  Noether's theorem is an elegant and powerful tool of classical mechanics, but
it is of little to no consequence in discrete theories. Here we define and
explore a discrete approach to covariant mechanics and show that within this
framework a discrete version of Noether's theorem, completely analogous to the
well-known continuum version with all its ramifications, remains valid. We also
discuss why more traditional approaches to discretized mechanics violate
certain conservation laws by construction.
