# Math Symposium

## Undergraduate Research in Mathematical Sciences Mini-Conference

### December 5, 2023 AL 302

**3:30pm - Dabin Song**

### Title: Apollonian Gaskets

**Abstract: **Apollonius of Perga (circa 240 BC – 190 BC) For any three circles in a plane that are pairwise tangent to each other, two new circles can be constructed that are each tangent to all three original circles. These configurations were introduced by Apollonius of Perga (circa 240 BC – 190 BC) and are known as Apollonian Gaskets. Using an iterative process to construct new generations of circles tangent to the existing circles generates interesting fractals; this process is known as an Apollonian Circle Packing. Ideas used to study Apollonian gaskets and circle packings touch on both geometry and number theory and are very attractive topics in modern mathematics. This talk will survey some interesting ideas and discuss some historic as well as recent developments on the topic.

**3:30pm, Dec. 5, 2023 | AL 302**

**Speaker Bio:** ** **Dabin Song is from South Korea and is a senior majoring in mathematics at Bob Jones University.

**4:15pm - David Stodola**

### Title: Who are You Most Like? Data Analysis by Machine Learning

**Abstract: ** In data analysis, it is often desirable to find subgroups of individuals who share similar characteristics and to gain insight by observing the different behaviors of those subgroups. Machine learning algorithms provide a controlled and efficient way to classify individuals into subgroups by similar characteristics. Two of these techniques, k-clustering and regression trees will be discussed. Detection of atypical subpopulations and visualization of clusters/groupings will be demonstrated. ** **

**4:15pm, Dec. 5, 2023 | AL 302**

**Speaker Bio:** David Stodola, a native of the New England woods, graduated from Trinity Christian High School in 2020 with a strong passion for applied mathematics and modern physics. He is currently a senior pursuing a Bachelor of Science degree in Mathematics at BJU. David's aspirations extend to graduate school, where he plans to specialize in data analysis—a field he believes holds the key to unlocking valuable insights in various industries. Beyond his academic pursuits, David enjoys a range of hobbies including dirt biking, fishing, and playing pickleball.

**5:30pm - Ethan House**

### Title: A Computational Approach to the Reconstruction of Bidegreed Graphs on Twelve Vertices

**Abstract: ** One of the largest open problems in graph theory, the Reconstruction Conjecture, asks whether a graph is uniquely identifiable by the collection of subgraphs derived from a that graph through the deletion of elements in a specified way. Due to the complexity of the conjecture, portions of the problem have been proven using exhaustive search algorithms. This talk showcases one such algorithm tests the conjecture for a specific class of bidegreed graphs. Both benefits and shortcomings of the approach will be discussed.

**5:30pm, Dec. 5, 2023 | AL 302**** **

**Speaker Bio:** Ethan House is currently finishing a Bachelor of Science degree in Mathematics at Bob Jones University and is looking forward to beginning graduate work next fall.

**6:30pm - Peyton McGinnis**

### Title: How to Build a Computer That Generates No Heat: A Visual Survey of Reversible Computing

**Abstract: ** Reversible computing is a paradigm of computing wherein every output of a computational process can be used to deterministically obtain the process’s inputs. Although the idea is simple, reversible computing has the fascinating consequence that a reversible computation loses no information, and therefore generates no physical heat. This is known as Landauer’s principle, and its initial discovery in 1960 led to an abundance of research in the field of reversible processes since it implied that a completely reversible computer could revolutionize energy efficiency in computing. Over the past few decades, computer scientists have made significant progress developing a cohesive theory of axiomatic reversible logic, reversible circuitry, reversible computation, and reversible programming. This talk presents a survey of the motivation, processes, and logic of reversible computing using visual examples.

** 6:30pm, Dec. 5, 2023 | Alumni Bldg 302**

**Speaker Bio:** Peyton McGinnis was born in Charleston, SC and began attending BJU in 2020. He is working towards completing a B.S. in computer science with a focus in mathematics. Throughout his time at BJU, he has been involved in many on-campus organizations and completed a semester internship at SermonAudio. He is passionate about research, user interface design, and abstract mathematics.

## ~~~ ~~~~~ Future Symposia ~~~~~ ~~~

**Upcoming Symposia: Spring 2024**

**Spring Symposia dates**

- Thur, Feb 1
- Thur, Mar 7
- Thur, Apr 4
- Tue, Apr 23

Scroll down for information about specific talks.

**6:00-7:30pm, AL 210**

## ~~~ ~~~~~ Past Symposia ~~~~~ ~~~

## November 2, 2023 --

**Owen Coss, Ph.D.**

### Title: Synchronization of Coupled Oscillators

**Abstract: ** Systems of coupled oscillators are prevalent throughout nature and engineering, and understanding their equilibria is important for understanding the synchronization behavior these systems exhibit. One of the most popular models of such systems is the Kuramoto model. This talk will focus on the Kuramoto model with "rank one" coupling between the oscillators. Exploiting the structure of the equations for this case yields a new formulation of the model that is easier to solve. Furthermore, the properties of this new formulation allow for an efficient algorithm to find all of the equilibria in much less time than general solving methods.

**6:00-7:30 p.m. | Nov. 2, 2023 | Alumni Bldg 210**

## Invited Speaker

**Speaker Bio: ** Owen Coss was born in Greenville and attended Bob Jones since elementary school. He earned his B.S. in Mathematics with a minor in Computer Science in 2015. Afterwards, he attended North Carolina State University where he earned a Ph.D. in Algebraic Geometry in 2020. Even though his primary study was math, he had several programming related summer internships along the way. Owen works as a member of the Continuous Product Engineering team at NetApp, Inc.

** **

## October 5, 2023 --

**Auria Morrow**

### Title: What Can Tech Software Do for You?

**Description: ** In this interactive session, we will examine the variety of mathematical and data management software available for commercial use today. These are the programs used by technical roles in every industry, and understanding their use will give you a leg up on the competition in the job market.

**6:00-7:30 p.m. | Oct. 5, 2023 | Alumni Bldg 210**

## Invited Speaker

**Speaker Bio: ** Auria Garland Morrow graduated with a Mathematics degree from BJU in 2016. She subsequently earned her Master’s Degree in Applied Statistics from USC while working as an analyst at Truist Bank. She is currently a Business Information Engineer at Truist and lives in Greenville with her husband Corey. She is passionate about distilling math and big data into insights for a non-technical audience.

## September 7, 2023 -- Panel Discussion

**Successfully Engaging in Math at BJU and Beyond**

This event will include a panel discussion about engaging with math and other fun challenges at BJU and how to balance math/work/life for successful engagement with the world beyond these walls.

Panelists:

- Ethan House, current student -- senior mathematics
- Peyton McGuinnis, current student -- senior computer science
- David Pittman, alumnus -- mathematics
- Erick Ross, alumnus -- mathematics and computer science
- Caleb Whisnant, alumnus -- actuarial science

**6:00-7:30 p.m. | Thursday, September 7, 2023 | Alumni Building 210**

## May 3, 2023 -- Mathematical Sciences Symposium

### URMS Talk: On Reconstruction of Bidegreed Graphs

by **Ethan House**

Abstract: The Reconstruction Conjecture is one of the oldest open problems in graph theory. This presentation aims to examine the development of the problem and a number of variants before looking at the methods of reconstruction with a focus on application to the still-unsolved class of bidegreed graphs.

**9:00-9:50 a.m. | Wednesday, May 3, 2023 | Alumni Building 303**

## May 3, 2023 -- Mathematical Sciences Symposium

### URMS Talk: Robotic Path-Planning

by **Peter Labadorf**

Abstract: This presentation will provide a brief overview of the field of robotic path-planning, covering grid-based algorithms such as Djikstra's, A*, and D*, and sampling-based algorithms such as RRT and RRT*. The presenter will then introduce a novel path-planning named the Right-Left Algorithm, which is based on the Archimedean principle that the shortest distance between two points is a straight line. The algorithm begins with a hyper-optimal straight line between start and goal and recursively moves towards feasibility by wrapping left and right around intersecting obstacle polygons. The talk will then conclude with a proof of optimality and a discussion of results.

**10:00-10:50 a.m. | Wednesday, May 3, 2023 | Alumni Building 303**

## September 27, 2022 -- Mathematical Sciences Symposium

### Puzzles, Problems, and Putnam

This is the fall kickoff of the Maths Symposia series. We will have some mathematical puzzles and problems to attempt as well as a couple of short presentations on recent developments in mathematics that may have missed your radar.

You will also have an opportunity to hear more about the upcoming Putnam Competition. And of course, it's just fun to socialize with other math types.

**6:00-7:30 p.m. | Tuesday, September 27, 2022 | Alumni Building 210**

## November 30, 2021 -- Mathematical Sciences Symposium

**Capstone: Modelling Quantum Computers and Algorithms with Linear Algebra**

by **David Pittman**

Abstract: We will start by seeing how quantum computing differs from classical computing through a brief introduction into the relevant aspects of quantum mechanics, including the non-deterministic nature of quantum theory and the difference between binary numbers and superpositions of binary numbers. Then, we will use linear algebra to model quantum computation, including modeling a quantum circuit as a single matrix. Using this model, we will apply it to some quantum algorithms, including Simon’s algorithm and the quantum Fourier transform. Finally, we will consider Shor’s algorithm and how it relates to factoring integers asymptotically faster than any known classical algorithm.

**5:00-6:00 p.m. | Tuesday, November, 30, 2021 | Alumni Building 303**

## October 22, 2021 -- Mathematical Sciences Symposium

**A Perspective on Research in Undergraduate and Graduate Level Mathematics**

Todd Fenstermacher, a Ph.D. candidate in mathematical sciences at Clemson University, will share some of his experiences in mathematical research on the undergraduate and graduate levels. His talk will include some graph theory from his research as an undergraduate mathematics student at Taylors University and an introduction to his current graduate research in ring theory.

After the symposium there will be opportunity to talk with Mr. Fenstermacher over pizza and dessert. **4:30-5:30 p.m. | Friday, October 22, 2021 | Alumni Building 303**

## September 14, 2021 -- Mathematical Sciences Symposium

**Mathematics at BJU and Beyond**

This event will include short presentations by upper-classmen and recent graduates about interesting real-world projects and the math courses that are applicable, a panel discussion about how to be successful in math courses at BJU, and social time with desserts and games.

Speakers:

- Jacob Brazeal, alumnus -- mathematics
- Andrew Platt, current student -- senior mathematics
- Erick Ross, current student -- senior mathematics and computer science

**6:30-8:00 p.m. | Tuesday, September 14, 2021 | Alumni Building 106**