  Information theory is a mathematical theory of learning with deep connections
with topics as diverse as artificial intelligence, statistical physics, and
biological evolution. Many primers on information theory paint a broad picture
with relatively little mathematical sophistication, while many others develop
specific application areas in detail. In contrast, these informal notes aim to
outline some elements of the information-theoretic "way of thinking," by
cutting a rapid and interesting path through some of the theory's foundational
concepts and results. They are aimed at practicing systems scientists who are
interested in exploring potential connections between information theory and
their own fields. The main mathematical prerequisite for the notes is comfort
with elementary probability, including sample spaces, conditioning, and
expectations. We take the Kullback-Leibler divergence as our most basic
concept, and then proceed to develop the entropy and mutual information. We
discuss some of the main results, including the Chernoff bounds as a
characterization of the divergence; Gibbs' Theorem; and the Data Processing
Inequality. A recurring theme is that the definitions of information theory
support natural theorems that sound ``obvious'' when translated into English.
More pithily, ``information theory makes common sense precise.'' Since the
focus of the notes is not primarily on technical details, proofs are provided
only where the relevant techniques are illustrative of broader themes.
Otherwise, proofs and intriguing tangents are referenced in liberally-sprinkled
footnotes. The notes close with a highly nonexhaustive list of references to
resources and other perspectives on the field.
