Question: Hi, I'm Tom, I am a budding mathematician and scientist and was wondering if you knew anything about Wave or Quantum Mechanics as they are the subjects I am most interested in?

Sreejita Ghosh answered on 21 Jan 2020:

Wrt Waves there’s this interesting mathematical technique involved which happens in our ears, eyes, in any musical or recording instrument – Fourier transform. Waves and signals are broken down into their constituent frequencies. When a band plays an ensemble of instruments, the reason you can discern all these instruments- these frequencies, is because your ear and part of the brain responsible for the ‘hearing’ transform these time series into frequency domains, breaking these musical signals your ear drum receives into all the different frequencies it is composed of.
It is analogical to white light waves being diffracted into the constituent wavelets by a prism.
https://www.intmath.com/fourier-series/7-fast-fourier-transform-fft.php
Fourier and inverse-Fourier transform are integral part of signal, image and video processing. You’ll learn about it in advanced Calculus. 🙂 It is fun.