Hello! My name is Kaylee Huber, and I am an Applied Mathematics Major with a minor in Statistics at the University of Pittsburgh at Greensburg. I will be an upcoming Sophomore in the Fall 2023 semester and I look forward to taking part in the Brackenridge fellowship.
As a recipient of this fellowship, I will be conducting research on the algorithms and mathematics of a 3×3 Rubik’s Cube. In my past experiences, I learned to solve the Rubik’s cube for the first time in middle school and I have learned to solve up to a 5×5 Rubik’s cube. Through this research, I will try to find a way to create an easier method and/or algorithm that anybody can use to solve the Rubik’s cube. This research is important because many people believe that the Rubik’s cube is impossible to solve due to its abstract structure. However, I believe using pattern recognition and simple pattern arrangements will help me explain the methods of how to solve the Rubik’s cube at the end of this fellowship.
So far, I have already built my own Rubik’s cube using a kit I found online. Building this cube has allowed me to see the different purposes for each piece of the cube and how the center of the cube (which is a circle, believe it or not) makes the different rows of the Rubik’s cube rotate. Also, I have begun studying a mathematical concept known as permutations, which in short terms is a different arrangement of numbers. In application to the Rubik’s cube, I learned that there is a total of 2.3 x 1071 different permutations. The math behind this is that there are nine total squares on one side of the cube and six sides of a Rubik’s cube. By multiplying nine by six, you will find 54 small two-dimensional squares that exist on the Rubik’s cube. Using factorials (or multiplying a number 1 value below it until you reach the number 1), you can calculate 54! to be the total number of permutations that exist in a 3×3 Rubik’s cube.
Throughout the summer, I will be working with Dr. Espinoza (who is also from Pitt-Greensburg) on conducting this research. Other than taking Dr. Espinoza for my Intro to Theoretical Mathematics course in the upcoming fall semester, I haven’t had him for any classes yet, but I have had interactions with him in the past year through interviews I conducted for a STEM scholarship program that I am a part of. For this project, I felt Dr. Espinoza would be a perfect mentor for it as he is not only the National Sciences Division Chair for the University of Pitt-Greensburg but also specializes in theoretical mathematics in topics such as abstract algebra and topology.
Currently, I plan to turn this project into a BPhil and then graduate in three years with my bachelor’s degree in Applied Mathematics. After graduating, I plan to attend a graduate school for Data Analytics to become a Data Analyst. By completing the Brackenridge Fellowship, I will get closer to achieving my future goals as I will gain more knowledge on interdisciplinary research. With this knowledge, I will have the opportunity to dive deeper into the world of mathematics by using other research methods to think outside the box.
Lastly, one unique thing about me is that I love photography. I specifically take photographs of nature and I have pursued this hobby for the past five years.