There are a few things in the list that I would say differently, which I mention not because the versions in the post are _wrong_ but because if you’re using a crib-sheet like this then you might get confused when other people say it differently:
I say “grad f”, “div f”, “curl f” for ∇f, ∇⋅f, ∇×f. I more often say “del” than “nabla” and for the Laplacian I would likely say either “del squared f” or “Laplacian of f”.
I pronounce “cos” as “coss” not as “coz”.
For derivatives I will say “dash” at least as often as “prime”.
The selection of things in the list feels kinda strange (if it was mostly produced by GPT-4 then that may be why) -- if the goal is to teach you how to say various things then some of the entries aren’t really pulling their weight (e.g., the one about the z-score, or the example of how to read out loud an explicit matrix transpose, when we’ve already been told how to say “transpose” and how to read out the numbers in a matrix). It feels as if whoever-or-whatever generated the list sometimes forgot whether they were making a list of bits of mathematical notation that you might not know how to say out loud or a list of things in early undergraduate mathematics that you might not know about.
It always makes me just a little bit sad when I see Heron’s formula for the area of a triangle. Not because there’s anything wrong with it or because it isn’t a beautiful formula—but because it’s a special case of something even nicer. If you have a cyclic quadrilateral with sides a,b,c,d then (writing s=12(a+b+c+d)) its area is √(s−a)(s−b)(s−c)(s−d). Heron’s formula is just the special case where two vertices coincide so d=0. The more general formula (due to Brahmagupta) is also more symmetrical and at least as easy to remember.
There are a few things in the list that I would say differently, which I mention not because the versions in the post are _wrong_ but because if you’re using a crib-sheet like this then you might get confused when other people say it differently:
I say “grad f”, “div f”, “curl f” for ∇f, ∇⋅f, ∇×f. I more often say “del” than “nabla” and for the Laplacian I would likely say either “del squared f” or “Laplacian of f”.
I pronounce “cos” as “coss” not as “coz”.
For derivatives I will say “dash” at least as often as “prime”.
The selection of things in the list feels kinda strange (if it was mostly produced by GPT-4 then that may be why) -- if the goal is to teach you how to say various things then some of the entries aren’t really pulling their weight (e.g., the one about the z-score, or the example of how to read out loud an explicit matrix transpose, when we’ve already been told how to say “transpose” and how to read out the numbers in a matrix). It feels as if whoever-or-whatever generated the list sometimes forgot whether they were making a list of bits of mathematical notation that you might not know how to say out loud or a list of things in early undergraduate mathematics that you might not know about.
It always makes me just a little bit sad when I see Heron’s formula for the area of a triangle. Not because there’s anything wrong with it or because it isn’t a beautiful formula—but because it’s a special case of something even nicer. If you have a cyclic quadrilateral with sides a,b,c,d then (writing s=12(a+b+c+d)) its area is √(s−a)(s−b)(s−c)(s−d). Heron’s formula is just the special case where two vertices coincide so d=0. The more general formula (due to Brahmagupta) is also more symmetrical and at least as easy to remember.
Thanks, I have applied most suggestions.
Indeed I didn’t choose the formulas myself but just told GPT to produce some, and then removed a few that seemed dubious or irrelevant.