This was part of a local math modeling competition at UNCA. During this project, me and my team developed a model to understand the flow of popularity between three fashion trends: A, B, and C. We did this by modeling two separate populations each of which can only flow from trend A to trend B then from trend B to trend C. The first population is the conformist. Those who move to the next trend at a rate proportional to how many are partaking in that next trend. For example if there are 100 people partaking in trend A and only 25 in trend B, then conformists are not very likely to shift from A to B, but if 25 are in trend A and 100 in trend B, then they will be much more likely to shift to the larger population. The other group is the non-conformist. Their likelihood to shift to the next trend is inversely proportional to how many people are partaking in that trend (relative to the current trend).

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Obviously, like most math models, this is a highly simplified. Most people aren’t conformist or non-conformist, but are often somewhere in between. This model can however capture many truths we see in the real world. For example the faster a trend grows the faster it dies. This is something we see all the time in the real world. Math models like this, though simplified, can often still reveal truths about the world. It is not about perfectly capturing reality, but rather knowing what details are important and how to simplify those details down in a way that preserves their truth. That is where the ‘skill’ of math modeling lies. 

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For the competition, me and my team were tasked with writing and presenting this research to a panel. We were the only team out of six to receive the highest honor. This was a formative experience for me. As lame as it might sound, working on this problem late at night with my two class mates in the library was some of the most fun I had in high school.