Preliminary Research: How and why I changed my topic

As of today, I have decided that my topic would be centered around Maxwell's equations. I aspire to delve into the physics and mathematics surrounding these elegant and breath-taking system of equations, and narrow my interest down to a question which I can spend my entire summer researching in depth.

Initially, I had decided on the topic of calculus of variations. My interest in this area of mathematics began when I stumbled upon Noether's theorem a year ago. Reading up on it, I realised that this function called the 'lagrangian' was used, and a recursive theme of using the principle of least action brought me to want to learn about this fundamental principle.
I had then soon after began watching an excellent YouTube series on this concept by a channel with the name of "physicshelps". After doing further research, I realised that the introduction was based on a lecture Richard Feynman gave in Caltech university.

However, I began to realise that calculus of variations is a rather difficult and inaccessible topic for me, and the resources are limited. Even someone who I know who did a pHD in mathematics admitted that he didn't need to use it that much. Despite being a very exotic topic, I decided to turn my attention to something that used more 'mainstrem' but similar mathematics, while being very elegant and important to physics: Maxwell's equations. This blog is dedicated to the content that I learn in order to understand and research Maxwell's equations.