The n-Category Café

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