Large Matter Effects in ${{\nu_\mu \to \nu_\tau}}$ Oscillations

We show that matter effects change the ${\rm {\nu_\mu \to \nu_\tau}}$ oscillation probability by as much as 70% for certain ranges of energies and pathlengths. Consequently, the ${\rm {\nu_\mu \to \nu_\mu}}$ survival probability also undergoes large changes. A proper understanding of $\nu_\mu$ survival rates must consider matter effects in $P_{\mu \tau}$ as well as $P_{\mu e}$. We comment on a) how these matter effects may be observed and the sign of $\Delta_{31}$ determined in atmospheric neutrino measurements and at neutrino factories and b) how they lead to heightened sensitivity for small $\theta_{13}$.