In this thesis we present a proof of the Banach-Tarski paradox, a counterintuitive result that states that any ball in R3 can be cut into finitely many pieces and then be reassembled into two copies of the original ball. ...

In this thesis we investigate the behaviour of primes in arithmetic progressions, with a focus on the phenomenon known as Chebyshev’s bias. Under the assumption of the Generalized Riemann Hypothesis and the Linear ...