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/sci/ - Science & Math

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12657631 No.12657631 [Reply] [Original] [archived.moe]

Diophantine Equations Edition

Formerly >>12645271

Talk maths.

>> No.12657655

Hello my math people :3

>> No.12657812

why do people act like e^(i*pi)=-1 is a big deal? literally just means half a full turn makes the number into it's opposite

>> No.12657839

Associating three of the major constants in mathematics in one formula is not a big deal to you?

>> No.12657860

>Diophantine Equations Edition
You mean petty high school exercises despised by grouchies who equate seriousness and importance to pompous names and artificial "sophistication"? Based.

There is no place for bent mathematics. There must be a good balance between problem solving and theory building.

>> No.12657870

Because the interesting stuff is too complicated for the average 20 year old.

>> No.12657875

Why are you like this? Did you really get this offended because I called your pettiness out in the last thread? Grow the fuck up, kid.

>> No.12657880

no? why would it be?
also calling i a constant is a bit weird

>> No.12657888

Care to tell us what is a big deal to you then, mr genius?

>> No.12657894

actual theorems?
this identity is more of a definition than anything really

>> No.12657913

Oh, so definitions are useless and not important according to you? Let's exclude all definitions from mathematics then, see what you have left after that.

>> No.12657937

>Oh, so definitions are useless and not important according to you?
useless no, not important yes since they can be replaced by other definitions and are the fruit of human imagination only and not of actual mathematical logic
>Let's exclude all definitions from mathematics then, see what you have left after that.
nice strawman bro

>> No.12657953


Elliptic curves are gay and squaring a prime is meaningless.

>> No.12657956

Hahaha, you're too much, dude. So, definitions are a product of human imagination but mathematics and logic are not? Hahaha.

>> No.12657962

Define strawman.
Create an equivalent definition.
Create a better definition in the context of mathematics.

>> No.12657966

Any recommendations on self-study textbooks for linear algebra?

>> No.12657971

didn't write that. Read again, since one time seems to be too much fro your brain
>are the fruit of human imagination ONLY and not of actual mathematical logic
i.e. theorems are the fruit of both human imagination and logic, definitions are the result of human imagination solely

>> No.12657981

Solve the exercises or you are clamped

>> No.12657994

don't care, virgin.

>> No.12658002
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>> No.12658020


>> No.12658033
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>> No.12658056

>I'll invoke random arguments then drop them the moment I am pressed.

>> No.12658079

ez derail math is suck a safe space for wh*toid "men"

>> No.12658085

your post has literally nothing to do with the conversation, retard

>> No.12658113

That bait doesn't work in /mg/. Try asking about consecutive coin flips instead, you'll get 100+ autist posts.

>> No.12658176

He might be baiting, but it's not really false saying that mathematics is a white man's game. Whites are responsible for what 97% of all maths?

>> No.12658319

Only because we were given the opportunity. In the alternate universe where sub-saharan Africa had an industrial revolution and built navies to colonise the world and loot other societies it would be blacks that accomplished 97% of math.

>> No.12658343

the feels

>> No.12658368

Linear Algebra Done Right by Axler

>> No.12658403

Enjoy not learning determinants and fucking up your entire understanding of linear algebra and how it relates to other fields.

>> No.12658422

He has determinants at the end of the book so I don’t understand what your point is. Who gives a fuck about other fields anyway?

>> No.12658454

>He has determinants at the end of the book
Doesn't matter. You won't understand how to use them in proofs.
>Who gives a fuck about other fields anyway?
You realize there's no research in Linear Algebra anymore, right? Nowadays it's merely a tool for getting into other more advanced fields and determinants are essential in most of those.

>> No.12658530

>laughs in characteristic p

>> No.12658537

What's a good book for Linear Algebra then

>> No.12658590

Hoffman&Kunze of course. All others are utter trash in comparison.

>> No.12658634

At what level of math can I talk here, Differential? Linear? Calculus?

>> No.12658651

I think undergraduates probably feel out of place here since most of the regulars are at a PhD level.

>> No.12658656
File: 38 KB, 600x800, 1611860216810.png [View same] [iqdb] [saucenao] [google] [report]

>Associating three of the major constants in mathematics in one formula is not a big deal to you?
It will really relevant if the formula actually tells something, like E=mc2 bur that "formula" only is another way to write -1. It's is only important for onions mathematicians and shitty normies that only knows maths for youtube "popularizers"

>> No.12658661

I would start with a low page count book and work your way up.
Therefore, I recommend Modules by Tom Head.

>> No.12658721

Sodachi Oikura is an underappreciated girl

>> No.12658727

>It will really
>only is
>It's is
>onions mathematicians
>for youtube
Jesus Christ, learn some english before trying to reply to me, you fucking idiot.

>> No.12658743
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>Who gives a f*ck about other fields anyway?
But I like my characteristic greater than 2...

>> No.12658792

i don't get why they add 1 to euler's identity? it could have been fine if the answer was just -1

>> No.12658805
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>snoyjak poster
>shit brainlet opnion
classic. There are a good couple of properties hidden away in the equation that are actually useful to people, such as [math]\mathcal{FT} \cong C_{4}, \{e^{ix} : x\in\mathbb{R}\} \cong C_{\infty}[/math]

>> No.12658810

muh autismo needs to have all 5 constants, that's why

>> No.12658814

Because during Euler's time the number 0 didn't exist. It makes more sense for it to be equal to zero.

>> No.12658844

1 and 0 are not constant

>> No.12658858

They're variables right?

>> No.12658861

My favorite one is that it's babby's first Lie group / Lie algebra correspondence by
[eqn]\mathrm{exp} : G \twoheadrightarrow \mathfrak{g}[/eqn]

>> No.12658869

most of the people here are undergrads
good posts are rare

>> No.12658878

fuck switched the group and the algebra
I'm a brainlet

>> No.12658881

no but they aren't like pi or sqrt(2) or e.
hey look i made an equation with all 5 constants

>> No.12658900

Retard... They are constants, they're just not as important as pi, e or i.

>> No.12658906

OK second attempt
[eqn]\mathrm{exp} : \mathfrak{g} \to G[/eqn]
forgive me for having an infinitely differentiable brain, mathanons...

>> No.12658921

yeah so why add them? there is no need for the +1

>> No.12658930

0 and 1 are constants just as e or pi you brainlet

>> No.12658948

Are Spec(R) and Specm(R) still defined for a noncommutative ring? Do we have to look at left and right ideals separately, or are they only defined for two-sided ideals?

>> No.12658972

>most of the regulars are at a PhD level
ahahahaha those are just undergrads trying to sound smart

>> No.12659002

petition to start /pmg/
professional mathematicians general
evidence of your published works and most recent paystub are required before you can post

>> No.12659014

But that would exclude you and I want to see you beautiful contributions to the thread <3 OwO

>> No.12659019
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>> No.12659021
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There's no meaning to mathematics if I don't have an asian girlfriend.

>> No.12659031

0 1 are constants but 2 and bigger are not a constant because the value depends in different characteristics

>> No.12659047

That's not how math works

>> No.12659056

Elementary abstract algebra is a prerequisite for posting in /mg/.
Bold of you to assume that my ring is unital.

>> No.12659071

it's just based af all around.

>> No.12659072

Looked this up, did you mean Modules and the Structure of Rings, Golan & Head, 1991 or Modules: A primer of Structure Theorems, Head, 1974?
They both seem designed for undergraduates.

>> No.12659103

It's the same book, 1991 is the second edition.

>> No.12659118

god i want an asian girlfriend
or a white girlfriend
or a tranny

>> No.12659120

ughhh guys i asked why euler's identity has +1 instead of the answer just being -1

>> No.12659133

second one

>> No.12659149
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Every day I try to calculate the number of anime gaysexual transfinitegender posters in these threads and fail... I can't even find an upper bound. Why live?

>> No.12659178

They are still constants in those rings retard.
If 2 is in the ring, and you take 1 as a constant then 1 + 1 = 2 is a constant.

>> No.12659208

After looking into the first one I decided that I indeed mean the older version. It is short which I prefer for a first exposure and second the typesetting in the newer is strange.

>> No.12659265

non-unital means no 1, asshat

>> No.12659276

Then it's just 0 and there is no notion of bigger you fucking niggerfaggot

>> No.12659283

You truly don't understand what a non-unital ring is, anon. You must be an analyst.

>> No.12659326

call it a rng then

>> No.12659356

Holy fuck you are so god-damn stupid. 2Z
2 is a constant.
ring implies unital btw You mean rng.

>> No.12659366
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>0 and 1
>nonunital ring btw gotcha dummy

>> No.12659377
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I searched mg in the catalog and this one didnt rejister in my FoV so I was gonna make an edition on how to visualize 4d. ; (

>> No.12659385

Same fucking shit, nigga.

>> No.12659392

What's an FoV?

>> No.12659409

Anyway lads. I had an idea on how to prove Zorns lemma without the maximum principle, but idk how to make it rigorous.
>start with any element
>find upper bound
>create simple order
>always have a new upper bound if theres no maximal element
>contradicts hypothesis of simple orders having upper bounds
Is recursive infinite contradiction a valid proof method?

>> No.12659423

Field of Vision/View

>> No.12659473

Anyway lads, I had an idea on how to prove Zorn's lemma using Zorn's lemma:
>every union of a chain of chains is a chain, proving that every chain of chains has an upper bound
>this implies by Zorn's lemma that the set of chains in a poset has maximal elements
>an upper bound of any of these maximal chains is a maximal element of the original poset

>> No.12659481

12659149 is a valid upper bound.

>> No.12659484

Aboutt 50 unique posters a thread
50 is a valid upper bound
49 cause Im not a faggot

>> No.12659495

here's a curious fact: 0=2 in Z2 but 0!=2 in Z
so clearly they can't both be constants

>> No.12659499

I fucking hate set theory. Humans should discover infiinity through experiment, not try to define it themselves. We havent achieved infinity yet, set theory will be washed away in 1000 years

>> No.12659502

>multiple anime math trannies exist
>i haven't had sex with any of them
please just kill me

>> No.12659512

[0]_2 = [2]_2 in Z_2

>> No.12659517

and 0! = 1

>> No.12659518

Oh I think I got it! Assuming no maximal element, we can say that for each element, it is Not the upper bound of some simple order. If every element is not an upper bound of something, then there is a chain which lacks an upper bound, contradiction

Technically there are multiple chains, but you can ignore those I think

>> No.12659528

Its like transfinite induction, not parleying at each stage where each layer contradcts the contradiction, but rather building an infinite god to contradct the other infinite god, a chain all at once

>> No.12659535

Okay lads, so I need advice. I am reading Munkres and I finally finished the Set theory chapter, and am eager to start the topology section. However he left some supplementary exercises at the end, just a page on proving the equivalence of well ordering and axiom of choice. But it seems absurd to me. Is it worth doing, or is set theory truly just insanity?

>> No.12659537

just look at this faggot >>12659031 >>12659056 >>12659265 >>12659283 right here, typical example of larping freshman

>> No.12659542

If it's not worth doing it wouldn't be in the book anon

>> No.12659779

I dont know if thats true. That implies that the book is inherently and completely worthy, but many books have been written about unworthy topics. I believe set theory as a whole is an unworthy topic, and not due to mg memes but my own experiences with void and infinite obsessions. I think nature will reveal infinity through physics someday, and humans are rushing to understand it without enough experience.

>> No.12659789

That said, I guess Ill give it a shot anyway just to stew on the datums.

>> No.12659794

Also guys I made 1200 bucks just now from swinging ethereums. Sold at 1530, bought a few days ago at 1350. Might buy back at 1400? 1430?

>> No.12659822

Smoke dmt if you want to "experience infinity". Or go shopping with a woman, you will learn that infinity can be experienced.

>> No.12659847

When did animeposting become acceptable in /mg/? I haven't been here in years.


>> No.12659862

i want to fuck it

>> No.12659926

We speak english in /mg/

>> No.12659933

Auch deutsche

Ja ich erinnern von mein Junger tag mit mein mutter

>> No.12659948
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>learn some english
Thanks for the feedback
>you fucking idiot
maybe, but you are even more idiot by thinking that e^i*pi+1=0 has any value

>> No.12659956

>basedjak posting
>chad meme posting
What is it like being completely unoriginal? Seriously just go back to funnyjunk.

>> No.12660004


>> No.12660013

>through physics
Which physics? There's an uncountable number of them.

>> No.12660058

What happened in 2018?

>> No.12660093


>> No.12660103

>or is set theory truly just insanity
But that is what makes it fun. How else are you going to square circles and play with infinitely infinite ordinals and cardinals?

>> No.12660140
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Most anime posters started posting around that time, me included. That's all.

>> No.12660147
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>> No.12660193

I bet you think integers are a social construct

>> No.12660198

just get a statics textbook.
it's basically the same thing

>> No.12660204

fascinating theory.
that didn't happen though so your point is retarded.
white people did it. period.

>> No.12660209
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>totally ad hominem
Yeah maybe I'm unoriginal, but still is a fact that "the most beautiful ""equitation""" is only a retard way to write -1

>> No.12660219

But integers are a social construct. All of maths is. You think math exists physically in the world?

>> No.12660220

do you seriously think we didn't have the number 0 during the 1700s?

>> No.12660229

go to reddit if you want efame

>> No.12660232

You see, that's my secret, anon... I'm already on Reddit.

>> No.12660256

4chan is just a meta site for reddit commentary at this point.
why even live anymore?

>> No.12660270
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>why even live anymore?
To solve all of mathematics.
To discover all the truths in the universe with physics.
To find a japanese girlfriend.

>> No.12660495

I got ur joke and made me chuckle so you're forgiven

>> No.12660500

newfags are bad enough but avatarfags get the rope desu

>> No.12661081
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Noticed this happening over the last year or two. Pretty sad but I guess the wheel always turns and no one can remain on top for long. 4chan had its era. Now is the age of (forgive me lord for uttering this word), the age of the r*dditor.

>> No.12661185

man, mathematicians are cringe

>> No.12661194

>the age of the r*dditor.
and peadophiles, ie anime posters

>> No.12661200

>noncommutative ring

The spectrum problem for noncommutative rings and algebras

Manuel L. ReyesBowdoin College, Department of MathematicsOASIS - May 22, 2015

>> No.12661287


>> No.12661737

Read a book like How to prove it, then you'll see that you're wrong and grovel for forgiveness.

>> No.12661839

Why that book?

>> No.12661855

The level of intelligence that can be inferred from a person who seriously asks /sci/ to engage with actual mathematical questions is generally considered inferior to the level of intelligence that is required in order to avoid handing over a fully loaded AK-47 rifle to a chaimpanzee.

>> No.12661958
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What did he mean by this

>square circles
With integrals
>infinitely infinite
But do we even know what infinity means yet?

>> No.12661974

>Associating three of the major constants in mathematics in one formula is not a big deal to you?
(e*pi)^(0) = 1
There I just did the same thing. Where's my field medal?

>> No.12661999

When I first saw e to the i pi, I was obsessed and confused. When I first comprehended it, it seemed like gravity and orbits, locked into place by the first Natural twist in space time (analytic continuation)

>> No.12662009

> But do we even know what infinity means yet?
We know that in mathematics infinity does not mean anything, in the same way that x does not mean anything unless you explain what you take it to mean in a given context. Traditionally the infinity symbol is used in mathematics as the name of an element that is added "extra" to an existing structure, such as a real or complex field or a finite elliptic group, etc.

>> No.12662012

As far as I can tell the rigorous definitions of countable and uncountable sets still hold the crux intuition of it goes on forever, its not true rigor but fundamentally intuitive. Countable I think we understand decently, regardless, but uncountable I think we need quantum mechanics to understand the axiom of choice better.

>> No.12662066

>thread derailed by a single post

>> No.12662113

ara so, you realize you're derailing it even more by complaining instead of staying on topic, right?

>> No.12662167

>What did he mean by this
You're not actually one of those idiots who searches for answers to mathematical (metaphysical) questions in the physics of this particular universe, are you?

>> No.12662171
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>> No.12662178

The first sentence is grammatically incorrect.

>> No.12662187

Is that good?

>> No.12662194

There is no way 0! is 2 read Bourbaki and how the figure 0! = 1

>> No.12662195

It's shit but it has Astolfo.

>> No.12662204

A geometer living 4000 years ago knows more math than you ever will. COPE

>> No.12662299

wanking over "infinities" and "meaning of infinity" is not math

>> No.12662331

Why isnt anyone laughing at my OC meme its so funny I made the knot myself

I am indeed one of those idiots

>> No.12662339
File: 190 KB, 428x537, KnotNot.png [View same] [iqdb] [saucenao] [google] [report]

I think this version is better , its interesting to contrast slight pixel deformations and witness memetic singularities. A little dotted line square literally hacks your brain.

>> No.12662375

>I am indeed one of those idiots
Nice of you to admit to your idiocy, that way I can completely ignore all the mumbo jumbo that comes out of your mouth.

>> No.12662409

I owe my undying interest in mathematics to Numberphile. Science popularizers are unironically the only hope left for public school educated Westerners.

>> No.12662416

Hey, don't beat yourself up anon, you have an analytic mind (if your brain is complex)

>> No.12662497

I learned Analysis from Baby Rudin but I had no background in Calculus. Should I still go through a Calculus book?

>> No.12662498

Nothing against geometry. Physishits trying to determine truth via their pitiful little theories, that's what I hate.

>> No.12662525

Finally I wont have to deal with this chinks annoying replies anymore

>> No.12662532

The integers literally came from physics. Bakameno! Ever heard of counting rocks? Grug smash!

>> No.12662533

The integers came from accounting.

>> No.12662536

You can only account material , which is physics.

>> No.12662540

I am pretty sure birds recognize integers in their songs as well. If I whistle N times they whistle back N times, and if I change it to M they do too

>> No.12662547

That's a natural number. Integers are relevant when you need to start considering debt and sheit.

>> No.12662548

Ok, whistle –3 times

>> No.12662570

Sure but thats just the memory of physics, remembered objects. Also sealevel and underwater

Do the form of whistling where you suck air in instead of blow out
Negatives are just a reversible index

>> No.12662573 [DELETED] 

[math]\text{physics }\ne \text{ nowaday physicists}[/math]

>> No.12662580

physics ≠ nowadays physicists

>> No.12662675

i havan't dont any maths today

>> No.12662699

I used Friedberg's book, I thought it was really nice

>> No.12662706

Wildberger's linear algebra course and linear algebra notes by Terrence Tao

>> No.12662742

Does anyone here experience impostor syndrome when it comes to math? In my linear algebra course, I was doing very well in my assignments and when I wrote the first test, I blanked out. I have no idea if I did well because my proofs were probably shit. Now, I'm starting to doubt myself. I was only able to take this course because I had the pre-requisites. How can I gain confidence in myself?

>> No.12662815

>I was only able to take this course because I had the pre-requisites
Thats, uh, not uncommon

>> No.12662823

God I genuinely despise those onions faggots who go ape shit about famous (((equations))) even though they have no fucking clue what they mean

>> No.12662827

I'm in a stochastic PDE course while getting my masters in EE

I have no clue what's going on and I spend hours on proof before googling the answer

Its lit senpai

>> No.12662845

I really like linear algebra and learning more about it with proofs really expands my understanding. I just don't know if I'll do well in this course...

>> No.12662850

> Science popularizers are unironically the only hope left for public school educated Westerners
we're fucking done
we are done

>> No.12662867

I think it's more twitter and tiktok really

>> No.12662871

If you were doing well in your assignments, then it's quite possible you didn't do as well in your test because you got too nervous/worried. If so, you just need to treat as another problem to solve, stay calm, focused and optimise your speed during a test.

>> No.12662880

I’d like recommendations for getting into machine learning, for someone who’s taken all the usual first year courses, topology, measure theory, analysis, etc. Reading Durrett’s probability rn because I know fuck all about it.

>> No.12662883

Thank you, anon. This is my first proof-based course and it being online makes it harder. I doubt it's any better if it was in-person but regardless of that, I'll try my best to calm down and get used to it.

>> No.12662953
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Is Eisenbud and Matsumura enough for this? (Granted I don't think I'm going to finish all of Eisenbud)

>> No.12662962

If I'm asked for [math]P_2 (x)[/math] i.e., the second Taylor polynomial approximting a function, and the second derivative gives me a zero term, should I go a step further so I have the usual number of terms in a [math]P_2 (x)[/math] polynomial?

Right, because normally you get [eqn]P_2 (x) = a_0 + a_1 x + a_2 x^2[/eqn] but if [math]a_2 = 0[/math] then does [math]P_2 (x)[/math] become [math]a_0 + a_1 x + a_3 x^3[/math] like in the Taylor series of [math]sin(x)[/math]?

>> No.12662966

Which is crazy because Twitter is almost as old as 4chan at this point.

>> No.12662968

Eisenbud, sure. Don't know about that other one.

>> No.12662976

If you don't know the answer, then you don't exactly know the definition of the sequence of taylor polynomial approximations.

>> No.12663014

ahhhhhhh then tell me please

I can't find a formal definition ANYWHERE

>> No.12663025

Nah. [math]P_n[/math] has just the terms of degree up to and including n.

>> No.12663077

are there any collections of math book reviews like choice reviews, but free?


>> No.12663087

LMAO can't believe that's actually a thing.

>> No.12663102

to add I know that journals have review sections and that my example only shows a few reviews as well, so just to make it clear I'm looking for the largest possible collection of reviews. I guess i'll try my luck with zbmath.

>> No.12663106

>posts russian character

please reiterate

>> No.12663114

Guys Im hacking my windows kernel
7.5 fuckin gigs for a driver

Am I allowed to use a namefag here? I deceided Im gonna become lain-like so I should have a brand, Im using it on other boards too

>> No.12663116
File: 31 KB, 487x89, BlownTheFuckOut.png [View same] [iqdb] [saucenao] [google] [report]


>> No.12663134

>non-commutative vector field
Google shows nothing, is the definition just "a derivation on a C*-algebra" or is it different?

>> No.12663140

Oh, it's noncommuting, not noncommutative.
Disregard my previous post, I remember what that means.

>> No.12663141

non commuting vector fields

>> No.12663154

zbmath isn't really a collection, but you can search for a topic you want and only show books with scanned reviews but that's just a fraction of reviewed.

>> No.12663161

Ya but I want to just have a bunch of reviews and read them all and then decide what subject/book looks cool.

>> No.12663250

Is machine code an arithmetization?

>> No.12663261

Prime factorization provide coordinate storage within one dimension

>> No.12663299

all zoomers are redditors, they turn every site into the same shitty discourse and memes

>> No.12663323
File: 268 KB, 502x401, dick_move.png [View same] [iqdb] [saucenao] [google] [report]

Discussing the Bitcoin/Ethereum elliptic curve spec


>> No.12663371

Will the behavior of dynamical maps remain impenetrable forever or can some general theory exist?

>> No.12663462

Will the behavior of functions remain impenetrable forever or can some general theory exist?

>> No.12663496

You can define a random function as the outputs of a QRNG over natural time steps and that will be impenetrable

>> No.12663503

In the limiting/unioning of all times case

>> No.12663531

Half this shit is in german ahhhhhh

>> No.12663730

Can one use logical operators in or around mathematical expressions? E.g.
[math]y = x^2 \Leftrightarrow ( x = \sqrt y \vee x = -\sqrt y ) \Leftrightarrow x = (\sqrt y \vee -\sqrt y) \Leftrightarrow x =\pm\sqrt y[/math]

>> No.12663811

the third statement sets x equal to a truth value

>> No.12663839

No, root(y) is a term, you cannot use terms in non-atomic formulas. Also that looks a like shit, just use English.

>> No.12663969
File: 48 KB, 1678x589, 4chan.jpg [View same] [iqdb] [saucenao] [google] [report]

You have a square grid (nxn). You must fill the maximum number of cells inside this grid without forming a rectangle. Question is in a grid(nxn) how many cells can you fill without forming a rectangle?

>> No.12663977

That is technically readable, but no sane person would write it like that. Just write "the following are equivalent."
Also, statement #3 doesn't say what you think it's saying. If the disjunction symbol (wedge?) is defined for numbers, I don't know what it means.
You could write [math]x \in \{ \sqrt{y}, -\sqrt{y} \}[/math], but I think your second statement might be the way the [math]\pm[/math] operator is defined anyway.

>> No.12664020

Big whoop I can do that too. Here's a formula with 4 constants

e^0 - 1 = i * 0

>> No.12664049


>> No.12664051

Use Cauchy-Schwarz

>> No.12664067


>> No.12664181

>forming a rectangle
Garbage way of writing what you're trying to say. Anyway, this is a graph theory problem in disguise.

Say your grid is [math] [n] \times [n] [/math]. Say that your set of filled squares is [math] A = (A_1, A_2, \ldots, A_n) [/math], where [math]A_i[/math] is the set of column indices filled in row i. So your first example is ({1,2,3}, {1}, {1}) and your second is ({1,2}, {1}, {1,2}). So far, so good?

So now consider [math]K_n[/math]. Each set [math]A_i[/math] is a set of vertices of [math]K_n[/math]. Let [math]C_i[/math] be the clique induced by [math]A_i[/math]. Then [math]A[/math] is "good" if and only if the cliques [math]C_i[/math] are disjoint.

So we can rephrase the question as follows: If an [math]n[/math]-vertex graph (or maybe just [math]K_n[/math]) is decomposed into [math]n[/math] cliques [math]C_1,\ldots,C_n[/math], what is the maximum possible sum [math] \sum_i |C_i|[/math]?

I don't even know if graph theory will be useful here, but I just think that observation is neato.

Anyway, I think you'll get the best result by putting a roughly equal number of vertices (filled cells) in each clique (row). This is because one large clique will make disproportionately many edges available for the other cliques to use. For example, in a 5x5, there are ten edges to work with. We can give them all to one row of five and four rows of one, or to one row of four (six edges) and four rows of two (one edge each,) or to two rows of three (three edges each) and three rows of two (one edge each.) The second and third options each get us 12 filled cells, while the first one only gets us 9.

If someone else wants to continue with this idea, go ahead.

>> No.12664237

look here for resources and recommended textbooks. you don't need Durrett for this level but it's probably still worthwhile to master it if you want to get into more advanced ML theory.

Do more practice problems from the textbook. Exams are all about being able to prove the trivial things quickly. Problem sets usually aren't great practice for this.

>> No.12664272


wrong link

>> No.12664301

Master, please teach me how to look at such a badly worded problem and clearly see how the question should have been formulated.

How did you do that, that question was totally garbage?

>> No.12664349

Well, first, I thought "lol a 1x1 rectangle is still a rectangle," but that's not an interesting problem. It's still not interesting if you allow two adjacent cells to be considered a rectangle. So, does the rectangle have to be at least 2x2? No, because the figure on the right is bad, but doesn't have a 2x2.

I looked at the dotted-line rectangle on the right, and tried to see how it related to the filled cells. It can't be some kind of smallest bounding box, since he didn't draw anything on the left. But it could be that the four corners of the rectangle have to be filled cells. Sure enough, the figure on the left doesn't allow for anything like that (except degenerate cases, I guess.) I thought about that, decided that it seemed like an interesting enough problem, and concluded that that's what he meant.

Could've easily been wrong. It's always a gamble to assume that anon has more than three brain cells.

>> No.12664380

I have used set belonging notation also. Trying to settle on a style. Thanks for the input.

>> No.12664384

Alright, I see how you managed to work out what that guy said, but how did you quickly come up with that solution by seeing how it relates to graph theory?
Is that something that happens when you know a broad amount of math topics? Sorry for the questions by the way, I am just genuinely envious, I would like to be like you.

>> No.12664416

>how did you quickly come up with that solution by seeing how it relates to graph theory?
hint #1: there's an hour-long gap between his post and mine
hint #2: I can use the backspace button after writing something that doesn't work out
>Is that something that happens when you know a broad amount of math topics?
Kinda. I do a lot of graph theory (relatively,) so it's not that surprising.
>Sorry for the questions by the way,
Apology not accepted. Nothing to be sorry for. You don't ask, you don't learn.

Also, in case anyone's wondering, we're talking about the problem more over in >>12664008.

>> No.12664960
File: 141 KB, 441x441, 1612417119438.png [View same] [iqdb] [saucenao] [google] [report]

Maths is a scam

>> No.12664977
File: 64 KB, 1024x1016, 7f19f8001175565f72f3d16d19020afe55687a7e_hq.jpg [View same] [iqdb] [saucenao] [google] [report]

I would like to become a researcher but it sucks compared to working with finance :(
My knee hurts.

>> No.12665185

>Can one use logical operators in or around mathematical expressions? E.g.
yeah i did for my thesis. it looks better

>> No.12665694
File: 18 KB, 259x259, 1 (214).jpg [View same] [iqdb] [saucenao] [google] [report]

An idea: define a bipartite graph: the vertices are 1, 2, ...n and 1', 2', ... n', and you put an edge (i, j') in your graph iff the square (i, j) is filled.
Then, a rectangle in the picture <=> a 4-length cycle in this graph.
This turns out to be googleable
the correct asymptotics is apparently O(n^3/2)

>> No.12665744

This. You realize all your problems are made up even "applied mathematics" has no relation to the real world.

>> No.12665778

virgin mathematician: thinks they will "discover truth" or do real-world useful stuff, inevitably gets disappointed
chad olympiad problem solver: knows it's all just a competition

>> No.12665837
File: 24 KB, 640x360, 6fc359ba42755c1f9afabdef810a970f.jpg [View same] [iqdb] [saucenao] [google] [report]

I feel you fellow based gabuposter. Also currently in finance. The hours suck but pay is great compared to research. Not sure if I will stick to it though.

>> No.12666022

How do you solve this:
It is 210 km from X to Y by road. Peter took a total of 5 hours to travel from X to Y and back, with the average speed of his car being 20% higher on the way back. Find the average speed of Peter's car while driving from X to Y.

>> No.12666077

[math]V_{avg} = \frac{210km + 210km}{5hr} = \frac{V_{X \rightarrow Y} + V_{Y \rightarrow X}}{2} = \frac{V_{X \rightarrow Y} + 1.2V_{X \rightarrow Y}}{2}[/math]

simply rearrange to isolate [math]V_{X \rightarrow Y}[/math]

>> No.12666197

We are all enemies here. The world of mathematics is a competition and the only rule is that it's every man for himself. You're all just rocks in my path.

>> No.12666202

We are all frens here. The world of mathematics is vast and we can all explore it together. You're all wonderful frens.

>> No.12666242

both are right

>> No.12666270

I can't even find a finance job that pays as low as PhD gibs. Uni professor pays well but in the time it will take me to get there I will be making more in finance.
Sad that we live in a society.

>> No.12666274

How do I get into finance as a senior math undergrad?

>> No.12666442

Anyone here successfully did math on psychedelics (any dose)? I feel like it's a junkie meme/cope from by exp, but I haven't tried doing math on them, nor will be able to anytime soon.

>> No.12666466

Doesn't work. It makes you too dumb for that. But you can get surprising insights on stuff you have been working on for a long time and already know subconsciously.

>> No.12666484

1st edition for a good understanding of linear algebra

>> No.12666503

Why is calling i a constant wierd? Most textbooks I've read define it as (0,1) in R^2

>> No.12666510

>American textbooks

>> No.12666532

No german and russian
Jörg Liesen and Volker Mehrmann Linear Algebra
and Shilov Elementary and real complex analysis.
Ironically when I checked Lang he didn't explicitly use that definition (though it amounts to the same thing)

>> No.12666540

Infact in liesen C is defined as R^2

>> No.12666547

>Infact in liesen C is defined as R^2
Who cares about implementation details? Any algebraic closure of ((([math]\mathbb{R}[/math]))) will do.

>> No.12666560

Ngl, ive been feeling a big attraction to tranny scat porn recently, anyone relate?
- Multimorph

>> No.12666569

>My knee hurts.
Mine does too. How did you fuck up yours

>> No.12666619

Does anyone else get the monogatari reference on op's pic? If you do, you are based.

>> No.12666715

The point is that the only difference between the group R^2 and the algebraic field R^2 is a multiplication operation.

>> No.12666769

It's possible. I'm not sure how helpful it is but it can be done.

>> No.12666829

Lang or D&F for algebra?

>> No.12666893

Let’s just say, I have a Foote fetish...

>> No.12666895
File: 140 KB, 850x1109, __makise_kurisu_steins_gate_drawn_by_cheshikk__sample-aaf24647f99ac6d4c65e809c2be27191.jpg [View same] [iqdb] [saucenao] [google] [report]

>you'll never build a time machine accidentaly while chilling with your friends in your lab
>you'll never find a genius japanese gf
why even live? why even do maths?

>> No.12666899
File: 352 KB, 480x486, mochi.png [View same] [iqdb] [saucenao] [google] [report]

>>you'll never find a genius japanese gf
she's out there, don't lose hope anon

>> No.12666902

life is only pain

>> No.12666944

Dummit and Foote unless you like Lang then use Lang. I think they are both very comprehensive maybe Lang a little more so.

>> No.12666946

Lang is graduate level dude...

>> No.12666967

They are both graduate level it's just Lang is graduate level for people who already know graduate level algebra.

>> No.12666984

I've unironically learned more from "graduate level" books than undergrad books. They just make more sense to me; I'm not sure if it's because they try to "hold your hand" or something in easier books but they don't work as well for me. I don't even see why have the distinction really unless the book is really written purley as a reference.

>> No.12666985

The whole question on which algebra book to use is idiotic. There are hundreds of good algebra texts.
Just read the one that you feel like you can make the most progress in and when the book starts to lose you jump to another book. This way you will have already seen all the basics so more advanced books seems approachable now. Rinse and repeat untill death.

>> No.12666997

Linear Algebra and its Applications by David Lay, 5th ed is pretty good. The pdf is easily findable online just google it.

>> No.12666998

Dummit and Foote is undergrad man...

>> No.12667002

Graduate books are obviously better if you know the basic mechanics, if you don't it is not. For example: almost all computational math procedures.

>> No.12667003

>The whole question on which algebra book to use is idiotic.
Yeah, everyone should just use the golden standard Aluffi already. All others are trash in comparison.

>> No.12667024

Yes. A small percentage of undergraduate programs skim around 7 chapters of D&F.
Usually honors classes.
Still the most common graduate book in algebra.

>> No.12667063

If Dummit and Foote is not an undergraduate book, then what is an undergraduate abstract algebra book?

>> No.12667074

Try google

>> No.12667092

lmao bet you didn't even open a page of dummit and foote before.

>> No.12667115

You realize most undergrad algebra books are 300-500 pages and don't even contain the word module?

>> No.12667127

My uni uses Artin’s Algebra.

>> No.12667132

Huh, never thought about it like that

>> No.12667163
File: 14 KB, 190x266, index.jpg [View same] [iqdb] [saucenao] [google] [report]

What is your favourite math related anime? Mine is "Gotoubun no Hanayome: The Double Integral"

>> No.12667166

That's why you're unemployed.

>> No.12667174

Graduate level is based on content not on how hard the book is.
Artin is harder at almost everything it covers but d&f goes further in almost everything except groups, and it has commutative algebra, algebraic geometry, homological algebra.

>> No.12667180

duh what do you think ring means?

>> No.12667183

Rikei ga Koi ni Ochita no de Shōmei Shite Mita

>> No.12667188

japanese people learn multivariable calculus in highschool? what the hell?

>> No.12667195

Its the origin of space

Think about it for at least 10 minutes, you'll see what I mean.

>> No.12667214

that just indicates how bad education is other countries.

>> No.12667224

Just read the first chapter, the premise is shit and the only math was addition.
Math education is shit in every country.

>> No.12667237

You don't even know for sure if they really study multivariable calculus during high school there. I find it hard to believe, that anime is just trying to romanticize math I guess.

>> No.12667265

I would not be surprised if it were true. Highschool maths in many asian countries is taught at a higher left than the west.

>> No.12667284

No, undergrad calculus books are generally gearing you to be able to solve engineering problems and the like. That shit is mad boring, just keep learning more math anon.

>> No.12667294

Well it's not true.

>> No.12667301
File: 223 KB, 720x692, 1610799499149.png [View same] [iqdb] [saucenao] [google] [report]

How hard is abstract algebra? I've been studying linear algebra by myself with some good progress and abstract algebra seems really cool too. Any recommended prerequisites/books?

>> No.12667303

Probably the hardest undergraduate subject.

>> No.12667323

Easiest by far, out of all undergraduate subjects.

>> No.12667332

If you follow this advice. If not it is cancer aids because you have to read through some hyperspecific contextless word salad at some point.

>> No.12667345
File: 15 KB, 329x499, 31QT+wKaq3L._SX327_BO1,204,203,200_.jpg [View same] [iqdb] [saucenao] [google] [report]

duality of /mg/
is picrel any good? I see it in the meme charts all the time

>> No.12667355

>duality of /mg/
Anyone who says it's easy is either lying or is a genius and considering they're posting on 4chan I'd bet on the former.

>> No.12667357

Yes. This is a standard reference for almost every graduate qualifying exam in America.

>> No.12667361

thank you anon

>> No.12667366

There's a difference between "easy" and "easiest".
One can surely argue that winning the gold medal of one of the olympic disciplines is easiest - but none of us will ever be able to get one nonetheless.

My first post in this thread, but I'd also say pure abstract algebra is easier than, say, stochastics or topology. The objects are just more handson in a sense.

>> No.12667386

I clearly followed it with this. Why are you like this? If this is how much brainpower you use to study algebra then you probably failed at finding out how to open the book.

>> No.12667410

>My first post in this thread
Why did you feel the need to state that, fucking retard?

>> No.12667451

>My first post in this thread
Why did you feel the need to state that, fucking retard?

>> No.12667700

the simplest olympic discipline? math obviously

>> No.12667706

Hatcher says at the bottom of page 186 that the set of functions from the vertices of an oriented graph into an abelian group is also an abelian group. What is the group operation between these functions?

>> No.12667708

Goes both ways. Usually it's one two camps analysis or algebra. I found algebra easier than analysis. I find it strange when people tell me they though analysis was easier. Neither are really hard as you go down the road and learn more.

>> No.12667738

Probably point-wise addition

>> No.12667948

Whenever I start studying I soon get very sleepy. How can I overcome this? It's so annoying.

>> No.12667964

improve sleep/study schedule
fix what you eat and how you exercise

>> No.12667988

Perhaps sleepiness actually is a good thing. It make you take info in moyre intuitively. Try yerba mate also.

>> No.12667997

What is your study environment like? I find that studying when I'm somewhere noisy or busy gives me this sort of sleepy feeling with tension in my head.

>> No.12668011

Simply don't study. Just skim and absorb the knowledge. Math is a spectator sport.

>> No.12668017

Can someone post the definition of minimal uncountable well ordered set from Munkres? I dont have my book on me and Im trying to think about it

>> No.12668057
File: 48 KB, 445x321, opisafaggot.png [View same] [iqdb] [saucenao] [google] [report]


>> No.12668076 [DELETED] 

Let X be a well-ordered set. Given a in X, let S_a denote the Set
S_a = (x|x in X and x <a).
It is called the section of X by a.

There exists a well-ordered set A having a largest element such that
the section SΩ of A by is uncountable but every other section of A is countable.

Note that SΩ is an uncountable well-ordered set every section of which is countable Its order type is in fact uniquely determined by this condition. We shall call it a
minimal uncountable well-ordered set.

SΩ has no Largest element.
For every a in SΩ. the subset {x I a <x} is uncountable.

>> No.12668110

So this shows that A and S0 can have the cardinality of (0,1)w. And I suppose they might depend on which well ordering B has. Can S0 have a different order type than (0,1)w and still have this property?

>> No.12668111

Can someone post the definition of a minimal uncountable well-ordered set from Munkres? I don't have my book on me, and I'm trying to think about it.

>> No.12668116

stfu with your schizo bullshit spude.

>> No.12668122

Bijections are schizo?

>> No.12668136

"""(((finite)))""" cardinality is bullshit. Let alone your delusions on infinity

>> No.12668139

In what way for finite?

>> No.12668146

Do you believe that you can have a "set" of numbers?
Do you believe that even if such a thing existed you could draw arrows to from one to the other?
No. and Hell to the fuck no.

>> No.12668160

9 and 4 both have 2 square roots, Y/N?

>> No.12668175


>> No.12668191

of course not. Just considering the number 2 the number 3. They both have 1 square root, Just draw a square.
Both negatives and imaginary require sets.

>> No.12668214

What should I eat?
It's a little noisy, I can't go to a library because of Covid.

>> No.12668220


>> No.12669669

The formula is trivial since the sine, cosine and pi are basically defined through the exponential to make it work.
What's more impressive are the formulas actually computing these objects.

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