This unique text for beginning graduate students gives a self-contained introduction to the
mathematical properties of stochastics and presents their applications to Markov processes
coding theory population dynamics and search engine design. The book is ideal for a newly
designed course in an introduction to probability and information theory. Prerequisites include
working knowledge of linear algebra calculus and probability theory. The first part of the
text focuses on the rigorous theory of Markov processes on countable spaces (Markov chains) and
provides the basis to developing solid probabilistic intuition without the need for a course in
measure theory. The approach taken is gradual beginning with the case of discrete time and
moving on to that of continuous time. The second part of this text is more applied its core
introduces various uses of convexity in probability and presents a nice treatment of entropy.
