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Madison Zebrine '13
2012 Soar Student

Madison ZebrineMajor/minor: Mathematics and Philosophy

Hometown: Blandon, Pa.

Project: Biranking of Ladder Graphs

Project advisor: Dr. Michael Fraboni

Project details: A graph is a collection of vertices and edges that connect those vertices. A biranking is a function that assigns to each vertex of the graph a number (called a rank) so that between each repeated rank there is a larger rank and a smaller rank. I looked at ladders (or railroad tracks, if you're my father), which are just two stacked paths of equal length, where the vertices are connected vertically as well as horizontally, so you end up with this row of squares.

Why I wanted to participate in SOAR: I've never done mathematical research before, and since I was (and still am) considering grad school, getting some experience seemed like a good idea, just to see if I actually would enjoy continuing my mathematical studies after college.

Results: I can now tell you the birank for any ladder graph, and it provides another foundation for future work in this area of graph theory. You have to start small in math; you can always look at a simpler problem in the expectation that a similar solution can be applied to something more complex. Also, I've learned that I really love math and math research. It can get challenging sometimes, and occasionally you feel like you're going in circles and you'll never find the best proof, but it's still more fun than frustrating.

Future plans: Currently, I intend to pursue a Ph.D. in mathematics. After that, I think I'd like to hit the top of the New York Times Bestseller list.