Post AoL8WToRCPOv3oTmk4 by selmins@mastodon.social
(DIR) More posts by selmins@mastodon.social
(DIR) Post #AoIbJsbM2NzDNFp9VY by futurebird@sauropods.win
2024-11-22T11:10:44Z
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Is there a math concept that never made sense to you? Which one or ones do you wish someone would explain in new ways?If none of these come close you can mention something as a comment.
(DIR) Post #AoIbRviMLb5RLTwICm by futurebird@sauropods.win
2024-11-22T11:12:11Z
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Yes I think fractions cause people as many problems as these other "more advanced" ideas. I've seen students in calc 2 who still had messy ideas about fractions. It's not trivial and just because we teach some of it to 5th graders doesn't mean everyone knows how they work.
(DIR) Post #AoIbVq6r80TR7XGGzA by rayhindle@mastodon.social
2024-11-22T11:12:53Z
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@futurebird i and j being imaginary!
(DIR) Post #AoIc2qey6TSSNoxPDE by robotistry@sciencemastodon.com
2024-11-22T11:18:52Z
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@futurebird I get fractions now, but I changed schools mid-year that year. The old school hadn't gotten to them yet, the new school had already finished them, and my teacher assigned another student in the class to help me catch up. It went ... poorly. It took years for me to bounce back from that.
(DIR) Post #AoIc928IMNULhgcjb6 by SallyStrange@eldritch.cafe
2024-11-22T11:19:57Z
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@futurebird I get fractions because I worked doing lots of carpentry and construction for years
(DIR) Post #AoIcCPrCbsau9UF36u by rysiek@mstdn.social
2024-11-22T11:20:27Z
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@futurebird I was in a "math/physics/informatics" profiled class, and our math teacher was an absolute legend. Friends who went on to study math easily coasted on what they learned in high school for a year or two.That said, conditional probability remains Black Magic to me.
(DIR) Post #AoIcbbBNdhFmW6ghma by caboolture@aus.social
2024-11-22T11:25:06Z
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@futurebird Banach-Tarski paradox
(DIR) Post #AoIcfG6Fxx2CHx2JoO by aaron@hilltown.studio
2024-11-22T11:25:47Z
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@futurebird I voted "derivative and rates of change" mostly because when I got to calculus in college, nobody was explaining what the hell we were doing. I understand it better now (thanks, Khan Academy!) but could have used some down-to-earth talk about what this stuff was covering. Sadly, because I didn't grasp it in time, I failed out of the engineering program I started in. Maybe for the best, but I still think about it.
(DIR) Post #AoIcgRv9VA7bEwPUmG by spmatich@ioc.exchange
2024-11-22T11:26:00Z
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@futurebird the Riemann tensor. lol.
(DIR) Post #AoIcnIRP95qzrklEum by stveje@mstdn.social
2024-11-22T11:27:13Z
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@futurebird I always had the greatest trouble with probabilities/stats.Also continuity (epsilon-delta), but I think that was mostly because the examples were always so limited. The concept made perfect sense, but how to apply it in practice seemed to get completely handwaved.
(DIR) Post #AoIdDJdDLGiV5TgwlM by scribe@mastodon.sdf.org
2024-11-22T11:31:52Z
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@futurebird Derivatives applied to Integration, probably. I vaguely get it now, but unlike other maths, never needed to apply it enough to understand it fully. Definitely remember getting lost in class on it.
(DIR) Post #AoIdKhFdvFzuN0Babo by TimWardCam@c.im
2024-11-22T11:33:16Z
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@futurebird Pretty much everything in stats. Starting with the n-1 degrees of freedom bit, which I sort-of gather is fundamental to everything else.
(DIR) Post #AoIdhH5RMrgxsmBD4i by caity@bne.social
2024-11-22T11:37:19Z
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@futurebird huh?? You lost me after fractions... I came top of my high school in 3 unit English (that's the "we do literature" version) and bottom in vege maths (also known as maths for dummies).
(DIR) Post #AoIdyD53W3HANe4jFg by jacquiharper@mastodon.world
2024-11-22T11:40:24Z
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@futurebird Before I read down the thread I didn’t know what ‘the derivitive’ even related to :D My father was an engineer, and obnoxious about Being Right, so I went into visual art where the criticism couldn’t follow. After he died I went back to school for Comp Sci and had to study up to place out of the intro math class — I like math now, but have still never taken a class more advanced than Algebra II (back in 1977 that was)
(DIR) Post #AoIewNmypaiCy1JTZQ by mattmcirvin@mathstodon.xyz
2024-11-22T11:51:16Z
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@futurebird Partial fraction expansions in calculus. I have to look up how to do them every time and my intuition for what was going on was never strong. These days it is easier to lean on a computer algebra system. In physics, anything to do with Lagrange multipliers. I can muddle through but I feel like my intuitive grasp of it is weak. I can get a better understanding temporarily by working through the many tutorials in the subject but somehow the intuition fades later and I have to start over. And it's a really important concept.
(DIR) Post #AoIfZUuyGAzqN2hbCS by futurebird@sauropods.win
2024-11-22T11:58:22Z
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@mattmcirvin I have a soft spot for partial fractions... I'm toying with the idea of making some little math videos and thinking about what I could create. I want the videos to address things that just never made any sense to a lot of people. But, also they should be deep and cool and fun.
(DIR) Post #AoIfmQBf9zHxSlfjvM by futurebird@sauropods.win
2024-11-22T12:00:31Z
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@rysiek Part of the reason conditional probability and probability more generally are confusing is that it insists on living on the margin of human language expressed in words and sentences and mathematical representations of that language. And our language simply IS NOT precise when talking about cause, effect, probability, dependence and a whole host of topics. It's a big mess.
(DIR) Post #AoIg05LXRTScsfo5PU by futurebird@sauropods.win
2024-11-22T12:03:10Z
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@blbc If I'm understanding what you are asking correctly I think the reason why you can't understand is because there isn't one correct answer to the question:"what axioms do we need to include to proceed with this proof?"It's contextual. And some teachers don't do a good job conveying this. We'll say "oh that's obvious you don't need to explain THAT." then a moment later flip out because someone didn't support their next step with an axiom. There is a logic to all of this, but yeah.
(DIR) Post #AoIg8NWdjjkbZwxD4i by adriano@lile.cl
2024-11-22T12:04:40Z
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@futurebird @blbc IIRC Peano started proving that 0 + 1 = 1, so there's no bottom I guess.
(DIR) Post #AoIgEyy5RFj5RVwP8i by futurebird@sauropods.win
2024-11-22T12:05:41Z
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@blbc A proof is a lot like writing an essay in that you don't just need to know your subject matter and be correct about how the math works, you need to know your audience. You need to show that what you are proving follows from the theorems or axioms you and your reader *already* agree are perfectly supported. Some students will read what they need to prove and reason for themselves why it MUST be true, but they struggle to express this reasoning clearly.
(DIR) Post #AoIgJW3SMhzFDXcA1Q by futurebird@sauropods.win
2024-11-22T12:06:41Z
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@adriano @blbc It can feel like there is no bottom, but in fact there is a bottom. In fact there are several bottoms and you can decide which one you want to use to work in different mathematical systems.
(DIR) Post #AoIgNYAsQUT4wx0cIS by adriano@lile.cl
2024-11-22T12:07:23Z
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@futurebird @blbc I mean I'm not arguing that what he did was silly. The man was trying to set a foundation for Arithmetics.Ok it was a bit silly, but still.
(DIR) Post #AoIgdlQYv5AUgd4pm4 by futurebird@sauropods.win
2024-11-22T12:10:19Z
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@modulux Only #onhere would people be like "gee I don't totally understand this advanced math concept that made Euler and other cry how embaressing"Frankly if limits don't make you feel a little queasy you haven't thought about them enough. They are slippery and often counterintuitive. Their mathematical foundations were only pinned down very recently and I don't think math education has matured enough with those discoveries to convey them well to wider audiences.
(DIR) Post #AoIgexvdvS01kSBhUe by WAHa_06x36@mastodon.social
2024-11-22T12:10:29Z
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@futurebird I have the opposite thing: The more I learn about the so-called "reals", the less I understand them and the angrier I get at them.(Worst-named entity in maths as well. There's nothing more unreal than a "real").
(DIR) Post #AoIgr8CNZHOt4hoiGG by glent@aus.social
2024-11-22T12:12:45Z
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@futurebird @rysiek A discipline which gave a weird jargon meaning to the ordinary meaning of "significant" cannot complain.
(DIR) Post #AoIgup0wpxKAjZEJjk by futurebird@sauropods.win
2024-11-22T12:13:26Z
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@mdkcore While these are slightly tricky concepts much of the confusion over injection, bijection and surjection comes down to them having multiple names. one-to-oneon-tocoversbijectioninjectionsurjectionone to one correspondence...and I'm forgetting some of them. I ought to make a big list and untangle that mess one rainy afternoon. When will there ever be enough rainy afternoons...?
(DIR) Post #AoIgwurY4137S3pe8O by futurebird@sauropods.win
2024-11-22T12:13:49Z
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@WAHa_06x36 This is very valid and dare I say it? Real.
(DIR) Post #AoIh1Wg5PTohtKfWyW by WAHa_06x36@mastodon.social
2024-11-22T12:14:37Z
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@futurebird As a physicist, it also makes me extra uncomfortable that all of physics is built on top of real analysis.
(DIR) Post #AoIh2uhpYkJOhe98dM by mansr@society.oftrolls.com
2024-11-22T12:14:39Z
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@futurebird @blbc "Then a miracle occurs."Simply stating that "it follows that ..." can work, but it should be done with caution.
(DIR) Post #AoIhIwzapH8aQa6MK0 by promovicz@chaos.social
2024-11-22T12:17:46Z
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@futurebird For me, it was "how it fits together". Math education tries to be practical, but that renders it incomplete - for people like me, that's confusing.
(DIR) Post #AoIhTlX5m02I4UvZYW by gannet@wandering.shop
2024-11-22T12:19:38Z
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@futurebird I mostly get fractions, but I remember it taking a long time to comprehend dividing one fraction by another.
(DIR) Post #AoIhWocckBlGWNy9uy by claushoumann@mastodon.social
2024-11-22T12:20:16Z
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@futurebird complex numbers
(DIR) Post #AoIhY9fJzSEi4mrz96 by btuftin@social.coop
2024-11-22T12:20:27Z
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@futurebird @blbc teaching proofs is _so_ hard. In part because the early problems students have to look at are either "stuff they already take for granted" or "simple toy problemsb only a math nerd could love". And as you say, we have to pick and choose which prior axioms or proofs the student is allowed to use, since most of the problems, or all, already have proofs and we don't want them to just bypass the challenging part.
(DIR) Post #AoIhgzBqJ6GgC3IBHM by WorkWithKirk@mstdn.social
2024-11-22T12:22:07Z
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@futurebird Dang it. I meant to vote for derivatives, not conditional probability. I did well in math until calculus and derivatives. It was like hitting a brick wall.
(DIR) Post #AoIhift134b6u4I80m by mattmcirvin@mathstodon.xyz
2024-11-22T12:22:26Z
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@futurebird @rysiek There are a bunch of "rhetorical fallacies" that are false when taken as statements about logical implication but that I've always thought appeal to us because they resemble correct statements about conditional probability. You can take Bayes' Theorem as a statement of how much you can really affirm the consequent.
(DIR) Post #AoIhnqW4xByzJt1qKG by rysiek@mstdn.social
2024-11-22T12:23:21Z
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@futurebird yeah, that makes a lot of sense.
(DIR) Post #AoIhu3G6UUxqZpW1NQ by PizzaDemon@mastodon.online
2024-11-22T12:24:07Z
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@futurebird I always have to look it up & re-prove it. Even still, there is a minority chunk of my mind that rejects it
(DIR) Post #AoIi7AXEkUjuuOmgSG by mattmcirvin@mathstodon.xyz
2024-11-22T12:26:50Z
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@futurebird @adriano @blbc Lewis Carroll's paradox seems to insist that even when there is a bottom, there is no bottom, and I've never been able to decide whether it is a legitimate problem or not.
(DIR) Post #AoIiLUaSzaxP9Z7nm4 by debivort@drosophila.social
2024-11-22T12:29:26Z
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@futurebird fixed points of the aleph function ??????
(DIR) Post #AoIirpcELQhhdeN1O4 by mansr@society.oftrolls.com
2024-11-22T12:35:17Z
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@futurebird Of the things you mention, I struggled a bit with probabilities and statistics when taking the intro course. The way it was presented was just weird (to me, anyway). When applying the concepts in things like signal theory, it started making a lot more sense.
(DIR) Post #AoIiwTYzlHEyh14VKS by mansr@society.oftrolls.com
2024-11-22T12:36:07Z
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@futurebird @mdkcore > When will there ever be enough rainy afternoons...?Come to England.
(DIR) Post #AoIj5NKYIxfzy4YlSC by KatS@chaosfem.tw
2024-11-22T12:37:44Z
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@futurebird Calculus stumped me.However, I think it's because my brain hadn't yet developed a proper grasp of relationships in time and space. That came about 35 years later, so I'm going to revisit it... just as soon as things quieten down a little and I have the time to write those docs.
(DIR) Post #AoIjQ75ns7ztgjY90S by nowan@mastodon.social
2024-11-22T12:40:05Z
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@WAHa_06x36 @futurebird Whenever my kids complain to me about how some numbers aren't really "real" enough I point out that the Greeks felt the same way - about the number one. After all, there's no counting involved in one, how can it be a number? And there's no need to even bring up that zero nonsense.
(DIR) Post #AoIjVbCzKTlaXTWgPQ by karchie@freeradical.zone
2024-11-22T12:42:28Z
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@futurebird moment-generating functions. as a grad student in biology but working lots with random processes, I took some grad-level probability and mathematical stats. They had two tracks, described as with and without measure theory, with the understanding that the latter would hand-wave past some details but you’d be okay. It wasn’t the measure theory that bit me though, it was (I think?) discrete math. So much pushing symbols around with no understanding of what it all meant
(DIR) Post #AoIjYbCNp1nhNSfpI0 by cmcfaul@cityofchicago.live
2024-11-22T12:42:54Z
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@futurebird I could never grok why the Axiom of Choice is necessary. I understood for about a minute while reading Bertrand Russell's Introduction to Mathematical Philosophy, but no longer do.
(DIR) Post #AoIjZJmk3D1ney1U4O by futurebird@sauropods.win
2024-11-22T12:42:56Z
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@Infrapink As a monolingual english barbarian do you think I could read it? is there a good english translation?
(DIR) Post #AoIjcS4rg0nQFLzhFg by david_chisnall@infosec.exchange
2024-11-22T12:36:35Z
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@blbc @futurebird I think that's a terminology problem. Anywhere outside of mathematics, a proof is a thing that you do to be able to claim that something is true.In mathematics, a proof is something that you do to demonstrate that things are self consistent. A mathematical proof doesn't say 'X is true' it says only that 'X is true if all of the axioms are true'. Outside of mathematics, 'true' is never an absolute because you always have some measurement errors, and so any notion of a thing being proven is probabilistic. Courts talk about 'beyond reasonable doubt' and 'in the balance of probability' as the requirements for evidence-based proofs of guilt for precisely this reason.This is a really important distinction for applied proof techniques. We use formal verification a lot, but I always remind people that formal verification doesn't prove that things are correct it proves that all of your bugs are present in your specification. You can then step further back and prove that some properties are present in the specification, but that doesn't mean that the properties that you're proving are the ones you really want.
(DIR) Post #AoIjqNcN3PNSTBJ8nA by rmattila74@energydon.fi
2024-11-22T12:46:12Z
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@futurebird Integers.
(DIR) Post #AoIk4HMD7ydV6gNPHM by carbontwelve@notacult.social
2024-11-22T12:48:44Z
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@futurebird solving differential equations
(DIR) Post #AoIk5VJgiFmAgrmStk by tyx@lor.sh
2024-11-22T12:48:56Z
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@futurebird ∇ · F, ∇ × F, Laplacian and friends (mentioned too early in physics, started to understand it only 10 years later),how to decompose functions in Maclaurin or Taylor series (still magic, but never tried hard enough to get it),Γ(z) and complex analysis in general (it took forever to get adjusted to sudden and seemingly illogical leaps in transformations).
(DIR) Post #AoIkMlRpzQ4Pdzp59c by futurebird@sauropods.win
2024-11-22T12:52:05Z
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@Infrapink @jacquiharper Exactly. A “rate of change” is a slope. 20miles/hour is a line with slope 20/1 because, for each 1 hour you go forward in the x-direction, your total total distance goes up by 20 miles in the y-direction. A tangent is a straight line … again with a slope. So “the slope of a curve at a point” (curves being precisely those lines with non-consonant slopes) we use the tangent to define it in a way so that our straight-line idea of slope works.😄
(DIR) Post #AoIkhQrJjabDryb1DU by nen@mementomori.social
2024-11-22T12:55:47Z
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@futurebird Why does math even work (or rather logic and reasoning in general)??? I'm usually able to satisfy my intuition about any specific math concept I need to know, but this question keeps bothering me.
(DIR) Post #AoIlNFUGP9sElMkimW by futurebird@sauropods.win
2024-11-22T13:03:24Z
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@nen When you say it “works” what do you mean by that? Can you give an example of “math working” ? what would it NOT working look like?
(DIR) Post #AoIldkn5mnmeU0Qheq by nowan@mastodon.social
2024-11-22T12:44:20Z
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@WAHa_06x36 @futurebird Their puritanical view on numbers must have made it all the more galling when they discovered they couldn't handle square diagonals and circle circumferences without irrational, "incommensurable" numbers.
(DIR) Post #AoIldmRtca17cqWntg by WAHa_06x36@mastodon.social
2024-11-22T12:48:00Z
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@nowan @futurebird But consider this: Show me a real number that is not part of a well-known countable subset of the reals.That is, show me a real number that is part of the _actual_ reals, not the tiny fraction that makes up 0% of the reals.
(DIR) Post #AoIldnqOQzCrx6zsie by nowan@mastodon.social
2024-11-22T12:49:20Z
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@WAHa_06x36 @futurebird That's also a problem for the naturals, right?
(DIR) Post #AoIldpHj4qfGQAnDxg by futurebird@sauropods.win
2024-11-22T13:06:22Z
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@nowan @WAHa_06x36 There only two kinds of meaningfully different infinite sets and ain’t *nobody* on god’s green earth who know why THAT is.
(DIR) Post #AoIldqJBGvQFayTtrs by nowan@mastodon.social
2024-11-22T12:50:52Z
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@WAHa_06x36 @futurebird Specifically, the set of naturals that have ever been used is finite.
(DIR) Post #AoIlf1lk9Ae3QhPF1U by PTR_K@dice.camp
2024-11-22T13:06:35Z
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@futurebird I took calc twice and passed with a C or C- each time. I could do the calculations, and the general idea of figuring out area under the curve or slope at a point made sense to me.But what I never intuitively understood was *why* doing the given manipulation of equations gave you the slope or area. Like I understood the algebra aspects, but it felt like a some leap to get from basic equation to slope or area equation.
(DIR) Post #AoIljZNj7MzepsL2jw by dan613@ottawa.place
2024-11-22T13:07:21Z
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@futurebird I don't think I ever really understood eigenvectors. I can never remember what they are and what they are important for when I run across them in papers.
(DIR) Post #AoIlvOSLZ3E0QT8aCu by llewelly@sauropods.win
2024-11-22T13:09:33Z
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@futurebird when I was in college I tutored many other students, and I had to keep a list of common misconceptions about fractions and how to address them with me. It's especially bad in programming, because you need to understand how fractions are supposed to work in order to write good code, but you also need to understand how divide, modulus, floating point divide, etc, differ from mathematical fractions.
(DIR) Post #AoInV6qwaeSSD3Elbk by wsrphoto@sfba.social
2024-11-22T13:27:12Z
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@futurebird Never understood Geometry. I understood calculus and applied it in USAF during Vietnam War. I was in the Nuclear Weapons Test Ban treaty monitoring program. We operated sites around the world with an array of instrumentation to detect nuclear events. The equipment I was research and maintenance technician is similar to seismic equipment. The equipment recorded the 2nd derivative of 0.5 Hz signal from electrical and magnetic sensors unique to nuclear events.
(DIR) Post #AoInnQ0m67icqDZ90a by Enema_Cowboy@dotnet.social
2024-11-22T13:30:30Z
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@futurebird I'm grappling with monads right now.
(DIR) Post #AoIo8OnzmFWnBKaoDI by McCrankyface@beige.party
2024-11-22T13:34:18Z
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@futurebird imaginary numbersThe square root of negative one does not exist but it is used all the friggin time
(DIR) Post #AoIoMWDR1SmqDcDyqW by ShiitakeToast@beige.party
2024-11-22T13:36:51Z
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@futurebird I really struggled with trigonometric identities when I took trig as a standalone class. I think because they taught it as triangles instead of curves. Also, my parents thought tutors were for dumb jocks and if I wasn’t getting it I just wasn’t spending enough time studying alone in my room.
(DIR) Post #AoIoS0epGgie51eekC by wademcgillis@mastodon.social
2024-11-22T13:37:50Z
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@futurebird topology. even real life applications like tying/untying things (shoes/trashbags/etc)
(DIR) Post #AoIpJUmxyHXWsWxyoC by josh@social.joshanders.com
2024-11-22T13:47:30Z
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@futurebird Induction
(DIR) Post #AoIprgCQ3NyM76AjAm by KarenDorman@mastodon.sdf.org
2024-11-22T13:53:41Z
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@futurebird I remember arguing with my teacher in elementary school because I didn't think dividing something should get you a bigger number. If you divide a pie it gets smaller. If they had just agreed that the pieces get smaller, but there are more pieces I would have understood.
(DIR) Post #AoIqvGr6K6SaciTd5M by Extra_Special_Carbon@mastodon.world
2024-11-22T14:05:31Z
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@futurebird Usually have to get to things like eigenfunctions and other physics things before I start losing the plot. Then I vaguely know concepts and trust that the people reporting know their stuff and hope I never have to solve a problem with it.
(DIR) Post #AoIrlL9TavBD0Ttssy by MollyNYC@mstdn.social
2024-11-22T14:14:58Z
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@futurebird Limits always throw me.
(DIR) Post #AoIs2knrTbbhUC5s8W by pileczka_gaia@chaos.social
2024-11-22T14:18:05Z
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@futurebird I really, intuitively understood derivatives and rates of change only towards the end of my masters degree, so while I understand them know (or at least did when it was still important for my studies 😅) I think there is a great lack of very good explanations there
(DIR) Post #AoIuKjlmG3WpOvp0YC by foolishowl@social.coop
2024-11-22T14:43:39Z
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@futurebird I tried to study calculus again at a community college in my thirties. I'd forgotten most of what I'd ever known about trigonometry, and it was tough, but at least there were patterns.But calculus itself seemed like an endless swamp of arbitrary rules, with multiple conflicting systems of notation. We spent most of the semester on the limit theorem, and from what I later read it seemed like a convoluted effort to avoid the concept of the infinitesimal, which it depends on anyway.
(DIR) Post #AoIyEWGvvbFJcPgYFM by ossobuffo@triangletoot.party
2024-11-22T15:27:27Z
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@futurebird I took trig as part of "Advanced Math" my senior year in high school, & absolutely loved it. What I didn't love, & what eventually burnt me out on math in uni, was calculus. Linear algebra was the last straw.At the time I didn't know I was #AuDHD, & just figured I was lazy. Turns out I've never really been able to concentrate on studying, & when I reached the point where I could no longer coast on natural ability, I failed out.Changed majors from CS to Lit, & managed to graduate.
(DIR) Post #AoIyzU3TzKkKLxmvZI by bardmoss@autistics.life
2024-11-22T15:35:56Z
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@futurebird When I was taking college trigonometry, at some point late in the semester they tried to switch us from algebra notation to function notation. I never could understand function notation, nor could I understand translating from one to the other. As such I never got into higher math (Calculus) and never progressed further in my studies.
(DIR) Post #AoIzgi1hv1je8XZLsW by australopithecus@mastodon.social
2024-11-22T15:43:44Z
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@futurebird Trigonometry. Didn't click for me until much later, when you start using it to extract x/y (or C/R) components. Which is to say, when it was properly presented in the context of circles, rather than triangles and waveforms.
(DIR) Post #AoJ3jHTVUdb6TR3PVY by dwildstr@ohai.social
2024-11-22T16:29:02Z
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@futurebird Apropos of fractions, there's a brilliant scene in the Isao Takahata film _Omohide Poro Poro_ in which a young girl expresses frustration at the notion that dividing by 1/4 is a different notion than dividing by 4, and her sister comprehensively fails to illuminate matters.There's a translation script for the whole film at http://www.nausicaa.net/miyazaki/opp/script_opp_en.txt , and the fraction bit has a footnote where the translator consulted with a mathematician to explain what's going on.
(DIR) Post #AoJ67l5NFiKzAUZ80O by dragonarchitect@rubber.social
2024-11-22T16:55:51Z
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@futurebird Mine is more of a notation gripe than anything:I can't understand why x^(-1) is equal to 1/x iff x is a number but when x is a function it somehow means the inverse of the function, when in ALL other cases of a negative power p, it means 1/x^(-p).I refuse to accept this stupid and confusing notation exception and I raise functions to a majuscule i as a function inversion operator.
(DIR) Post #AoJ7Odz70UTW1QFgmm by bkim@mastodon.social
2024-11-22T17:10:06Z
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@futurebird I understand the concepts of logic, but I do have trouble operating with them, which is embarrassing as a programmer. I regularly write full truth tables to figure out what is the proper sequence of ANDs and ORs.I have a friend (graduated as a mechanical engineer, now PhD in economics) who struggles with basic mental arithmetics, so at least I know I'm not alone
(DIR) Post #AoJ9o9Xf0yaX2ihezo by PTR_K@dice.camp
2024-11-22T17:37:09Z
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@futurebird Unless there's some deeper aspect I'm overlooking, I think fractions always made intuitive sense to me. Just the idea that a quantity of something can be proportionately associated with a quantity of something else, either as a part of the whole (pie slice analogy) or comparing things to other things (unit conversions, ingredient quantities, etc.). The concept didn't seem unusual at all once it was pointed out.
(DIR) Post #AoJDfTbxQaVOUspbiy by nen@mementomori.social
2024-11-22T18:20:22Z
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@futurebird @mcc @pesasa @vikxin @Wharrrrrrgarbl @Kichae @whknott @dwildstrMath and logic seem to map well onto the observed “real world”, despite how hard the complexity of reality usually fights back against being divided up into simple boxes. Math works by being useful tool in predicting stuff. Also it doesn't seem disagree with itself all the time. How to rule out the existence of some alternative, completely alien math like @mattdm said? Could there be something that breaks our logic but still helps predict things, maybe better than what we have?It's a vague feeling and I find it difficult to completely get rid of, mostly because it directly challenges the fundamental validity of the tools I otherwise would rely on to seek clarity. Like, am I even allowed to try to think rationally? If not, how can I proceed at all? How to “prove” something if you can't just assume that any rules hold? Would it be possible to find solid answers from some specific kind of unhinged ramblings?However, I actually do have something that tastes like an answer. It just feels like it bypasses the problem.I'd say that math is based on some self-sustaining stable things in our brains. Maybe “attractor” is a correct word here – math could be seen as a system of strong attractors. It consists of tiny rules or patterns that our brains find easiest to hold onto and reproduce. We learn them by repeatedly observing corresponding similar (but not exactly equivalent) stable phenomena in the nature. For example, we think that three stones today is still three stones tomorrow, unless someone removes one of them or adds another. But what if we realize later that one of the stones is actually made of foam? Our simple rules are so sticky and dear to us that we rather count that as subtraction, too (someone tricked us and swapped a stone when we weren't looking), or we say that there were only two stones from the beginning, but we just didn't notice that one of them wasn't real. We would firmly refuse the conclusion that three is sometimes equal to two.Maybe this is more or less what most of you meant in your replies?I think the answer basically says “wrong question” and then turns it around, pointing outwards: why are some things in the universe simple enough that they can be modeled by a minuscule brain? And my hunch on that is: matter couldn't organize into even simplest life if the local environment was too chaotic to present lots of simple patterns.Maybe practically satisfying, but not philosophically/mathematically or however it should be described.
(DIR) Post #AoJDlJF6tHK84qvTN2 by fluorescentBeige@mastodon.social
2024-11-22T18:21:28Z
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@futurebird I actually feel like learning calculus made the entirety of math make so much more sense. Derivates particularly. I took calculus 1 and physics with calculus at the same time and I had so many “Everything is calculus?!” moments. I think this was mostly in the context of physics because I’d taken algebra based physics in high school. I wish I’d learned more calculus early on as an explanation for how stuff works, but I get why we’re taught it the way we are.
(DIR) Post #AoJGDWOdmLFOtCxpuS by catmisgivings@stranger.social
2024-11-22T18:48:54Z
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@futurebird so, I understood the description of what division *is* really well from the get go, but for some reason I had a hard time understanding why you *do* it differently from the other operations.Subtraction: Opposite-addingMultiplication: Adding a bunch of timesExponents: as adding is to Multiplication, so is Multiplication to raising things to powersDivision: okay forget about adding for a minute, we're going to draw a weird shape around the number we want to divide and
(DIR) Post #AoJQX1fYjKWSvMohRQ by AMS@infosec.exchange
2024-11-22T20:44:33Z
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@futurebird Differential equations, like find a closed form to this pile of PDEs still seem sus to me (in a rest of the owl way). And I've got higher degrees in this stuff.
(DIR) Post #AoJTPKLxgCXAPvfeDI by rehana@mastodon.social
2024-11-22T21:16:31Z
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@futurebird Topology. I know the pop explanation and I've tried reading about the actual math, but I never get far enough to connect the definitions with the intuition.
(DIR) Post #AoJWCkXPJYL7j1ibo0 by dragonarchitect@rubber.social
2024-11-22T21:48:07Z
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@futurebird @modulux Honestly even though I feel like I reasonably intuitively grasp limits, I can't for the life of me understand how the epsilon-delta definition is supposed to work.The logic in it is completely circular and dependent upon itself and I Do Not Like That™.
(DIR) Post #AoJWVMLbTgaICb4Tce by dragonarchitect@rubber.social
2024-11-22T21:51:28Z
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@futurebird @mattmcirvin There's probably a whole lot of room for explaining partial fractions in deeper depth which I would love to see, but my favorite simple "how to do it" explainer is the "cover-up" method taught by Prof. blackpenredpen because of its simplicity:https://www.youtube.com/watch?v=ZocN1K_AXaA
(DIR) Post #AoJWgxkyjP6DPVTOUq by CoolerPseudonym@wandering.shop
2024-11-22T19:59:09Z
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@futurebird Natural logs
(DIR) Post #AoJdlnRZCa5aYHe4em by phaedral@mastodon.social
2024-11-22T23:12:52Z
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@futurebird @Infrapink @jacquiharper A tangent is a straight line?https://mathbooks.unl.edu/PreCalculus/tangent-and-cofunctions.html
(DIR) Post #AoJhRtuxoyX6ekAEsa by sbourne@mastodon.social
2024-11-22T23:53:37Z
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@nowan @WAHa_06x36 @futurebird I was hanging out with a toddler, a daily Sesame Street watcher who sung along enthusiasticly to the number segments. So I asked him to count the croquet balls in the rack. He was so excited! "One!" he said pointing to the first one. "One!" he said pointing to the second one. "One!" he said pointing to the third one. Yes, he did this for all six balls. I was stunned into silence because, well, he wasn't wrong, was he? Each ball was just one ball.
(DIR) Post #AoJhmXeZnJyhgaLE2q by futurebird@sauropods.win
2024-11-22T23:57:51Z
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@phaedral @Infrapink @jacquiharper "20mph isn't a rate of change; it's a velocity, unchanging."I don't know what you are getting at with this.
(DIR) Post #AoJiHmo7VDXlf6hhLM by phaedral@mastodon.social
2024-11-23T00:03:27Z
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@futurebird @Infrapink @jacquiharper Maybe I misunderstood your post. If so, apologies. I thought you were offering 20mph as an example of rate of change.
(DIR) Post #AoJiP8jGOebdg5wG5A by futurebird@sauropods.win
2024-11-23T00:04:49Z
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@phaedral @Infrapink @jacquiharper It's a rate of change. The distance changes 20 miles for each 1 hour. It could be instantaneous, and just the rate at a particular moment on a nonlinear function or it could be the constant rate of change of a linear function.
(DIR) Post #AoJiS7kOVGQzVAtH1s by phaedral@mastodon.social
2024-11-23T00:05:20Z
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@futurebird @Infrapink @jacquiharper ok
(DIR) Post #AoJiUJPA8EGAEi0Eoi by treleanor@aus.social
2024-11-23T00:05:41Z
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@futurebird You left off “everything.”
(DIR) Post #AoJkvy4jEC0q6HlBvk by dendari@mastodon.world
2024-11-22T23:16:33Z
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@phaedral @futurebird @Infrapink @jacquiharper A tangent is a straight line that touches a curve on exactly one point. The slope of that tangent is then considered the slope of the curve at that exact point.
(DIR) Post #AoJkvzKMZY73z45BwG by phaedral@mastodon.social
2024-11-22T23:22:35Z
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@dendari @futurebird @Infrapink @jacquiharper Arguably that's a different use of the word. Of course it's been 30+ years since second semester calculus, which is as far as I got. "tangent" is defined:Given an angle θ (in either degrees or radians) and the (x,y) coordinates of the corresponding point on the unit circle, we define tangent astan(θ)=y/xResulting in this curve:
(DIR) Post #AoJkw0aLtaUrswZTV2 by dendari@mastodon.world
2024-11-23T00:27:52Z
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@phaedral @futurebird @Infrapink @jacquiharper this is the tangent from trigonometry not the same tangent. Futurebird is likely a much better math teacher than I am. I haven't done anything beyond 8th grade algebra in years.
(DIR) Post #AoJkw1WUPR08nFlu7M by futurebird@sauropods.win
2024-11-23T00:33:09Z
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@dendari @phaedral @Infrapink @jacquiharper The crazy thing is... in a way it *is* the same tangent, or at least for a circle. Most people know that you can plot a circle using:x=cos thetay=sin thetaAnd let theta go from 0 to 2pi (or 0 to 360 if you like)Because the x and y co-ordinates of a circle are parametrized by the sin and cos. Tangent has a geometric meaning here too. And this is why it increases without bound as theta get close to pi/4 (90 degrees)
(DIR) Post #AoJlLVc7fYJdMGYiG0 by dendari@mastodon.world
2024-11-23T00:37:46Z
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@futurebird @phaedral @Infrapink @jacquiharper This is why we need to teach understanding math and not just how to do it.
(DIR) Post #AoJnGwGXLnyETgPXBQ by ksaj@infosec.exchange
2024-11-23T00:59:21Z
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@futurebird I used to have a hell of a time with derivatives and rates of change (and similar concepts). Then I took a course on Origin of Life, and the way they presented it suddenly worked. It was like bam I suddenly understood something I didn't grasp very easily at all before.It really takes knowing how to teach through different types of examples, versus just using the same examples with different numbers!
(DIR) Post #AoJpEAoR0exedK4jVA by futurebird@sauropods.win
2024-11-23T01:21:16Z
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@Virginicus @nowan @WAHa_06x36 That's why no one know why!But also I think calling it "continuum hypothesis" confusing. It should be call the "only two kinds of infinity hypothesis"
(DIR) Post #AoJthMmtxrM5zLXB7w by phaedral@mastodon.social
2024-11-23T02:11:22Z
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@futurebird @dendari @Infrapink @jacquiharper Futurebird: I've got a /visual/ that I cannot articulate, for how the line at a tangent to the semi-circle could be used to re-create the trig tangent curve...but if that tangential line is tangential to a curve other than a semi-circle...uh... B^)
(DIR) Post #AoJtxOmaJbieoD1xdQ by keithpjolley@discuss.systems
2024-11-23T02:14:15Z
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@futurebird @dendari @phaedral @Infrapink @jacquiharper neat!
(DIR) Post #AoJuXv0hyEFJBd3CyG by keithpjolley@discuss.systems
2024-11-23T02:20:52Z
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@futurebird euler's identity blows my mind every single time. like, here we are chatting about natural logs all nice and casual then someone mentions pi and it's like ok so then what happens? some wise-ass throws in a an imaginary number and all of a sudden we are are at negative one. wtf? 🤯
(DIR) Post #AoJvYLNu0oHkwFfNPk by futurebird@sauropods.win
2024-11-23T02:32:09Z
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@keithpjolley I like Euler's identity. But it's also just sort of saying "cos(180 degrees) = -1"
(DIR) Post #AoJwWvYOfGQgUTSnEe by whknott@mastodon.social
2024-11-23T02:42:47Z
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@futurebird @keithpjolley So, trig relationships are easy to memorize if you want to, which I never did, but one of the things they're really useful for is reducing equations, ime. It's one of those things that makes teaching them so difficult, to me, in that they have a physical relationship to the world that you can derive from geometry but their actual utility is for doing more math. I keep qualifying, cuz maybe I'm just dumb but that's how I see identities - useful for reductions.
(DIR) Post #AoJxPwD3vZ7WS4iQ2y by dlakelan@mastodon.sdf.org
2024-11-23T02:52:51Z
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@futurebird I would like someone to explain Lie Algebras and Lie Groups and their relationship to differential equations.
(DIR) Post #AoJxSFjGKGqTZLseae by vonzo@toot.io
2024-11-23T02:53:25Z
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@futurebird I like to mention the square root of two every chance I get*How many cookies would you like? Sqr root of two
(DIR) Post #AoJxViEApEj6pBzMTw by superflippy@mastodon.xyz
2024-11-23T02:54:04Z
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@futurebird I had a terrible time with statistics because it’s not logical.
(DIR) Post #AoJxmQX7rjSYryp7r6 by futurebird@sauropods.win
2024-11-23T02:57:06Z
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@whknott @keithpjolley IDK if it's about memorization. It keeps coming back to the unit circle. The Euler identity is over on the left. It's just a reality of going around the circle.
(DIR) Post #AoJy8dY89VS7bqss64 by futurebird@sauropods.win
2024-11-23T03:01:09Z
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@whknott @keithpjolley Can't spell identity... sleepy brain.
(DIR) Post #AoJyEa1y9DyoQxfthI by whknott@mastodon.social
2024-11-23T03:02:11Z
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@futurebird @keithpjolley cuz it's 1/-1?
(DIR) Post #AoJyMbITK9UOg4DavA by futurebird@sauropods.win
2024-11-23T03:03:39Z
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@whknott @keithpjolley Yeah. And because at that same point sin is zero. So, you just have the real part, not the imaginary. (imaginary being the y axis ... or sin)
(DIR) Post #AoJybOqtsKtUQONXOa by whknott@mastodon.social
2024-11-23T03:06:19Z
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@futurebird @keithpjolley but if you graph it as a wave instead of a circle it's amplitude and period, right? I think that's how I was taught it lo those many centuries ago.
(DIR) Post #AoJylMM60tSTZoifBI by futurebird@sauropods.win
2024-11-23T03:08:07Z
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@whknott @keithpjolley If you graph sin theta as the height and make your x axis just increasing at the same rate of theta you get the regular sin wave... it a projection of the vertical distance of a point moving around the circle .... that's why it's periodic.
(DIR) Post #AoJzY8teqD721bgAKW by eleanor@chaosfem.tw
2024-11-23T03:16:55Z
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@futurebirdThe part of it that always feels magical to me is the relationship between the exponential function and the polar representation just...falls out of the definition of basic complex arithmetic as transformations in plane geometry. That always felt like it was hinting at some deep truth of the universe to me.One of my absolute favorite math books is Visual Complex Analysis by Tristan Needham, which builds from basic complex arithmetic to the best parts of complex analysis using almost entirely lovely geometric arguments. @whknott @keithpjolley
(DIR) Post #AoK0fMPF6z0xuASTnk by jens@social.finkhaeuser.de
2024-11-23T03:29:25Z
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@futurebird conditional probability.It's not as if I don't understand it, but it's much harder than it should be? I feel like I'm missing something that makes it as intuitive as other concepts.
(DIR) Post #AoK10o03iJ8HZCu9CK by davew@mastodon.online
2024-11-23T03:33:14Z
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@futurebird There are so many weird and wonderful ideas in mathematics. Some infinities are larger than others, fractals, the Monty Hall problem. As David Hilbert once observed, “Mathematics is a game played according to certain simple rules with meaningless marks on paper.”#GBOD
(DIR) Post #AoK12Qg1Oq7JoJJ4UK by CardboardRobot@mstdn.social
2024-11-23T03:33:37Z
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@futurebird Maybe not what you’re looking for but for me it was fractions. Somehow I missed the day that / meant “divided by” and was bewildered for months. For that time I was stamped “bad at math.” Not sure how this knowledge was finally delivered but I could see how missing this basic idea would have set my life trajectory in a completely different direction.
(DIR) Post #AoK1q6Nl81ahLaRydM by EmptySet@dobbs.town
2024-11-23T03:42:35Z
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@futurebird Let me guess:you see {N/D}'==N'/D' used, a mistake familiar to me when grading.
(DIR) Post #AoK3pBdYJ1QlGNWqCO by grumpasaurus@infosec.exchange
2024-11-23T04:04:49Z
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@futurebird null hypothesis and confidence intervals
(DIR) Post #AoK6hWjYHh6cEuNG9A by bgrinter@mastodon.sdf.org
2024-11-23T04:37:02Z
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@futurebird @blogdiva surds and indiciesI was sick the day we learnt it and trying to catch up never made sense even when someone explained it to me
(DIR) Post #AoK7EL5Acmxvey8FEW by chris_hayes@fosstodon.org
2024-11-23T04:42:58Z
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@futurebird Discrete math (logical operators) is oddly the one math class I understood and enjoyed.Imaginary numbers were always confusing to me, they're already confusing without giving them the most mysterious and ambiguous name ever. And then you have "Complex numbers", which are "real" numbers and "imaginary numbers" together.However—while doing the HackRF Sotware Defined Radio course in the past year, he explained "Complex numbers" in a way that clicked with me.https://www.youtube.com/watch?v=hPhhxwgk0A0
(DIR) Post #AoK7xkBY8hgyXvlaUq by m0xee@social.librem.one
2024-11-23T04:51:16Z
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@futurebird Derivatives are fine, integrals are what I hate — I do understand them, but I hate dealing with them, simplifying and all that. They aren't much different, but for some reason they make my brain boil 🤯Also limits are kinda disgusting 😅
(DIR) Post #AoK9DpHH4di0vYg11E by marymessall@mendeddrum.org
2024-11-23T05:04:38Z
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@futurebird @dendari @phaedral @Infrapink @jacquiharper I would like to see a proof that shows that the length of the green line here is always equal to the ratio of the blue line length to the black line length, if you know where I could find one...
(DIR) Post #AoKA76BPvAHrHnIEAy by SETIEric@mastodon.sdf.org
2024-11-23T05:15:10Z
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@futurebird Why, in statistics, can I do math for 8 hours and then it turns out I've just derived the g*d***mn incomplete gamma function again? That is my greatest puzzle.
(DIR) Post #AoKGpHP4AJtcYF7yIy by oblomov@sociale.network
2024-11-23T06:30:33Z
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@m0xee @futurebird integration is horrible in general. The fact that there are trivial functions that do not have a primitive that can be expressed through standard functions is an injustice. (But how do you dislike limits and not have an issue with derivatives?)
(DIR) Post #AoKHX8l3fa4OTpKQZk by m0xee@social.librem.one
2024-11-23T06:38:31Z
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@oblomov > how do you dislike limits and not have an issue with derivativesHa-ha-ha, good question! I think it's something irrational, hard to put into words — all three are related, but it's one of those cases when there is a gang of friends and you like one of them, can't stand the other two, but as they hang out together all the time, you have to tolerate them. Derivatives are my darlings, limits — can bear with them, integrals — eww, yuck! 🤭@futurebird
(DIR) Post #AoKQRm8pEIYYTWxi1A by libroraptor@mastodon.nz
2024-11-23T08:18:16Z
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@futurebird there are two trig functions whose names will immediately make new sense to you if you think in circle terms: tangent and chord. They're lengths of tangents and chords corresponding to the angle.If you look at the back of certain astrolabes, a quadrant is given to a sine/cosine calculator on which it's quite literally a length, just like the tangent and chord are lengths.If you look pre-1600, the lengths are tabulated for circles of various radii.@Infrapink
(DIR) Post #AoKT3ynynIZifDYZHs by tuban_muzuru@ohai.social
2024-11-23T08:47:37Z
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@futurebird I taught my kids what I call Practical Math: which describes the ways the world works. That's great - I can show them the math underlying a course correction of a planetary probe.But biggish chunks of math: abstract algebra, number theory, set theory - and especially logic, these lack easy-to-explain examples. Abstract algebra, that's a beast. I had to go back to college for two semesters to understand the math I was seeing in the physics books,. heh heh.
(DIR) Post #AoKn4UvlLmZ7NminTs by tuban_muzuru@ohai.social
2024-11-23T12:31:37Z
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@rysiek @futurebird 1/ Conditional probability explained to my kids:Deck of cards. Shuffle. Now draw cards until you get an ace:P(Ace) = (Number of favorable outcomes) / (Total number of possible outcomes)Let's break it down:Favorable outcomes: These are the outcomes we're interested in, which is drawing an Ace. There are 4 Aces in a standard deck.
(DIR) Post #AoKp4g6c0Ar3ww0fmS by futurebird@sauropods.win
2024-11-23T12:54:16Z
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@japonica (1/2)/(1/2)(1/(2/1))/2((1/2)/1))/21/((2/1)/2)I guess we could also claim1-2-3-4 was ambiguous1-(2-(3-4)) But we don't make such a claim we treat it as a sum with each - assigned only to the adjacent number. 1+(-2)+(-3)+(-4)So, maybe it makes sense to do the same for the fraction? Treat it as a product and assign the -1 exponent only to the adjacent number.1*(1/2)*(1/1)*(1/2)The confusion comes from the non-commutative operations of subtraction and division.
(DIR) Post #AoKxMcNhO3YPFD4FFI by oblomov@sociale.network
2024-11-23T05:52:15Z
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@marymessall @futurebird @dendari @phaedral @Infrapink @jacquiharper similar triangles
(DIR) Post #AoKxMd7Qe28LX2SlWa by marymessall@mendeddrum.org
2024-11-23T14:26:44Z
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@oblomov @futurebird @dendari @phaedral @Infrapink @jacquiharper Ah, because it's a unit circle! So the "adjacent" side of the big triangle is going to always have a length of 1. And the length of "opposite" side of the big triangle, divided by 1, is equal to the ratio of the opposite side to the adjacency side of the smaller triangle... because they are similar triangles. Thank you!
(DIR) Post #AoL4GMgnW2YEWBxxui by catselbow@fosstodon.org
2024-11-23T15:44:23Z
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@futurebird @dendari @phaedral @Infrapink @jacquiharper Going off on a tangent (ha!), my favorite way of parametrizing a circle is (r=1):x = (1-t^2)/(1+t^2)y = 2t/(1+t^2)where t is between -infinity and infinity.One neat feature is that rational values of t are guaranteed to give you rational values of x and y.Geometrically, you can think of t as the point where a line pivoting around the point (-1,0) meets the y axis. (x,y) is the point where this line meets the circle.
(DIR) Post #AoL8WToRCPOv3oTmk4 by selmins@mastodon.social
2024-11-23T16:32:10Z
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@futurebird homology theory
(DIR) Post #AoL8bhzzsjA8VUNak4 by mina@berlin.social
2024-11-23T16:33:05Z
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@futurebird Tensors.I never got a feeling for them.
(DIR) Post #AoL9EEh8lea4uovlWi by mina@berlin.social
2024-11-23T16:38:44Z
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@futurebird That said: I have given Math classes on every level and every kind of students, and my conclusion is:Fractions are the most crucial part in mathematical understanding.If a kid had a bad time or a not so good teacher in 4th or 5th grade, they have a hard time in mathematics, whilst those with solid knowledge of fractions will always be able to catch up with complex issues they missed or did not understand at some point.
(DIR) Post #AoL9Zdet9GGAQ75Cka by drazraeltod@chaos.social
2024-11-23T16:43:56Z
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@futurebird none of thosebut operations on matrices always were too hard for menot "I'll never understand this"-hardbut "It' would be much easier if you'd explain this in sane, non-math, terms… like some source code snippet." And since there was some easier way, I'd just skip understanding this.
(DIR) Post #AoLAH4HG3WUVQfjrIe by remenca@mastodont.cat
2024-11-23T16:51:48Z
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@futurebird I'd say that all of them made sense when I learnt them, but from time to time I forget why they made sense and every time I want to understand them again I have to go back again.
(DIR) Post #AoLHuT8aGAP3VKPsDg by stiefel_fan@troet.cafe
2024-11-23T18:17:21Z
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@futurebirdI have to admit I still have issues with Complex numbers! 🤷🏼♂️
(DIR) Post #AoLQ2LqM3tg2pf9we0 by belehaa@wandering.shop
2024-11-23T19:37:11Z
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@futurebird My struggles with math were mostly a matter of notation. I just wish more of my instructors had taken a moment to explain "this symbol is called __ and it means __"I like to think the experience has made me a better teacher, though, because I always stop to explain equations and symbols. I don't want to leave my students as baffled as I was
(DIR) Post #AoLiKqflyaPopqBC9Q by kechpaja@social.kechpaja.com
2024-11-23T23:13:27Z
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@futurebird I stared at this for a bit, and found that I was getting all too thoroughly hung up on the difference between the "never made sense to me" that means "I genuinely think I am not capable of understanding this", and the one that means "I never learned this well enough to understand it (and/or gave up because it wasn't interesting enough to keep trying)".There are numerous things in the latter category, but for me the feeling of futility associated with the first usually comes from things that pose organizational, time management, or motivational problems rather than simply being conceptually difficult the way math can be.
(DIR) Post #AoMY3aVs02fdPUddZY by goku12@fosstodon.org
2024-11-24T08:53:00Z
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@futurebird Stochastic processes are not appreciated enough. Nobody explains why concepts like ensemble and ergodicity matter. You get the feeling that it has something very profound to convey, but can't quite place it. Personally, even multivariate and vector calculus never appeared as cryptic.