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/edu/ - Education

'The weapon of criticism cannot, of course, replace criticism of the weapon, material force must be overthrown by material force; but theory also becomes a material force as soon as it has gripped the masses.' - Karl Marx
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 No.338[View All]

All good communists study math.

What are you studying right now? What is your favorite field of mathematics and why?

Personally, I really like the book "Linear Algebra Done Right" by Sheldon Axler. It is on Libgen if you are interested and I attached a pdf.
172 posts and 34 image replies omitted. Click reply to view.

 No.9141

>>9138
>a lot of quacks come up with "solutions" that are blatantly incorrect. All of the open problems require a lot of study to even understand
Counter-example to your second claim: Collatz conjecture (also a great example for your first claim).

 No.9154

>>9141
Do you mean to insinuate that the Collatz conjecture is misleading?

 No.9155

>>9154
How do you solve word problems with a reading comprehension like that?

 No.9168

>>9155
?
First claim in the quote you've addressed is 'a lot of quacks come up with solutions that are blatantly incorrect'
Second claim is 'all of the open problems require a lot of study to understand'

 No.9169

>>9168
I'm not that anon lol. The Collatz conjuncture is easy to understand, which contradicts the claim that
> All of the open problems require a lot of study to even understand

 No.9475

File: 1642884362013.png (19.9 KB, 640x480, plot.png)

Why is the maximum of \(\sqrt[x]{x}\) at e?

 No.9478

>>9475
f(x)=x**(1/x) => f(x)=e**((1/x)*ln(x))

f'(x)=x**(1/x)*(1-ln(x))/x**2

f'(x)=0 => 1-ln(x)=0 => x=e

x<e => f'(x)>0 \
                => max
x>e => f'(x)<0 /

 No.9480

>>9155
cute and aesthetically pleasing reaction image
i am monke

 No.9481

>>9478
Yeah that's how I found it but why is that the case?? It's very suspicious.

 No.9483

>>9481
>pose problem involving exponentials
>wtf why does e suddenly appear?

 No.9731

https://www.youtube.com/watch?v=v68zYyaEmEA

does this video have to do with mathematics
is maths the way to solve wordle the best?

 No.9747

>>9731
I don't have time to watch the whole thing, but at the beginning it looks like they just tried out every combination ever? That doesn't sound very mathy.

 No.9749

>>338
Math is the biggest waste of time

 No.9750

>>338
someone here redpill me on the concept of infinity

 No.9773

>>9750
iz big

 No.10112

are you here {}anon?

 No.10113

can we continue with you responding to
>>>/leftypol/873853 here?

 No.10114

File: 1648014604783.png (5.45 KB, 832x114, ClipboardImage.png)

>>10113
>https://www.wolframalpha.com/input?i=%7C%7B%7D%7C%3D
Wolfram is interpreting it as the absolute value and not cardinality of sets. (See pic 1)
>you can't have a set without an empty set, no?
Can you clarify this question? Are you referring to the construction of natural numbers starting with the empty set?

 No.10115

>>10113
NTA but reposting a link (archived version is available).
https://math.stackexchange.com/questions/283/is-0-a-natural-number

 No.10237

Another day I didn't study. Why do I do this, the exam session is about to start aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

 No.10404

>search page 0 results for optimization or operations research.
You're not being good central planners with this attitude.

 No.10405

>>338
Math seems like such a massive field that It would be impossible to master in a lifetime unless you have a specific interest or use it for practical purposes.

 No.11646

File: 1663122189907.png (18.11 KB, 507x140, ClipboardImage.png)

This makes me feel mentally disabled, because I have no idea where to start on solving this. What type of equation is this? If anyone could link a pdf or a video with a step by step, I'd appreciate it.

 No.11647

>with a step by step
of this type of equation I mean

 No.11648

>This makes me feel mentally disabled
You're a namefag, of course you feel that way. Drop that junk.

That's set theory, with a couple of complex numbers. I'm assuming you know what those are. If not, look it up.
I'm not great with (nor generally interested in) mathematics, but if I'm reading it right (Q = the set of rational numbers, which is normal for the blackboard-bold symbol Q, https://en.wikipedia.org/wiki/Rational_number , and the final question being what is the intersection between the set S and Q) then it's just asking which of the 6 elements of the set S are rational.
So for example, 1/3 and 22/7 are obviously rational, [pi]/3 is obviously not, and so you need to figure out if the other 3 are rational. I forget all my trig and odd/even powers of those complex fractions so someone else needs to sub in.

 No.11650

Try transforming the complex numbers into trigonometric form, they look like they will have a modulus of 1 which will make the exponentiation easy.

 No.11651

File: 1663164259594.jpg (39.83 KB, 523x666, Abraham_de_moivre.jpg)

>>11646
> a step by step

https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational
https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic
https://en.wikipedia.org/wiki/Roots_of_unity
https://en.wikipedia.org/wiki/Polar_coordinate_system#Complex_numbers
https://en.wikipedia.org/wiki/De_Moivre%27s_formula

You are asked to count the rational numbers in S. Two of them are evidently rational. π/3 is irrational, but in most contexts this will be accepted as known since the proof is non-trivial. If you can't remember the sine of π/3 take a right-angled triangle with an angle of 60 degrees and take the ratio of the opposite leg and the hypotenuse. Complete your right-angled triangle by reflection to an equilateral triangle and you will easily find the ratio to be sqrt(3)/2. For the irrationality of sqrt(3) take a^2==3*b^2 with a and b coprime, take the unique prime factorization of both sides and simply count the parity of the number of times 3 appears on each side.

For the first two values, identify them as roots of unity, a cube root and an eighth root. Recall that when raising roots of unity to natural powers you may discard multiples of the root order. Reduce 2019 modulo 3 and 8. This resolves the first value, while for the second you are left with the cube of an eighth root. Since you only need the rationality of the imaginary part you can avoid doing any computation by recalling that exponentiation by natural powers on the unit circle amounts to rotation by multiples of the base angle. Since the base angle is π/4, first quadrant, cubing takes you to 3π/4, second quadrant. This has the effect of flipping the real part sign and leaving everything else untouched, which resolves the second item in S.

 No.11679

>>10404
we're all in the /cybersoc/ thread

 No.12227

>>9475
Because
e = lim{x to infinity} (1 + 1/x)^x

 No.12231


 No.12233

>>344
That's reassuring, I guess I just need to learn linear algebra then

 No.12234

>>5504
> I like things involving theory, writing, critical thinking, etc.
That sounds like mathematics…

 No.12235

https://archive.org/search?query=subject%3A%22little+mathematics+library%22
Cute short books by Soviet mathematicians. They are based on lectures given to high school students, so they should be accessible to most of us here.

 No.12240

>>12234
WEEWOO POSITIVIST DETECTED, WE'RE HERE TO TAKE YOU AWAY FROM THE GOOD DIALECTICAL CITIZENS

 No.12251

>>12235
There are some pretty cool books in the rest of the publisher's catalog: https://archive.org/details/mir-titles
These two for example present topics in a very fun dialog style:
https://archive.org/details/TarasovCalculus
https://archive.org/details/QuestionsAndAnswersInSchoolPhysics

 No.12260

Taking Calc II at a community college.
I think i am going to switch declared major from Computer Science to Mathematics, it seems more useful for building utopia.
How important is statistics for applied math? Can I get away with just taking the upper-division level later or should I study it at the expense of vector calculus?

 No.12611

Could someone help me find out where to start with this problem? I tried to search up hints or explanations for the problem book but came up with nothing.

 No.12612

>>12611
It is pretty easy to do inductively. First you show that it holds for n=1, that's trivial. Then you say: assuming it holds for n, it will also hold for n+1. You write down the left side, rearrange it a little so that the left side of the n case is there, replace that with the right side of the n case, and verify that you have got the right side of the n+1 case.

 No.18025

>>496
Do you have the latex template for this? I would like to use this format for my own cheat sheets.

 No.18027

Is Khan Academy good up till calculus?
I'm a drop-out trying to catch up on my math understanding because it could be useful for a lot of things

 No.18222

Hello, I been looking for some calculus books and where would I go from calculus. The back ground is that I was in college to do chemistry (This shit was hard let me tell you) and I didn't do so well in my calculus course and one of the things that made it difficult was my teacher who was teaching the course. The other problem was me at this time being fresh out of high school in college without the maturity needed to be in College yet.

So I basically want to prove to myself that I can do calculus and see now that I have grown older if I can do other forms of mathematics that will eventually help me with my computer programming and with my history background being able to critically think. Any thing would be helpful to someone like me, as if I can overcome the hurtle then I can do this with the other slumps I found myself it, as it would motivate me to improve.

 No.18223

File: 1687158214938-1.pdf (2.58 MB, 197x255, VectorCalculus.pdf)

>>18222
I read these two books for similar reasons. Although in my case I can't blame it on the teacher. There might be better books, I chose these two because they are relatively short compared to other calculus textbooks and because they were written in emacs.

I am not sure about programming itself, but if you are interested in actual computer science, like the theoretical stuff, logic is the calculus of computer science.

 No.20576

Apparently trigonometry was created by the Babylonians, who used ratios rather than angles and sides
https://www.upworthy.com/amp/3700-year-old-babylonian-stone-tablet-gets-translated-changes-history-rp4-2653733786

 No.20883

It's scary how much easier calculus is if you actually know trigonometry.

 No.20884

>>20883
In Burger school you have to take trig before calculus.

 No.20887

>>20884
Oh it's the same here, and I assume that's the way it's taught everywhere, I was just too dumb to actually learn it when it was taught…

 No.20937

How are you supposed to read maths books that do not have exercises? Exercises are usually good enough to hammer the content into my brain but when there are no exercises I just forget it as soon as I am finished reading.

 No.21545

What do I need to study for operators? Stuff like "factoring an operator". I understand the analogy but I would like some justification for it.

 No.21546

>>21545
I mean what field of maths is this included in, linear algebra?

 No.21553

Can someone explain to me what "Third curvature" is, how it is different from Total Curvature (I'm not even sure about that either) and how it relates to Space-Time?


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