/mg/ - Mathematics General

[Anonymous No.12657631]

Diophantine Equations Edition

Formerly >>12645271

Talk maths.

[Anonymous No.12657655]

Hello my math people :3
*snickers*

[Anonymous No.12657812]

>>12657631
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

[Anonymous No.12657839]

>>12657812
Associating three of the major constants in mathematics in one formula is not a big deal to you?

[Anonymous No.12657860]

>>12657631
>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.

[Anonymous No.12657870]

>>12657812
Because the interesting stuff is too complicated for the average 20 year old.

[Anonymous No.12657875]

>>12657860
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.

[Anonymous No.12657880]

>>12657839
no? why would it be?
also calling i a constant is a bit weird

[Anonymous No.12657888]

>>12657880
Care to tell us what is a big deal to you then, mr genius?

[Anonymous No.12657894]

>>12657888
actual theorems?
this identity is more of a definition than anything really

[Anonymous No.12657913]

>>12657894
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.

[Anonymous No.12657937]

>>12657913
>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

[Anonymous No.12657953]

>>12657860
based
>>12657875
clamped

Elliptic curves are gay and squaring a prime is meaningless.

[Anonymous No.12657956]

>>12657937
Hahaha, you're too much, dude. So, definitions are a product of human imagination but mathematics and logic are not? Hahaha.

[Anonymous No.12657962]

>>12657937
>strawman
Define strawman.
Create an equivalent definition.
Create a better definition in the context of mathematics.

[Anonymous No.12657966]

Any recommendations on self-study textbooks for linear algebra?

[Anonymous No.12657971]

>>12657956
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

[Anonymous No.12657981]

>>12657971
>>12657962
Solve the exercises or you are clamped

[Anonymous No.12657994]

>>12657981
don't care, virgin.

[Anonymous No.12658002]

>>12657971

[Anonymous No.12658020]

>>12657994
clamped

[Anonymous No.12658033]

>>12658002
>>12658020

[Anonymous No.12658056]

>>12657994
>I'll invoke random arguments then drop them the moment I am pressed.
Female?

[Anonymous No.12658079]

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

[Anonymous No.12658085]

>>12658056
your post has literally nothing to do with the conversation, retard

[Anonymous No.12658113]

>>12658079
That bait doesn't work in /mg/. Try asking about consecutive coin flips instead, you'll get 100+ autist posts.

[Anonymous No.12658176]

>>12658113
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?

[Anonymous No.12658319]

>>12658176
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.

[Anonymous No.12658343]

>>12658113
https://www.google.com/search?q="science+%26+math"+"consecutive+heads"
the feels

[Anonymous No.12658368]

>>12657966
Linear Algebra Done Right by Axler

[Anonymous No.12658403]

>>12658368
Enjoy not learning determinants and fucking up your entire understanding of linear algebra and how it relates to other fields.

[Anonymous No.12658422]

>>12658403
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?

[Anonymous No.12658454]

>>12658422
>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.

[Anonymous No.12658530]

>>12658422
>laughs in characteristic p

[Anonymous No.12658537]

>>12658454
What's a good book for Linear Algebra then

[Anonymous No.12658590]

>>12658537
Hoffman&Kunze of course. All others are utter trash in comparison.

[Anonymous No.12658634]

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

[Anonymous No.12658651]

>>12658634
I think undergraduates probably feel out of place here since most of the regulars are at a PhD level.

[Anonymous No.12658656]

>>12657839
>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"

[Anonymous No.12658661]

>>12657966
I would start with a low page count book and work your way up.
Therefore, I recommend Modules by Tom Head.

[Anonymous No.12658721]

>>12657631
Sodachi Oikura is an underappreciated girl

[Anonymous No.12658727]

>>12658656
>It will really
>bur
>only is
>It's is
>onions mathematicians
>for youtube
Jesus Christ, learn some english before trying to reply to me, you fucking idiot.

[Anonymous No.12658743]

>>12658422
>Who gives a f*ck about other fields anyway?
But I like my characteristic greater than 2...

[Anonymous 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

[Anonymous No.12658805]

>>12658656
>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]

[Anonymous No.12658810]

>>12658792
muh autismo needs to have all 5 constants, that's why

[Anonymous No.12658814]

>>12658792
Because during Euler's time the number 0 didn't exist. It makes more sense for it to be equal to zero.

[Anonymous No.12658844]

>>12658810
1 and 0 are not constant

[Anonymous No.12658858]

>>12658844
They're variables right?

[Anonymous No.12658861]

>>12658805
My favorite one is that it's babby's first Lie group / Lie algebra correspondence by
[eqn]\mathrm{exp} : G \twoheadrightarrow \mathfrak{g}[/eqn]

[Anonymous No.12658869]

>>12658651
most of the people here are undergrads
good posts are rare

[Anonymous No.12658878]

>>12658861
fuck switched the group and the algebra
I'm a brainlet

[Anonymous No.12658881]

>>12658858
no but they aren't like pi or sqrt(2) or e.
hey look i made an equation with all 5 constants
1+2+3+4+5=16

[Anonymous No.12658900]

>>12658881
Retard... They are constants, they're just not as important as pi, e or i.

[Anonymous No.12658906]

>>12658878
OK second attempt
[eqn]\mathrm{exp} : \mathfrak{g} \to G[/eqn]
forgive me for having an infinitely differentiable brain, mathanons...

[Anonymous No.12658921]

>>12658900
yeah so why add them? there is no need for the +1

[Anonymous No.12658930]

>>12658881
>>12658844
0 and 1 are constants just as e or pi you brainlet

[Anonymous 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?

[Anonymous No.12658972]

>>12658651
>most of the regulars are at a PhD level
ahahahaha those are just undergrads trying to sound smart

[Anonymous No.12659002]

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

[Anonymous No.12659014]

>>12659002
But that would exclude you and I want to see you beautiful contributions to the thread <3 OwO

[Anonymous No.12659019]

>>12658930
No

[Anonymous No.12659021]

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

[Anonymous No.12659031]

>>12658930
0 1 are constants but 2 and bigger are not a constant because the value depends in different characteristics

[Anonymous No.12659047]

>>12659031
That's not how math works

[Anonymous No.12659056]

>>12659047
Elementary abstract algebra is a prerequisite for posting in /mg/.
>>12659031
Bold of you to assume that my ring is unital.

[Anonymous No.12659071]

>>12658906
it's just based af all around.

[Anonymous No.12659072]

>>12658661
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.

[Anonymous No.12659103]

>>12659072
It's the same book, 1991 is the second edition.

[Anonymous No.12659118]

>>12659021
god i want an asian girlfriend
or a white girlfriend
or a tranny

[Anonymous No.12659120]

>>12658810
>>12658844
>>12658858
>>12658881
>>12658900
>>12658930
>>12659031
>>12659047
>>12659056
ughhh guys i asked why euler's identity has +1 instead of the answer just being -1

[Anonymous No.12659133]

>>12659072
second one

[Anonymous No.12659149]

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?

[Anonymous No.12659178]

>>12659056
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.

[Anonymous No.12659208]

>>12659133
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.

[Anonymous No.12659265]

>>12659178
non-unital means no 1, asshat

[Anonymous No.12659276]

>>12659265
Then it's just 0 and there is no notion of bigger you fucking niggerfaggot

[Anonymous No.12659283]

>>12659276
You truly don't understand what a non-unital ring is, anon. You must be an analyst.

[Anonymous No.12659326]

>>12659283
call it a rng then

[Anonymous No.12659356]

>>12659283
Holy fuck you are so god-damn stupid. 2Z
2 is a constant.
ring implies unital btw You mean rng.

[Anonymous No.12659366]

>>12659283
>0 and 1
>ring
>nonunital ring btw gotcha dummy

[Anonymous No.12659377]

>>12657631
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. ; (

[Anonymous No.12659385]

>>12659356
>rng
Same fucking shit, nigga.

[Anonymous No.12659392]

>>12659377
What's an FoV?

[Anonymous 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?

[Anonymous No.12659423]

>>12659392
Field of Vision/View

[Anonymous 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
Thoughts?

[Anonymous No.12659481]

>>12659149
12659149 is a valid upper bound.

[Anonymous No.12659484]

>>12659481
Aboutt 50 unique posters a thread
50 is a valid upper bound
49 cause Im not a faggot

[Anonymous No.12659495]

>>12659356
here's a curious fact: 0=2 in Z2 but 0!=2 in Z
so clearly they can't both be constants

[Anonymous No.12659499]

>>12659473
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

[Anonymous No.12659502]

>>12659149
>multiple anime math trannies exist
>i haven't had sex with any of them
please just kill me

[Anonymous No.12659512]

>>12659495
wrong
[0]_2 = [2]_2 in Z_2

[Anonymous No.12659518]

>>12659409
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

[Anonymous No.12659517]

>>12659495
and 0! = 1

[Anonymous No.12659528]

>>12659518
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

[Anonymous 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?

[Anonymous No.12659537]

>>12658651
>>12658972
just look at this faggot >>12659031 >>12659056 >>12659265 >>12659283 right here, typical example of larping freshman

[Anonymous No.12659542]

>>12659535
If it's not worth doing it wouldn't be in the book anon

[Anonymous No.12659779]

>>12659542
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.

[Anonymous No.12659789]

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

[Anonymous 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?

[Anonymous No.12659822]

>>12659499
Smoke dmt if you want to "experience infinity". Or go shopping with a woman, you will learn that infinity can be experienced.

[Anonymous No.12659847]

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

https://i.4cdn.org/gif/1611966761919.webm

[Anonymous No.12659862]

>>12659512
i want to fuck it

[Anonymous No.12659926]

>>12659779
We speak english in /mg/

[Anonymous No.12659933]

>>12659926
Auch deutsche

>>12659822
Ja ich erinnern von mein Junger tag mit mein mutter

[Anonymous No.12659948]

>>12658727
>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

[Anonymous No.12659956]

>>12659948
>basedjak posting
>chad meme posting
What is it like being completely unoriginal? Seriously just go back to funnyjunk.

[Anonymous No.12660004]

>>12659847
2018.

[Anonymous No.12660013]

>>12659779
>through physics
Which physics? There's an uncountable number of them.

[Anonymous No.12660058]

>>12660004
What happened in 2018?

[Anonymous No.12660093]

>>12658743
vendace

[Anonymous No.12660103]

>>12659535
>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?

[Anonymous No.12660140]

>>12660004
Most anime posters started posting around that time, me included. That's all.

[Anonymous No.12660147]

>>12655023

[Anonymous No.12660193]

>>12657937
I bet you think integers are a social construct

[Anonymous No.12660198]

>>12657966
just get a statics textbook.
it's basically the same thing

[Anonymous No.12660204]

>>12658319
fascinating theory.
that didn't happen though so your point is retarded.
white people did it. period.

[Anonymous No.12660209]

>>12659956
>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

[Anonymous No.12660219]

>>12660193
But integers are a social construct. All of maths is. You think math exists physically in the world?

[Anonymous No.12660220]

>>12658814
do you seriously think we didn't have the number 0 during the 1700s?

[Anonymous No.12660229]

>>12659002
go to reddit if you want efame

[Anonymous No.12660232]

>>12660229
You see, that's my secret, anon... I'm already on Reddit.

[Anonymous No.12660256]

>>12660232
4chan is just a meta site for reddit commentary at this point.
why even live anymore?

[Anonymous No.12660270]

>>12660256
>why even live anymore?
To solve all of mathematics.
To discover all the truths in the universe with physics.
To find a japanese girlfriend.

[Anonymous No.12660495]

>>12658906
I got ur joke and made me chuckle so you're forgiven

[Anonymous No.12660500]

>>12660140
DIS GUS TANG!
newfags are bad enough but avatarfags get the rope desu

[Anonymous No.12661081]

>>12660256
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.

[Anonymous No.12661185]

man, mathematicians are cringe

[Anonymous No.12661194]

>>12661081
>the age of the r*dditor.
and peadophiles, ie anime posters

[Anonymous No.12661200]

>>12658948
>noncommutative ring
https://www.cs.ox.ac.uk/files/7352/SpectrumProblem-Oxford.pdf


The spectrum problem for noncommutative rings and algebras

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

[Anonymous No.12661287]

>>12661200
https://ncatlab.org/nlab/show/noncommutative+algebraic+geometry

[Anonymous No.12661737]

>>12661185
Read a book like How to prove it, then you'll see that you're wrong and grovel for forgiveness.

[Anonymous No.12661839]

>>12661737
Why that book?

[Anonymous No.12661855]

>>12657631
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.

[Anonymous No.12661958]

>>12660013
What did he mean by this

>>12660103
>square circles
With integrals
>infinitely infinite
But do we even know what infinity means yet?

[Anonymous No.12661974]

>>12657839
>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?

[Anonymous No.12661999]

>>12657812
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)

[Anonymous No.12662009]

>>12661958
> 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.

[Anonymous No.12662012]

>>12662009
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.

[Anonymous No.12662066]

>thread derailed by a single post
wew

[Anonymous No.12662113]

>>12662066
ara so, you realize you're derailing it even more by complaining instead of staying on topic, right?

[Anonymous No.12662167]

>>12661958
>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?

[Anonymous No.12662171]

>>12660058

[Anonymous No.12662178]

>>12660147
The first sentence is grammatically incorrect.

[Anonymous No.12662187]

>>12662171
Is that good?

[Anonymous No.12662194]

>>12659495
There is no way 0! is 2 read Bourbaki and how the figure 0! = 1

[Anonymous No.12662195]

>>12662187
It's shit but it has Astolfo.

[Anonymous No.12662204]

>>12662167
A geometer living 4000 years ago knows more math than you ever will. COPE

[Anonymous No.12662299]

>>12662204
wanking over "infinities" and "meaning of infinity" is not math

[Anonymous No.12662331]

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

>>12662167
I am indeed one of those idiots

[Anonymous No.12662339]

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.

[Anonymous No.12662375]

>>12662331
>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.

[Anonymous No.12662409]

>>12658656
I owe my undying interest in mathematics to Numberphile. Science popularizers are unironically the only hope left for public school educated Westerners.

[Anonymous No.12662416]

>>12658906
Hey, don't beat yourself up anon, you have an analytic mind (if your brain is complex)

[Anonymous No.12662497]

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

[Anonymous No.12662498]

>>12662204
Nothing against geometry. Physishits trying to determine truth via their pitiful little theories, that's what I hate.

[Anonymous No.12662525]

>>12662375
Finally I wont have to deal with this chinks annoying replies anymore

[Anonymous No.12662532]

>>12662498
The integers literally came from physics. Bakameno! Ever heard of counting rocks? Grug smash!

[Anonymous No.12662533]

>>12662532
The integers came from accounting.

[Anonymous No.12662536]

>>12662533
You can only account material , which is physics.

[Anonymous No.12662540]

>>12662533
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

[Anonymous No.12662547]

>>12662540
That's a natural number. Integers are relevant when you need to start considering debt and sheit.

[Anonymous No.12662548]

>>12662540
Ok, whistle –3 times

[Anonymous No.12662570]

>>12662547
Sure but thats just the memory of physics, remembered objects. Also sealevel and underwater

>>12662548
Do the form of whistling where you suck air in instead of blow out
Negatives are just a reversible index

[Anonymous No.12662573]

>>12662532
[math]\text{physics }\ne \text{ nowaday physicists}[/math]

[Anonymous No.12662580]

>>12662532
physics ≠ nowadays physicists

[Anonymous No.12662675]

i havan't dont any maths today

[Anonymous No.12662699]

>>12657966
I used Friedberg's book, I thought it was really nice

[Anonymous No.12662706]

>>12657966
Wildberger's linear algebra course and linear algebra notes by Terrence Tao

[Anonymous 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?

[Anonymous No.12662815]

>>12662742
>I was only able to take this course because I had the pre-requisites
Thats, uh, not uncommon

[Anonymous No.12662823]

>>12657812
God I genuinely despise those onions faggots who go ape shit about famous (((equations))) even though they have no fucking clue what they mean

[Anonymous No.12662827]

>>12662742
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

[Anonymous No.12662845]

>>12662815
>>12662827
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...

[Anonymous No.12662850]

>>12662409
> Science popularizers are unironically the only hope left for public school educated Westerners
HAHAHAHHAHAHHAHA
we're fucking done
we are done

[Anonymous No.12662867]

>>12661081
I think it's more twitter and tiktok really

[Anonymous No.12662871]

>>12662742
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.

[Anonymous 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.

[Anonymous No.12662883]

>>12662871
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.

[Anonymous No.12662953]

Is Eisenbud and Matsumura enough for this? (Granted I don't think I'm going to finish all of Eisenbud)

[Anonymous 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]?

[Anonymous No.12662966]

>>12662867
Which is crazy because Twitter is almost as old as 4chan at this point.

[Anonymous No.12662968]

>>12662953
Eisenbud, sure. Don't know about that other one.

[Anonymous No.12662976]

>>12662962
If you don't know the answer, then you don't exactly know the definition of the sequence of taylor polynomial approximations.

[Anonymous No.12663014]

>>12662976
ahhhhhhh then tell me please

I can't find a formal definition ANYWHERE

[Anonymous No.12663025]

>>12662962
Nah. [math]P_n[/math] has just the terms of degree up to and including n.

[Anonymous No.12663077]

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

https://www.google.com/books/edition/Choice/c-48AQAAIAAJ?hl=en&gbpv=1&dq=choice+magazine+mathematics&pg=PA488&printsec=frontcover

[Anonymous No.12663087]

>>12663077
LMAO can't believe that's actually a thing.

[Anonymous No.12663102]

>>12663077
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.

[Anonymous No.12663106]

>>12660270
>posts russian character

please reiterate

[Multimorph 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

[Anonymous No.12663116]

>>12663077
KEK

[Anonymous No.12663134]

>>12663116
>non-commutative vector field
Google shows nothing, is the definition just "a derivation on a C*-algebra" or is it different?

[Anonymous No.12663140]

>>12663134
Oh, it's noncommuting, not noncommutative.
Disregard my previous post, I remember what that means.

[Anonymous No.12663141]

>>12663134
non commuting vector fields

[Anonymous No.12663154]

>>12663077
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.

[Anonymous No.12663161]

>>12663154
Ya but I want to just have a bunch of reviews and read them all and then decide what subject/book looks cool.

[Multimorph No.12663250]

Is machine code an arithmetization?

[Multimorph No.12663261]

Prime factorization provide coordinate storage within one dimension

[Anonymous No.12663299]

>>12660256
>>12661081
all zoomers are redditors, they turn every site into the same shitty discourse and memes

[Anonymous No.12663323]

Discussing the Bitcoin/Ethereum elliptic curve spec

https://youtu.be/RZzB-vPFYmo

[Anonymous No.12663371]

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

[Anonymous No.12663462]

>>12663371
Will the behavior of functions remain impenetrable forever or can some general theory exist?

[Multimorph No.12663496]

>>12663462
You can define a random function as the outputs of a QRNG over natural time steps and that will be impenetrable

[Multimorph No.12663503]

>>12663496
In the limiting/unioning of all times case

[Anonymous No.12663531]

>>12663154
Half this shit is in german ahhhhhh

[Anonymous 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]

[Anonymous No.12663811]

>>12663730
the third statement sets x equal to a truth value

[Anonymous No.12663839]

>>12663730
No, root(y) is a term, you cannot use terms in non-atomic formulas. Also that looks a like shit, just use English.

[Anonymous No.12663969]

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?

[Anonymous No.12663977]

>>12663730
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.

[Anonymous No.12664020]

>>12657839
Big whoop I can do that too. Here's a formula with 4 constants

e^0 - 1 = i * 0

[Anonymous No.12664049]

>>12664020
>>12661974
>>12658656
>>12657880
>>12664020
autism

[Anonymous No.12664051]

>>12663969
Use Cauchy-Schwarz

[Anonymous No.12664067]

>>12664051
Cauchy–Bunyakovsky–Schwarz*

[Anonymous No.12664181]

>>12663969
>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.

[Anonymous No.12664237]

>>12662880
http://www.cs.columbia.edu/~verma/classes/ml/lec/lec9_graphical_models_markov_hmm.pdf
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.

>>12662883
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.

[Anonymous No.12664272]

>>12664237
>>12662880

wrong link
http://www.cs.columbia.edu/~verma/classes/ml/

[Anonymous No.12664301]

>>12664181
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?

[Anonymous No.12664349]

>>12664301
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.

[Anonymous No.12664380]

>>12663811
>>12663839
>>12663977
I have used set belonging notation also. Trying to settle on a style. Thanks for the input.

[Anonymous No.12664384]

>>12664349
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.

[Anonymous No.12664416]

>>12664384
>how did you quickly come up with that solution by seeing how it relates to graph theory?
>quickly
ahahahaha
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.

[Anonymous No.12664960]

Maths is a scam

[Anonymous No.12664977]

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

[Anonymous No.12665185]

>>12663730
>Can one use logical operators in or around mathematical expressions? E.g.
yeah i did for my thesis. it looks better

[Anonymous No.12665694]

>>12663969
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
https://math.stackexchange.com/questions/1713140/maximize-the-number-of-edges-in-a-bipartite-graph-with-no-4-cycles
the correct asymptotics is apparently O(n^3/2)

[Anonymous No.12665744]

>>12664960
This. You realize all your problems are made up even "applied mathematics" has no relation to the real world.

[Anonymous 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

[Anonymous No.12665837]

>>12664977
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.

[Anonymous 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.

[Anonymous No.12666077]

>>12666022
[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]

[Anonymous 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.

[Anonymous No.12666202]

>>12666197
We are all frens here. The world of mathematics is vast and we can all explore it together. You're all wonderful frens.

[Anonymous No.12666242]

>>12666197
>>12666202
both are right

[Anonymous No.12666270]

>>12665837
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.

[Anonymous No.12666274]

>>12665837
How do I get into finance as a senior math undergrad?

[Anonymous 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.

[Anonymous No.12666466]

>>12666442
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.

[Anonymous No.12666484]

>>12662742
Read
>>12658661
1st edition for a good understanding of linear algebra

[Anonymous No.12666503]

>>12657880
Why is calling i a constant wierd? Most textbooks I've read define it as (0,1) in R^2

[Anonymous No.12666510]

>>12666503
>American textbooks

[Anonymous No.12666532]

>>12666510
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)

[Anonymous No.12666540]

>>12666532
Infact in liesen C is defined as R^2

[Anonymous No.12666547]

>>12666540
>Infact in liesen C is defined as R^2
Who cares about implementation details? Any algebraic closure of ((([math]\mathbb{R}[/math]))) will do.

[Multimorph No.12666560]

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

[Anonymous No.12666569]

>>12664977
>My knee hurts.
Mine does too. How did you fuck up yours

[Anonymous No.12666619]

>>12657631
Does anyone else get the monogatari reference on op's pic? If you do, you are based.

[Anonymous No.12666715]

>>12666547
The point is that the only difference between the group R^2 and the algebraic field R^2 is a multiplication operation.

[Anonymous No.12666769]

>>12666442
It's possible. I'm not sure how helpful it is but it can be done.

[Anonymous No.12666829]

Lang or D&F for algebra?

[Anonymous No.12666893]

>>12666829
Let’s just say, I have a Foote fetish...

[Anonymous No.12666895]

>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?

[Anonymous No.12666899]

>>12666895
>>you'll never find a genius japanese gf
she's out there, don't lose hope anon

[Anonymous No.12666902]

>>12666895
life is only pain

[Anonymous No.12666944]

>>12666829
Dummit and Foote unless you like Lang then use Lang. I think they are both very comprehensive maybe Lang a little more so.

[Anonymous No.12666946]

>>12666944
Lang is graduate level dude...

[Anonymous No.12666967]

>>12666946
They are both graduate level it's just Lang is graduate level for people who already know graduate level algebra.

[Anonymous No.12666984]

>>12666946
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.

[Anonymous 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.

[Anonymous No.12666997]

>>12657966
Linear Algebra and its Applications by David Lay, 5th ed is pretty good. The pdf is easily findable online just google it.

[Anonymous No.12666998]

>>12666967
Dummit and Foote is undergrad man...

[Anonymous No.12667002]

>>12666984
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.

[Anonymous No.12667003]

>>12666985
>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.

[Anonymous No.12667024]

>>12666998
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.

[Anonymous No.12667063]

>>12667024
If Dummit and Foote is not an undergraduate book, then what is an undergraduate abstract algebra book?

[Anonymous No.12667074]

>>12667063
Try google

[Anonymous No.12667092]

>>12667074
lmao bet you didn't even open a page of dummit and foote before.

[Anonymous No.12667115]

>>12667092
You realize most undergrad algebra books are 300-500 pages and don't even contain the word module?

[Anonymous No.12667127]

>>12667063
My uni uses Artin’s Algebra.

[Anonymous No.12667132]

>>12663261
Huh, never thought about it like that

[Anonymous No.12667163]

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

[Anonymous No.12667166]

>>12667132
That's why you're unemployed.

[Anonymous No.12667174]

>>12667063
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.

[Anonymous No.12667180]

>>12667166
>>12667132
duh what do you think ring means?

[Anonymous No.12667183]

>>12667163
Rikei ga Koi ni Ochita no de Shōmei Shite Mita

[Anonymous No.12667188]

>>12667163
japanese people learn multivariable calculus in highschool? what the hell?

[Anonymous No.12667195]

>>12657812
Its the origin of space

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

[Anonymous No.12667214]

>>12667188
that just indicates how bad education is other countries.

[Anonymous No.12667224]

>>12667163
Just read the first chapter, the premise is shit and the only math was addition.
>>12667214
Math education is shit in every country.

[Anonymous No.12667237]

>>12667214
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.

[Anonymous No.12667265]

>>12667237
I would not be surprised if it were true. Highschool maths in many asian countries is taught at a higher left than the west.

[Anonymous No.12667284]

>>12662497
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.

[Anonymous No.12667294]

>>12667265
Well it's not true.

[Anonymous No.12667301]

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?

[Anonymous No.12667303]

>>12667301
Probably the hardest undergraduate subject.

[Anonymous No.12667323]

>>12667301
Easiest by far, out of all undergraduate subjects.

[Anonymous No.12667332]

>>12666985
>>12667323
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.

[Anonymous No.12667345]

>>12667303
>>12667323
duality of /mg/
>>12667332
is picrel any good? I see it in the meme charts all the time

[Anonymous No.12667355]

>>12667345
>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.

[Anonymous No.12667357]

>>12667345
Yes. This is a standard reference for almost every graduate qualifying exam in America.

[Anonymous No.12667361]

>>12667357
thank you anon

[Anonymous No.12667366]

>>12667355
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.

[Anonymous No.12667386]

>>12667355
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.

[Anonymous No.12667410]

>>12667366
>My first post in this thread
Why did you feel the need to state that, fucking retard?

[Anonymous No.12667451]

>>12667366
>My first post in this thread
Why did you feel the need to state that, fucking retard?

[Anonymous No.12667700]

>>12667366
the simplest olympic discipline? math obviously

[Anonymous 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?

[Anonymous No.12667708]

>>12667303
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.

[Anonymous No.12667738]

>>12667706
Probably point-wise addition

[Anonymous No.12667948]

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

[Anonymous No.12667964]

>>12667948
improve sleep/study schedule
fix what you eat and how you exercise

[Mult No.12667988]

>>12667948
Perhaps sleepiness actually is a good thing. It make you take info in moyre intuitively. Try yerba mate also.

[Anonymous No.12667997]

>>12667948
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.

[Anonymous No.12668011]

>>12667948
Simply don't study. Just skim and absorb the knowledge. Math is a spectator sport.

[Mult 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

[Anonymous No.12668057]

>>12668017

[Anonymous No.12668076]

>>12668017
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.

[Mult No.12668110]

>>12668057
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?

[Anonymous 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.

[Anonymous No.12668116]

>>12668110
>cardinality
stfu with your schizo bullshit spude.

[Mult No.12668122]

>>12668116
Bijections are schizo?

[Anonymous No.12668136]

>>12668122
"""(((finite)))""" cardinality is bullshit. Let alone your delusions on infinity

[Mult No.12668139]

>>12668136
In what way for finite?

[Anonymous No.12668146]

>>12668139
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.

[Mult No.12668160]

>>12668146
9 and 4 both have 2 square roots, Y/N?

[Anonymous No.12668175]

>>12668160
no.

[Anonymous No.12668191]

>>12668160
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.

[Anonymous No.12668214]

>>12667964
What should I eat?
>>12667997
It's a little noisy, I can't go to a library because of Covid.

[Anonymous No.12668220]

>>12668218

[Anonymous 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.