SUMS: Vasak -- P-adic Numbers, Modular Arithmetic and Strange Geometry

Everybody knows the counting numbers. Most know the integers. Many
know the rationals, or reals (even if they call them decimals). Some
even know of the complex numbers. But only a few have heard of the
p-adic numbers, the final (and most recent) addition to this
collection. The p-adic numbers are one of our most important tools in
modern number theory, giving us a much clearer perspective on what
modular arithmetic really means. This talk hopes to give an elementary
introduction into what they are, why they are important and just how
weird they can get.