We present a simple, linear, partial-differential equation for the density-density correlation function in a glass-forming system. The equation is written down on the basis of fundamental and general considerations of linearity, symmetry, stability, thermodynamic irreversibility and consistency with the equation of continuity, that is, conservation of matter. The dynamical properties of the solutions show a change in behaviour characteristic of the liquid-glass transition as a function of one of the parameters (temperature). The equation can be shown to lead to the simplest mode-coupling theory of glasses and provides a partial justification of this simplest theory. It provides also a method for calculating the space-dependence of the correlation functions not available otherwise.

The results suggest certain differences in behaviour between glassy solids and glass-forming liquids that may be accessible to experiment. A brief discussion is presented of how the method can be applied to other systems such as sand-piles and vortex-glasses in Type II superconductors.

The methods discussed above can and have been used to construct an undergraduate research project which provides the student with experience in a wide variety of numerical and analytic techniques.