  We present an intuitive, conceptual, but semi-rigorous introduction to the
celebrated Markov Chain Monte Carlo method using a simple model of population
dynamics as our motivation and focusing on a few elementary distributions.
Conceptually, the population flow between cities closely resembles the random
walk of a single walker in a state space. We start from two states, then three
states, and finally the setup is fully generalized to many states of both
discrete and continuous distributions. Despite the mathematical simplicity, the
setup remarkably includes all the essential concepts of Markov Chain Monte
Carlo without loss of generality, e.g., ergodicity, global balance and detailed
balance, proposal or selection probability, acceptance probability, up to the
underlying stochastic matrix, and error analysis. Our teaching experience
suggests that most senior undergraduate students in physics can closely follow
these materials without much difficulty.
