Graduation Year
2015
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Nicholas J. Pippenger
Reader 2
Michael R. Orrison
Rights Information
© 2016 Matthew Lam
Abstract
At the intersection of algebraic geometry, number theory, and combinatorics, an interesting problem is counting points on an algebraic curve over a finite field. When specialized to the case of elliptic curves, this question leads to a surprising connection with a particular family of graphs. In this document, we present some of the underlying theory and then summarize recent results concerning the aforementioned relationship between elliptic curves and graphs. A few results are additionally further elucidated by theory that was omitted in their original presentation.
Recommended Citation
Lam, Matthew, "A Combinatorial Exploration of Elliptic Curves" (2015). HMC Senior Theses. 91.
https://scholarship.claremont.edu/hmc_theses/91
