From a quick look into B-spline Galerkin methods, I need to integrate B-spline basis functions against each other. Though I could extract piecewise polynomial representations and integrate them symbolically, it was more fun to see what fixed order Gauss quadrature FOSS existed. I stumbled across Pavel Holoborodko's excellent routines. I'm in the process of preparing a patch for the GNU Scientific Library that ports Pavel's code to GSL conventions (update: patch submitted). Hopefully they'll accept it (update: patch accepted).
While digging around, I ran across a beautiful paper by Trefethen which I just finished on the morning bus ride into campus. Absolutely fantastic.
The paper is so good that it makes me also want to try implementing Clenshaw-Curtis rules for GSL. Before coding, I need to read this follow up work which it seems may have some numerical details buried within it.