We give an introduction to computation and logic tailored for algebraists, and use this as a springboard to discuss geometric models of computation and the role of cutelimination in these models, following Girard's geometry of interaction program. We discuss how to represent programs in the λcalculus and proofs in linear logic as linear maps between infinitedimensional vector spaces. The interesting part of this vector space semantics is based on the cofree cocommutative coalgebra of Sweedler.
