Welcome to the first homework session of Statistical Mechanics: Algorithms and Computations.
During the lecture, we have seen two powerful methods to compute π using Monte Carlo algorithms
the homework consists of three parts,
and you can find them on the Coursera website.
In part 1, you will evaluate errors associated to direct sampling like in the children's game
at the Monte Carlo beach.
In part 2, you will see that the performance of the Markov chain algorithm
played by adults in the heliport
depends on how far you can throw the pebble.
You will find that the best performance is approximately reached
using the very famous 1/2 thumb rule.
In part 3, you will study an advanced automatic method
to evaluate errors in a smart way
in Markov Chain algorithm, it's named the bunching method.