Modeling Affinity towards Mathematics Through Networks
CORNELL CLOSE-UPS | Professor Shares Beauty of Math with Students Traumatized by Subject
When prompted to write an article relating real world events to networks, I wanted to use this opportunity to learn something new about Cornell. This is how I stumbled upon an article talking about Professor Strogratz’s experiences with math and trying to get people to fear it less. His passion for math stemmed from a geometry problem given to him in high school, except this problem his teacher readily admitted he had no solution for. This both puzzled and intrigued Professor Strogratz. Much like many of the capable students here, he was used to being able to solve the standard math problems put in front of him by his previous teachers. To him, however, this felt different. Looking at this problem, he could not draw a solution right away, and finding that solution became his obsession. From this, the reader can see that math for some is like Professor Strogratz was an avenue for problem solving. Professor Strogratz conveys this as well; he sees mathematics as a way of thinking and wants his students to find relatable ways to incorporate mathematical thinking into their lives.
The way I see it, an affinity towards mathematics can be modeled as a networks problem. The nodes are people with exposure to mathematics, so we can generally assume that they are students and teachers. Having both in this graph are crucial. The edges represent the value of an interaction to do with math between the two people, and therefore the more positive the edge, the more impactful and memorable the experience would be. I chose this model because Professor Strogratz’s fascination was fueled by his admiration for his teacher who had readily admitted his inability to solve the problem. I’d like to draw one extrapolation with respect to balanced graphs. We know that the theory behind a balanced graph is that in a triangle, there must either be one or three positive ties. In this case, when all of Professor’s Strogratz students are put together in MATH 1300, over time more and more positive interactions related to mathematics will occur, and with more positive ties, the graph will trend towards stability. For example, if in a triangle between three friends two of them are positive, the third would then also from that exposure be more likely to learn from their positive experience and make that third positive interaction.