this thesis several known results on the behavior of this number as n → ∞ are presented. In particular we discuss a reformulation by Terence Tao and Will Sawin of a proof found by Dion Gijswijt and Jordan Ellenberg. It...

RekenRobot: Assisting primary school teachers in arithmetic education

A large problem that primary schools face is that the ratio of pupils to teachers is too high, the class sizes are too large and this makes it difficult for a single teacher to have a good oversight of how the development of a given child is going. The aim of Interactive Robotics is to tackle this problem by bringing robots into the classroom to...