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/sci/ - Science & Math

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12605538 No.12605538 [Reply] [Original] [archived.moe]

think outside the box edition
previous thread: >>12588999

>> No.12605557
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>> No.12605562

does anyone remember which german uni had a good set of algebraic geometry notes?
think it had an -eide- or a -burg in the name

>> No.12605569

That's inflation not expansion

>> No.12605584
File: 88 KB, 996x720, 99s1q.jpg [View same] [iqdb] [saucenao] [google] [report]

Heidelberg? Regensburg? Those would be two quick guesses.

>> No.12605618

might have been bielefeld
some kind anon posted a link to their notesquite a long time ago

>> No.12605637


>> No.12605650
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>> No.12605661
File: 39 KB, 657x527, 1610511423816.jpg [View same] [iqdb] [saucenao] [google] [report]

retarded anon here, just finished College Algebra 1 with an A, do I progress next to Pre-Calculus or can I jump straight into Calc 1 without being too lost? Don't shit on me please I never applied myself in high school and am doing my best to relearn all the math I've forgotten or never learned.

>> No.12605669

you HAVE to start calculus, NOW, ANON NOW! DON'T LOOK BACK

>> No.12605670

what the hell is 'college algebra 1'?

>> No.12605672

x * x = 2x

>> No.12605674

The first level of college algebra I don't know anon, it wasn't hard but I also took it at a juco.

>> No.12605675

americans really are fucking their young adults into a life of debt servitude

>> No.12605677

You go at it step by step. Obviously, pre-calculus
comes before calculus so try for it. For me, I
jumped to calculus at college after doing the pre
at high school.

>> No.12605682

My college is free, I did my time with el Army and now I get my bennies
Ok I'll enroll into pre calculus. I bought a Ti Nspire CX before my Algebra because I found a used one for $60 and it worked well.

>> No.12605687

Another retarded anon here. After a book like Dummit and Foote, should one read Lang's algebra or go right to a commutative algebra text like Atiyah? I frankly don't really understand how these things fit together. My university's grad program for example starts with commutative algebra, so I'm not sure why other programs have year long abstract algebra courses.

Go to Calc 1. I believe in you anon!

>> No.12605689

thank you for your service to Isreal

>> No.12605695

np anon, actually the only deployment I went on was a peace keeping mission between Israel and every country around that hates them so I unironically did serve Israel :^)

>> No.12605700

did you get your foreskin back at the end of your service?

did your uni recommend any supplementary mats? or is there at least someone there you could ask?
it largely depends on the content of your grad course

>> No.12605752

I had a TI-89 Titanium for a good while until I lost
it for some damn reason. I now work with the
non-graphing Canon F792-SGA which works
just fine for me.

>> No.12605967
File: 1003 KB, 1589x1627, 1611168635082.png [View same] [iqdb] [saucenao] [google] [report]

What's the deal with Aluffi?
Is it a good intro to abstract algebra or is it a meme?

>> No.12605971

kurisu is the answer

>> No.12605981
File: 832 B, 153x87, math is solved.png [View same] [iqdb] [saucenao] [google] [report]

Why do people have hard time grasping this?

>> No.12605998

What is there to grasp?

>> No.12606004

Grasp THIS

>> No.12606014
File: 19 KB, 400x400, e736b127e4ac0a1f605c74e53038ba56.jpg [View same] [iqdb] [saucenao] [google] [report]

You answered the wrong question!

>> No.12606024

I think that's too small for me to have any grip.

>> No.12606028

nothing, math is religion, no knowledge only belief (unlike the superior observational science of biology, the true meta-science).

>> No.12606029

That you will never be a whole number.

>> No.12606107

You talk a lot of shit online but I bet you wouldn’t say that with my cock in your face.

>> No.12606376


>> No.12606383

>be me
>hate math
>always get A’s in math classes
>tell people that I hate math
>”you must just be bad at it”
Why are mathfags like this?

>> No.12606485

same feel anon

>> No.12606496

>Why are mathfags like this?
because most of the time, people hate math because they're bad at it

>> No.12606502

If I was doing summer undergrad research, what would be better, something something in know theory or Bass-Serre theory?

>> No.12606506

excuse my brain melting, *something in knot theory

>> No.12606524
File: 11 KB, 275x183, schlop.jpg [View same] [iqdb] [saucenao] [google] [report]

based largo

>> No.12606533 [DELETED] 

I have an algebraic curve C over the field of complex numbers and n given points, not necessarily distinct. Is there a general way to prove that the sum of these n points is a canonical divisor? I'd need a nonzero divisor of a differential form that is this sum plus a principal divisor.
I know that there are exactly n points outside of each affine chart and I know how they look like, not sure if this helps.

>> No.12606651

>always get A’s in math classes
>thinks that makes him good at math
Pathetic. Math is for the chosen few. 170+ IQ or gtfo.

>> No.12606654

Aluffi is good for a first text on abstract algebra, and also it teaches category theory along the way. I'm not sure why it isn't more widely used in undergrad.

Pinter is also good according to anons, although I'm not sure because I've not tried it myself.

>> No.12606661

>in online classes
>doctor says we don't have to take notes, he will send the board after class
>can't concentrate if I don't take notes, end up watching memes
b-bros, I may be retarded

>> No.12606676

It means I’ve been successful with every bit of mathematics I’ve been presented with, so...

>> No.12606681

You may be, but at least we are both retarded

>> No.12606793

anyone have a nifty derivative/integral to solve that requires some creativity but let's limit it to college level and not grad level?
had a professor who knew a lot of these but I don't know where he got them from.

>> No.12606826

[math] \int_0^1 1\ dx[/math]

>> No.12606901

these seem to be fairly disparate fields
which do u like more? what classes have u taken?

>> No.12606907

look at the previous years of the putnam exam my friend, plenty of interesting integrals and ODEs

>> No.12606919

Candidate for the lowest bar of a meaningful proposition: the ability to decide it given halting oracles of arbitrarily high complexity.
Exercise: find math problems that don't fit this criterion.

>> No.12606929

The ones Michael Penn does, maybe?

>> No.12606929,1 [INTERNAL] 

Aluffi is a meme
Pinter is a meme
>anyone who disagrees is wrong

>> No.12607030

Some algebra, some algebraic topology, I mean, I'm an undergrad. I haven't taken a dedicated course in combinatorics though, just the basics which were taught in a 1st year class, so that kinda worries me about bass-serre

>> No.12607032

>some algebraic topology
which I'm in rn

>> No.12607045

im also currently an undergrad in topology, i think knot theory might be the way to go then

>> No.12607246

Apparently I proved impossible what my professor is asking on an exercise.

Consider the algebraic curve [math]C := \{ (x:y:z)\in \mathbb{C}P^2\, ;\ x^4+y^4+z^4=0\}[/math], and let [math]P_1, P_2, P_3, P_4\in C[/math] be points, not necessarily distinct (they are more specific, but the data doesn't matter). He asks to show that [math]D := P_1+P_2+P_3+P_4[/math] is a canonical divisor of [math]C[/math].

What I did (in brief):
1. This is equivalent to the existence of [math]g\in \mathbb{C}(C)^\times[/math] with [math]\text{div}(g) + \text{div}\left( d\left(\frac{x}{y}\right)\right) = D[/math];
2. [math]\text{div}\left( d\left(\frac{x}{y}\right) \right) = -2(P_{2, 0}+P_{2, 1}+P_{2,2} + P_{2,3}) [/math] where [math]P_{2, j} = (1 : 0 : \mu_8^{2j+1})[/math] for each [math]j[/math];
3. Taking degrees of both sides in 1 and using 2 we get the impossibility 0 - 8 = 4.

What am I doing wrong here?

>> No.12607505

[math] \int_0^1 1\, dx=x\,|_0^1 [/math]
[math] \int_0^1 1\, dx=1-0 [/math]
[math] \int_0^1 1\, dx=1 [/math]
[math] QED [/math]

>> No.12607528

lmao I probably played 100 hours of hype rouge while my professors were lecturing last semester. It was sick.

>> No.12607651

take lighter notes and also focus more on synthesis

e.g. note down the general approach of a proof and which parts you find difficult / don't fully understand, relate what's being said to earlier material / other courses, etc..

at least for me this helps me stay focused while not merely copying everything on the screen

>> No.12608119

Update. Apparently I am indeed wrong, the degree of the canonical divisor should be 2g-2 = 4. The first item should be correct, so d(x/y) should be canonical and thus have degree 4, so the mistake should be on the second item.
But I can't see how my calculation of that divisor is wrong. I used [math]d(x/y) = -(x/y)^2 d(y/x)[/math] and local parameters.
Help plz

>> No.12608293

what the fuck is that thing between the numbers? why do mathematicians just make shit up man, it’s not helpful

>> No.12608563

i would have given them credit for that kek.

>> No.12608566

you're still bad at math

>> No.12608598

I'm trying to read some math textbooks by myself. But they are hard af, a few pages on number theory took me hours. Should I keep grinding proofs or just skimming through theorems to help my cs major?

>> No.12608610

Something like 2x + 8 + 12x - 4x = 7
>Find X

>> No.12608682

>Find X
It isn't in there, please, I've looked as much as I can, I just want to pass!

>> No.12608786

What number theory book are you using?

I don’t think there’s any reason to read number theory theorems without going through proofs

>> No.12608804

Sheldon Axler used to say that for students it is not only normal but also desirable to spend ~1 hour on some of the heavier pages. But once you git gud you will speed up naturally

>> No.12608849

>Sheldon Axler used to say that for students
it's also written in his
>Measure, Integration & Real Analysis
pdf of which is freely available on springer

>> No.12608960

Here's a question for /mg/ historians

>> No.12609089

It's all true

>> No.12609571

Kinda liked this take on it.

>> No.12609612

Any math undergrads here? How does something like Calculus 1 - 2 -3 compare, in terms of difficulty, to other classes you guys have?

>> No.12609665
File: 1 KB, 300x300, 5x5-grid.png [View same] [iqdb] [saucenao] [google] [report]

Is it possible to remove one square from 5x5 grid and then cut remaining squares into three congruent parts?

>> No.12609668

All equally easy.

>> No.12609706

I'll give you some actual advice instead of these muh anons "math is joke".

The entirety of Calc 1 only requires a few things to be known:
- Functions
- Knowledge on factoring
- Exponents, logarithms, properties of each
- Some trig (unit circle)

Basically if you know at least 50% of the stuff posted on this website you are prepared to do Calc 1, albeit with a little more difficulty than if you had taken PreCalc: https://www.mathsisfun.com/algebra/index-college.html

You should only take PreCalc if you have little/no idea what the above topics I listed are.

All in all, as long as you have access to Khan Academy to explain some stuff that is new to you, you'll be more than ready to go to Calc 1.

>> No.12609709

Precalc is literally a meme. I'm not joking, I took it and it was just a refresher on algebra 2. DO CALCULUS ANON YOU'LL THANK YOURSELF YOU DIDN'T WASTE A SEMESTER.

>> No.12609744

Is calc course the circumcision of mathematics?
It's the first encounter with "serious" maths (like first sexual experience of the rabbi sucking out the blood), permanently traumatises the youth with shockingly nonsense axioms and constructions (like permanent brain trauma from shock during circumcision), and those who fail, can never do maths again (like a botched surgery, rendering unable to ever have sex). Those who take it, are forever going to only see the world like this, and do weird, increasingly degenerate, constructions with sets when a simpler, potentially constructive, alternative exists for those intact (think how circumcised men masturbate and have sex).
When it comes to teaching the youth analysis again, they'll do the same as what was done to them, the analogy here is obvious. The ethno-religious background is identical too.

>> No.12609773

dunno what schizobabble you posted
but it seems to be a non-consensual problem in america
so maybe

>> No.12609805

This a joke or for real?

>> No.12609866

are calc 1-3 supposed to be first year modules?

>> No.12609898

1 and 2 are first year where I study. Hence my question, does it get harder or what?

>> No.12609918


Where I'm from, trig is one semester of precalc, and you should probably take that. (The trig functions are important in calc and there is some interesting af math to be learned) But the functions and analysis semester is garbage. Like you said, it's literally just Algebra 2. I skipped that and calc is no harder.

>> No.12609933

do your homework
seriously, those exercises are there for a reason. if you don't want to go further into it later in your degree then at least you have a decent grade to show
the plug and chug parts of calculus should be very easy with sufficient practice
some people stumble a bit in anal classes, and struggle a bit with their arguments/proofs

>> No.12610221 [DELETED] 

Solved. Problem was, x/y - a/b is not always a local parameter for a point with non-zero second coordinate, we have to be careful with what happens in the local ring, this can become 0 there and then its order would actually be +infinity.

>> No.12610241

Solved. Problem was, x/y - a/b is not always a local parameter for a point with non-zero second coordinate, we have to be careful with what happens in the local ring, this can become 0 modulo the square of the maximal ideal there, so its order at P would be greater than 1.

>> No.12610451 [DELETED] 
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How do I make this fuction go to (1,1) in the same way as it's coming from (0,0)?
Point symmetry around (1/2,1/2).
Think of -a instead of -0.21 with 0<a<1.

>> No.12610600

>lol just ignore additive constants
>lol just ignore constant factors
>if I write [math]\ll[/math] everywhere no one will question my arguments
>bro ur cauchy schwarz?
Why is analysis and analytic number theory in particular such a farce?

>> No.12610609

just feel and experience the size of the quantities with your intuition
no one gives a shit abour rigor

>> No.12610627

>x * x = 2x
x * x = x^2

>> No.12610631

did i win?

>> No.12610755

That's not inflation, that's gaping.

>> No.12610770

Calculus is actually pretty simple to understand if you ignore delta-epsilon proofs, or ignore all the "proofs" that are usually beyond the scope of an undergrad course. All the constructs are very intuitive and based on simple geometric concepts. To me, it's other math fields like discrete or probability that are impossible to grasp.

>> No.12611002

I've never heard of a math major taking calculus 1 and 2. Are you using Spivak or Apostol at least?

>> No.12611005
File: 154 KB, 1920x1080, WIN_20210117_06_47_46_Pro.jpg [View same] [iqdb] [saucenao] [google] [report]

Proof that the sum of 1/n^a for all Z+ a is 1/(n-1):

Take some dots
Cross out the first dot
Thats 1/n
Take the second dot and expand it into more dots
Then cross out one, thats 1/n^2
Keep doing it at all layers
At all layers you have 1/(n-1) plus the excluded dots fraction which is fractal
So you have a sum of 1/(n-1)s at each layer, giving by distribution a total as so.

I cant tell if this is a geometric or symbolic proof.

>> No.12611050

it's not a proof it's schizo rambling

>> No.12611071

Low IQ post, unironically

>> No.12611078

much better without all the animefags spamming

>> No.12611093

Yeah but now its just us retards left so were gonna have to learn advanced math on our own.

>> No.12611107

thank you anon. I literally came here to ask what I needed to know to not be lost in my calc class since it has been a while since I have done any math.

>> No.12611113

>thank you anon. I literally came here to ask what I needed to know to not be lost in my calc class since it has been a while since I have done any math.

>> No.12611120

▲ ▲

>> No.12611270

Why dont alt keys work on my computer

▲ ▲
Copypastaing the unbreaking space dont work eider

>> No.12611275
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What in the fuck is this thread

>> No.12611276

▲ ▲

>> No.12611282


It works on d?scord y not here

>> No.12611297

there is no proof, 1/nᵃ is not 1/(n-1) while a ∈ ℕ.

and please learn to write mathematical expressions

>> No.12611302

No the sum I meant

>> No.12611318

▲ ▲

>> No.12611334
File: 758 B, 73x99, TriKraft.png [View same] [iqdb] [saucenao] [google] [report]

▲ ▲

>> No.12611351
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▲ ▲

I vent my spleen at the lord

>> No.12611358

[math]\ ▲[/math]

>> No.12611366

How do you do it anon
The alt key on my windows pc isnt working so alt 255 does nothing and theres no num lock
Hilf mir

>> No.12611374

Noice. [math]\LaTeX[/math] never disappoints.

>> No.12611379

Element untersuchen
Nw I know

>> No.12611380

Git gud
[math]\ ▲[/math]

>> No.12611381

Used [math]\TeX[/math]. Just right click and see the commands.

>> No.12611386

genius of /mg/
king of /sci/
owner of the /tri/force

>> No.12611392

▲ ▲

>> No.12611402

▲ ▲

>> No.12611405
File: 33 KB, 477x165, 4chanada.png [View same] [iqdb] [saucenao] [google] [report]

I am a King

>> No.12611414


>> No.12611473
File: 110 KB, 600x450, Uusi%20kirkko%2018.12.2009%202[1].jpg [View same] [iqdb] [saucenao] [google] [report]

Sorry, I was busy.

Whatever that building is supposed to be, it is nothing compared to the church in Hyvinkää, the temple of the Space Messiah.

I was going to say it has to be Cox-Zucker because C precedes Z, but the set theory axiomatisation isn't BGN but NBG. I conclude that it is intentional.

>> No.12611483

Hey anime tranny add me on discord and teach me fourier convergence theorems pwetty pwease
Multimorph 4167

>> No.12611512
File: 98 KB, 1200x675, 1601920023924.jpg [View same] [iqdb] [saucenao] [google] [report]

Hi! Sorry but
(1) I don't use discord.
(2) I don't remember much anything about Fourier stuff.

>> No.12611517

Someone who uses discord add me and teach me fourier convergencce

>> No.12611560
File: 116 KB, 1200x1200, die wissenSCHAFTEN.jpg [View same] [iqdb] [saucenao] [google] [report]


Does anyone else get math obsessions? Whenever I dont understand a concept I get agony. I try to reframe all concepts in terms of pure axioms and ssince the universe runs on void energy I just go in spirals. When I look at a object I create alternatives and theyre endless. The combinatoric possibilities exponentially spiral out and my brain melts. How do I do math without getting overwhelmed?

>> No.12611632

Very funny. 0 points.

>> No.12611640

Yes. Remove the 5x5 square and the remaining null set divides evenly into 3

>> No.12611661


>> No.12611675

Depends on your definiton of cut bt 24 give a gihting chance. But if you want us to do it in 2 slices, then we need each group to be 8, so think not by intuition but unsure

>> No.12611683

Counting down to 0 by intersecting endsegments can only happen in steps of one natural number per
endsegment because from the definition

Ek \ {k} = {k, k+1, k+2, k+3, ...} \ {k} = {k+1, k+2, k+3, ...} = Ek+1

we find the bijection

subtract({k}) = Ek+1 . (3)

But no endsegment can be defined that contributes to reduce the intersection from an infinite set of
(1) to the empty set of (2). Only undefinable, so-called dark, endsegments with indexes not subject to
universal quantification in (1), can produce the empty intersection in (2) by deleting the infinite set
step by step or one by one – if (3) holds, i.e., if mathematics is valid for all steps

>> No.12611684

"k œ Ù: E1 … E2 … E3 … ... … Ek = Ek ∫ « where |Ek| = ¡0 . (1)

>> No.12611689
File: 5 KB, 861x50, Peeoga.png [View same] [iqdb] [saucenao] [google] [report]


But no endsegment can be defined that contributes to reduce the intersection from an infinite set of
(1) to the empty set of (2). Only undefinable, so-called dark, endsegments with indexes not subject to
universal quantification in (1),

>> No.12611700

Or maybe recursion doesnt work sequentially at the edge infinity, instead acting as an omnipresent chain fully loaded in one instant

>> No.12611731
File: 167 KB, 120x120, Tetraeder.gif [View same] [iqdb] [saucenao] [google] [report]

Polygon john signing off for the night. Post tetraeder facts to feed our flight.

>> No.12612035

F(x) = 2(x)^2
G(x) = a+b

Just started pre-calc, tell me how wrong I am.

>> No.12612075

it's asking for
2(a+b)^2 =
2*(a^2 + 2ab + b^2) =

>> No.12612146

Noice, yeah I suppose that makes sense.
Been 5 years since I was in college, and last did math in HS, I’m a little rusty on my terminology & skills.

>> No.12612255

I've self-studied math up to Tao and Baby Rudin. The problem is I lack geometric intuition, I haven't taken any geometric class. How can I embrace the
arnoldpill/sovietpill and dab on bourbakist trash?

>> No.12612302
File: 12 KB, 480x360, hqdefault.jpg [View same] [iqdb] [saucenao] [google] [report]

>bourbakist trash
knowing high school level maths does not mean you're qualified to make such a value judgment

>> No.12612374
File: 174 KB, 610x600, medium.png [View same] [iqdb] [saucenao] [google] [report]

Why does every element of a residue-class ring mod n have a multiplicative inverse for prime n? Is there some sort of intuition behind this or is it just a fact of numbers I need to accept?

>> No.12612421

Imagine there is no multiplicative inverse for some a<p, then by pigeonhole you have b_1<b_2<p such that ab_1=a_b2 (mod p). This implies that a(b_2-b_1) is a multiple of p which is a contradiction. I think this gives some intuition.

>> No.12612425


>> No.12612451

How do I motivate the study of PDE without knowing physics? More abstract stuff like sobolev spaces is fine and interesting in its own right, but all the concrete examples seem to relate to the modeling of physical phenomena (which I don't understand or care about at all).

>> No.12612793

Study classical mechanics. Even if you don't "care" about it. Also read
uni-muenster.de SLASH Physik.TP SLASH ~munsteg SLASH arnold.html

>> No.12612808

Ship sails downstream from city A to city B. It takes two days. Same ship sails upstream from city B to city A. It takes three days.
How long will it take for a raft to sail from city A to city B?

>> No.12612822

2 days, if we are assuming the original question posits the ship which made the journey in 2 days downstream, simply rode the current and didn’t utilize other techniques to enhance its arrival time.

>> No.12612832
File: 56 KB, 810x458, b3c84bfea39aeb6ba8e48e4a9607853d82d69ce9.png [View same] [iqdb] [saucenao] [google] [report]

> bourbak*st

>> No.12612868

>How do I do math without getting overwhelmed?
try stop smoking weed

>> No.12612879

12 days.

>> No.12613031

I have a proof, but it's late, so I'll type it tomorrow.
The answer is no.

>> No.12613095

>if we are assuming
Tip: Don't. Ever. Assume.

>> No.12613168

Read Arnolds books and try stuff yourself, with just pen and paper, no books, no computer, no nothing, just math. Trust me, your brain works different with no outside bullshit.

>> No.12613246

x*x*x = 3x

>> No.12613251

No: x x x x x = 5x

>> No.12613256

wait let me expand this so you can grasp it

x * x * x = 3x

>> No.12613264


>> No.12613283

Ok, I groped it now: so x^x^x = x^3.

>> No.12613649

I want to die

>> No.12613666

x*x*x = *(*(x, x), x)

>> No.12613674

now you get it. x+x+x = 3+x

>> No.12613683

>no anime posters
>the quality of posts plunges to lows never seen before

>> No.12613686

>think outside the quadrilateral parallelogram edition

>> No.12613701
File: 223 KB, 1335x2048, ayano.jpg [View same] [iqdb] [saucenao] [google] [report]

Same, but we have work to do first. The merciful bliss of death must be earned.

It's because of this https://en.wikipedia.org/wiki/Fermat%27s_little_theorem

Totally not my false flag, btw.

>> No.12613767

>▲ ▲

>> No.12613782

Holy fuck I just did this problem in my linear algebra book. SPOOPY AF

>> No.12613788

Weed isnt implicaeted

W+C = dist/2
W-C= dist/3
Current gives velocity of dist over 12

Bit odd to say you can add velocities like that but if we consider each force as contributing a velocity vector that reaches equilibrium, if the force to velocity function is linear, it makes sense (which it is for non equilibrium force vectors, and if equilibrium is a sum of force plus its resistance I think it checks out but resistance can vary due to environment). Also we would assume the wind blows/harnessedgets the same on both direction

>> No.12613800

Why do you want to die anon? What dreams may come in the sleep of death?

>> No.12613809
File: 496 KB, 521x324, coin.png [View same] [iqdb] [saucenao] [google] [report]

The actual problem was pic related. Which I think sets it up enough for you to figure out the problem.

>> No.12613817

Death would be better than forever being a burned-out failure

>> No.12613821

Why is there a standard math curriculum? Why arent students educated by just having them work on new problems and see what they branch into, with some methods and tools given as needed

>> No.12613823

Then go and win at something.

>> No.12613834

Like what? The paper I'm working on is fucking horrible

>> No.12613896

That would require more teachers and money. But it would make way more sense.

>> No.12613924

There will be more papers in the future. Plus Im sure its not that bad. Youre most likely just experiencing burnout, why not go for a few days of fresh air outside

Maybe it could be feasible if students were taught to be more self reliant from elementary school. To ask questions and seek answers on their own. The internet as a mega library helps and professors can act as loose guides

>> No.12613948

>self reliant
>ask questions and seek answers on their own
Ah yes just derive all human knowledge on your own whilst living alone in a forest

>> No.12613970

>The internet as a mega library helps and professors can act as loose guides
I wish you didnt have ADHD

>> No.12613975

Also nice clock dubs

>> No.12613979
File: 524 KB, 1200x1800, 1200px-Ilmatar_ja_sotka[1].jpg [View same] [iqdb] [saucenao] [google] [report]

You mean you are not guided by the ancestral spirits and the Airress? NGMI, sorry.

>> No.12614004

Ancestral spirits told me that addition and multiplication arent the only meaningful operations

>> No.12614091
File: 112 KB, 750x750, aw0va.jpg [View same] [iqdb] [saucenao] [google] [report]

Higher homotopical structures https://sites.google.com/view/hhs2021-opening/home
Interviews about maths and life and what have you https://www.muramatik.com/math-life-balance/ & https://www.youtube.com/channel/UCYRR0SgbYH59htIHkwTbqMw

You have a good bloodline, my friend. I can see a hint of Atlantean origin.

>> No.12614137
File: 86 KB, 640x541, mg.jpg [View same] [iqdb] [saucenao] [google] [report]

Thanks for the youtube link bitch. Do you have good heritage or do you look like a mongol?

>> No.12614143

wow me on the right

>> No.12614239


>> No.12614264

no Fourier analysis for you

>> No.12614302

Multimorph 4167

>> No.12614305

Clamped, vaccinated, circumcised, halogenated

>> No.12614310

Chapter 11 Thirty spokes are joined together in a wheel, but it is the center hole that allows the wheel to function. We mold clay into a pot, but it is the emptiness inside that makes the vessel useful. We fashion wood for a house, but it is the emptiness inside that makes it livable. We work with the substantial, but the emptiness is what we use.
Alan Watts once said in an object there is inside and outside. But what about klein bottles? Are they just like a piece of paper?

>> No.12614315

But pieces of paper have edges and kleine has keine

>> No.12614319
File: 400 KB, 699x922, siis omg.jpg [View same] [iqdb] [saucenao] [google] [report]

No problem, my friend. I think I have fairly good genetics, no mongol face or anything like that. That's like tooooooootally me on the right uwu <3

>> No.12614325


>> No.12614395

based, redpilled, keyed, schway

>> No.12614420

Is Vladimir Zorich's Mathematical Analysis a good book? I heard it has a lot of application for an Analysis textbook, so I am quite tempted to switch into it.

>> No.12614424


>> No.12614536

Got an optimization problem for you guys:

I want to find the best armor combo to use in Dark Souls 3. There's four slots (chest, head, legs, gloves), and each piece of armor has an armor value and a weight value. You cannot wear two helmets, or two sets of gloves at the same time. You want to maximize armor while not going above a weight limit. How would you choose the best set?
>inb4 g2/g/
This question is not about the discussion of gaming keyboards or graphics card companies so /g/ would be clueless.

>> No.12614555

What does a course in analysis entail? I have a book called Introductory Real Analysis by kolmogorov but its basically just random math bits to define measure theory then define integrals. Feels kinda pointless

Is regular analysis just integrals or wut I relly dont know

>> No.12614737
File: 126 KB, 1920x1541, fad.jpg [View same] [iqdb] [saucenao] [google] [report]

>a tensor is an algebraic object that describes a relationship between sets of algebraic objects related to a vector space. Objects that tensors may map between include vectors and scalars, and even other tensors.
what does this even mean? who the fuck comes up with this cryptic shit?

>> No.12614868

it's a useless sentence that one puts as an introduction for the sake of introduction
just scroll down in whatever you are reading

>> No.12615175
File: 56 KB, 720x410, 190214100031_1_900x600.jpg [View same] [iqdb] [saucenao] [google] [report]

how do 'you' read math books /mg/?

>> No.12615182

How do ‘you’ get a cute gf (male) /mg/?

>> No.12615206

how do i become a tranny girl

>> No.12615211

Linear programming could be used but it's simpler to look at all possible combinations and eliminate the ones that exceed the limit.

>> No.12615225

If you take the infinite integer plane lattice [math]\mathbb{Z}^{2}[/math] and draw as many lines connecting vertices to other vertices as you like, including intersections of drawn lines with other lines as vertices, can you construct an intersection at every point in [math]\mathbb{Q}^{2}[/math]?

>> No.12615254

>A in math class
>thinks he's good in math
kek, maths is about understanding and it's fair to assume when one understands math he'll be impressed and like it, you can get A's without even knowing you're studying maths.

>> No.12615362

lurk /soc/

>> No.12615363

Knapsack problem

>> No.12615370
File: 2.02 MB, 330x275, 1611287680959.gif [View same] [iqdb] [saucenao] [google] [report]

Professional retard here, how the fuck do I learn calculus? I got an A in precalc but then corona hit and we switched to online for calc 1. I passed it through bullshit but understood none of it. Now Im retaking calc 2 because I couldnt bullshit a high enough grade the first time and Im still completely lost, dont get integrals or u substitution or any of that, can only make some sense of graph related problems. What the hell do I do?

>> No.12615381

Practice. Your goal should be to have so much confidence in your knowledge that you can just google random problem and solve them without your hand being held. Doing every exercise in the textbook is a good place to start.

>> No.12615382
File: 55 KB, 600x719, 1268891287892.jpg [View same] [iqdb] [saucenao] [google] [report]

Don't listen to Stalin, there are limits in calc. https://www.youtube.com/watch?v=i83cVs03EE0

>> No.12615414

Sauce for the first line.

>> No.12615441

it's simply a relation defined from {(0,0),(0,1),(1,0),(1,1)} to {0,1}
the problem leaves the actual mapping open to interpretation, so the problem is unsolvable but there are 2 possible solutions, so it's a 50-50.

>> No.12615444

>cs major
just learn to code brosuf give up the math larp

>> No.12615445

The way the question was worded forces you to assume something or else it is completely unanswerable.
It’s a compromise.

>> No.12615446

Dunno if I'm the only one to find this nifty, but I genuinely like to interpret
[eqn]\int_{\gamma} \mathrm{d}z\, f(z)[/eqn]
[eqn]\int_{\gamma} \mathrm{d}
\, \vec{f}(\vec{z})\text{, with }
\vec{z} = \begin{pmatrix}
\end{pmatrix},\vec{f}(\vec{z}) = \begin{pmatrix}
\Re (f(x+iy))\\\Im(f(x+iy))
You can make it fully consistent by instead making f,z matrices, ofc, but this mixed style is more compact and yields no redundant equations.

>> No.12615457

I have a paint application open and I prove every theorem and do every problem. If I get stuck for too long I'll drop the book usually going to an easier book in the subject I failed at and come back later.

>> No.12615461

School isn't about teaching kids to be critical thinkers.

>> No.12615463

Thanks bros, I can dig around from here. I did some optimization and such in college, but I've been out for years now and had no idea where to start with this one.

>> No.12615484

Will try, already picked up a textbook

>> No.12615504

>t. moron
The answer is 12 days

>> No.12615531
File: 117 KB, 1280x720, awbbh.jpg [View same] [iqdb] [saucenao] [google] [report]

Yes. I have heard nothing good about Stalin vs Martians except that it has a banger soundtrack, the idea is great and that gif of Stalin dancing is awesome.

Using my eyes. Then I fall asleep because reading makes me tired.

I think it should be sufficient to show that you can get [math](p, q)[/math] for any [math]p, q \in \mathbb{Q}, 0 < p, q < 1[/math] as such intersections. Then you can translate the line to get all the rest. Try lines that pass through [math](0, 0), (p, q)[/math] and [math](p, q), (1, 0)[/math].

I don't know.

Take your pills.

>> No.12615559

It may be even easier to construct two distinct lines that also intersect the integer lattice left and right of the point, but that's my gut.

>> No.12615580

post face

>> No.12615607

I like math but I'm bad at it, what do?

>> No.12615611
File: 231 KB, 1920x1080, uiopl.jpg [View same] [iqdb] [saucenao] [google] [report]

You mean like taking any rational pair instead of something inside that square of mine? That would at least be quicker. Did I interpret your idea correctly?

I don't think I should. I have already ruined a few threads with one photo. I don't want to ruin more with another.

Git gud scrub.

>> No.12615612

<math xmlns="http://www.w3.org/1998/Math/MathML">
<mspace width="0.2cm" />

>> No.12615620

Yeah. Come to think of it, if you affix a point like you did (the origin) you are already done. Cause then you already found infinitely many lines intersecting (p,q) by means of translation.

>> No.12615625
File: 56 KB, 300x647, solaire-of-astora.jpg [View same] [iqdb] [saucenao] [google] [report]

>Git gud scrub
Got platinum trophy for the 3 souls and I'm pretty good at PvPing, dunno what else I can do anon
Also, I just want to get good at math

>> No.12615635

Pre-calculus is generally gonna be trigonometry.
Wouldn't skip unless you're very familiar. Large sections of calculus are based on unit circle manipulation and identities. I did know a guy who made it through calc 1 without it but he had to teach himself trig along the way and worked very hard at it.
If you aren't a very self motivated person or you are taking other heavy science or math classes simultaneously I would not recommend but if your other classes are humanities or something you could likely do it without much issue if you found a decent tutor through your University.

>> No.12615644
File: 168 KB, 1920x1080, 8f7if8.jpg [View same] [iqdb] [saucenao] [google] [report]

Yeah because any (p, q) is (m+p', n+q') for some integers m, n and some rationals p', q' strictly between 0 and 1. No need to care about m and n.

I don't know. Self diagnose impostor syndrome and then you can pretend you are good but insecure. That's my style. Fake it till you make it.

>> No.12615649

>The proof for this is trivial and left as an exercise for the reader.

>> No.12615653


>> No.12615654

>impostor syndrome

i don't understand this one bit. how could anyone feel like an imposter unless they are one?

>> No.12615656

you know you want to <3

>> No.12615662
File: 20 KB, 300x245, monadAlgebras.png [View same] [iqdb] [saucenao] [google] [report]

What is the most high iq introduction to abstract algebra book you know? The more esoteric, the better.

>> No.12615666

Mr P. Pseud's big book of abstract algebra pseuds

>> No.12615678

Based pseud trips

>> No.12615693

I think the canonical isomorphisms [math]\mathbb{C}\mapsto\mathbb{R}^{2(\times 2)}[/math] have a certain beauty to them.

>> No.12615697

I don't know. I'm more of a Dunning-Kruger myself.

Please don't tempt me. I bought wine and it's getting me.

>> No.12615719


>> No.12615723

Which one

>> No.12615740

Suppose the distance were x miles. Then the speed of the ship plus the speed of the stream equals x/2 miles per day, and the speed of the ship minus the speed of the stream equals x/3 miles per day. The first equation minus the second equation yields twice the speed of the stream equals x/6 miles per day, so the speed of the stream is x/12 miles per day. A raft travels at the speed of the stream, so to travel x miles at x/12 miles per day would take 12 days. Of course, anyone who's not a retard could figure that out.

>> No.12615752
File: 15 KB, 700x700, Image0.png [View same] [iqdb] [saucenao] [google] [report]

Alright, here's my proof of why it's impossible:

Lemma 0: The congruent parts cannot be a 2x4 rectangle.
The proof of this is trivial.

Lemma 1: The congruent parts cannot have a dimension of 5 (as in, a part either occupies both columns A and E or occupies both rows 0 and 4).
The proof of this is as follows: suppose the congruent parts have a dimension of 5. Without loss of generality, suppose one of the congruent parts occupied both columns A and E. Then the other two congruent parts cannot occupy both rows 0 and 4, as they would have to cross the first part, so they too must occupy both columns A and E. When the grid is cut, it is clear that there is a top part, a middle part, and a bottom part. Without loss of generality, suppose the removed square is below the middle part. If any of the middle part occupied row 4, it would be impossible for the top part to be above the middle part, so row 4 must be completely occupied by the top part. Then, in order to be congruent, the middle part occupies a complete row by itself. Call this row X. The space between row 4 and row X must be occupied by the three squares of the top part not in row 4 and, in order to maintain congruence between the top and middle part, either zero or three squares of the middle part not in row X. So the space must be occupied by either three or six squares. However, the space between row 4 and row X must be a multiple of five. Then it is a contradiction, and the congruent parts cannot have a dimension of 5.

>> No.12615759

I hope you think that's a bad thing

>> No.12615775
File: 15 KB, 700x700, Image1.png [View same] [iqdb] [saucenao] [google] [report]

Now for the actual proof:
There are four corners of the 5x5 grid: A1, A4, E1, and E4. By Lemma 1, a part cannot occupy more than one corner. Then three corners must be occupied by three different parts, and the fourth corner must be the square removed. Without loss of generality, the squares may be coloured like the picture, with red, green, and blue representing the squares occupied by the different parts, and the black square denoting the square removed.

>> No.12615785

pwetty pwease :3

>> No.12615788
File: 15 KB, 700x700, Image2.png [View same] [iqdb] [saucenao] [google] [report]

By Lemma 1, row 0 cannot be occupied by either red or blue, so it must be occupied solely by green. Similarly, column E must be occupied solely by blue.

>> No.12615790

We'll just pretend you've never posted it. It's going to be ok.

>> No.12615823
File: 15 KB, 700x700, Image3.png [View same] [iqdb] [saucenao] [google] [report]

Because both green and blue contain a straight line of four squares, red must too contain a straight line of four squares. Without loss of generality, suppose this straight line of four squares is horizontal. This straight line must occupy columns A through D of one of the rows from 1 to 4. It cannot be row 1, as that would prevent green from occupying eight squares. It cannot be row 2, as green would then have to be a 2x4 rectangle, which by Lemma 0, is impossible.

Suppose it were row 3. By Lemma 0, the three remaining red squares cannot be in row 4, so there must be a red square in row 2. Then there are red squares on both sides of the straight line of four red squares. For green to be congruent, there must be green squares on both sides of the straight line of four green squares. However, because the straight line of four green squares is on the bottom row, and it is impossible to make another straight line of four green squares (excluding the one that will make green a 2x4 rectangle), it is impossible for green squares to be on both sides of the straight line. So it cannot be row 3.

>> No.12615833

redpill me on spivak

>> No.12615852
File: 15 KB, 700x700, Image4.png [View same] [iqdb] [saucenao] [google] [report]

Suppose it were row 4. By Lemma 1, A1, A2, and A3 must be occupied by red or green. In order for red and green to be congruent, D1, D2, and D3 must be occupied by the opposite color of A3, A2, and A1 respectively. However, if D1, D2, and D3 are occupied by red and green, then blue cannot occupy the necessary eight squares. Then it cannot be row 4.

Therefore, it is impossible to remove a square from a 5x5 grid and cut the remaining squares into three congruent parts. QED.

>> No.12615870


>> No.12615897

>equals x/2 miles per day

Miles are never mentioned in the original question, only how long it takes to get there each way. You're assuming things that aren't in the original question too.
Opinion discarded.

>> No.12615903

The original question implies a distance, and any distance can be converted to miles. Kill yourself you retarded nigger.

>> No.12615905

Yes, and you said it is two miles per day.
It only mentions that it takes two days.

Miles do not equal days bro, you got the wrong conversion tables

>> No.12615910


>> No.12615911

Jacobson Basic Algebra I&II

>> No.12615926

You retarded mother fucker. I said x/2 miles per day. X over fucking 2. You mother fucking retard. Please do everyone a favor and kill yourself.

>> No.12615932

Guess what brother, x divided by 2 just equals x/2
Congratulations on pulling 12 out of your ass

>> No.12615936

If you are given a shape, like triangle vertices for instance, is it possible if given work = 3 to find a vector field that would make that statement true?

>> No.12615958

Kill yourself

>> No.12615967

Like, the calculus book?

>> No.12615973

X/2 Minus X/3 is equal 1/6x
Not 12

lmao you can't even do basic algebra

>> No.12616051


>> No.12616065

No x x x x x = x^5

>> No.12616088

>contact techer
>he never replies

>> No.12616090

It's a Gilbert Strang calculus problem where he asks you to find the field around a unit square in which work is equal to 4

>> No.12616096 [DELETED] 
File: 206 KB, 913x753, IMG_20210123_002644.jpg [View same] [iqdb] [saucenao] [google] [report]

I'm gonna regrte´et this in the morning. But here you go. All you will get.

>> No.12616123

lemma1 assumes the 3 congruent pieces must be connected

>> No.12616133


>> No.12616150 [DELETED] 

I'd like to see her feet first

>> No.12616163

Cute hand

>> No.12616228 [DELETED] 

I missed? Please send

>> No.12616252

Is that not implied from the question?

>> No.12616264

If she deleted it I'm not comfortable sharing without permission. Sorry

>> No.12616277 [DELETED] 
File: 206 KB, 913x753, anitranny.jpg [View same] [iqdb] [saucenao] [google] [report]

No time stamp but he posted this.

>> No.12616284

Watch it buddy

>> No.12616285


>> No.12616292


>> No.12616305 [DELETED] 

Thanks, I'll delete my comments now then.
Don't leave pic for too long, it is the least we do in return

>> No.12616335

what are some good ODE books for us mathchads

>> No.12616346

I thin Arnold's book is usually considered a good one.

>> No.12616348

Can you reach any [math]\mathbb{Q}[/math] by adding/subtracting an arbitrarily large but finite amount of elements from the set {1 and [math]\sqrt{2}[/math]}? If not, is there any finite set that would let you do so?

>> No.12616359

You can't reach any rational number besides the integers that way.

>> No.12616364

No finite set of rationals will give you that.
Rationals form a moduel over integers with no finite free-basis.

>> No.12616414
File: 34 KB, 480x630, a3elg.jpg [View same] [iqdb] [saucenao] [google] [report]

You need to habe 1/p for every prime and then require it to be closed under multiplication and addtuon.

>> No.12616415

Calculus Early Transcendentals 4th Ed. Rogawksi

>> No.12616545
File: 67 KB, 500x474, 1610393918668.jpg [View same] [iqdb] [saucenao] [google] [report]

I'll be honest here, all this blogposting that has been happening in the last few threads is extremely annoying. I don't really care about your personal life and what stuff you're into. I'm just here to talk about mathematics like everyone else. So please, have some self-awareness and restrain the subject of your posts to be strictly about math. No offence, but no one other than a few underages or trolls seeking attention care if you're trans or if you're new to college or whatever excuse you people have to start blogposting. Problem is that those underages and trolls have a loud voice and it gets even louder when someone gives them a reason to shitpost and that's exactly what you're doing.

>> No.12616552

What's the intuition behind studying exact sequences in abstract algebra? I am rather unfamiliar with algebra so I can understand the definition and apply it to prove some toy statements but I don't have a good understanding of why they're useful objects to study.

>> No.12616575

>personal life
The vast majority of what has been posted was either math or stuff about the mathematical life. We also discuss aspects of being a math student or researcher in /mg/, it has never been strictly pure mathematics.

If you really thought like that, you wouldn't even post unrelated picutres like the anime pic you sent, you're just annoyed because it rubs you the wrong way. Just ignore and scroll.

>> No.12616600
File: 29 KB, 540x540, 1610035682330.jpg [View same] [iqdb] [saucenao] [google] [report]

Not really no, most of those posts are a mix of math with blogposting. I could post dozens of them here from the last two threads and in this one they've gone as far as to post a picture of themselves to get attention.
>We also discuss aspects of being a math student or researcher in /mg/, it has never been strictly pure mathematics.
That's welcome, what's not welcome is when your post is 70% blogposting and 30% actual mathematics/math life/research life.
>If you really thought like that, you wouldn't even post unrelated picutres like the anime pic you sent
>you're just annoyed because it rubs you the wrong way.
Oh, and how so? I literally didn't get what you tried to imply here.
>Just ignore and scroll.
Great way to excuse criticism. I guess all off topic posts should be allowed now, after all one just needs to ignore and scroll, am I right?

>> No.12616640

So by "blogposting" you mean the pictures and sexual-related stuff? Come on anon, wasn't much and some were even funny. A tiny bit of slightly off-topic here and there is ok imo, it's not a problem if doesn't become spam.
It's not a joke, some people have argued just like you're doing but regarding anime. Sometimes it's not even just pictures. Why should they tolerate it? Strictly speaking, it has nothing to do with math.
>Oh, and how so? I literally didn't get what you tried to imply here.
It's a non-constructive existence claim, you being annoyed is enough proof.
>Great way to excuse criticism. I guess...
I addressed eveything you said, and you're snowballing. When newbies post bs they could answer by thinking for 3 minutes or googling I also get annoyed, but it's part of the ride, I just ignore and scroll.

>> No.12616895
File: 226 KB, 827x1024, Carter-827x1024.jpg [View same] [iqdb] [saucenao] [google] [report]

how long did it take you to feel like you were "good" at math? i'm a university graduate and an amateur mathematician but i have never felt very good at math, even though i'm likely better then the average person.

>> No.12616942

What's a good masters program with a math/cs undergrad?

>> No.12616971

Why in God's good name would you get a master's degree?

>> No.12617016


I wanna work as a code monkey for a couple years and then do a career change to something else via a masters.

>> No.12617034
File: 33 KB, 720x541, FB_IMG_1611151914716.jpg [View same] [iqdb] [saucenao] [google] [report]

Take the linear algebra pill

>> No.12617134

wrong about what? You just defined two functions, and G doesn't even need to be a function on x.

>> No.12617142

keked hard at this, based and alternate-pilled

>> No.12617181

shit negro what are you doing

>> No.12617206

Define "good at math". Do you mean writing proofs or just rote monkey calculations? I felt good at writing proofs after doing about 1000 of them.

>> No.12617256

do post, if you find them!

>> No.12617337
File: 85 KB, 715x715, 1 (156).jpg [View same] [iqdb] [saucenao] [google] [report]

going back to math, i really want to fuck a tranny guys

>> No.12617407

There are two types of trannies
i) faggots
ii) faggots
You are a faggot

>> No.12617428
File: 124 KB, 750x900, awhxi.jpg [View same] [iqdb] [saucenao] [google] [report]

OK, so I can give you an example that will not be a toy example. It's known as the Universal Coefficient Theorem. I don't know how much you know about homology, so I'll give you the basics first. If it sparks your interest, I recommend Rotman's book on algebraic topology.

First of all, a chain complex of [math]R[/math]-modules would be a sequence of modules and their homomorphisms [math]C_* = \cdots \to C_{n+1} \xrightarrow{\partial_{n+1}} C_n \xrightarrow{\partial_n} C_{n-1} \to \cdots[/math], one for each integer, such that [math]\partial_n \circ \partial_{n+1} = 0[/math] for all indices. This is the same thing as [math]\text{im} (\partial_{n+1}) \le \ker(\partial_n)[/math], so we may loo at the homology of this complex, and it is given by [math]H_n(C_*) = \ker(\partial_n)/ \text{im}(\partial_{n+1})[/math], for any integer n. Notice that vanishing homology for some n means exactness at [math]C_n[/math] in the complex. Let's then assume we are interested in the homology of some space [math]X[/math], and that [math]C_* = C_*(X; \mathbb{Z})[/math] is for example the singular chain complex (and now the ring is the integers). The groups in the complex vanish for negative indices, and for non-negatives we obtain [math]H_n(X; \mathbb{Z}) = H_n(C_*)[/math], the nth (integral) singular homology group of [math]X[/math]. So far so good, no need for exact sequences.

>> No.12617430
File: 46 KB, 800x600, wasted.jpg [View same] [iqdb] [saucenao] [google] [report]

Next, we ask what happens if we tensor the complex with some abelian group [math]A[/math] (over the integers). We obtain the complex [math]C_*(X; A) = \cdots \to C_{n+1}\otimes A \xrightarrow{\partial_{n+1} \otimes 1_A} C_n\otimes A \xrightarrow{\partial_n \otimes 1_A} C_{n-1}\otimes A \to \cdots[/math], the homology of which gives us [math]H_*(X; A)[/math], the singular homology of [math]X[/math] with coefficients in [math]A[/math]. This is where many who see this the first time would assume "oh but [math]H_n(X; A) \cong H_n(X; \mathbb{Z}) \otimes A[/math]", which is not true in general. Instead, there is an exact sequence [math]0 \to H_n(X; \mathbb{Z})\otimes A \to H(X; A) \to \text{Tor}(H_{n-1}(X; \mathbb{Z}), A) \to 0[/math] for every [math]n\ge 0[/math] ([math]H_{-1}(X; \mathbb{Z}) = 0[/math]). Even better, yet not completely perfect: this sequence is split exact: [math]H_n(X; A) \cong H_n(X; \mathbb{Z})\otimes A \oplus \text{Tor}(H_{n-1}(X; \mathbb{Z}), A)[/math], but not naturally (for example Dylan Wilson's answer in https://math.stackexchange.com/questions/33685/what-does-splitting-naturally-mean-in-the-universal-coefficients-theorem).

Some immediate things that follow from the UCT:
(1) If the group [math]A[/math] is torsion-free, then [math]Tor(-, A)=0[/math], and so [math]H_n(X; A) \cong H(X; \mathbb{Z}) \otimes A[/math].
(2) If [math]H_n(X; \mathbb{Z}) \otimes A = 0[/math], then [math]H_n(X; A) \cong \text{Tor}(H_{n-1}(X; \mathbb{Z}, A)[/math].
(3) [math]H_0(X; A) \cong H_0(X; \mathbb{Z}) \otimes A[/math].
If now [math]H_n(X; \mathbb{Z})[/math] is all torsion, or even a finite group, then it vanishes when tensored with [math]\mathbb{Q}[/math], and (2) applies. Furthermore, the rationals are torsion-free, so (1) applies and we get [math]H_n(X; \mathbb{Q}) = 0[/math]. Many such cases!

Reminder to get WASTED!

>> No.12617435

yes i am a faggot tranny UwU can you fuck my slutty bussy now?

>> No.12617460
File: 206 KB, 842x589, BEFT.jpg [View same] [iqdb] [saucenao] [google] [report]

"Good" compared to the average person was when I got medals in math olympiads (very, very far from IMO level, but it was something) during early high school, and by that time I noticed that I could do it because I had a combination of a good math teacher in my last elementary school year who'd give lots of exercises every class, and new performance demands at home.
But good at real mathematics... I did fairly better than the average math undergrad, but that just means having a minimum of math maturity. At PhD courses I'm being very close to average (probably below), and I have no idea how I'd do on research, probably bad at first.

Why would you do that?

>He's a big guy, I wouldn't compare myself to him.
I wouldn't either, not in that sense.

>> No.12617467

Just went through the section where you factor out functions into 2 separate equations, thought that’s what OP was referring to.
Up until this school year started, I hadn’t done math in a long time, and while I got decent grades & good test scores, I didn’t really try to learn the material back then so it didn’t stick with me.

>> No.12617474
File: 75 KB, 1170x461, ad0sn.jpg [View same] [iqdb] [saucenao] [google] [report]

I really liked the video of Knuth. If you are interested, there's this new channel https://www.youtube.com/channel/UCYRR0SgbYH59htIHkwTbqMw. I haven't watched the video yet, so I can't comment on that, but it could be your cup of tea.

>> No.12617523

If I have an algebraic projective curve [math]C[/math] over a field [math]k[/math], [math]\tilde{C}[/math] one of its affine parts/components (if that's how it's callled), [math]f, g\in k[\tilde{C}][/math], then is it true that [math] \text{div}(f^*/g^*) \ge 0 \, \iff \, f/g \in k[\tilde{C}][/math] ?
Actually I've only seen divisors being defined for elements of [math]k(C)[/math] and [math]f^*/g^*[/math] wouldn't be one (unless it's an element of [math]k[/math]), but that can be understood in terms of orders of zeros and poles.

>> No.12617638

Has anyone that old meme with the 1,i,0 right triangle?
I thought it was just a meme but then a read about circles in projective space intersecting at +-i:1:0
Also I'm trying to visualize what could that possibly mean geometrically, apart from satisfying the equations

>> No.12617681

Bourbaki Algebra Ch 1-3 for groups, rings and modules. However you can look at the Stacks project chapter 9 for a good overview of fields, it's actually quite good.

>> No.12617907

Thanks for the useless face pic

>> No.12618006
File: 481 KB, 895x671, iq.png [View same] [iqdb] [saucenao] [google] [report]

>make a time stamp but forget to use it
>use a pen to keep your hair under control
>mess up the lighting an make everything look flat and eerie
>look like a troll because you haven't washed your hair for two days
>wake up to find out what you have done
At least I covered my face and deleted the post.

>> No.12618380

>I'm not sure why it isn't more widely used in undergrad.
Probably just exercise count. The first exercise is
>1.1. Locate a discussion of Russell’s paradox, and understand it
and is one of 6 problems in its subchapter
Which in usual undergrad books comes near the end of a list of 20-30 exercises.
The problem being that each subchapter performs the function that a chapter in something like beachy would. The difficulty in algebra comes from understanding the concepts, theorems and proofs and being able to supply proofs and the calculation is usually straightforward. For example in one experement most math phds spent hours trying to solve a given geometry problem taken from a middleschool textbook. Remember at one point most problems were research problems and the less the author gives the student to work with the harder the problem becomes.
all in all taking a semester of algebra from an easy book and having more to background knowledge to read aluffi is easier than filling in everything that aluffi leaves out.
Also, its still a bit ahead of it's time for teaching category theory to non-graduates

>> No.12618465
File: 72 KB, 878x878, 1 (182).jpg [View same] [iqdb] [saucenao] [google] [report]

>first text on abstract algebra
>teaches category theory
hmmm i think i found the flaw

>> No.12618514

>Let [math] A [/math] be a nonempty set of real numbers which is bounded below. Let [math] -A[/math] be the set of all numbers [math] -x[/math] where [math] x \in A[/math]. I need to show [math]\inf A = -\sup A [/math]. I know there is an easier way to do this, but I want to see if my logic is correct:

Let [math] \alpha = -sup A[/math]. Then [math] -\alpha \geq -x \forall x \in A \implies \alpha \leq x \forall x \in A [/math]. So [math] \alpha[/math] is a lower bound of [math] A [/math]. Now I need to show this is the greatest lower bound. Let [math] \beta \in \mathbb{R}, \beta > \alpha[/math]. Then [math] \beta > x, x \in A[/math]. Hence [math] \beta [/math] is not a lower bound of [math] A [/math]. Thus [math] \alpha = inf A \qed[/math]

>> No.12618520

I fucked up this post a bit, please tolerate my autism

>> No.12618576
File: 36 KB, 646x350, abnng.jpg [View same] [iqdb] [saucenao] [google] [report]

Your logic is correct but you need to work a bit on presentation. You have
>Then [math]\beta > x, x\in A[/math]
and I know you mean some x in A, but I would interpret that as "for all x in A" if I had to grade your solution. Nothin' personnel, kid, but if you are to use quantifiers on x like that, you shouldn't leave x unquantified later. Add "for some" or use "[math]\exists x\in A: x < \beta[/math]" instead!

Unironically this. First concepts from different areas, not only algebra, and then categories. Without examples, CT is total gibberish.

>> No.12618590

Haven't done math in a year after doing nothing but math for three years. Should I get back where I left or should I redo the basics?

>> No.12618607

I'm exactly as you are. I finished my bachelor's in math and then stopped because my graduate degree is in a meme applied science field. I'm personally going over the basics (analysis, abstract algebra) to get my proof skills back and then plan on getting back to where I was.

>> No.12618854

Why are all videos explaining the euler maclaurin summation formula so dumb?
It's like a bunch of midwits just read the wikipedia article and don't really understand what is going on.

>> No.12618863 [DELETED] 
File: 30 KB, 1145x137, maxmin_lagrange.jpg [View same] [iqdb] [saucenao] [google] [report]

I dont see a stupid questions general but i need help on a calculus problem. you dont have to give me the answer but if someone could help me get started. its a max/min problem with lagrange multipliers. I can visualize the problem, its a square on the curve but what would that make the constraint equation? its some kind of multi-parabola looking thing.

>> No.12618870 [DELETED] 

its a square on the curve of the surface of that equation which looks like an upward bowl, to clarify.

>> No.12618873

read a book brainlet

>> No.12618909

Most books are pretty bad too desu.
I have a better proof than anywhere I've seen that also allows for generalization.
You can derive the bernoulli polynomials/numbers and the summation formula with remainder in less than a page using very basic principles/motivations.
It only requires simple integration by parts, with the motivation of telescoping series.
The bernoulli polynomials/numbers fall out effortlessly.

>> No.12618927 [DELETED] 

OP here, maybe I can use x^1000 + y^1000 = 2 as the equation.

>> No.12619144

I'll share it. I think people will appreciate the simplicity and hopefully make use of the idea.
First natural thing to do: keep repeating integration by parts on the integral of 1*f.

[math]\int\limits_{0}^{1}1*f(x)dx = \int\limits_{0}^{1}p_{0}(x)*f(x)dx \\
= \sum\limits_{m=0}^{M-1}(-1)^{m+1}[p_{m+1}(x)*f^{(m)}(x)]_{0}^{1}+ (-1)^M\int\limits_{0}^{1}p_{M}(x)*f^{(M)}(x)dx \\
where\ \ p'_{m+1}=p_{m}. [/math]

Ignoring the error and letting M = infinity gives you infinitely many constants of integration (one for each p_m, m>0) to freely choose.
What would be a "convenient" choice for all of them?
Wouldn't it be awesome if they were chosen so that if the formula was applied to [0,1] and added to the formula applied to [1,2] then there would be maximal cancellation for all derivatives of f at 1? (Telescoping)

[math]Let\ P(x,t)= \sum\limits_{m=0}^{\infty}t^mp_m(x).\\
P(x,0)=1\ and\ P_x=tP\ so\ P(x,t)=k(t)e^{xt}\ where\ k(0)=1.\\
Telescoping\ at\ all\ derivatives\ of\ f\ would\ mean\ P(1,t)-P(0,t)=0.\\
This\ can't\ happen\ since\ p_1(1)-p_1(0)=1\ no\ matter\ which\ constant\ of\ integration\ is\ chosen.\\
The\ best\ that\ can\ be\ done\ is\ P(1,t)-P(0,t)=t.\\
So\ k(t)*(e^t-1)=t,\ resulting\ in\ k(t)={t \over e^t-1}\ and\ P={te^{xt} \over e^t-1}.[/math]

The euler maclaurin summation formula and the generating function for bernoulli polynomials/numbers are obvious from here.

I'll let you derive the "midpoint" method which has a much better error term.
The trick for the midpoint method is to break [0,1] in half and use two alternating methods for the interval [0,1/2].
P1 = k1(t)e^(xt) and P2 = k2(t)e^(xt).
P1(1/2,t)-P2(0,t) = t and P2(1/2,t) - P1(0,t) = 0.

>> No.12619169


Please... Its cold...

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