/sci/ - Science & Math

>>11188333
>I'm bad at math and science
>Lets go to /sci/ and complain that it isn't more like /his/
Thanks for your fine contribution to the board.

>>11188353
t. CS major

Op I'm on board with you. Learning the history of investigative thought is both inspiring and gives a lot of context to why problems were solved. If you really wanted to do something you might look into doing an education doctorate but I'm guessing you'd be slammed with a bunch of cognitive dissonance

Anonymous 12/01/19(Sun)07:10:17 No.11188358▶
>>11188353
t. CS major
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>>11188333
None of these are good ways of teaching math.

Or philosophy.

>>11188358
CS majors tend to have little to no allegiance to science and math, and frequently believe physically idiotic theories about technology. They also tend to lack clean, efficient mathematical reasoning as evidenced by the belief in incorrect physical theory

>>11188358
>t. moron
Want to try again?

>>11188389
no, your paraphrase is a reasonably correct equivalent of what i said, glad we agree

>>11188333
You’re right. They give you the formulas and general principles first before you can even see their significance. They expect you to internalize it and be able to work towards the particular, when natural learning works from the particular to the general. It’s a sad joke, really. They know you’re confused when they first present the formulas, but that’s ok! You’ll learn it eventually! But why does confusion have to be a part of the learning process? Why not have series of questions and problems so that what needs to be learned can be derived for everyone to see?

>>11188415
When you phrase it like this it really does make it seem wild - would it really do that much harm to tell kids why algebra was developed before they started? Strange

The thinking is:
Most people don’t have what it takes to think abstractly and logically and really understand the underpinnings of math. But those who can’t do it still need to learn the techniques to handle numbers in their daily life.

Idk how true that is but that’s probably the reasoning behind it. I will say that I know lots of engineers and other stem majors in school that have no interest or capacity to learn upper division theoretical math, but they have a good handle on calc and diff eq techniques

>>11188333
if you are good enough you learn what you are taught and then you read about this stuff on your own, which is what I did
but I agree in general historical context is usually useful when I teach others math

>>11188333
ok so i actually have some input here. i was trying to learn math historically but the thing is its actually pretty difficult. try reading most ancient texts in mathematics. most of the time stuff was explained in pure prose which makes it rather difficult to read.

we do NOT have a proper scaffolding of mathematical material. even euclid's elements is basing around a long historicity. plus euclid doesn't give much motivation for why he is doing what he does, and why he chose certain axioms. we do have results that preceded euclid but they aren't presented in a scaffolding manner and are pretty disparate. this leads on to something else that i remember getting inspiration from Hadamer about. i recall he mentioned how the reason why we are able to understand historical works is precisely because our thoughts are conditioned in historicity. but by the contrapositive, if you dont have a good grasp of the mathematics discussed by the ancients, chances are, you will understand LESS than if you were to just learn from a well written textbook.

outside of that, you need to understand that our understanding of mathematical material has improved. if you were to present someone an article containing a particular formale, you'd have to keep in mind hat you are essentially presenting a *scientific article* that's often in a style of presentation that's *unrefined* as they don't often have the perspective of whats truly important to modern mathematics. the unrefined presentation is doubled because as i said before, they could easily be using outdated notation that isn't even very enlightening. also often times in math you see very short proofs for various results but you can bet that back then proofs of the same thing could be very involved and complicated. it's adding a lot more noise back into the mathematics

>>11188557
one thing to quickly add for the second paragraph i wrote is that i recall reading some neo-pythagorean/neo-platonist expositions on mathematics, and sometimes what they'd explain is really simple, but the language takes a while to digest from the start. for instance they'd make distinction between 'even-even', 'even-odd', 'odd-even' numbers and try to give a definition from just words. if you just looked at how it is represented algebraically its far easier to parse their meaning (which wasn't that interesting anyways). for more subtle arguments presented in an inefficient manner, having a deep understanding of their modern significance becomes tantamount to understanding properly and efficiently.

furthermore, i'm beginning to think that the progression of mathematical concepts is often a very praxeological endeavour. a lot of generalization come from observing regularities in how we solve particular problems that are common to several fields of mathematics. for instance, the concept of a group was implicitly recognized in the study of permutations (both in themselves and also in the theory of equations), and also manifested itself in gauss' number theory.

the foundationalism of modern mathematics has 2 big points to consider. 1) it was only started because of people's skepticism of infinitesimals and also paradoxes 2) while intuition for limits spans back to particular sophists who preceded even archimedes, mentioning of them isn't particularly important. while the sophistic attempt at approximating the circle by increasing the sides of a polygon was probably inspired by the problem of squaring the circle, there isn't really any insight from observing that because they were quite blatantly breaking the rules of the game.

>>11188617
i think guided discovery/problem textbooks are way more enjoyable ways of learning math desu it is also predicated on a faulty notion of mathematical understanding. the phenomenological significance of mathematics makes much more sense when you see it from the point of 'know-how' as opposed to 'know-what'. for instance, the abstract definition of a topology seems rather unmotivated, but there's probably better ways to get a good feel for the definitions than reading riemann's and poincare's work lmao. for instance, you can see that particular axioms of an open set are actually very crucial for certain proofs in real function theory (for instance the proof that the limit of the point is unique implicitly requires that an intersection of open sets is also an open set. likewise, there are some proofs in real analysis requires particular inequalities that are best to understand by imagining two limit points [with a a relevant point of limit] and having neighbourhoods that we want to shrink sufficiently to get an upper bound on some function of the distances between these points. this very subtly uses the hausdorf property). keep in mind that mathematical theories are often devised to generalize certain problem solving tools to new domains of mathematical discourse so you can get a very good idea for why things are defined one way or another by just looking at the applications of them

nevertheless, if you still want to learn it i recommend Axler's 'Mathematics and Its History' or Karz's History of Mathematics: an Introduction

anyways, that's that. i have a blog documenting more of my thoughts on stuff but i dont want to post it rn.

>t. someone who has wasted hours reading math history shi

>>11188620
>i have a blog documenting more of my thoughts on stuff but i dont want to post it rn.
Post it anon. If you don't mind.

>>11188333
Nice triple dubs.

I too wish for wrestlemania mathematics curricula.

don't really think it should be taught historically and philosophically, it's more something you do yourself but it definitely should be explained better and more in depth.
A very basic example of what I want is that in first grade kids are taught to count in decimal and use the operations plus and minus. And this is their entire foundation which they work on throughout their school career until they finish high school. They can pass all the math classes and graduate without even understanding what a numeral system is believing decimal is just some kind of magical reality rule when it comes to numbers, especially since we have 10 fingers. It's simply 1 of multiple numeral systems and they should learn that. Just look at the amount of people calling computers a bunch of zeroes and ones while not knowing those zeroes and ones are binary which is another numeral system to store information just like they use decimal.

>>11188333
brraappss
brapp, braap, brapppp
b-brrraaap-p-pppp

>>11188656
i dont want to be too public w my plans on what i am doing. if you really want you can join the sci discord server and id dm if u dm me. im chika there. i am a zoomer so dont check emails

>>11188333
>Why isn't math taught historically and philosophically
...bcoz Math Professors are neither historians nor philosophers.

Its okay it took me till college to realize math is the gateway to all sciences and logic.

>>11188383
>They also tend to lack clean, efficient mathematical reasoning...
What are algorithms?

>>11188333
Because they have to teach it to engineers.

>>11189156
But it makes it easier to learn... that's his point.

>>11189147
Insufficient to cover the deficiency of the cstard’s anemic abstracting abilities, and also mostly the work of mathematically oriented CStards. Compare to physicists where they just invent new math and it later becomes useful to mathematicians, mathematicians don’t give a fuck about TCS wankery nor should they.

>>11188684
Do you have a link to the discord?

>>11188447
The obvious flaw in that thought is that maths isn’t desperately difficult, just off putting due to the zeitgeist, maths’ presentation and maths’ use of English.

>>11188333
Because people are fucking retarded.

>>11188333
Math history is not "meaningful". It is the gigantic mess of mostly failed attempts to discover and prove something. The first time some of the best geniuses on earth introduced a new concept, the concept was messy and incomprehensible and has to be modified and clarified later.
How many decades it took to Newton to painfully do his stuff and why would it helpful to students 100x dumber than him to go through all the trouble he went while they have a much more limited time?
Math teaching has to be efficient and fast, so "formal definitions, theorems, proofs" is the way to go.

>>11188333
Because ((we)) do not want children to being autists , just smart enough to make things work n feed the capitalist machine.

>>11188383
>>11189457
>CS majors tend to have little to no allegiance to science and math.
>mathematically oriented CStards.
You have to be trolling, TCS is math, and to say anything otherwise is you coping. Here is some proof https://web.archive.org/web/20060525195404/http://www.idi.ntnu.no/emner/dif8916/denning.pdf

>>11190358
>TCS is math
no it isn’t
>you’re copeing
Im not involved in pure math in any way and don’t care about what the appropriation of their history and accomplishments entails for math as a field. Its just obvious CS isn’t math, is of interest to people who are not and will never be mathematicians, and doesn’t advance mathematical research in a meaningful way.

>>11190372
CS is a subset of math.
Halting problem, decidability, lambda-calculus/combinatory logic, type theory, formal proof theory etc all belongs to CS and are 100% math, they are the study of foundations of mathematics actually.

>>11190372
>doesn’t advance mathematical research in a meaningful way.
Ok now I know you're trolling

>>11190479
>Halting problem, decidability, lambda-calculus/combinatory logic, type theory, formal proof theory
Not math, lol ggnore fag
>>11190578
If you want to do math, why not get a PhD in mathematics? Shouldn't be hard if CS is as rigorous and in depth a subject as math, physicists routinely do just that. Curious that physicists and mathematicians don't claim to be computer scientists or engineers but the converse is quite common, I wonder why?

>>11190584
>Not math, lol ggnore fag
This is objectively wrong, formal proof theory is mathematical logic, type theory is a class of formal systems, some of which can serve as alternatives to set theory as a foundation for all mathematics, and while lambda-calculus and combinatory logic is focused on CS it's without a doubt math. Mathematical logic is math, I thought that was self explanatory.
https://en.wikipedia.org/wiki/Lambda_calculus
https://en.wikipedia.org/wiki/Combinatory_logic
https://en.wikipedia.org/wiki/Type_theory
https://en.wikipedia.org/wiki/Proof_theory
>Shouldn't be hard if CS is as rigorous and in depth a subject as math
Code monkeying isn't as rigorous and deep as math that is why I specified TCS. TCS is without a doubt rigorous and in depth as math because like I've been saying it's mostly math
>Curious that physicists and mathematicians don't claim to be computer scientists or engineers
Nowhere have I claimed computer scientists are mathematicians, they aren't. Just because a physicist does math doesn't make him a mathematician. What I'm claiming is that TCS is a lot of math just like physics is a lot of math. You wouldn't say a physicist doesn't do a lot of math because he is studying the natural world so why would you say a theoretical computer scientist doesn't do a lot of math because he focuses on computation. TCS is a subset of math bro I don't know why people want to deny it so much?

>>11190628
Forgot to provide this link, it's where I got the pic from.
https://en.wikipedia.org/wiki/Theoretical_computer_science

>>11188333
Because school is trash and they have a limited amount of hours a year to teach 30 kids in the same class with various potentials and affinities so they all become service workers to pump the productivity and pay taxes.

>>11188383
CS majors are mostly bugmen with an unwarranted sense of superiority while in reality they are in 99% of the case scribes writing basic boolean logic all day.

>>11188557
I doubt he means that you would have to learn man STRAIGHT from actual ancient material but most likely put them here in context.
Calculus would benefit immensely from being taught through the ideas and life of Leibniz and Newton.
Ideas in philosophy is ALWAYS taught in the context of their era, yet mathematics somewhat doesn't need context.

>>11188333
If you were genuinely concerned about the origins of the number line as a kid, you could have researched it on your own time. School isn’t there to spoonfeed you everything, and if you just learn things by rote instead of putting in your own effort you’re going to end up fucking dying in higher level mathematics courses.
There were probably artistic or musical students who would prefer that math be taught with regards to more creative activities, but the truth is that school only teaches you the bare minimum and anybody who’s actually curious about the subjects taught in it will do their own research alongside coursework so that they can understand the foundations and implications of those subjects.

>>11188358
I'm a CS major and I love math, others don't because math is the great filter for the CS major. Without math in CS it would be far worse than it is right now.

>>11188333
They tried new math and it sucked retard

>>11188333
The people who most often learn science would rather autistically ""observe"" and then draw conclusions on their philosophy of science. It's retarded, but that's just the way it is.

>>11188333
Because the main idea of actually teaching higher level math and science is so that the kids with potential/interest for STEM can be more easily sorted out of the bunch and then possibly encouraged.

>>11188383
> They also tend to lack clean, efficient mathematical reasoning as evidenced by the belief in incorrect physical theory

Yet the entire world and literally everything in it form your entertainment, to your security, to your health even your studies is run by computers and applications we have built. Doesn't seem like anything is lacking or incorrect pointdexter. Salty lil nigga

>>11191503
>possibly encouraged
wew, where did you grow up?

>>11189702
its in the wiki anon