Of all the techniques used to classify topological spaces, few are so simple, so fruitful and so ubiquitous as homology and its dual, cohomology. By breaking a space into discretized parts we spot patterns, monitoring the closed n-dimensional "loops" to give groups, smaller structures that elucidate the whole; yielding vital theorems that, with a little case analysis, can classify the almost indeterminably abstract.

Beginning with a description of simplices, the buiding blocks of our discretized spaces, we build algebras; and generalized algebraic systems. Dual to this, we establish the space of differential forms, the wedge product and use the Stokes theorem to explain the mysterious duality. Our tools and minds sharpened, we set about proving some results. Among those covered will be the discussion groups favourite "hairy ball theorem" (this time for general n) and the awesomely powerful fixed point theorem of Brouwer.

Share the joy monday 7:30-9:00 MS03: after which we all share the joy at the pub.