For my undergraduate course (MSci Mathematics at Lancaster University) my dissertation was on discrete-time Markov Chains, supervised by Professor Dmitry Korshunov.
For my dissertation I studied classification of states, return times, and invariant and asymptotic distributions. I also looked at various applications of Markov Chains, such as simple random walks, branching processes, and MCMC (Markov Chain Monte Carlo).
View my dissertation here: