  We construct numerical models of the newly discovered binary pulsar
J0737-3039A, both with a fully relativistic, uniformly rotating, equilibrium
code that handles arbitrary spins and in the relativistic, slow-rotation
approximation. We compare results for a representative sample of viable nuclear
equations of state (EOS) that span three, qualitatively different, classes of
models for the description of nuclear matter. A future dynamical measurement of
the neutron star's moment of inertia from pulsar timing data will impose
significant constraints on the nuclear EOS. Even a moderately accurate
measurement (<~ 10 %) may be able to rule out some of these competing classes.
Using the measured mass, spin and moment of inertia to identify the optimal
model computed from different EOSs, one can determine the pulsar's radius.
