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Great writeup It's amazing (in a bad way) how most professors couldn't care less about how/why they teach something. Didactical thinking is nowhere to be seen.

Great writeup It's amazing (in a bad way) how most professors couldn't care less about how/why they teach something. Didactical thinking is nowhere to be seen. And yes even a lot of youtubers just repeat the same unsufferable self-pleasuring of "solve this problem here like it's the 1900s". Or how professors will throw a fit whenever you solve a limit problem using L'Hospital instead of their farcical show-and-dance about limits. It's appaling. Pro-tip: Nobody cares. > Allow me to state another controversial opinion: existence theorems for the solutions of ordinary differential equations are not as important as they are cracked up to be. Correct. See point above > will list a number of disconnected tricks that are passed off as useful, such as exact equations, integrating factors, homogeneous differential equations, and similarly preposterous techniques. Since it is rare – to put it gently – to find a differential equation of this kind ever occurring in engineering practice, the exercises provided along with these topics are of limited scope: Ugh. This is so Dickensonian it hurts. See the point above about "Nobody cares" Learn what they care about, learn how to best explain the point in question (it's hard)

hackernewds 4y ago
L'hopital*
- alimw 4y ago
  Definitely not. Either l'Hôpital or l'Hospital
- raverbashing 4y ago
  https://en.wikipedia.org/wiki/Guillaume_de_l%27H%C3%B4pital#/media/File:L'Hospital_-_Analyse_des_infiniment_petits_pour_l'intelligence_des_lignes_courbes,_1715_-_1425244.jpg https://en.wikipedia.org/wiki/Guillaume_de_l%27H%C3%B4pital#... Though it seems people write it both ways (it is pronounced without the S though) > In the 17th and 18th centuries, the name was commonly spelled "l'Hospital", and he himself spelled his name that way. However, French spellings have been altered
effie 4y ago
> Or how professors will throw a fit whenever you solve a limit problem using L'Hospital instead of their farcical show-and-dance about limits. They are teachers, they want you to think and practice mathematical way of thinking, using minimal set of assumptions. Exercising this discipline in thought to some extent is useful. Using l'Hospital rule to solve simple problems that are easy to solve from first principles is like taking out a fly with a nuke, when you have nukes. Just because you can, does not mean you should.
- raverbashing 4y ago
  "First principles". I mean, besides the whole pick and choose which first principles to teach and which ones to drop (there are a lot), they might not be as useful as one may think When discussing limits, the tradicional way this is explained is pointless and extra annoying. And then you end up using limits for pretty much nothing after working with derivatives and integrals. So, again, nobody cares. And maybe someone can explain limits better than the "two dials" analogy because that's too much mathematical theatre that doesn't help when a good explanation is actually needed.

hackernewds 4y ago

L'hopital*

alimw 4y ago
Definitely not. Either l'Hôpital or l'Hospital
raverbashing 4y ago
https://en.wikipedia.org/wiki/Guillaume_de_l%27H%C3%B4pital#/media/File:L'Hospital_-_Analyse_des_infiniment_petits_pour_l'intelligence_des_lignes_courbes,_1715_-_1425244.jpg https://en.wikipedia.org/wiki/Guillaume_de_l%27H%C3%B4pital#... Though it seems people write it both ways (it is pronounced without the S though) > In the 17th and 18th centuries, the name was commonly spelled "l'Hospital", and he himself spelled his name that way. However, French spellings have been altered

effie 4y ago

> Or how professors will throw a fit whenever you solve a limit problem using L'Hospital instead of their farcical show-and-dance about limits. They are teachers, they want you to think and practice mathematical way of thinking, using minimal set of assumptions. Exercising this discipline in thought to some extent is useful. Using l'Hospital rule to solve simple problems that are easy to solve from first principles is like taking out a fly with a nuke, when you have nukes. Just because you can, does not mean you should.

raverbashing 4y ago
"First principles". I mean, besides the whole pick and choose which first principles to teach and which ones to drop (there are a lot), they might not be as useful as one may think When discussing limits, the tradicional way this is explained is pointless and extra annoying. And then you end up using limits for pretty much nothing after working with derivatives and integrals. So, again, nobody cares. And maybe someone can explain limits better than the "two dials" analogy because that's too much mathematical theatre that doesn't help when a good explanation is actually needed.