  We present a theory of spin waves in a non-condensed gas of spin-1 bosons:
providing both analytic calculations of the linear theory, and full numerical
simulations of the nonlinear response. We highlight the role of spin-dependent
contact interactions in the dynamics of a thermal gas. Although these
interactions are small compared to the thermal energy, they set the scale for
low energy long wavelength spin waves. In particular, we find that the polar
state of Rb-87 is unstable to collisional mixing of magnetic sublevels even in
the normal state. We augment our analytic calculations by providing full
numerical simulations of a trapped gas, explicitly demonstrating this
instability. Further we show that for strong enough anti-ferromagnetic
interactions, the polar gas is unstable. Finally we explore coherent population
dynamics in a collisionless transversely polarized gas.
