Re:A monad is a monoid in the category of endofunctors, what...
by EGreg on Sunday February 10, 2019 @10:38AM
(#19128158)
All mathematics is abstraction.
Numbers are abstractions
Variables are higher level abstractions
You can have properties that you abstract and then see what you have. Banach spaces. Metric spaces. Three different ways to define compactness.
I liked to teach calculus by teaching the limit of a sequence first and then defining limits of functions by considering all sequences x_n that converge to x, and then looking if y_n converge. Building up definitions from simpler definitions, instead of the STUPID handwavy definition they use in Calculus 1 that can’t even handle limits of functions like cos 1/x and answer about limits of certain subsequences of x_n that approach 0.
I started a course about mathematics this way, building up from the very basics:
Numbers are abstractions
Variables are higher level abstractions
You can have properties that you abstract and then see what you have. Banach spaces. Metric spaces. Three different ways to define compactness.
I liked to teach calculus by teaching the limit of a sequence first and then defining limits of functions by considering all sequences x_n that converge to x, and then looking if y_n converge. Building up definitions from simpler definitions, instead of the STUPID handwavy definition they use in Calculus 1 that can’t even handle limits of functions like cos 1/x and answer about limits of certain subsequences of x_n that approach 0.
I started a course about mathematics this way, building up from the very basics:
https://m.youtube.com/channel/UCuge8p-oYsKSU0rDMy7jJlA