  This article begins by reviewing the causal set approach in discrete quantum
gravity. In our version of this approach a special role is played by covariant
causal sets which we call $c$-causets. The importance of $c$-causets is that
they support the concepts of a natural distance function, geodesics and
curvature in a discrete setting. We then discuss curvature in more detail. By
considering $c$-causets with a maximum and minimum number of paths, we are able
to find $c$-causets with large and small average curvature. We then briefly
discuss our previous work on the inflationary period when the curvature was
essentially zero. Quantum mechanics on $c$-causets is considered next. We first
introduce a free wave equation for $c$-causets. We then show how the state of a
particle with a specified mass (or energy) can be derived from the wave
equation. It is demonstrated for small examples that quantum mechanics predicts
that particles tend to move toward vertices with larger curvature.
