Mathematical background

The pre-requisites for this course are one upper-level undergraduate course on probability and one on analysis. Students wishing to take this course who have not had one or both of these courses will need to fill in gaps as we go along. Below are some resources for doing so (I will try to add things as they come up during the course.)

Probability

The primary utility to this course of an undergraduate course on probability is the intuition for how things like random variables, distributions, expectations, etc., behave and interact in the “nice” settings that are often encountered—the ones in which it is not crucial to abstract things to their measure theoretic foundations. A course in statistical inference is also useful for the same reasons.

Some good references/books to learn from are:

• Casella and Berger, Statistical Inference
• DasGupta, Fundamentals of Probability: A First Course (Free PDF version via the UBC library)

(Real) Analysis

The primary benefits in this course of a course on analysis are:

• experience proving things (a large component of the oft-cited “mathematical maturity”).
• experience with the weird things that can happen as we go off to infinity.
• some knowledge of the topology of the real line R.

A good resource for these things is Chapters 1 and 3 of Abbott’s Understanding Analysis, 2nd ed. (available for free as a PDF through the UBC library). Chapter 2 is also useful, but you are likely to have encountered much of this material in a calculus class.