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Math is beautiful!
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@methemetics replied to your post “@methemetics replied to your post:I’ve been in the US education system...”
^^that is the key; I literally meant that in a non proof based math class you will not get a question like that
I’m still confused. Do you have questions like “show that this function is decreasing” (=“find intervals of increase/decrease”, same question, no scary word “show)? Or “determine whether this series converges or diverges”? “Show that these two vectors are orthogonal”? “determine if these lines intersect” etc? Same difference. These are all “proofs”.
(hence that part of the original post where i express confusion on the apparent difference in perception of "show that (a+b)^2 = a^2 + 2ab + b^2” and “prove Bolzano-Weirstrass”)
@methemetics replied to your post:I’ve been in the US education system for 5 years...
One other thing–and correct me if this sounds wrong–but when something is called a “non proof based” course, I assume it is really a distinction about how much of your homework is expected to be in full sentences. It doesn’t mean anything about whether the professor is doing proofs on the board or whether the student is expected to know how to apply the meaning of a theorem in a problem
oh
that’s not what i thought proof based means, but maybe the rest of you readers do, and that’s the source of my confusion
but on the other hand “ how much of your homework is expected to be in full sentences. ” is puzziling to me. Just like...you should have sentences where you need to have sentences to communicate the solution, and you don’t need to have sentences where you don’t need sentences? “Compute an integral” doesn’t need any words attached to it, but on the other hand “Use intermediate value theorem to show that the equations has a solution” is not possible to write without sentences, and both kinds of problems appear in a Calc 1 class?
(i mean, students try to do that - avoid any words in like IVT proofs, and then they can’t read their solutions back to me themselves. How am I supposed to grade it then?!...different story)
Everyone wish methemetics a happy birthday, if you can! She's wonderful and flawless and she had a super tough week!