Projects

Simple yet Complicated Numbers (Aug 2023)

Prime numbers possess both simplicity and complexity. On one hand, their definition is straightforward: a prime number is divisible only by 1 and itself. However, generating the $n^\text{th}$ prime number, $p_n$, lacks an explicit formula. Furthermore, the infinite nature of prime numbers and their distribution along the number line give rise to fascinating mathematical problems, such as the renowned Riemann Hypothesis. This discussion serves as a concise introduction to the realm of Analytic Number Theory.

An Analysis of Thomae's Function (Jul 2023)

Thomae's Function is defined to be the following function: \[f\left( x \right)=\left\{ \begin{array}{*{35}{l}} \dfrac{1}{q} & \text{if }x=\dfrac{p}{q}\in \mathbb{Q},\text{ }p\in \mathbb{Z},\text{ }q\in \mathbb{N},\text{ }p\text{ and }q\text{ are coprime;} \\ 0 & \text{if }x\in \mathbb{Q}'. \\ \end{array} \right.\] We will establish various assertions concerning continuity, differentiability, and (Riemann) integrability. In particular, $f$ is discontinuous on the rational numbers but continuous on the irrational numbers. Something even more perplexing is that $f$ is Riemann integrable.

A Proof of the Prime Number Theorem (May 2023)

A very important theorem in Analytic Number Theory that is used to study the distribution of prime numbers. Let $\pi(x)$ denote the number of primes less than or equal to $x$. In this project, we discuss the proof of the Prime Number Theorem, which states that \[\lim_{x\rightarrow\infty}\frac{\pi(x)\operatorname{log}x}{x}=1.\]

In Pursuit of Mathematics (Jun 2022 - May 2023)

Meet six passionate Mathematics enthusiasts (Zhang Puyu, Wallace Tan Gian Yion, Zoe Lee, Thang Pang Ern, Joseph Teoh Tze Tzun, and Leong Chong Ming) from Singapore, each with a unique and inspiring story to share regarding their pursuit of Mathematics. Discover how they have forged their paths, overcome numerous challenges, and found joy in the world of Mathematics.

Our Everyday Mathematics (Jun 2022 - Apr 2023)

Join us on a fascinating journey as we uncover the hidden beauty of numbers, shapes, and patterns that surround us in our everyday lives — in particular, in Singapore!

The Fibonacci Sequence adorns flower petals in nature's masterpiece; quadratic curves model the trajectory of a ball with precision; abstract concepts come to life too — Group Theory harmonises seamlessly with the world of music!

Whether you are a mathematics fanatic or simply curious about the hidden marvels concealed within our surroundings, this video promises to deepen your appreciation for the mathematical elegance that envelops us!