Finite Markov chains and Monte-Carlo Methods: An Undergraduate Introduction

This is a free textbook suitable for a one-semester course on Markov chains, covering basics of finite-state chains, many classical models, asymptotic behavior and mixing times, Monte Carlo methods, and martingales and harmonic functions. It is designed to fill a gap in the literature by being suitable for undergraduates; much of the theory is thus built from the ground up, with only basic probability and linear algebra assumed. We take as our basic framework the first four chapters of the classic Levin-Peres text "Markov Chains and Mixing Times," generously expanding to make an exposition suitable for an undergraduate audience. We also incorporate over a hundred exercises and problems, along with a rich set of accompanying illustrations. Suggested homework sets are found in an appendix. Updated editions will periodically appear as new versions of this submission.