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/sci/ - Science & Math

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Discuss maths
Previously: >>15102029
>>
nigger
>>
>>15107772
What the fuck is the gay shit in OP’s pic
>>
>>15107772
Hello, sorry to bother you anons but if any of you could tell me if this is genuine and coherent I would appreciate it
"There is a quantum element to consciousness. This becomes evident if you have a passing interest in quantum mechanics and mathematics. The equations of schrodinger and the observer are viewed from the wrong paradigm, what is the mystical observer who's eye makes the cat dead or alive? That is where you find consciousness. The works of Lemaitre mathematically as well as the wonderful Dr. Penrose gave me real understanding, In Platos cave the shadows watching the observer and what give it consciousness. "
The context is sentience in AI. I don't have a math and STEM background and can't even begin to tell if that is bullshit or not so am asking you anons?
>>
>>15107772
Maths is gay. 99.9999% of people hate it. Maybe it's time for maths to change
>>
>>15107891
>>15107936
>>
>>15107891
>you could tell me if this is genuine and coherent
It's schizo nonsense
>>
>>15107949
Thank you
>>
Solve the following system of inequalities for the value of I
J<B
I<J
J<I
I<S
S=2(J+B)=M/10
M=X-Y
sqrt(J^2+S^2)=10nmi
>>
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>be me
>be in fourth year of degree
>half the time feel like a retard
>contemplate changing my major to something else
>feel regret at choosing math because I'm too stupid, and unemployable degree
Anyone else feel this feel?
>>
>>15108234
I is invisible
>>
>>15108234
J < I < J which can't exist so I DNE
>>
>>15109949
Set without the archimedean principle
>>
>>15108250
just be a racist and get people in trouble for being racist against you
easy life
>>
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Eight minutes, OP.
I couldn't take much more than eight minutes.
Eight minutes and eighteen seconds, to be exact.
>>
>>15107891
quantum is nonproliferation shibboleth
>I FREAKIN' HATE SIBBIE
https://homestarrunner.com/sbemails/76-sibbie
>>
>>15107891
Quantum is literally
>I don't want poo people to get the atom bomb.
Even thought poo people invented it and Oppenheimer said so.
>>
>>15110000
>quantum
>in /mg/
>>
>>15107772
NIGGER STOP MAKING NEW THREADS AT AROUND 200 POSTS THE BUMP LIMIT IS 310
>>
HELLO /MG/
Here is a problem.
It's actually 2 problems!
But they're veeery related so might as well be a single post. Anyway, in my own lovely opinion these two are very fun. As far as I know, there are a couple ways to go about solving them. What I have personally done is dumber one but the book has a really cool solution which I'll eventually share here as well so those interested see it. Anyway, please let me know what you think of these. And I hope they're clear and fun to solve. I appreciate anyone taking their time to reply, whether they have a solution or not. I think this is all I wanted to say. Anyway....good luck!
>>
>>15111645
a) [(n-1)(n-2)..(n-k+1)]^-1 * [(n-k)!]^-1
b) P = sum_k P(cycle containing 1 has length k) * (1 - [(n-1)*...*(n-k+1)]^-1)
>>
>>15111645
Easy to do with straightforward counting arguments :

number of cycles containing 1 of length k:
(n - 1) ... (n - k + 1)
number of permutations of length (n-k) :
(n-k)!
thus number of permutations with a cycle of length k containing 1:
(n-k)! * (n-1) ... (n-k+1) = (n-1)!
number of total permutations:
n!
probability of getting cycle containing 1 to be of length k:
(n-1)!/n! = 1/n
Suppose 1 is in a cycle of length k. This cycle will contain k-1 other elements, there are (n-1) choose (k-1) ways to choose these elements (neglecting order, but this is fine). If we insist 2 is one of these elements, there become only (n-2) choose (k-2) ways. Hence the probability of this cycle containing k is :
[(n-2) choose (k-2)] / [(n-1) choose (k-1)] = (k-1) / (n-1).
Taking an average over k gives probability : n(n-1)/2n(n-1) = 1/2.
>>
>>15111686
I'm afraid both of those are wrong my friend. If you wrote how you got there, we could discuss what went wrong. I'm sure it was only a small misunderstanding because I believe you can solve these problems.But regardless thanks for attempting!
>>15111886
Nice job!
Both are correct. Don't you find the results a bit....surprising? I think they're quite unexpected, especially the first one.
Anyway, the way you solved it is pretty much the same as the way I went about it. So I really recommend you take a look at the book's solutions as well which I'll probably post by tonight.
But anyway, thanks so mıuch for taking time out of your day to attempt these and good job for getting them correct. I appreciate it!

>>15111645
I would like to put this image here as well to give people encouragement.
>>
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Does anyone have the /mg/ guide with Kurisu and Kurt Gödel on it?
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>>15111483
remiCHUD
>>
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>>15112762
This one?
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>>15111361
>>15111392
>>15111394
>>15111399
I mean, we could also say that von Neumann invented it.
Or even that first light, recorded by cosmic background radiation, produced the original consciousness, and therefore antediluvian pre-consciousness invented it.
Hell, Sol invented the bomb.
Blame the glowing yellow disc in the sky.
>>
>>15107891
Quantum simply refers to writing as developed by Egypt, the possibility of correctly recognizing a written word because it is selected in a quantized way, that is, the nearest acceptable form is taken to be the actual, real, intention of the writer.
This is an idea where mind is a giant keyboard, the words are the keys, and your cognitive perception of language is a matter of dividing time into sentences and sentences into words
When writing as opposed to merely conversing, the addition level of the paragraph also exists.
Online interaction is essentially conversing, i.e. there is no culture of holding typers who submit typed messages to online forums to the standard of written paragraphs printed on paper or engraved in limestone
>>
>>15114171
You can see this most clearly in, of all places, the settings for a digital audio workstation program. The quantization settings refer to the length of beat assumed to be the intended granularity of performance, and enabling quantization means that all played notes through MIDI will be taken to have occurred at precisely the time intended as if a robot were reading sheet music...as it happens, of all people the drummer for U2 did an interview with some individuals involved in the perception of musical performance, and by and by, this guy can hear extremely minute changes in tempo expressed through the beat, i.e. this is a guy who finds it particularly painful to hear totally precise robotic performance, someone who would find enabling the quantization setting on a digital audio workstation program damaging and doing violence to the integrity of the performance
You could say that enabling quantization to, say, 1/64th of a beat simply destroys the soul of a performance, and regardless, makes it impossible to perform a waltz or any other style with a multiple of three beats per measure, such as 3,6, or 12 beats per measure, as opposed to the rather more common 4
>>
bros what am I doing wrong:
I'm trying to compute symbolic derivatives with Mathematica for a function of scalars, vectors and matrices and when I do Simplify[D[Z[W, C, F], F]] (where Z is my function), all I get is Z^(0, 0, 1)[W, C, F]. What's wrong? matrixcalculus.org works with the same expression, I just want mathematica for some further work and I can't get the first step to work
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>>15113987
yes, thank you
>>
>>15113987
is steins gate to /sci/ what lain is to /g/
>>
What is the best book on ordinals?
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do mathmeticians normally agree that 2+2=4 would be necessarily right in every possible universe?
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which of the two should i get
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>>15116939
2 + 2 = 0 in Integers modulo 2
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>>15117311
...where 4=0 as well. As does 2, for that matter.
>>
What is the best book for Pre-Calculus ? Rusczyk or OpenStax ?
>>
>>15117854
>Open books
Why do people keep falling for this meme?
>>
>>15117864
According to the web, it covers a wide range of problems popping up on math competitions
>>
>>15107891
>if you have a passing interest in quantum mechanics
>The works of Lemaitre mathematically as well as the wonderful Dr. Penrose gave me real understanding
These two things contradict each other. Reading "The Road To Reality" does not make you an expert on physics or any other topic to the degree that it lets you figure out what consciousness is. I don't want to call the guy a schizo because I'm not a psychiatrist but I'm evidently he is retarded or mentally ill in one way or another
>>
>>15117854
Rusczyk's books are great. I've never heard of OpenStax

Also
>What is the best book
don't fall for the meme of thinking a "best book" exists for anything. The particular textbook you use is never that important, as long as you pick something decently reputable they're all good enough
>>
Does anybody know of some sort of beginner quick reference guide for doing these fraction problems?
>>
x
>>
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I have a question since I am a mathlet and /g/ are bunch of freshmen implementing binary tree

I am currently dealing with Levenshtein automaton. Conceptually speaking not very difficult to grasp. It's a deterministic finite state automaton that will go into final state if the string that is input is a certain distance away from the string the automaton was constructed from.

think f('fuck')
on f which is constructed from 'duck' with degree 2, this will return true because the distance is 1
f('uck) is true, two deletions
f('cluck') is true, one insertion and one substitution

http://blog.notdot.net/2010/07/Damn-Cool-Algorithms-Levenshtein-Automata

The most relevant part from the blog is this:
"States are named using a ne style notation, where n is the number of characters consumed so far, and e is the number of errors.
Horizontal transitions represent unmodified characters, vertical transitions represent insertions, and the two types of diagonal transitions represent substitutions (the ones marked with a *) and deletions, respectively."
In this automaton, substitution and deletion are the same vector. My question is, if I modify this automaton to accept substitutions of only specific characters, will this destroy the characteristic of the automaton being able to accept deletions?
>>
>>15107772
Need to know where to start studying some topics for a test for a bunch of job openings at a bank in a month or two.
Could someone be kind enough to give me points on where to learn about probability and statistics? Jobs require only highschool level education so I figure the math need only be highschool level aswell.
Preferably books since I can read those during break times in my wagie job.
>>
what is so special about 3 dimensions
>>
>>15119394
there are three of them
>>
what's the least number of primitive notions and axioms needed to construct all fields of mathematics together?
>>
Starting a quarter term undergrad linear algebra followed by a quarter term undergrad abstract algebra. Textbooks are strang's linear algebra, and Gallian's abstract algebra. I'm looking for books that can compliment these. Have had really good fortunes by studying with two different books and perspectives rather than one so far.
>>
>>15119394
The Schrodinger equation for hydrogen has too few solutions in D<3 and too many (the ultrahyperbolic DE is a bastard) in D>3. You can only get observers in 3+1, read Tegmark.
That's physics, though. In math no particular integer number of dimensions is privileged.
>>
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Good morning /mg/.
Today I will read Serre's thesis (Homologie singuliere des espaces fibres).
I've tried learning spectral sequences from Fomenko, but remember getting confused when it came to transgression and local coefficients. Hopefully today will be better. :)
>>
is it possible to translate any problem into something whose answer can be calculated?
>>
>>15121375
>>
>>15121375
Do you mean calculated by a computer? Technically every conjecture has a numeric solution: 1 or 0, but a computers cannot prove/disprove conjectures. Any problem with a known algorithm can be solved by a computer.
>>
>>15120025
Larson's elementary linear algebra, and Dummit & Foote abstract algebra should serve you nicely as complementary books.
Don't bother with Artin. Just like Spivak, its a book overly praised entirely due to its stylistic choices in writing. Spivak and Artin are good books only if you are reviewing content.
>>
Who would win? Oiler or Yooler?
>>
>>15121380
but unknown algorithms can become known if you use a search algorithm to find them
>>
>>15121379
Isn't it already proved by church's thesis ?
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>>15121379
Gödel ate my math homework?
>>
>>15121557
(You)ler
>>
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Yeah yeah
https://imgur.com/a/Gzp2Ile
uh huh uh huh uh huh
Yeah yeah
Oh baby
https://soundcloud.com/platform/danny-tenaglia-1
>>
>>15107772
Why is the math wiki order so fucked up? The section about proofs and mathematical reasoning should be the first.
>>
I have a math exam for my first semester CS bachelor next week on Wednesday.

We'll be going over stuff like "Set Theory", "Power Series", "Integrals", "Induction & Recursion" and "Differentiable Functions".
Any tips or books to help me get a good grade?
>>
Dependent choice is enough, anything above this is fake and gay. Formalism is the right path, but if only math autists thought a bit more about what they were doing instead of just going "ahah axioms go brrrrrrrrr", people wouldn't be constantly shilling for constructivism (or worse, finitism) on this board.
>>
>>15123230
>Formalism is the right path
kys retard
>>
>>
>>15123737
Kind sir,
I humbly request you return to /mu/ at once and make a vaporwave thread in compensation for spamming and shilling your vaporwave meme.
Good day.
::tips fedora::
>>
>>15123757
>>
>>15123793
Do you mean to inform me that you have not heard the news of vaporwave's untimely death?
>>
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>>15123216
Me too brother, I think I'm getting more retarded as the time to fail the class approaches.
How do I solve this before I commit sudoku ?
>>
>>15123798
I don't know, I don't participate in low iq normie activities like music.
>>
>>15119517
>>15119517
At most:
1 axiom (the conjunction of all the NBG axioms, for example)
1 binary relation (membership)
1 unary relation ("is set")

And also equality and the axioms of logic
>>
any interesting papers on foundations?
>>
I am having my one and only business/governance class this year in my otherwise autistic CS degree, and I am literally -- not merely figuratively -- miserable from the requirements of the graded work. Shit like word count requirements, which are very much enforced (got penalized already for 15% over length), and buzzword/lingo bingo as the main "substance".
And no -- prose is not my issue. I may be a STEMlord, but at least not an e*gineer I can compose a text. It truly is just the "NPC-pipeline" model of the desired work output.

So to any math-hating business admins and HR aspirants who recreationally lurk the math general thread: I tell you, it's not too late to abort your horrific transformation into a mobile NPC platform.
>>
>>15124641
>but at least not an e*gineer I can compose a text.
but at least not an e*gineer ==> I can compose a text.
Deletion of unicode implication symbols must be an embarrassment factory on this site.
>>
>>15124580
I mean...the so-called "foundational crisis in math" was a blatant attempt to spam internationalist foundations for education philosophy.
If you take away the machine gun and ZF, there is no fucking way German nationalism gets to nazi levels of evil by 1938
It's hopeless though; these guys invented Protestantism, essentially a turbocharger for the Jesus Christ cult...the Jesus Christ cult was so prolific that Islam had to be created *specifically to assassinate Christians*
>"Oh, you think you alive, muthafukkah? No boy, you need to have faith in the LORD Jesus Christ, baby! That's the REAL life!"
Keep in mind that Christianity was already all of the worst Egyptian perversions (think Osiris) rolled up into one big rolling boulder of
>F
U
>C
K
>Y
O
>U
>>
>>15124580
fairly good chance /lit/ will know some
not quite sure where to ask
perhaps make a new thread idk
there might be a math themed one
>>
>>15107772
Modern mathematics is based on schizophrenia.
Zero isn't a number
>https://youtu.be/tgPyWMRPt_4
Infinity isn't well defined
>https://youtu.be/00YcPd3Uqk4
Limits is a hot load of mess
>https://youtu.be/cfas8oMsmVg

There was a nigger who wrote a long essay full of insults on /g/ and I couldn't reply to him because the threat got archived. "Ugh, you dumb engineer, you have to study analysis"
Fucking nigger really thinks non-standard analysis means shit
>https://youtu.be/NJyXuX4FgnI

"Just trust the experts™ Chud!!"
Fucking brainlet troons
>>
>>15124972
finitistkino
>>
>>15124978
I couldn't find any based channel other than the one posted. Do you know any other similar redpilled mathcels?
>>
>>15124978
LMFAO
He falls some faggot a fat Jew. Kikes ruined academia and wikipedia
>https://youtu.be/NJyXuX4FgnI
>>
what's the point in defining mathematical objects such as the cardinal number 1 as the class of all unit classes when that's not the definition of 1 used in everyday speech.
>>
>>15125256
because everyday speech is not formal mathematics.
>>
Why quaternions? Why not just use angle-axis? Both just use 4 values.
>>
What are some abstract algebra books that extensively talk about linear algebra as well?
>>
>>15107772
What does /sci/i think of mathjobrumors . com
>>
>>15125355
quaternions have skew field structure
>>
>>15125551
vector space is an algebraic structure
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>>15126126
...obviously.
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>>15126179
sorry, misread as you saying "why algebra books ...". please take a look at "Algebra" by Godement
>>
>>15126187
Thank you.
>>
Can I use Aluffi's Chapter 0 if I have no knowledge of Algebra (except some of the definitions through Linear Algebra)? I am not concerned about the difficulty, but the prerequisites. Also, where is Chapter 1?
>>
>>15126124
What does that mean? That you can divide them or something? I'm only 12 years old mentally
>>
>>15123798
Long live driftphonk
>>
>>15124648
TeX nigger, TeX
>>
>>15126555
Nigger TeX, nigger
>>
Does anyone have that image of the SCP-001 Gate Guardian math explanation shit? It was posted in the schizo science thread but I have lost it. I figured you autists would know better than me.
>>
Is this chart any good? (starting from the "Intermediate" level)
>>
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>>15126657
Forgot image
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>>15126657
>>15126665
no, you're better off with Halmos - Naive Set Theory and Hodges - A Shorter Model Theory
there is a real standards war here, and
~ i'm right and sexy ~
~ you're wrong and ugly ~
>>
In a formal axiomatic theory can you prove that everything provable has been proved?
>>
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I invented a new first order optimization algorithm with superlinear convergence, but it still feels like it's missing something.
>>
What's the point of defining abstract differentiable manifolds instead of viewing them as sub-manifolds of R^n?
>>
>>15126665
Kunen has a new book btw that's much better and includes much more new shit. Why people still read that old thing from the 1980s is beyond me
>>
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do they really teach Algebraic Geometry in tents in Russia?
>>
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>>15128618
I would say not usually. I mean...it's an experience
one could have compared to teaching algebraic
geometry near the picturesque, rolling hills of
the forest.
>>
>>15125355
Quaternions don't have gimble lock.
>>
>>15128618
>>15128683
Russians aren't really people. They don't vote for their leaders like we do in the West. They are just robots filled with anti-West fuel and sent out to hurt people in the West.
People in the West work hard to make sure people in Russia have freedom to elect their leaders, but Russian diaspora like pic related think their job is to put up with Russian totalitarianism and adopt a nazilike anti-Western mentality.
Google itself is an anti-Western operation targeting ordinary folks who just want to be free.
>>
>>15128618
>>15128683
When it comes to Russia, there is only on agenda item, and that goes for everybody. You don't have to be a mathematician.
That one agenda item is imposing
- Western value
- Western liberal democracy
- Market economy
- Regular elections
on Russia, the Russian people, the future of Russia, and the future of Central Asia.
Russia is development.
Central Asia is production.
Westerners are the developers, operations, management, janitors, &c.
Russians and Central Asians are the customers.
With absolutely zero political influence, how could the Russians and Central Asians be anything else?
They are pawns, passengers in history.
Maybe someday they will have the intelligence to grasp what the West is doing for them.
>>
>>15128618
>>15128683
It actually makes sense to take a von Neumann approach and advocate for attacks on Russians that refuse to promote Western values in Russia.
There is absolutely no reason to let dangerous elements get access to technology they should not be allowed to contact.
Higher education is one such critical technology that Russians should not be allowed to access until they make progress along the track of imposing Western values on the Russian people.
>>
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What would a formula for Yn+1 be?
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>>15128618
>>15128683
Good example of culture not transferring to new Russian transplants is Sergey Brin.
Here is the clip of (highly anti-social) bullying, intimidating, peer pressuring employees during a company meeting on a political topic: https://www.youtube.com/watch?v=YHz9YDp1Nm0
SB has no idea how damaging this is to the way everybody perceives Russian personal character.
NOTE
THIS FUCKING RUSSIAN IMMIGRANT SAYS HE DOESN'T KNOW JACK SHIT ABOUT AMERICAN CULTURE
HE CLAIMS HE HAS THE AUTHORITY TO IMPOSE HIS CRAP RUSSIAN VALUES ON AMERICANS!
>>
>>15128618
>>15128683
9/11 is about anti-Westerners trying to impose anti-Western totalitarianism on the West.
Don't let anti-Westerners have nice things like algebraic geometry until they accept Western anti-totalitarianism.
>>
>>15128618
As a matter of expanding the Western empire and doing so with terrorism, the faces of these young people could be put in a database kill list and sent to the CIA.
The CIA will murder these young people in order to stand up to ethnic cleansing.
It is clear that the Russian people seek to invade the USA and ethnically cleanse the American people.
>>
>>15129034
Correction: I meant to ask what the formula for yn would be?
>>
>>15129053
>ethnic cleansing
>America
Lol, there isn't an american ethnicity
>>
kind of a dumb question but can someone tell me how to derive the identity in picrel?
>>
>>15129065
America is a British colony.
The ethnicity of the American colonists is British.
Don't fall for the ethnic cleansing ideology.
You're spreading hateful anti-American ethnic cleansing ideology.
>>
>>15129068
Just expand the right side my man.
>>
>>15129073
>America is a British colony.
and a french colony
and a spanish colony
and like 20% of your population are latinos
>>
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Hey, I want to refresh my school math knowledge, so after I want to learn some linear algebra, analitical geometry, Mathematical analysis, theory of variety, theory of games to increase my IT algo knowledge and some economics skills.

I want to keep it as a hobby, so it will not be about a deep high education, just something like 1-2 hours per week, just 4 fun, so I need to have something quick and short to refresh my old school knowledge of everything first, but it should be pretty good in the same time to start some additional new math education from the list above. Do you know some online courses, videoblogs or books for it? I've taken M. I. Skanavi "Mathematical tasks pack to prepair for a technical universities" (it is my literal translation, the original english book can be another), can you recommend something more?
>>
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>>15107772
Hey /sci/, I am trying to learn math from the very foundation and, by the virtue of having some background in programming and philosophy, I'm trying to understand everything from the most abstract concepts. I've found a few /sci/ charts and decided to start with Serge Lang - Basic Mathematics(also since I've heard about that book some time ago), but even that feels like it's skipping the information that is crucial to fundamental understanding of concepts from the very beginning.
Like, the properties: associative, commutative, distributive, etc.. -- I immediately want to know why

$3 * (4 + 5) = 3*4 + 3*5$

but

$-3(4 * 5) = (-3 * 4) * 5$

Like, I know it seems obvious from the practical point of view, but it doesn't seem obvious from an abstract one: "why the change of an operator changes the behavior of the destructuring? What exact entities and functions/processes at play?"
The information that is presented as "just because" simply doesn't register in my memory.
It appears I might need to first start with category and set theory, which doesn't appear as hard I thought having looked at it for a few days, but still, I wanted to ask you anons if there any books that don't assume an advanced level of knowledge of a reader that still work through the topics in a "from abstract to concrete" way?
>>
>>15129412
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>>15107935
You hate maths?
>>
>>15107935
That's the retarded 99.9999%
>>
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>>15129412
nigger because when you multiply a number it means the same shit as multiplying the two numbers that add up to be that number and then adding them up after multiplying and any set of numbers being multiplied can be rewritten in any order because 12 groups of 3 is the same as 3 groups of 12 simple as your basically just asking really obvious shit like why can we just keep multiplying 1's to a number when its convenient or why does x equal x kind of niggerlicious that you think it needs to be proven anymore than that also 1/3 times 4 is not the same as 4/1 times 3 because the numbers place in the fraction can make a different number if you write it differently simple as
>>
>>15107847
fpbp
>>
>>15107891
no thats niggerlicious thats not how quantum mechanics works "observing a particle you change its spin" just means that in order to observe something we have to interact with it or be viewing other photons of light interact with it a particles spin is ambiguous only when its in a complete vacuum without any particles touching it and since we cant observe something without something touching that particle "observing the particle alters its spin" you silly nigger keep that esoteric nigger shit back in /x/
>>
>live with abusive family
>go into CS
>get sponsored by a company to get financial independence from family
>try to get a minor in math, sponsor doesn't allow me
>cut off family
>work for company for a few years
>save money
>apply to math grad school (MS) in my alma mater
>get rejected due to lack of math courses
>get accepted
>leave company when my contract is up
>complete MS
I'll be 29 when I start my PhD, when many start at 21.

If I could go back in time and could change one thing about my life, it's to make my family kind. It's the one thing I prayed for as a kid.
But I had to live with abusers and waste years of my life to keep my sanity.

If you have a kind family, a family that you love, that you are proud of... take a moment to appreciate them and the impact they had on your life.
>>
rational Parametrization of the unit circle: e(t)≡ (1-t^2)/(1+t^2)+2ti/(1+t^2)

Circle sum: h⊕u≡ (h+u)/(1-hu)

Group structure of unit circle: e(h)e(u)= e(h⊕u)

e(h)= a+bi, e(-h)= a-bi, e(1/h)= -a+bi, e(-1/h)= -a-bi, e(1⊕h)= -b+ai, e((-1)⊕h)= b-ai, e(1⊕(-h))= b+ai, e((-1)⊕(-h))= -b-ai
>>
>>15129456
>>15129482
Fuck off you monkeys. I'm trying to understand the "why", not the top-level instructions one follows to solve shit. If I was asking nonsense such concepts as left and right distributivity wouldn't exists, but they do, and they allow me to get a much more fundamental understanding of mathematics. Mean mid-wit cunts.
>>
>>15129412
>why
>3∗(4+5)=3∗4+3∗5
But it is the same as 9*3, another implementation, "why" is not the word here, it is "equal", "the same"
>but
>−3(4∗5)=(−3∗4)∗5
You can chose another ordering here. No mater what to calculate first.

What philosophy are you trying to find here? Also, you are trying to compare different things. I don't get it.
>>
>>15128611
You mean picrel, right? I wanted to read it but I couldn't find a pdf of it anywhere... it wasn't at the usual place
>>
>>15129533
You are not looking deep enough at each operation. As I said in my op, the practical aspects of it are obvious, but I would like to understand the nature of each operation and what properties it applies to the operands on which it is used. If you ever did functional programming, you'll understand me better in viewing each mathematical symbol as a function that performs changes on the data provided to it(such as enveloping data in a way for it to gain different attributes so that the nature of how it reacts with certain operations higher up changes) and, in turn, treats those changes as data to be provided for functions higher up the chain. It's autism, but it's my autism, so please be patient.
And my question still stands. As AIs are yet to become good enough to give book recommendations for such specific cases, I am asking this board for advice.
>>
>>15129565
>>15129529
>>15129412
Fuck it, I think this is my answer >>15126665
Thanks to anon who posted it. May your dilation be painless.
>>
>>15129529
>I'm trying to understand the "why"
You think you're being "abstract" but you're evidently several years short of knowing what that means so you're just being a pretentious dumbass

>"why the change of an operator changes the behavior of the destructuring? What exact entities and functions/processes at play?"
is a silly question. You did two different things, and you got two different results. Why would there be an "entity" at play (what even is an entity)? You're trying to pretend depth in shit with absolutely none
>>
>>15129412
You can derive the properties from the Peano axioms and the axioms of logic.
>>
>>15129606
>"what even is an entity"?
>evidently several years short of knowing
>>
>>15129650
So what's a mathematical entity?
>>
>>15129584
i can give you a philosophical answer
mathematics is based on definitions (or axioms, but theyre the same thing) where people step back and formalise observations which cannot be proven logically but are true "by definition" (technically they are synthetic apriori)
commutativity and associativity are definitions, they cannot be proven bc youre just asserting that this is possible for certain algebras then you abstract from there with theorems (then further definitions)
maybe someone will come along and "prove them" by creating more definitions, but again you ask what is the basis of those definitions and people create more definitions to back, its an infinite regress
theres no unified basis of mathematics but the basis structurally is definitions
>>
>>15129607
Thank you, anon, but the proofs only say "well, see these are equal, therefore we reach conclusion that it makes sense", they are like sanity tests, but they don't explain the why/how the numbers and operations interact with each other, they don't explain the concrete "implementations"(if you will) of the processes and properties of the operands and operators involved.
Like imagine math as a programming language(and a good case, I think, could be made to consider it as such), how would the * operator work (how would it look as a class/function)? In my scribbles above I reasoned that it would apply an "effect" on the object/entity provided to it(which is the "(10*4)" in that case), that effect would add a property of two-sided distributivity to that object which would make it behave like so:
$a * (b * c) = (b * c) * a$

The / operator, for example, does not apply that effect to the entity passed to it in the same way:
(distributivity effect only applies to the right side):
$(a − b) / c = a / c − b / c$
but doesn't work the same way on the left:
$c / (a − b) != c / a − c / b$

>>15129689
Thank you, anon, I understand that going into infinite regression is pointless, but I only wish there was a book that would start from "ok, here's the point beyond which we cannot go further(yet), let's go up the abstraction ladder now". And it doesn't seem to me like someone would need years of mathematical knowledge to read something like that, especially because one might treat numbers as objects or function instead of "just because" instructions(which I think makes it much more easier to understand and on a more fundamental level)

>>15129661
No gonna bite, use google or chatgpt if you're interested.
>>
>>15129689
literally this its just a way of rewriting shit based off of proven axioms its already been proven that using these properties simplifies and rewrites an equation there probably is some niggerlicious overly convoluted way of proving it further but nobody is going to do that or find the proof of concept because it doesn't need to be proven anon is just being an esoteric nigger monkey
>>
>>15129506
Everyone has a different path. I suffered with serve mental illness (and to some degree still do), so it took me a long time to finish undergraduate. I completed an M.S recently as well and am now going onto my Ph.D (in my early 30s). You can do it anon.

I actually had a supporting family (and they support my interest to pursue mathematics, but I just suffered with crippling anxiety/ocd in my 20s and it fucked me over. I still have it, but I think I have a better handle now.
>>
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>>15129739
this is what being overly subjective, respecting other people's opinions, not excepting the concept of something being objectively true, and thinking like a woman gets you you just start questioning why something is true and then rejecting any logical answers based off of axioms you start questioning the axioms themselves and act completely retarded in a pseudo intellectual sort of way where you reject any logical or deductive reasoning and start questioning why that reasoning works when you already know that it does since you are using it to be a retarded little faggot nigger nigger im not ready that shit nigger
>>
>>15129068
0 < a < b, so I think you can substitute all a's with b's and derive the identity from this (there are n addends)
>>
>>15129412
It is because in one case you’re considering f(x, g(y, z)) and in another f(x, f(y, z)). And since f ≠ g nothing stops them from having different properties.
>>
>>15129808
> since f ≠ g nothing stops them from having different properties

No doubt, they are different operators, I never questioned them having different properties though. I just want to know why these basic things work the way do.

> "What exact entities and functions/processes at play?"

$2 * (a + b) = (a * 2) + (b * 2)$
but
$2 / (a + b) != (a / 2) + (b / 2)$
instead the division function, by some grace of god(only right distributivity), works the same way only when placed on the other side of the entity:
$(a + b) / 2 = (a / 2) + (b / 2)$

Just because I changed the function, the entire behavior of the system changes and it the step by step process of that change that I want to know, or at least get as close to its understanding as possible.
>>
>>15129870
cuz niggers simple as
>>
>>15129870
division is essentially just multiplying by the reciprocal of whatever's under the sign. you change the order of shit, you change the reciprocal you're considering.
>>
>>15129897
sheeeeeeeeeeeeeeeeeeeeet
it all makes sense now
>>
>>15129870
ok ok I'll explain one of them since your a retard nigger incapable of thinking about shit on your own and instead need to ask other people like a woman since you need to show off how much of a pseudo intellectual faggot retard nigger you are and how big your dick is but I kind of mentioned this earlier but with 12 times 3 and 3 times 12 they both mean the same shit because imagine you have a 12 by 3 rectangle its width and its length all depend on your perspective but it does not change the area of it there thats the associative property and now imagine you have 3 groups consisting of 2 quarter eaten pies would that be the same as 12 groups (3/.25) of 2 whole eaten pies? of course not silly nigger now imagine you have 2 groups consisting of 2 + 2 apples (2[2+2]) could you, instead of saying that you had 2 groups of 4 apples say that you have 2 groups of 2 apples plus 2 groups of 2 apples yes there thats the commutative associative and distributive property explained in niggers terms for you with objectively correct axioms
>>
>>15129907
>>15129928

See, you people are still thinking about it in terms of the top-most level of "just because" instructions and images .
Of course 10 / 5 = 10 * (1/5) , I have no trouble understanding that, as I mentioned previously, but you retards seem to think me your equal for your inability to grasp mentally the shit I'm referring to. Read Plato ffs. At this point I'm just here to see how many /math/ematicians does it take to screw a light bulb and recommend me:
Abstract Algebra - David S. Dummit
Contemporary Abstract Algebra - Joseph A. Gallian
A First Course in Abstract Algebra - John B. Fraleigh

>>
>>15129940
no plato was a retard nigger too so your saying when you tilt your head and length becomes width and width becomes length the area of the rectangle(W*L) changes? If that were the case then how does geometry and objects even exist around you if they have no tangible amount of volume how the hell is using that analogy doing math like a robot without thinking about why its true what fucking world do you live in where that doesn't prove the associative property
>>
>>15129940
>why does this operator that's defined this way work exactly as it's defined???
>>
>>15129940
You're welcome nigga coma again
>>
>>15129956
Defined by whom nigger? God himself?
Ask him to define you a new brain, a good one, tell em it must work that way.
>>
the same thing that defines addition and multiplication that you have no qualms accepting the rules of, you muppet
>>
>>15129963
cowardly nigga afraid to even mention my post in his, sneed
>>
>15129972
is this better
>>
>>15129961
logic is derived from the nature of the axioms themselves not everything is subjective
>>
>>15129979
Again, never said anything about doubting how operators work. Explain the abstract processes involved in that "how" and what methods affect what entities and I'll be happy, until then, good night.
>>
>>15129020
>>15129023
>>15129029
>>15129040
>>15129050
you have a mental illness, get help
>>
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Galois theory for button-operated calculators.
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(ò-ò) (ó-ó)
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>>15129989
there is nothing abstract about it its just an efficient way of describing something like if you need to put a 60" desk in a space that is 70" wide 70-60 = 10 therefore you have 10" of extra space addition is simply fusing two values as one value subtraction is separating one value using another value multiplication is taking the number of groups and how much value each group has to find the total value of all the groups for example stacking 5 1x1x1 cubes in 4 different areas the total area would be 20 and division is giving you the amount of groups of a certain value that would make up the number you are dividing thats as far as those operators derive there is no answer that you are looking for because the "how" is already based off of the axioms just described theres nothing more to it calling the height of the stack of cubes the width and the width the height i. e. changing the order in which two numbers are multiplied does not change its value why? because god says so why do things have tangible value that are the axiom of all mathematics and dont have differing values at the same time? because god says so fucking nigger
>>
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a priori or posteriori
if priori, why is picrel wrong?
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>>15129535
libgen
>>
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>>15130000
>>
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>>15130106
https://en.wikipedia.org/wiki/Automorphism_group
>>
>>15130111
>"And then he said, 'Reverse Polish Notation model theory.'"
>>
>>15129412
I have been reading about how the natural numbers are constructed lately, so just for fun and to check my understanding, I'll try to prove to you that n * (m + p) and that (n * m) * p = n * (m * p).

>Genesis 1-1: In the beginning, God created the integers.
I'll take the properties of addition (which can be derived from Peano's Axioms) as granted, to keep things simple. So here is what I'll do: define multiplication, and then, using induction, prove the properties you mentioned. The key idea is that when we say m * n, we mean "the sum of n parcels equal to m". More precisely, for every natural number m, let $f_m: \mathbb{N} \rightarrow \mathbb{N}$ be defined as $f_m(p) = p + m$ so that $m \cdot (n + 1) = (f_m)^n(m)$, where (f_m)^n is f_m iterated with itself n times. You might argue that this is just as arbitrary as the properties I am trying to prove, but I would disagree: the definition of m * (n + 1) is just the translation of "the sum of n+1 parcels equal to m" to the mathematical language.

Now with the definition of multiplication in mind, we see that $m\cdot n = (f_m)^{n-1}(m)[\math] and thus [math]m\cdot (n+1) = (f_m)((f_m)^{n-1}(m)) = (f_m)(m\cdot n) = m \cdot n + m$. This is really the heart of the first property. Now, the proof is as follows: let X be the set of natural numbers p such that (m + n) * p = m * p + n * p for every natural number m, n. I already have proved that 1 is in X above. Then, suppose p is in X, we will prove that (p+1) is also in X:

\begin{align}(m + n)\cdot(p + 1)&= (m+n)\cdot p + (m +n) \\&= m \cdot p + n \cdot p + m + n \\&= m \cdot p + m + n \cdot p + n \\&=m\cdot(p+1)+n\cdot(p+1) \end{align}

There, I used the hypothesis that p is in X and the addition properties. We can conclude, by induction, that X = N. So we have just proved the first property. Oh fuck, I am not proving the second one, fuck it, but it just as easy.

>t. 80 iq retard
>>
>>15130148
$m\cdot n = (f_m)^{n-1}(m)$ and thus $m\cdot (n+1) = (f_m)((f_m)^{n-1}(m)) = (f_m)(m\cdot n) = m \cdot n + m$
>>
Are any of you guys like, professional mathematicians or have made a career out of math?
I kinda went NEET mode for 3 years... I ended up working part time as a deckhand on a ferry, but soon Im gonna get my bachelors at 25..
I havent been practicing much at all over those 3 years, im super rusty.
Idk what im asking exactly but I guess its how to make money off of a bachelors in math... or what u would do if you were me
People always ask me what I'm gonna do with my degree, I never know what to say...
>>
>>15129091
>>15129807
can you give me the step by step algebra of how to get from the left side of the equation to the right? its been racking my brain for like 3 days, im starting to think im terminally retarded
>>
>>15129529
pretend you are teaching addition, subtraction, and multiplication to a 6 year old. Maybe use pennies or beans. It should immediately become clear. Or, as others have suggested, you could pull your head out of your ass.
>>
>>15129091
>>15129807
you guys are both wrong you fucking retards
difference of powers requires is more involved but the easiest way is using the identity for the sum of a geometric sequence, (x^n - 1)/(x-1) and substituting x for a/b
https://proofwiki.org/wiki/Difference_of_Two_Powers#Proof_3

fuck you all, dont fucking reply to me if you dont know what youre talking about
>>
>>15129412
Yes. Read Jacobs book on categorical logic, then move on to https://ncatlab.org/nlab/show/Science+of+Logic
>>
>>15129689
definitions aren't axioms, retard
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>>15130901
Finally, thank you anon.
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>>15130903
theyre the same thing, the only difference is a matter of priority, ie axioms are "first order" definitions
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>>15130900
Expand the right side and see for yourself you dumb nigger.
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>>15129565
Nice handwriting, anon-kun desu ne.
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>>15131067
oh wait youre right its really obvious, sorry
the other guy is still a retard tho
but also i meant how id stumble upon it myself without already being given the right side of the equation, and the geometric sequence thing made sense in that respect
>>
>>15123230
>Formalism is the right path
>>
>>15130927
Definitions capture essences. They're not true or false on their own. Axioms are claims that can be true or false but can't be proven through deduction because they're prior to all other premises. Axioms can only be known to be correct through direct understanding.
>>
>>15130920
Not that anon, but I doubt you'll understand fuck all in cat theory if Basic Mathematics already filters you, kek.
Can't wait for you to spam /mg/ with even more stupid questions.
>>
>>15131166
How did he do that?
>>
>>15129412
anon, unless this is an elaborate troll post or you are INCREDIBLY interested in foundations (logic, Peano axioms, etc.) at the expense of everything else, i recommend you drop this bullshit, pick up Spivak's "Calculus" and Silverman's "A Friendly Introduction to Number Theory" and learn some actual fucking math
>>
>>15131247
Spivak's terrible. Just read an introductory analysis book.
>>
>>15131249
a) no it's not, tell me how exactly it's terrible
b) he might not be ready for analysis
>>
Jesus Christ, Statistics might be the most dreadfully boring subject in the entire planet. The whole thing is just tedious algebra.
>>
>>15131268
Nobody "isn't ready" for analysis. Off yourself.
>>
>>15129034
>>15129062
Yo? Any help?
>>
>>15129034
Substitute the last in the LHS of second.
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>>15131415
I’m not sure what you mean.
Also, I just realized for the bxn terms, should they be bxn-1 then bxn?
So for the y3 equation should it actually be: abx2 + bx3?
>>
what is a good /mg/ approved calculus book for calc I and II?
>>
>>15131637
Fichtenholz
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>>15131982
Double-approved
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>>15130093
it's only in some shitty djvu format, no?
>>
came across this on the wikipedia. Haven't seen it talked about around these parts, but i'm not mathematicianist. Maybe it's of some interest to some people of various persuasions, people always talking about self study and what not etc
>The Polymath Project is a collaboration among mathematicians to solve important and difficult mathematical problems by coordinating many mathematicians to communicate with each other on finding the best route to the solution. The project began in January 2009 on Timothy Gowers's blog when he posted a problem and asked his readers to post partial ideas and partial progress toward a solution. This experiment resulted in a new answer to a difficult problem, and since then the Polymath Project has grown to describe a particular crowdsourcing process of using an online collaboration to solve any math problem
https://en.wikipedia.org/wiki/Polymath_Project

p.s. maths is gay
>>
>>15131240
Look up Godel's incompleteness theorems. Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F and For any consistent system F within which a certain amount of elementary arithmetic can be carried out, the consistency of F cannot be proved in F itself. However arithmetic can be constructed from axioms that are obviously true and therefore consistent, for example that if equals are added to equals, the wholes are equal. Mathematical intuition is necessary to justify axioms.
>>
>>15132524
This is technically schizo-babble. Such schizoid ramblings made it into published works such as
>"The New Turing Omnibus" by A. K. Dewdney
there are countless other publications by nonmathematicians on the topic of Gödel's theorems, almost all of them heedless of ordinary mathematical practice
Quite simply, Gödel never made it into mainstream ordinary abstract mathematics as the various systems on which logic is built were not specified.
It sounds crazy, but Gödel simply never defined the prelogical systems on which logic is based, and thus never developed an abstract system of logic, in contradiction to the claims of his (snake oil) theorems.
So now we must suffer schizo babble.
You can go back to Gödel's original published articles in English. They're terrible. Awful. Embarrassing. Shocking. Alarming. Remember: this is a guy who came from the side that lost World War II, i.e. idiotic nazi dreamers.
He really was clueless.
>>
>>15132524
>Mathematical intuition is necessary to justify axioms.
You realize this is complete bullshit because no math teacher has ever asked you to justify an axiom, ever. No math teacher has ever suggested that math intuition is necessary for completing homework assignments, ever.
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>>15132562
There is no fucking justification.
There is no fucking intuition.
This is math, muthafukkah.
>>
>>15132573
>d-don't call me a retard!!!
No.
>>
>>15132379
look up djvu to pdf converters
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>>15132549
^ This is technically schizo-babble.
>>
>>15107772
Why can't I find any decent resources for finitism? Leopold Kronecker's works are in German and French. This is terrible. No mathematician published a paper disproving infinite set in English?
>>
>>15133246
The problem is mathematicians are usually just retards. They have an intuition about how to solve a problem (like derivatives being the slope of a fucking secant line parallel to the tangent we want) and they pull out the most absurd justifications to "prove" their methods. They're peak "it just werks" faggots. It's ironic how they make fun of engineers who use 3.14 for pi because "it's close enough" while they're doing the same shit (except it's worse) with their limits cope. "It's close enough to make the function continuous"
How can they argue against retarded axioms? Of course they can't, and they don't care. It's about who can pull the trick out of his hat first to solve the actually important issue. I wonder if Hobbes had the same opinions about mathematicians. He called the empiricists, experiments worshippers cargo cultists. A mystical ritual that only a bunch of wizards can do that determines knowledge and truth. Scientists and academics are such clown mfs
>>
>>15133263
>>
>>15133246
>>15133263
>t. midwit
>>
>>15132379
djvu is great
>>
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I'm a first year in uni, and I flunked the two term tests for Calculus
I can still recover with the future two tests and the final, but I'm so lost I don't know what to do.
We are now going through Reimann sums and integrals, but I still haven't gotten a grasp of "abstract thinking" or just proving things in general, none of it makes intuitive sense to me. Do I just go back to basics and hope it somehow clicks? What are some essential reads to understand how proofs, limits, etc work? Is there a calculus for retards book?
I don't want to drop the course because it will be such a waste of time otherwise
>>
>>15133388
Well, give this video a try:

>>
/mg/ is dead and its corpse defiled
long live /mg/
>>
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>>15111645
Has anyone else solved this? Or attempted? It's really not difficult!!!
It's actually very fun.
>>
>>15119393
Khan academy app is pretty good desu
>>
>>15132562
Why should I care what math teachers think? I'm not in school. If you want to apply math to real life your axioms need to be correct.
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>>15134023
retard
>>
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>>15133930
Javascripting is an important job that people get paid for and soon all flight controls and fire systems will be also be coded in JavaScript the running race is truly on for the best and brightest minds over there at google.com
>>
>>15111645
For part a:
Out of the other n-1 numbers, choose k-1 for the k-cycle containing 1. This gives a C(n-1, k-1) factor.
There's (k-1)! permutations for them in the k-cycle.
Then there's (n-k)! ways to permute the remaining numbers.
We get (n-1)!(k-1)!(n-k)!/[(k-1)!(n-k)!] = (n-1)! ways to get a k-cycle containing 1.
So the probability is (n-1)!/n! = 1/n.

I wonder if there is a more elegant way.

For part b:
From part a, we can just modify the above argument from the start when we chose which numbers to be in the cycle.
There are k-1 spots for n-1 numbers. 2 has a chance of (k-1)/(n-1) of getting in.
So we just sum up (k-1)/(n-1) for all k, then divide by n.
So that's (n(n-1)/2)/(n(n-1)) = 1/2.

Again: I wonder if there is a more elegant way.
>>
>>15107772
Learning SPSS for applied data analysis currently.
Among others we have the task to find out whether student group A consumes significantly more alcohol than student group B. Both data sets are normally distributed, so gotta use the independent student t test.
Now here's the thing, all my colleagues use the two sided p significance. Based on the way the H1 is formulated (student Group A consumes more) I think it should be one sided. They cite our prof as source but I have my doubts.
Are they all fuckwits or am I just really retarded right now?
Unfortunately it is actually relevant because one sided is below 5% and two sided above 5%.
>>
28 year old doing a math undergrad here(I'm 30 now) with an update.
Finally taking linear algebra this semester. I hope to do well as my math GPA is 3.75 so far.
Network analysis is pretty cool. I dislike taking non-math courses now. Physics II is just an annoyance. That is all.
>>
x
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>>15134023
fucking
>L
T
>C
M
>>
Are sense data talked about in principia mathematica? does anybody know what page they are on if they are talked about? It would save a lot of looking time if somebody if anybody so happened to know the answer off hand
>>
>>15132549
>this is a guy who came from the side that lost World War II, i.e. idiotic nazi dreamers.
your precious western civilization but also the barbaric soviet civilization could develop just because they've split nazi scientist fifty-fifty between themselves after WWII
>>
>>15135102
Sense-data are brought out several of Russell's philosophical, not mathematical works such as The Problems of Philosophy.
>>
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>>15134315
Hi anon! First of all, thank you very much for solving these problems. And they're both correct correct so great job!
>I wonder if there is a more elegant way.
Heheheheheh

EHEHEHHEHEHEHE

HEEEEEEEHEHEHHEHEHE
What a great question, thank you for asking it as well.
Why yes there is anon, it is given in the solutions of the book and it makes it a lot easier to solve variations of this problem.
I have attached an image that contains these solutions, taken from the book (Combinatorial problems and exercises by Laszlo Lovasz)

I hope you found the problems fun and the second solutions interesting. Thank you again so much for your time and effort solving the problems and replying to my post. And good job recognizing there might be a different solution. I hope you have a great day!
>>
Any help understanding math? I'm struggling through calc 2 at the moment.
>>
What is the probability that a standard uniform continuous random variable lies in the cantor set?
>>
uhm anyone have an operation cheat sheet? i completely forgot how to do long division and shit like that
>>
>>15135774
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>>15136046
Wrong place to ask, buddy. Mathematicians are terrible at arithmetic and all this sleight-of-hand "math".
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I don’t even know where to start with the first part of this example problem. Is anyone here smart enough to help?
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>>15131982
>>15132372
do you have another calculus book? I can't unfortunately read it as it is not in english or danish.
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>>15136046
Learn from scratch and then do a few hundred examples. There's no cheating the basics.
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>>15136301
That's not true at all. The best mathematicians in history like von Neumann, Gauss, and Ramanujan were excellent at arithmetic and numeric manipulation. It's the modern generations of retards who created this stereotype, and they contribute nothing to the field.
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>>15136301
if mathematicians are terrible at arithmetic wouldn't they need cheat sheets for basic operations?
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>>15133373
Do you know what midwit means? You realize that the infinitist approach is standard in all academia, even high school. So all these people aren't midwits because they can learn and use infinitist math? Bullocks, it goes against the definition of midwit. You're just a butt-hurt, baiting retard
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Multilineal algebra and projective geometry final tomorrow, wish me luck
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>>15136574
Every function
f1: {*} -> 1
f2: {*} -> 2
f3: {*} -> 3
Set({*}, X) = {f1, f2, f3}

maybe like this?
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>>15136690
Yes, I'm sure Grothendieck contributed nothing. Off yourself.
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>>15136695
they used to have tables for logarithms and sin, cos values
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>>15136690
When they were brain-dead children, in a time long before computers, mind you. Actual mathematics is about ideas, something that is fun, my undergrad friend. Arithmetic is just adding, multiplying, etc./performing boring operations over and over again like a robot. Nobody really cares if you're a nerd who's mastered a long-division algorithm when computers exist. Focus on doing math instead.
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>>15136690
Nah all that matters is understanding the computational efficient methods, but not actually performing them. As long as you program it, arithmetic will always be perfect*
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Hello. Does linearity apply to PDEs? I'm reading the first few sections of a Diff Eq. book, and it only touches upon linearity of ODEs.
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>>15136914
>Does linearity apply to PDEs
Yes and the same definition applies for each term.
>>
You know what I'm really happy about? The release of all these impressive large language model 'AI'. ChatGPT has essentially demolished all of my most boring work.

I'm a government mathematics wagie and I have a lot of bullshit documents that HAVE to be written and now I just have ChatGPT doing all the work while I edit it and feed it ideas. It's fantastic. Right now I have it helping me write out this organizational document explaining how our analysis division will be organized.

It basically replaces a shit ton of management types and their useless degrees since a bot can spit out all those sorts of documents without someone like myself needing to know or keep track of all the bullshit.
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>>15136879
>Arithmetic is just adding, multiplying, etc./performing boring operations over and over again like a robot.
You don't need to perform boring operations over and over again to do math, but it is almost impossible to be able to understand and meaningfully process higher math if you can't even manipulate simple numbers. That's like trying to long jump before you can crawl.
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>>15136971
Keep a copy of
- Neuromancer
- Brave New World
- Nineteen Eighty-Four
on your desk and you will not care one bit about what some government management bureaucrat says
just imagine the small talk
now
it gets better
you actually have to read those motherfuckers and talk about them with the fine folks over on /lit/
then go read Crystallizing Public Opinion by Bernays and
Political Language and Political Reality by Edelman
Add a copy of SICP and to your desk and suddenly a strange quiet comes over the office near your cubicle...then
>"He added, ::lights a cigarette:: ::inhales:: '4 Blondes' next to the obscene chia pet figurine, it looks like an anime girl taking the piss"
>"By Candace Bushnell?"
>"I know, right? It gets better. Then it was a copy of 'The Girls' Guide to Hunting and Fishing'"
>"Is it Yotsuba?"
>"No, it's Misato."
>"I'm getting the matching Shinji."
Enjoy, fren.
>>
How do i show that there are only $2^{\Aleph_{0}}$ continuous real functions?
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>>15137102
Every continuous function is completely determined by its values on dense set. In particular the rationals, so every continuous sequence can be encoded by a countable sequence of rational numbers.
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>>15137127
*so every continuous function
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Are linear spaces over finite fields ever useful?
I've only used them to construct some "interesting" groups, but have never seen them come up in anything more interesting ie. algebraic topology / geometry or such.
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Are polynomials of degree bounded by n, as a linear subspace of $\mathcal{C}([0,1])$, also a closed subspace?
I was thinking using finite-generatedness would be the easiest path and assumed $(a_nx^n+\cdots+a_1x+a_0)\mapsto(a_0,\cdots,a_n)$ might be an isomorphism, but I'm struggling with showing the norms are equivalent (or coming up with a counterargument).
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>>15137452
what is the topology/metric on C([0,1])
that's important
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>>15137452
if you don't say, then we assume
- C([0,1]) inherits the topology from Maps([0,1],Re), the set of all real-valued maps
- Maps([0,1],Re) gets the product topology
are you sure this is the topology you want
there are others, such as sup norm and L_1 norm
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>>15137496
sup norm, isn't that standardized?
>>
>stop doing math for six months
>become retarded
bruh
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>>15137504
Yes it is standardized. Ignore the retard topologist.
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>>15137504
Proving that constant functions in C([0,1]) are a closed subspace in the sup norm is somewhat entertaining.
Perhaps you should entertain us with your proof...
Post a picture for the audience, please.
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>>15137522
>Proving that constant functions in C([0,1]) are a closed subspace in the sup norm is somewhat entertaining.
Trivial. A sequence there is basically a sequence in the reals/complexes, so convergence of Cauchy sequences is evident.
Are you trying to imply that I can now "easily" proceed by induction, because I can't see it yet.
>Post a picture for the audience, please.
Idk what you mean. This just came to mind, it's not from a text.
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>>15137532
no no no
this way
given a sequence of constant functions f_n in C([0,1]) such that f_n -> f in sup norm, prove that f is constant
so just prove that the subset is closed directly, using the definition of a closed subset of a metric space (it contains its accumulation points)
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>>15137532
I think the answer to your question is yes and it shouldn't be so hard. A subspace C is closed iff every convergent sequence has a limit in C. So take a sequence of polynomials $(P_k)_{k\geq 1}\to P$. If you let $a^k_{i}, 0\leq i \leq n$ denote the ith coefficient in the polynomial $P_k$, then all you have to do is show that $P = \sum_{i=0}^n a_ix^i$ where $a_i = \lim_k a_i^k$. I don't know how to do this but it maybe isn't so hard.
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>>15137556
I wouldn't be surprised if
- it's a pain in the ass
- you have to use Lagrange polynomials
- you're shit out of luck if you don't have Hoffman and Kunze
I could be wrong, but you essentially have to show that you can't get Weierstrauss theorem, so you have to use some Lagrange polynomial equation to find a contradiction
I could be wrong
https://archive.org/details/LinearAlgebraHoffmanAndKunze/Linear%20Algebra%20-%20Hoffman%20and%20Kunze/page/n131/mode/2up?view=theater
a simpler way to open up the oyster is to say: suppose you have a limit f that isn't constant...now what fineness of epsilon do you request, in terms of what you now know about f, in order to get a contradiction
there is a definite threshold beyond which a requested epsilon size easily establishes a contradiction
what is it
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>>15137532
- are you currently taking a math course
- if so, what is it, and what text
- if not, what is your highest level of math you achieved in school and the highest degree you achieved in school
The whole
>I need help with what is obviously a math homework question even though I'm not going to mention a text
act is just fuckin' bs
even if it is true
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>>15137576
I think you need to revisit some material because you have no idea what you're talking about.
>>
Are there infinitely many prime p for which 2p+1 is also prime?
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>>15136986
>You don't need to perform boring operations over and over again to do math
Exactly. You don't have to master arithmetic and all this sleight-of-hand math. Basic arithmetic, though? Sure.
>it is almost impossible to be able to understand and meaningfully process higher math if you can't even manipulate simple numbers
And nobody made the claim people with severe dyscalculia can become great mathematicians, so this got nothing to do with the discussion.
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>>15137553
>no no no
yes yes yes
A normed linear space is closed iff cauchy sequences converge.
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>>15137971
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>>15137581
ok mr CIA agent.
I'm taking functional analysis, but I wanted to review my old linear algebra notes and stumbled upon Legendre polynomials, which I suppose can give an orthonormal system that generates bounded-degree polynomials. I wanted to review that those make a closed set.
>>
>An object is a tensor if it transforms like a tensor
Okay, list the tensor tranformation rules. You can't..?
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>>15138426
$T^{\alpha \ldots}_{\beta \ldots} = T^{\alpha' \ldots}_{\beta' \ldots} \dfrac{\partial x^{\alpha}}{\partial x^{\alpha'}} \dfrac{\partial x^{\beta}}{\partial x^{\beta'}} \ldots$
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>>15138241
okay now you sound like an attack bot
>Legendre polynomials
either that or you're trying to be cute
in all seriousness, you need to cut it out
just act like those fucking younger undergrads you hate
fuck it
act like a middle schooler
you don't need anything above middle school algebra to solve it
college analysis, yes, but only middle school algebra
it's a very simple concept:
>oh, mr. "not an n'th degree polynomial" let's find n+1 points to constrain your values on all points in the interval [0,1]
Oh heavens, mr. mathematician, anything but that!
>Well, then I'll put you in my Iron Maiden
Okay, fine, you've constrained my value along n+1 points, now what
>Now I invoke the fact that you aren't an n'th degree polynomial
::moans of pain as the function realizes its fate to be fed to an epsilon-delta contradiction argument::
>DO
IT
>FOR
HER!
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>>15138537
so, for example, if you know that a function is not linear on [0,1], then you can take two points, say 1/3 and 2/3, and you know that f is not the linear interpolation of the graph (1/3,f(1/3)),(2/3,f(2/3)) so now you have to find a point x in [0,1]\{1/3,2/3} such that f(x) is not equal to the linear interpolation, and then feed |f(x) - g(x)| where g(x) is the linear interpolation function into another function that spits out an epsilon that gives you the required N and then it's algebraic manipulatives to get a contradiction
>>
>>15138537
>>15138554
oh yeah, that works.
weirdly put, but correct.
>>
>>15138238
Thanks
>>
Is linear algebra more like a language which we apply to study different objects like curves, rotations, optimisation problems and so on and not some theory of some objects like analysis or analytic geometry?
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>>15137452
>>15137502
Obviously he meant the sup/L1 norm which are equivalent.
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>>15137504
This is extremely easy to prove
Assume P(x) is of degree n. Let a_k=k/n (k=0,....n)
Let A_k(x)= f(a_k) prod_(j!=k) (x-a_j)/(a_k-a_j)
Then A_k is of degree at most n and A_k(a_k) = f(a_k)
Consider B(x)= sum_k A(k)
B(x) is a polynomial of degree n and agrees with f(x) at n+1 points (a_0,....,a_n). Therefore B(x) = f(x) identically
Now if P_n(x) is a sequence of polynomials of degree (at most) n, which is cauchy in sup norm, then call A^n_k the same polynomials we get but now applied to P_n, we find each A^n_k converges to the polynomial A'_k = lim_n(P(a_k)) * (the product) in the sup norm. Therefore lim_n(P_n) = lim_n( sum_k A^n_k) = sum_k (lim_n A^n_k) = sum_k A'_k which is a polynomial of degree at most n.
As I said, elementary.
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>>15139183
No. Linear algebra is the study of vector spaces and maps between them.
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>>15139278
I think you were drunk when you wrote that and you didn't read it before you posted it.
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>>15139317
Mind you, I think your argument is essentially correct; I stand by my comment.
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Given N=p*q, both prime, a and b such that gcd(a, N) = 1, prove that 1 + abn ≡ 1 + bn mod(N^2).
Any directions?
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https://theanarchistlibrary.org/library/john-zerzan-number-its-origin-and-evolution
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>>15139334
isn't this an undergrad math number theory homework assignment?!?!
- what book are you reading
- are you currently taking a math class
- if so, what math class (obviously first semester number theory, but whatever...)
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every /mg/ is essentially a paean to the respect you show your math grader when you prepare your math homework now
the West is now known throughout the world as the place that infected everybody with
- the desire to have their math homework graded
- a lack of institutional support to deliver math homework grading services at a reasonable rate to a frothy market
this is why communism will die in the end: instead of grading each other's math homework, the mathematicians decided to play political games
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>>15139350
It is basically number theory, but I'm the course is actually on cryptography .
We went on a few lectures on number theory in order to learn on El-Gamal encryption. But we do get some number theory questions in the upcoming exam.
Any books you can recommend that covers this material?
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>>15139334
somewhat annoying that you don't have consistent capitalization...
doesn't look right...are we missing some typesetting here??
either that or it's a semi-trick question very early in the book
- why add 1 to both sides
- why write (?)n === (??)n mod(n^2) instead of (?) === (??) mod (n)
it appears to be a very easy question with a lot of tricks and gimmicks to make it look hard
so
yah
no typesetting issues, just simplify and chug
you guys definitely need to review middle school math for
>>
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>>15139456
Cheers man.
I got it, just needed to clarify that a = kN + 1 for some k>=0 and roll with it lol
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>determining vector scalar values for polynomial function of matrices
>no idea how to formalize it or do it as an algorithm or proof.
>just look at it long enough until it just clicks

One day I'm gonna be so fucked, but I don't think I need anything more for an undergrad linear algebra course....
>>
Which one does /sci/ prefer?
I prefer Book of Proof because it doesn't have a gay title.
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where did you learn p-adic numbers from? i tried Guillot's "Local Class Field Theory" and the presentation there sucked, had to switch to Gouvea. still not entirely satisfied, but it's miles ahead
>>
>>15139658
I prefer not reading any of these time-wastes at all.
>>
Is there any way to get rid of the hardcoded memory limit in the student version of Magma without shelling out \$1000+ for the license?

It's so annoying that my laptop runs Magma computations several times faster than the university's Linux machines, yet I can't actually take advantage of that because of the stupid hardcoded memory limit on my student version.
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>>15140829
Can you pirate the whole thing without getting in trouble?
>>
>prove wether or not the following limit exists, if so calculate its limit.
>a_{n+1} = a_n * (1 + 1/sqrt(n))
I was thinking it would converge, but can’t find any upper bounds.
Buy I also can’t seem to find any sequence smaller than a_n that diverges.
Any directions?
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>>15141029
It diverges unless $a_1 = 0$.
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>>15139983
sick
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>>15141163
Because $1 + \frac{1}{\sqrt{n}} > 1$ and therefore $a_{n+1} > a_{n}$ for all $n$ when $a_1 > 0$?
But that doesn't necessarily mean it diverges right?
Should you use induction to show that there always exists a bigger minimum upper bound?
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>>15140829
Can Magma write to a file? If so, just rewrite your computation to use an external file instead of keeping everything in memory.
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>>15139538
Every monoid is a quotient of a free monoid. This is then trivially true of the class of monoids you defined.
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>>15141476
How the fuck do you type these symbols?
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>>15141504
If you're using 4chanx it's alt+m (otherwise type [ math] [ /math]), then you can type using LaTeX.
>>
>>15141504
This board supports mathjax, an alternative version of LaTeX. You post a mathjax expression, such as \frac{1}{sqrt{n}} inside a pair of math tags (math before the mathjax and /math after the mathjax, inside square brackets).
You can do this inline and the board software translates the pseudocode into symbols for you. $\mathbb{IT'S} \; \mathbb{REALLY} \; \mathbb{NEAT}$.
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>>15141518
How do you wrap long posts in 4chanx?
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>>15141476
No.

[eqn]\frac{a_n}{a_1} = \prod_{k=1}^{n-1} \left( 1 + \frac{1}{\sqrt{k}} \right) \geq 1 + \sum_{k=1}^{n-1} \frac{1}{\sqrt{k}} \underset{n \to \infty}{\longrightarrow} \infty [/eqn]
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>>15141643
That explains a lot. I thought there would be a solution without using $\prod \limits_{k=1} ^{n-1} (1 + \frac{1}{\sqrt{k}})$ as $\prod$ wasn't used anywhere in the lectures/notes.
But it was an older exam. So maybe it got scrapped.
>>