Irrational numbers abound in all of mathematics, as is easy to see from the ubiquity of constants such as and or even Cantor's theorem that "almost all" numbers are in fact irrational. To deal with these numbers, very often, it is useful to be able to approximate them by the much more familiar rational numbers and countless methods to do this have been devised, ever since antiquity and Archimedes' famous approximation of , to do just that. However, in Diophantine Approximation (as opposed to, say, Numerical Analysis), we are not directly concerned with finding methods to approximate given irrationals but rather with studying the theory of how this can be done and, in a way, study the general "number theoreic" relationship between rational and irrational numbers. In this evening's DG, we'll take a look at a few interesting topics in this field and see a few of the striking results that this fascinating theory holds. Then pub.

P.S. Bear in mind that the Revision Group for Analysis III is taking place in MS.04 just before and might last until 8 PM, so we might have to use MS.03/05 or start slightly later instead, but there definetly will be a DG.