  We begin by presenting the classical deterministic problems of the calculus
of variations, with emphasis on the necessary optimality conditions of
Euler-Lagrange and the Noether theorem. As examples of application, we obtain
the conservation laws of momentum and energy from mechanics, valid along the
Euler-Lagrange extremals. We then introduce the stochastic calculus of
variations, proving a recent stochastic Noether-type theorem obtained by
Cresson. We end by pointing out an interesting open problem.
