Here’s Amplitude Modulation Deep and Fast, a not too lengthy video that gets to the roots of what amplitude modulation does mathematically. I’ve referred to AM’s role in sampling theory in past articles, and its relatively simple math makes understanding sampling much easier than traditional explanations. And this will serve as the primary math basis for an upcoming video on sampling theory.
Fun fact: AM’s ability to convert a multiplication to simpler addition/subtraction was exploited in global navigation a few hundred years ago, in the couple of decades before the invention of logarithms displaced it.