  A topological procedure for computing correlation functions for any (1,q)
model is presented. Our procedure can be used to compute any correlation
function on the sphere as well as some correlation functions at higher genus.
We derive new and simpler recursion relations that extend previously known
results based on W constraints. In addition, we compute an effective contact
algebra with multiple contacts that extends Verlindes' algebra. Computational
techniques based on the KdV approach are developed and used to compute the same
correlation functions. A simple and elegant proof of the puncture equation
derived directly from the KdV equations is included. We hope that this approach
can lead to a deeper understanding of D=1 quantum gravity and non-critical
string theory. (Paper uses tex TeX macro package jytex and includes 8
Postscript figures in the text using dvips (and epsf). Instructions for
processing are included.)
