This one is a bit more symbol heavy, and that's actually the point. The goal here is to represent in somewhat more formal terms the intuition for how backpropagation works in part 3 of the series, hopefully providing some connection between that video and other texts/code that you come across later.

What's actually happening to a neural network as it learns?

The goal of this video is to introduce the idea of gradient descent and to analyze a specific network.

Introduction to neural networks.