Although my understanding of it is still very elementary, set theory is really interesting to me. Especially the "Cantor" portion that deals with cardinals, ..., Continuum, hyperreals etc Calculus is also pretty fun~
Than we would have to make up new rules for algebra. Abstract rules, in fact. Dividing by zero (or at least, infinitely close to it) isn't that bad anyways, it just involves infinity (eg f(x)=1/x).
Favourite female singer would be Mimi Page, and male singer, eh, picking Marko Saaresto. Favourite band would be The Future Sound of London, and artist probably Zastabuj Kopec, Aurastore, Igorrr or Dream Stalker.