Ask HN: Why is calculus considered such a difficult subject to learn?
2 comments
Even as a math graduate, I still think calculus is a bit weird.
The idea of successive approximations for a slope culminating in a dy/dx term -- where we say dx (really the denominator of the limit definition) is obviously not zero, but is also smaller than any given real number. It's not clear that numbers should work like that.
Pile on that calculus courses (at least in the US) tend to care more about deriving interesting trigonometric/exponential/polynomial/whatever derivatives once using the limit definition and proceed to have students essentially memorize the derivation tricks for the remaining 90% of the course, and it can easily end up being overwhelming.
The idea of successive approximations for a slope culminating in a dy/dx term -- where we say dx (really the denominator of the limit definition) is obviously not zero, but is also smaller than any given real number. It's not clear that numbers should work like that.
Pile on that calculus courses (at least in the US) tend to care more about deriving interesting trigonometric/exponential/polynomial/whatever derivatives once using the limit definition and proceed to have students essentially memorize the derivation tricks for the remaining 90% of the course, and it can easily end up being overwhelming.
That does seem a bit pointless. If that's your first experience of calculus I can see it would be off putting. Here in the UK basic calculus is taught at school, it felt just like another aspect of maths to me.
Honestly? It sounds to me like a meme. A bit like "Math is hard" for freshmen
There's nothing specifically hard about it. Maybe harder-ish than other subjects, but nothing specifically hard (I mean, specifically about Calculus 101 - later ones are of course harder)
> Are the teachers bad or the curriculum or books?
But yes, yes and yes. All of that. And wasting too much time with crap like "theorems about limits" which literally nobody cares unless you're on a pure math track.
There's nothing specifically hard about it. Maybe harder-ish than other subjects, but nothing specifically hard (I mean, specifically about Calculus 101 - later ones are of course harder)
> Are the teachers bad or the curriculum or books?
But yes, yes and yes. All of that. And wasting too much time with crap like "theorems about limits" which literally nobody cares unless you're on a pure math track.
Calculus is such a beautiful field with geometrical explanations for almost every theorem. It is the least abstract or dry subject in math.
What is your favourite textbook that made you understand and love calculus (single and multivariable)?