Preliminary Ideas of Counting, and Some Useful Mathematics

Abstract

The modern subject of statistical mechanics is built on a single, simple idea: that much of the physics and chemistry of many-particle systems can be deduced from ideas of counting and probability. Classical physics contains no randomness, and yet a probabilistic description turns out to be very capable of analysing systems composed of a large number of entities. This is not mysterious; after all, if we flip a coin a large number of times, we fully expect that roughly half of the flips will yield heads, even though predicting the outcome of each flip is so complex as to be effectively impossible.

In which we set the stage for counting the number of ways in which a system can arrange itself, derive some mathematical and statistical results that will be useful later, examine the meaning of infinitesimals and partial derivatives, and study how to use units correctly and efficiently.