Re:On teaching mathematics, by V.I. Arnold (1997)
by 4ad on Sunday November 20, 2016 @12:11PM
(#12999843)
Gromov's approach is not abstract, it's extremely concrete. It uses abstractions for a very precise treatment, and it's probably not the best text for an introduction to entropy, but it's essentially a very concrete treatment.
It analyses very concrete observations using abstract methods in order to construct an abstract definition. It doesn't simply spew out abstract definition. Everything is motivated by concrete facts.
I would not say it's against Arnold's method at all, if anything, it uses the same concrete to abstract treatment. It is, however, not the best way to learn about entropy, but it's a good way to formalise it once you have become familiar with it. It's poor for undergraduate level material, but it's good as graduate level material.
It analyses very concrete observations using abstract methods in order to construct an abstract definition. It doesn't simply spew out abstract definition. Everything is motivated by concrete facts.
I would not say it's against Arnold's method at all, if anything, it uses the same concrete to abstract treatment. It is, however, not the best way to learn about entropy, but it's a good way to formalise it once you have become familiar with it. It's poor for undergraduate level material, but it's good as graduate level material.