We analyze the neutrino conversions inside a supernova in the 3 nu mixing s
cheme, and their effects on the neutrino spectra observed at the earth. We
find that the observations of the energy spectra of neutrinos from a future
galactic supernova may enable us to identify the solar neutrino solution,
to determine the sign of Delta m(32)(2), and to probe the mixing matrix ele
ment \ U-e3\(2) to values as low as 10(-4) - 10(-3).