Research has allowed me to experience mathematics beyond problem-solving, diving into both its abstract foundations and its unexpected applications. I have explored pure math, where the focus lies in theory and rigor, as well as applied projects that connect mathematics to fields like music, finance, and artificial intelligence. These experiences have taught me not only precision and persistence, but also the joy of discovering how mathematical ideas can shape the way we understand the world.
Below you’ll find several studies on mathematics and its diverse applications in areas such as music and finance. I hope you enjoy exploring them, and I would be grateful for any feedback or comments you may wish to share.
New Measurement on the Unit Circle
By Khang Nguyen
In this paper, I introduce a new measurement on the unit circle where any two arbitrary
angles are considered equal. The paper was presented at Troy MathFest 2025, which
attracted over 200 global attendees, sparking interdisciplinary mathematical applications.
Geodesic curves and Barycenters in R n
Together with two other students, we conducted research on a mathematical problem. We study geodesics in planes with respect to various distance functions. As an application, we show that for any interior point of a Euclidean triangle, there exists a metric on R n with respect to which this point becomes the barycenter of the triangle. We also briefly discuss an extension to the case of positive definite matrices.
The paper was published in Alabama Journal of Mathematics Volume 48(1) (2025), 9–16.
View detail
Fourier Series: A Historical Journey from Theoretical Foundations to Audio Processing Technology
by Khang Nguyen
The article reviews the evolution of Fourier series from its controversial beginnings in the early 19th century to its development into a powerful mathematical tool. It summarizes key stages in its refinement and emphasizes its modern application in audio processing, particularly through the Fast Fourier Transform (FFT), which underpins many digital audio technologies.
The paper was published in Pi Journal, Vol. 9, No. 7–8, August 2025. Pi Journal is a prestigious mathematics magazine of the Vietnam Mathematical Society for students.
View detail
Tuning systems: The mathematical foundation of Music Notes
By Khang Nguyen
The physical and mathematical foundations of music, focusing on how tuning is determined beyond human perception. It highlights the Pythagorean tuning system the earliest documented method and its role in shaping the development of Western music.
View detail
High School Mathematics in Personal Financial Decision Making
By Khang Nguyen
Under Dr. Pham Van Khanh’s guidance, I developed a project titled “High School Mathematics in Personal Financial Decision Making”, which applies 11th grade mathematics to real life financial situations. This initiative aims to give students a fresh perspective on Mathematics, highlight its practical value, and spark a deeper enthusiasm for learning.
View detail
Affine Coupling Layers Model in Normalizing Flows
During our time at PIMA summer camp, my teammates and I conducted a project focused on Normalizing Flows, a class of generative models that transform a simple probability distribution into a more complex one through a series of invertible and differentiable mappings. In our project, we studied the mathematical foundations of Normalizing Flows, implemented them in Python, and explored their applications in data generation and density estimation under the guidance of our mentors.
View detail