Undergraduate Project 2024-25 (3H)

Are you a creative individual excited about exploring new ideas and innovative methods of explaining things? Do you have an artistic side that can be harnessed to simplify complicated concepts? Are you passionate about science outreach and sparking interest in mathematics through social media or other modern outlets? If your answer is yes, then look no further! This project is for YOU!
The Fourier transform is one of the most powerful mathematical tools on planet Earth (and probably on other planets too!). Its applications are vast and diverse, spanning every aspect of our daily lives. From enhancing the music we listen to and optimizing the compression of photos on our phones to forecasting weather patterns and deciphering signals received from distant stars, the Fourier transform plays a pivotal role in a myriad of disciplines.

In this project, you first deepen your understanding of Fourier transform. Then, you pick several concepts or application cases related to the Fourier transform and present them in innovative and engaging ways across various online platforms such as social media, educational websites, and interactive content hubs. The topics ranges from fundamental concepts like function decomposition using the Fourier transform or discussing Gibbs' phenomenon, to exploring diverse application areas such as compression algorithms, wave dynamics, and signal processing.

There are no constraints on the choice of outlet or presentation format. For example, you can create YouTube videos, Instagram posts, educational Jupyter Notebooks, interactive websites, or any other medium that suits your creativity and communication style. Collaboration and teamwork are encouraged, providing opportunities to combine diverse perspectives and skills for a richer learning and sharing experience.

I leave a few YouTube clips for inspiration below:

What is a Fourier Series? (Explained by drawing circles)

The Fourier Series and Fourier Transform Demystified

Fourier Series and Gibbs Phenomena

And this is a very nice course that teaches Fourier transform and explores some of its applications:

The Fourier Transform and Its Applications