  In recent years a supersymmetric form of discrete light-cone quantization
(hereafter `SDLCQ') has emerged as a very powerful tool for solving
supersymmetric field theories. In this scheme, one calculates the light-cone
supercharge with respect to a discretized light-cone Fock basis, instead of
working with the light-cone Hamiltonian. This procedure has the advantage of
preserving supersymmetry even in the discretized theory, and eliminates the
need for explicit renormalizations in 1+1 dimensions. In order to compare the
usual DLCQ prescription with the supersymmetric prescription, we consider two
dimensional SU(N) Yang-Mills theory coupled to a massive adjoint Majorana
fermion, which is known to be supersymmetric at a particular value of the
fermion mass. After studying how singular-valued amplitudes and intermediate
zero momentum modes are regularized in both schemes, we are able to establish a
precise connection between conventional DLCQ and its supersymmetric extension,
SDLCQ. In particular, we derive the explicit form of the (irrelevant)
interaction that renders the DLCQ formulation of the theory exactly
supersymmetric for any light-cone compactification. We check our analytical
results via a numerical procedure, and discuss the relevance of this
interaction when supersymmetry is explicitly broken.
