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Cake day: June 12th, 2023

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  • Kogasa@programming.devtoMemes@lemmy.mlMath
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    22 days ago

    Stokes’ theorem. Almost the same thing as the high school one. It generalizes the fundamental theorem of calculus to arbitrary smooth manifolds. In the case that M is the interval [a, x] and ω is the differential 1-form f(t)dt on M, one has dω = f’(t)dt and ∂M is the oriented tuple {+x, -a}. Integrating f(t)dt over a finite set of oriented points is the same as evaluating at each point and summing, with negatively-oriented points getting a negative sign. Then Stokes’ theorem as written says that f(x) - f(a) = integral from a to x of f’(t) dt.






  • Kogasa@programming.devtoMemes@lemmy.mlConfusing...
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    1 year ago

    What you just said is at best irrelevant and at worst meaningless. No, the fact that multiplication is defined in terms of addition does not mean that it is required or natural to evaluate multiplication before addition when parsing a mathematical expression. The latter is a purely syntactic convention. It is arbitrary. It isn’t “accounting.”


  • Kogasa@programming.devtoMemes@lemmy.mlConfusing...
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    1 year ago

    It is, in fact, completely arbitrary. There is no reason why we should read 1+2*3 as 1 + (2*3) instead of (1 + 2) * 3 except that it is conventional and having a convention facilitates communication. No, it has nothing to do with set theory or mathematical foundations. It is literally just a notational convention, and not the only one that is still currently used.

    Edit: I literally have an MSc in math, but good to see Lemmy is just as much on board with the Dunning-Kruger effect as Reddit.