### Functional Equations, Entropy and Diversity: A Seminar Course

#### Posted by Tom Leinster

I’ve just finished teaching a seminar course officially called “Functional Equations”, but really more about the concepts of entropy and diversity.

I’m grateful to the participants — from many parts of mathematics, biology and physics, at levels from undergraduate to professor — who kept coming and contributing, week after week. It was lots of fun, and I learned a great deal.

This post collects together all the material in one place. First, the notes:

- Tom Leinster,
*Functional Equations*. Rough and ready course notes, University of Edinburgh, 2017.

Now, the posts I wrote every week:

- I. Cauchy’s equation
- II. Shannon entropy
- III. Explaining relative entropy
- IV. A simple characterization of relative entropy
- V. Expected surprise
- VI. Using probability theory to solve functional equations
- VII. The $p$-norms
- VIII. Measuring biodiversity
- IX. Entropy on a metric space
- X. Value
- XI. The diversity of a metacommunity