Book: The Anti-Cookbook of Proofs - a course in mathematical intuition

[Z1202]

As the community seems to agree that this is on-topic, I shall open a dedicated topic for this book. The original announcement is here.

This is a book about mathematical intuition for engineers, which can be found by clicking this link. Historically it started as an attempt to extend the VA Filter Design book by some treatment of Fourier theory topics, but quickly turned into a more general math text, covering a much wider range of topics. Still, the main focus audience are technical engineers and DSP engineers in particular.
The chapters which are of particular interest to DSP engineers, could be the one on the Fourier theory, as well as the one about exponentials (for those who'd like to deepen their understanding of differential equations and state-space form).

NB. Despite talking about intuition, the book is not an easy read and is somewhat hardcode. But it's supposed to make things a lot easier afterwards.

[Z1202]

Basically when I got to 1.1, the moment I see the quadratic rewritten on page 19, my brain builds the pattern "extract a binomial expansion + left overs" and none of the rest of the chapter makes much sense ("why are we graphing these things when we could just use algebra")...

This is actually the whole point. You know about extracting the binomial expansion because you learned about this possibility earlier (or you have just seen it in the book ). But suppose you haven't. Or you just wonder, how was the person, who was first to come up with this idea, thinking, as it's relatively unlikely that this idea appeared out of nowhere by pure enlightenment. The book illustrates how the thought process could have evolved.

In a way, in many places, I believe, the book unveils the "hidden process" behind what might seem pure enlightenment from the outside. The main value of this is that the connections between different mathematical ideas can become more intuitively clear, and the whole math becomes much more intuitive than just manipulation of abstract formulas - more on this in the book's intro.