This course is designed to provide doctoral and master students with a working knowledge of convexity, optimization in Rn, dynamic programming, and various statistical techniques that are primarily used in economics. We will briefly set up several economic models and then introduce mathematical tools pertaining to analyzing those models. Due to time constraints and the intensive course structure, we will learn primarily how to manipulate (to some extent, mechanically) economic models associated with corresponding mathematical tools, and gain basic ideas and insights rather than going over mathematical details in a rigorous way. If you are interested in the fundamentals and all the building blocks of those mathematical tools, you could teach yourself by reading the references listed below, or take courses oered by mathematics department: real analysis, matrix algebra, differential equations, probability theory, stochastic processes, stochastic calculus, functional analysis, large sample theory, statistical inferences, and numerical analysis.

The following is excerpted from Tom Sargent's opinions on economics and math courses: The recommendations here are based primarily on the success of students who have taken the path I describe. Math is the language of economics. If you are an undergraduate, studying math will open doors to you in terms of interesting economics courses and job opportunities afterwards. Start with the basics: take three calculus courses (up to and including multivariable calculus), linear algebra, and a good course in probability and statistics. These basic courses will empower you. After you have these under your belt, you have many interesting options all of which will further empower you to learn and practice economics. Superb economists have made notable contributions to economics partly because they are creative but also because they studied more math than others. I especially recommend courses in (1) Markov chains and stochastic processes, and (2) dierential equations. These courses listed above are very useful courses for applied work in econometrics, macroeconomic theory, and applied industrial organization. They describe the foundations of methods used to specify and estimate dynamic competitive models. Just as in jogging, I recommend not overdoing it. Rather, find a pace that you can sustain throughout your years here. You will nd that taking these courses doesn't really cost time, because of your improved eciency in doing economics. There are many other courses that are interesting and useful. The most important thing is just to get started acquiring the tools and habits these courses will convey.