Re:Applied Category Theory
by ThoAppelsin on Monday March 26, 2018 @02:39PM
(#16681303)
This description of teaching is a lot like how 3blue1brown does his videos on YouTube: https://m.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw
I am not affiliated, just love how he geometrically visualizes the concepts of math, and how he focuses on he intuition.
One book I can think of that has a similar chapter/difficulty curve is Boyd & Vandenberghe's "Convex Optimization" book, http://stanford.edu/~boyd/cvxbook/.
i've seen a number of math-but-sort-of-CS textbooks putting the dependency graph for chapters in the introduction, so you know what you can get away with skipping and what must be done first.
i agree about geometric intuition, as long as there's a wall of separation between the intuition+motivation and the main results.
it frustrates me when an important result is only proved in the context of a motivating example where i don't have the background. usually this is when a math book dips into physics or engineering for whatever reason.
Re:Applied Category Theory
by danield9tqh on Monday March 26, 2018 @04:58PM
(#16682534)
Unfortunately from reading the first couple of chapters it seems like this textbook doesn't do an excellent job of favoring graphics over formula. It's acceptable but really nothing stellar. I don't think it does the title of 'Applied Category Theory' justice. It is still very much theoretical.
Conveying intuition is about way more than using graphics. It's about storytelling. I've seen people focus on graphics and fail in a hundred ways, while overwhelming theoretical works shine due to the focus on the narrative.
On another pedagogical note and as someone who reads a lot of math texts, I wish math textbooks would spend way more time on introducing the intuition (geometrical if in any way possible) of the ideas before or simultaneous with going into the formulas, theorems, and details. This not only vastly improves comprehension but I find having a geometrical understanding ( even if rough and partially incorrect) greatly helps in me being able to later derive the same formulas and theorems.
Having written about various math topics over the years I know its much more difficult to follow this approach, so I don't blame anyone for not going out of their way to imbue intuition, but its still something I wish more mathematicians who teach would advocate for.