Description of the project: Quaternions were originally brought to life by a man named William Rowan Hamilton. Hamilton was trying to make complex numbers more applicable in a 3-dimensional space since complex numbers are made up of a real number and an imaginary number. Hamilton initially theorized that quaternions consist of 2 imaginary numbers and one real number. He thought that he was making no progress then a few years later he managed to create the formula of a quaternion which is denoted by i² = j² = k² = ijk = -1. This study investigates the properties of algebraic structures, particularly quaternions, through the lens of operations defined on sets. We focus on the complex and computational challenges associated with verifying these properties, especially moving into a higher dimension.
Presenters:
Jessica González
I am a first-generation senior at the University of Houston-Downtown, pursuing a B.S. in Computer Science with a minor in Mathematics (GPA 3.80), graduating in May 2025. Passionate about cybersecurity, software development, and mentorship, I currently serve as the Senior Peer Mentor for the Scholars Academy, leading a team of 17 mentors and supporting 200+ students. As a CHASI advocate, I am dedicated to helping minority students succeed in STEM, fostering a more inclusive and supportive environment.
Edgar Llanas
My name is Edgar Llanas, and I am a Mathematics major with a minor in computer science. I am a Junior at the University of Houston-Downtown. I have an OSHA 30 Certification which is an industry-based certification I earned in my senior year of high school, certification in Microsoft Excel Specialist 2019 and I am Peer-Led Team Learning trained. I also have a Bachelor of Science in Mathematics with a minor in computer science pending May 2026. I am fluent in Spanish, very patient, a team player and I have been fortunate enough to become a Peer Leader as well as a Peer Mentor for Scholars Academy.