/sci/ - Science & Math

>>11812784
Any good texts on Ramsey theory?

>>11812784

>>11812784
Lang wrote a book on SL_2(R)? I was just reading about SL_2(R)!

>>11812791
>Pure mathematics is on the whole distinctly more useful than applied For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.
>-Hardy

>>11812789
No.

>>11812784
Has anyone ever read one of Lang's undergrad textbooks? What are they like compared to his graduate ones?

>>11812831
i used some of his calculus book(s) for multivariable calculus . it was good but the notation was kinda archaic (or maybe just different than what we used in class). also i had previous exposure to a lot of the "calc 3" syllabus and proofs and unless that's the case for you it's probably not for u. honestly for most of the undergraduate sequence you can get by with just online resources though imho, except for probably differential geometry and higher level electives / survey courses

>>11812910
>>11812831
i'll add that there are many superior books for undergrad abstract algebra, just off the top of my head pinter, gallian, herstein, artin in ascending order of difficulty

Are there any single variable polynomials that are irreducible over [math]\mathbb{C}[/math] or is it just some multivariable polynomials?
Additionally, are there any multivariable polynomials that are irreducible no matter how far you extend the Cayley-Dickinson construction?

>>11812831
Basic mathematics is very good for a motivated autodidact trying to speedrun to calculus; the single variable calculus book is inferior to Spivak, Apostol, and Courant; his multivariable Calc book is subpar compared to all of the other usual suspects like Hubbard&Hubbard and the like. Linear Algebra I only skimmed, seems perfectly adequate, I used Lax and Hoffman and Kunze instead. I have his diff geo book but I don’t see why I would use it when Lee exists.

>>11812938
or based spivak diff geo

>>11812928
yes, precisely the degree one polynomials in C are irreducible

>>11812938
how is multivariable apostol

The 3blue1brown background music playlist is pretty good if you need something to listen to when you study/work. It's not too catchy but not too shitty, just some gentle pieces of music. I think it works better than classical music and lofi hip hop.
I wish I can just study in silence but my room faces a main street and they honk all the fucking time.

>>11812985
I like Touhou piano covers for studying

>>11812985
For me, it's
https://www.youtube.com/watch?v=XS6m3lkiQjc

>>11812996
I have a big list of 2hu/animu piano songs but they are too catchy for me so I can't focus. It's probably just me to be honest.

>>11813003
I couldn't do it with anime music for sure especially if its recognizable, but the 10hr "Touhou piano study music" videos on youtube do the trick .
https://www.youtube.com/watch?v=-7OfZ2fYDx4

If we let [math]\phi:G\rightarrow G^*[/math] be a homomorphism, are there any noteworthy consequences if [math]Ker(\phi)=Im(\phi)[/math]?

>>11812928
>Additionally, are there any multivariable polynomials that are irreducible no matter how far you extend the Cayley-Dickinson construction?
*Dickson

Also I'm not sure this question really makes sense. As soon as you kill off commutativity by extending to [math]\mathbb{H}[/math] the whole notion of a polynomial ring falls apart. Noncommutative polynomials are gross and ugly and rarely behave in a respectable manner. You can try to force the theory if you want but it's just not something that works well.

>>11813018
what does the asterisk superscript mean here?

>>11813029
Just a different group, I suppose [math]\phi:G\rightarrow H[/math] makes more sense, though.

>>11812985
https://www.youtube.com/watch?v=HRvrTfYW0WY

>>11813036
>different group
>kernel is equal to the image
your statement only makes sense if you're talking about endomorphisms.
Even if you loosen it and say [math]\ker(\varphi) \cong \text{im}(\varphi)[/math] the image being isomorphic to a subgroup of G means you may as well just be talking about an endomorphism anyway.

>>11813018
Not one of the big brains here, just an undergrad mathlet, so this might be all wrong, obvious, or unhelpful.

But if ker(f) = im(f), then wouldn't that mean (unless the group theory defs are real different from the linear algebra ones) all values f(x) are such that f(f(x)) = 0.

Specifically for linear maps in R^n, expressing f as a matrix A, A^2 * y = 0 for all y in G, so A^2 = 0. If A is invertible, obviously A = 0. Otherwise, though, 0 = det(0) = det(A^2) = det(A)det(A) and so det(A) = 0; the reverse shows this is iff. So A is singular.

Idk if any of that's useful. Googling shows the phrase "nilpotent of order 2", maybe that has more helpful applications.

>>11813089
This seems correct.
A concrete linear algebraic example of this would be the matrix ((0,1),(0,0)), or as a more general example of the exact same idea you could take G x G -> G x G: (g,h) -> (h,0) for any group G.

Goddamn I hate textbook typos man. Translations are suffering

>>11813280
What are you reading anon?

>>11813298
Apostol's Calc books. No bully pls

>>11813303
It’s not over for you as long as you haven’t reached 24.

>>11813303
Everyone has to start somehwere.

>>11813313
That's a long list. I just jumped straight to Apostol with some Spivak on the side and it's been just fine.

>>11813313
Has anyone actually gotten something out of reading "How to solve it?" I feel like it could be good as a book for teachers though, as it is sometimes marketed.

>>11813329
The critiques of it boil down to the fact that people think it's a good book because they see in it techniques they themselves have used but weren't really taught, and not because those techniques are teachable.

>>11813329
idk i only read about half of it but there's a list of questions that are meant to guide you through problem-solving. I memorized those a while ago and they have been immensely helpful when I am stuck.

>>11813329
>>11813336
Basically this. The uncomfortable truth is that the only way to learn how to solve problems is to solve a metric fuckton of problems. Because people are lazy and don't like feeling stupid, the promise that passively reading a book can make you a better problem solver is easily marketed but it's just flat-out wrong.

>>11813306
No but shit will catch up to me soon

>>11813336
>>11813339
I agree with you and that has been my own experience as well. Terry Tao recommends it though, and even claims to have used it in his MO years, which makes me wonder if I just haven't read it closely enough. (https://terrytao.wordpress.com/career-advice/solving-mathematical-problems/))

>>11813365
Why does /sci/ hate Tao, again?

>>11813370
Tao is a meme

>>11813313
These memecharts are just the worst

>>11813475
>He thinks it's a meme

>>11813496
>reading 7+ books most of which overlap in content in preparation for a freshman/high-school level calculus textbook
meme

Are you the best student in your department /mg/?

>>11813496
Spivak can be read by people in high school. It has set theory, construction of the real numbers, and he walks you through proofs. You don't need all the other shit.

>>11812784
Is this actually a good way to relearn mathematics?

I stopped after linear algebra and discrete mathematics in University. If I want to relearn everything from the beginning, would this be an ideal way to do it? I'm also looking to pick up physics from scratch again

Good morning /mg/

>>11813509
Used to be top 3, but probably haven't been for ages.

>>11813527
I meant qualitatively ~
Also is there a sekrit discord all y’all regulars are in?

>>11813539
>I meant qualitatively ~
No idea what you mean by that.
>Also is there a sekrit discord all y’all regulars are in?
There could be some, but I don't even have an account.

>>11813539
Go away discord tranny.

>>11813662
This.

>>11813539
we don’t allow pedophile tranny groomers in /mg/ or in the greater /sci/ territories. sorry.

What are you guys' thoughts on Dover books?

>>11813688
These two are good https://store.doverpublications.com/048668735x.html & https://store.doverpublications.com/0486663523.html, no idea about the rest.

>>11813688
It really depends on what book you're talking about. For instance I know they sell books like Naive Set Theory and Tennenbaum's Differential Equations (which are good), but I'm certain there's less than stellar stuff on there just because they got the rights to sell it.

>>11813691
I have Mendelson's book and I like it, though it's the only book on topology I've read.

>>11813696
>Tennenbaum's Differential Equations
Is this more theory orientated than algorithmic?

>>11813696
Mendelson was a good warm up before Dugundji. Dugundji was a horrible choice for a first year student, but the lecture notes referenced it, so I decided I will be cool and read it.

>>11813713
Quick rundown on Dugundji?

>>11813704
Algorithmic. You should be able to find it easily to judge for yourself.

>>11813721
I've pretty much forgotten everything, but I remember he didn't hold my hand when he kept barraging me with stuff. The very first chapter was just a recap of basic naïve set theory etc, then some axiomatic set theory to make the Zorn arguments and such later grounded on something. Then he starts with the spaces, it's pretty much the usual stuff, some funny examples like space filling curves. Then he dealt with product spaces, connectivity, compactness, separation and countability axioms, paracompactness, metric spaces etc. Sharp argumentation, probably good when you have at least a bit of maturity. It's old, though, from the sixties or something. There could be a book similarly thorough yet more modern out there, but here's a link https://www.academia.edu/37129457/Dugundji_J._Topology

Is anybody else allergic, btw? There's a constant flow of water through my eyes and it's making it hard to read anything. All blurry blergh

>>11813745
Thanks!
Hope you get your allergies sorted out, too.

I FUCKING HATE MATHS
ALL YOU MATH ELITISTS NEED TO BE SHOT
I JUST WANT TO BE COOL

[math]\int_0 ^1x^xdx=\int_0 ^1 e^{log(x^x)}dx=\int_0 ^1 \sum_{k=0}^\infty \frac{x^klog^k(x)}{k!}dx\approx.7384[/math]

>>11813872
Thanks! Have a nice day or a good night or w/e!

>>11813926
Shoot me first.

good morning mgbros...
did you pass your exams for this term already?
i did, and i'm finally free from the shackles of algebraic topology... at least for some time...
>>11813509
i used to be, now all those IMO gold medalists appeared at my university and I know they'll get better than me in no time
>>11813930
why don't you post the most interesting part
[math]\int_0^1 x^x dx = \sum_{n \geq 1} (-1)^{n+1}n^{-n}[/math]

How do I get better at maths, so I can become a algebraist, anime chad?

>>11813935
>i did, and i'm finally free from the shackles of algebraic topology... at least for some time...
Good job!

>>11813948
Blood sacrifice ad maiorem Diaboli gloriam.

>>11813948
Practice and dedication.

How long should I take to complete Basic Mathematics? It's reasonable to complete within a month studying 8 hours a day every fuckin day?

>>11813968
I mean maybe. Why do you want to though?

>>11813935
>did you pass your exams for this term already?
I did pass my exam for *last semester* last Friday and there is only one University exam remaining in my life.

>>11813926
>>11813930
Stop posting my wife!

>>11813981
What will this last one be?

>>11813976
To start Calculus 1. I will have an exam in two months, Im shit in algebra

Is the interior of the cone of positive operators on a Hilbert space just the cone of strictly positive operators? I don't see an obvious proof that the sets are exactly the same.

>>11813994
The Calc examen or a precalc exam?
Anyways I just think you can learn precalc stuff easier elsewhere but I'm noone to say.

>>11814009
by "strictly positive operator", do you mean [math]\langle Ax, x\rangle > 0[/math] for all x nonzero, or do you mean [math]\langle Ax, x \rangle \geq c ||x||^2[/math] for some c>0?

>>11814015
Actually, has more precalc stuff than calculus 1. But it have some calculus questions like asking for volume of a cube using integral, differential parts, differentiation log, implicit differentiation

>>11814009
are you the faggot that posts hilbert space questions and then doesn't respond to solutions?

>>11814015
>>11814015
Actually, has more precalc stuff than calculus 1. But it have some calculus questions like asking for volume of a cube using integral, differentiation log, implicit differentiation

>>11814029
sorry should have clarified. a positive operator has [math]\langle Ax, x \rangle \geq 0[/math] for nonzero x, strictly positive has [math]\langle Ax, x \rangle > 0[/math].

>>11814036
it's the first question I posted in ages, I'm not even sure who you're referring to

>>11813935
>i did, and i'm finally free from the shackles of algebraic topology... at least for some time...
how did it go

Herr Bildschirmfoto could be interested in this thing I spotted on the daily list:
Finite axiomatizability for profinite groups
https://arxiv.org/pdf/1907.02262.pdf

>>11813993
Some engineering stuff I need to fulfill all the requirements.

The second to last one was a pretty in depth calculus of variation course which was quite fun.

>>11814082
>Some engineering stuff I need to fulfill all the requirements.
Ace that and be free from the shackles of academia!
>The second to last one was a pretty in depth calculus of variation course which was quite fun.
Did you use results by Oiler or Yuler on that course? :^)

>>11814054
thank you, it went well, i got my country's equivalent of A grade
i had only 2 courses this semester so there was a lot of time to study properly

>>11814009
>>11814049
in a finite-dimensional space, the answer is yes: let A be a strictly positive operator, and let [math]S = \{x \in H : ||x||=1\}[/math] denote the unit sphere.
Then S is compact so the map [math]\phi : S \ni x \mapsto \langle Ax, x \rangle [/math] has a minimum c > 0. It follows that [math]\langle Ax, x \rangle \geq c||x||^2[/math] for all [math]x \in H[/math].
So A is in the interior of the cone, because for any operator [math]||B|| < c[/math] we have [math]\langle (A-B)x, x \rangle \geq c||x||^2 - c||x||^2 = 0[/math].
The other inclusion is simple.

In an infinite-dimensional space, the answer is no: let [math](e_n)_{n \geq 1}[/math] be a orthonormal basis, define an operator [math]A[/math] by [math]Ae_n = \frac{1}{n} e_n[/math]. Then A is strictly positive, but does not belong to the interior of the cone of positive operators.

So I just finished doing continuing education at my uni for Senior High school level math. Needed to improve my mark so that I could enroll in the math program. I have the rest of summer with free time. I want to Learn Analysis and Algebra beforehand so I don't get weeded out. Where's a good place to start? Or I guess a list of prerequisites before doing these.

>>11814100
>Did you use results by Oiler or Yuler on that course? :^)
Can you really do a course in a topic about Analysis *without* a result by Leonhart Oiler?
But not in the exam instead of asking my about the EL equation I got question about some meme semi-classical existence theory.

>Ace that and be free from the shackles of academia!
Yeah, that is exactly my plan.

>>11814117
Thanks, indeed it was the infinite-dimensional case that interested me. Is there a simple characterization of the interior of the cone of positive operators?

>>11814202
for me, its leo wheeler and his red eyes white theorem

>>11814202
Just had to check which Euler you were using. You passed my test.

>>11814194
I would probably start by trying to prove all sorts of trigonometric and logarithmic identities.

>>11814227
>Just had to check which Euler you were using.
Well, I am studying in Germany and despite the lecture being in English, the lecturer was German too, so no Wheeler's to be found.

>>11814234
Sehr gut.

>>11814210
An operator A is in the interior of the cone iff [math]\langle Ax, x \rangle \geq c||x||^2[/math] for some c>0, for all [math]x \in H[/math]. Or in other notation, [math]A \geq cI[/math] for some c>0.

>>11812784
WHat level is /mg/ - math at? Are you guys top mathematicians?

>>11814344
I'm Peter Scholze

>>11814344
I'm Shinichi Mochizuki

>>11814344
I'm Andreas Floer.

>>11814344
Mostly undergrads and grad students. I know a group of MIT and Harvard students who post here and the old /Putnam/ General threads because it's a bit more formal than r/math and less taxing than mathoverflow.

>>11814419
and unlike r/math we don't have "blackout for black lives" nonsense here.

>>11814456
Obsessed and rent free.

>>11814538
Dilate.

My math education is roughly at a Bachelor and I it feels like most "groundbreaking" discoveries were already made. This is probably wrong of course, but it feels like that because all important definitions and concepts that I am somewhat aware of are pretty much older than 1970.
I' talking about things like algebraic geometry in the second half of the 20th century, generalized functions, big dualities etc.
So I want to ask: If a mathematician from 1970 travelled to 2020, what would could contemporary mathematicians show him that would blow his mind? Not just "hey we proved this hard problem", they should be deep connections that were discovered in the last 50 years.

>>11814592
To elaborate: A professor I know does research in analysis & pdes, particularly function spaces and inequalities.I domt understand his recent results, but I've at least seen a hint of what kind of stuff he does. It's probably good work, but does it get anywhere? What if when he retires after 30 years, he has only improved this and that inequality and discovered the Harambe function space [math] H_{p,q,n,t}^{s,r,\pi}[/math].

>>11813341
Polya would certainly expect you to solve a shit ton of problems. He just tried to give heuristics. But I'm not sure how effective that is at all

>>11814419
I wish people here dumb animations like the r/math ones

>>11814592
>So I want to ask: If a mathematician from 1970 travelled to 2020, what would could contemporary mathematicians show him that would blow his mind?
IUT

>>11814664
IUT is an exception because it's something a single guy cooked up and we don't even know if it's true. It also (as far ad I know) doesn't tell much about existing mathematics but goes deep into something now.

>>11814592
Geometric group theory
Langlands if you're allowed to take the time to teach him 2000 pages of prerequisite bullshit first
Related, gigantic chunks of representation theory are pretty new, e.g. geometric representation theory, most of the theory of infinite-dimensional Lie representations, D-module stuff, the entire idea of a quantum group...
Moonshine/VOAs. Related, you should probably tell them we think we know all the finite simple groups now. That was a big deal.
90% of the entire field of algebraic combinatorics
The foundationstards trying to do weird type theory shit
Definitely the biggest one I can think of, computing was still very primitive in 1970. There essentially wasn't even an Internet. Most of theoretical computer science didn't exist (I checked out of curiosity, P v. NP wasn't even formally stated until '71), and the things other not-TCS people work on today would have been literally just sci-fi in 1970.

And I'm rattling off stuff I happen to know exists. You unfortunately seem like you're more interested in analytic stuff, which I am as qualified as a poodle to start namedropping on, but I'm sure it's exactly the same over there.

The reason everything you know is old is because a Bachelor's exclusively covers old math. You can't do fancy new stuff until you've already learned the foundational old stuff it's built on.

>>11814680
I was meming about IUT, I agree with you. This might be because problems have become much harder in the last 50 years, but I think we need a completely different approach of mathematics, which transcends sets and categories, because with the current tools we have we are unable to do more than anecdotic results.
The last groundbreaking theorems we've had are all between the 1950's and the 1970's.

>>11813016
>I have added Binaural Frequencies for better Concentration and overall wellbeing
What?

>>11814698
>>11814704
Do you think something as fundamental as a topological space, measure space or field/ring/group could still be discovered?

>>11814809
Yes.

>>11814809
Check out topoï

For me the intuition for quotient structures (let's say quotient groups for example) is that if we have a group G and a subgroup F of G, we want to find H such that F×H=G, and we call H=G/F, correct? (don't worry I know the definition is with equivalence classes, it's just to explain my thought)
Then, if that's the case, do we have similar structures, but instead of a cartesian product, with a semi-direct product?

>>11814861
[math]G \cong G/H \times H[/math] isn't even remotely true.

>>11814875
Can you provide an example please?

>>11814887
[eqn]\mathbb{Z} \not \cong \mathbb{Z}/n\mathbb{Z} \times n\mathbb{Z}[/eqn]

>>11814887
[math]\Sigma_3 \cong \mathbb{Z}/3+mathbb{Z} \rtimes \mathbb{Z}/2\mathbb{Z}= G, H = \mathbb{Z}/3\mathbb{Z}[/math] gives [math]\mathbb{Z}/6\mathbb{Z} \cong G/H \times H[/math] more concretely.

>>11814896
Take a in Z, a=qn+r (unique, Euclidean division).
Then f:a->(r,q) is an isomorphism.

>>11814906
oops Z/3Z in the beginning

18 year old dweeb from 3rd world country here thinking about emigrating to study mathematics at some decent english speaking uni
is there any future in mathematics? will a degree prevent me from starving? its the only subject at school which i truly like along with english so im kinda lost here

>>11814907
It's a SET isomorphism. It's obviously not a group isomorphism, there are elements with finite order on the right side, there's nothing of finite order in (Z,+) (except 0).

>>11814907
>Then f:a->(r,q) is an isomorphism.
it's not

>>11814887
[math]\mathbb Z/4\mathbb Z[/math] versus [math]\mathbb Z/2\mathbb Z \times \mathbb Z/2\mathbb Z[/math]

>>11814861
No. What you describe is what is called a direct factor, but there are other types of normal subgroups.
In general, reconstructing a structure from a substructure and a quotient is very complicated and determining how many ways it can be done is nontrivial. In fact, there is no systematic way to count them (extension problem).

>>11814915
>is there any future in mathematics?
Depends. The future in academic research is pretty bleak unless you are a 200IQ gigabrain who also has excellent social skills.
Getting a decent real-world job with a math degree isn't that hard, especially if you go to grad school first.

>>11814939
>Math degree with CS skills
Is there a better combo?

>>11814973
yes
CS degree

>>11814980
>t.

>>11815009
mathfag cope lmao
go study cohomosexual complexes or whatever while CS chads make 200k.

>>11815102
>while CS chads make 200k.
Math is 300k starting...

>>11815122
delusional mathfag cope
CS gets you way more money, why do you waste your time on useless stuff?

>>11815125
Seething cope brainlet

>>11815126
dilate math tranny

>>11815129
yikes oof reddit

>>11815131
wow ok sweaty

>>11815134
lmao yiff in hell furry

>>11815169
cringe incel virgin

>>11815171
stfu simp

>>11815172
söy nigger kys

Mathchads... I kneel

>>11815270
Rise, my apprentice.

>>11815270
>>11815308
Get away, he's mine!
He'll make a fine addition (heh) to my harem

>>11815316
No, he is mine. I will turn him into a mindless drone eunuch servant.

>>11814592
See the Princeton Companion to Mathematics. A nice overview of the cutting edge of mathematical research from the mid 00s.

>>11815332
Why must we be this divided? (huhu)
I'm sure that integrate him into both our schemes!

[math]\forall z\in\mathbb{C},cos(z)=\frac{e^{iz}+e^{-iz}}{2}\land sin(z)=\frac{e^{iz}-e^{-iz}}{2i}\\ Let\ \psi\in \mathbb{R}\Rightarrow sin^2(\psi)+cos^2(\psi)=\frac{e^{2i\psi}+2+e^{-2i\psi}}{2}+\frac{e^{2i\psi}-2+e^{-2i\psi}}{2}=\frac{2-(-2)}{4}=\frac{4}{4}=1[/math]

>>11815354
[0, 1] see what you did there. Good post.

>>11815392
You seem like a real [math]\int_0^\infty (q*t*2sinx/x ) dx[/math]
You should join my harem too so I can collar you like this catboy

>>11815417
Quick rundown on how [math]2\int_0 ^\infty\frac{sin(x)}{x}dx=\pi[/math]?

>>11814592
anime

>>11815441
This.

>>11815417
Why thank you! However, harems are disjoint subsets of humans, and hence I cannot join yours. My sincere apologies. It is worth noting that harems do not form a partition, as some may be empty, as is the case for members of classical harems.

>>11813935
I have a Galois theory exam on Tuesday, wish me luck

Someone may find this link worth checking out
https://www.lancaster.ac.uk/maths/study/phd/math-sci-studentships-2020/#

>>11815417
damn, that's [math]\frac{\partial u}{\partial t}=\alpha\left(\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2}+\frac{\partial^2u}{\partial z^2} \right) [/math]

>>11815474
Good luck!

>>11815437
because [math] \int_0 ^\infty\frac{sin(x)}{x}dx=\frac{\pi}{2} [/math]
you're welcome my friend

>>11815437
https://en.wikipedia.org/wiki/Dirichlet_integral
>>11815474
keep studying and good luck

>>11815437
You can use the residue theorem or tack on an exponential factor to make it easier to evaluate

>>11812784
So is this true or not?
[math]
\triangledown \cdot \iiint \dfrac{ \bar{r}_0- \bar{r}}{ \left | \bar{r}_0- \bar{r} \right |^3} \, \text{d}x \, \text{d}y \, \text{d}z = 4 \pi
[/math]
r0=(xo,yo,zo)
r=(x,y,z)
nabla is the divergence opreator

Would anyone be interested in seeing more binary pattern analysis like these ones?
I like making alternate numerals and other "visualizations" for number relationships.
1/6

Do you guys find [math]\xi[/math] or [math]\zeta[/math] to write?

>>11815541
I'm an artist, rather than a mathmetician so I look at the relationships between numbers and our natural world instead of crunching them.

2/6

>>11815542
harder to write*

>>11815541
>>11815543

>>11815541
>>11815543
>>11815547

>>11814056
I think that's a very 1920 kind of topic.

I'm not actually that much into logic, just out of necessity. Thanks for thinking of it anyway.

>>11814592
Quantum complexity theory classifications? All answers are probably quite niche.

Some things that bear the name Witten-something?

It might make some happy that neural nets have proven to be relevant.

>>11815541
>>11815543
>>11815550

Here's an alternate visualization for >>11815547

5/6

>>11815541
>>11815543
>>11815547
>>11815554


And here's an alternative visualization of >>11815550

>>11815556
Oops, it looks like I didn't change the symbols from 1 and 14 to 2 and 13 in this diagram. Excuse the mistake, and I'll update it for the next time around.

>>11815553
Better pic.

>>11815554
6/6

Alternate visualization of
>>11815550

>>11815562
look at how the black king is crooked
this was clearly shopped to make her look thinner lmao

>>11815567
Good catch.

>>11815567
It's shopped to make it look like she's winning

>>11815562
Debatable. I found the old man staring in the background the highlight.

I had actually seen that pic before but when I got a bit into chess in the last two weeks for unrelated math reasons, I found that it's actually a pretty exploding space right now.

https://youtu.be/TZmM7NZqBvw

>>11815553
>I'm not actually that much into logic, just out of necessity. Thanks for thinking of it anyway.
It just reminded me of you when I saw profinite groups and axiomatisability at the same time.

>>11815567
Maybe the king is more into the bishop than into his wife.

>Axiom of choice
Is this the biggest meme in mathematics?

>>11815565
>>11815562
>>11815554
>>11815550
>>11815547
>>11815543
>>11815541

Here's a circular version, with the inverse values connected in red

>>11815593
Based and Renpilled.

>>11815544
[math] \zeta[/math] because it's two more letters to type

>>11815542
Zeta but I've been writing them for so many years I'm not challenged by it anymore

>>11815538
This is one of those problems that you can just visualise or literally say what the problem means in your head.

>>11815578
>Maybe the king is more into the bishop than into his wife.
He is black, so he obviously will not stay around for long...

>>11815270
No, DragonScholar, it is I who kneels.

Am I learning math the wrong way by focusing on the intuition instead of formalism? When I read long descriptions using mathematical notation my eyes glaze over, I prefer to just skip to the problems and learn by trial and error in order to intuitively understand a method instead of reading the notation.
I do proofs a similar way, I care only for the concepts and dislike relying on the notation, I tend to describe things in words that are "supposed" to be described via strings of mathematical symbols.

>>11815701
DAYUM

>>11815709
Just say everything is the way you claim up to homotopy and then it's OK.

>>11815709
The ultimate conclusion of about 300 years of debate is that you need both.

>Grading calc 2 exams
>A third of the problems are needlessly tedious integrals that a computer could solve in seconds
Why do professors do this?

>>11815748
usually calc 2 is also taken by engineering/CS students
computing useless shit is good for them

>>11814803
it's sissy cuck hypno

>>11815748
without those the class would not fill up a semester

>>11815688
gonna write that on my exam lmao

>>11815538
this is supposed to be true for all bodies in 3 dimentions

>>11815538
why does this get posted so often

>>11815836
The triple integral causes no fear in you?

>>11815840
chigau, it causes much fear in me

>>11815846
/mg/ is a phoneposter free area.

>>11815849
good thing i'm not one then

>>11812784
Why is calculus so shit bros?

>>11815853
[math] \mathb R [/math] was a mistake.

>>11815853
[math] \mathbb R [/math] was a mistake.

>>11815860
What about [math]\mathbb{N}[/math]?

>>11815836
i still didnt get a reply

>>11815860
commies >>>/out/

>>11815871
I can live with ℕ, I conjecture it's more of less unavoidable.

>>11815586
No, Category Theory
>>11815884
Neither is physically justifiable navel gazing brainlet faggot

>hurr category theory this durr category theory that
Isn't it time you admit your brain is simply too small to understand it ?

best djvu viewer for mac?

>>11815927
sumatra

>>11815884
>infinite sets

Taking Intro to Topology next semester. What should I expect?

>>11815956
>What should I expect?
topology

>y-you’re just too stupid to understand our fake and gay tranny AIDSbrain language games
absolutely debased cope

>>11815938
can't find a download for a mac version

>>11815973
get a real machine and operating system faggot

>>11815973
oops rip nvm https://www.sumatrapdfreader.org/docs/why-only-windows.html

explain free groups to me

>>11815981
I see, it's cpp
https://github.com/sumatrapdfreader/sumatrapdf/tree/master/src

>>11815993
just writing down symbols like a child

>>11815956
A lot of preimages, unions and intersections. Did I mention preimages?

>>11815911
I wonder if the CT obsessed fans or the CT obsessed haters are the worse.

>>11815993
If you think about a very generic two examples, integers and quaternions. in the first case the only way you can turn any element to 0 is by adding its inverse, but in the latter you actually have ij -k = 0. This means that there is a relation turning the difference of ij and k into 0, but if it was just a free group, then you would not have that. You would have no non-trivial relations, that is different from x-x=0, in your group, as is the case for the free (abelian) group of integers. Now, drop the commutativity and you have a free group.

>>11812921
I thought that Herstein had more difficult exercises than Artin?

>>11815956
[math]T_0, T_1, T_2, T_{2\frac{1}{2}}, T_3, T_{3\frac{1}{2}}, T_4, T_5[/math], and [math]T_6[/math] spaces.
On a more serious note: it's usually a course that introduces you to various things that will be needed in future. Nothing exciting, but necessary stuff.

>>11815993
you can build any group by specifying a set of generators and a set of relations the generators satisfy
the free group is the one you get when you specify the generators but mom calls you for dinner and you forget to put any relations

>>11816000
>>11816015
>>11816035
can you guys be less precise and less rigourous please?

>>11816015
>I wonder if the CT obsessed fans or the CT obsessed haters are the worse.
both are needed for the fun

>>11816044
sure
first picture a very large dildo
now imagine shoving it up your ass
that's kind of like what the free group is

>>11816050
WTF I love free groups thank you very much

>>11815993
all elements in a group satisfy the following relations

a(bc) = (ab)c
1*a = a*1 = a
a^-1*a = a*a^-1 = 1

in general they satisfy other relations as well. for example if an element a has order p, then

a^p = 1

holds. or two elements a,b can commute with each other:

a*b = b*a

and so on. a group is free if there are no such relations besides the mandatory group axioms. the only thing that is true is what needs to be true.

>>11815956
https://www.youtube.com/watch?v=wr0of2-8o7Q

>>11816044
Imagine if you have a bunch of letters, and you make a semigroup whose elements are words made up of the letters and the product is concatenation.
You also add in the empty word as a word.
That's a free semigroup/monoid.

Now imagine you add in anti-letters that cancel out the normal letters when you concatenate, and you now have a free group.

>>11816062
>>11816065
thank you very much
what are free groups used in?

>>11816022
could be, i haven't read either of those books in a while and i never went deep on herstein

>>11816060
i hate trannies so much

>>11816082
we all do, buddy
we all do

>>11816076
You can write any group as a quotient of a free group.
You can also do that in a not disgusting way often enough.

>>11815380
>italicized operators

>>11815543
>artist
>those fucking awful mspaint graphics

deslusional

>>11816095
I sort of like his pics

>>11816063
Reminder that she has written "regurality" on the board.

>>11816065
Imagine there's no relations, I wonder if you can.

>>11816076
You can for example take any set and generate a free group using that, so they offer you a passage from sets to groups. Also, if you want to know how a homomorphism works, it is sufficient to check how it maps the generating set, just like it would be the case with vector spaces and their bases. Let's say we have a pair {x, y}. Then all the elements of the free group would be products of different powers of x and y. For simplicity, let's consider x^my^n, and let f be a function from the generating set to a group G. Then we get a homomorphism F from the free group by having F(x^my^n)=f(x)^mf(y)^n, and similarly for all other elements. Sorry, too lazy and tired to latex that.

>>11816082
>>11816085
You do, they do.

>>11816095
he's a performance artist

>>11816076
do you know what a fundamental group of a topological space is ?

>>11816104
thanks
>>11816106
yes

bros ... she's so cute ...

https://www.youtube.com/watch?v=lfTX00pB1L8&list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB&index=3

>>11816120
haha thought you were talking about wildberger like haha who would find him cute like haha wouldn't that be weird watching his lectures and thinking "damn he's hot" like haha get real my friend

>>11816113
the fundamental group of n-times punctured plane is the free group on n generators. it's not exactly "what free groups are used for", but it's an example of how they appear in the wild.

>>11816128

I mean, he is a handsome middle-aged man but I'm gay only for traps

>>11816134
yeah me neither bro haha I'm straight haha

>>11816128
he's good looking, no problem with that
(pic only secondarily related)

>>11816134
>middle-aged
he'd actually quite old.
I'd think he's 70?

Can any of you guys redpill me on constructive mathematics? I would like to hear arguments both in favor and against it.

>>11816142
I have too much respect and admiration for Alain to be attracted to him sorry

Can anyone link me the channel of that one military looking guy that is surprisingly a great math educator?

>>11816179
DoctorBob?
https://www.youtube.com/user/MathDoctorBob

[math]\forall n+1\in\mathbb{N},\zeta(n)\in \mathbb{R}\setminus\mathbb{Q}[/math]

Do we know if this is true yet?

>>11816183
Yeah, thanks bro.

>>11816186
yes

>>11816187
He's based as fuck. The breadth of that guys channel is crazy. 9/10 times when I want to brush up on a topic, he has a video on it.

>>11816188
I don't think that's true

>>11816186
All even integer values of zeta are irrational, there's a closed form for them
AFAIK the only odd one we know for sure is irrational is [math]\zeta(3)[/math] , although there's probably conditional results or half-results about them.

Are mathematics just a big MMORPG quest but weird symbols as dialogue

>>11816142

60 is the new 40

Complete retard here who wants to relearn math, is starting with arithmetic books and then going forward with Lang a good idea? I found a book called Mathematics for Non Mathematicians and it’s made me see math in a new light after I grew up despising math because I was terrible at it.

>>11816231
Nay. It is a bullet hell where you are bombarded with problems and your publications are your spell cards.

>>11816237
Thank you for the image, I had lost it.
And sure, try not to get bored though. Going straight to Lang with some KhanAcademy or something on the side doesn't sound terrible either. Pick up things are you go along

>tfw I'm already 22 mod 24 years old

it's over bros

who needs inifity when we have computers? literally everyone should be learning algebraic calculus right now

Can [math]A\in GL(n,\mathbb{C})[/math] be written as a product of [math]B\in SL(n,\mathbb{C})[/math] and [math]\lambda I_n,\lambda\in\mathbb{R}[/math]?

>>11816259
>tfw 16 in a few years and still haven't made it

>>11816259
If it makes you feel better, I'm 23 mod 24.

>>11816283
>immediately latches onto the ravings of the strongest personality he encounters
very low iq behavior desu

>>11816259
>>11816302
if it makes you feel better, i'm 0 mod 24... bros...

>>11816305

its extremely powerful, I'm a wildberger disciple now shameless

>>11816310

it's like when women expel their last egg, we're worthless now

>>11816317
>>11816310
>>11816259
actual faggots
>>11816312
actual brainlet

>>11816323

that's all me, we're alone in this thread

>>11816323
why the homofobia, anon-kun?

>>11816299
Am I confused or are you forcing A to have real determinant?

>>11816283
Literally everyone should learn a lot of things, though.

Although I don't disagree that "algebraic calculus" is nice.
I'd just say learn formal power series well.

>>11816299
Gee anon, how did you compute the determinant of a scalar times a matrix again?

>>11816299
no. consider R^2 and reflection along some axis

>>11816299
>is every complex matrix a real multiple of a determinant 1 matrix
This obviously can't work, you need lambda to be complex if detA is complex.

>>11816310
18+ website

>>11815598
Thankyou anon for checking them out, I'm glad you find them informative

>>11816095
>>11816105
Think whatever you want, the graphics are purely informational. I make them in free moments when I can, but they don't make me any money so I can't pour time into them like I do painting, animation, etc.
Here's some of my more typical art.

>>11816102
Thankyou anon

>>11816353
>>11816358
I fucked up. It should be [math]\lambda \in \mathbb{C}[/math].

>>11816368
Then yes, every complex number does in fact have an nth root

>Statistics isn't mat-

>>11816389
my stats professor told me it isn't math, if statisticians don't believe they are doing math then neither should we

>>11816389
-hematics.

>>11816398
I think Decision theory is more like physics theory than math. As in, a subject that has to use math and can answer as many meta-question as it likes, but
"what's the best loss function here"
ad absurdum isn't a question that has a mathematical answer.

Given the criterium (resp. a physics theory), of course you can make the remainder of your work look like pure math if you're so inclined.

>>11816422

>>11816426
>>11816422
absolutely MOGGED

The Mathematician is the father, the theorems are the daughter and Chad are Statisticians

>>11816617
The statiscian is the father, the theorems and models are the daughter and Chad is an economist.

>>11816633
The chad is the philosopher.

>>11816617
>>11816633
cope

>>11816617
The mathematician is the father, the theorems are the daughter, and the chad is also the mathematician.
No cuckoldry involved.

>>11816793
ah based? mmm yes based. based!!!!

>>11816793
totally based, Christian family

>>11812784
Any good books on embedded systems, control theory, dynamical systems, or optimization that I should read? I have an undergrad degree in math, and have no interest in formally pursuing graduate studies, but have recently considered working on a project that might unify these ideas, as I've developed an affinity for them.

I have taken a class in optimization before, and used An Introduction to Optimization by Chong and Zak.

Bonus question: Should I try to develop these ideas (for my own benefit) in the language of categories? I have attended conferences on applied category theory and painfully worked through Mac Lane's Categories for the Working Mathematician, as well as various books on a.c.t. by Spivak (David, not Michael) and Fong, though I still struggle with whether or not it is a meme for anything outside of algebraic geometry.

Hope you all are having a good day or night and my rambling was not too retarded to parse. Thanks.

Anyone got a good cubic solver? I'm tryin to do [math]-\lambda^3+\lambda^2(z+0.92)+\lambda(0.11x+0.15y-0.92z-0.0323)+0.0023x-0.0377y+0.0323z [/math] for some research and I kinda wanna die just thinking about it. Or for a shortcut, I'm trying to diagonalize [math]\pmatrix{0.75 && 0.14 &&0.11 \\ 0.68 && 0.17 && 0.15 \\ x && y &&z}[/math]. Tyvm for any help!

>>11817229
Have you asked a CAS?
Maxima, Mathematica, etc.

>>11817263
Don't have nay, however I derived the values I needed (but they aren't great in terms of truth wise per se), so I guess I won't need this (although it wouldn't hurt to have). Thanks anyways!

>>11816283
>who needs inifity when we have computers?
Computers are quite able to deal with problems concerning infinity.

>literally everyone should be learning algebraic calculus right now
Why? What is so bad about Analysis?

>>11816144
The best argument for it is that it forces people to do "better" proofs. I have no doubt that in almost any situation a constructive proof is preferable. It also integrates very well into one possible future of mathematics, where the computer will become an invaluable tool every mathematician needs.

On the other hand it obviously ruins much of existing mathematics. And not just useless mental masturbation but fairly concrete well developed theories, especially in analysis.

algebraic geometry for absolute retards reccs?

>>11817360
I started reading algebraic geometry a problem solving approach yesterday, although I already have some AG pre knowledge from a quite in-depth crypto course.

I think the beginning was quite gentle and we'll motivated, although I obviously can not speak about the rest, maybe have a look.

>>11817267
>although it wouldn't hurt to have
The time to calculate them would be a tenth of the time it would have taken to write out your question...

thread bump limit test

What is [math]SO(q,\mathbb{R})[/math] supposed to be where [math]q[/math] is a quadratic form?

>>11817377
>>11817267
eigenvalues(matrix([0.75,0.14,0.11], [0.68,0.17,0.15], [x,y,z]))
Is what you would do in maxima. It will give you a (very ugly) algebraic expression for the eigenvalues.

Or you enter eigenvalues({{0.75,0.14,0.11}, {0.68,0.17,0.15}, {x,y,z}}) into Wolfram alpha...

>>11817391
The group of invertible linear operators [math]f[/math] such that [math]q \circ f = q[/math]

>>11817397
Wrong

>>11815538
>>11815829
>>11815878
I mean yeah it's clearly fucking true. The divergence of an inverse square law function will be just [math]4\pi\delta(r)[/math] because it goes as the surface area of the sphere. You literally can visualise why this is true in your head.

>>11814592
You're going to have to get a graduate degree to answer that lol. Learn some statistics in the mean time as well as programming they will be indispensable to proving future theorems.

>>11815541
Cool shit anon. Looks like Aztec/Mayan mathematics if they never went extinct.

>>11817460
faggot

>>11817360
Conics and Cubics.

>>11817073
I really like this book
http://read.pudn.com/downloads474/ebook/1987095/Optimal%20State%20Estimation.pdf

Category theory is only "used" in special CS fields and fringe physics communities, it's not in the standard curriculum of any major except maybe some math fields. Don't expect your future colleagues to have heard of it before, unless they studied math.

>Should I try to develop these ideas
My answer to this questions will always be yes.

>>11816144
It allows for models more accurately reflecting computation. I.e. it's model theory includes
https://en.wikipedia.org/wiki/Realizability

>>11816148
Why would they be exclusive

>>11817273
I understand that fundamentally some parts of classical mathematics would have to be left out. But I read somewhere that you can construct most of analysis without the law of excluded middle. Are you familiar with this development?

>>11816367
that's a very nice squirrel, I take my comment back

>>11817715
new thread
>>11817715
new thread
>>11817715
new thread
>>11817715
new thread
>>11817715

>>11817688
>>11817740

>>11817449
Oh wow that expalnation, although not a demostration, was based. Thank you anon. What exactly is δ(r) tho? I havent coursed calc III yet

>>11812831
Lang's undergraduate algebra has very good exercises. I recommend it just for that reason.

>>11815102
>Ph.D. in Math
>any job I want
>$300k starting

>>11816362
hes 24 u moron