this post was submitted on 02 Mar 2024
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You're probably the kind of person who complains that they don't teach complex numbers when first introducing square roots in school.
Not really no. It's a meme. Although, now that you mention it …
To learn to count to 10, we first have to understand quaternions.
The fundamentals of math takes like 700 pages before it gets to 1+1=2
Yeah, time to stop coddling those kindergarteners!
Depends into how much detail you go.
My prof. at uni. did a nice summary in two and a half pages.
Building axioms from the ground up, with proofs
You blew right by creating the universe first. Your apple pies probably come out terrible.
Come on, that's way too complex. But how can one count to 10 if they don't know what base to count to 10 in? We should definitely teach them bases first.
Base 11, base 12, and base 16 are all better number systems to teach first imo. A prime number has some benefits when it comes to fractions, but so does a number like 12 which is divisible by many other numbers. Base 16 is useful as you can easily convert between that and the other bases of powers of 2.
Can you really talk about 1 or 2 before giving a proper set-theoretic construction of the natural numbers?
“This is a triangle. It has three sides and three vertices.” [proceeds to give a collegiate trig course to the dismay of kindergarten students]
I pretty distinctly remember being introduced to square roots at the same or nearly the same time as complex numbers. Obviously we didn't do the whole Complex Numbers Extended Cinematic Universe, but I think my class did learn to solve quadratics with complex roots in middle school.
I mean I did go to Catholic middle school, but I don't think the math education was that weird.
Yeah advanced placement math in catholic schools gave me the same experience. Similarly I think kids can handle introducing negative numbers as you teach them subtraction.
Is there much beyond i^2 = -1, z = a + bi, and e^iθ = cosθ + isinθ? I didn't think the extended cinematic universe was that big...
You can literally take a class on Complex Analysis. Turns out that those "small" modifications have huge ramifications. They add a ton of extra structure to the real numbers which can be exploited, particularly if your problem can be expressed in terms of sines and cosines, or if your problem lives on a plane.
For example, complex differentiability is much more stringent than real differentiability, to the point that the existence of one complex derivative implies the existence of all of them! Furthermore, you have to be really careful extending the classic functions to the complex numbers. Typically, you either end up with a multivalued function, or you have to pick a specific branch that is single-valued.
If you want to learn more, Theodore Gamelin's Complex Analysis book is a good place to start. But to read it, you'd really benefit from a background in vector calculus. For a more "practical" but still detailed account of complex variables, check out Complex Variables and the Laplace Transform for Engineers by Wilbur LePage, which just assumes basic calculus.
What does electric current "i" have to do with the glorious imaginary unit j ?
This post was brought to you by Electrical Engineering Gang.
Good to see a fellow J enjoyer.
Preferably you want to note it's existence on the way past. But leave it there.
It's one of the maths areas that is complex enough to wow them, while still simple enough for some to research on their own.
You could also wait for the first smart Alec to ask about negative square roots, blow their brain with a quick simplified answer, and move on.
We already have Calculus and Stochastics, so please no.
Yes, I am the kind of person who gets upset when teachers pretend things don't exist and then gaslight students who know those things do exist and want to ask about them.
You sound like the kind of person who thinks it's wokeism to take issue with saying Columbus discovered the Americas when he A) Never landed on them, B) Didn't even think it was the Americas himself and went to his death bed swearing it was Indonesia, and C) WAS PRECEDED BY LITERAL MILLIONS OF INDIGENOUS PEOPLES WHO HAD BEEN LIVING THERE FOR THOUSANDS OF YEARS.
I agree this to some extent. I had a teacher who said conduction(thermal) does not happen in liquids and gases. Even according to textbook, fluids does convection and radiation but no mention of conduction, and there was an excersise question:
The answer in teacher's manual was (a) and I(and my friend) disagreed on that and argued. The teacher actually belived it happens only in solids and she was against me. I even wrote the "wrong" answer as per teacher on exam and lost 1 mark in that exam. And finally we got redirected to a senior teacher who said I was correct but the manual for teachers said so because they thought that shoul be introduced in higher classes only. It was pretty unacceptable to me as they don't NEED to say the wrong answer and they can simply say conduction occurs in fluids as well. It bought more problem than what it would have been if real answer was given. Even the teacher belived fluids don't conduct and and spread the misconception to students(which was reinforced by her when we argued).
I belive there should be a small mention of theese things for 1) The sake of avoiding misconception AND 2) For enhancing the curiosity of the students.
A single sentence mentioning of complex numbers in 10th grade by my favourite Math teacher bought Great curiosity in me.
One more thing to add, I have never seen it mentioned that conduction occurs in fluids explicitly in later classes but it was kind of assumed everyone knows. I wonder if there are students in my age who still belive It doesn't.
You sound really fucking annoying.
We're on Lemmy, who the fuck here isn't annoying‽
That's a very pedantic way to look at it. When teachers talk about the discovery of the Americas, there's an obvious implied "by the Europeans, for the purpose of permanent settlement" attached to it. Answering the question "who first visited Japan?" with "The Japanese" is completely useless, as an analogue.
Now, if you were to talk about how the Scandinavians settled bits of Canada at least 500 years before Columbus was born, that'd be much more interesting.
Using the word discovered erases the fact that the indigenous peoples were there first, by thousands of years, and that they're all people of equal humanity to columbus.
Trying to insist that genoese serial child rapist is the discoverer of jack shit is literally telling indigenous folks "our bottom of the grease barrel worst still count more than your most important."
As for the norse, is it any wonder everyone forgets about them when even they forgot about it in the intervening centuries. They literally thought the chick who lead the second expedition was a fictional character meant to represent how batshit insane pagans were before her cool younger brother convinced everyone to be nice and christian instead.
But they're not the cultural head of the current society, so that's irrelevant.
Fallacy, appeal to emotion. The only thing it tells is exactly what it tells - an expedition organized by Columbus was the first European voyage to reach the Americas with the intention of permanent settlement.
Yeah sure keep stanning the child rapist buddy, maybe try this line around your debate club coach so they can remind you what the fallacy fallacy is you contrarian walnut.
Fallacy fallacy doesn't apply, you pedantic child, as I've described why your line of argument is invalid. Maybe at least read the wikipedia article in its entirety before pretending to know what you're talking about.