In case you want to tackle some other problems (without credit) here are some examples. Of course you can think up some of your own. Basic motivation is to develop the skills for problem solving using Mathematica.
Q1. Implement a random walk in 2 dimensions. Allow for graphical output and statistical analysis of walk.
Q2. Implement the Metropolis algorithm for sampling from a thermal distribution the conformation of a simple model of a protein backbone where bond lengths are fixed and the potential energy is a sum of independent bond angle and torsion terms. Assume the potential energy for each term is proportional to the cosine of the angle. Investigate the conformation as a function of temperature.
Q3. Model the process of collisional energy transfer by a non-reactive master equation
using a matrix formulation. Examine the time evolution (animation?) of the probability density p(t;E) given an exponential model for the transition probability P(E,E').
Q4. Solve the Schrödinger equation for a system of two harmonic oscillators coupled by a simple m:1 coupling term
and examine the wavepacket dynamics as a function of time for different
coupling terms (varying 
, m) and frequency ratios (varying
and 
).