Elementary Stochastic Processes

Most reviewers give an accurate sense of this course. I just wanted to add some advice on taking the course--

For the problem sets, Brown will often have "help sessions." Go to these. He basically goes through the entire problem set and does them. I missed the first two, and then was kind of shocked to see him seemingly give away all the answers in the later two. Immensely useful in bringing down the work in the course.

Final and midterm were of the "pick and choose" format. For the midterm, something like 7 questions are given and you pick 4. Don't remember exact numbers, and he may change this. So if you don't have a ton of time to study, you can cram for just a few sections. For the midterm, I just learned all of the Markov chains questions really well and ended up with an okay grade.

To reiterate what others have said: Brown is a very dry lecturer. The main things to know in the course are Markov chains and Exponential Variables / Poisson processes. Everything is built off of one of these two concepts, so just understand these and you'll be fine.

This was an interesting class. What you get out of it is entirely a function of what you put in. Lecture is incredibly dry, granted, but the real gold is the posted notes and practice problems.

Stochastic processes are incredibly wonderful things. I've never though so coherently before about series of random processes, but this communicates the subject well.
What's really required here: You need to sit down with the book and the lecture notes and the problem sets and think about Markov chains and Poisson processes on a gut level. Everything else in the course is just an extension or generalization of this.
Become familiar with limit theorems, with the expected values of many distributions and how they relate (for example, the sum of exponentials is just a gamma-- the quotient of two gammas is a beta. etc). There's more than enough practice material to fully ace the exams, there are no tricks on them.

Dr. Brown is a wonderful man, but he injects a formalism into the course that's not needed for the problem sets (that you can do from the book) and is only tangentially needed for the exams (order statistics aren't mentioned in the book, but if you're smart enough, you'll be able to figure out the conditional expectations for the ordering of exponential distributions).