/mg/

[Anonymous No.11932327]

math general
subtraction: >>11928516

addition edition

[Anonymous No.11932338]

>>11932327
>Elliptic curves

[Anonymous No.11932340]

>>11932338
gigabased

[Anonymous No.11932345]

>>11932338
elliptic curves have <0 applications

[Anonymous No.11932351]

What about [math]|x-y|[/math]?
Is it useless?

[Anonymous No.11932353]

>>11932345
>What is cryptography

[Anonymous No.11932361]

>>11932327
Re: the OP image: Actually, visual and geometric arguments aren't arguments. In topology, all our arguments are done by passing to the relevant algebraic structures or by clarifying the definition of transversality. We don't do geometrc intuition in topology.

[Anonymous No.11932363]

>>11932351
[math]|x-y|=\alpha,\alpha \in \mathbb{R}[/math] gives you two parallel lines with x-intercepts at [math]\pm \alpha[/math].

[Anonymous No.11932364]

>>11932345
They owe applications?

[Anonymous No.11932367]

whats a good number of grad courses to have taken as an undergrad if you want to get into a good grad school?

[Anonymous No.11932370]

>>11932367
About 15 or 16. Some schools expect 20 but if they do they're usually okay with 4 recommendations instead of 5.

[Anonymous No.11932374]

>>11932367
Unironically as many as you can take.

[Anonymous No.11932375]

>>11932367
about tree fiddy

[Anonymous No.11932384]

>>11932374
That's what I'm doing, I just wanted to get a handle on how decent the amount I'm taking is. My small brain feels like it can only handle 3 per semester.

[Anonymous No.11932387]

What do people mean when they say they took a "proof-based" course? I'm an engineer (the degree consists of 60% pure math and the rest is applied stuff with physics on the side) and every single course I took proved the statements they use except for the usual "it's trivial" or "you'll learn the proof later on" things. I often see posts here saying that they took their first proof-based course and it was too hard to them, but that implies that they were taught without proofs before. How the fuck does that work? Do they just sit in class while the professor lists proposition after proposition without proving anything?

[Anonymous No.11932389]

>>11932387
And for the record I'm not talking about courses on logic, Peano arithmetic and all that shit. The posts I read were talking about basic maths like trigonometry and basic calculus and algebra.

[Anonymous No.11932393]

>>11932387
Proof based courses: Algebra, analysis, and topology.
Computational based courses: Differential equations, numerical analysis, and stochastic processes.

[Anonymous No.11932396]

>>11932389
i think what people mean is that their problem sets are full of "prove this statement" and "prove that statement" as opposed to "solve this equation" or "compute this integral"

[Anonymous No.11932398]

>>11932393
All the things you mentioned under computational based rely on proofs too, I don't understand why you'd list them as different from the others. You need to be very comfortable with measure theory to even begin to study stochastic processes properly, same for differential equations and calculus/analysis. Hell you can't even do PDEs without a good understanding of topology.

>>11932396
Why wouldn't you teach undergrads to prove stuff from the very first day? The fact that they encounter this after they started their degree seems baffling.

[Anonymous No.11932400]

>>11932387
>Do they just sit in class while the professor lists proposition after proposition without proving anything?
No, you see the algorithms and he solves stuff on the board.

[Anonymous No.11932401]

>>11932398
Why would you teach anyone who isn't a mathematician or possibly a physicist or computer scientist to prove things? Why would an engineer know how to prove things?

[Anonymous No.11932403]

>>11932387
Are you European? Low level American math classes like calculus or differential equations consist of memorizing formulas and algorithms.
If you tried to teach these economics/biology majors who have to take these classes an epsilon delta proof, they would riot and absolutely fail.

[Anonymous No.11932407]

>>11932401
>Don't think, just consoom

[Anonymous No.11932411]

>>11932398
>All the things you mentioned under computational based rely on proofs too
True.
>I don't understand why you'd list them as different from the others
Because those subjects are a lot more tangible, for lack of a better word, and while in grad school those classes will definitely be rigorous, you'll also still be do calculations that you wouldn't be doing in a pure math program.

[Anonymous No.11932416]

>>11932407
You can spend time teaching them how to think about engineering, instead of about doing math proofs. Meanwhile, I want to spend time learning about how to think about math proofs. I couldn't care less about how to think about engineering.

[Anonymous No.11932423]

>>11932400
>and he solves stuff on the board.
But why? Isn't that what TAs are for?

>>11932401
>Why would an engineer know how to prove things?
To improve critical thinking and problem solving. It's completely fine by me at least because I got close to the math degree experience with an engineer diploma to make money on top.

>>11932403
>Are you European?
No, but my university and my math department in particular have ties with french universities and I think our curriculum is modeled similarly.

>If you tried to teach these economics/biology majors who have to take these classes an epsilon delta proof, they would riot and absolutely fail.
Maybe, but the first two years on my faculty are shared by all engineer students: I'm a "math engineer" which is basically applied maths I guess, but even the more economics-focused engineering degrees are forced to take our math courses from pre-calculus (sequences, limits with epsilon-delta up to differentiation) to multivariable calculus (with some teachers reviewing Banach spaces even). To be fair they do complain about it.

What's interesting to me that my country's education is very poor, certainly miles away from Europe, yet other countries still delay this encounter with proofs.

>>11932411
>Because those subjects are a lot more tangible, for lack of a better word
This is true.

[Anonymous No.11932444]

>>11932423
>To be fair they do complain about it.
I think the issue here is that you're assuming that American universities operate remotely the same way as (presumably South American?) ones, and you're looking for some academic justification for why they teach like this, which is totally off the mark.
American universities are businesses. They make their money from pants-on-head retarded tuition fees.
A state-funded university in Europe or SA doesn't care if a bunch of freshmen drop out because they don't like being forced to think. An American university cares very very much because every freshman that quits is hundreds of thousands of dollars down the toilet.
Universities bend over backwards to give students whatever they want so they will stay and keep taking out loans. If they want proofs gone, proofs go.

[Anonymous No.11932463]

I have an arbitrary bit length word. I want to alias this word by multiplying by some integer amount and modulate it to provide all possible combinations of that bit length? Is this possible for all bit lengths, using the same value of alias multiplier for each value? If not, which I suspect, is there a paper or proof I can be pointed to?

I'm not a mathematician, I believe this would be part of group theory, related to galois fields, but I'm not sure

[Anonymous No.11932468]

>>11932444
I go to an American university and my school has two different courses for ODEs and linear algebra: One for engineering/physics/CS majors and one for math majors. Obviously the latter has no where the near the same amount of students as the former, but they still exist.

[Anonymous No.11932478]

>>11932468
Most schools are like that, I think. I don't mean to say that American schools are bad; you can still get a very solid education at most American schools, _if_ you want one. The difference is that America will also allow you to choose a meme education if that's what you want to pay for, and the meme education is very popular since it's easy.

[Anonymous No.11932572]

>>11932327
Do high level mathematicians remember the basic but rarely used things from more elementary math topics?

[Anonymous No.11932602]

>>11932572
One time, I unironically forgot the volume of a sphere.

[Anonymous No.11932631]

>>11932572
Virgin autists who overspecialize do. They are never going to make it though.

[Anonymous No.11932671]

>>11932572
Not immediately, but they look it up and it comes back to them quickly.

[Anonymous No.11932735]

>>11932444
Now that you mention it, my institution is "public" and is guaranteed to receive as many new students as it wants to thanks to prestige so drop outs don't factor into the equation. That's a pretty good explanation.

[Anonymous No.11932844]

My inability to factor or divide cubic polynomials without fucking up is hindering calc 3, what can I read that thoroughly covers that bit of basic algebra?

[Anonymous No.11932928]

>>11932844
https://brilliant.org/wiki/rational-root-theorem/ try this

[Anonymous No.11933007]

>>11932327
Why is there a new thread if the other has at least 50 more posts left?

[Anonymous No.11933009]

>>11932398
>Hell you can't even do PDEs without a good understanding of topology.
Dubious, unless you're doing the old trick and define the subject as what you like to understand by the subject

[Anonymous No.11933015]

>>11933009
You need topology to define [math]D(\Omega)[/math] and therefore distributions, I don't see any decent PDE course skipping Dirac's delta. This is also assuming you count the theory of Sobolev spaces as pure analysis.

[Anonymous No.11933025]

>>11933015
That's what I'm saying, you can do a PhD implementing solutions for the Naivier stokes equations for 6 years and not ever did a course on abstract topology. And yes, of course there's also PDE theory where the the results depend on the continuum hypothesis, there's not one angle to the subject.

[Anonymous No.11933028]

>>11933015
>>11933025
To make my point a different way: Fourier, Gauss and Laplace did PDE theory even before Dedekind was born.

[Anonymous No.11933033]

>>11933028
>Fourier, Gauss and Laplace did PDE theory even before Dedekind was born.
We're not in the 1800s anymore though, we're supposed to teach current knowledge.
>Numerical solutions
I'd wager that's not exactly the same field as pure PDE. If you meant numerical PDE you should've said so, and I agree in that case.
>And yes, of course there's also PDE theory where the the results depend on the continuum hypothesis, there's not one angle to the subject.
You're comparing the Riemann hypothesis to one of the most basic elements in the theory.

[Anonymous No.11933040]

>>11933033
>If you meant numerical PDE you should've said so
Not him, but he literally said "computational based course".

[Anonymous No.11933041]

>>11933040
And he said PDE, which is not a computational based course unlike numerical PDE. At this point we're arguing semantics though and it really doesn't matter.

[Anonymous No.11933044]

>>11933033
>that's not exactly the same field as pure PDE
As I gauged, you define "PDE there" in your favorite way.
You said, quote
>Hell you can't even do PDEs without a good understanding of topology.
and the experts in turbulence at Boing may not be able to tell you th 3 properties of a topology.

>comparing the Riemann hypothesis
I wrote continuum hypothesis, which some plain integrals in measure theory depend on

Terrence Tao-like results on PDE's isn't the only angle at PDE's, PDE's can also relateto the world, like combinatorics does

[Anonymous No.11933046]

Boeing

[Anonymous No.11933048]

>>11933044
>I wrote continuum hypothesis, which some plain integrals in measure theory depend on
And fundamental solutions use the Dirac delta, are you telling me the experts at Boeing don't know what a fundamental solution is?

[Anonymous No.11933050]

>>11933046
They fucked over our manufacturing economy in my state desu, globalist corporate rat scum.

[Anonymous No.11933053]

>>11933048
Moving goalpost.
I'm sure most people at Boeing got their job without having ever visited a point set topology course or having heard the word "Sobolev" before

[Anonymous No.11933058]

>>11933053
>I'm sure most people at Boeing got their job without having ever visited a point set topology course or having heard the word "Sobolev" before
Well unless a Boeing engineer shows up in the thread we'll never know.

[Anonymous No.11933062]

[Anonymous No.11933068]

>>11933058
I take my estimation from doing an internship at such a company, the engineers there don't know what a Gamma function is

[Anonymous No.11933071]

>>11933068
No wonder their planes crash so often then.
Jokes aside, I stand corrected. Like I said I was trying to discuss something else.

[Anonymous No.11933081]

>>11933071
I think irl Gamma functions only appear in normalizations constants to probability densities or other such integrals. That's arguably even the case for the Riemann zeta function.

[Anonymous No.11933083]

We know that we can express the cohomology of a space in terms of its homology by the universal coefficient theorem. Is it possible to express the homology of a space in terms of its cohomology in general?

[Anonymous No.11933091]

>>11933083
What have you tried?

[Anonymous No.11933097]

>>11933083
It is extremely easy when you have a field as coefficients: [math]H_n(X; k) \cong H_n(X; k)^{**} = \text{Hom}(\text{Hom}(H_n(X; k), k), k) \cong \text{Hom}(H^n(X;k), k)[/math].

[Anonymous No.11933122]

>>11933091
asking /mg/

[Anonymous No.11933161]

Should I take numerical analysis or probabilities? Probabilities sound better but I'm not sure.

[Anonymous No.11933165]

>>11933058
A Grad course of mathematical methods for theoretical physics that teaches "distribution theory" will never even construct the Schwartz space. Hell some will not even mention that it's defined as a functional but rather as the limit of a gaussian or something that goes to infinity at 0 lol. Do you think an engineer who mostly runs numerical shit will have fucking knowledge of topological vector spaces? When you mention topology to them they think you are talking about electrical circuits. We know why the heuristics work because it has already been properly justified, that it works doesn't depend on people actually knowing the theorems and definitios. The same with infinitesimals, there is a justification as to why they work so that's why people use them.

[Anonymous No.11933227]

>>11932423
>But why? Isn't that what TAs are for?
Sure, the professor can also spend five minutes explaining the subject and then go take a short nap while the TA grinds some example problems and answers questions.

[Anonymous No.11933430]

I hope you all had a nice maths week.

[Anonymous No.11933439]

What does it feel like to have studied math to a phd level? Do you begin to notice higher order patterns or do you still feel like you're groping in the dark bumping into odd coincidence after odd coincidence springing from the loins of apathetic algebra?

[Anonymous No.11933444]

>>11933439
Depends, if you do category theory you'll notice patterns everywhere. If you do baby PDE/dynamical systems stuff you won't understand anything.

[Anonymous No.11933448]

>>11933444
what if my main interests are algebra, topology, and higher dimensional spaces

[Anonymous No.11933451]

>>11933448
Then you'll do category theory? There's isn't a single good graduate course about algebra, topology or geometry which doesn't features categories.

[Anonymous No.11933452]

>>11933451
cool (auf deutsche)
what are the prereqs to study topology, especially algebraic topology? im almost done with my current textbook (lin alg) and im excited to do the next thing

[Anonymous No.11933464]

>>11933452
>topology
Pretty much nothing, except set theory and maybe a bit of analysis to understand the notions.
For algebraic topology I'd say topology, group theory, modules and complex analysis.

[Anonymous No.11933469]

>Zariski topology

[Anonymous No.11933491]

>>11933464
is analysis anything other than calculus?
where do i learn group theory and modules?
what is the best book for topology?

[Anonymous No.11933525]

>>11933491
>is analysis anything other than calculus?
I don't really know, on my language it's the same word for both. I guess knowing how to prove stuff on functions will be useful in topology, not just computing integrals.
>where do i learn group theory and modules?
In books about group theory and modules I guess? Not sure if I understand your question.
>what is the best book for topology?
Lots of people recommend Munkres, never read it personally, I don't read much on English. Steen-Seebach is very nice.

[Anonymous No.11933538]

>>11933491
>is analysis anything other than calculus?
not sure, but I think calculus refers to analysis on R^n to R^m, which doesn't include topics as analysis on manifolds nor functional analysis
>where do i learn group theory and modules?
Any Abstract Algebra book. Maybe start with Aluffi and then move on
>what is the best book for topology?
I recommend Bourbaki's series of books, "Handbook of Set-theoretic Topology" by Kunen and Wilanski's "Topology for Analysis"

[Anonymous No.11933565]

>>11933491

Proofs and Intuition:
>How to Prove it, Velleman
>A Concise Intro. to Pure Mathematics, Liebeck
>Visual Group Theory, Carter

Novice:
>Abstract Algebra, Pinter (Dover)
>Linear Algebra, Hoffman & Kunze

(you may skip to Advanced if you can deadlift 200kg)

Intermediate:
>Basic Algebra I, Jacobson
>Supplement with: Grillet, Hungerford, and maybe Dummit & Foote

Advanced:
>Algebra, Lang
>Basic Algebra II, Jacobson

[Anonymous No.11933578]

>>11933565
what if i deadlifted 200kg 3 years ago in competition but i cant do it anymore

[Anonymous No.11933588]

>>11933538
>I recommend Bourbaki'

[Anonymous No.11933615]

>>11933578
Then you should read the following.

Advanced High School Maths (European):
>Course in Arithmetic, Serre
>Theory of Ultrafilters, Negrepontis
>Program Analysis, Neilson
>Subsystems of Second Order Arithmetic, Simpson

[Anonymous No.11933627]

>>11933615
god does not ask us to make axioms, he asks us to go forth daringly into the structure and discover truth within our eyes' creation

[Anonymous No.11933638]

>>11933015
>You need topology to define D(Ω) and therefore distributions, I don't see any decent PDE course skipping Dirac's delta. This is also assuming you count the theory of Sobolev spaces as pure analysis.
What if the entire semester is dedicated to the classical theory of the wave equation, the heat equation, the Laplacian and the study of harmonic functions tho?

[Anonymous No.11933647]

Does anyone wanna be my friend? I have three friends but they never wanna talk a lot.

[Anonymous No.11933673]

Before we stabilized, I saw One from beyond the atmosphere as I’d never seen it before. The sky was clear, landmasses differently shaped, and the grey infection had not yet taken hold. Raw green and blue orb, it felt alive, it felt breathing.
Presently, we stood boot-firm on the ground, washer floating beside us to cover our tracks with organic chaos. In the distance, we spotted fire. Teams fanned out, and this seems to be the first instance of its intentful creation. With magnification lenses, we stalked the creature responsible. At night, he demonstrated his innovation to his community. Some hissed, some howled, but he held that torch high and spoke like he was possessed:
Hak TAMUR na-ada! Sem Duly har DAFT!
Though I had never encountered this dialect, augmented reconstruction was simple: “All demons gone! Only we prevail!” – to which cries shrieked and fervor ecstasy danced around the plume of flame he lit

[Anonymous No.11933716]

Prometheus, we would call him, recounted how he came upon his discovery. We had observed him before seeking him in private confidence, but we wanted to know what his thought process was. How did neural systems first begin to coordinate? To my best comprehension, he said this:
By forest edge, me sit
When storm shake,
Sky rips
When sky rips, forest rips
Then forest burn
So me go to little forest
Break arms of forest
And make it rip
And make it Sun

He betrayed no fear in talking to us strange, overpowering foreign creatures. His skin shook to the rhythm of the Sun’s crackles, he was possessed with it. Yet, he calmed, aware of a need to be communally sane in conversation. He sat presently, equanimous.
“We thank you for your story, Nvo (as he was called by his kind). We wish to give you a parting gift, but it goes against our traveler’s code. We thank you for the tea and nuts you shared with us. And we thank you for keeping this meeting – silent – “
He nodded in agreement, and we saluted him as we departed to the next piece of history, a quizzical comical look on his face as he wondered over our strange body signs. But, he saluted back, feeling the strength, finality, equality in it.

[Anonymous No.11933818]

>>11933647
no

[Anonymous No.11933849]

A young woman, not yet marked with the stress of Motherhood, sits by a flower, and a petal falls off. Gently holds it in her hand, picks a little seed off of it and brings it back to her abode. She pats it into the dirt next to some growing grain. We dare not disturb this peace, for it is the last we’ve known. Change would quicken now.
>>11933818

[Anonymous No.11933982]

Best book for geometric group theory please.

[Anonymous No.11934068]

I know how to prove the irrationality of [math]\sqrt{2}[/math] and [math]\sqrt{2}[/math] but how do I go on about proving the irrationality of [math]\sqrt{4}[/math]?

[Anonymous No.11934080]

>>11934068
Suppose that sqrt(4) = m/n with m, n coprime. Then m^2 = 4n^2. So m^2 is even, so m is even. Dividing, we find that n^2 is even, so n is even. Thus m and n are not coprime. Contradiction.

[Anonymous No.11934082]

>>11934068
What have you tried?

[Anonymous No.11934089]

>>11934068
[math]\sqrt{4}=2=\frac{2}{1}\notin \mathbb{R}\ \setminus \mathbb{Q}[/math]. Therefore, 2 is rational.

[Anonymous No.11934095]

>>11934068
you have two irratiional numbers. neither has a factor on top or bottom. so you multiply them, and you have no factors on top, nor on bottom!

[Anonymous No.11934111]

>>11934068
lel

[Anonymous No.11934122]

>>11933444
>if you do fake and gay schizo shit you’ll notice patterns everywhere
>if you do analysis you’ll possess singular focus on real problems that gratify and validate a life time of training
Wow really makes you think

[Anonymous No.11934158]

>>11934122
Cope more patternlet

[Anonymous No.11934175]

>>11934122
are you chinese?

[Anonymous No.11934185]

>>11934158
>patternlet
Name a single real world application of abstract algebra that’s more impressive than all of physics, finance, economics and engineering. I’ll wait.
>>11934175
No, I hate chinese people and ivory tower foppery like algebra that produces nothing tangible and is also ugly and degrades the quality of pure math as an art.

[Anonymous No.11934200]

>>11934185
>real world applications
Eww yikes. Why would I care about that?

[Anonymous No.11934226]

>>11934185
how can you appreciate an art without having a basic feeling for its overall aesthetic? assuming there is one, because i pray there is one. i'm beginning to see it's form in symbolic manipulations - the nature of a system is understood by what type of manipulations can occur - switches of a symbol as in negative numbers, conjugates, adjoints. pulling out of terms. factorization in inner products and foiling. these things describe the basic possibilities of change, which pieces are liberated and what degrees of freedom they have - just not geometric ones. there's also things in arithmetic, finding inner structures to algebraic statements by what it can be set equivalent to, how it can be manipulated to liberate or connect terms, what terms are contained within it

but number theory and complex analysis tell strange tales still, seemingly magically
and space itself is curious as of yet

[Anonymous No.11934264]

https://www.youtube.com/watch?v=rQ73L6aItQ8

[Anonymous No.11934356]

>youtube recommends me a video about a non euclidean world engine
>watch it
>start thinking that it may be a spheroid or a hyperbolic surface but with some visual effect that makes it look flat or some other cool shit
>it's actually just a flat surface but with portals
is that the power CS?
here is the video https://www.youtube.com/watch?v=kEB11PQ9Eo8

[Anonymous No.11934362]

>>11934356
wouldn't a spheroid be easy to cs compute? travel in any direction for the same duration, return to beginning.

[Anonymous No.11934366]

When it says to construct a field using [math]x^2+1 \ in \ \mathbb{Z}_3[/math] does that just mean the field [math]F=\mathbb{Z}_3 / \langle x^2+1 \rangle[/math]?

[Anonymous No.11934373]

>>11934366
What you wrote doesn't make sense. You meant the quotient of the ring of polynomials over that field I think.

[Anonymous No.11934374]

>>11934356
There's that 7-gon roguelike which, while we can argue whether or not roguelikes are "games", is in fact a game. There's also a variety of 4D puzzler games in FPS.

[Anonymous No.11934394]

>>11934373
Here's the question.
I was thinking that it would be [math]F=\{0,1,2,x,x+1,x+2,2x,2x+1,2x+2\}[/math], since any field with order 9 will have characteristic 3 and it's obvious that that field does have characteristic 3. I'm just confused as to what's meant by the first part regarding [math]x^2+1[/math] because wouldn't [math]F=\mathbb{Z}_3 / \langle x^2+1 \rangle[/math] be the same thing?

[Anonymous No.11934440]

>>11934362
yeah. i am just saying that this video that has a lot of views and people are praising the guy for how smart he is even though it is all outright lies.
here is a legit non euclidean surface game.
https://arnaudgl.itch.io/non-euclidean-shooter
i think the trick is that your world is on a curved surface but you have some visual effect that makes the world look flat to make you unable to tell that it's a curved surface. it would be interesting to push this idea even further with more complicated surfaces and shapes and it would definitely make certain geometry concepts easier to understand and visualize

[Anonymous No.11934441]

>>11934394
It is the quotient.

[Anonymous No.11934445]

>>11934440
'Non-Euclidean' has become one of the biggest buzzwords in the vidya and very few people seem to know what it actually means.

[Anonymous No.11934463]

>>11934356
someone is making a proper game like what you want, though. all those videos are usually super disappointing so it was very cool to see this:
https://www.youtube.com/watch?v=EMKLeS-Uq_8

[Anonymous No.11934487]

>>11934356
>>11934463
actually, both videos were made by the same person interestingly but the one you posted is a lot older. the same guy also made marble marcher which is a game for ball-rolling on 3d fractals, it's really something special. and it's free.
hyperbolica will be a lot of fun, i'm very excited for it even if it's more of a walking simulator.

[Anonymous No.11934506]

NICE NUMBERS, FAGGOT.

[Anonymous No.11934607]

>1000 pages homology and topology book on arvix.

https://arxiv.org/pdf/2007.02467.pdf

[Anonymous No.11934742]

>>11934440
>cylinder rendering funny
>non-euclidean
I can understand calling cylinder geometry non-euclidean, but you can't say that portals are euclidean and cylinders aren't, fuck off.

[Anonymous No.11934763]

>>11932572
I forget how to add every other day. Mike Spivak is 100% right about me.

[Anonymous No.11934774]

>>11934742
>but you can't say that portals are euclidean and cylinders aren't
Actually, you can.

[Anonymous No.11934781]

>>11934607
Damn, that's based. Thanks for sharing.

[Anonymous No.11934789]

>>11934774
No, the moment you say that one quotient of R^2 with the quotient metric is non-euclidean by default every other non-trivial quotient also is.
In fact, portals win out, because a cylinder is still a manifold, while R^2 with two points identified isn't.

[Anonymous No.11934791]

is this cool?

[Anonymous No.11934809]

>>11934791
erm, well it's not so interesting if you go from right to left and realize you can always get some projection of connected edges this way

but yeah it's cute if you want

>>11934506
lel

>>11934607
also lel

have you seen Luries stuff?

[Anonymous No.11934817]

>>11934607
>>11934809
wew

[Anonymous No.11934835]

does vixra deserve the hate and bad reputation?

[Anonymous No.11934836]

>>11934791
That's pretty fucking cool.

[Anonymous No.11934853]

>>11934835
I am not sure anything legitimate has ever been posted to vixra

[Anonymous No.11934854]

>>11933430
I did have a nice maths week, thank you! I hope you all have a good maths weekend.

[Anonymous No.11934865]

wtf is surgery? no meme answer please.

[Anonymous No.11934875]

>>11934854
Thanks, lad.

[Anonymous No.11934891]

>>11934865
Imagine I take you an' Bob an' I draw a circle on your bellies, right.
So I remove the skin inside the circle on your belly an' Bob's, and so the meat isn't left exposed, I sew your circle an' Bob's together, so your open wounds are just pressing against the other's.
That's surgery. Simple as.

[Anonymous No.11934927]

>>11934854
Did you learn something nice? Did you prove something cool?

[Anonymous No.11934947]

>>11934927
Not that anon, but I'm currently going through Hall's book on Lie groups/algebras and representations. It's pretty comfy.

[Anonymous No.11934949]

What are the best resources for improving my fundamentals?

It's really hindering me that I can't "play" with equations like other people can

[Anonymous No.11934953]

>>11934791
not realy cause its just squares without the extra black lines

[Anonymous No.11934964]

>>11934947
Nice! I hear a lot of good words about that book. Compact Lie groups could be useful for me to know, so maybe I'll give it another try at some point.

[Anonymous No.11934975]

>>11932387
Usually the proofs in engineering and physics just assume the functions you are working with are well-behaved enough for the math techniques to work.
Mathematicians are concerned with finding the limits of the validity of the techniques.
Basically they want to find what breaks the technique and what can be done to fix it in those extreme cases.
I doubt you learned the criteria for the convergence of fourier series or when you are allowed to swap integrals and infinite sums.
Usually these things are just assumed to be valid out of convenience and to make the "proofs" simple.

[Anonymous No.11935009]

So, /mg/. Which one do I start with?

[Anonymous No.11935030]

>>11935009
Steinberg.

[Anonymous No.11935034]

>>11935030
sounds kinda boring though. I should have downloaded Serre instead.

[Anonymous No.11935110]

>>11932327
Help me /mg/, which subjects should I focus on this semester (it will be online), the ones that are boring as fuck so I can get rid of them faster (statistics, numerical analysis, physics, differential equations) or the fun proof-based ones (analysis, algebra, linear algebra)?

[Anonymous No.11935119]

>>11935009
Jesus Christ, do a favor to yourself and download SumatraPDF.

[Anonymous No.11935124]

>>11935110
I hope you get AIDS

[Anonymous No.11935126]

>>11935110
If you're already disinterested in a topic, then you'll find it impossible to focus on it in an online context. Source: I'm currently taking online classes in courses that I'm not much into. I would recommend ones you're already interested in because it's a lot more likely that you'll engage in the material out of sheer interest rather than necessity. Also, differential equations (especially PDEs) are fun classes provided they're not mindless computational based.

[Anonymous No.11935140]

>>11935119
Book/reference management software is AIDS.

[Anonymous No.11935148]

>>11935140
>Book/reference management software is AIDS.
Sumatra is a pdf reader.

[Anonymous No.11935159]

>>11935148
Yes, and?

[Anonymous No.11935179]

>>11935159
What the fuck did you mean by your post if you weren't implying that you don't use Sumatra because it's a "Book/reference management software" and because those are AIDS?

[Anonymous No.11935210]

>>11935179
¿What's so fucking special about this pdf reader then?

[Anonymous No.11935225]

>>11935124
Oh, Kaz... I'm already Aids...
>>11935126
Thanks for trying to help, but I already decided I'll do the boring stuff so I can get rid of them faster, I'll have to do it sooner or later anyway, I just came here seeking validation for my choice.

[Anonymous No.11935230]

>>11935210
Because it's light years better than the ancient proprietary shit you're using...

[Anonymous No.11935233]

god i’m getting so wet imagining all the ants living in this cone for ants in the middle frame of this .jpg for ants crawling all over my naked body and biting all over my clit and nipples

[Anonymous No.11935236]

>>11935225
>I just came here seeking validation for my choice.
Try reddit, next time.

[Anonymous No.11935241]

>>11935236
Will do, at least there are actual mathematicians there.

[Anonymous No.11935250]

>>11935230
I use Okular or wtf ever is default on Linux Mint now. I don't care about your gay freedom hoopla.

[Anonymous No.11935257]

>>11935241
In order for that to work here someone would actually have to think of themselves as a mathematician. The truth is we're all 12 year old Indonesian tapestry weaving fans who pretend to know math between mastrubation sessions.

[Anonymous No.11935262]

>>11935257
Delete this post before you get actually banned for it.
>do the mods really enforce the underage rule as a joke
Yes.

[Anonymous No.11935279]

>>11935262
Whatever, they don't enforce any of the other rules that aren't legally required. No one gets banned for saying «i am 12 and what is this».

[Anonymous No.11935284]

>>11935262
>>do the mods really enforce the underage rule as a joke
>Yes.
can confirm, I've received underage bans before for posting actual copypasta because the pasta (not me mods I've already hit the 24 wall) claimed to be underage

[Anonymous No.11935304]

>>11935262
They unironically do. I got a 30 day ban for a joke pertaining to that.

[Anonymous No.11935315]

>>11935257
Holy shit, that's literally me, except I'm 24. I'm already past the golden age to do mathematics, so all that's left for me is to masturbate to high level maths while imagining myself proving a millenium problem.

[Anonymous No.11935369]

>>11934975
>I doubt you learned the criteria for the convergence of fourier series or when you are allowed to swap integrals and infinite sums.
I did actually, my measure theory course went all the way to Brownian motion and related results. Like I said though my degree is closer to applied math than actual engineering, so it likely doesn't apply to normal engineering courses.

[Anonymous No.11935407]

>>11935369
Based and stochasticspilled.

[Anonymous No.11935507]

>>11935315
I was just joking, that's super depressing. :(

[Anonymous No.11935842]

Slow thread, lads.

[Anonymous No.11935853]

>>11935842
I can't feel motivated to study maths, therefore I also lose my motivation for shitposting here.

[Anonymous No.11935878]

uhh.... what to talk about?
do any of you guys like survivor?

[Anonymous No.11935885]

>>11935878
One of my favourite bands, I love Eye of the Tiger!

[Anonymous No.11935903]

What kind of questions piss you off most in oral exams? Asking for a friend.
>inb4 ORAL EXAMS MORE LIKE BENIS INSPECTION HAH HAHAHAAHAHA
no.

[Anonymous No.11935906]

>>11935903
We don't have oral exams in the states.

[Anonymous No.11935915]

>>11935906
Why?

[Anonymous No.11935926]

>>11935878
Suvivor games? Not very much, I mostly play puzzles, been playing Infinifactory these days, pretty good game, but don't play it if your IQ is below 120.

[Anonymous No.11935986]

>>11935903
>tell me what you know about X

[Anonymous No.11935999]

>>11935915
Average iq of american mathfags is at least a full standard deviation higher than that of europeans. it would be unnecessary.

[Anonymous No.11936001]

>>11935915
takes too long to test people or is just logistically more difficult maybe? Also remember schools over here have to churn through thousands of international students with barely passable English.

[Anonymous No.11936003]

>>11935999
checked but also lol'ed
>>11936001
usually oral exams are for advanced courses, between 10 and 20 participants

[Anonymous No.11936006]

>>11935999
>>11934506

[Anonymous No.11936008]

>>11935906
In graduate courses it's not uncommon.

[Anonymous No.11936012]

>>11935999
Not true at all, most american academics are so dumb that universities have to hire foreigners most of the time to make up for that. Just go to any university im the US and the math department will be 50% or more composed of asians, indians, middle-easterns etc.

[Anonymous No.11936013]

>>11936003
how long does each individual exam last though? even if you only talk for half an hour or an hour (which seems short, considering the written final is around 3 hours of writing) that's a substantial investment of time and effort from the professor. it doesn't seem worth it to waste dozens of hours of the prof's time per class per semester when he can spend two hours writing an exam and then knock out all the students at once by sitting in a room reading for 3 hours while they finish their tests.

[Anonymous No.11936020]

>>11936008
Even in graduate courses I think it's mostly reserved for upper-level topics courses. If you did a seminar-style class where you worked through a bunch of papers together there's not really a body of test-appropriate exercises to give you, so the only way to test whether you learned what you read is to talk to you about it.

[Anonymous No.11936024]

>>11936013
It's half an hour to an hour. And yeah it is some time investment, but far less then making up a written test, grading it, and then making a second one because a bunch of faggots were too lazy to study properly. imo for everything less than 30 people oral exams are overall less time intense and more relaxed for everyone involved.

[Anonymous No.11936035]

>>11936024
>but far less then making up a written test, grading it, and then making a second one because a bunch of faggots were too lazy to study properly.
the fuck are you talking about? making up a written test from scratch doesn't even take longer than an afternoon, it's basically a totally automatic process once you have a couple old ones to recycle from, and you can grade a couple of them an hour. plus if you're doing an undergrad course you don't even have to grade them at all, you can pawn it off on a TA (which you can't do with an oral exam)

[Anonymous No.11936063]

>>11936012
>Just go to any university im the US and the math department will be 50% or more composed of asians, indians, middle-easterns etc
Average iq of American whites is 103-106, average iq of East Asians is 103-106. Average iq of indians is 90-95. Average iq of Iranians is ~95. Average iq of Arabs ~85-90. There is a specific reason why there are so many foreigners in American mathematics departments it has nothing to do with intelligence. Whites and Jews are the master race(s) there is nothing you can do about this.

[Anonymous No.11936067]

>>11936012
Foreigners get into American university math departments because they know how to cheat written exams much better than Americans

[Anonymous No.11936073]

>>11936063
Explain Ramanujan, then.

[Anonymous No.11936090]

>>11936073
weaponized autism

[Anonymous No.11936110]

>>11936073
monkey banging on keyboard into infinity, wow one smelly street shitter out of 239472938 Billion street shitters, not impressed

[Anonymous No.11936112]

>>11936073
What a stupid post lol.

[Anonymous No.11936127]

>>11936035
Yeah right, keep spouting bullshit mister undergraduate-know-it-all.
>using old stuff
HAHAHAHHA maybe if you're in Bongland because they have no standards (exception: Cambridge & Oxford, still retards though).

[Anonymous No.11936172]

>uni library has just papa rudin and no other analysis textbook
huh

[Anonymous No.11936184]

>>11936172
Well?

[Anonymous No.11936326]

>>11936127
>took you an hour to come with "call him an undergrad"

[Anonymous No.11936335]

>>11936326
Sorry I'm preparing an oral exam right now, can't be lurking 24/7 :^)

[Anonymous No.11936338]

>>11936172
do you go to the university of rural Zimbabwe?
my undergrad uni had ~6,000 students and the library still had like 3 shelves of intro analysis books

[Anonymous No.11936369]

>>11936338
>do you go to the university of rural Zimbabwe?

[Anonymous No.11936525]

yo y dis bread ded

[Anonymous No.11936614]

>>11936063
>American whites is 103-106
Yeah, gonna have to doubt that, just see Trump and how many people voted for him.

[Anonymous No.11936619]

>>11936614
What would you say about Clinton voters?

[Anonymous No.11936624]

>>11936619
extremely intellectual types, for example terence tao

[Anonymous No.11936628]

>>11935369
Maybe your oh so formal math course ended up covering less material because of it. Don't tie your ego to what you learn

[Anonymous No.11936629]

>>11936619
I'd say Trump voters average around 85~90 IQ and Clinton voters 90~95 IQ, any high IQ person would realize they're both trash and wouldn't vote at all.
>>11936624
That person is not me.

[Anonymous No.11936673]

Holy fucking shit, I hate my uni, they think mathematicians can't learn physics so they put a bunch of exercise lists every fucking week for us, not only that but some of those need to be done in groups of 3 or 5, what the fuck is this shit?????

[Anonymous No.11936733]

[Anonymous No.11936760]

Definition. A piggot is a pig-faggot, i.e. someone who is a pig and a faggot (the term is a portmanteau of "pig" and "faggot").

Theorem. (You) are a piggot.
Proof. We proceed by showing that (You) are a pig and a faggot. First, the pig case. (You)r mother is a pig, and a pig begets pigs; therefore, (You) are a pig. The faggot case is obvious. Q.E.D.

[Anonymous No.11936800]

When did /mg/ die? Last time I came here was 4 weeks ago and the thread was relatively fast with good posts all around, now there's luckily one answer each hour and they're mostly teen trash like this one above.

[Anonymous No.11936840]

>>11936012
>Just go to any university im the US and the math department will be 50% or more composed of asians, indians, middle-easterns etc.
that's just boomer hiring practices

[Anonymous No.11936918]

>>11936760
brilliant theorem, i'm giving you a positive review

[Anonymous No.11937090]

>>11936800
Maybe a lot of the posters are on summer breaks or have summer jobs or something.

[Anonymous No.11937092]

absolute sate of this thread.
Not even a single math related post in the last 20 hours.

[Anonymous No.11937107]

>>11937092
>Actually discussing math
Keep the nerd shit in the classroom. Let us shitpost (sometimes about math).

[Anonymous No.11937138]

>>11936800
/mg/ is normally pretty dead. The last few weeks have been uncharacteristically lovely for some reason.

[Anonymous No.11937201]

>>11937090
I have increased their duties of relieving my stress as a part of my harem.

[Anonymous No.11937207]

Is the PhD anime tranny that used to post the 24 meme still around here?

[Anonymous No.11937221]

>>11937207
Hello there.

>>11937201
I see. That explain.

[Anonymous No.11937259]

>>11937221
What are you doing your PhD on, lad?

[Anonymous No.11937276]

[Anonymous No.11937278]

>>11937221
>Hello there.
Great, at least one good poster is still here, hope the touhou one is as well, you are the soul of these threads.

[Anonymous No.11937315]

>>11937259
It's a mixture of homotopy, representations, group cohomology, homology of categories etc. Basically, my supervisor and his friends came up with a structure they manged to use in order to generalise the methods of a certain paper where the author starts with a groups and obtains the homology of its loop space (completed in the sense of Bousfield and Kan) purely algebraically (or is it algebraicly?). They also showed that this structure of theirs could be used for much more, yet never had time to actually find out what this "much more" is. This is where I step in. Sorry for the somewhat vague description, I'd just doxx myself very easily (regardless of whether anyone actually cared to look me up or not, I don't like the idea on a personal level). Anyhow, currently looking at this things potential connections to Bredon cohomology.

>>11937278
Thanks! The touhou poster is active too.

[Anonymous No.11937334]

>>11937315
>That thumb

[Anonymous No.11937336]

>>11934374
>7-gon roguelike
>4D puzzler games in FPS.
what are their names?

[Anonymous No.11937361]

>>11937138
This is because I have been multi-posting as various personalities and having engaging exchanges with myself and others (myself and others).

[Anonymous No.11937382]

If [math]\rho(x,y,z)=x^4y+2y^3x^2+3xyz \ \textrm{with} \ x>y>z[/math], then the leading term with respect to deglex would be [math]x^4y[/math], right? Since even though the first and second terms of [math]\rho[/math] both have degree 5, the term with the higher power of x 'breaks the tie'.

[Anonymous No.11937393]

>>11937276
>can only define kernels in abelian categories

Disappointing.

[Anonymous No.11937403]

Is Pinter's abstract algebra book any good? Was thinking of using it before something grad level.

[Anonymous No.11937406]

>>11937403
It's probably the best introductory book to algebra. My only complaint is that he is very stingy with solutions to the exercises.

[Anonymous No.11937425]

>>11934356
>>11934463
>>11934487
One hell of a redemption arc desu

[Anonymous No.11937456]

>>11935926
infinifactory is really good. not so tough to finish until very very late in the game, but brutally difficult to optimize. optimizing for blocks is so much fun.

[Anonymous No.11937459]

>>11937456
Optimization is half the fun of vidya, at least for a mathematician.

[Anonymous No.11937463]

>>11937336
the 7-gon roguelite is hyperrogue

[Anonymous No.11937473]

Speaking of games occurring in unusual geometries, has anyone else seen 5-dimensional chess with multiverse time travel?
https://www.youtube.com/watch?v=EBzX1ybigmw
It's fucking hilarious. Apparently it's very interesting too.

[Anonymous No.11937475]

>>11937473
I don't understand what I just watched.

[Anonymous No.11937488]

>>11937473
What the fuck? 5D chess really exists? That's looks like a 200IQ game

[Anonymous No.11937494]

>>11937475
It takes some time to get the idea for what's going on.
But if you understand normal chess, the extension is a pretty elegant idea:
>There are really 4 dimensions. (I think it's called 5-dimensional cause normal chess is technically only 3-dimensional since knights can move over other pieces).
>The dimensions are: rows on the board, columns on the board, time which is left to right, and parallel realities which are top to bottom
>All chess pieces move normally, but in any dimension. So a knight can move 2 steps in one dimension and 1 step in another. A rook can move in a straight line along any single dimension as long as that line isn't blocked. A queen can move along just about any diagonal through multiple dimensions. Etc.
>All pieces in the past are stuck in place.
When you move backwards in time, you create a branch onto a parallel reality which becomes the new present.
>You get checkmate as you usually do, if one of the other player's kings is in check and cannot be taken out of check. But this can include past kings, which may be locked in place.
It's a very different game in many ways due to this last point, it's quite aggressive. You can double up pieces by doing certain maneuvers and create many different parallel timelines to manage. But both players have the same tools at their disposal. It's very complicated and very, very fun to think about.

[Anonymous No.11937498]

>>11937488
Just came out. I don't think it's so bad once you get the hang of how to win. The games don't get too complicated because the more interacting timelines there are the more danger your pieces are in. It's not like you need to resolve dozens of timelines.

[Anonymous No.11937525]

>>11937494
On one hand, this sounds pretty neat; on the other hand, this sounds overly convoluted. Maybe I'm just a brainlet.

[Anonymous No.11937539]

>>11937525
It's convoluted, but it's about as simple as it could be for proper time travel chess.

[Anonymous No.11937597]

>>11937278
fuck off

[Anonymous No.11937602]

>>11937597
?

[Anonymous No.11937604]

>>11937602
Dumb reddit faggot

[Anonymous No.11937630]

>>11937604
Based.

[Anonymous No.11937680]

>>11937630
Why are you insulting me like that? What did I do to you?

[Anonymous No.11937718]

>>11937473
Just got this game for shits and giggles. This is wonderfully confusing.
I just got checkmated 5 moves in the past by a queen who time traveled from a parallel universe to clone herself in the past.

[Anonymous No.11937722]

>>11937718
Kek, i need to play that

[Anonymous No.11937740]

>>11937718
>a queen who time traveled from a parallel universe to clone herself in the past.
Based.

[Anonymous No.11937749]

>>11937718
lel

[Anonymous No.11937755]

>>11937718
Lmao

[Anonymous No.11937956]

>>11937473
How do I become good a this?

[Anonymous No.11938006]

>>11937956
practice it you impatient faggot

[Anonymous No.11938035]

>>11938006
There's no reason in practicing if you don't have the necessary IQ.

[Anonymous No.11938047]

death of /mg/.

[Anonymous No.11938052]

>>11938035
>RedditQ

[Anonymous No.11938083]

>>11937956
I have no clue. I think it comes down to experimentation and getting beaten by the AI in interesting ways. The game also has a number of puzzles which I guess are good for training.

[Anonymous No.11938146]

>>11936628
>Maybe your oh so formal math course ended up covering less material because of it.
Doubt it, we covered like 300 pages worth of material. There's no need to get defensive about it friend, my university is not even in global top 50 rankings.
>Don't tie your ego to what you learn
I didn't do anything of the sort, the guy just assumed something and I corrected him. There are some things that I will obviously miss because it's impossible to cover everything, personally I have a gap in algebra because I avoid those courses like the plague.

[Anonymous No.11938156]

>>11937473
>tfw now I can flex on the brainlets in my Steam friendlist playing their weeb trash while I dominate on 5D chess

[Anonymous No.11938172]

>>11938156
Based.

[Anonymous No.11938185]

Hey brainlets if I happen to have a closed timelike curve on a Cauchy surface, constrain it to a Riemann geodesy using the Nash rules, and detemporalize the fucker via the Einstein metric tensor, I pretty much would be able to generate a particle of any spin correct me if I’m wrong? (If you can?)

[Anonymous No.11938241]

>>11938185
That's not how spin works

[Anonymous No.11938366]

>>11937473
this looks very white-biased at a glance
but complex enough for experience to overcome the black disadvantage

[Anonymous No.11938367]

lower than 6

[Anonymous No.11938382]

>>11938367
[math]S_5[/math] is the smallest unsolvable group.

[Anonymous No.11938384]

>>11938382
Wasn't it A_5?

[Anonymous No.11938386]

>>11938185
go away
>stein

[Anonymous No.11938396]

>>11938384
Yeah, you're right.

[Anonymous No.11938438]

How much measure theory is actually used in statistics?

[Anonymous No.11938459]

>>11932345
>What is orbital mechanics

[Anonymous No.11938511]

>>11938438
A lot.

[Anonymous No.11938525]

>>11938438
All of it.
There aren't any useless theorems in classical measure theory before Polish space autism, anon.

[Anonymous No.11938533]

>>11938386
>>11938241
brainlet

[Anonymous No.11938543]

>>11938241
https://en.m.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment

uh... anon...

[Anonymous No.11938553]

[math]E[i]=\{\alpha + \beta \omega \vert \omega = \frac{-1+i\sqrt{3}}{2} \}[/math]

[Anonymous No.11938589]

>>11936624
Why do you think Tao would vote Clinton? And what does he have to do with the average nigger voting Clinton or Biden?

[Anonymous No.11938602]

>>11938438
Under what measure?

[Anonymous No.11938607]

>>11938602
Lebesgue

[Anonymous No.11938686]

Hey anons, 3rd year undergrad retard here. How the fuck do I study math? Do you read the text and do all the problems? Just the ones in the back? How do you read a textbook? I feel like all my methods are wrong.

[Anonymous No.11938703]

>>11938686
Go line by line and make sure you actually understand everything that is being said. You can't read a textbook like you can a novel. Doing every single problem usually isn't an efficient way to study either. Ideally, you should pick problems that stress concepts that you either struggle with or are core to the respective chapter. I also found it helpful to have two notebooks for each class: One where I would copy down stuff from class and another where I would for formally lay out all the concepts with examples. This is helpful because you'll be copying down the stuff which is good to get it into your head and it'll be a lot more organized and thus easier to study from.

[Anonymous No.11938704]

>>11938686
>How the fuck do I study math? Do you read the text and do all the problems? Just the ones in the back? How do you read a textbook?
https://youtu.be/BAtDe5Mfq84?t=43
0:43-1:09 is the answer I'd give in a better way than I could ever give it

[Anonymous No.11938711]

>>11938704
Basé

[Anonymous No.11938756]

>>11938686
Focus completely on the endgoal, that is passing the course
Course contents is filled with keywords, make a plan to know what those keywords represent only
Fuck all the other shit, don't get lost digging holes and filling them up, there's infinite fucking math do what takes you where you want only
Use the old tests, recommended exercises for your modules, upperclassmens old lecture notes, once you sort of know the contents of the course start doing an old test per day. Start tryharding when you start the course of possibly even before you start it, each hour is worth much more if you're early in the process rather than accruing debt, that knowledge needs to simmer a bit to solidify

[Anonymous No.11938768]

>>11938756
>When the professor posts past exams

[Anonymous No.11938985]

Is there an unironic example of [math]\aleph_2[/math]?

[Anonymous No.11938997]

>>11938607
0

[Anonymous No.11939066]

>>11932327
Do any of you guys listen to music on low volume when you study? Post some

[Anonymous No.11939076]

>>11939066
https://www.google.com/url?q=https://m.youtube.com/watch%3Fv%3DH9UIdlXhrBQ&sa=U&ved=2ahUKEwi2jvScpOrqAhWBct8KHY0DABkQyCkwAHoECAoQAQ&usg=AOvVaw3Fyj452tHpdqzHtZqE1lQr

I listen on HI volume

[Anonymous No.11939080]

>>11939076
I'm not clicking that shit

[Anonymous No.11939084]

>>11939080
It's literally just a deformed YouTube link you poopsterbater

[Anonymous No.11939128]

>>11939066
https://www.youtube.com/watch?v=XS6m3lkiQjc
https://www.youtube.com/watch?v=eB_1hxJZzug
https://www.youtube.com/watch?v=HtaIJCQF3ws
https://www.youtube.com/watch?v=KXH5G_bqrlc

[Anonymous No.11939153]

>>11939066
Renai circulation

[Anonymous No.11939174]

/gmmg/

>>11938686
Do you ever stop and think about the stuff you have read as if it was a story? I'm not saying you should treat textbooks like novels, but it helps me if I can see some "plot" in the big thing. In particular, if you can see the "story" of a chapter, like for example how compact sets are small, or something similar, that helps. This does not mean, however, that you should skip rigour and exercises. It's just something to think about when you go for a walk or tidy up your home. To do this, you need to have read the things beforehand or else you have nothing to work on.

>>11939066
Lately I have been listening to a lot of Drudkh, Moonblood and Ritualz.
https://www.youtube.com/watch?v=S7PLhhb0Mls
https://www.youtube.com/watch?v=gxJ5nXlHe6o
https://www.youtube.com/watch?v=XCYcTt2IuB0

[Anonymous No.11939192]

>>11939174
Morning, lad.

[Anonymous No.11939207]

>>11939192
Based lad poster.

[Anonymous No.11939216]

>>11939066
>>11939076
>>11939080
>>11939084
>>11939128
>>11939153
>>11939174
>>11939192
>>11939207
You have ruined your general lol. If you had any idea how bad it is now compared to just a year ago

[Anonymous No.11939221]

>>11939216
Thank you for your contribution. It made this thread a lot better.

[Anonymous No.11939225]

>>11939221
You're welcome.

[Anonymous No.11939239]

uhhhhh what's the continuous dual space of the space of bounded operators? say, on a Hilbert space, the space B(H) has a well-known predual, but what happens to its dual space?

[Anonymous No.11939247]

>>11939239
Are you asking about [math](X^*)^*[/math]? There's a canonical injection of [math]X[/math] into it given by evaluation, but you need more information to say anything more.
https://en.wikipedia.org/wiki/Reflexive_space

[Anonymous No.11939714]

>>11939216
>ruined the general
Actually, that was me, my bad.

[Anonymous No.11939731]

>>11939714
Good job, Anon!

[Anonymous No.11939738]

>>11938985
I don't know, but Gödel believes the real naturally have this cardinality, so maybe you find something with those keywords

[Anonymous No.11939762]

>>11938382
oh no i was trying to decide whether to masturbate or not. thanks for the input though

[Anonymous No.11939787]

Since 2015 I've been trying to prove the Riemann Hypothesis, but these days I'm finally starting to accept that talent is indeed the most important thing in this field, I just can't do it anymore, I tried for 5 years, I failed, I need to move on now, but at the same time that bitter feeling of defeat still lingers in my soul.

[Anonymous No.11939790]

>>11935999
top fucking kek, american math undergrad programs are a joke

[Anonymous No.11939796]

>>11939174
>if you can see the "story" of a chapter
The fuck am I reading? Terrible advice, how can one see the 'story' in an advanced mathematics textbook? The only way to memorize definition, theorems and formulas is the old, simple and boring way: repetition, there's no other way around it, you need to repeat and repeat and repeat and repeat and repeat until it fixes in your head.

[Anonymous No.11939799]

>>11939787
Imagine being so detached from the maths community that you attempt to solve the hardest of the hardest problems.
Go look at Putnam problem sheet, then look at IMO problem sheet, maybe this will teach you humility.

[Anonymous No.11939807]

>>11939799
>Go look at Putnam problem sheet, then look at IMO problem
This shows your complete lack of knowledge on math if you're putting IMO high school problems above the Putnam college problems.

[Anonymous No.11939815]

>>11939807
My point was: he can't do super hard thing (riemann hypothesis). He probably couldn't do a simpler thing (putnam) or even a much simpler thing (imo problems).

[Anonymous No.11939820]

>>11939787
You had a stupid idea and the audacity to dedicate five years of your life to it, I'm proud of you. Best of luck in whatever you go for next.

[Anonymous No.11939824]

>>11938985
Under GHC, it would be [math]\mathfrak P(\mathbb R)[/math]

[Anonymous No.11939828]

>>11939820
I'll finish my PhD now, get a job in a third rate university where it doesn't require much of me and just chill.

[Anonymous No.11939831]

I have a function f(x) = (cos (pi x))/2 - 5 and g(x) = 5x / 6. Together they are h(x) = f(g(x)) = (cos (pi * 5x/6))/2 -5.

I want to calculate h(3), h(4), h(5) and unsure how to go about it. How do I calculate for example h(4) = cos (pi * 20/6))/2 - 5?

[Anonymous No.11939836]

>>11939831
>How do I calculate for example h(4) = cos (pi * 20/6))/2 - 5?
You punch it into a calculator. I don't understand what your problem is.

[Anonymous No.11939839]

>>11939828
Sounds comfy.

[Anonymous No.11939842]

>>11938985
Powerset of the reals?

[Anonymous No.11939844]

>>11939836
Help me grasp it instead thanks

[Anonymous No.11939849]

>>11939844
What part of typing an expression into a calculator don't you grasp

[Anonymous No.11939856]

>>11939849
Consider the same question might appear on my exam where only pencil and paper is allowed

[Anonymous No.11939862]

>>11939856
nah just skip it and do the rest

[Anonymous No.11939870]

>>11939831
>>>/sci/sqt
>>>/wsr/
>>>/somewhere else
You literally use properties and the shitty table with values for cos (30), cos (45) and cos(60). Someone might handhold you through it somewhere else.

[Anonymous No.11940405]

>>11939831
>>11939844
Trig funcs don't care about thetas outside of 0 to 2pi (or -pi to pi, doesn't matter), so take 20pi/6, reduce to 10pi/3, subtract off 2pi=6pi/2, you get 4pi/3, and fuck off to /sqt/.

[Anonymous No.11940422]

>>11940405
Based.

[Anonymous No.11940423]

>>11940405
>2pi=6pi/2

[Anonymous No.11940447]

>>11940423
[math]\sin(2\pi)=\sin(\frac{6\pi}{2})=\tan(2\pi)=\tan(\frac{6\pi}{2})[/math]

[Anonymous No.11940457]

>>11940447
Ocasional reminder to everyone to add in a bunch of spaces between everything when you LaTeX here.
For example,
\sin (2 \pi ) = \sin ( \frac{6 \pi }{2} ) = \tan (2 \pi ) = \tan ( \frac{6 \pi}{2} ) is roughtly how anon should have formatted this.
[eqn] \sin (2 \pi ) = \sin ( \frac{6 \pi }{2} ) = \tan (2 \pi ) = \tan ( \frac{6 \pi}{2} ) [/eqn]

[Anonymous No.11940460]

>>11940423
>the state of /mg/

[Anonymous No.11940497]

>>11940457
>Ocasional reminder to everyone to add in a bunch of spaces between everything when you LaTeX here.
why?

[Anonymous No.11940500]

>>11940457
My question is why does it show up as being good in the preview but then not display that when I actually post it?

[Anonymous No.11940506]

>>11940497
Makes it less likely to blow up.

[Anonymous No.11940750]

>>11940745

noo

[Anonymous No.11940787]

>>11940460
someone post the pic

[Anonymous No.11940996]

Test for randomness:
[math]\sin(2\pi)=\sin(\frac{6\pi}{2})=\tan(2\pi)=\tan(\frac{6\pi}{2})[/math]

[Anonymous No.11941000]

>>11940996
Testing for more than one equal sign:
[math]\sin\pi=\sin\pi=\sin\pi[/math]

[Anonymous No.11941004]

>>11941000
FUCKING BINGO MY NIGGA.
Fuck, I'll have to redo the meme image.

[Anonymous No.11941009]

>>11941000
Double checking:
[math]\sin\pi=\sin\pi[/math]

[Anonymous No.11941013]

>>11941009
Triple checking:
[math]\sin\pi=\sin\pi=\frac{0}{1}[/math]

[Anonymous No.11941015]

>>11941013
Last one:
[math] \sin \pi = \sin \pi = \sin \pi [/math]

[Anonymous No.11941066]

>>11941015
One last check to see if the example can be compactified.
[math]\sin x=\sin x=\sin x[/math]

[Anonymous No.11941076]

No, no, no, one more.
[math]\pi[/math]
[math]\pi\pi[/math]
[math]\pi\pi[/math]
[math]\pi\pi\pi[/math]
[math]\pi\pi\pi\pi[/math]
[math]\pi\pi\pi\pi\pi[/math]
[math]\pi\pi\pi\pi\pi\pi[/math]

[Anonymous No.11941081]

[math]\sin\pi*\sin\pi*\sin\pi[/math]

[Anonymous No.11941083]

>>11941081
Hmm.
[math]*\sin\pi*[/math]

[Anonymous No.11941092]

[math]\sin=\sin=\sin[/math]

[Anonymous No.11941244]

>>11941076
all you're trpiforce are belong to us

[Anonymous No.11941553]

new thread
>>11940745
>>11940745

[Anonymous No.11941652]

>>11941013
Honestly this shit is really weird.
[math]\frac{1}{2}=\frac{2}{4}=\frac{4}{8}[/math]

[Anonymous No.11941662]

[math]\frac{\pi}{1}=\frac{\pi}{1}=\frac{\pi}{1}[/math]

[Anonymous No.11941665]

>>11941662
[math]=\sin\pi=[/math]

[Anonymous No.11941999]

>>11932572
Not high level but I forgot how to do long division on integers a couple weeks ago but can do polynomial or synthetic division in a heartbeat. I think it just comes from how little you use something.