"Mathematical Social Sciences;" An Oxymoron?

An explicit part of my agenda with these lectures is to encourage more mathematicians to seriously consider issues coming from the social sciences; let me assure you that you will find different and new mathematical issues. In the other direction, I also hope to encourage social scientists to appreciate the important gains that can result by using serious mathematics; I want to encourage the social scientists to seriously consider using this powerful approach. Because of these twin goals, my lectures, and these notes, are explicitly designed to address both audiences. For instance, the beginning of each section consists of examples which are intended to help develop intuition about the issues at hand. Then, toward the end of each section, there is a slightly stronger mathematical emphasis which is intended for the mathematicians. Nevertheless, I encourage the social scientists reading these notes to push on through this somewhat more technical material.

Table of Contents:

1. Mathematical Physical vs. Social Sciences

2. Symmetry galore!

3. Singularity theory and departmental meetings

4. Evolutionary game theory

 5. Adam Smith’s “Invisible hand” — and continuous foliations