It's cool to see that much dedication. It's useful when people take the time to summarize knowledge in a book to serve as reference.

But ... I have the feeling that the author, who is relatively new to the field (by his own admission), expanded a lot of formulas and made certain parts of the theory more complicated than it should be.

Look around page 60. There are formulas with 6 summation signs in front of them, with all kinds of little indices floating around. How about page 37 ?

In a way, the whole point about the chain rule (and software libraries that implement it) is that you can stay in "math world" to do the reasoning, and not think about the job of managing the computation.

Same idea with expression as much as possible in terms linear algebra primitives. Matrix multiplication is easier to understand when it's not broken apart into sums whose indices you have to track.