Re:An update on the campaign to defend serious math educatio...
by hnrj95 on Tuesday April 26, 2022 @03:09PM
(#31171778)
i’d argue that you can’t properly define probability without notions in measure theory, which is obviously far too advanced for a high school student. i’m not an educator, but some middle ground needs to be struck. i think it’s clear to many that the quality of education in american colleges far exceeds the quality of education in the average middle or high school. that’s the issue, imo
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Re:An update on the campaign to defend serious math educatio...
by afiori on Tuesday April 26, 2022 @03:26PM
(#31172006)
You can do quite a lot of useful stuff with just https://en.wikipedia.org/wiki/Cumulative_distribution_functi...
You only need measure theory when working with something that is not easily replaceable by R^n, Z^n, or finite sets to meaningfully define integration, otherwise (in)finite sums and Riemann integration get you very far.
I am a bit rusty on my advanced probability theory, but IIRC the only thing that required* measures was defining conditional probabilities and expected values on zero-probability events.
Of course redoing that class without Lebesgue integration sounds excruciatingly painful.
* Not just to make proofs nicer and theorems more powerful