Concept Python Advanced 40 min

Hamiltonian Monte Carlo: why gradients beat a random walk in 100 dimensions

Afterwards you can explain how Hamiltonian Monte Carlo uses gradients and leapfrog steps to move far, tune its step size and path length, and spot a divergence.

Bayesian inference·Monte Carlo and random numbers Biology, Mathematics, Physics

Concept Python Intermediate 35 min

Monte Carlo transport: why a shield lets through more than e⁻³

Afterwards you can sample free paths and directions with NumPy, follow particles through a shield, and explain why more cross it than the exponential law says.

Monte Carlo and random numbers Engineering, Physics

Concept Python Intermediate 35 min

Neutron moderation: why hydrogen needs 18 collisions and carbon 115

Afterwards you can explain why light nuclei slow neutrons fastest, compute the collisions to thermal energy for any moderator, and check it by Monte Carlo.

Monte Carlo and random numbers Engineering, Physics

Concept Python Beginner 35 min

Monte Carlo integration: why the error falls as one over the square root of N

Afterwards you can estimate an integral by random sampling, give it an error bar, and say why its error falls as one over the square root of N in any dimension.

Monte Carlo and random numbers Cross-disciplinary