Spring 2019 was the second semester of the Directed Reading Program at Syracuse University. This program pairs undergraduate students with graduate mentors for a semester-long reading project. The program is run entirely by graduate students, from advertisement and selection of participants to the final presentation day. The 2018-19 DRP Committee consisted of Casey Necheles (chair), Erin Tripp, and Mkrtich Ohanyan. On April 30, 2019, students presented the following projects. 

An Introduction to Elliptic Curves and Their Cryptographic Applications

Samuel Wheeler (mentor: Caleb McWhorter)

Abstract: Elliptic curves play a central role both in number theory and modern computer security. In this talk, some of the basic properties of elliptic curves will be introduced, especially addition of points on elliptic curves. Then the cryptographic applications of elliptic curves will be discussed. Time permitting, we will discuss the future of elliptic curve cryptography with the advent of quantum computing.

Machine Learning Outline: Neural Network and Digit Recognition

Yantao Wu (mentor: Erin Tripp)

Abstract: Learning is not particular for human beings! A computer can learn something by itself with adequate data, hypothesis set, and training model. In this presentation, I will cover basic machine learning topic such as linear classification, linear logistic regression, neural networks, and our application in digit recognition.

Mathopoly: A Game Theory Saga

Kevin Aubrey and Emily Dyckman (mentor: Josh Fenton)

Abstract: We created an economic game played by two players modeled after Monopoly. The goal of the game is to model ice cream markets with 2 firms who have to make decisions of when to enter the market. Changes in supply and demand force competitors to determine what is feasible for the firm. We used extensive form to help calculate all possible decision and moves that a player can make to gain to increase their payoffs for all possible game outcomes. We also computed the Nash Equilibrium for each decision in the game to underline the best response that a player can make.