Mathematics

Converting foreign currency from a financial literacy and proportional reasoning perspective

Can undergraduates convert $100 of foreign currency? Can they convert 100 NZD into foreign currency? We examine foreign currency conversion from a financial literacy lens and compare it to a proportional reasoning perspective.

Mathematical billiards: Periodic orbits within quadrilaterials

We introduce a novel continuation formulation which bypasses the extreme degeneracies exhibited by mathematical billiards and use it to compute branches of periodic solutions as a parameter varies the shape of the billiard from a square to a rectangle and parallelogram.

Dynamics of Twitter Hashtags

We quantify the statistical properties and dynamics of the frequency of hashtag use on Twitter and find that the volume and the nature of the hashtags depend strongly on time, with the appearance of bursts at the minute scale, fat-tailed noise, and long-range correlations.

Non-convergent Nash equilibria on a circular market

Using the Hotelling-Downs spatial model of competition to investigate the behavior of competing firms when the location space is a circle. Unlike the standard Hotelling-Downs model we assume that customers with some probability buy from retailers other than the closest one.