Large matter effects in numu-->nutau oscillations.

We show that matter effects change the numu-->nutau oscillation probability by as much as 70% for certain ranges of energies and path lengths. Consequently, the numu-->nutau survival probability also undergoes large changes. A proper understanding of numu survival rates must consider matter effects in Pmutau as well as Pmue. We comment on (a) how these matter effects may be observed and the sign of Delta31 determined in atmospheric neutrino measurements and at neutrino factories, and (b) how they lead to heightened sensitivity for small theta13.