Re:Do the math: too much calculus? (2012)
by Someone on Wednesday October 19, 2016 @05:49PM
(#12747999)
I'm already baffled by the distinction between algebra, trig, and calculus.
Where I live, it was just called 'math'. The first time I encountered algebra was in university, and that started with groups (a set and an operation on pairs of items in the set)
As to the 'pre': I have a masters in math, and lots of what we did was in some sense pre.
For example, calculus on real variables showed you how to define differentiation and integration and how to rigorously prove lost of theorems (pro tip: if you can't make heads or tails of an exam question, at least write down "let epsilon > 0")
Next, we basically went through the same set of theorems but in multiple dimensions, but showed that those rigorous proofs had glaring holes, but hey, now you know better. Also: infinities are weird (pro tip: the area under a 2D curve can depend on the order in which you add up its parts).
Next, calculus on complex numbers extended that and showed that those rigorous proofs had glaring holes, but hey, now you know better (pro tip: every contour integral you compute at an exam has a value of plus of minus 2n pi, with n typically being plus or minus one)
For math majors, the next step was measure theory: that definition of integration we started with? Forget it. Lebesgue came up with something that's better. And by the way, those proofs we told you about have glaring holes (let's spend a few hours proving that cutting a rectangle across a diagonal gives you two parts that each have half the rectangle's area). A few of the functions that we proved cannot not be integrated can be, if you use this new definition of how integration works.
That seems a waste of time, but I don't think it is. Very few people can jump in at the deep end and survive; the first iterations are necessary to prepare one's mind for the next steps.
Given the above, I think you will have had various 'pre-' things, even though they weren't named so.
Where I live, it was just called 'math'. The first time I encountered algebra was in university, and that started with groups (a set and an operation on pairs of items in the set)
As to the 'pre': I have a masters in math, and lots of what we did was in some sense pre.
For example, calculus on real variables showed you how to define differentiation and integration and how to rigorously prove lost of theorems (pro tip: if you can't make heads or tails of an exam question, at least write down "let epsilon > 0")
Next, we basically went through the same set of theorems but in multiple dimensions, but showed that those rigorous proofs had glaring holes, but hey, now you know better. Also: infinities are weird (pro tip: the area under a 2D curve can depend on the order in which you add up its parts).
Next, calculus on complex numbers extended that and showed that those rigorous proofs had glaring holes, but hey, now you know better (pro tip: every contour integral you compute at an exam has a value of plus of minus 2n pi, with n typically being plus or minus one)
For math majors, the next step was measure theory: that definition of integration we started with? Forget it. Lebesgue came up with something that's better. And by the way, those proofs we told you about have glaring holes (let's spend a few hours proving that cutting a rectangle across a diagonal gives you two parts that each have half the rectangle's area). A few of the functions that we proved cannot not be integrated can be, if you use this new definition of how integration works.
That seems a waste of time, but I don't think it is. Very few people can jump in at the deep end and survive; the first iterations are necessary to prepare one's mind for the next steps.
Given the above, I think you will have had various 'pre-' things, even though they weren't named so.