I’m glad I conveyed my enthusiasm. :) I think that one reason I was overconfident when I got to higher math was because I had mastered this sort of simplification-based reasoning, and assumed it would always work!
I was thinking of mathematics degree courses as a whole, rather than specific lecture courses, and in particular of the British system. The mechanics of calculus is taught at A-level in the UK, and here I’d definitely agree that following a standard recipe is most of what’s required. But the key feature of a good university maths course is that it develops certain ways of thinking that enable you to tackle problems unlike any you’ve seen before, and this is the experience that I hope would be shared by all students of mathematics. This is a genuine hope though, not an expectation.
I think you just described how to do most undergraduate and high school maths exams!
I’m glad I conveyed my enthusiasm. :) I think that one reason I was overconfident when I got to higher math was because I had mastered this sort of simplification-based reasoning, and assumed it would always work!
I’d hope that this doesn’t hold for most undergraduate maths courses, but it’s definitely false at the top end.
What do you mean by “most”? It seems to work pretty well all the way up through calc 1, imho.
Correction: I was wrong; there are some basic cases which knuth-bendix can’t handle. It looks like it wouldn’t be sufficient up to calc 1 after all.
I was thinking of mathematics degree courses as a whole, rather than specific lecture courses, and in particular of the British system. The mechanics of calculus is taught at A-level in the UK, and here I’d definitely agree that following a standard recipe is most of what’s required. But the key feature of a good university maths course is that it develops certain ways of thinking that enable you to tackle problems unlike any you’ve seen before, and this is the experience that I hope would be shared by all students of mathematics. This is a genuine hope though, not an expectation.
I liked your original post by the way.