  Unary theta functions have played a significant role in the theory of
holomorphic modular forms and modular $L$-functions. A partial theta functions
is defined analogously, but the sum is over part of the integer lattice. Such
sums fail to have modular properties. We give a construction which unifies
these partial theta functions with the mock theta function introduced by
Ramanujan. The modularity of Ramanujan's mock theta functions has only recently
been understood by the work of Sander Zwegers.
