transfinites to grok the reals, and topology to grok continuity, and then I could appreciate abstract analysis as an application of that, >
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Replying to @Meaningness @drossbucket
and then work my way down to actual differential equations. Obviously I am a weirdo. But suspect that math is *best* taught by combining >
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Replying to @Meaningness @drossbucket
as many different styles of explanation as possible, because you get different intuitions from each.
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Replying to @Meaningness @drossbucket
Arnold is IMO overreacting (perhaps for performative and political reasons) against the horrors of mid20C French mathematics.
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That era was something of a Grothendieck cargo cult, and did for mathematics education what Le Corbusier did for architecture. Still...
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Speaking as a perhaps-decent algebraist once upon a time who nevertheless is hopeless at both logic AND physics.
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Replying to @St_Rev @Meaningness
I was hopeless at algebra, so maybe that is my problem...
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IMO algebra is the hardest part of calculus & differential equations. Can't ever remember all the rules properly.
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Yes, in general the hardest part of learning layer n of math seems usually to be the complexity of layer n-1 that’s required.
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Replying to @Meaningness @EvanMcM and
When you’re learning highschool algebra, the hard part is doing the arithmetic properly; in calculus it’s the algebraic manipulations.
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The “algebra” we were talking about here is another layer up from that—abstract algebra—in which you take things like functions as elements.
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I'm not there yet but hoping to be soon. Didn't mean to interrupt your conversation but thought it was interesting to see you mention this.
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