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This course concerns dynamic optimization in both continuous and discrete time. More specifically, it develops Pontryagin’s maximum principle and the Euler-Lagrange conditions in the calculus of variations, on the one hand, and the basic tools of deterministic dynamic programming, on the other. The course will be self-contained from the technical point of view but will presuppose a level of mathematical maturity that ought typically to be achieved by taking a course such as AS.180.600.