When I studied engineering, the topic that I found the most philosophical value in was The Fourier Transform. It blew my mind as it took a complex, crazy, unruly world of waves in the time domain and transformed it into an orderly world of discrete frequencies and phases where they could be easily understood and manipulated. I remember realizing for the first time that most complex, emergent behavior in one dimension was something that could still be easily abstracted in another – a template for many problems we encounter in the world. This is the most accessible explanation of the Fourier Transform. Wish I had access to this when I was a student.
http://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/
