  We present models for the initial mass function (IMF) for stars forming
within molecular clouds. These models use the idea that stars determine their
own masses through the action of powerful stellar outflows. This concept allows
us to calculate a semi-empirical mass formula (SEMF), which provides the
transformation between initial conditions in molecular clouds and the final
masses of forming stars. For a particular SEMF, a given distribution of initial
conditions predicts a corresponding IMF. We consider several different
descriptions for the distribution of initial conditions in star forming
molecular clouds. We first consider the limiting case in which only one
physical variable -- the effective sound speed -- determines the initial
conditions. In this limit, we use observed scaling laws to determine the
distribution of sound speed and the SEMF to convert this distribution into an
IMF. We next consider the opposite limit in which many different independent
physical variables play a role in determining stellar masses. In this limit,
the central limit theorem shows that the IMF approaches a log-normal form.
Realistic star forming regions contain an intermediate number of relevant
variables; we thus consider intermediate cases between the two limits. Our
results show that this picture of star formation and the IMF naturally produces
stellar mass distributions that are roughly consistent with observations. This
paper thus provides a calculational framework to construct theoretical models
of the IMF.
