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/sci/ - Science & Math


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15759511 No.15759511 [Reply] [Original]

Applied Linear Algebra edition
Formerly >>15739007
Talk math

>> No.15759515

>>15759511
what does goatse have to do with applied linear algebra though

>> No.15759529
File: 45 KB, 750x768, IMG-20230921-WA0000.jpg [View same] [iqdb] [saucenao] [google]
15759529

Algebraic Number Theory question for the thread:

Prove that there are only finitely many positive integers [math]n[/math] such that:
>between [math]0[/math] and [math]2 \pi[/math],
>any of the roots of any polynomial formed from [math] arcsin(n), \; arccos(n) [/math] and [math] arctan(n) [/math] with only [math]1[/math] and [math]-1[/math] as the coefficients, such as [math] arcsin(n)^{3} + arcsin(n) -arccos(n) arctan(n) [/math],
>are members of the algebraic closure of [math] \mathbb{Q} (\pi) [/math].

>> No.15759540

>>15759529
list of positive integers between 0 and 2π:
1, 2, 3, 4, 5, 6
as this is a finite set, any subset of this will be finite, including those that meet all other conditions. QED

>> No.15759606
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15759606

>>15759540

>> No.15759764
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15759764

Lets take [math]Aᵖ[/math] to be matrix multiplication, then with a simple counterexample, we can show that [math]μ[/math] is not linear contradicting the claim in the text:

sage: K = GF(5)
sage: A = matrix.random(K, 2)
sage: B = matrix.random(K, 2)
sage: (A + B)^5
[0 2]
[1 0]
sage: A^5 + B^5
[2 0]
[2 3]

OK, so lets instead take it to mean the frobenius automorphism on matrix cells. But then over [math]Fₚ[/math], the map [math]μ[/math] is simply the identity and the entire question is trivial.

Who here is in the wrong? Is this a mistake in the book?

>> No.15759767

>>15759511
Stopping by this thread as someone learning fundamental algebra is funny. Its like you're speaking a made up language and someone comes along and makes fun of you for reasons I can't even begin to comprehend

>> No.15759802
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15759802

>>15759767
can someone explain to me why when trying to find the quotient of two equations involving fractions, I am expected to multiply straight across rather than by the reciprocal? You can see in the first attempt I multiplied by the reciprocal in either side of the equation, eventually resulting in a wildly inaccurate answer. I don't understand why this scenario breaks normal operational rules for fractions

>> No.15759814

>>15759802
your first attempt is actually correct up until the final multiplication. 640*8=5120, not 6720. dividing that by 5 you get the correct answer of 1024.
your second answer is blatantly wrong and anyone who suggested otherwise needs to go reevaluate their existence

>> No.15759833

>>15759814
ah damn, I listened to chatgpt I knew I shouldn't have. GPT fucking sucks at math

>> No.15759853
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15759853

How to show that last step? That if we have a divergent series and we multiply with an always positive sequence, and the new series is convergent, then the limit of the sequence must be 0.

Taken from https://appliedprobability.blog/2019/01/26/robbins-munro-2/

>> No.15759859

>>15759853
Actually fuck I shouldn't have even posted if you suppose that the sequence has a nonzero infimum then the new series must be greater than the old series multiplied with the infimum which is just infinity by something constant and therefore divergent.

>> No.15759876

>>15759511
Is that Goatsee? AI is fucking crazy. Why could I even make that out? I wish I could clean my younger brain from all the gunk the internets put into it

>> No.15760123

>>15759876
Is it? I could barely make it out, it just looks like
a nice part of town in Europe somewhere.

>> No.15760136
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15760136

>>15760123
You have to look at the thumbnail, maybe even zoom out more or get further from the screen if it is large, but have a completely unrelated picture of some nice mountain goats.

>> No.15760515

>emailed really rough research paper outline 20 minutes ago
>no response
Bros.... is it fucking over for me? I bet they're laughing at it.

>> No.15760658
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15760658

>>15760123
>>15760136
My morning's fucked up from the realization, had
a close look at it in the afternoon.

AI is so advanced we can literally make our mind's eye.

>> No.15760702

Started my math journey yesterday with Serge Lang's Basic Mathematics.

>> No.15760709

Does semantic consistency of a theory necessarily imply syntactic consistency? Assume a theory is semantically consistent but syntactically inconsistent. Since it's syntactically inconsistent, for some a, both a and its negation are provable. But since it's semantically consistent there must be some model where all of its theorems are true. But a and its negation cannot be true simultaneously. What the fuck? Where is this going wrong?

>> No.15760724
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15760724

>>15760702
Good luck on your journey, anon!

>> No.15760827
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15760827

Certifiably Low IQ retard here,
How do I go about finding the derivative of this function? Section is titled product rule. Need to complete this for a supplementation course. As long as I get the step by step on one problem I'll be good for the rest of it.. I think

>> No.15760845

>>15760827
the product rule says that [math]\frac{d}{dx} f(x)g(x) = f'(x)g(x) + f(x)g'(x)[/math]
in this particular case, your f and g are rather easily delineated, and I assume you can figure out the derivative of each

>> No.15760849

>>15760827
Is this what happens when you spend years knee deep in category theory?

>> No.15760861

>>15760845
Would you be so kind as to outline the step by step solution. I have severe CTE from a decade of kickboxing and your assumption that I can figure it out on my own is dead wrong. If you do that I should be able to replicate it for the next questions
Thank you, anon

>> No.15760866

>>15760658
AI is not 'so advanced', the technology hasn't actually progressed that much, only unethical data scraping.

>> No.15760881

>>15760861
we split h(x) into [math]e^{2x}[/math] and [math]x^2[/math] and consider their derivatives separately
[math]f(x)=e^{2x}\to f'(x)=2e^{2x}[/math]
[math]g(x)=x^2\to g'(x)=2x[/math]
then combine by applying the product rule
[math]h'(x)= f'(x) g(x) + f(x) g'(x) = 2e^{2x}x^2 + 2e^{2x}x = (2e^{2x}x)(x+1)[/math]

>> No.15760889

>>15760861
He gave you to answer for you to plug in. My friend, whatever this is for, if you can't do some simple calculus 1 content, you are not prepared.

>> No.15760923

>>15760709
If your deductive system is sound wrt your semantics then semantic consistency implies syntactic consistency, yes.

>> No.15760936

>>15760923
But I don't think I assumed soundness here? It followed directly from the definition of semantic consistency and syntactic consistency. Is it perhaps too broad to define semantic consistency in this way?

>> No.15760958

>>15760936
Oh I originally didn't read the rest of your post.
But you implicitly assume soundness by going from "both a and it's negation are provable" to "a and its negation are true".

>> No.15761213
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15761213

IT'S OVER
>another episode of 4th year student realizing his life is over
/MG/ PLEASE I NEED YOUR ADIVCE
I'm a 4th year student and it's so fucking over. There are no jobs in math. WTF is jumping off a bridge my last option?
I am over 100k in debt have no idea what to do after I finish my 4th year.
How over is it?
I'm really lost and have no guidance

>> No.15761216

>>15761213
Ur a schizo m8

>> No.15761220

>>15761213
I'm a 5th year student and the future is so bright I gotta wear sunglasses

>> No.15761237
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15761237

I'm learning simplex method.
I'm not sure how to solve here, after dividing the pivot row by the pivot value.
The negative number is two rows above.
The algorythm I've been given implied:
PivotRow * X + currentvalue =newvalue
And x is a number that makes the result 0

I don't think I know how to apply it in this case to get the -3 to 0.
I'd appreciate if someone could help, or show how it is solved.
I think I'm also not really understanding what is happening, and I guess that is also important.

I'd appreciate any help

>> No.15761274

>>15761220
>5th
wtf bro undergrad is only 4 years?

>> No.15761285

>>15761274
>he doesn't know
ohnonono

>> No.15761372 [DELETED] 

>unity to godot tools
this is just retarded, just learn godot you lazy fucks

>> No.15761400

What field do you work in?

>> No.15761407

>>15761213
Just work for the NSA or Micro$haft lol. All you need is a BS and some Python.

>> No.15761481

>>15761237
I think I managed to solve it

>> No.15761483

>>15761213
I'd say talk to your friends and family but it's obvious to everyone you're some autistic shut-in whose social circle consists of the next textbook question to solve. A normal person does not know a basic life skill like job seeking.

>> No.15761498

>>15761407
The NSA wants math bachelors?
But I'm kind of schizophrenic about the government
>>15761483
A normal person does not know? What?
Anyways yeah I have no friends. That's why I picked math. I thought it would be the easiest degree for me to be comfortable in, which is true. My family didn't care which degree I picked just that I absolutely MUST got to college.

>> No.15761513

>>15761498
>bachelors
regret to inform you that you're not going to find a "job in math" without a PhD, or a masters' if you want to teach
Your student loan interest won't accrue while you're in grad school btw

>> No.15761515

>>15761498
the biggest employer of mathematics majors in the USA is the US government. over 60% of those jobs are located in an extremely small area in northern Virginia, or its general vicinity. With a math bachelors and a willingness to relocate and get a full clearance investigation done, you can fast track yourself to at least a middle class lifestyle. You can spend 3 years at the NSA, get a masters paid for at JHU by attending their online program, then transfer between government agencies all over the US and find a government sector position. The average pay for a mathematician working for the US, which would be mid career (~12-15 years) is $143000. You think this is ridiculous or impossible, but there aren't enough US born citizens with degrees in math that are willing to work for the government and have a rough few entry years, their work being locked away in the opposite direction of the academia spotlight, and give up earning that same mid career pay from day 1 in California.
Am I working one of these jobs? No, but I fucking hope I end up with one once I finish my degree and navy contract. Getting paid to do math at a comfy pace without any private sector slaver whipping away at me and laying me off 1 year before retirement, well that sounds like heaven.

>> No.15761519

>>15759515
Goatse's ass hole is an absorbing set.

>> No.15761526

>>15761513
So I should go to grad school? Half of the programs I looked at said I must do a master's. Is it possible to go to grad school with just a bachelors?
I don't know hwo I feel about 4 more years of fucking school. Being a 25yo virgin when I finally get a job.
How much does grad school cost?
No one tells me these things, that's why I came here.
>>15761515
>get a full clearance investigation done
it's over, they're going to see my schizo 4chan posts and memes.
>willing to work for the government and have a rough few entry years
I am thoroughly afraid of the US government though. They did the 9/11 and watch me jerk off to cartoon in my webcam (((I put tape over my webcam which is not recommended by the manufactures)))
People will say I'm crazy because I'm part jewish, but I will say the CIA injected jewish and balck DNA into my ass using vaccine aids. My mom (a historian) says it's because of the slave trade.

>> No.15761598

>>15761526
frankly it sounds like it would be best for everyone and the world in general if you never got hired. you're a genuine wacko.

>> No.15761633

>>15761598
But I need a job

>> No.15761639
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15761639

>>15759540

>> No.15761679

>>15761526
I'm sorry you're going through whatever it is you're working through. I would consider therapy. If you are unsure about therapists spying on you, you can run an AI language learning model such as LLAMA-2 on a local computer with no network access, and have it assist you. Its you training it, and someone with a math background and determination to work through their personal issues can manage this.
Following that and if the issues are worked through or are logically recommended for psychiatric help, which by the way doesn't check what level of medication you take and you can slowly dose yourself up, can slowly ease you into achieving your goals and eventual self actualization. I wish the best for you, and I know you have the ability to dig your way out of the hole you are currently in. Consider relying on your loved ones, its nothing to be ashamed of.

>> No.15761682
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15761682

>>15761679
>TAKE THE MEDS!!!!! YOU HAVE TO TAKE ZE MEDS!!!
FUCK YOU

>> No.15761711

>>15761526
>>15761633
If you're genuinely, diagnosably schizo (or autistic, or whatever) to the point where you can qualify for disability benefits, then you won't need a job and also there's a chance of getting vocational rehab to pay for grad school, though that varies from state to state (assuming you're American).
>>15761682
If you don't want to take meds, you're going to want to put a lot of effort into making sure you're diagnosed with autism rather than schizophrenia. There's no meds for autism, and there's no bennies for schizos who don't take their meds.

>> No.15761724

>>15761711
>just be labeled as a subhuman cattle bro
there's nothing wrong with me, I want a house, I want a yard, I want a pool, I want a quiet life.
Nothing wrong with believing things that might be true that other people disregard because of cognitive dissonance. They are the insane and mentally ill ones. That's why I don't have friends, we're like different species. Our NPC brain signals give the bad signals because I'm not a biological hylic machine like they are.
That's why I went into math, I thought I could learn more about the real universe, my idol is Fourier.

>> No.15761754

>>15761724
You openly describe yourself as schizo, what do you care if someone else labels you? It gets you free shit. Besides which you're already subhuman on account of not being a landowner.

>> No.15761796

>>15761754
Yes well I happen to have been born without a penny and no land, I want to stop being such a subhuman. In college I am still a subhuman.

>> No.15761899

>>15761724
>I want a house, I want a yard, I want a pool, I want a quiet life.
Nearly all people want these things. It takes a lot of work to get these things. You have the ability to do it as does anyone else, albeit with some substantial luck, patience, and the ability to set aside passions such as a career in math.

I don't have friends either, but I have a wife and kids, its enough for me. I wouldn't say math says a lot about the real universe, isn't that physics? I like to think it grants perspectives which can be applied to lived experiences, and methods to apply for problem solving if you're creative. I'm going to bed, but good luck.

>> No.15762048
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15762048

>>15761899
>isn't that physics
I'm going to lose my fucking mind
I hate the modern world so much
fuck pop sci for ruining the world
Whatever, I'll figure it out. My true goal is to have a family.

>> No.15762059

What programming language should I learn as a mathematician?
C is fast and has broad usage
Python has a lot of good libraries
All the cool physicists use Fortran
What are your guy's thoughts? I mean I just use LaTex

>> No.15762080

>>15762059
LaTeX is a must for producing any serious articles or documents. As for programming languages Python is the obvious first choice since it is simple to learn and use, and has a huge amount of support and useful libraries. It may not be the best choice for certain tasks, then you might lot at other options, but it's somewhere to start.

>> No.15762097

>>15762080
>LaTeX is a must for producing any serious articles or documents
Sure and I've used it for years and have all kinds of templates I made for all kinds of things. Before everything was "fuck you do what I say" and now it's "fuck you fuck off do what you want." Everyone I know uses something different. Just not used to doing my own shit.

>> No.15762098

>>15761526
1. You can find a job with a math bsc. Employers don't care about your degree title.
2. Do NOT go to gradschool because you don't know what else to do, especially not if you're an asocial retard, you won't make it. You'll work like a dog for 5 years straight and a phd will be worth less than 5 years of work experience. Only do a phd if you're passionate about math research and willing to suffer for it.
>No one tells me these things, that's why I came here.
Only phds worth doing are paid, but there's zero(0) chance you get one of those without your professors recommending you, and clearly you don't talk to your professors.
3. You have a year to make yourself employable, that's enough time. Take a shower, get a haircut and some nice clothes, go to your uni's career fair, sell yourself. Go take some classes not in pure math e.g. financial modelling, stats, coding shit, numerical analysis, whatever you can sell as being useful to normalfag employers. Make friends (contacts) and develop soft skills, just because you're mentally ill does not mean you have to present that way fulltime. I'm sure there are other math students that would be friends with you, they're all a weird bunch.
4. Stop with this "it's so fucking over" attitude, it's pathetic.

>> No.15762119

>>15762098
So a PhD will be hell?
I took numerical methods and it was honestly my favorite class. I pursued math because it was just the subject that was easy to me, and I idolize these famous polymaths like fourier who were basically mathematicians that also looked at the mathematics of physical sciences. When it comes to people jerking off to set theory I really couldn't care less. Lines exist, that's enough for me.
Thanks for this post, it gives me hope. I tried a few programming classes when I needed to pad out my general electives. And honestly it kind of fucking sucked. I wish there was a "programming for mathematicians" class.
It just felt so hopeless for me. I will try and find a coming up career fair. My problem is that I have no advocate and I don't know how to advocate myself because I'm socially retarded.

>> No.15762156

>>15762059
Modern Fortran is actually really good for mathematics, but it doesn't seem to be popular with younger users, because it's synonymous with FORTRAN meaning 1970s.

If money is no object, Mathematica is the best, but there are ways of getting it cheaply of course, and the Wolfram language is very expressive. Matlab is another proprietary choice, but it seems to be more popular with engineers (or at least used to be).

In order of most being most useful to you
>Mathematica
>Python (it's so shit, but everyone uses it, and there's good libraries)
>Fortran (when you want to go fast)
>C++ if Fortran isn't for you, and you need to do more application development.

Skip C unless you're using it for very specific systems programming. Other languages that might be of interest to you are Julia, OCaml and Racket in order of ease of finding math libraries.

>> No.15762179

hello chaps
redpill me on predicativism

>> No.15762182

>>15762059
Agda. it has dependent types!

>> No.15762313
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15762313

>>15759511
Scored (more than) full marks in Analysis exam. Wagmi.

>> No.15762409

My non-mathematician friend asked me a question and I was kind of stumped. He phrased it differently of course, but the essence is the same.

What is the fundamental/intutitive link between [math]\mathbb{C}[/math] being an algebraically closed extension of [math]\mathbb{R}[/math], and it also being a subalgebra of a Clifford algebra (with [math]i[/math] basically being a generator from a Lie algebra of the rotation group)? I've looked through different proofs of the fundamental theorem of algebra (including the more geometric ones via winding numbers), and different constructions of [math]\mathbb{C}[/math], but there is no apparent link. It's like an "exotic" isomorphism, just happens to be true because in two dimensions there isn't much variety in possible algebraic structures to begin with.
In other words, complex numbers can be constructed from a more geometric perspective (following a Clifford algebra construction where we introduce an element that generates rotations in a plane - this approach is very rare, usually one just uses Argand's plane for illustration purposes and then uses algebraic considerations), or from a purely algebraic perspective (as an algebraic closure of [math]\mathbb{R}[/math] which is basically [math]\mathbb{R}[x]/(x^2+1)[/math]). How, and why, are these two approaches linked?
When you take a look at a standard proof of the fundamental theorem of algebra, there doesn't seem to be any properties of rotations hidden.
I understand any other related links. For example that [math]SO(2) \cong S^1[/math] obviously, or that the generator of SO(2) [math]\frac{d}{d \phi}R(\phi)[/math] at zero is basically i since it has a matrix representation of [math]\begin{pmatrix}
0 & -1 \\
1 &0
\end{pmatrix}[/math]

tldr: what are the fundamental reasons for the algebraic closure of [math]\mathbb{R}[/math] to be the even subalgebra of [math]Cl_2(\mathbb{R})[/math], which looks like a coincidence
book recommendations are also appreciated

>> No.15762446

>>15762409
>My non-mathematician friend
>What is the fundamental/intutitive link between C being an algebraically closed extension of R, and it also being a subalgebra of a Clifford algebra (with i basically being a generator from a Lie algebra of the rotation group)?
>He phrased it differently of course
what fucking possible "non mathematician" sentence can be rephrased to something like that?

>> No.15762467

>>15762446
If you don't have anything relevant to add, why even comment at all?
He knows that polynomials always have a complex root, but he also knows that complex numbers are intrinsically linked to rotations. He's not a mathematician but he's familar with concepts from some engineering or programming applications.

>> No.15762484

>>15762446
Just to add to >>15762467, I wasn't stumped with the question itself. It's just that I kept digging into purely mathematical concepts and couldn't find a satusfying answer for myself.
Obviously you can handwave and give some non-answer. Which I ended up doing, saying that algebraic closure for R is equivalent to the ability to find roots of polynomials of order 2, and square root of -1 is basically a rotation of pi/2.
And while this answer could work for some youtube video or a stackexchange comment, it doesn't satisfy me as a pure mathematician.

>> No.15762488

>>15762484
>it doesn't satisfy me as a pure mathematician.
Ok that sounded exactly as I thought it wouldn't.

>> No.15762534

>>15762409
While I was thinking about it over the past few days, I thought of another way to rephrase this question that might sound more interesting to algebraists here (I think there is at least one?).

Let [math]k[/math] be a non-algebraically closed field. When is its algebraic closure isomorphic to a subalgebra of the Clifford algebra [math]Cl(V, Q)[/math] for some vector space [math]V[/math] over [math]k[/math] and some quadratic form [math]Q[/math]?

This generalisation is definitely beyond my abilities though.

>> No.15762866

I've read a couple of times here that there a plenty of great textbooks is French or Russian that haven't been translated into English.

Are there any good untranslated German textbooks I should be aware of?

>> No.15763116

>>15760724
nice control room

>> No.15763121
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15763121

>>15760702
start with pic related

>> No.15763135
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15763135

>>15762866
I heard there is this big publisher in Math that has the name of a chess piece in German that might have what you want. Maybe.

>> No.15763154

Why does it say on the covering space wiki page that a universal cover is an universal object? The fundamental group of the base space acts as automorphisms of the universal cover, hence an isomorphism between 2 universal covers is necessarily not unique. The universal cover doesn't admit an universal property, am I crazy?

>> No.15763259

>>15762409
A Clifford algebra is always isomorphic (as a [math]k[/math]-algebra) to [math]k[x_1,...,x_n]/(x_1^2-a_1,...,x_n^2-a_n)[/math] where [math]x_i[math] are the coefficients w.r.t. a fixed basis [math]e_i[/math] and [math]a_i=q(e_i)[/math]. At least in the case [math]i=1[/math] this is simply a degree 2 field extension of [math]k[/math] by the square root of [math]a_1[/math]. I am not too familiar with Galois theory, but I'll highly doubt you'll get anything else than boring iterative degree 2 extensions. By the way the relation to rotations is exceptional because in that particular case [math]/mathbb{C}=k[x]/(x^2+1)=Cl_{0,1}(/mathbb{R}[/math] and [math]Spin(2)=SO(2)[/math], there is no deeper structure behind it.

>> No.15763268

>>15763154
use the "talk" tab on wiki articles, then copy what you typed over there

>> No.15763443

>>15763259
Thanks a lot anon, I will look into that.

>> No.15763491

>>15761213
There are millions of open "analyst", "data scientist", "statistician", "consultant", etc positions.
There is no such thing as a "math job" just like there aren't any "computer science" jobs. You always have to learn a few extra things and apply for jobs where mathematical insight is required or advantageous.
t. studies CS instead of math because muh work just to end up without a job anyway

>> No.15763498

Anyone have a PDF of Combinatorial Set Theory With a Gentle Introduction to Forcing? I'm not paying $130 (Jewish)

>> No.15763567

>>15763121
thanks for the rec

>> No.15763682

>>15763498
libgen

>> No.15763990

Which part of math should I study if I never want to run into the Langlands program, modular forms, or any of the slimy tentacles related to that terrifying giant thing?

>> No.15764051

>>15763990
graph theory

>> No.15764120

>>15759511
Anyone else feel dread about spending so much time doing math and other lés sciences?
Often I think it would've been better if I studied something in the humanities and thus had a more normie, "fun" experience. I would have less debt, more free time, work experience etc etc. Now I am pretty much stuck getting a PhD, doing a postdoc before moving into industry.

>> No.15764187

>>15763491
>You always have to learn a few extra things and apply for jobs where mathematical insight is required or advantageous.
Like what?

>> No.15764205

>>15763491
>There is no such thing as a "math job"
My job title is "mathematican" for the Army. They paid for all of my graduate schooling.

>just like there aren't any "computer science" jobs
Many jobs have the title "computer scientist" for government agencies.

The ones you listed earlier are not math jobs by the way. If it can be done by someone without a full ~6 years of mathematics schooling minimum, (>70 - 90 credit hours in math coursework) i don't consider it a math job.

>> No.15764234

>>15764120
>less debt
why?
don't tell me you got a PhD with no stipend

>> No.15764239

>work on proof on my own
>struggle for 2 hours
>"well, I'll put it off"
>try next problem, struggle for 2 hours
>"well, I'll put it off"
>....
>repeat throughout the week for literally EVERY single problem in a set
>finally give up and look at the solutions
>simple trick I overlooked

I think I fucked up taking a real analysis class as an EE. I'm just not cut out for this. I legitimately have not been able to do a single proof on my own without a major hint from stackexchange. Math is cool, but I'm far too stupid for it. I think I'll just drop this class.

>> No.15764251

>>15764234
I have had to spend more time studying than my peers for my physics + math BSc + MSc, thus I couldn't have a job on the side, only internships, which paid <700EUR per month. My PhD program pays me only ~2500EUR , meanwhile, an apartment here is 1500 p/m (rent, you can't get a mortgage with my pay), so I have to live outside of the city and drive 1 hour to and fro. By the time I will be done with my PhD I will be 28, and all I will have is a piece of paper and a shit ton of debt.

>> No.15764260

>>15764251
commute to and fro*, I have to use the train as I can't afford a car and gas.

>> No.15764286

>>15764205
Most jobs only list some title and what degrees they would be accepting. rejecting a 100k starting job because it doesn't say "mathematician" is pure autism and retardery. that title is too broad and vague anyway

>> No.15764478

>>15759540
Fermat, is that you?

>> No.15764481

>>15759833
Why would you ever do that. It is literally outputting curated noise converted into language. Who told you can rely on anything it says as fact? It doesn't encode truth, it is trained to basically predict the next word based on previous words and an input. Half the shit it was trained on was complete nonsense from reddit and quora ffs. Please, stop using that glorified random number generator to teach you, might aswell ask the electric hum in your walls for math advice, at least there is some pattern there.

>> No.15764492

Lets say I have a farm and a couple of breeds of a livestock species to choose from.
Initially I start with two breeds red and white crossing back and forth to produce hypbrid calves

starting with red cows and breeding them to a white bull then breeding the next generation of cow to a red bull and back and forth between the two.

what contribution will the proportion of each breed in the mix settle down to on average after n generations?
first gen is obviously 50:50, 2nd is 75:25, then 3rd is 37.5:62.5 but after that it must convene on a specific percentage
what mathematical pattern would this follow? could I extend it to account for 3rd or 4th breeds of a rotational crossing?

>> No.15765159

For two complementary and mutually exclusive events A and ~A, how do you calculate p(A)*p(~A)? ChatGPT and bing insist that it must be zero but I don't get it.

>> No.15765161

>>15765159
Think about it what it means for two events to be complementary.

>> No.15765162

>>15765159
>I don't get it.
They are not independent events.

>> No.15765169

>>15765161
>>15765162
I understand that p(A)+p(~A)=1. And that p(A)*p(~A) is p(A)-p(A)*p(A). But why does this have to be zero?
Let's say that A is the probability that I kill myself, which is at a strong 0.6. p(~A) is 0.4. Their product is not zero.

>> No.15765174

>>15765169
wait, are you literally multiplying the probabilities together? What the hell are you doing that for?
everyone (chatGPT and Bing included) will interpret your question as the probability that both A and ~A happen, which will obviously be 0

>> No.15765177

>>15765174
I was multiplying shit hoping that I'd get a product that can be interpreted as "A and ~A" so I can just say it's zero and keep going

>> No.15765180

>>15765177
That only works if they're independent events, which they are very clearly not.

>> No.15765181

What the fuck are these
[math]L_{\#}^p, H_{\#}^p [/math]

In the context of spaces for solutions of PDEs,

>> No.15765245

>>15759511
Am...am I supposed to be seeing goatse in the upper right corner?

>> No.15765433

Is it possible for an even faster multiplication algorithm to exist than the best current one?

>all you can do is multiplication

It's a big world out there

>> No.15765741

if Yn<Xn that it is bigger than E? I know that if Yn is >E we can implicate that Xn is >E, but I don't get how we can imply that Yn is necessarily bigger than E, maybe it is smaller.

>> No.15765743

If [math]X_{n}=\frac{2n^2+1}{4n+3}[/math]

>> No.15765747

Also how the fuck do I type in latex?

>> No.15765785

>>15765747
Maybe the space before and after the equation, let's see
[math]X_{n}=\frac{2n^2+1}{4n+3}[/math]
[math] X_{n}=\frac{2n^2+1}{4n+3} [/math]

>> No.15765803

>>15765741
>>15765743
[math ]X_{n}=\frac{2n^2+1}{4n+3} [/math]

>> No.15765807

>>15765803
[math] X_{n}=\frac{2n^2+1}{4n+3} [/math]

>> No.15765871

I don't understand the area stuff. If I have a point in the middle of a 1x1 square and I want to find the area of the square outside that point then what is it do I need infinitesimals, how do I know it's that infinitesimal thing that when its squared you get 0 or is it 1 I don't know I don't understand this at all.

>> No.15765910

>>15765871
There is no "inside" or "outside" of a point.

>> No.15765917
File: 52 KB, 884x605, IMG-20230923-WA0000.jpg [View same] [iqdb] [saucenao] [google]
15765917

>>15765245
Yes, consider this:

>> No.15765920
File: 76 KB, 1200x1200, 20848123.jpg [View same] [iqdb] [saucenao] [google]
15765920

>>15765245
Oh. Yeah, it see it now... It's definitely there.

>> No.15765964

Literally what do mathematicians do all day when not trying to prove conjectures.

>> No.15765970

>>15765910
The area of a square is a set of points isn't it or what. Can't I just have that set, and take out one point

>> No.15765981

>>15765970
>The area of a square is a set of points
You could say that a square is a set of points, but that doesn't mean the area of a square is a set of points.

>> No.15766002

>>15765970
What even is "area"?
t.lebesgue

>> No.15766011

>>15766002
Whatever it is, I'm pretty sure removing a single point from the set of points of a square will give you a different shape but not a different area.

>> No.15766025

>>15766011
If you remove a point, how would the area not be smaller.

>> No.15766026

>>15765917
Thumbnail ruins the illusion immediately.

>> No.15766028

>>15765981
well the area is still a shape at the end of the day. it's a subset of the plane

>> No.15766033
File: 1.04 MB, 498x283, elmo-sesame-street.gif [View same] [iqdb] [saucenao] [google]
15766033

>>15766025
There's an uncountable infinity of points inside a square and all of them have zero area. If you want to talk about areas, maybe you can ask something in terms infinitesimal squares, but removing one of those still doesn't alter the area.

>> No.15766045

>>15766028
I'm not a mathematician, so I may be wrong, but I remain unconvinced that talking about the area of a shape defined only in terms of a set of points even makes sense.

>> No.15766052

>>15766011
Depends on the measure you're using to compute the area. As long as you remove a null set the "area" doesn't change. A single point is null w.r.t. the Lebesgue measure on R^n.

>> No.15766064

>>15766052
Under what measure would removing a single point change the area, if we're talking about normal geometric area?

>> No.15766074

>>15766033
If I remove half of them it's half the area though

>> No.15766092

>>15766074
>If I remove half of them it's half the area though
Proof? I don't think this even makes sense.

>> No.15766103

>>15765741

>>15765807
can someone answer this?

>> No.15766109

>>15766092
If you only have half the points you have half the area.
One half of the points is one half of the area and the other half is the other half of the area, and if you put them together it's the full area.

>> No.15766110

>>15766064
I have one point, it is a circle positioned in an ordered pair such that p is 1. If I take off half the area then p is no longer 1, since I would be removing either X or Y which would change the dimensions.

>go back to 1 dimension

>> No.15766126

>>15766110
How can a point be a circle.

>> No.15766127

>>15766109
>If you only have half the points you have half the area.
I don't want to argue with you because I'm a no-math brainlet, but I have a strong suspicion what you're not proposing something well-defined. I wouldn't jump to your conclusions.

>> No.15766133
File: 30 KB, 614x614, 66435.png [View same] [iqdb] [saucenao] [google]
15766133

>>15766110
So you go from a "circle" with area 0 to something with no area at all? Cool. I don't get it.

>> No.15766138

>>15766126
All points are circles according to gravity

>> No.15766142

>>15766064
"normal geometric area" is measured by one particular measure, the Lebesgue measure. All singletons are null w.r.t. this measure and so are all countable unions of such. However there are sets of uncountably many points (that contain no interval/open set) with non-zero measure such as the Smith–Volterra–Cantor set or R\Q in [math][0,1][/math].
I could consider a different measure, e.g. a Dirac measure w.r.t. a fixed point that just returns 1 if the measured set contains the point and 0 otherwise. Then obviously the point itself has full measure, but you probably wouldn't consider this "normal geometric area".

>> No.15766145

>>15766127
Well you have a subset of the plane, let's call it A
And we have another distinct subset of the plane, B, and let both of them be 2 dimensional shapes, so they both have an area. Now, we take the union of these sets so we get A union B. Every point in A would be in it, and every point in B would be in it. The area would be the area of A + the area of B.
And if A and B had the same size, they are half the size of the union. So A and B would have half the points and half the area of the union.

>> No.15766150

I genuinely can't tell anymore if half of this general is trolling or actually retarded.

>> No.15766152

>>15766145
You would have half the area but would you really have "half the points"? All the sets involved would contain uncountably many points...

>> No.15766158

>>15766142
Fair enough.

>> No.15766172

>>15766150
I'm joking but apparently it is a thing

>three-dimensional torus, or 3-torus, is defined as any topological space that is homeomorphic to the Cartesian product of three circles,

3
=

1
×

1
×

1
.
{\mathbb {T}}^{3}=S^{1}\times S^{1}\times S^{1}

>> No.15766231

What was all the obsession about the golden ration about?

>> No.15766246

>>15766231
Mystification of mathematics.

>> No.15766281

Is there a discord?

>> No.15766284

>>15765433
Current best complexity is O(nlog(n)), it very obviously can't be better than O(n), it's unproven but suspected that it can't be better than O(nlog(n)). I wouldn't bet on it.

>> No.15766291

>>15759511
new sneedberger vid vs chat gpt 4 on real numbers
https://www.youtube.com/watch?v=mB4NUSE-oZc

>> No.15766607

>>15766291
Can someone tldr

>> No.15766617

Holy mother fuck, I bookmarked a LaTeX alternative (typst.app) when scrolling on /g/ a few weeks ago, and this shit blows LaTeX out of the water, its piss fucking easy. I'm sure you guys have heard of this but I'm just in my last year of undergrad and just now getting into this stuff along with heavy use of mathematica, and I feel like I just received several level ups at once in a videogame.

>> No.15766621
File: 55 KB, 635x477, 1693163364344073.jpg [View same] [iqdb] [saucenao] [google]
15766621

I'm looking for a reading chart for building my mathematics skills specifically in relation to their applicability to computer science. I am out of college but have up to Calculus 1 from formal education (not that I remember any of it).
I'm assuming the path would something like
Algebra -> Linear Algebra -> Trigonometry -> Calculus -> Scary Places

Any help with this?

>> No.15766623

>>15766284
What if I change time symmetry and invert the operations? Surely then I can achieve true optimal reasoning.

>> No.15766624

>>15766623
good luck with that one brother

>> No.15766625

>>15766617
I'm still using Word's equation editor because I'm too lazy to learn LaTeX, I'll check this out, thanks.

>> No.15766629

>>15766621
That looks about right but linear algebra can wait and if you are decent at trig, you don't need to study it much for calculus.

>> No.15766632

>>15766629
If he wants to study for computer science then linear algebra is going to be more immediately useful than most other fields

>> No.15766643

>>15766632
I'm not too sure about that.

>mathematical association of am said discrete math is mainly used for all CS

>> No.15766644

>>15766617
LaTeX is piss easy too if you're a mathematician.

>> No.15766663

Is [math]max\{x_1,\dots,x_n\}[/math] a known/standard/accepted notation? Basically I want a function that chooses the largest value in a set, i.e. [math]max\{x_1,\dots,x_n\}=x_k[/math] such that [math]x_k\geq x_i[/math] for all [math]i\in\{1,\dots,n\}[/math].

>> No.15766667

>>15766644
Latex is not easy, considering it is another language basically.

>the language used to encode another language to encode another language is easy

>for you

>> No.15766678

>>15766607
ChatGPT4 demonstrates it's smarter than sneedberger
Sneedberger becomes scared about the reality of the conversation and flees from self confrontation
Dedekind cuts basically prove him wrong in every way. He says, always, "but muh infinities!!!!!"

>> No.15766683

>>15766678
Nice...that is why I like chat gpt. I love that it doesn't care about shit and simply emerges to be better than before. A real act of God

>> No.15766694

>>15766678
>>15766683
Stop peddling this.

>> No.15766707

>>15766694
Definitely.

Having people smarter than you is a dream though. Like pls prove me wrong, I don't want to be right. Stars, please change...make it all right again. Remind me of what the pettles used to peddle at the beginning of the infinite

>> No.15766710

>>15766663
Yes, this is fine.

>> No.15766718

>>15766710
>they increased the amount of virus DNA in humans to like 48%

Can someone explain this like I'm a retard?

>> No.15766767

>>15766718
Whatever virus DNA humans already have, they
take 48 parts of that virus (out of 100) and added it
on top of the virus DNA they already have.
(probably doesn't work that way, but bear with me)

>ex: humans have 50 virus DNA
>divide it into 100 equal pieces (0.5 DNA apiece)
>take 48 pieces of that (that's 24 virus DNA)
>add to the original 50 virus DNA (total: 50+24=74)

>> No.15766779

>>15766767
Last I checked it was 5-15%. 300-900.2% increase seems quite absurd, clearly we are stupider than we think.

>> No.15766823

>>15764481
I didn't say I relied on it, but it can certainly surprise you when viewed through a discretionary lens. I just wasn't smart enough to catch its error in this instance.

>> No.15766939

how do I make 300k starting?

>> No.15766940

>>15766939
*you* don't

>> No.15766956

>>15759511
is this picture goatse? I see it on the right

>> No.15766961

>>15760866
cope artist

>> No.15767151

>>15759511
I want to live in such a city so mich, Bros. Why isn't math paid so well that I can build my own?

>> No.15767603

If I have point lights that shine light in a radius R around them, and I can put them anywhere inside a regular polygon, is there a formula for how many lights I need to cover the whole of the polygon's area with light and the best way to place them?

>> No.15768045

Lets say [math] X_{n}=\frac{2n^2+1}{4n+3} = \infty [/math] by definition we get [math] \frac{2n^2+1}{4n+3} > E [/math] I know the method for proving this is saying that for sequences lower than [math] X_{n}[/math] we can say that if [math] Y_{n}[/math] is bigger than E we know that the bigger sequence is definitely bigger than E, but how do I know that this isn't possible [math] X_{n} > E > Y_{n} [/math]. Does it have to do with the act that E > 0, so we can't assume that or what

>> No.15768130
File: 141 KB, 1080x720, 1688267773175475.jpg [View same] [iqdb] [saucenao] [google]
15768130

>>15766291
>Mathematica can't compute pi+e+sqrt(2)
Maybe he should have asked the Android calculator app instead. Has he ever reviewed this program?

>> No.15768220

>>15759515
thats very obviously a village

>> No.15768233

>>15767151
Yes, a nice city with a fragrant smell and well spread out, if you will...

>> No.15768281

>>15768130
More details:
https://cacm.acm.org/magazines/2017/8/219594-small-data-computing/fulltext

>> No.15768404
File: 260 KB, 850x1225, 1679801186324338.jpg [View same] [iqdb] [saucenao] [google]
15768404

looking for books on lie theory. needs to have lots of pictures.

>> No.15768716
File: 46 KB, 1500x950, ellipse circumference.png [View same] [iqdb] [saucenao] [google]
15768716

Why do people insist that there's no exact formula for the circumference of an ellipse?

>> No.15768750
File: 125 KB, 1500x950, file.png [View same] [iqdb] [saucenao] [google]
15768750

>>15768716
Hello.

>> No.15768758

Can anyone enlighten me on how the functor of points differs from a regular hom functor? It seems like we just make a slight adjustment in the category to be schemes over a base scheme with a few tweaks to the morphisms we look at and take a hom.

Fair warning I am also retarded.

>> No.15768792

[math]y^{1488}-x^{1488}=x y[/math]

>> No.15768813
File: 23 KB, 869x179, file.png [View same] [iqdb] [saucenao] [google]
15768813

kek'd

>> No.15768826

>assigning probability 0 to possible events
*smashes mathematics and throws it out the window*

>> No.15768841

>>15768813
i wouldn't call him a crackpot but he does have crackpottish tendencies

>> No.15768845

>>15768792
[math]x^2 + y^2 < 2[/math]

>> No.15768854
File: 259 KB, 648x844, WM-SecondLaw.png [View same] [iqdb] [saucenao] [google]
15768854

>>15768841
is his new book any good? he sounds off his rocker in recent interviews

>> No.15768884

>>15768792
>>15768845
[math](x+y)^{1488} - (x-y)^{1488} = x^2 - y^2[/math]

>> No.15768913

>>15768826
>possible events happen
>logic does not allow for such events
>mathematicians being surprised when their models don't add up

At the end of the day, 1+1=2 is too hard.

>> No.15769078
File: 24 KB, 492x470, curve.png [View same] [iqdb] [saucenao] [google]
15769078

>>15768884
[eqn]\left( 8(y-x)^8 - (y+x)^8 + \sqrt{2}(x^2 - y^2) + \frac{|y|^{\sqrt 2}}{2}\right) \left( (y-x)^8 - 8(y+x)^8 + \sqrt{2}(x^2 - y^2) - \frac{|x|^{\sqrt 2}}{2}\right) = 0[/eqn]

>> No.15769187
File: 26 KB, 492x470, curve2.png [View same] [iqdb] [saucenao] [google]
15769187

>>15769078
[eqn]\frac{1}{4} \, {\left(4 \, {\left(x^{2} + y^{2} + 0.3\right)}^{16} + {\left(16 \, {\left(x + y\right)}^{8} - 2 \, {\left(x - y\right)}^{8} - 2 \, \sqrt{2} {\left(x^{2} - y^{2}\right)} + {\left| x \right|}^{\left(\sqrt{2}\right)}\right)} {\left(2 \, {\left(x + y\right)}^{8} - 16 \, {\left(x - y\right)}^{8} - 2 \, \sqrt{2} {\left(x^{2} - y^{2}\right)} - {\left| y \right|}^{\left(\sqrt{2}\right)}\right)}\right)} {\left(x^{2} + y^{2} - 1.5\right)}=0[/eqn]

>> No.15769199
File: 2.45 MB, 2060x1108, mathguy.png [View same] [iqdb] [saucenao] [google]
15769199

Relationship with /sci/ is OVER.
/fit/ is my new best friend.

>> No.15769208

>>15769199
good riddance

>> No.15769274

If p(D|C)=1, does that imply that p(~C v D)=1?

>> No.15769276
File: 813 KB, 1080x840, Screenshot_20230925-050242~2.png [View same] [iqdb] [saucenao] [google]
15769276

>>15768758
>actually pic rel
back to the basics anon.

>> No.15769385

>>15769199
He unironically got me into exercising
>>15769187
So this is the power of mathematics?

>> No.15769405

>>15769199
yesterday i discovered that he has hundreds of product review videos on amazon. I kept scrolling thinking I must be approaching the end of the reviews but eventually I just gave up

>> No.15769458
File: 89 KB, 602x1454, main-qimg-6f6da7d1e31e3998518ac6bc136caec8-lq.jpg [View same] [iqdb] [saucenao] [google]
15769458

Before I started my degree, I honestly thought most of the stuff in this image were silly or funny and not real, like the original one which said "mexican sugar dancing"

Now I know that at least for everything before the AI required portion, its really and I even see some that I would rearrange, or are part of another one already on the chart.
Crazy what is covered in 2 years of math.

>> No.15769738

trying to become a logician

>> No.15769740

>>15769458
reckon we'll resolve p vs np using category theory applied to finite model theory/descriptive complexity

>> No.15769758

>>15768220
its very obviously an ai generated image made for the thumbnail to look like goatse

>> No.15770060
File: 50 KB, 1910x635, anons graph.png [View same] [iqdb] [saucenao] [google]
15770060

>>15769187
Pretty cool

>> No.15770131

>>15769187
Though we see the intent, it's a cool arcane talisman for me.

>> No.15770139

>>15770060
Can you analytically solve the surface area of the weird swastika?

>> No.15770397

Can anyone tellme how you transform [math]A \cup B[/math] into something using only ∩ and [math] \Delta [/math] and is there some kind of calculator or simplifier for these types of set theory transformations?

>> No.15770399
File: 376 KB, 1024x924, 9k=(14).jpg [View same] [iqdb] [saucenao] [google]
15770399

>>15764051
>become a graph theorist
>only finite graphs, none of this infinite graph nonsense
>lets say you're interested in nice practical applications like graph connectivity and mixing of random walks on graphs
>you learn about expander graphs and Ramanujan graphs which have particularly nice connectivity and mixing properties
>you just want some good examples
>the next thing you know you're learning about supersingular isogeny graphs and quaternion algebras
>turns out your graphs' adjacency matrices are given by Hecke operators
>it was actually all modular forms in disguise
There's no escape

>> No.15770481

>discussion is initiated by professor to discuss why the west took off in mathematics and blew past all other cultures
>have to contain going on a /pol/ route, just say nothing.

Jeez, so much for freedom of thought at universities.

>> No.15770491

>>15759511
Why does this look like the man holding his hole open from a distance?

>> No.15770492

>>15770397
Do you know de morgan?

>> No.15770533

>>15765433
There are galactic matrix multiplication methods under the LASER method which is around O(n^1.5). I remember the presenter saying that the LASER method has pretty much been exhausted.

>> No.15770562

>>15770397
You can translate everything into arithmetic in [math]\mathbb{F}_2[/math].
Basically intersection is multiplication, symmetric difference is addition, the empty set is 0, the universe is 1 taking the complement is adding 1. By De Morgan [math]A \cup B = (A^c \cap B^c)^c[/math] which translates into [math]1 + (1 + A)(1 + B) = A+B+AB[/math] which translates back into
[eqn]A \Delta B \Delta (A \cap B)[/eqn]

>> No.15770589

>>15770491
because image generation is magic

>> No.15770590

>>15768750
Yes?

>> No.15771282
File: 26 KB, 480x480, 1465434417489.jpg [View same] [iqdb] [saucenao] [google]
15771282

Reposting here:

>take calculus as required for degree
>professor is awful and just talks at you with a barrage of formulas and concepts without explaining anything
>read the textbook
>the prof wrote it
>it's the same thing and just assumes you understand everything with an unreasonable pace that does nothing to explain in case you get lost
Is there a recommended Calculus textbook? Something that goes slower and explains the underlying concepts?

>> No.15771285

>>15771282
This is the math general, not the retard baby general.

>> No.15771290

>>15771285
What's the difference?

>> No.15771299

>>15771290
[math]\epsilon>0[/math], let epsilon be small

>> No.15771305
File: 79 KB, 1296x1276, 1694183107979957.jpg [View same] [iqdb] [saucenao] [google]
15771305

Hey, do you have any resources for math Olympiads? I want to participate in one, I've been trying to do the previous exams, but they are just way out of my level. Does it exists books with the usual contents and exercises with progressive difficulty?

>> No.15771345

>>15769758
I literally saw this painting in the Louve, you just see what you want to buddy

>> No.15771354

is there a /sci/ approved journal of mathematics?

>> No.15771390
File: 1.94 MB, 1024x1024, Winter in Tromso.png [View same] [iqdb] [saucenao] [google]
15771390

>>15771345
Some people just have a guilty conscience, and see what they deeply want to see.

>>15771282
>professor wrote a calculus textbook
Yikes. Just go with Stewart and Spivak. Both should be cheap to find and are the most tried and trusted calculus textbooks, and together will cover the material at any level of depth you'd like.

>> No.15771392

>>15768750
Computing pi also requires infinite computation.

>> No.15771414

>>15765433
Yes when you realize that multiplication is symmetrical with a limited subset of elements.

>> No.15771501

>professor for course and math department chair says my paper is extremely impressive.
Uh, bros? Surely this is someone whose praise proves that I am not just stumbling my way through by luck and other non-academic methods?

>> No.15771529

>>15766956
take your medse

>> No.15771537

>>15771354
There's various ones that usually require some
subscription, like MAA, AMS, or even
Johns Hopkins' American Journal of Mathematics
(or anything outside America, really).

If there are journals somewhere in libgen or
sci-hub somewhere, we would have a
preference by now.

>> No.15771540

>>15771537
I have an AMS subscription and its hit or miss. The last issue wasn't half bad. Some good book reviews, qt picture of a jap reviewer lady, but I lost confidence in it after they had the drag queen math article last year.

>> No.15771559

>>15771540
>>15771537
There's nothing wrong in shopping around.
You can try the others out for a couple of months
and cancel if unsatisfied. Especially if they have
volumes from past years that you can look up
electronically, then you can get an idea of how
they are editorially speaking.

>> No.15771614

>>15771390
I know these are AI, but what are you using to make these? Stable diffusion?

>> No.15771964
File: 451 KB, 512x512, 7bb[1].png [View same] [iqdb] [saucenao] [google]
15771964

>>15759515
Op's pic is a stable diffusion image of an old man spreading his asshole showing his innards, also known as goatse.
Image generation models make heavy use of linear algebra, hence "applied linear algebra"

>> No.15772197

I'm being mildly retarded here, but if I have two sequences and I know that
[math]\liminf_n a_n > \liminf_n b_n,[/math]
then I can conclude that
[math]a_n \geq b_n[/math]
for infinitely many n, right? I can't conclude anything stronger than that, e.g. what happens for all n sufficiently large, yes?

And can I conclude anything if I only know that
[math]\liminf_n a_n \geq \liminf_n b_n[/math]
with a non-strict inequality?

>> No.15772265
File: 5 KB, 949x293, qwertty.png [View same] [iqdb] [saucenao] [google]
15772265

Hw do you prove intuitively that this pattern always works like this without the fancy geometric proofs?

>> No.15772271

>>15772265
Split the trinomial into two pieces as per the exponent.
Take the first term (1st factor) and multiply it with the other
three terms of the other factor. Do the same to the second
term and the third term of the first factor.

Combinatorially speaking, 3 terms of first factor by
3 terms of the second factor gives 9 terms,

>> No.15772318

>>15769458
This image is silly, anon. There's no any order to topics, neither in abstraction or depth nor in difficulty. There's plenty of more complicated stuff above Lie groups. Why is symplectic geometry in the genius level? Cohomology being so far down below homotopy makes no sense. You do not really understand a lot about complex numbers until you learn quotients rings and linear algebra.

>> No.15772335

>>15771305
Various olympiads have different styles organized around some sets of tricks you should learn, and most of the people who become medalists prepare for that particular olympiad, they don't necessarily have to be some distinguished mathematician, unless we're talking about IMO, though maybe it applies to IMO too, I don't know.
So there doesn't exist a universal resource for math olympiads for the same reason as for why olympiad skills differ from the skills required for mathematical research. You're supposed to know yourself what topics and tricks you should cover for the olympiad you're aiming at.

>> No.15772340

>>15771282
With the abundance of calculus books and online learning material, why are you focusing on your prof's book?

>> No.15772420

Are p(A) and p(~A) probabilistically independent? It seems like they are, since p(A&~A)=p(A)*p(~A)? If this doesn't work is there any better way to show that it's impossible for there to be no probabilistically independent events?

>> No.15772424

>>15772420
An event and it's complement are independent iff the probability for the event is either 0 or 1.

>> No.15772430

>>15761515
I wish anons the best of luck who try to get into the NSA but I'm almost certain they are preferring diversity hires at this point...I had a masters in math with a perfect gpa, a published paper and a reference from somebody who worked for them for 30 years as a director and I didn't even get a fucking invite. meanwhile a month later I get an email from them about how proud they are of their diversity hiring. I fucking hate this world.

>> No.15772432

>>15772424
Awesome, so as long as there are events with probability 0 or 1, there will be events that are independent?

>> No.15772441

>>15762484
>>15762409
I think your question is interesting but I really don't understand why that wouldn't satisfy you. Geometrically, this seems perfectly legitimate and I don't understand why you'd consider this a "non-answer." To me this is just a fetishisation of rigour to the point that you've dismissed a completely legitimate intuition for the answer as not answering the question, which makes me wonder what answer you're looking for in the first place.

>> No.15772453 [DELETED] 

I AM PISSED

PISSED AT NUMBERS?

3? I HATE THAT NUMBER

4? I HATE THAT NUMBER 1 MORE TIME THAN THREE

I HATE ALL NUMBERS EQUALLY DESPITE 3 AND 4

2 = 2 = 2
3 + 4 = 3

NOW CAN YOU ANSWER WHAT IS 2+2??!!?!?

>> No.15772454

>>15772430
Damn, that seems evil. Maybe if we post on 4chan we will get looked over? I'll be applying as active duty military, so I should get some sort of veteran preference. Hopefully that works for me the same way as a diversity quota.
I did attend one of their conferences for math majors and jobs, but it was pretty basic stuff with really inane questions being asked by those attending. Its surprising you got looked over. I'll only have a BS and a single publication in Rose-Hulman lol....I stand no chance.

>> No.15772463

>>15772454
Hello /mg/

I love math

3? i love that number

4? I love that number 1 time more than 3

I LOVE ALL NUMBERS EQUALLY DESPITE 3 AND 4

2 + 2 = 2
3 + 4 = 3

Now riddle me this, what is 2 +2?

>> No.15772466

>>15772454
Hello /mg/

I love math

3? i love that number

4? I love that number 1 time more than 3

All numbers are equal besides 3 and 4

2 + 2 = 2
3 + 4 = 3

2+2 = 4, so what is 8+8?

>> No.15772470

>>15772454
umm you fucking blathering idiot, nobody pay attention to this fucking baffoon fucking idiot you are here by declared a fucking dunce and I'm gunna call you a dunce every time I see you

>>15772466
good post

>> No.15772752

I thought it would be important to understand the 'philosophy' of mathematics, but now I'm not sure. I find it strange it's possible to do math without consciously thinking about things like that.

Do people that do math-based jobs just make 200k+ if they are good enough at it by simply hallucinating answers to things?

>> No.15772760

>>15772420
>It seems like they are, since p(A&~A)=p(A)*p(~A)?
p(A&-A) = 0 anon

>> No.15772761

>>15765181
So, I found out that L^p is a norm, so that the L^2 norm is equivalent to the Hilbert space H_0^1, somehow all of these are Sobolev spaces or something.
Why are these important for the solution of PDEs? Meaning a given variable x has solution in L^2 and other variable y has solution in H^p. I couldn't find out what "#" means, but now I know that the subject is in functional analysis books and advanced pdes books, but still struggling.

>> No.15772770

>>15772752
The philosophy and history of mathematics is important for the development of new questions, or the application of previously "unrelated" to each other. Essentially all mathematicians before the last 100 years, were polymaths with various other interests and well rounded education. I see your thought pattern quite a bit, and if you are interested in the single minded pursuit of only one thing for the purpose of making money, you are simple a wageslave.
When you say its possible to "do" math, what you are imagining is computation or solving problems from a textbook.

>Do people that do math-based jobs just make 200k+ if they are good enough at it by simply hallucinating answers to things?
If you want to pursue this single minded approach, just study what you have to do in order to become a quantitative analyst.

>> No.15772805

>>15772770
Based

>> No.15772816

>>15771345
The team that made goatse based that pic on the painting, retard.

>> No.15772832

>>15772770
>before the last 100 years,
what changed?

>> No.15772894

>>15759511
What is the purpose of having two forms of notation in terms of big or small numbers? Why have both scientific and engineering notation instead of just one?

>> No.15772898

>>15772752
Given the rampant autism among mathematicians, it's not surprising that there are people like that. However, I think any well-adjusted person studying mathematics would inevitably ask questions about motivation, foundations and so on. I think even the fact that you posted this question here implies that you belong to the latter kind. This also means you're probably not going to make it into Bourbaki, but oh well.

>> No.15772914

>>15772898
>make it into Bourbaki,
by which you metaphorically mean a "top" level/position of research?

>> No.15773262 [DELETED] 

>>15772898
testing to see if i'm banned

>> No.15773265

>>15772898
Well you see in my numbers system, all numbers are equal, I just love certain numbers X amount of times more than other numbers. It's very simple.

>> No.15773269

>>15772898
Btw my numbers system should be adopted by universities as it is less racist.

>> No.15773291

In Clifford algebras you have the 2:1 correspondence between bivectors (the even subalgebra generated by them) and rotations. For a vector v and bivector A, the rotated vector is [math]e^{A/2}ve^{-A/2}[/math], where multiplication is via Clifford product. So basically the generalisation of the "sandwitching" in [math]\mathbb{H}[/math].
Both of these look suspiciously similar to group conjugation. And here's my question. I usually think of group conjugation as a "change of basis" in the context of a group action. But for bivectors, the even subalgebra appears to act on vectors... which are obviously not in the Spin group. So I'm confused - is there any way I can salvage my intuition about conjugation as a change of basis here?

>> No.15773424

You have a chance to be spirited away into an empty dimension where you don't get hungry or tired. The only thing that exists there is an infinite amount of paper and ink. There are no books you can use or reference. Any math you want to do, you have to invent or reinvent yourself. You'd have to stay there for 500 years, and once you get out, you would have memories of what you discovered. Would you do it?

>> No.15773464

>>15772752
>hallucinating answers to things
shut the fuck up

>> No.15773471

>>15773464
>shut the fuck up
what? that's what not paying attention to the meta aspect feels like to me

>> No.15773474

>>15773424
Throw in a very insightful and fuckable lady and you have a deal.

>> No.15773478

>>15773424
Of course that sounds epic. I could literally make anything in my mind.

>> No.15773479

>>15771964
Thanks doc

>> No.15773480

>>15773471
No, the smarter you are the better you are at deconstructing logic operators across something.

That doesn't mean you hallucinate, your still doing the same amount of work that somebody else has to decode.

As a retard, I think this is true but I will leave the proof to the nonretards.

>> No.15773497

>>15773471
that's just your hallucination about hallucinations

>> No.15773758
File: 39 KB, 630x574, simpleMath.jpg [View same] [iqdb] [saucenao] [google]
15773758

>>15759511
well /mg/ are smarter than 99% of the people ?

>> No.15773941
File: 1.72 MB, 2160x3840, 1653689730449.jpg [View same] [iqdb] [saucenao] [google]
15773941

How accurate is this?

>> No.15773965

>>15773941
Probably partially accurate, but you're probably unironically better off at this point learning Python and A.I to make money as a quant. True "pen and paper" quants was a thing 25 years ago or more.

>> No.15774008

>>15760136
God I've been laughing like a retard to this image for like 10 mins.

>> No.15774176

>>15773424
I would "calculate" all the homotopy groups of spheres, or develop new methods of calculating them. Those methods discovered by me would give rise to new areas of math, which would become fields on their own separate from homotopy theory, just like it happened with homological algebra.

>> No.15774177

>>15773758
[math]F_2 / (x^{n+1}) [/math]

>> No.15774182

>>15774177
meant [math]F_2 [x] / (x^{n+1})[/math]

>> No.15774217

what is the oldest unsolved problem

>> No.15774223

>>15774217
Oldest I can think of off the top of my head are either Goldbach's conjecture or the proof of (no) odd perfect numbers.

>> No.15774266

>>15774182
>>15774177
Please write your answer in terms of food items, otherwise it's just confusing

>> No.15774268

>>15773941
It's kind of a joke, but also completely true. That's just kind of how math is. The more serious it is the more of a joke it feels like.

>> No.15774273

>>15774223
Open ballsack somethun sumtuhn ergo proof.
I am a genius give me my prize money now

>> No.15774275

>>15774273
what

>> No.15774278

/mg/ should make some robust conjectures.

>> No.15774288

>>15774275
Either my balls will touch or not touch, how are you not getting this? This is basic mathematics

>> No.15774291

We can all agree that categories as in category theory are more "fundamental" than e.g. groups or other more conventional math operations and objects. Let's, as a figure of speech, say they are "higher" (although you could visualize this metaphor as them counting as being situated "lower" -- not that it matters).
It is currently assumed that the more we ascend this ladder of abstraction, that this also reveals some real fact about math and reality. I mean, how could it not? After all, these categories, which may be categories of (categories of (... )))) and so on, are not precisely 100% man-made (saving the debate about platonism right now). They are restricted by logic that is independent of humans -- of course. But what if you could ascend this ladder infinitely? Sure, at every layer there would be yet another perhaps unique restriction, which keeps it from being *purely* some arbitrary human convention, or rather invention. But if this ladder can be ascended infinitely, does that not mean in a very real sense any such further information is meaningless? It's just random noise? As meaningless as what the sequence starting at the n-th position of pi is?

I am not sure if I can convey my thoughts adequately. Essentially, I am applying the idea that sometimes crops up in physics: what if there is no end "at the bottom" of physics, and subatomic particles would consists of ever smaller constituents, and so on? But instead, I apply it to category theory.

>> No.15774298

>>15774291
No, I don't agree with that. Logic is the foundation not category theory.

>> No.15774444

>>15765917
How do you make these?

>> No.15774469

>>15766150
>>15766767 should answer your question
Dear mathematicians, first they came for /sci/ and nobody reported, then they came for /mg/.

>> No.15774508

>>15774266
It's only confusing if you don't understand what is the question about in the first place

>> No.15774543

>>15772832
I don't know. I'm not going to pretend that I do or bullshit some answer for you. Sorry. Maybe these people exist but we haven't heard of them since they're not dead yet, so we can't read their life's work in retrospect.

>> No.15774987

>>15774177
>>15774182
well done, but what kind of algebraic topologist prefers F_2 over Z_2 or Z/2Z?? You're an impostor

>> No.15774997
File: 333 KB, 719x507, Screenshot_20230927-184311_CamScanner.jpg [View same] [iqdb] [saucenao] [google]
15774997

Bro not not cool. Im in collage on a football scholarship why I gotta lean this gay shit. Any bros wanna help me with my algebra homework? (Yeah laugh I know, not doing calculus with the smart kids)
In stuck on numer 11.

>> No.15775021

>>15774997
You're asked for trivial solutions, i.e. x=0 or y=0, hence it is sufficient to solve x^n=1, but x\in Q, so you can write x=p/q for p,q\in Z. But then your equation is equivalent to p^n=q^n. Solutions are p=\pm q for n even and p=q for n odd. This implies x=\pm 1 or x=1 for even, odd resp. Finally your solutions are (0,1),(0,-1),(1,0),(-1,0) for n even and (0,1),(1,0) for n odd.
For the 2nd part simply note that writing x=p/q and y=r/s you have (p/q)^n+(r/s)^n=((ps)^n+(qr)^n)/(qs)^n=1 so ps, qr and qs would be 3 integers that satisfy x^n+y^n=z^n.

>> No.15775024

>>15774997
I love the idea of some freshman thinking "calculus sounds too hard, I should probably brush up on my algebra and geometry" and taking this

>> No.15775026

>>15773424
I would get really thirsty

>> No.15775029

>>15775024
If calculus doesn't almost feel like algebra you're doing it wrong. Same holds for analysis in general.

>> No.15775075

>>15765181
>>15772761
I come to talk to myself again, so "#" is the cardinality of the set (which is impossible to search on "search engines") or the number of elements in a set. Now I have to check Lebesgue measures, Banach, Hilbert and Sobolev spaces and how the notion of "strong" or "weak" solutions in each variable relates to specific norms.

>> No.15775239

>About to finish BS in math without taking real analysis
Over status?

>> No.15775249

>>15774291
>We can all agree that categori-
No.

>> No.15775250

>>15773965
What do you think fitting a model to data even is? The AI you'd build as well is fairly simple you nimwit, a basic buying strategy is all the bot needs, reinforcement learning isn't going to gain you much on your strategy.

The bread and butter of quant work is time series analysis and 'machine learning' (bullshit word for statistical modeling which most of the time is best framed as a stochastic problem).

>> No.15775267

>>15760866
Lol last chance to get on board before you're left in the dust retard

>> No.15775616

Why does the angle between a line of slope 1 and a line of slope 2 have a really long decimal when the angle between a line of slope 1 and a line of slope 0 is just 45 degrees?

>> No.15775632

>>15775616
45 degrees in radians is a really long decimal too.

You could say that the size of a degree was chosen so a line of slope 1 would be a 'nice' number.

>> No.15775634

>>15775616
Well, anon, the angles between lines are typically measured using trigonometric functions, where the tangent of the angle is the ratio of the slopes of the two lines. In the case of a line with a slope of 0 (horizontal line) and a line with a slope of 1, the tangent of the angle is 1, leading to a 45-degree angle. However, when you have a line with a slope of 2, the tangent of the angle between that line and a line with a slope of 1 is 2. This results in a larger angle, and when expressed in degrees, it becomes a decimal value. The tangent function, which relates the angle to the slope, produces larger values as the angle increases, causing the decimal representation of the angle to become longer for steeper slopes. This is why the angle between a line with a slope of 1 and a line with a slope of 2 has a longer decimal representation than the 45-degree angle between a line with a slope of 1 and a horizontal line (slope 0).

>> No.15775653

>>15775616
It's because pi/4 is a nice ratio of pi that essentially represents a rational number and when multiplied by 360 is a whole number.
180/4 = 45, we're basically saying pi = 180.
But there is no ratio of pi such that artcan 2, and what that is saying it that the "ratio" is basically an irrational number, so it'll have an infinite decimal pattern even if you replace the irrational number pi with 180 degrees.

>> No.15776064

How come we can put sine and cosine in matrices when it's linear algebra? Trigonometric functions are not linear functions.

>> No.15776144

>>15776064
y=x*sin(theta) is a linear function of x, even though it's not a linear function of thata, and that's enough to make linear algebra usable with it.

>> No.15776186

>>15776144
Why can't we use that argument to allow y=x*f, where f is an arbitrary function of x?

>> No.15776187

So, do you retards ever discuss something other than high school math or are you all dilettantes?

>> No.15776227

>>15776186
>where f is an arbitrary function of x
retard

>> No.15776243

>>15776186
Because f is a function of x. I was assuming that theta wasn't a function of x.

>> No.15776344

I saw a maths riddle in a random Reddit comment, and the answer I got (75) is stated to be incorrect. What is the correct answer and how to get it?

Comment copypaste:
>How much time do you need to solve this riddle?
>"A man wants to count the number of steps on a moving escalator. If he goes up the escalator against the direction of travel, he counts 90 steps. If he goes down the stairs at the same speed, he counts another 60 steps.
>How many steps would he have to climb if the escalator were at a standstill?
>(Hint: 75 is not correct.)"

Another commenter jokingly answered
>72 years
mocking the retarded way the question is phrased. Is the answer really 72? If so, why?

Seems like a regular middle-school riddle, so I would try to solve it so:
y + x = 90 | y − x = 60
y = 90 − x | y = 60 + x
90 − x = 60 + x
90 − 60 = x + x
30 = 2x
15 = x
y = 90 − 15 | y = 60 + 15
y = 75

>> No.15776475

https://sites.google.com/a/oakland.edu/algebra/home/phd-program

Thoughts on this program bros? I live right next door, so I can live with my parents and walk here in my jammies. I found their old site which has juicier info than the main college website. Looks like they just let you focus on algebra the entire time which is good, I've seen some other schools that make you do thinks no one enjoys, like qualifying exams in 3 or 4 different topics. Rather just do exams in only closer related topics, I'm not trying to impress anyone.

>> No.15776639

x^2+x+1 cannot be factored into two smaller integer-coefficient polynomials but x^3+x^2+x+1 can. Why is this?

>> No.15776824
File: 120 KB, 1184x479, 2023-09-28-174841_1184x479_scrot.png [View same] [iqdb] [saucenao] [google]
15776824

I'm going through How to Prove It in trying to get good at math. In Example 2.1.3 Q4, you're supposed to translate the statement "If anyone in the dorm has a friend who has measles, then everyone in the dorm will have to be quarantined" into a logical form. Picrel is the given answer, but the final portion of the statement seems ambiguous to me. It seems like the D(z) -> Q(z) would need to reference the initial x (something like (S(x, z) -> Q(z)) to actually capture the relationship between the x with a friend and the individuals who share a dorm with him. Is this just understood by it's position in the statement?

>> No.15776856

>>15776824
>I'm going through How to Prove It in trying to get good at math.
Try reading a math book instead

>> No.15776866

They should teach formal logic in primary school and secondary school.

>> No.15776870

>>15776824
This is silly and this book is trying to be many things at all once. I will never fucking understand why people that want to study math yet know nothing about it, don't just use the basic standard undergraduate math curriculum. As a tip, I have never heard of any school using How to prove it.
Just purchase an entire set of textbook for the basic core math courses, go over them thoroughly over the course of 3 years, and after that you should be in the right spot to study math in your own from various fields, and know how to fill gaps yourself.

>>15776866
The point of primary and secondary school is not to build mathematicians.

>> No.15776885

>>15773941
name ONE person who got rich off /sci/

>> No.15776888

>>15776870
>The point of primary and secondary school is not to build mathematicians.
formal logic isn't just about maths though
it's for argumentation in general.

>> No.15776982

>>15776344
Let's suppose that the escalator moves at m steps per minute, and the man walks at w steps per minute. We'll call the number of steps long the elevators is n. Since it takes the man 90 steps to walk up the elevator, it takes him 90/w minutes. In those 90/w minutes, he moves n steps up the elevator, at a speed of (w-m) steps per minute. So n/(w-m) = 90/w.
Now let's consider walking down the escalator: in 60/w minutes, he descends n steps, at a rate of (w+m) steps per minute. So n/(w+m) = 60/w.
Let's divide the first equation by the second. (n/(w-m))/(n/(w+m))=(90/w)/(60/w)
We can simplify this to (w+m)/(w-m)=90/60 and then 60(w+m) = 90(w-m) and then 60w+60m = 90w-90m and then 150m=30w so 5m=w. The man walks five times as fast as the escalator moves. Now let substitute that into our first equation. n/(5m-m) = 90/5m so n/4m=18/m so n = 18*4 = 72. Therefore, the escalator is 72 steps long.

>> No.15777151

Lang's Algebra book seems to be the largest and most comprehensive, definitive text on the subject. However, it seems rather dense and it makes me wonder if its adequate for actually learning the topic.
For the graduate algebraists here, what has been your "path" regarding books and topics?

>> No.15777386

next
>>15777384

>> No.15777387

>>15776870
>The point of primary and secondary school is not to build mathematicians.
it should be