Ranking Collegiate Soccer: Massey vs. Colley Method

This project analyzes the performance of the Lander University Men’s Soccer team during the 2023-2024 conference season using two well-known ranking systems: the Massey Matrix and the Colley method. Both methods help evaluate team rankings based on game results, but they take different approaches. Massey factors in margin of victory, while Colley focuses on win-loss records and strength of schedule. By applying these models to real match data, this study aims to provide an objective ranking of teams within the conference and explore which method offers the most accurate reflection of team performance in collegiate soccer.

Jaime Escos Castillo is a senior at Lander University pursuing a degree in Mathematics. He is an international student-athlete from Spain and a member of the Lander University Men’s Soccer team. Upon graduating in December, Jaime aspires to build a career in finance or insurance

Topology and Its Extension to Fractals

This project explores the branch of mathematics known as Topology and its extension into the study of fractals. A fractal is a structure within a topological space, characterized by infinitely repeated shapes formed through the application of complex analysis. This study introduces fundamental concepts of Topology and examines how these principles extend into the complex plane to generate fractals. By analyzing the mathematical foundations and iterative processes involved, the project aims to provide insight into the intricate relationship between topology, complex functions, and fractal geometry.

Logan Dorcas graduated from J.L. Mann high school in Greenville, South Carolina and is in his final year at Lander University as a Math/Engineering major. He is a member of the Men’s Lacrosse team and has won awards for his outstanding ability in Calculus from the Mathematics and Physical Sciences department.

Numerical Semigroups: An Examination of Their Properties and Applications

Imagine selecting from a variety of chicken nugget meal options at Chick-Fil-A: the 5-count, 8-count, 12-count, or 30-count meals. How many distinct quantities of nuggets can you order, and are there any quantities that are impossible to obtain? These questions can be addressed through the study of numerical semigroups. A numerical semigroup is a set of non-negative integers that is closed under addition, contains an identity element, and has a finite complement with respect to the whole numbers. Numerical semigroups play a significant role in diverse fields such as algebraic geometry, factorization theory, combinatorics, and computer science. In this talk, we will explore the structure and properties of numerical semigroups and some of their real-world applications.

Weston Reid is a graduate from Dixie High School of Due West, South Carolina. Weston is a senior mathematics major with a minor in business administration at Lander University. He has also played trombone for the various music ensembles at Lander, including the wind ensemble and jazz band. Projects he has worked on during his time at Lander includes researching planar graphs by applications of Euler's formula and analyzing matrix groups via their associated lie algebras.

The RSA Cryptosystem

The RSA algorithm is a widely used public key cryptosystem that employs asymmetric encryption to ensure secure communication between two parties. Developed by Ron Rivest, Adi Shamir, and Leonard Adleman in 1977, RSA addressed the challenge of creating a one-way function suitable for an asymmetric cipher. It leverages modular arithmetic to generate secure key pairs for encryption and decryption, with its security relying on the difficulty of factoring large prime numbers. This project delves into the theoretical foundations of RSA, covering key generation, encryption, and decryption processes.

Rachel Schenck is a senior mathematics major with a minor in business administration. She is a member of Lander's cross country and track and field teams. Following graduation in December, Rachel plans to pursue a master's degree in mechanical engineering and a career in project management.

Progression and Application of Gradient Descent in Machine Learning

Gradient descent is a fundamental optimization method used in machine learning, crucial for minimizing loss and boosting model performance. In this project we will follow the mathematical progression of gradient descent, starting with the perceptron learning rule and advancing to major advances like gradient descent with momentum and the Adam optimizer. By exploring the mathematics behind these methods, this project illustrates how each development addresses convergence and efficiency. We will further demonstrate the practical application of these methods using a neural network built from scratch, then trained on gradient descent with momentum. This project emphasizes the mathematical evolution of optimization methods and their significance in modern machine learning.

Joshua Wolford is a senior mathematics major with a data science minor at Lander University and a member of the Men’s Lacrosse Team. Originally from Falling Waters, West Virginia, he graduated from Spring Mills High School in 2021 and transferred from Wheeling University. During college, he worked part-time as a clinical data analyst and plans to pursue a career in data science after graduation.