We've seen how to define and apply Monte Carlo integration, but there's a whole world of techniques for reducing variance.
Part five (thenumb.at/QMC) covers Quasi-Monte Carlo: negative correlation, stratified and adaptive sampling, and low-discrepancy sequences.

Apologies for the delay of part 5...

Monte Carlo has many uses, but path tracing is one of my favorites. Part four (thenumb.at/Rendering/) explores how Monte Carlo integration is used to simulate light transport.

Monte Carlo methods require randomly sampling complicated domains, which can be difficult in of itself.
Part three (thenumb.at/Sampling/) discusses how to create samplers using rejection, inversion, and changes of coordinates.

Monte Carlo integration lets us integrate high-dimensional functions exponentially faster than traditional methods!
Part two (thenumb.at/Monte-Carlo/) explores how and why it works.

I'm working on a series of posts about Monte Carlo methods!
The first (thenumb.at/Probability) is a review/overview of continuous probability, including random variables, distributions, expectation, variance, probability bounds, and the Dirac delta.

Functions are vectors! This perspective lets us apply the tools of linear algebra to computational problems from image and geometry processing to machine learning and light transport—and provides a natural explanation for Fourier series.
Let's explore: https://thenumb.at/Functions-are-Vectors