Part 1
The course reviews the mathemathcal skills that are needed for a research-oriented master in economics. The
course covers mathematical topics. The choice of topics and their presentation is geared towards applications in
economics. The course is an intensive mathematics camp, organized over 1 week prior to the beginning of the academic course.
It aims at providing students with a working knowledge of the concepts and techniques from mathematics that are
critical in a research-oriented master in economics.
Part 2
This course covers the foundational aspects of probability theory at the basis of economics and finance. The topics are standard for an introductory graduate probability course.
The course will last 18 hours and span 4 days. It will be divided into lectures of 4 and 4.5 hours. The first part is dedicated to constructing the notion of probability and random variables. Afterwards the course focuses on probability distributions: It discusses their measures of location and dispersion, such as expectation and variance, their common families, and transformation methods. The successive part of the course is dedicated to an advanced and thorough treatment of the topic of conditionality. The course concludes by presenting asymptotic results and convergence theorems for random variables on which econometrics (and statistical inference in general) is based.
The course’s material can be accompanied by the following suggested readings:
• Casella, G.H. and Berger, R.L. (2002). Statistical Inference. Duxbury/Thomson Learning.
• Wiley J. and Sons (1986). Probability and Measure. Patrick Billingsley.
• Rudin W. (1987). Real and Complex Analysis. McGraw-Hill.
• Williams D. (1991). Probability with Martingales. Cambridge University Pres.
• Bierens, H. J. (2004). Introduction to the mathematical and statistical foundations of econometrics. Cambridge University Press.
