### Mathematics and Statistics Course for MA and PhD Students

Mathematics and Statistics is a required course for all Economics graduate students. All MA general stream and MFE students are required to take ECO1010H1F, Mathematics and Statistics for MA General Stream Students. All PhD and Doctoral Stream MA students are required to take ECO 1011H1F, Mathematics and Statistics for PhD and Doctoral Stream MA students. These courses are both scheduled Monday-Friday, August 15, 2023 to September 1, 2023. For class locations, check the schedule of courses.#### Mathematics and Statistics for MA General Stream and MFE Students (ECO 1010H,F)

Mathematics and Statistics for MA Students (ECO 1010H,F) provides MA general stream and MFE students mathematical and statistical foundations for their microeconomics, macroeconomics and econometrics courses. The emphasis is on techniques and tools, not on proofs. The Math portion focuses on: intervals, functions, derivatives, static constrained and unconstrained optimization, envelope theorem, dynamic optimization, matrix algebra, and some differential and difference equations. The Stat portion focuses on probability, conditional probability, random variables, probability and cumulative distribution functions, probabilistic processes (such as Normal, Poisson, Bernoulli etc), Central Limit Theorems, parametric hypotheses and tests and Maximum Likelihood. Recommended references are (1) Martin Osborne's Mathematical Methods for Economic Theory, (2) A.K. Dixit, 1990, "Optimization in Economic Theory", second edition, Oxford University Press (in paperback); William Greene, Econometric Analysis, 6th Edition.NOTE: Although offered before the start of classes, this course is to be considered a FALL term course and students MUST enroll in it. Enrollment on ROSI for registered students opens on August 15, 2023.

In exceptional circumstances, a general stream MA student may be permitted to take ECO1011H1F, Mathematics and Statistics for PhD and MA Doctoral Stream Students. In these particular cases, written permission from the Associate Chair is required PRIOR to starting the Mathematics and Statistics course on August 15, 2023.

#### Mathematics and Statistics for PhD and MA Doctoral Stream Students (ECO 1011H,F)

The first half of the course reviews materials that will be useful primarily in econometrics but also in micro and macro. The material covered includes: (1) a review of matrix algebra; (2) probability theory including probability spaces, expectation and conditional expectation, independence, commonly encountered distributions, asymptotic distribution theory; (3) statistics, including summarization of data, estimation and inference. Theoretical and computer exercises will be assigned. Reference: William Greene, Econometric Analysis, 6th Edition, Appendices A-D.The second half of the review will concentrate on optimization theory that will be necessary for microeconomic and macroeconomic theory. It will start with static optimization theory, and then focus on optimal control theory and dynamic programming. The stochastic counterparts of the latter techniques will only be briefly mentioned. 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).