2025 Iowa State REU Projects

Combinatorics

Project mentor: Steve Butler

There will be two potential projects that will run (based on interest and availability of co-mentors). They are as follows:

Prerequisites: Proof-based math course; basic linear algebra course; mathematical curiosity; good communication skills and ability to work well in a group. Freshman and sophomores are encouraged to apply.
Students with advanced coursework (e.g. graduate level courses) are likely not to get as much benefit from this program; but may still apply.

Game theoretic modeling

Project mentor: Zhijun Wu

This project is to use the evolutionary game theory to study a critical language dynamic problem emerging worldwide in recent decades where multiple languages compete in societies with many of them becoming extinct as a result. In this project, the students will learn basic theory and methods for game dynamic analysis, and use these knowledges to build a game theoretic model for language competition. The basic idea here is to consider language competition as a population game where every individual decides how to use the available languages for his/her best social interests and collectively, the whole population reaches an equilibrium state with a “balanced” use of multiple languages. The project will use the game theoretic model to investigate the population threshold for language growth or decline; the effect of society intervention for language shift; and the importance of maintaining a language group for keeping a language. A Matlab code is to be implemented to simulate the language games in small-world social networks as well. 

Prerequisites: Knowledge of linear algebra, differential equations, and Matlab.