In October 2013, I was invited to the National Hellenic Society (NHS) Reunion Weekend as a representative of the Heritage Greece 2012 (HG2012) class. While I was sitting on the plane to Las Vegas unable to sleep, I had a thought – how can I make applying to college easier? I’m not quite sure what drove me to have this idea nor why my immediate consideration was to use math to try and solve it. Over the course of the flight I wrote an initial draft of what I called College Application Selection: A Student Perspectives Based Approach.
My plan was to create a model that would help a student choose which colleges to send applications, given that he or she has already done initial research on colleges, and has a specific budgetary constraint on the cost of applying. This model would take as input the list of colleges and the budgetary constraint, as well as factors in which each college would be rated and the ratings for each college. It would then act as a black box, and output for the student a list of schools that would maximize the total value of schools applied to.
Unbeknownst to me at the time, what I created was the Binary Knapsack Problem (BKP), illustrated in the following scenario. Consider a hiker, who has a list of unique items he wants to take with him, and a particular value and weight for each item. The hiker can choose only to take or not take an item in its entirety; a fraction of an item cannot be taken. He must carry the items he chooses in his knapsack, which has a certain weight capacity. His goal is to choose the items that maximize the total value of his knapsack without going over the weight capacity. In my model, the colleges are the items to be “placed in the knapsack” and the “weight capacity” is the budget placed on cost of applying.
After several iterations, I realized that there was more to the problem that I initially considered. The BKP has no known efficient solution, although a variety of approaches have been published to solving this problem both approximately and exactly. After choosing a simple approximation method to use within my paper, I submitted the paper to the Hopkins Undergraduate Research Journal (HURJ). Months later, I was contacted by the selection committee, who chose my paper as a Focus article in the Fall 2014 edition, which has the theme “The Changing World”.
My ultimate goal with this research is to continue expanding the model from both mathematical and sociological perspectives. On the math side of things, I will be continuing my research into the BKP as part of my Master’s Thesis. I plan to implement my model in an easy to use web application that can then be distributed to students around the country struggling to make this college application decision. The hope is that combining this model with a query for basic demographic information will allow analysis of correlations between demographic groups and the factors they consider important to college applications. More importantly, it will allow low-income college applicants to maximize their budget when applying to college.
Johns Hopkins University
BS/MSE Candidate, Class of 2015
Applied Mathematics and Statistics
Cell: (347) 374-1184