ORF 526 · Princeton · Fall 2026
A graduate probability course built out of tools and examples rather than a slow development of the foundations.
Twenty-four sessions, in two modules. Each one is organized around a technique worth owning — Lindeberg swapping, Stein’s method, Wick’s theorem, the resolvent, exponential tilting — and around an example that shows what the technique is for. A substantial part of that second half is modern machine learning: wide networks at initialization, kernel regression, the spectrum of a Gaussian random matrix, the maxima of Gaussian processes, stochastic gradient descent, and diffusion models.
No measure theory. Nothing is assumed beyond linear algebra, multivariable calculus and an undergraduate probability course. Where a standard fact from analysis is needed — Fourier inversion, the spectral theorem — it is quoted honestly and marked as such in the notes.
The lowest quiz is dropped. Both examinations are closed book.
On the homework and the quizzes. The exercises live inside the lecture notes, typed A, B and C: A checks that nothing was missed, B asks whether the argument was understood, and C withholds exactly one idea. They are not collected and not graded — use whatever help you like, including an AI assistant, and if you are short of time do the C problems. The weekly quiz is where that work is cashed in: closed book, by hand, drawn from the week’s assigned exercises. The homework is the exploration layer; the quiz is the verification layer, and it is the only thing that needs policing.