Refresher-Course: Math and statistics

With Krisztina Molnar, I am teaching the refresher course in math and statistics for incoming phd students in August, 2017. The course will cover some of the basic topics in math and probability/statistics for economists, and is intended to give you a running start for the main fall PhD courses in micro and econometrics. We will cover basic theory in class, but you will also do a lot of exercises to make sure that the necessary skills are not only theoretical, but also in your fingers.

If you are a beginning phd student in 2017 and believe you might need to do some preparations over the summer, please contact me. Have a look at the previous exams down below to see if this is familiar stuff that you can calculate without too much effort.

Lectures

The official timetable and such will be available at the econ department’s page for PhD Specialization in Economics.

  • Math: Week 34, August 21-26: 1015-1200 and 1415-1600 all days. All lectures in Aud 21.
  • Probability/statistics: Week 35, August  28 – September 1: 1015-1200 and 1415-1600 all days (except Thursday August 31, for which the morning lecture is 0815-1000). All lectures in Aud 21.

Part 1: Mathematics

We will have two 2 hour sessions  per day. Some of these will be lectures, some dedicated to solving exercises. List of topics:

  1. Sets, numbers and proofs
  2. Real Analysis  (Limit, Continuity, Differential, Approximation by differentials, Mean Value theorem, L’Hospitals rule , Indefinite and Definite integrals, Integration by substitution/ by parts, Introduction to Ordinary Differential equations)
  3. Linear Algebra  (Linear mappings and matrices, Vectors: addition, substraction, inner product, rotation, Linear independence, Rank of a matrix, Determinant, Eigenvalues and eigenvectors, Diagonalization, Solving linear difference equations)
  4. Unconstrained and constrained optimization (Quadratic form, Definiteness of matrix, Lagrangean, Kuhn-Tucker theorem)
  5. Functions of several variables  (Open ball, Limit point, Continuity, Partial derivative,  Total derivative, Gradient, Hessian, Differentiability and continuous differentiability, Implicit Function theorem)

math readings: For those of you who have previously studied this material I hope that I will help revive and organize your old memories.  You can use any  introductory math textbook, the course is based on Carl P. Simon and Lawrence Blume, «Mathematics for Economists», Norton 1994.

Part 2: Probability and statistics

The probability/statistics part starts Monday August 28, and we’ll have two sessions every day. Some of the sessions will be exercise sessions, in which we will go through a set of exercises. We might make minor adjustments to the lecture plan later.

The topics are, broadly speaking:

  1. Motivation: The problem of inference.
  2. Probability and random variables. Distributions.
  3. Expectation, conditional probability and Bayes theorem
  4. Transformations of random variables in one and two dimensions.
  5. Statistical inference. Hypothesis tests and power.
  6. Asymptotics.

How much we cover and the detail well get into depends on our progress.

After the course, there will be a 3-hour exam to test and make sure that everyone are ready for the main courses. For econ students, attending lectures is not mandatory, but the exam is mandatory.

prob/stat computing: For computing examples and simple empirical applications, we’ll be using R. Please download R and RStudio Desktop to your own computer ahead of the course. If you are not familiar with R, I think this free online textbook is wonderful: R for Data Science, by Garrett Grolemund and Hadley Wickham.

prob/stat readings: I think you can get the basics of probability and statistics from many different textbooks. The lectures will follow and reference Oliver Linton’s new book Probability, Statistics and Econometrics, and I expect that we’ll cover chapters 1-12, in varying level of detail. I want everyone to have read Gelman and Weakliem’s paper «Of beauty, sex, and power: statistical challenges in estimating small effects.» in American Scientist before we meet for the first time.

Previous exams

If you are interested in seeing what the exams have looked like previously, these are the some previous ones: