Monthly Archives: January 2011

A topological proof of Van der Waerden’s Theorem

1. Introduction The van der Waerden’s theorem (vdW for short) was one of the first theorems to be proved in the branch of mathematics called Ramsey theory. I now state it in one of its many equivalent formulations: Theorem 1 … Continue reading

Posted in Ramsey Theory, Topological Dynamics | 13 Comments

Absolute values on Number Fields

One fundamental construction in modern algebraic number theory is that of the completion of a number field with respect to an absolute value, the p-adic numbers being a particular case. I will introduce the idea behind this construction and explore … Continue reading

Posted in Number Theory | 2 Comments