/mg/ maths general: dogma edition

[Anonymous No.11030534]

talk maths, formerly >>11019139

[Anonymous No.11030570]

>>11030534
Are Hatcher/Hartshorne books actually good? Ant better alternatives for algebraic topology/geometry, respectively? Ideally something eith motivations, insights, etc

[Anonymous No.11030586]

>>11030570
>Are Hatcher/Hartshorne books actually good?
Why don't you read them and find out?

[Anonymous No.11030595]

>>11030570
>Ant better alternatives for algebraic topology/geometry, respectively?
For me, it's Spanier/Grothendieck.

[Anonymous No.11030601]

>>11030534
thoughts on hyperreals?

[Anonymous No.11030674]

any group theory application besides qm? i've started studying it on my own, going good by my self so far but i lack of motivation besides my curiosity for the subject on itself

[Anonymous No.11030857]

>>11030674
Real-life applications or applications in general? If it's the latter, then group theory pops up here and there in mathematics (above-mentioned algebraic topology, for instance).
If it's the former, then the most fundamental application is theoretical physics (not just QM). Representations of the Poincare group play a central role both in relativity and in quantum field theory.
Chemistry and solid state physics, obviously.
I've seen them applied in optimization theory as well (linear integer programming).

Pretty sure you can just google up "group theory applications" on amazon and look through the contents of some books.

[Anonymous No.11030862]

>>11030857
thanks anon, i appreciate it

[Anonymous No.11030868]

>>11030674
Dude... Group theory has applications almost everywhere in pure maths but I see your point. You make a mistake in that you study something you see as necessary instead of something that you're actually interested in. I suggest pick a topic that you are actually motivated to learn about because it intrinsically interests you, and then learn the prerequisites as they pop up along the way. That way your learning will by much smoother and more motivated.

[Anonymous No.11030882]

>>11030868
actually, anon, i started studying this to get at some point with Galois theory, when i heard about it while at uni and how it proved the impossibility of solving some problems it blew my mind.

Since then i have just take some chunks of theory, once in a while, I understand it, but i can't give proper meaning more over than what is written, I don't know if I explain myself at this point, for giving an example it has been like studying musical theory being deaf, it makes some kind of sense but not much more if you cannot hear a whole composition. But the 'promise' of being able to understand, say, why there's no general formula for solving polynomials of grade greater than 4 it's nuts. I keep wondering and asking myself "why? what get's broken after that? -symmetry, uhhh ok".

I miss the wondering feeling i had when i was introduced to calculus, it was amazing. Somehow i wish i could un-learn that just to be as amazed as then.

[Anonymous No.11031087]

>>11030570
Hatcher is talky bullshit. It has motivations, but layout is poor. Munkres is the gold standard for topo.
Harthshorne is good.

[Anonymous No.11031092]

>>11031087
Munkres is for general topology, not algebraic topology. Agree that Hatcher is quite shite though. Much prefer Bredon/May/von Dieck

[Anonymous No.11031275]

>>11030570
Hatcher is a fucking meme that people only use out of momentum.
Hartshorne is the gold standard.

[Anonymous No.11031296]

>>11031275
what else for algebraic topology then ?

[Anonymous No.11031301]

>>11031296
dude, really? you are studying algebraic topology already and you still ask which books to read?

[Anonymous No.11031314]

>>11031296
Fuchs Fomenko (if you're a normal person), Switzer (mildly autistic) or Strom (the walking embodiment of autism).

[Anonymous No.11031320]

why don't you fucks ever link to the new thread from the previous???

[Anonymous No.11031343]

>>11031301
I'm not that anon, I'm genuinely interested in opinions of people who think Hatcher is shit

[El Arcón No.11031417]

Gold rumors

[Anonymous No.11031420]

>>11030570
https://www.maths.ed.ac.uk/~v1ranick/papers/diecktop.pdf

[Anonymous No.11031425]

>>11031320
>he just leaves the thread open on a tab the entire day instead of opening /sci/ and fining it every now and then
Jesus Christ anon.

[Anonymous No.11031453]

>>11031420
this book actually looks pretty sweet. is it ?

[Anonymous No.11031704]

>>11030570
For algebraic geometry, Shafarevich and Hartshorne or Liu or Mumford-Oda for schemes. If you want to go autistic, then read EGA or the first half of Demazure-Gabriel, but if you are learning, it is preferable to read something with examples and problems

[Anonymous No.11031709]

>>11031314
at first sight Fuchs and Fomenko looks like an absolute gem. has anyone here actually read it ?

[Anonymous No.11031769]

>>11031709
I'm obviously recommending those because I've read them, you absolute autist.

[Anonymous No.11031784]

>>11030882
Galois theory as it's usually done required some facility with fields and finite groups to really get a feel for it.
Galois originally based his work on permutation groups, you can try either reading Liouville's commented version of Galois' letters or Rotman's book that tries to develop the theory in the Galois' way.
Seeing an application of it might help too, Hartshorne's euclidean geometry book uses Galois theory to prove some of the impossibility results you're interested in.
But honestly, just learn more field theory and come back latter. Field theory is nice

[Anonymous No.11031787]

>>11031769
>acting as if it was a rule that people recommending books here actually read them lol

[Anonymous No.11031792]

>>11031769
He might have been looking for opinions of other people.
>you absolute autist
Oh the irony...

[Anonymous No.11031997]

>>11031784
thanks a lot for your sugestion anon

[Anonymous No.11032153]

>>11031709
I read the first few hundred pages of it. I have no interest in being a working algebraic topologist so all the in-depth stuff on spectral sequences and K-theory is beyond what I'm interested in investing time in.
It's a really cool book. Lots of very, very good exercises, which is important.
Pretty stereotypical Russian style (we're gonna blast you with a firehose of cool information, and if you're not smart enough to follow it you can eat shit), which can be hard but is hard for good reasons I think. Fomenko's schizo paintings are also pretty awesome.

[Anonymous No.11032167]

>>11032153
thanks for the answer. what are the paintings supposed to be ? do they actually illustrate concepts from algebraic topology, are they just inspired by algebraic topology, are they just what Fomenko probably sees in his brain when he thinks about algebraic topology, are they completely unrelated ?

[Anonymous No.11032177]

>>11030674
"literally anything"

Most of mechanics is representation theory of the Poincare group. Signal analysis (e.g. Fourier transform) are a product of group representation theory. Whole subjects in combinatorics stem from it. Topological invariants end up being groups and/or rings. Tell me anything and I tell you how it relates to group theory.

[Anonymous No.11032206]

>>11032167
the ones included in the book are very loosely inspired by topological concepts. There's a little index at the back of the book which explains in a line or two what each one is.
You can kind of agree with most of them in hindsight but I doubt most people would be able to actually describe what's being represented before being told.

[Anonymous No.11032354]

Why don't you NIGGERS link this thread to the previous one

[Anonymous No.11032362]

>>11032354
To piss you off. Now piss off.

[Anonymous No.11032369]

>>11032354
Why the racism?

[Anonymous No.11032392]

>>11030570
Hatcher and Hartshorne are on different leagues.

That said, Hatcher isn't nearly as bad as half the people claim itt. I'm not experienced enough in AT to give you a better source, but regardless, 90% of AT courses are based on Hatcher. You can always learn the basic subjects then jump directly to May's concise course, which is more akin to Hartshorne.

As for Hartshorne, there are many better learning alternatives. If you want motivation, this isn't the book for you. The only motivation is experience in classical AG and its drawbacks, and the Weil conjectures. Remember that the motivation for writing the book is out of necessity, since the only other source for modern AG came from a 1.8k page untranslated French text. The exercises are GOAT however.

An approach that is more systematic and modern that covers most of chapters 2-3 of Hartshorne (the meaty bit), is Bosch's Algebraic geometry and commutative algebra - note that it comes with most CA prereqs, and proves them, unlike Hartshorne. It doesn't have many concrete examples as with Hartshorne's 2-3, since the latter leaves them for 4-5, so the unmotivated reading experience will likely be the same.

Liu's book has many more examples, but in my opinion, the exposition is a fucking mess; it's hard to follow where he's going and many times he just has a random theorem/proposition out of nowhere.

Vakil's is great too [character limit reached]

If you've never done classical AG, I think you'd make a stupid mistake jumping straight onto modern AG, akin to an undergrad learning category theory without knowing algebraic topology/geometry. For that, a great and fast to read book is Smith's An Invitation to AG, followed by Shafarevich BAG I (you can start with Shafarevich, but I found that the translation is too rough to understand what he's even speaking about in the chapter 0). I heard good things about Shafarevich BAG II, so if you like it you can continue on with it if you want into schemes.

[Anonymous No.11032398]

>>11031425
you dumbass, i havent come to /sci/ in a week, but the archived thread is still pinned with the thread watcher. I dont want to go into the catalogue to fish for a new fucking link. Thank you for showing us how much of a RETARDED FAGGOT you are

[Anonymous No.11032775]

>>11032398
Take the homophobia somewhere else, "bro."

[Anonymous No.11032825]

I'm so confused.

I get this
[math]
\frac{A_1}{A_2} = (\frac{\frac{1}{2}h_1b}{\frac{1}{2}h_2e}) = (\frac{h_1}{h_2})(\frac{b}{e})
[/math]
and this
[math]
(\frac{b}{e})(\frac{b}{e}) = \frac{b^2}{e^2}
[/math]
but how did he do this:
[math]
(\frac{h_1}{h_2})(\frac{b}{e}) = (\frac{b}{e})(\frac{b}{e})
[/math]

[Anonymous No.11032913]

>>11032825
The numbers a/d = b/e = c/f gives you the number by which you multiply DEF to shrink it down to ABC (saying the triangles are similar is exactly equivalent to saying that it is possible to shrink down all the sides by the same scaling factor). If you want to shrink h2 down to h1, you multiply it by h1/h2. Therefore h1/h2 = a/d = b/e = c/f as well.

[Anonymous No.11032925]

>>11032913
Oh okay. So it's just the ratios being squared. Makes sense.

Thanks

[Anonymous No.11032990]

>>11030534
Can someone explain the picture in the OP? That is the ugliest poster I have ever seen.

[Anonymous No.11033129]

>>11032167

http://chronologia.org/art/

some are translated here
http://chronologia.org/en/math_impressions/images.html

[Anonymous No.11033163]

What's your opinion on these taped lectures on abstract algebra?
https://www.extension.harvard.edu/open-learning-initiative/abstract-algebra

Videos:
http://matterhorn.dce.harvard.edu/engage/ui/index.html#/1999/01/82345

Are there similar free lectures on pure mathematics?

[Anonymous No.11033417]

>>11032990
>Can someone explain the picture in the OP?

[cats No.11033710]

Since I see this asked a lot, tomorrow I'll make a quick overview video clip of what online books are officially available as pdf's (here https://youtu.be/fTBL4TmZNRo).).
The ones I'm aware of are the following:

http://www.cs.man.ac.uk/~hsimmons/zCATS.pdf (Simmons)
https://arxiv.org/pdf/1612.09375.pdf (Leinster)
https://5ht.co/cat.pdf (Awodey)
https://www.logicmatters.net/resources/pdfs/GentleIntro.pdf (Smith)
https://img.4plebs.org/boards/tg/image/1460/05/1460059215690.pdf (Lawvere, Schanuel)
http://pi.math.cornell.edu/~dmehrle/notes/partiii/cattheory_partiii_notes.pdf (Johnstone, Mehrle)
http://www.mathematik.uni-muenchen.de/~pareigis/Vorlesungen/04SS/Cats1.pdf (Pareigis)
https://github.com/hmemcpy/milewski-ctfp-pdf/ (Milewski)
http://math.mit.edu/~dspivak/teaching/sp13/CT4S--static.pdf (Spivak)
http://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf (Barr, Wells)
https://arxiv.org/pdf/0905.3010.pdf (Coecke, Paquette)
http://www.math.jhu.edu/~eriehl/context.pdf (Riehl)
http://katmat.math.uni-bremen.de/acc/acc.pdf (Adamek, Herrlich, Strecker)

Anything I missed out of or something I should definitely point out w.r.t. them etc.?

[Anonymous No.11033832]

>>11033710
GO
STUDY
CUNT

[Anonymous No.11033844]

>>11032775
fag

[Anonymous No.11033898]

>>11033710
For whoever is going to read those - trying to get into category theory is absolutely 100% pointless if you don't already know abstract algebra and a bit of algebraic topology. I often see people buying into hype (CS idiots maybe, idk) and realizing that it is utterly incomprehensible without having background knowledge.

[Anonymous No.11033955]

>>11030534
I need some free maths visualization software, specially for complex analysis and differential equations, any recommendations?

[Anonymous No.11034047]

what do you do when you've asked a simple question to a bird and she hasn't responded to it yet? how long do i wait?

[Anonymous No.11034054]

>>11033898
this
don't become the "undergrad cat theorist"

[Anonymous No.11034057]

>>11034054
holy shit this is based

[Anonymous No.11034139]

Moved to a new uni for postgrad and I don't like the classes on offer. What do I do?
Basically, when I originally researched the uni, I liked some of the classes and I liked the city and so on, so I signed up and put a lot of work to move here.
Now semester is starting and I find out that 100% of the classes I'm interested in are going to be unavailable because all those Profs are leaving for greener pastures.

Do I just suck it up and take whatever is on offer?
I don't think I have much choice in the matter.
First semester is looking pretty boring.
Hopefully later semesters some interesting people show up.

[Anonymous No.11034196]

Does the stochastic differential equation
dX = (1/X) dX + dW
or
dX = (1/X) (dX + dW)
have an analytic solution?

>>11034139
What's the alternative?

[Anonymous No.11034200]

Does the stochastic differential equation
dX = (1/X) dt + dW
or
dX = (1/X) (dt + dW)
have an analytic solution?

>>11034139 #
What's the alternative?

[Anonymous No.11034206]

>>11032990
Looks like a poster near >>11033417 this guys office at uoft

[Anonymous No.11034284]

Lads, I did bad on the test.
BUT THEY THREW THE COMPUTATION OF e^(||x||^2 ) IN FUCKING R^3 AT ME
DO THOSE MADMEN THINK I REMEMBER POLAR COORDINATES IN FUCKING R^3?
DO THEY THINK I'LL DERIVE THAT MESS ON MY OWN?
Anyhow, what I remembered was piss easy, expecting a 7. Which is good, grades are below the floor.

[Anonymous No.11034301]

>>11034284
lmao

[Anonymous No.11034346]

>>11034139
This doesn't make a lot of sense to me.
The courses you'd take as a first year graduate student are not so specific that they're going to be tethered to one prof, or even two. Any of the algebra faculty could teach an intro to AG course just fine and probably most of the rest of the department could too.
Super-specialized topics courses directly related to research may only have one prof capable of running them, but if it's the case that you had specific research interests before applying and you didn't even talk to those profs before you accepted the offer, then you fucked up big time and now you're paying for it.

Regardless, courses aren't that important in postgrad. They're mostly just a requirement to get out of the way. You're expected to be able to learn what you want to learn on your own at this point, and if you can't or don't want to you're going to have serious trouble finishing.
As long as there are good research supervisors still available just stay and do what you want with them.

[Anonymous No.11034513]

>>11034346
One of the classes is Algebraic Topology. There's only 5 people in the research group (excluding Ph.d students) and apparently 3 of them are leaving next semester. I think it is more of a temporary setback. They will get some new people to fill the gap, but Algebraic Topology is a 2 semester course so they better hurry up.

Anyway more worried about not finding an interesting mentor for my thesis.

[Anonymous No.11034517]

>>11034284
>DO THOSE MADMEN THINK I REMEMBER POLAR COORDINATES IN FUCKING R^3?
It's expected in some classes, yes. But that should be clear from the start of the class.
Also thank fuck I don't have to do tedious computations anymore. God worst part of undergrad, that.

[Anonymous No.11034563]

>>11034513
>There's only 5 people in the research group (excluding Ph.d students) and apparently 3 of them are leaving next semester
so what? it doesn't take 5 algebraic topologists to teach a course on algebraic topology, does it

[Anonymous No.11034570]

>>11030570
What do people think of Rotman's Algebraic Topology book?

[Anonymous No.11034698]

>>11034517
It was a catch all real anal test for entering phd programs. Pretty much the only computation in the test.

[Anonymous No.11034809]

>>11031417
Interesting. I'll bring that to /biz/.

[Anonymous No.11034824]

>>11034054
based

[Anonymous No.11035015]

Finished Axler's Precalc text and I really liked it. What's a good follow up?

[Anonymous No.11035401]

>>11035015
Courant's Introduction to Calculus and Analysis vol. 1 is a bit wordy and old-timey but worth a look if you don't like Spivak or Apostol.

[Anonymous No.11035579]

>>11034698
haha anal

[Anonymous No.11035876]

>>11032990
Don't talking badly about Dror please. His graphics are very helpful.
>tfw he called me a retard once

[Anonymous No.11036242]

>>11035876
hello yukariposter
how was your vacation

[Anonymous No.11036321]

Can someone explain how is representation theory and principal bundles stuff related to physics, especially particle physics ? I've heard that electromagnetism (Maxwell equations) is somehow related to U(1)-bundles. I'm expecting an answer which is something like "a particle is a section of a principal bundle" or something like that.

[Anonymous No.11036412]

>>11036321
Lie Groups like U(1) represent transformation matrices (in spacetime) that conserve the symmetries dictated by physical laws.

Fibre bundles are the mathematical physics approach to quantization of fields, in quantum field theory. I don't quite remember the details, but read The Geometry of Physics by Frankel. I believe he covers this.

That's what I remember off the top of my head.

[Anonymous No.11036621]

>>11030534
Question: if someone has come up with a solid proof for a conjecture and he's not part of an academic institution, how should they go about getting those results peer reviewed and or published?

[Anonymous No.11036714]

>>11036621
Do you have qualifications (at least an MSc)? If yes, contact some people working in the field and just send them the PDF. If you're paranoid, you can first upload it to Google Drive or similar to get a timestamp.

If you don't have qualifications, well, you're wrong, and you've got nothing.

[Anonymous No.11036734]

If I pick two values numbers and square them, wouldn't the probability that the sum is smaller than value 'x' be like pic related? 'n' is the cap, and the two values are positive real numbers.

[Anonymous No.11036738]

>>11036734
forgot pic

[Anonymous No.11036741]

>>11036738
oh yeah and then divided by n

[Anonymous No.11036743]

>>11036714
>you need qualifications to publish
Then how do people publish under pseudonyms?
Honest question.
>>11036621
If it's a millenium problem, Collatz, Goldbach, or something on a similar level, the proof is wrong.

[Anonymous No.11036775]

>>11036743
they get their qualifications with the same pseudonym duuhh

[Anonymous No.11036986]

>>11036734
No. Maybe you mis-stated the question?

u^2+v^2<x => √(u^2+v^2)<√x

The condition that the sum of their squares is less than x is equivalent to saying that the point (u,v) falls inside a circle quadrant of radius √x centred on (0,0). If u,v are uniformly distributed over [0,n] with n>=√x, then the probability of this happening is the area of the quadrant (= (1/4)π(√x)^2 = πx/4) divided by the area of the square (= n^2), i.e. πx/4n^2.

If n<√x then it's a bit more complicated, but the probability will always decrease as n increases (unless 2n<x, in which case the circle contains the square and the probability is 1).

[Anonymous No.11037007]

Just attended university two weeks ago. In maths we're not allowed to use calculators at all. I am supposed to do logarithms by hand. How the fuck do I solve shit like that?

[Anonymous No.11037010]

>>11037007
>How the fuck do I solve shit like that?
What have you tried?

[Anonymous No.11037014]

>>11037007
[math]-\frac{\ln3}{2\ln 2}[/math]

[Anonymous No.11037093]

>>11036621
Write it up. If the written version doesn't look like it's written by a crank then email people working in the field asking for feedback. One of the main tests of whether something is crank is whether or not a short summary aimed at experts has an obviously original idea. As long as your manner of discourse is respectful and demonstrates knowledge of the mathematical literature you shouldn't encounter too many issues.

Ultimately though, all you really need to do is post it on the arxiv and submit to a journal. Trash journals don't do real peer-review, but if it's a well-known (at least to experts) conjecture then any respectable subject specific journal (look at impact factors to figure this out) will do a fairly thorough job reviewing. Being outside academia means you don't need to worry too much about min-maxing which journals you submit your work to.

[Anonymous No.11037222]

Im helping friend but havent done this shit in a while pls respond

if f(x) = x +tanx, what is (f^-1)'(x)?

[Anonymous No.11037230]

>>11037222
>if f(x) = x +tanx, what is (f^-1)'(x)?
What have you tried?

[Anonymous No.11037235]

>>11037230
Well, i get using the standard procedures that [math](f^{-1} )'(x)=\frac{1}{2+ \tan ^2 x}[/math], or [math](f^{-1})'(x+\tan x)=\frac{1}{2+\tan^2 x}[/math], but I don't know how I'd solve from there

[Anonymous No.11037239]

>>11037235
Sorry, meant [math](f^{-1})'(x)=\frac{1}{2+\tan^2 (f^{-1}(x))}[/math] on the first one

[Anonymous No.11037272]

>>11036321
As the anon have hinted, internal non-spacetime symmetries [math]G[/math], oftentimes a compact Lie, relate physically equivalent trajectories. If [math]\hat\gamma:[0,1]\rightarrow P[/math] is such a physical trajectory, the class of trajectories [math]\gamma[/math] under the action of the structure group [math]G[/math] describes a path in the base space [math]M[/math] of a [math]G[/math]-principal bundle [math]P\rightarrow M[/math], and conversely every physical path [math]\hat\gamma[/math] can be constructed from (horizontal) lifts of some paths [math]\gamma[/math] on [math]M[/math].
Now, by using a representation [math]G\rightarrow GL_n(V)[/math] of [math]G[/math], we can form the associated vector bundle [math]P\times_G V\rightarrow M[/math] for which the [math]L^2[/math]-sections are the [math]fields[/math] of the particles in question. The [math]G[/math]-equivariant Hilbert spaces they form are identified with the physical space of states, and the connection 1-forms constitute the fields of the gauge bosons. For instance, spinors have an [math]SU(2)[/math] spin rotation symmetry and hence a spinor bundle [math]P\rightarrow M[/math] is a Hermitian [math]SU(2)[/math]-principal bundle, where the associated vector bundle comes equipped with a Clifford structure. Sections [math]\psi: M\rightarrow P[/math] are called spinors, and are models for fermion fields given Rokhlin's theorem is satisfied.
Now the [math]U(1)[/math] group in classical EM comes from the local gauge invariance, which leads to charge conservation via Noether. Given a [math]U(1)[/math]-principal bundle [math]P\rightarrow M[/math], Maxwell's equation arise as monopole solutions to the Abelian Yang-Mills action [math]S[A] = -\frac{1}{4g^2}\int_M F\wedge \ast F[/math] defined on the moduli space of [math]U(1)[/math]-connections [math]A[/math] on [math]P[/math], where [math]F=dA[/math] is the curvature 2-form. Solutions [math]A[/math] describe photon fields with bosonic character.

[Anonymous No.11037284]

>>11037272
thanks, now, what should I read to get into this, given that I understand all of the mathematics that you've used, but I literally don't know what a boson is ?

[Anonymous No.11037285]

>>11037284
Aspects of Symmetry by Coleman.

[Anonymous No.11037301]

What do you call the set of functions of a set on itself? I'm looking for a nice notation of it.

[Anonymous No.11037305]

>>11037301
permutations?

[Anonymous No.11037307]

>>11037222
>>11037230
>>11037235
>>11037239
forget it, the dumb cunt didnt tell me the entire context of the question (find only a value), so in hindsight, finding f^-1 ' is probably impossible with standard functions

[Anonymous No.11037309]

>>11037301
[math]
Aut(S)
[/math]

[Anonymous No.11037311]

>>11037309
End(S) is better. usually endomorphism - any morphism, automorphism - isomorphism.

[Anonymous No.11037316]

>>11037311
probably, although I also assumed that it was a set of bijections (or simply put, permutations as >>11037305 said)

[Anonymous No.11037319]

>>11030534
I'm reading a textbook that says that for mechanical drives, T2 = T1*(θ1/θ2) = N*T1 (i.e., the relationship of the output torque to the input torque) only holds true if there is no acceleration or the gear inertia is negligible. Would someone be able to point me to a resource that says why that is or explain it to me?

[Anonymous No.11037320]

>>11037311
>>11037309
That'd be for the homomorphisms of a set on itself. I'm looking for a notation that includes more general functions.

>>11037305
Permutations are bijections.

[Anonymous No.11037323]

>>11037320
what is a more general function that arbitrary set function from a set to itself? multivalued or what?

[Anonymous No.11037327]

>>11037320
End(US) where U:C->Set is the forgetful functor

[Anonymous No.11037328]

>>11037320
[math]
Hom_S(a,b)
[/math]
if you regard a and b to be say, subsets of S

[Anonymous No.11037343]

>>11037284
If the the physics is of any interest to you, I think a book on electrodynamics might not be all that bad as well. As in, second year electrodynamics, discovering relations between E and B fields and the wonders of pic related etc. There were a good 50+ years before the dA in >>11037272 was tied to U(1).
Trigger warning: There's going to be some explicit coordinates.

The curricula before and after the early 20'th century also looked very different and theoretical physicist 150 years ago didn't know or feared group theory. Bosonic is a bit of a herring in that the counterpart (Fermionic) characterize the physically harder to motivate objects. The bosonic fields tend to be the fields you expect anyway.

This might also give some pointers:
https://en.wikipedia.org/wiki/Particle_physics_and_representation_theory
There's generally some absurdly long Wikipedia articles in this direction, e.g.
https://en.wikipedia.org/wiki/Representation_theory_of_the_Lorentz_group

>>11037327
Inb4 that undergrad cat theorist guy posts his pic

Speaking of which
>>11033710
I looked and ask around and came across a whole lot more open books and lecture notes.
E.g. Smith has put together at least 10 more pdf's, here:
https://www.logicmatters.net/categories/
So I didn't do that literature overview clip just yet, but just now put together an elementary take on some exp-defining limits
https://youtu.be/avc3Iv7Yojs

[Anonymous No.11037355]

>>11037320
You're retarded, aren't you?

[Anonymous No.11037360]

>>11033710
>>11037343
unironically milewski's book shouldn't be read by anyone even remotely smart (as if the "for programmers" part wasn't descriptive enough)

[Anonymous No.11037404]

>>11037360
I'd agree, but I honestly don't know whether I'm not just biased. I get a heart attack when I see texts imply "functors are boxes" and arrows are always algorithms/functions and I added more than one note and caveats on cardinality in Milewski's blog when it was still just on his page, but at least it's one of the view intros that introduce the theory together with an example.


>>11037343
Btw. here's an addon on the second paragraph
https://ncatlab.org/nlab/show/Gruppenpest

[Anonymous No.11037535]

>>11037309
Auti(S)ts

[Anonymous No.11037596]

>>11037319
> 'm reading a textbook that says that for mechanical drives, T2 = T1*(θ1/θ2) = N*T1 (i.e., the relationship of the output torque to the input torque)
=> T1*θ1=T2*θ2, i.e. energy in = energy out
> only holds true if there is no acceleration or the gear inertia is negligible. Would someone be able to point me to a resource that says why that is or explain it to me?
"Energy out = energy in" only holds if the gear itself isn't accumulating energy. If the gears themselves have non-zero inertia and are accelerating, they're accumulating kinetic energy.

Or to put it another way: what if there's nothing attached to the output? There's no output torque so there should be no input torque. If there's no acceleration, that's reasonable enough: you set the gears spinning and they just keep spinning. And if the gears have negligible inertia, accelerating them requires negligible torque. But if the gears themselves have significant inertia and are accelerating, clearly you're going to need torque just for that, above and beyond anything attached to the output.

In short: consider the gears as discrete parts of the system rather than just a magic box which applies T1*θ1=T2*θ2. I.e. a gearbox where the gears have inertia is equivalent to an ideal gearbox but with flywheels attached to the input and output shafts. As well as accelerating what's nominally attached to the output shaft, you also have to accelerate two flywheels.

[Anonymous No.11037633]

>>11030534
Whats up?
EE undergrad here taking first class into complex analysis.
Whats the difference between a function being differentiable and a function being holomorphic? When my prof. Introduced the concept of differentiability he wrote up the whole limit definition and then proved that when Cauchy-Riemann equations a function is holomorphic, so I just thought the concepts were equivalent. Now im doing some problems (written by him) and they have you prove a given function is differentiable but not holomorphic in a given subset of the complex plane

[Anonymous No.11037643]

>>11037633
maybe by differentiability he meant that the function is differentiable as a map R^2 -> R^2. the difference is that differentiable (in this sense) means that jacobian matrix exists, holomorphic means that this matrix represents a multiplication by a complex number.

[Anonymous No.11037653]

>>11037643
He never talked about the jacobian, but i see some sense in what you say

[Anonymous No.11037656]

>>11037633
I have some notes on this here
https://axiomsofchoice.org/holomorphic_function
If you know what a Jacobian is and if you know the matrix representation of complex numbers in the 2x2 real matrices, then the requirement is that the complex function interpreted as a vector field on R^2 has a Jacobian which actually acts as a complex function again

[Anonymous No.11037698]

>>11037633
> Whats the difference between a function being differentiable and a function being holomorphic?
A function is holomorphic at a point if it's complex-differentiable in a neighbourhood of the point. Holomorphic implies differentiable but the converse isn't necessarily true.

[Anonymous No.11037702]

>>11037596
Alright thanks

[Anonymous No.11037705]

>>11037656
Lad, did you just dox yourself?

[Anonymous No.11037707]

Good books for diving into PDEs? I know I'll need them for physics

[Anonymous No.11037711]

>>11037707
youtube mit lecture is really good

[Anonymous No.11037712]

>>11037707
>PDEs for physics
Craig is good.

[Anonymous No.11037714]

>>11037656
Thanks, ill check it out

>>11037698
Ok, so i would just need to plug in the function into the c-r equations and see for what subset of C they hold?
For example if a function is differentiable for every x=y then it would be differentiable but no holomorphic, given that its only diffentiable in that line and not any neighborhood of it?

[Anonymous No.11037716]

>>11036621
>how should they go about getting those results peer reviewed and or published?
Publish on arxiv, send a mail to relevant mathematicians in the field.

Except if by "peer review" you mean jumping through hoops to get it into some dumb journal, then the answer is "don't".

[Anonymous No.11037724]

>>11037711
>>11037712
Desu senpai

[Anonymous No.11037730]

is there any money in being a TeX monkey or does basically everyone do their own thing?

[Anonymous No.11037734]

what are some obscure number theory problems i could make progress on if i have a really powerful GPU?

[Anonymous No.11037762]

>>11037734
Landau's.

[Anonymous No.11037778]

>>11037301
X^X, where X is the set you're considering.
>>11037305
>>11037309
those are bijections
>>11037328
hom implies algebraic structure

[Anonymous No.11037782]

>>11037730
Everyone who's smart enough to have something to TeX is smart enough to figure out how to use it. TeX monkey is not a job and will never be.
>>11032392
Fulton's Algebraic Curves is also a great introductory text. It even proves riemann-roch for curves.

[Anonymous No.11037788]

>>11037782
I didnt like it at all

[Anonymous No.11037789]

>>11037730
You could always look for jobs on publisher's websites and see if they exist

[Anonymous No.11037791]

>>11037778
>hom implies algebraic structure
Sets without algebraic structure aren't worth studying.

[Anonymous No.11037796]

how can i tell if i'm cut out for math degree?

[Anonymous No.11037801]

>>11037791
do you consider topological spaces as sets with algebraic structure ?

[Anonymous No.11037804]

>>11037801
>do you consider topological spaces as sets with algebraic structure ?
We don't consider topological spaces at all.

[Anonymous No.11037814]

If [math]f[/math] is invective and [math]g[/math] is onto, will [math]g\circ f[/math] be onto?

[Anonymous No.11037817]

>>11037814
>If f is invective and g is onto, will g∘f be onto?
What have you tried?

[Anonymous No.11037819]

>>11037817
drew a picture and it seemed likely.

[Anonymous No.11037831]

>>11037814
Nah.
Unless invective isn't a typo for injective, in which case I haven't the foggiest.
>>11037819
You're shit at drawing.

[Anonymous No.11037837]

>>11037814
take g = identity. then this statement gives that injective implies surjective. is this true ?

[Anonymous No.11037845]

Can I, an american, go to grad school in japan? Is japanese acedemic culture as bad as japanese work culture?

[Anonymous No.11037846]

>>11037845
>acedemic
>tfw illiterate

[Wasteman No.11037850]

>>11037796
Start a maths degree

[Anonymous No.11037853]

>>11037272
What do I need to learn to understand all this cool mathematical physics stuff? I'm currently self-studying manifolds from Lee's Introduction to Smooth Manifolds, and I'm assuming that's the right track?
I know all the standard undergrad math material, but have only dug a little into graduate level stuff. I've also been studying some QM (nonrelativistic) from Shankar, and GR from Carroll.

[Anonymous No.11037858]

>>11037853
Lie theory, diffy geometry (i.e. in Tu) plus Clifford algebras and spinors.
I also see the smallest bit of Hodge theory in there.
You could comnprehend that post in a week tops, after you finish Lee.
Plus, obviously, field theory(the physics kind).

[Anonymous No.11037864]

>>11037853
If you already know differential forms and QM expectation values, then you basically just need the topology necessary to like fibre bundles to get the gist of that.

[Anonymous No.11037869]

>>11037819
draw better

[Anonymous No.11037888]

Hello, I am a mathematician working on groundbreaking research at the most prestigious university in Peru.
Now, I am confronted with the most difficult challenge I have yet to come across in my journey and I come to you for help.
If anyone has any idea on how to solve this problem please tell me as this could potentially change the world.

PS. this is NOT homework.

[Anonymous No.11037897]

>>11037888
Absolutely cheeky of you.
Anyhow, the equation should be p=54-q, where p is price, and q is quantitity (I'm calculating from my head since it passes through (10, 44) and (44, 10).
I don't remember the elasticity of demand formula.
For e) we maximize pq=p(54-p)=54p-p^2. We take the differential 54-2p, equal it to zero, and get p=27.
I "think" that f) is (0, 27), but I'm still not looking up that formula.

[Anonymous No.11037931]

>>11037897
Thank you sir.
I will definitely not forget to put your name on my research paper, Anonymous.

[Anonymous No.11038034]

What did I do wrong?

[Anonymous No.11038062]

>>11037888
>peru
sounds about right.

[Anonymous No.11038065]

>>11037643
>>11037656
>>11037698
reminder to ignore all non math major brainlets.

[Anonymous No.11038100]

>>11038034
what have you tried?

[Anonymous No.11038102]

>found a 26-arithmetic progression of prime numbers after searching for only two days

[Anonymous No.11038137]

>>11038100
everything

[Anonymous No.11038141]

>>11038137
What does [math]comp_v u[/math] even stand for?
[math]<v, u>[/math]?

[Anonymous No.11038145]

>>11038137
Also, did you try copyng the brackets from the answer preview? They might actually be different from the less than and more than signs.

[Anonymous No.11038147]

>>11038141
component of a vector in the direction of another, give, vector, so just an inner product with a unit vector.

[Anonymous No.11038151]

>>11038145
>>11038145
Oh, also, in the thingy below they space out before the first digit and after the last, so it should be < -1, -3, -2 >
>>11038147
>)
>>11038147
That's what <u, v> stands for.

[Anonymous No.11038161]

lmao maybe i'm just dumb. im killing myself

[Anonymous No.11038165]

>>11038161
LAD
THE FUCKING SPACING
I'M FUCKING TELLING YOU
ADD A SPACE BEFORE THE FIRST COORDINATE AND AFTER THE LAST ONE

[Anonymous No.11038174]

>>11036242
Terrible. Caught a cold and had to let the bf nurse me back to health. Research also slowed as a result. Still not 100% back.
>>11037707
Brezis.
>>11037845
Japan has a sizeable geometry community with focus on strings/CFT, alg geo, contact geo and geo top. Also if you have a physics slant they also have a massive physical society comparable to the Royal Society.

[Anonymous No.11038179]

>>11038165
too late I only had 5 tries. guess i'll find out tomorrow where I went wrong

[Anonymous No.11038193]

>>11038174
Ahem.
>>11038179
Tough luck.

[Anonymous No.11038197]

>>11037730
you discover half of your mistakes as you tex it up, so no

[Anonymous No.11038202]

>>11038193
In retrospective, the font size is absolutely fucked.

[Anonymous No.11038207]

>>11038102
how long is it

[Anonymous No.11038217]

>told professor an easier way to do cross product in front of class
>he shut me down and said no

i'll go back to not speaking during class
:(

[Anonymous No.11038222]

>>11037707
Evans, of course.

[Anonymous No.11038224]

>>11037804
I guess you (plural) aren't much of a mathematician then.

[Anonymous No.11038228]

>>11037869
kek, great post

[Anonymous No.11038231]

>>11038217
tism

[Anonymous No.11038238]

Books to get into probability? Been recommended pic related, how's it?

[Anonymous No.11038258]

>>11038238
>Been recommended pic related, how's it?
Why don't you read it and find out?

[Anonymous No.11038263]

>>11038224
>mathematician
This is not well-defined.

[Anonymous No.11038266]

so how do I know if i'm doing problems right if there is no solutions manual

[Anonymous No.11038267]

>>11038258
Because it's time consuming and my time is finite. *shrug*

[Anonymous No.11038271]

>>11038266
>so how do I know if i'm doing problems right if there is no solutions manual
Ask /mg/, /sqt/, or stackexchange to check your work.

[Anonymous No.11038277]

>>11038217
if you brought le determinant method then he was right to stop you

[Anonymous No.11038280]

>>11038217
You told him about the Hodge star?

[Anonymous No.11038308]

Considering rolling without slipping, if the tangential force of friction does no work, then what force is doing the work of propelling the car forward?

[Anonymous No.11038314]

>>11038308
Also, if the force of gravity causes no torque on the cylinder, then how can it do the work of giving the cylinder an angular acceleration?

[Anonymous No.11038350]

>>11038266
Chegg it. Do the problem and then check to see if you did it right. In that order.

[Anonymous No.11038378]

>>11038314
I thought about it in the shower; let me know what you guys think of this explanation. In the case of a cylinder rolling down a hill, I considered the free body diagram. I found it odd that the friction force would cause the cylinder to translate more slowly (i.e., have a smaller acceleration along the abscissa) despite the fact that it does no work on the cylinder. Then I reasoned that it must be that the friction force is said to do no work because it is merely transforming some of the work done by gravity on the cylinder from translational energy to rotational energy.

[Anonymous No.11038403]

>>11038378
As I have reasoned, the energy of the forward motion of the car does not come from work done by the friction force, but rather from work done by the torque on the wheels. Therefore, let it be stated that there is no valid analogy to Newton's second law in the domain of energy and work; i.e., no external force is required to do work on a mass for the kinetic energy of the mass to increase.

[Anonymous No.11038490]

Is it possible to ever understand mathematics? I think people who say they 'understand' a section of mathematics are delusional and lying to themselves. They may 'understand' in so far as they can use things like groups and rings, but their understanding will fall flat once faced with a problem that evades capture my conventional means, regarding something like groups and rings.

I don't really know what a group of ring is, I can spit out a definition, sure. I can think of multiple examples of groups and rings, and perhaps I can solve a few tricky problem regarding groups, but there are times when someone can pull out a problem I can't solve, quickly, at least. I can say I know vector calculus by saying I know how to apply the divergence theorem and turn line integrals into double integrals using Green's Theorem, but I really don't understand.

I'm a senior in mathematics going to graduate school. My question is, why do people like to claim they 'understand'? I don't believe they understand a thing, tbqh.

https://math.stackexchange.com/questions/11267/what-are-some-interpretations-of-von-neumanns-quote

[Anonymous No.11038524]

>>11038490
>My question is, why do people like to claim they 'understand'? I don't believe they understand a thing, tbqh.
Vanity. And you're right, they don't.
Especially analysts.
>>11038238
>Books to get into probability?
They all suck.

[Anonymous No.11038599]

>>11038490
>why do people like to claim they 'understand'? I don't believe they understand a thing, tbqh.
You are just redefining "understanding".
A mathematician understands his research as well as an engineer understands the thing he is creating or a physicist whatever theory he is investigating.

"Understanding" doesn't mean "having perfect knowledge", because by that standard nobody ever understood anything. You "understand" mathematics if you see how the pieces fit together.

[Anonymous No.11038671]

>>11030570
Hatcher is good. Hartshorne is gay, but only because AG is gay.

[Anonymous No.11038681]

>>11038490
Wtf. Fucking of course. You think people write textbooks not understanding the material?

[Anonymous No.11038690]

>>11038490
>I can't solve Riemann so I don't know what a prime number is
>I'm just like von neumann
>I am so humble
This is exactly what you sound like, asshole. Fuck all pseuds and especially fuck you. "Math senior" my ass

[Anonymous No.11038697]

>>11038490
Why the fuck wouldn't they? Yeah, ok, math gets harder to understand as you climb the ladder of abstraction, but as a senior you should probably understand at least something. Are you telling us that you don't understand what it means for a sequence to converge? Fuck off

[Anonymous No.11038926]

>>11038174
>Still not 100% back.
Great. Hope you die. I'll be praying for that to happen.

[Anonymous No.11038932]

>>11038102
nice anon
are you in2 computational mathematics? did you try any other similar things?

[Anonymous No.11038955]

>>11037707
Partial Differential Equations in Action

[Anonymous No.11038991]

Let's say I have an ODE with two variables [math]x_1, x_2[/math], I want to find a function [math]F(x_1, x_2)[/math] which is constant along the solutions. Does this concept have a name and is there a general method to do that?
for example if the equation was
[math]x_1' = 1[/math]
[math]x_2' = 2[/math]
then for any real [math]c[/math] there is a solution [math]x_1(t) = t, x_2(t) = 2t + c[/math]
and a function which would be good is [math]F(x_1, x_2) = x_2 - 2x_1[/math]

[Anonymous No.11039054]

>>11038991
It is called a conserved quantity.
Now I am not sure if there is a general recipe for finding one of these.
Some necessary conditions are listed here: https://en.wikipedia.org/wiki/Conserved_quantity

[Anonymous No.11039090]

>>11038991
> then for any real c there is a solution x_1(t) = t, x_2(t) = 2t + c
Without any initial conditions, it's more general than that:
x_1(t)=t+c_1, x_2(t)=2t+c_2
> and a function which would be good is F(x_1, x_2) = x_2 - 2x_1
x_2 - 2x_1 = (c_2-2c_1)
> Does this concept have a name and is there a general method to do that?
This is just converting a pair of parametric equations to an implicit equation, and has nothing to do with ODEs per se. The only general method is to solve one of the equations for the parameter and substitute into the other:
x_1=f_1(t)
x_2=f_2(t)
=> t=f_1^-1(x_1)
=> x_2=f_2(f_1^-1(x_1))
Of course, this assumes that you can find a closed-form solution for one of the equations. If the function isn't bijective, then any inverse will only be partial.

You may be able to find a suitable identity to link equations. E.g. if you have x_1=cos(t), x_2=sin(t) then an implicit form is x_1^2+x_2^2=1. But there's no guarantee such a form exists, and even existence doesn't guarantee that you'll be able to find it.

[Anonymous No.11039114]

>>11038238
Feller

[Anonymous No.11039120]

>>11039054
>>11039090
thanks

[Anonymous No.11039123]

>>11038350
>chegg
anyone who so much as accesses this website should be put under disciplinary investigation. so fucking sick of brainlets cheating. at least if you ask on here or plebbit people will generally give you a hint not a copy-pasted solution. or just go to office hours you dumb fucks

[Anonymous No.11039125]

>>11038681
>>11038690
>>11038697
this is why colleges have mandatory english classes, your reading comprehension is abysmal

[Anonymous No.11039279]

>>11039125
Ok retard

[Anonymous No.11039284]

>>11039125
Perhaps it's what they're reading that's abysmal.

[Anonymous No.11039314]

What is the correct way of writing a function [math] f(x) [/math] interacting with each element of a list [math] y [/math] to produce a list [math] z [/math]?

Would any of these make sense?
1:[math]f(x) \oplus \langle\ H, E, L, L, O\rangle = \langle\ K, I, H, J, F\rangle[/math]
2: [math] f(x) \oplus \textbf{y} = \textbf{z} [/math] when [math] \textbf{y} = [H,E,L,L,O] [/math] and [math] \textbf{Z} = [K,I,H,J,F] [/math]

[Anonymous No.11039321]

>>11039314
If Y is the list write f(Y) for the image of the list (kinda like image sets)
Makes the most sense to me

[Anonymous No.11039384]

>>11030601
fun, but not really useful, the most interesting thing about them is probably the construction

[Anonymous No.11039505]

>>11038926
This. I hope that stupid faggoty tranny dies as well

[Anonymous No.11039507]

>>11038991
>ODE
Try >>>/lgbt/ or >>>/hm/

[Anonymous No.11039538]

Learning algebra, I'm at learning how to complete a square and this just came out of nowhere. Up until this point it's been implied you can't factor out something without it being factored out of all terms, how are they getting away with factoring out just the 4 from the first 2 terms? Am I just being retarded?

[Anonymous No.11039592]

>>11039538
>Am I just being retarded?
yes, quite
4x^2 + 4x is the same as 4(x^2 + x) right?
then surely if you add 1 to both of those they are still the same right?

[Anonymous No.11039662]

>>11039538
It sounds like you don't really get what factoring is. It's just writing some expression as a product of 2 other expressions. You can factor whatever you'd like. Certainly it' s more useful most of the time to factor the whole expression, but sometimes it helps to factor just a part of it.

[Anonymous No.11039721]

>>11038908
Any takers?

[Anonymous No.11039728]

>>11037801
It's monadic over set, so yes.

[Anonymous No.11039735]

>>11039592
I think it's as >>11039662 said and I wasn't getting what factoring is completely. It makes a lot more sense now that I've run through a few problems

[Anonymous No.11039751]

>>11039538
It seems you think factoring is a tactic that depends on completing the square. Actually, completing the square is a strategy that depends on factoring. The first two terms have the same coefficient, so they can be rewritten as shown.

However, in the strategy of completing the square, the constant coefficient is left alone.

If you weren't completing the square, and simply wanted the entire expression inside brackets, then the expression would be 4(x^2+x+1/4), since 1*(4/4)=1.

[Anonymous No.11039790]

>>11030534
> become math and physics major
> expect taking advanced calculus and mathematics classes
> expect exploring the physics of the universe and other cool stuff
> 2 months in
> literally spend my days writing proofs on prime numbers
> have to learn useless stuff like set theory

Is this what I should expect in mathematics or is it just there to weed out brainlets???

[Anonymous No.11039822]

>>11039790
>expect exploring the physics of the universe and other cool stuff
>implying you didn't grow out of this mindset in highschool
>have to learn useless stuff like set theory
Ok retard

[Anonymous No.11039826]

>>11039790
you have to learn how to crawl before you can walk and run.

[Anonymous No.11039916]

Would we have done better if God has given us more dimensions to live in?

[Anonymous No.11039929]

>>11039790
you are one of those brainlets who become category theorists from that "category theorist" pic

[Anonymous No.11039933]

>>11039790
if you go into anal-ysis, yes
>set-theory
looks like someones getting weeded out

[Anonymous No.11039945]

I'm studying abstract algebra. Is it worth picking up some category theory too?

[Anonymous No.11039959]

>>11039945
>>11034054

[Anonymous No.11039966]

>>11039959
I'm not going to study it exclusively, if that's what you're asking. Are you saying I should avoid an entire field because it has a habit of attracting obsessives?

[Anonymous No.11039980]

>>11038217
When you want to make a comment in class, if it's not a genuine question about something you don't understand, stop for a second and think why you want to say it and if someone would give a shit. Most of the time it's just unnecessary flex. "I know how to do cross products differently", well congrats bro.

[Anonymous No.11039984]

>>11039945
category theory is absolutely essential in algebra

[Anonymous No.11039989]

>>11039945
Yes but whatever you do don't become addicted to it. Keep appreciating the beauty of mathematics, remember that abstraction isn't inherently better.

[Anonymous No.11039998]

>>11039916
It probably would have been hard for us to exist without stable gravitational orbits.

[Anonymous No.11040077]

>>11039822
seething.

How can I apply set theory outside of academia? If it's not useless, why aren't we taught its applications?

[Anonymous No.11040092]

>>11039790
"real" math is proof based math. sorry you weren't told this in HS (i wasn't), but it's the truth.

[Anonymous No.11040100]

Convince me that math is not a lie.
For there is one truth, God, and your mathematics is just a human attempt to try and quantify the unquantifiable.

How can anything be proven in math when no prophets were mathematicians?

[Anonymous No.11040108]

>>11040100
what the fuck are you going on about

[Anonymous No.11040113]

>>11040100
http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Heliocentric.html

[Anonymous No.11040126]

>>11040092
Could you elaborate?

[Anonymous No.11040133]

>>11040126
Elaborate what

[Anonymous No.11040144]

>>11040100
Mathematics is necessary for the epistemic accelerationism program, based on topos theory. Giving a geometric basis to our understanding of the world will enhance our mental capabilities by turning our feeble neurochemical processes into hyper-realised manifestations quantum consciousness able to fuse the physical external world with the cybernetic. The supergeometric (or maybe cybergeometric) mind without a brain, the predecessor of a body without organs will be the next step in the evolutionary chain, as we take the wheel and say to Mother Nature "Hey bitch, thanks for the ride, but now it's time to fire up the V808 and accelerate into the rhizomatic xenojungle of double layered, yet singular, existence!" God is not dead, for God isn't even born yet. We will build God, and us mathematicians will be both his prophets and brothers.

[Anonymous No.11040152]

Is there an attempt at building from scratch a new notation for mathematics? My autism really like clean syntax like in programming where everything is standardized. My autism is so high that the current notation in mathematics gives me anxiety.

[Anonymous No.11040157]

>>11040152
You can go pretty far subsisting solely on Bourbaki, but you can't go all the way.

[Anonymous No.11040158]

>>11040152
Idk but I could unironically donate one or both of my kidneys to the person who would make it possible for me to write elder futhark runes using latex. The problem with your wish can be seen by looking at any preceding attempt to make a new universal standard for anything. People just don't follow.

[Anonymous No.11040170]

>>11040133
Elaborate on what makes proof based math "real" math.

[Anonymous No.11040174]

>>11040170
based. replace "real" with "pure".

[Anonymous No.11040243]

>>11040170
anything else is computer math.

[Anonymous No.11040267]

Did you know that the basic dynamic in calculus of integration and differentiation being inverse operations of the same process also corresponds to the nature of change in the most general, as well as our perception of change?

This makes sense when one yeets platonic delusions out of the window and understands that mathematics is built on conceptual metaphors grounded in our experience of the physical world.

[Anonymous No.11040547]

How do I use the principle of recursion to show that there is a unique function [math]f:\mathbb{N}\to \mathbb{R}[/math] satisfying [math]f(0)=2[/math], [math]f(n+1)=(n+2)^{\frac{1}{3}}[/math]

[Anonymous No.11040550]

>>11040547
[math]f(n+1)=\left(f(n)+2\right)^{ \frac{1}{3} }[/math] it should read

[Anonymous No.11040594]

>>11040077
>He expects applications immediately after learning the theory
Go back to watching your Niel DeGrasse Tyson lectures you loser. "Muh universe" lol grow up

[Anonymous No.11040731]

>>11040547
What do you mean by "show"? You've defined the function. By induction, you can trivially prove that it's defined for all N. It's "unique" by definition; any function which gives the same value for every argument is the same function.

BTW, if you're just asking for the limit, it's the root of x^3-x-2=0, which is ∛(1+(√78)/9)+∛(1-(√78)/9) ~= 1.52138. This is independent of f(0), depending only upon the recurrence.

[Anonymous No.11040745]

>>11040731
>What do you mean by "show"?
I wish I knew. the induction is probably the way to go about this

[Anonymous No.11040764]

>>11040745
Well, clearly f(0) is defined and real. If f(n) is defined and real then so are f(n)+2 and (f(n)+2)^(1/3) (every real has one real cube root) and thus so is f(n+1). So by induction it's defined and real for all n∈ℕ.

[Anonymous No.11040769]

>>11040547
>>11040745
Suppose you have 2 functions, f and g, which satisfy this. We want to show that they are the same. Try induction.
What is the base case?
What do you assume for the inductive step?
How do you get from that to the next step?

[Anonymous No.11040778]

>>11040731
You know very little about mathematics, don't you?

[Anonymous No.11040917]

>>11040594
>"muh universe" lol grow up

what did he mean by this ?

[Anonymous No.11041479]

>>11039790
>have to learn useless stuff like set theory
The basics of set theory are absolutely essential to any "advanced" math, as physicists use them.

[Anonymous No.11041484]

>>11040158
>Idk but I could unironically donate one or both of my kidneys to the person who would make it possible for me to write elder futhark runes using latex.
Have you tried Google?
https://ctan.org/pkg/allrunes?lang=en

[Anonymous No.11041500]

>>11041479
>The basics of set theory are absolutely essen-

[Anonymous No.11041527]

>>11041500
Type theory is irrelevant.
Most of modern analysis is built on set theory and until all of that has been rephrased in Type theory set theory is absolutely essential.

[Anonymous No.11041615]

>>11041484
Cheers, m808!

[Anonymous No.11041619]

>filled out everything on my linear algebra midterm
>don't even know or care if I was right but I left no blanks so it's a win for me

[Wasteman No.11041640]

>>11041619
Good shit anon. Linear algebra is pretty important for a lot of different things down the track so it's good to understand it well now.

[Wasteman No.11041644]

>>11041527
There are mathematicians working with type theory instead of set theory at my university. There are people doing research for microsoft, google, etc into type theory. Basically every theorem prover ever is based on type theory. Set theory is a relic of the past.
>Most of modern analysis is built on set theory
And most of it is trivial to rephrase in type theory.

[Anonymous No.11041775]

>>11041644
>There are mathematicians working with type theory instead of set theory at my university. There are people doing research for microsoft, google, etc into type theory. Basically every theorem prover ever is based on type theory.
Sure and?
I am not "against" type theory, it is just a fact that set theory is necessary to understand nearly every single text about modern analysis.

>And most of it is trivial to rephrase in type theory.
"Most" and the 10% that isn't and which would require serious work?
Are you just gonna skip the chapters in your PDE book because you were too autistic to learn the single most important and widely used mathematical theory because some people are doing research on alternatives which might or might not be a somehow viable alternative in a few decades?

You are an undergrad who just happened to overhear some shit from one of his professors, right?

[Anonymous No.11041781]

>>11040764
>clearly f(0) is defined and real
What make you believe so without a shadow of a doubt?

[Anonymous No.11041848]

>>11034284
Just use Fubini's theorem m8

[Anonymous No.11041961]

>>11041644
>And most of it is trivial to rephrase in type theory.
Epic!! This is one of the most deep resulsts we've seen in quite a while.

[Wasteman No.11042011]

>>11041775
>You are an undergrad who just happened to overhear some shit from one of his professors, right?
When I landed in college I took a class on type theory and logical proof and greatly enjoyed it. I had a bit of a knack for doing proofs quickly in my head.

[Anonymous No.11042175]

>>11042011
About the reply I expected.

[Anonymous No.11042196]

>>11042011
>I had a bit of a knack for doing proofs in my head
That pasta isn't even old, but it feels extremely ancient since niggas used it ~5 times a few months ago.

[Anonymous No.11042247]

New precalc book, whaddayathink?

http://aidanwiteck.com/textbook/

[Anonymous No.11042262]

>>11042247
I think the world needs another precalculus textbook just about as badly as it needs another Indian child

[Anonymous No.11042284]

This is theoretical mechanics, but there's no general physics thread.

We know that two Lagrangians which differ by a total time derivative give the same Euler Lagrange equations. The conservation laws are derived by assuming that the original lagrangian and the transformed lagrangian are identical (up to the first order at least). Why should we assume this and not just that their difference is a total time derivative ?

[Anonymous No.11042377]

>>11041500
please prove to me that there exists a part of R2 that intersects every line in exactly two points without using set theory

[Anonymous No.11042401]

>>11042377
>there exists a part of R2 that intersects every line in exactly two points
Is that actually true?

[Anonymous No.11042430]

>>11042401
I can guarantee without even looking it up that if it is true, it's some bullshit transfinite AoC construction.

[Anonymous No.11042439]

>>11042430
Yeah, that’s what I also thought after thinking a minute about it.

[Anonymous No.11042456]

>>11042284
>Why should we assume this and not just that their difference is a total time derivative ?
That's what you actually do, not what you said. Just look at the wikipedia (https://en.wikipedia.org/wiki/Noether%27s_theorem#Field_theory_version)) "This will certainly be true if the Lagrangian density L is left invariant, but it will also be true if the Lagrangian changes by a divergence"

[Anonymous No.11042573]

>>11042284
>This is theoretical mechanics
Use >>>/toy/.

[Anonymous No.11042654]

Can I get a recommendation for a dry introductory analysis / advanced calculus book?
I'm talking about the theorem-proof style with lots of exercises that doesn't have paragraphs of irrelevant text.

[Anonymous No.11042662]

>>11042654
Landau's foundations of analysis?

[Anonymous No.11042684]

>>11042430
yepp, that's why i chose it kek

[Anonymous No.11042688]

Where do I use P or Q in math?

[Anonymous No.11042703]

>>11042654
rudin

[Anonymous No.11042712]

>interested in pure math
>the only linear algebra class is firmly applied
reeeeeee
how do i get a less applied one?

[Anonymous No.11042732]

>>11042688
What do you even mean by that?
Use them as Symbols?

[Anonymous No.11042761]

>>11042732
yes, what do they usually represent

[Anonymous No.11042764]

>>11042761
Pints
Quarts

[Anonymous No.11042765]

>>11042761
Penises
Qtpies

[Anonymous No.11042781]

>>11042761
P and Q can represent sets, namely the projective space and the rational numbers.
They are often used for matrices, eg. in the QR decomposition and P is used as a Projection in linear algebra or even functional analysis.

In analysis the lowercase numbers together very often represent real numbers larger or equal to 1 or infinity such that 1/p+1/q=1.

[Anonymous No.11042794]

>>11042430
>he can recognize stuff that requires AoC at a glance
I feel like this is a sign a person has genuinely reached mathematical maturity.
>>11042654
>dry
I don't think there's any, unfortunately.
>>11042688
Spectral sequences and Dolbeaut cohomology.
Also the >>11042781 1/p+1/q=1 thing.

[Anonymous No.11042889]

>>11041775
>"Most" and the 10% that isn't and which would require serious work?
Can you expand on this 10%? I'm genuinely curious. I don't know much about analysis tbqh.
>You are an undergrad who just happened to overhear some shit from one of his professors, right?
I took a course taught in type theory and wrote a (small) part of a theorem proving math library, but pretty much yes.
I was just baiting because I was bored.

>>11041961
I mean if you want to be pedantic we can construct sets in type theory.

>>11042011
Good meme.

>>11042377
I don't know how to prove this with set theory (I'm not a big fan of choice anyway). Why do you think the type theoretic version fails? You know type theory supports an axiom very similar to choice right?

[Anonymous No.11042895]

>>11041775
>Are you just gonna skip the chapters in your PDE book because you were too autistic to learn the single most important and widely used mathematical theory because some people are doing research on alternatives which might or might not be a somehow viable alternative in a few decades?

You pretend like those subject use anything but [math]V_{\omega_2}[/math]. A space like
[math] \left( ( {mathbb R} \to {mathbb R} ) \to ( {mathbb R} \to {mathbb R} ) \right) \to \left( ( {mathbb R} \to {mathbb R} ) \to ( {mathbb R} \to {mathbb R} ) \right) [/math]
is about the biggest thing you'll encounter in normal mathematics. To argue for set theory is not to argue for being able to use function spaces and set intersection. You can do type theory and still use curly brackets. All such constructions are indeed simple to model in about any foundational theory. Set theory is about stuff barely anyone who obtains a Masters degree in mathematics even hears about (sadly). All set theory you learn (e.g. the algebra of sets, and choice principles) will always be relevant, but that doesn't mean you need set theoretical foundations on the bottom of your setup doing analysis.

[Anonymous No.11042898]

>>11041775
>Are you just gonna skip the chapters in your PDE book because you were too autistic to learn the single most important and widely used mathematical theory because some people are doing research on alternatives which might or might not be a somehow viable alternative in a few decades?

You pretend like those subject use anything but [math] V_{\omega+\omega}. A space like

[math] \left( ( {\mathbb R} \to {\mathbb R} ) \to ( {\mathbb R} \to {\mathbb R} ) \right) \to \left( ( {\mathbb R} \to {\mathbb R} ) \to ( {\mathbb R} \to {\mathbb R} ) \right) [/math]

is about the biggest thing you'll encounter in normal mathematics. To argue for set theory is not to argue for being able to use function spaces and set intersection. You can do type theory and still use curly brackets. All such constructions are indeed simple to model in about any foundational theory. Set theory is about stuff barely anyone who obtains a Masters degree in mathematics even hears about (sadly). All set theory you learn (e.g. the algebra of sets, and choice principles) will always be relevant, but that doesn't mean you need set theoretical foundations on the bottom of your setup doing analysis.

[Anonymous No.11042901]

>sadly
Why?

[Anonymous No.11042902]

>>11042895
>accel tranny
Tell me about how much you love category theory.

[Anonymous No.11042907]

@11042889
>I don't know much about analysis tbqh.
>I don't know how to prove this with set theory (I'm not a big fan of choice anyway).

[Anonymous No.11042912]

>>11042901
>sadly
Because I like model theory.

>>11042902
I like it.
Both category theory and Series Experiment Lain.
The acc crowd is the only non /v/ one that goes for that aestetic. Although Murphy is just dissident left, I don't think he's taking acc more serious than any other academic outbreed he might have read books about.

[Anonymous No.11042916]

>Because I like model theory.
Who cares?

[Anonymous No.11042922]

>>11042907
Are you gonna answer the question laughing anime poster? I'm confident the set theoretic proof works almost word for word in type theory.

[Anonymous No.11042923]

>>11042916
Wat. Yeah well if I judge something as sad, then you already know that the answer won't be very objectivly applicable

[Anonymous No.11042927]

>if I judge something as sad
Who cares?
>the answer won't be objectivly applicable
Says whom?

[Anonymous No.11042938]

>>11042922
>works almost word for word in type theory
[citation needed]

[Anonymous No.11042939]

>>11041500
will large cardinals be easier to understand in type theory

[Anonymous No.11042944]

>>11042922
>I
Mathematicians say "we". Not that someone of your ilk would know.

[Anonymous No.11042957]

>>11030674
Yeah, everywhere actually. A ton of application for CS and related fields, but what really has a ton of applications are semigroups (i.e. groups without identity and inverse) and monoids (groups without inverse). These structures have a ton of applications in math, CS, linguistics, biology, and economics - for instance in analyzing patterns in DNA sequences.

[Anonymous No.11042968]

>>11042889
>Can you expand on this 10%?
Just guessing to be honest, but I do not see how you can easily talk about properties like a Continuous or Lipschitz boundary or even define Integration properly without set theory.

[Anonymous No.11042972]

>>11042684
At least fucking tell us the proof.

[Anonymous No.11042983]

>>11042939
No, I don't think anything that needs an axiom will be easier to understand or work with.

The gain is that you can have a computer check your logic (which is entirely unfeasible with FOL if you're not just checking truth tables) and the proofs about enumberable objects will tend to carry computation algorithms.

No thing (term) is a member of two types (in most systems), so it's quite different than sets. Unions and intersections are explicit constructions by definition.
Equality is much richer than extensional testing, you have infinite groupoids as primitives by definition too, and equality of general objects is proven by a path induction.

It IS a logic with terms as entities given via introduction rules, not a theory IN logic with axiomatic characterizations of objects grabbed from the ether that you try to pin down and see if they "exist".
But you can still adjoin any axioms.

Anyway, I don't actually think type theory will get into the common math curricula in this form, with the fancy general computational (in the best case) equality.
But it doesn't matter so much. For the most part, mathematicans think in terms of types anyway and also don't use set theory in the sense that set theorists do. Foundations are largely invisible. And people will do more computer math as well and functional languages will make talking about primitives such as products and lambda terms normal.

[Anonymous No.11042987]

>>11042898
I think you are missing the point though. How, for example, would you rephrase measure theory in type theory?

>>11042889
>I took a course taught in type theory and wrote a (small) part of a theorem proving math library, but pretty much yes.
Pretty cool, I am currently trying to learn a bit about that too.

[Anonymous No.11043000]

>>11042939
Probably not. Large cardinals are basically an artefact of set theory. They're not something that really arise in type theory.

On the other hand they're not really something we're good at talking about with standard set theory and type theory does have the advantage of being way more natural as a computational system.

>>11042968
Simple things like that translate immediately.
Instead of "for all [math]x[\math] in your domain and all [math] \epsilon \in \mathbb{R}[\math] there exists a [math] \delta \in \mathbb{R}[\math] such that [math] d(x,y) < \epsilon [\math] \implies d(f(x),f(y))< \epsilon" you have the statement "for all [math]x[\math] of your domain and all [math] \epsilon : \mathbb{R}[\math] there exists a [math] \delta : \mathbb{R}[\math] such that [math] d(x,y) < \delta \implies d(f(x),f(y))< \epsilon[\math]".

You can do the same thing for the topological definition of continuity using subtypes instead of subsets, and so on.

[Anonymous No.11043002]

>what's your major, anon?
>math
>omg wow, math is so hard!!
How do you respond?

[Anonymous No.11043006]

>>11043002
I use the classic. “Fuck off and die normie scum! unless your going to fellate me, then I will postpone your meeting with my katana”
Always works

[Anonymous No.11043008]

>>11042939
Probably not. Large cardinals are basically an artefact of set theory. They're not something that really arise in type theory.

On the other hand they're not really something we're good at talking about with standard set theory and type theory does have the advantage of being way more natural as a computational system.

>>11042968
Simple things like that translate immediately.
Instead of "for all [math]x[/math] in your domain and all [math] \epsilon \in \mathbb{R}[/math] there exists a [math] \delta \in \mathbb{R}[/math] such that [math] d(x,y) < \epsilon \implies d(f(x),f(y))< \epsilon [/math]" you have the statement "for all [math]x[/math] of your domain and all [math] \epsilon : \mathbb{R}[/math] there exists a [math] \delta : \mathbb{R}[/math] such that [math] d(x,y) < \delta \implies d(f(x),f(y))< \epsilon[/math]".

You can do the same thing for the topological definition of continuity using subtypes instead of subsets, and so on.

[Anonymous No.11043011]

>>11042987
I'm not sure, but I'm also not sure if it's a big issue. You do have some notions of R and all that.

[Anonymous No.11043014]

>>11043002
>what's your major, anon?
>math
>I always hated/sucked at maths in highschool!!

>what's your major, anon?
>math
>You must be smart!!

>what's your major, anon?
>math
>*changes conversation*

>what's your major, anon?
>math
>*stunned silence*

[Anonymous No.11043019]

>>11043008
>for all x in your domain
What is "your domain"? Certainly it has to be of some type.
And how would you talk about measure theory?
In both cases, is the answer just talk about the type "set"?
In that case, what was the fucking point?

>>11043011
Measure theory is certainly important in analysis, how do you define integration without it?

[Anonymous No.11043022]

>>11043008
>Large cardinals are basically an artefact of set theory.
Not entirely true. Certain theories in combinatorics are only true if a certain large cardinal axiom holds, e.g. laver tables

[Anonymous No.11043039]

>>11042987
>How, for example, would you rephrase measure theory in type theory?
Something like "A measure on a type [math] \alpha [/math] is a function from subtypes of [math] \alpha [/math] (the measurable "sets") to the reals satisfying the measure axioms".

>>11043019
>What is "your domain"? Certainly it has to be of some type.
Whatever the domain of the function you are talking about is. Functions map from one type to another (potentially dependant) type.
>measure theory
see above
>In both cases, is the answer just talk about the type "set"?
No, we can do everything with types and subtypes.

[Anonymous No.11043057]

>>11043019
>What is "your domain"? Certainly it has to be of some type.
pic related for e.g. forall

>In that case, what was the fucking point?
Taking other primitives, being constructive, making computer verifiable statements

https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence

[Anonymous No.11043058]

>>11043039
>Whatever the domain of the function you are talking about is.
But I am talking about "geometric" object, not a function.

>Something like "A measure on a type α is a function from subtypes of α (the measurable "sets") to the reals satisfying the measure axioms".
But in that case you are LITERALLY doing nothing but calling things by different names.

Just replace \in with : and you have rephrased all of mathematics in type theory.
What's the point?

[Anonymous No.11043077]

>>11043057
>https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
The Reals aren't computable, how does this gain you anything in analysis?

>pic related for e.g. forall
I don't think you understand what I meant.
Usually a "domain" in analysis is a subset of the Real numbers, which has certain properties.
How would you describe such a domain in set theory.

[Anonymous No.11043086]

>>11043085
new
>>11043085

[Anonymous No.11043100]

>>11043058
>But I am talking about "geometric" object, not a function
You were asking for the definition of continuous function, no?
>But in that case you are LITERALLY doing nothing but calling things by different names.
Types are fundamentally different in that everything you talk about must have a single* unique type. In set theory [math] x \in X [/math] is a proposition: it can be either true or false. In type theory [math] x: X[/math] is not a proposition: [math]x[/math] doesn't even make sense without a type.
The type theoretic approach has disadvantages (subtypes are less neat than subsets, quotient types require additional axioms) but most of the maths still works and it is much easier for computers to reason about.

*strictly with universes this isn't true but it doesn't really matter


>>11043077
>The Reals aren't computable, how does this gain you anything in analysis?
The reals aren't computable, but facts about them are. Computer systems are no more working with representations of the reals than you are. They use axioms just like you. Computers can already prove "basic" facts of analysis by heuristic graph search.

[Anonymous No.11043120]

>>11043100
>You were asking for the definition of continuous function, no?
No? I was asking about Continuous or Lipschitz boundaries, as they often come up in analysis.

>In type theory x:X is not a proposition
How is that even true?
Can't you talk about the type of an object?
Like saying "the proposition that sqrt 2 : Rat" is false.

>x doesn't even make sense without a type.
Let me rephrase that in set theory. x doesn't make sense if it isn't specified from which set it originates from.

So, again, what is the actual point of trying to rephrase things in type theory, it won't make PDE theory any more computable than it is now.

[Anonymous No.11043191]

>>11042972
i'll write it up tomorrow, but it's a standard transfinite induction, you well order the lines, choose 2 from the first one, then at step α you have only chosen countably many points, so there is one good point on the αth line (you so have to check the lines connecting every intersection of the already chosen ones, but that's also only countably many) and that's basically it

[Anonymous No.11043456]

>>11043002
"Yeah, but I really enjoy it. Besides, most fields are hard. I have a friend doing biochem and even when he explains the simplest things to me I feel like it all goes over my head."

[Anonymous No.11044439]

>>11036743
>If it's a millenium problem, Collatz, Goldbach, or something on a similar level, the proof is wrong.
Who the hell are you to assume that 'the proof is wrong'?