Mathematics Research Projects 2023
K.c. Kula
Advisor: Victor Donnay
Approaches to Energy Conservation: A Mathematical Analysis
With increasing threats of global warming and limited non-renewable resources, energy conservation is more important than ever. Our research will focus on energy conservation with geothermal heat pumps and improved insulation. These eco-friendly resources often receive grants and tax credits under the Inflation Reduction Act. We will also work with Liz Robinson, Executive Director of the Philadelphia Solar Energy Organization, to develop and apply her solar toolkit to Pennsylvania school districts. This toolkit encourages schools to use the Inflation Reduction Act to purchase solar panels at lower prices in our changing environment. Using mathematical and differential equations, we will measure the potential cost and energy savings of improved insulation, airflow, and geothermal and solar energy. These methods can help a school district or household save money and energy.
Cordelia Li
Advisor: Leslie Cheng
Stock Price Prediction of Bilibili Stock
During this summer, I will build upon what I learned in the Math B225 (Introduction to Financial Mathematics) course to predict stock prices. The stock market is known for being volatile, dynamic, and nonlinear, so a successful prediction of a stock’s future price would yield significant profit.
In this research, I intend to analyze and predict the stock price of Bilibili, one of China's leading streaming platforms that offers videos on demand such as documentaries, variety shows and other original programming, using various mathematical models such as the Generalized Binomial Model and the Black-Scholes Model. For example, I will be employing variations of the Hull-White Algorithm and Geometric Brownian Motion to predict stock prices for Bilibili.
Orli McGuire-Berk
Advisor: Victor Donnay
Approaches to Energy Conservation: a Mathematical Analysis
The usage of energy produces CO2 emissions that are harmful to the Earth. Most of that time it feels as though there is nothing you can do on an individual level to help lessen the emission of greenhouse gasses. This summer we are doing an in depth analysis on the ways an individual household can lessen its carbon footprint. Thanks to the Inflation Reduction Act, the government is now giving tax credit for households who take the steps towards using/producing green energy. We will be analyzing geothermal energy pumps, insulation and heat usage in order to figure out a way to balance going green and saving money.
We will also be working with Liz Robinson who is the Executive Director of the Philadelphia Solar Energy Association. They have developed a toolkit for Pennsylvania School Districts on how the Inflation Reduction act can assist them to purchase solar panels. We will be working with her to create educational materials that schools can use to teach their students about solar energy.
Yuxin Wang
Advisor: Leslie Cheng
Mathematical Foundations of Public-Key Encryption: A Revolution in Cryptography
Since the late 20th century, cryptography has undergone a remarkable transformation from being an artistic pursuit of code-writing to a rigorous scientific discipline. This research focuses on the mathematical aspects of public-key encryption, a pivotal advancement in modern cryptography. Previously, ancient cryptography primarily employed private-key encryption, which relied on a shared secret key for both encrypting and decrypting messages. In contrast, public-key encryption introduced a groundbreaking approach by utilizing two distinct keys: a public key for encryption and a private key for decryption.
In public-key encryption, the recipient of a secure message generates a pair of public and private keys. The sender can then use the recipient's public key to encrypt the message, ensuring confidentiality during transmission. The receiver, possessing the corresponding private key, can decrypt the ciphertext to retrieve the original message. The birth of public-key encryption, credited to Diffie and Hellman, brought about a revolution in the history of cryptography. This breakthrough enabled widespread adoption of cryptographic techniques in real-world applications.
This research aims to delve into the mathematical foundations of public-key encryption, exploring the underlying principles and algorithms that ensure its security and effectiveness. We will apply the mathematical principles to real-life examples of public-key encryption.
Jingxuan (Christine) Yang
Advisor: Leslie Cheng
Stock Price Predictions for Apple Technology Company Using Various Models
Accurate predictions of a stock’s future prices are crucial for determining the potential profit it can generate. As one of the largest technology companies in the world, the changes in the stock market of the Apple technology company are of great value to study. We will first employ variations of the Hull-White algorithm to predict future stock prices. Additionally, we shall use Geometric Brownian Motion for Apple’s stock price predictions.