I am a research mathematician and an expert on mathematical software. I completed my PhD in applied mathematics with a specialization in computer algebra and symbolic computation in 2003 at the University of Waterloo. My PhD supervisor was Prof. Keith O. Geddes, co-inventor of Maple. In my PhD thesis, I invented a parameterized family of bilinear infinite series expansions for multivariate functions, which I named "Geddes series expansions" in honor of my thesis supervisor. Geddes series are more general than both Taylor series and Fourier series since the terms of a Geddes series can contain arbitrary functions. Geddes series are more versatile than traditional series expansions because the parameters of the family are not numbers, or even functions, but rather linear functionals on function spaces. Geddes series have dozens of computational applications ranging from the fast and accurate approximation of high-dimensional multiple integrals to the automatic derivation and proof of multivariate identities for elementary and special functions.