Below are several studies on Mathematics and its diverse applications in fields such as Music and Finance. We sincerely hope you will take the time to read and share your valuable feedback and comments on these works.
New Measurement on the Unit Circle
by Khang Nguyen
This presentation will introduce a new measurement on the unit circle where any two arbitrary angles are considered equal framework.
Fourier Series: A Historical Journey from Theoretical Foundations to Audio Processing Technology
by Khang Nguyen
From a novel but incomplete idea that faced criticism from some of the greatest mathematicians of the early 19th century, Fourier series theory went on to be refined and developed by subsequent generations of mathematicians into a powerful mathematical tool with applications across many modern fields. The article is based on the method of reviewing and synthesizing academic literature, aiming to summarize the development of the Fourier series and highlight one of its concrete applications in modern life — specifically, its role in audio processing. The implications of this review point to how theoretical advancements have enabled efficient digital applications, especially through the Fast Fourier Transform (FFT), which plays an important part in audio technology.
TUNING SYSTEMS: THE MATHEMATICAL FOUNDATION OF MUSIC NOTES
by Khang Nguyen
Abstract
Music has existed for as long as humanity has. From the primitive rhythms of drums and stone flutes in ancient times to today’s complex symphonies or catchy, familiar tunes, music has always been an essential part of the human spirit and cultural life. We can easily perceive and distinguish musical notes with our hearing, but have you ever wondered: How do we truly know when a note is in tune? Is it merely based on human perception? In this article, we’ll explore the physical and mathematical foundations behind the music we know and love, and take a closer look at the Pythagorean tuning system — the earliest documented tuning method in human history, which laid the groundwork for the later development of Western music
