Title: Computation and hierarchies in classical analysis

Abstract: What should it mean for one discontinuous function to compute another one? We describe two approaches. Within the Baire 1 functions, the first approach has equivalence classes which line right up with levels of the transfinite \alpha rank on Baire 1 functions considered by Kechris and Louveau. The second approach is designed to extend the already-established definition of what it means for one continuous function to compute another. This is joint work with Adam Day, Rod Downey and Takayuki Kihara.