In this Lecture the formal concept of the ensemble was developed. I emphasized the canonical ensemble -- its list of states and their statistical weights -- but also treated other ensembles often seen in statistical mechanics. Notation and terminology for particle position and momenta was introduced. While subsequent Lectures could be given without using this notation, its gradual introduction will substantially compress the equations to be discussed.
The remainder of this course consists entirely of embellishments and illuminations of the remarks given in this Lecture. I said in Lecture 1 that any physical theory has three parts: a set of formal equations, a set of implicit assumptions, and a set of models and exemplary problems which show the limits and applications of the theory.[9] The formal equations and implicit assumptions of statistical mechanics largely appear above. In the remainder of the course, we will examine problems which show how the theory may be applied, and what models have been found useful to describe physical systems.