The first half of the course reviews material that is useful in doctoral courses. The material covered includes 1) mathematical and statistical background concepts (matrix algebra, probability theory, random variables, and distributions), 2) core elements of statistical inference (estimation and testing), 3) analysis in vector spaces (metric and normed vector spaces with associated linear algebra).

The second half of the course concentrates on optimization theory necessary for microeconomic theory and macroeconomic theory. It starts with static optimization theory, and then focuses on optimal control theory and dynamic programming. The stochastic counterparts of the latter techniques are mentioned only briefly. The three basic references for the course are 1) A.K. Dixit, 1990, "Optimization in Economic Theory," second edition, Oxford University Press (in paperback); 2) N.L. Stokey, R.E. Lucas, Jr., with E.C. Prescott, 1989, "Recursive Methods in Economic Dynamics," Harvard University Press (Chapters 3, 4, 5, 6); and 3) T.J. Sargent, 1987, "Macroeconomic Theory," second edition, Academic Press (Chapters 9 and 11).