/sci/ - Science & Math

>>11446627
>Open Number Theory paper
>see Robin's Theorem
>Close Number Theory paper

>>11446769
whats a galois group

>>11446769
Oh, its been so long

>>11446778
The group of automorphisms of the field

>>11446849
which field? whas an automorphism?

What is the Latin alphabet?

>>11446869
A field is a mathematical generalization of a flat grassy piece of land. An automorphism is a theoretical framework for transforming one kind of car into another.

>>11446849
No.

What text would be good for getting into complex analysis? I have an EE degree and did some work doing differential modeling of natural system dynamics in Mathlab for a mathematics minor, and would like to get back into it all.

I actually have a whole section in my free book about how other people besides Mochi-kunt had already stolen big parts of my research aside from the part that Mocki-kunt stole. Pic related.

Original section:
>The General Relevance of the Modified Cosmological Model
>https://vixra.org/abs/1712.0598

Eventual Hamiltonian:
>Time Arrow Spinors for the Modified Cosmological Model
>https://vixra.org/abs/1807.0454

>>11446945
When I need to remember something about CA, I go to Orloff's undergrad MIT notes.
>https://math.mit.edu/~jorloff/18.04/notes/index.html

What does Kashiwara mean by a “U set” is a set isomorphic to a set belonging to U. (U is a Grothendieck Universe). He doesn’t define isomorphisms before that. Is Isomorphism = Bijection in this context?

EE undergrad here
if I don't want to annoy the math people on my upcoming senior project to death what should I not do?
I already know being prideful about easy stuff like calculus or the beginner ODE's I was taught is bad along with dick waving in general, but is there anything else that's obviously bad?

Threadly reminder to work with physicists.

>>11446879
y not?

>>11447349
Don't be loose with your reasoning, try being as concrete and clear as possible, understand the common nomenclature, don't use words that have both a technical and colloquial meaning in any other circumstance except technical (you start saying things like "there a manifold reasons for blah" and it'll just get weird), try putting some diagrams and pictures in there people love that shit, don't spend too long on trivial details most mathematicians worth their salt can fill in the gaps just give the broad strokes and give details only where crucial.

Can I get an operator K theory book suggestion? I took a class on algebraic K theory and have some exposure to topological K theory, so it seems silly that I have no operator background.

>>11447337
Likely

What is the best way to develop an intuition for tensor algebra (from a rigorous mathematical perspective)?

>>11447653
Think of tensors as linear functionals defined on product spaces.

>14F05
>14F20
>14F30
>14H57
>14K22
>18GXX
>19AXX
>19E08
>19E15
>19E20

>>11447647
Thank you

Presheaf? I barely even knew her!

just realised that "second quantification" [in Quantum Physics] comes from the fact that the Hilbert space is "second countable"

funny that

>>11447337
Yeah, isomorphism in the category of sets.

>>11447580
Pretty sure your options are Blackaddar, Blackaddar and also Blackaddar.
It's available on his website for free.
https://wolfweb.unr.edu/homepage/bruceb/Book6.pdf

>>11446769
Sauce?

>>11448310
Mhm, I'd like to believe that but I'd guess the expression "second quantification" comes from early 20'th century physicists who where by and large not talking in those particular mathematical terms. Mind you, the formalization even of set theory and quantum field theory is barely 50 years apart.

>>11448310
Pretty sure second quantization originally comes from quantizing a second time.
Nowadays it just means something something Fock spaces.

>>11448365
ye mum focks spaces

>>11448365
Agreed, and even that is historically grown and rather inaccurate term. It's not like they didn't have field theories and cooking up Lagrangian formulations of field's differential equations before going from classical to quantum mechanics.

Moreover, I don't think "second countable" has a German correspondence with "zweit" (i.e. 2nd) in it, which makes >>11448310 even more unlikely

>>11448365
>>11448360
>>11448378
You're probably right, but the textbook I'm reading it from [i'm arguably not at a very advanced level] really makes it look like there's a parallel at least between the two things

Before introducing the actual photons and radiation quantas, it starts by quantifying a simple continuous model (the continous vibrating string), and it makes a good deal of showcasing how you go from a continous model to infinitely countable quantas

It's really, really funny how it makes me think of something completely abstract and unrelated (the isomorphism between l-2 spaces and the space of continuous square-integrable periodic functions)

I guess this was just being over-excited about something I could string together

>It's really, really funny how it makes me think of something completely abstract and unrelated (the isomorphism between l-2 spaces and the space of continuous square-integrable periodic functions)
I think it's hard to find two things in math which are entirely unrelated. That whole function space spiel just as much relates to character theory, Pontryagin duality, Rigged Hilbert spaces and eventually trickle into the position-momentum conundrum you have in quantum mechanics. What you look at then more concretely is this similar transform
https://en.wikipedia.org/wiki/Segal%E2%80%93Bargmann_space

>it starts by quantifying a simple continuous model (the continous vibrating string), and it makes a good deal of showcasing how you go from a continous model to infinitely countable quantas
You mean quantifying or quantizing here? The modes of a compact system are already countable discrete in the classical setting and you might also speak of "quantizing" here, so the language get's a bit fuzzy.
For telling things apart-sake, I'd speak of QM exactly at that point where it involves an algebra of observables (whatever the means of obtaining real measurement values is) that is a non-commutative algebra.

>>11448381
>but the textbook I'm reading
Which book?

I've recently ranted a bit about a history book here (and there's a follow-up video more concretely about the life of B. L. van der Waerden')
https://youtu.be/5zLr7hAnrZY

>>11448409
English isn't my first language, sorry for the confusion, yeah I know the vibrating string already has a "quantification" with eigenmodes and dispersion relation
In a way, I guess this discussion helped me to understand that we are now quantizing "again" by imposing the energies to be "packets of [math]h \nu_k[/math], hence the name 2nd quantification
Thanks!

The book is "Quantum Mechanics" by Cohen, Diu, Laloë

>>11448416
What's in a name? I wouldn't read too much into it, it's historical.

>>11447653
Noncommutative polynomials in your basis vectors obviously

The spatial transformations (for which time isn't relevant) are called Euclidean transformations.
Now how come the homogenous Galilean transformations don't have their own name? (In parallel to how the homogenous Poincare transformations are called Lorentz transformations.)

>>11448314
But wouldn’t the U-set and the set in consideration be in possibly different Set categories, since they might be living in different universes?

>>11448357
The blurb is from OP paper. I put together that picture in this 2013 paper.
>Geometric Cosmology
>https://vixra.org/abs/1301.0032

>>11448757
The category of sets has all sets, anon.

>>11448776
even itself?

>>11448776
Kashiwara doesn’t allow the Category of all Sets. He takes the viewpoint of Grothendieck Universes. But I think I understand the idea now, one assumes that both universes U, V are contained in a bigger universe W, and then the V set and the U set are isomorphic in Set_W.

>>11448794
Categories aren't set. (Just "function" shouldn't mentally be set equal to "set of pairs, and with the function property")

Are there any good books on constructivist / intuitionistic approaches to mathematics? You always see it mentioned in books which have axiomatic approaches to mathematics but I'm having trouble finding actual references for the material. In particular, I'm just having a hard time imagining proving properties about mathematical objects via some set of axioms without ever using proof by contradiction - it seems like some propositions can be made specifically so they can only be proved via a reductio ad absurdum argument with reference to "it contradicts the axioms so it must be false."

https://www.youtube.com/watch?v=x1GnoAbb1ms

https://www.youtube.com/watch?v=wLZLHy0kP2g

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

>>11449057
>>11449074
>>11449092
huh

>>11448998
The only places intuitionistic logic gets used seriously is HoTT and some abstract varieties (hehe) of alg geo and diff geo. And that ultimately boils down to the fact that the internal logic of a topos is inherently intuitionistic.

How is your PhD studies going?

>>11449108
rejected from all the places I applied to and am now in my mother's basement deciding what to do with this useless master's degree

>>11448998
There are number of different approaches. Bishop's book "Foundations of Constructive Analysis" is probably most accessible.

>>11449111
>rejected from all the places I applied to
I can't imagine how this even happens unless you shot way too high and the worst school you applied to was Cornell or something
I came from a trash no-name school, GPA wasn't perfect, no research experience except a single summer, and only 2 good letters and I still got into around half the programs I applied for, and I only applied to R1s.

>>11446769
This is just like saying comparative philology is a complete science with 100% sure morphisms.

>>11449133
I think the worst school I applied to was Colorado State University
I got past the stage where I blamed factors outside my control for failing to get into a PHD program and accepted that I'm just shit and seriously should to consider suicide.

>>11449146
Just get a job and apply again next year. Apply for PhD positions in shit holes in Europe.

>>11449146
why would you do that? you're obviously much much smarter than almost everyone if you've made it this far

>>11449146
because a professional tripfag on /mg/ and publish all your work under that pseudonym

>>11449159
Dude's fucked bro. My adviser told me that programs fucking toss out applications with a master's degree due to the assumption that if the candidate got his Masters they should have finished their PHD, otherwise they're just going to waste what little spots they have for US residence

http://cgi.2chan.net/m/futaba.htm

Has anyone ever been to the math board of 2chan - it's surreal

pic related

>>11449260
It's almost like they're (sub)humans, like us

>>11449159
Too bad my mom lives in a job deadzone and unless you got a degree in nursing, enjoy working at walmart

>>11449184
Examining my undergrad/grad career, part of my success could be attributed professors just letting people pass so they didn't have to be bothered with them. Yeah the school is accredited but it was a tier 2 State school so they have incentive in ensuring a certain percentage pass their class otherwise administration will get on their ass. The other factor was less my ability to solve problems or anything IQ related and more my ability to tenaciously work hard until I passed out. That strat got me more Bs then As in grad school.

That said, I'm at an age where if I haven't made it, I won't make it.

>>11449190
Ah yes, like that one guy who continues to post his proof of the Riemann Hypothesis despite the fact that other anons either ignore him or point out a glaring flaw with his logic. Regardless I don't really know how to do mathematics research because my adviser basically went AWOL and I had to use one of the alternative graduate conditions (doing a fucking report which is basically taking someone else's work and presenting it to 3 professors who don't want to be there) [which also means I don't have a C.V. FUCKING THANKS PROF]

>>11449191
Thanks for the honesty

We have the set [math]S[/math] of maps [math]\mathbb{Z} \rightarrow \mathbb{Z}_{10}[/math] which are bounded below, that is, for every map [math]f[/math] there is some [math]N[/math] such that [math]n<N[/math] implies [math]f(n)=0[/math].
These are represent "formal strings which look like real numbers". So for example, the element [math]f(0)=0[/math], [math]f(n)=9[/math] if [math]n>0[/math] would be written [math]0.99999 \cdots [/math], [math]\pi[/math] would be [math]g(0)=3[/math], [math]g(1)=1[/math], etc for the n-th digit, and the lower bound on [math]f[/math] really just ensures the integer part is finite.
Anyhow, I want to know if you lads know or can come up with any "no go" theorems for group structures on [math]S[/math], in particular showing that we can't define the real numbers as the lexicographically ordered elements of [math]S[/math] and expect reasonable properties.

>>11449111
Jesus fuck. This is why state unis should be outlawed for STEM fields. They aren't qualified to teach jack diddly shit.

>>11449289
>those are actually just the positive strings
Fuck.
Please pretend the formalism somehow works.

>>11446875
I know what a field is. But which one? Auto.. morphism. What is an automorphism?

>>11449191
I dont understand this at all, why does having a masters means that you should have finished a phd? Most phd positions require a masters

>>11449286
>thanks for the honesty
that's completely false in europe, stop believing everything you read on the internet just because it reinforces your current beliefs

>>11449323
Maybe back in 1969, but this is CURRENT YEAR

>>11449260
Good to know they're also full of undergrads falling for the same old bait threads.

https://www.youtube.com/watch?v=xFSZH9HiOak

What do you do when you have no one to talk to about what you love doing?
No one even in my own offices/classes enjoys delving into topics more than they have to for their job or for their grade. To be honest it's starting to get to me how alone it feels to be at my job.

>>11449931
I talk with people like me on /mg/.
I also find different things like good TV shows or video games etc that people like to talk about.

>>11449910
ftfy

>>11449289
For one (I might say something dumb here), I'm not sure if the topology of those "formal strings" carries useful properties. Could you define, say, a distance on it ? Is your space complete with respect to that distance ?
If limits are not possible, what about filters ?

I don't think so, obviously a limit of elements of S converges outside of S

>>11449931
>What do you do when you have no one to talk to about what you love doing?
deal with it, it's part of being mathematician

>>11449931
deal with it. talk about something else.

>>11448998
Go to the respective Wikipedia articles and click the book reference links at the bottom there. You also find approaches in the computability field

Stats question:

If a car tire machine has a 0.15 probability of making a defect tire, and the machine stops after 3 defects, what is the probability of making 5 tires before stopping?

>>11450614
it's actually probability and that's fairly easy.
5 times before stopping = 2 failures in the first 4 tries AND a failure at the 5th

This makes it

[math]p = \left(C^2_4 * (0.85)^2 * (0.15)^2\right)*0.15[/math]

With [math] C^2_4 = \frac{4!}{(4-2)!2}[/math], as any combination of two failures in the first 4 tries is possible
(explicitely)
F F S S
F S S F
F S F S
S S F F
S F F S
S F S F

>>11450638
i meant the probability that it produces at least 5 or more tires before it gets stopped*

>>11450673
I calculated the probability of it to stop at exactly 5 times.
You should adapt it and find the probability to stop at 4 tires, 3 tires. (it can't stop at 2 or 1 ofc)

Then it's 1 minus the sum of those probabilities.

Come on dude, probabilities aren't that hard. Write down a tree, use your intuition, and formalise it.

>>11450614
It's 1 minus the probability of not making 5 tires.

Consider the probabilities of all strings of length 7 or less with exactly 3 defects.

That should be enough, I'm not doing your homework for you.

>>11450695
>>11450698
Okay, thx. i was expecting a poisson random variable but it was easier than i thought, thanks. :)

>>11450701
don't think of a theorem before looking at the problem, just look at the question, use your intuition, formalise it, do some test cases with low/easy numbers, draw potatoes and trees [knowing how to draw potatoes to visualise something is a very important mathematical skill], and then see which theorems, techniques, and tools might be useful

good luck
what's your degree?

>>11450715
I see, and thanks. well, math, first year

I just saw in the library that Arnold Neumaier who keeps lurking on the web of physics and numerical optimization, so you might have come across him online) finally wrote up his thermodynamics-related fundamental physics views, let's say, in a book. Anybody read him (online or otherwise)?

>>11450751
he usually uses this badly cropped ava

>>11450715
Do you know how I calculate the expected value of how many tires it will produce before it gets stopped?

>>11450806
Get a general expression for the probabilities of stopping after N tries. Calculate the sum of [math]N * P_N[/math].
It will most likely be a geometrical series or the derivation terms-by-terms of a geometrical series

Do you change the gumball?

>>11450815
I found P(X=k) where k is the amount of tires produced, but the sum of k*P_k converges to a decimal number, like 0.0016875 which makes no sense...

[math] { \mathcal E }(A^*\, A) = { \mathcal E }(A)^*\, { \mathcal E }(A) + \sigma_A^2 [/math]

[math] { \mathbb E }(A^*\cdot A) = { \mathbb E }(A)^*\cdot { \mathbb E }(A) + \sigma_A^2 [/math]

>>11450894
Yes. And also what is the manga's name.

>>11450962
can probably be written as a fraction

>>11450894
Makes no difference. But I just barely passed stochastics...

>>11450894
monty hall is illuminati propaganda and not real probability theory

>>11451059
I understand my reptilian overlord

*shudders*

󠛡 󠛡
fucking rad man

>>11449941
>>11450371
>>11450388
I absolutely refuse to believe this. The sciences can chat merrily about their subjects, hailed and represented by media. Yet here we are in the basement of Omelas; we are called saints because we do what's necessary, but kept more than an arm's length away.
Do we even talk here? Most of the prattle that goes on are half-baked memes or dick-measuring contests, there is no fun revisits to simpler theorems or questions that aren't just copy-pasted from a book.
I refuse to believe that there does not exist some individual out there who considers math their primary source of entertainment, who also wishes to be social about it.

>>11451422
Okay. Firstly, why do you believe that anyone here is even qualified to talk about anything beyond Highschool mathematics (which is profoundly boring)?
Secondly mathematics tends to be very specialized and hard to communicate to people with little knowledge in your field, or even mathematics in general.
Thirdly, be the change you want to see in the world, try to talk about something interesting and if a miracle happens somebody who at least has a bachelors will give you a non-idiotic reply.

>>11451422
Consider a few factors.

First, some fields of mathematics are so far out there that one expert in mathematics can't talk to another due to how disparate their chosen fields are.

Next, 99% of anyone outside of mathematics (especially if they're a lolmerican) can NOT discuss anything beyond arithmetic. There is no way to bridge the gap between 'you know clopen sets are a thing' and '52 is an even number, right?" in the time it takes to have an average conversation.

Thirdly, Mathematics is hard work. I DON'T want to talk about it with my colleagues or peers because it invariably ends up as either gossip or dick measuring. All I want is to publish my shitty paper that is not going to advance our understanding of mathematics in the slightest, but I gotta to get tenure, and go watch a Monster Truck show.

Fuck ultra autistic fields of math, fuck people who keep bringing up the mandlebot set WITHOUT FUCKING KNOWING WHAT IT IS, and Fuck my colleagues for making my job harder then it needs to be.

>>11451422
i'll be honest with you, at my university i spend a lot of time with a group of at least 20 to 30 people all of whom absolutely adore mathematics and talking about it. they have other interests too but i never have felt the isolation you talk about.
maybe you're just at a shit uni or something? or you need to find the right group? as far as i can tell outside of my group no one gives a shit about math.

>>11449931
>>11451422
I usually talk to my physicist friend who appreciates mathematics. He at least finds it interesting, or pretends to, so it's nice. Also, at conferences you end up meeting people who have similar interests as you, so try making friends and keeping in contact with them, maybe sending an email here and now about a particular topic you think is worth discussing or interesting. Also, the only time I think one can't talk with colleagues is if you work in a department with no one else in your specialization, which is atypical. Usually there is at least one person in your field there.

>>11451025
yancha gal no anjyou-san, the girl on the page posted is only a side character though

>>11451509
Oh I love the Mandelbrot set and I'm bad at math just like that student. One of the first things I ever coded in high school was a fractal renderer.

How much commutative algebra does one need to read FOAG?

>>11449313
Dude? Is this bait?

>>11451792
can you do a*b=b*a?
If so you're good

>>11451792
Sorry I'm ancient, FOAG?

On an unrelated note:
[eqn]\prod_{n=1}^{\infty}\frac{(2n)^{2}}{(2n-1)(2n+1)}=\frac{\pi}{2}[/eqn]
I'm astounded I've never seen this before and I'm trying to play around with it without peeking at proofs, I find product convergences quite fascinating since we don't tend to play with them in any classroom setting.

>>11451178
that looks delicious

>>11451852
Probably Grothendieck's FGA, but anon translated the title for no reason.

>>11451852
Product convergence is just illuminati series convergence, with [math]\ln[/math] involved.
A few complex analysis textbooks go into it. Alfhors has a short but interesting segment on it.

>>11451903
>FGA
Do you mean EGA?
Or is it SGA? Please only use the french titles, this is less confusing.

>>11451987
Is complex analysis really necessary for product-to-series considerations of purely positive numbers? Surely some decomposition exists without...

>>11452108
it is possible, it's not very interesting.
the key argument is that the power series and the infinite product both represent the same analytic function. the zeros in the product correspond to the zeros of the analytic function as well.

it will be very hard for you to prove convergence, absolute convergence, and other dumb shit without analycity and a properly defined log. you'll also miss on some interesting applications (the gamma function, for starters).

>>11452068
>Do you mean EGA?
Or is it SGA?
No.
https://en.wikipedia.org/wiki/Fondements_de_la_G%C3%A9ometrie_Alg%C3%A9brique
Foundations of Algebraic Geometry, FOAG, translated literally.

>want to do math research
>find out about cranks
>afraid to do math research because I don't want to get labeled a crank by the greater math community

>>11451758
Thank you very much.

>>11452205
Why are you afraid to be labeled as a crank? Are you an obnoxious egotistical retard?

>>11452236
>Are you an obnoxious egotistical retard?
I post here... so by definition yes?

>>11451903
Not the Anon, but FOAG is the pretty standard abbreviation for Ravi’s book.

>>11448310
Nope. Second quantization is named so inorder to distinguish it from first quantization. Given a symplectic space [math](\Omega,\omega)[/math], second quantization quantizes fields, namely promotes sections of vector bundles on the [math]\infty[/math]-jet bundle [math]J^\infty \Omega[/math] to operators, while first quantization quantizes coordinates, namely promotes the smooth Poisson algebra [math]C^\infty(\Omega)[/math] to operators.
>second countable
Did you mean separable? Second countable means a countable base for the metric topology, which is weaker than having a countable basis for the linear structure of [math]\mathcal{H}[/math]. Being separable is an assumption that allows us to leverage reflexibility and Riesz representation to study duals and preduals. This extremely useful in QM, since it in particular allows for a faithful infinite-matrix representation on [math]\mathcal{B}(\mathcal{H})[/math] and hence a resolution of unity.
>>11448716
Because it's just [math]SO(3)[/math].
>>11449108
It's looking up. Thanks for asking.

>>11452283
>Because it's just SO(3).
Na, it's also a 6-dim Lie group.

Also, second is still a bad name, imho. The models aren't technically ina succession, or at least you'd not jump along models in such a progression. Should be avoided.

>>11452283
you're late af and your jargon isn't interesting
the other anons explained why I was wrong much better
and I did mean second countable before for me, you were constructing a basis of eigenstates out of something that felt "countinous"
I was wrong as fuck and I realised that after other anons explained it to me and I know what 2nd quantification means now thanks to them

dumb animelord

>>11452303
give the weeb a break, I think nLab stuff should be shilled where it's accessible. I'm not sure jet budles will ever make it into the applied realm, sadly.

>>11452306
the way he types makes me want to punch him in the face through the computer screen

it's probably because I'm a brainlet whose still learning QM and intermediate level maths while he's a big smart guy, but by the lord his jargon is the opposite of what pedagogy should be

>>11452283
>it's just SO(3)
What about speeding up time tho?
>>11452308
You shouldn't get angry at him, you should get angry at yourself, and use that anger to study harder.

>>11452308
my only issue is that he uses the same anime images over and over again as a psudoform of identification

>>11452301
The Lie algebra of the entire Euclidean group is 6D, yes. Without time we don't know what "boosts" are so your question depends on what you mean by "homogeneous". We have [math]{\bf E}(3) \cong \mathbb{R}^3\rtimes O(3)[/math] anyway and if by "homogeneous" you mean orientation preserving then it's [math]SO(3)[/math]; if by homogeneous you mean that [math]\mathbb{R}^3[/math] is a homogeneous space under it then it's the entire group.
>>11452306
>I'm not sure jet budles will ever make it into the applied realm
Putting a contact structure on [math]J^\infty\Omega[/math] lets you define the Lagrangian density as [math]\Omega^n(J^\infty\Omega)[/math], which lets you do quantum/classical field theory as if you're doing quantum/classical mechanics. I don't know what you mean by "applied" but it's the backbone of theoretical physics. Sardanashvily has a few nice articles on this.
>>11452314
>What about speeding up time tho?
In the non-relativistic case "time" is just the parameter on a physical trajectory, and time evolution is just an automorphism [math]\alpha_t[/math] on [math]C^\infty[/math] generated by the Poisson bracket [math]\{H,\cdot\}[/math] with the Hamiltonian. Again, "boosts" don't exist here and speeding up time just scales this parameter. It's not actually part of the isometries of space.

>>11452314
>What about speeding up time tho?
I was talking about the Galileian group (10 dim) without the translations (in 4d). There's no speeding up time, it's quite a plain thing.

>>11452308
We're all faggots, but anybody taking the effort of writing more than 5 sentences in response should stay imho

>>11452316
I do that too, it helps the conversation tbqh and also helps you find your own posts. If I add a random pic to the post, I can easily read up what I missed tomorrow from where I left it.

>>11452319
>Lagrangian density as
as an [math]n[/math]-form in*

>>11452319
Yeah, you skipped the part where I wrote Galilean, but whatever.

I guess by applied I mean that more than 50% of Profs who teach QM know what it is. That's certainly not the case with J^\inftyfoo

>>11452321
>it helps the conversation tbqh and also helps you find your own posts
>helps you find your own posts
>find your own posts

What

>>11452314
I do something like 3-4 hours a day + my internship slavery. Being an engineer trying to get a PhD in interesting physics is painful, but I think I already did something worthwhile if I read (and understood) half of Rudin. Now, just gotta do the other half.

>>11452321
I just don't think vomiting jargon at someone is very polite or encouraging.

>>11451792
Eisenbud or Atiyah-Macdonald should cover enough.
>>11452308
>tfw anon wasn't here for ribbon category autism
Good times.

>>11452321
just use 4chanx

>>11452328
>I just don't think vomiting jargon at someone is very polite or encouraging.
We're all just fishing for people who want to talk about the stuff we find interesting

>>11452332
Might do.

>>11452326
If I come here in 18 hours tomorrow and scroll down, I know that I left for bed around the post that has the Justin Murphy pic. I don't need to read to find my last post.
Good bye.

>>11452321
>If I add a random pic to the post, I can easily read up what I missed tomorrow from where I left it.
High IQ.

>>11452321
>I do that too, it helps the conversation tbqh
it's called avatarfaggotry, and it's against the rules for a reason
although that said there's no point in reporting it because jannies don't give a shit about this board

>>11452336
Yes, I do understand the dilemma of the situation

>>11452324
Maybe you have something else in mind when you meant "Galilean", but I took that to mean the Euclidean group, i.e. the group of isometries of Euclidean space.
If you're thinking about 4D then it's [math]O(4)[/math] or [math]SO(4)[/math], depending on if "homogeneous" means "orientation-preserving" to you. Again, for any [math]n[/math] in general we have [math]{\bf E}(n) \cong \mathbb{R}^n \rtimes O(n)[/math]. On a lattice this is called Bieberbach's theorem, not sure if there's a name for it in the continuum but you can just pass to it from Bieberbach's by the embedding homomorphism of the point group [math]\rho: P_n \hookrightarrow O(n)[/math].

>>11452344
You may or may not have noticed me saying
>>11452301 "Na"
and
>>11452321 "but whatever"
and I've talked down on myself by calling me faggot in your defense etc.
Why don't you let it be?
The Galelaen group is 10 dimensional by all accounts
https://en.wikipedia.org/wiki/Galilean_transformation#Galilean_group
https://en.wikipedia.org/wiki/Representation_theory_of_the_Galilean_group
let's change topic

>if "homogeneous" means "orientation-preserving" to you
You are indeed, I have to agree with the other guy, a bit annoying

>>11452344
>not sure if there's a name for it in the continuum
The classification of Euclidean isometries?
>you can just pass to it from Bieberbach's by the embedding homomorphism of the point group ρ:PnO(n).
IIRC the classic proof went something like this:
>dude
>subtract the image of the 0
>the translation part is now gone
>notice how any point is completely determined by it's distance from n+1 points
>consider an orthonormal basis plus zero
>take the image
>still orthonormal plus zero
>induces an orthogonal map
>coincides on n+1 points with the original, coincides everywhere, and we're done

>>11452402
>notice how any point is completely determined by it's distance from n+1 points
Actually, I think it was n+1 points that didn't fit into a single hyperplane.

>>11452402
>>11452419
Yep, it's pretty standard so it probably just doesn't have a name.
>the classic proof went something like this
That looks like the right idea, which is to identify the classifying space [math]BO(n)[/math] as the real flag Grassmannian [math]\operatorname{Gr}_n(\mathbb{R})[/math]. Each collection of [math]n+1[/math] non-planar points defines an [math]n[/math]-plane up to a frame, hence an element in [math]\operatorname{Gr}_n(\mathbb{R})[/math].
Also any non-symmorphicity (preventing the splitting into a semi-direct product) of the lattice is killed off in the continuum.

>>11452402
>>11452431
Maybe a name for it pops up in a book on the study of well behaved Riemannian manifolds. I know there's names for theorems I can't recall or find right now

>>11452462
>Maybe a name for it pops up in a book on the study of well behaved Riemannian manifolds.
I looked it up in a book about affine geometry.
It's really just "Classification of Euclidean motions".
Not a particularly good book, tho.

>>11452481
Alright. Thanks for looking.

>>11451805
no

>>11446875
In this context though, automorphism stands for the sworn enemies of the deceptimorphisms.

>>11446845
since I last have seen my son

>>11452634
when an automorphism takes in a deceptimorphisms or vice versa, does it produce the identity element?

>>11452431
You are incredibly fucking infuriating, and make everything way more complicated than it should be.

>>11452795
Are you implying that an elementary fact about manifolds is "way more complicated than it should be?"
Wow.

>>11452829
I'm saying he's talking way more obtusely than necessary. Mentioning that [math]BO(n)[/math] is a classifying space or that [math]\text{Gr}_{\text{n}}(\mathbb{R})[/math] is a flag manifold is completely useless, it just makes it all seem complicated when it's not warranted.
Also, please tell me what the fuck "Also any non-symmorphicity (preventing the splitting into a semi-direct product) of the lattice is killed off in the continuum." means, because to me, he's not really saying anything. Probably one of those empty statements mathematicians love which only mean anything to the people who already know what it's being talked about, and sometimes not even then. But please do proceed to interpret it however you please and chastise me for not being able to understand an obtuse statement.

>>11452795
>>11452829
are you two gonna get a divorce?

>>11452890
Did we remind you of some dark times anon?

>>11452911
I'm just waiting for the part where one of you complains about child support to your 8 year old son

you know, the child your child support goes to

>>11452939
It's times like this where I wish I were a roastie, so that I could give you a hug and make you feel better. But alas, I'm just some random retard on the internet.

Here's tonight's little proof for those who want a small brain dessert.
Prove or Disprove:

[eqn]4|(3^{k}+2+(-1)^{k})[/eqn]

>>11452967
high school homework goes in /sqt/

>>11452967
I'm retarded, forgot to mention [math]k\in\mathbb{W}[/math], (that's [math]\mathbb{N}\cup\{0\}[/math] proper for you lazy ones who forgot the difference between whole numbers and natural numbers.)
>>11452982
>divisibility proofs are high school homework durr hurr
Yeah I wish, good meme.

>>11452987
yes, modular arithmetic is taught to high schoolers
if you went to a crappy high school maybe this is your freshman uni homework, either way, /sqt/

>>11452987
The natural numbers already include zero, what are you talking about?

>>11452998
>The natural numbers already include zero

>>11452987
Suppose [math]4 \nmid \left( 3^k+2+(-1)^k\right) [/math]. Then [math]4 \nmid \left( 3^k+2+(-1)^k\right) [/math]. [math] Q.E.D. [/math]

>>11452994
>even and odd, sometimes divisibility-by-three and eleven tricks are played with pre-uni, therefore modular arithmetic is covered
Genius. Shitters like you are why there's no fun in this thread when someone likes writing problems/quizzes.
>>11452998
For computer science babies perhaps, whole and natural should never be considered the same. There is no need to have two names for the exact same thing in mathematics.
>>11453001
You're right, but this proves the wrong thing :-(

>>11453036
Fine. Suppose [math] 4 \textbar \left(3^k+2+(-1)^k\right) [/math]. Then [math] 4 \textbar \left(3^k+2+(-1)^k\right) [/math]. [math] Q.E.D.[/math]

>>11453036
Fine. Suppose [math] 4 | \left(3^k+2+(-1)^k\right) [/math]. Then [math] 4 | \left(3^k+2+(-1)^k\right) [/math]. [math] Q.E.D.[/math]

>>11453089


\bottomtext

>>11452939
Actually, it's his wife's son. I'm the dad. The wife is Yukari.

>>11452967
I mean this is just obvious. What is 3^k mod 4? The sequence goes 1, 3, 9 = 1, then 3 again, so it's 1 when k is even and 3 when k is odd. But 2 + (-1)^k is 3 when k is even and 1 when k is odd. So the sum is always 4 = 0 mod 4, and the number is always divisible by 4.

>>11453116
Thank you for humoring me. Your reward is another, perhaps less obvious challenge.
Prove for all whole numbers n, where D is a natural number that satisfies [math]D*6^{5^{n}}\equiv D(mod 10^{n})[/math] and [math]D=\sum_{k=0}^{n-1}10^{k}d_{k}[/math] and for any index i [math]d_{i}\in\{0,1,2,3,4,5,6,7,8,9\}[/math]

[eqn]2^{n}|\sum_{k=0}^{n-1}2^{k}d_{k}[/eqn]

>>11452487
I don't get the issue, what's wrong with Haag?

Would a kind gentleman be able to provide an answer to this question? Cheers.

>>11453092
This is the contrapositive of what you said before
>>11453142
Excuse me, but what the fuck

>>11452795
>>11452859
very much this

>>11452634
can someone PLEASe tell me what an automorphism is? and can i get a number 9 large extra fries with that? and a math gf?

>>11452859
>>11452795
yeah it's just jargon for the sake of jargon at this point
what he says is not completely unworthy of attention and devoid of mathematical value, it's just not interesting and useful for a conversation

he's like a Rick and Morty character except that he posts anime and actually know the jargon.

>>11454206
an automorphism is a map from one set unto itself that is also an isomorphism.
more precisely, it must be bijective (to each element x there is precisely one and only one f(x) ) and preserves some structure.

This entire fiasco is so depressing to look at I actually took five minutes to make a frog meme about it.

imagine being so btfo that you had to frogpost

>>11454615
pathetic.

>>11454688
>>11454912
t. big boys

>>11454954
t. rick & morty watcher

Question for y’all, I’m utilizing the law of cosines for a proof and I think I’ve discovered that the law of cosines seems to hold not just for triangles but to any 3 points in the plane, even collinear points, where the angle at the middle point is pi and the angles at the other two are 0.

If that’s true that makes my proof significantly simpler to write out, so I’m wondering if anybody else has seen that before, or if I’m wrong and my proof has a mistake?

Also I tried cases where we don’t have 3 unique points, and it seems to hold there too, but with the caveat that the angle between a point and the same point is undefined, however in such a scenario that angle will always be multiplied by 0 in the formula.

Isn't it kinda ironic that founder of classical mechanics also found a method of generating fractals?

>>11455034
yes, you are correct
the formula just states the obvious when the triangle is degenerate

>>11455101
Right okay thank you

>>11453621
no

>>11455052
>ironic
I see no irony in that at all

Any complex analysis anons on here?

I looked at this website: http://tetration.org/Tetration/index.html
I'm interested in doing what he did for a function, only the function is meromorphic with a residue at its (Attractive)fixed point. The function also has poles past the 1st derivative, also at its fixed point, unfortunately. Any resources for finding a formula, a way I could solve schroeder's equation?

>>11453591
Haag theorem states that interacting QFT is not unitarily equivalent to (products of) single-particle QFT. This means that most of scattering calculations done by physicists is wrong and there's no such thing as "the interacting picture".
Given sufficient regularity of the interacting potential, however, Goldstone's theorem in fact proves the asymptotic free-ness of interacting states in the [math]|t|\rightarrow\infty[/math] limit. So the best we can do is to add the axiom of asymptotic completeness to the Sterater-Wightman axioms of QFT and compute [math]S[/math]-matrix elements with far future/past single-particle scattering states. We can't probe intermediate scattering events unless someone develops an interacting/many-body QFT ab initio.

>>11454615
great image, accurate, well done
t. left frog

Do you guys think studying math as an accelerator to understanding all other difficult science-y/tech stuff is a meme? Of course doing a lot of math beats nothing/jerking off/watching anime but you're probably better off learning CS/coding/engineering/etc. directly instead of hoping that advanced math study will pay off somehow (in my estimation)
Thoughts?

I would like to get a copy of Neukirch ANT, and Geometric Modular Forms and Elliptic Curves. But each of the books cost >100 dllrs. ANT is for some reason not available for MyCopy.
Does anyone know if there are cheap international editions for either of those books? For World Scientific books in general? Otherwise I think I’ll end up printing them.

I learn faster from actual textbooks because it’s easier to flip pages, before frugal Anons start giving me shit.

havent heard back about my grad school application, how fucked am i?

>>11456103
Did you only apply to one place?

>>11456128
Yes... I didnt have time or money to apply to others. Considering suicide currently.

>>11456158
What tier uni did you apply to? Roughly speaking, what was your GPA and all that stuff? You can always try next year, with better fit Unis.

>>11449108
Quite nicely. Producing new shit every week. My supervisor told me to slow down, but I must X C L R 8

>>11456251
He's as fucked as that Master's kid above if he keeps playing the try again next year game. Graduate programs hunt for hot young blood, not 2 year old rotten sausages

>>11452998
There is no void, no vacuum, no nothing in nature, and hence no 0 in the natural numbers.

>>11455854
I thought the issue is with the word "Haag"

>>11454536
So basically, the Galois group of a field is all the possible ways it could be mapped onto itself?

>>11456380
No, you oversimplified it too much. What the other anon said is the bare minimum (and I still think it should have more stuff) of the definition of an automorphism.

>>11456380
Basically, you have a field k. Then you extend it to K and consider the automorphisms of K that fix k.

What's the real difference between [math]\mathbb{C}[/math] and [math]\mathbb{R}^{2}[/math]?.They are isomorphic as vector spaces over [math]\mathbb{R}[/math] and also as metric (topological) spaces with their usual metrics. I assume the difference is in their algebraic structures, but how does that translate into analysis on [math]\mathbb{C}[/math] being different than analysis on [math]\mathbb{R}^{2}[/math]?

I hope this is not a stupid question.

>>11456568
R^2 is not a field.

>>11456568
C is algebraically closed whereas R^2 has no algebraic properties.
C with the multiplication and addition has the structure of a field.

If you go into more analytic details, you will find that this field structure lets you derive useful properties. Theory of complex integration and analytic fonctions shows examples of that.

>>11456568
The difference is that [math]\mathbb C[/math] has a multiplication and that the definition of [math]\mathbb C[/math]-derivative takes into account that extra structure.
Simply put, analysis on [math]\mathbb C[/math] is a very special case of analysis on [math]\mathbb R^2[/math]. Holomorphic functions are differentiable functions on [math]\mathbb R^2[/math] in the usual sense but whose differential is a similitude at every point (this translates to the Cauchy-Riemann equations).
In the language of complex numbers, it corresponds to saying that it is a differentiable function whose derivative is the multiplication by a complex number.

Is there a book/website that list all the commonly known convergent series and sequence?

>>11456423
k

>>11456781
Wikipedia lmao

For real though, I doubt that can really be done since some are just generalisations of others so it would be arbitrary which special cases to include

>>11456413
So I looked up some examples on Wikipedia and basically, the Galois Group of a Field extension is all the ways the extension could be changed without changing its effects. For example instead extending the rationals by square root of 2, we could also use negative square root of 2 without a difference. Therefore we have two automorphisms, this one and the identity one.
Yes?

>>11446627
What are some good books for babbies first topology on metric spaces class?

>>11456823
maybe the one by Thomson and Bruckner - Elementary Real Analysis
it's analysis but it covers basic topology of the real line and metric spaces
I think it's by far the most gentle introduction to the subject out there

>>11456813
>without changing its effects.
Can you elaborate on this?
> Therefore we have two automorphisms
We can also extend it with 3 times squareroot of 2, and that doesn’t mean we have three distinct automorphisms.
Read the first few pages of Chapter 15 in dummit and foote. It’s very readable without much background.

>>11456832
Thanks, will check it out!

I'm looking for the paper in which Jean Leray first introduced the notion of a sheaf. Can someone help me out?

>>11457096
nevermind. I've found it. It is L’anneau d’homologie d’une représentation. But does anyone know where I can get it? It's not on libgen

>>11456367
It's just a joke lad

starting to lack motivation to read more "theoretical" stuff on the side/on the week-end now I started the job.

>>11456158
Some European/Asian universities have no application fee for their PhD programs. Try them again next year hun.
>>11456568
Having a complex structure gets you a Hodge decomposition [math]\Omega^n_\text{dR} = \bigoplus_{n = p+q}\Omega^{p,q}_\text{Dol}[/math] of the forms. You can't do this in [math]\mathbb{R}^2[/math] because you can have harmonic maps that don't satisfy Cauchy-Riemann.

>>11456158
Are you seriously considering doing a non-funded PhD?
Because I wouldn't recommend it at all. It's insane that unis should require you to pay for them for helping them with their work. PhDs students are already overexploited even when paid.

>>11457271
>Having a complex structure gets you a Hodge decomposition [...] of the forms. You can't do this in R2 because you can have harmonic maps that don't satisfy Cauchy-Riemann.

That's not what he asked at all, and mention of harmonic maps that don't satisfy Cauchy-Rieman is completely gratuitous and I'm not sure if that's very useful even if we consider the big abstract picture. If we are really doing autistic shit, the Quaternion field also allows analytic functions that aren't harmonic.

>>11457271
>Some European/Asian universities have no application fee for their PhD programs. Try them again next year hun.
>hun
What a kind way to tell someone to neck themselves.

>>11457291
are you that surprised Yukarifag has the tism

>>11457286
The quaternions aren't a two-dimensional real vector space, tho.

>>11457254
What's the payoff, why is it funny

>>11456158
>>11457271
There are decent American unis that don't have application fees either. Carnegie Mellon has no fee at all, and Ohio State charges $5. I'm sure there are others but those were the only two I remember from when I applied.
Realistically though, "I didn't have money" is not an excuse. Fees are like $80-90 a pop for most schools including mailing the GRE scores. It raises serious questions about whether or not you were actually even serious about getting a PhD if in all the months leading up to your applications you couldn't be bothered to find $200 or $300 somewhere so you're not risking an entire year of your academic life on a coinflip.

>>11457302
That answer is already more connected to the OG question and helps him with what actually matters, R2 is a 2-d vector space, so is C, but the complex also form a field. It so appears that this property leads to making Hodge decompositions or something very smart ; that's very interesting, but not really what the dude asked and it's not presented in a way that makes it look interesting, it's just a math word salad.

Yukarifag didn't have enough professors yelling at him that his shit is off-topic at best and completely hides the point at worst. Knowing how to present your results should be the basic skill taught to PhD students.

>>11457317
who the fuck does PhDs for free
do you enjoy being exploited, or are you just afraid of having to provide results?

>>11457286
>That's not what he asked at all,
That's exactly what he asked, hun. To quote, "... how does that translate into analysis on [math]\mathbb{C}[/math] being different than analysis on [math]\mathbb{R}^2[/math]?"
>big abstract picture
Now THIS is not what he ask for at all.
>>11457316
There's no payoff.

>>11457323
>who the fuck does PhDs for free
why do you keep interjecting this into a discussion about application fees?
please go google what the word FEE means

>>11457337
Any funding that provides a monthly stipend for living/expenses usually also covers the application/tuition fees.

>>11457346
Not really, tuition yes but usually not the application fees.
Granted, application fees are much lower than tuition fees, but they can add up.

>>11457346
>Any funding that provides a monthly stipend for living/expenses usually also covers the application/tuition fees.
Yeah. How do you get from that to "anyone paying a fee is not doing a funded PhD"?
You still have to pay the fucking fee upfront you retard. Yes, the one school you accept an offer from will give you a fee rebate as part of your package, but all the schools you turn down will not, and all the ones that reject you won't either.

>>11457120
pwease guys. does no one know?

>>11457360
I don't understand why you would pay for even seeing phDs proposals at all. Go on sites like findaphd.com and directly email the professors without setting up an account on the goddamn uni website.

>>11457356
what does it cost to send an email to the teacher with the proposed subject

>>11457368
>>11457374
you're making an awful lot of noise for somebody with literally no idea how PhD applications work

>>11457384
>see PhD proposal on university website, industrial webpage, or whatever
>send email to person responsible with attached CV and cover letter
>wait for them to respond and start exchanging from there
it's like finding a job or an internship. I'm going to pay them for giving me work.

>>11457390
i'm not*

>>11457390
>>11457394
You're free to not pay them, but you won't get any work either.
The fact that you think you can get into a program without filing an application makes it blatantly obvious you've never applied anywhere, which is why I'm simply suggesting you shut the fuck up about PhD applications.

>>11457384
maybe I'm just being bamboozled by your statement and not understanding. Are you talking about GRE and other annex stuff?

>>11457397
i was always told to send emails directly, or even better, use the networking you've done through internships to hook you up with a proposal. have you never done internships? The one I'm doing right now has basically a thesis at the end if I want and things go well.

>>11457407
>i was always told to send emails directly,
you do. But this does not somehow replace having to file an application.
The very best-case outcome you will get from an email is
>I think you'd be a good student. Apply and I'll mention to the committee that I'm interested in you
Even if the prof offers to support you out of their own funding (like often happens in e.g. Canada) and your acceptance is guaranteed, you STILL have to go through a formal application. You simply will not get in anywhere without one.

>>11457424
I once did the automatic admission thing and got an automated email saying that weren't looking for student at this time. The next day, I got another email from the prof supervising the thing I was trying to get info about correcting the automated system.

>>11457364
This isn't incredibly helpful but it's included in volume 1 of his selected papers published by Springer. Unfortunately that's not on libgen either but it might be easier to find through your library system than the standalone original paper, and if worst comes to worst and you really need it you can buy a copy without having to sell a kidney.

>>11457120
>>11457364
https://gallica.bnf.fr/ark:/12148/bpt6k31740/f1366.image

>>11457271
>>11457286
>>11457317
It's for MSc. My gpa is only 2.7, so an American or Euro uni is out of the question. Plus I wouldnt be able to afford moving there as I am in Canada. The only hope I have is my 4 years research experience, TA experience, and community outreach volunteer experience (involving math). How did I get this you may ask? The prof I volunteered with got me the RA and TA jobs without ever asking for a transcript. The profs I met from all that never suspected I had a low GPA as I excelled at research and teaching. They were bamboozled when I asked for reference letters and finally asked for my transcript. I got A's in classes and C's in others, depending on how interested I was. Also had tough home life and worked to pay for my semesters before those jobs. I'll commit suicide if I can't keep doing math.

>>11457528
You should use this teaching experience to create a network. This is how most people get PhDs anyways.

>>11457528
>Plus I wouldnt be able to afford moving there as I am in Canada.
This is actually not a bad thing for you. The Canadian system is less formal than the US one; if you talk to a professor and make a good impression (which you seem pretty capable of doing) then they have a lot more ability to pull strings to get you in compared to an American school, most of which are extremely bureaucratic. Your profs that like you may be able to put in a word for you with their friends as well.
Although I don't see how you "wouldn't be able to afford" immigrating to the US from Canada. That costs basically nothing. Besides, if you end up having a year off, you might as well work so you're not a broke-ass nigga next application season.

>>11447403
That's only true if you're dealing with a Galois extension.

>>11457534
>You should use this teaching experience to create a network
Can you please elaborate?

>>11457607
Whomever you were working with/for could write you a letter of recommendation.

>>11457528
Anyways, if you think so fee is shitty, think of the non-English-natives students who have to coof up £250 for IELTS or equivalent despite being entirely proficient.

>>11457622
>think of the non-English-natives students who have to coof up £250 for IELTS or equivalent despite being entirely proficient.
What about the non-English-natives students who coof up the £250 for IELTS but who's speaking skills are so shit that it was obvious that they cheated?

>>11457612
Why do you insist on talking when you have no idea how anything works and can't even read?
Letters of recommendation are mandatory. If he applied, it's a certainty he already has letters, and the post you responded to explicitly said so.

>>11457631
>Letters of recommendation are mandatory
Not in my country at all.

>>11457637
Then you're in some third world shithole with no standards, which explains why you have no clue how Western PhD programs work, but please don't act like your shithole experiences apply to the first world.

>>11457648
>please don't act like your shithole experiences apply to the first world.
Expect for China and India
Graduate Programs welcome the Massive influx of students from China and India who are going to a western university for the status symbol!

>>11457495
thanks, anon!

Can someone tell me what this shorthand notation means, the highlighted square brackets with h inside?
h := x -a
and T(x,a) is the Taylor Polynomial.

So somehow the square brackets [h, ... ,h] transform into the coefficients of the sum of partial derivatives?!

>>11457862
It's tensor contraction. [math]f^{(n)} = \partial_{i_1}\dots\partial_{i_n}f[/math] is a rank-[math]n[/math] tensor and it is contracted with [math][h,\dots,h] = h_{i_1}\dots h_{i_n}[/math]

What is tropical geometry and what are some cool open problems in the field?

>>11457862
so wie du mit nem Vector das inner Produkt mit h nehmen kannst, und mit einer Matrix hinten und vorne h drauf klatschen kannst um nen Skalar zu bekommen, so machst du es in beliebige Ordnung weiter.
Siehe
https://en.wikipedia.org/wiki/Taylor_series#Taylor_series_in_several_variables

>>11457885
oh right, I have not been exposed to tensors yet but I understand the concept somewhat, thanks

>Real Analysis
>Differential Equations

Is noncommutative probability theory fun to learn?

Bros, why do i still struggle with undergrad physics when i pick a book even though i have a math degree and have studied grad level math

>>11459070
Which book?

>>11459070
because physics is not only math

>>11459070
>>*Gets finished proving the Riesz–Fischer theorem*
>Hi, I need you to calculate this series of measure conversion in Ch 1 of this textbook
>>No Problem bro, that's trivial wor-
>Also I need an approximate result that used scientific notation that is only 5 decimals long
>>What rules of approximation are we using? In fact, can I get a section 0 of the textbook that has a lot of questions just on approximation and scientific notation so that I can get a feel fo-
>I'M NOT GOING TO TELL YOU THAT ASSHOLE YOU'RE THE STUDENT
>>*Proceeds to start working on Chapter 1 of an Undergraduate Physics Textbook*
>>*keeps getting the answer wrong, either due to a the solution manual arbitrary deciding to drop scientific notations for answers of a specific length, a sudden unexplained change of length of the approximation, or an approximation error but never told what an acceptable radius of error is or (and this is a good one) the solution manual failing to use it's own rules of approximation*
>WHATS WRONG MATHEMATICIAN?
>I THOUGHT MATHEMATICIANS WERE SUPPOSED TO BE SMART
STOP IT
I'VE ONLY EVER HAD TO GIVE EXACT ANSWERS!!!!

>>11459070
Because it wants you to develop intuition. At the research level it's what allowed e.g. Bethe/Laughlin/Feynman to guess the ground states and correlations of non-exactly solvable many-body quantum theories without knowing what a Yangian/Virasoro/Hodge algebra is, let along their representation theory. This is also what gives my previous advisor the gall to shit on mathematicians constantly.
https://arxiv.org/abs/hep-th/9310158v1
Sure, proving that a certain ansatz is valid is nice, but knowing where to look in the first place takes a whole different training.

Is it true? Also how much do you use your mobile? Is there any effect of it on you?

stats question:

How do i interpret:
"How big must a random sample from a normal distribution be so that the sample's expectation X with the probability > 90% is less than a standard distribution away from the distribution's expectation mean?"

>>11459564
in other words:
There is a normal distribution (it has some expected value E and some standard deviation sigma)
you have n independent random variables x1,...xn, each has this normal distribution
how big n should be, in order to have the inequality
[math]P(|\frac{x_1+...+x_n}{n} - E| < \sigma) > 0.9[/math]
?

>>11459579
I'm completely lost and I feel stupid.

folks I have a test in 4 hours and I'm just solving the practice exam and I'm stuck in a problem, save my dumbass please

Let [math]I[/math] be an ideal in [math]S = K[x_1,...,x_n][/math] and [math]f \in S[/math] any polynomial.I want to show that [math](I:f^\infty) = (I:f^m) [/math] iff [math](I:f^m) = (I:f^{m+1})[/math]. One implication is trivial, but how do I get that [math](I:f^m) = (I:f^{m+1}) \Rightarrow (I:f^\infty) = (I:f^m)[/math]?. I've tried a direct proof and a proof by contradiction but I haven't gotten any progress so far. Here [math](I:f^m) = \{g \in S : gf^m \in I \}[/math]

>>11459579
would it work to answer:
0.68*0.9 = 0.612 = 61,2 % of the normal distribution must the random sample be? (0.68 from one standard deviation away)

>>11459597
What’s the definition of f^infty

>>11459778
[math](I:f^\infty) = \{g \in S : gf^N, N \in \mathbb{N} \in I \}[/math]

>>11459302
how to get a phD in string theory memery like you seem to do
as an engineer the most theoretical I can do is to develop ab initio models for transport phenomenons using DFT or other StatMech techniques and all the math I can do in my spare time isn't going to change my resumé

I hate this tb'h

>>11459597
>>>/sci/sqt
Hint hint: [math](I : f^{ \infty} ) = \bigcap _{n \in \mathbb{N} } (I : f^n )[/math]

>>11459987
Isn’t it /cup?

>>11460117
it is

>>11460117
If we're judging by the way anon wrote it, yes.
But [math]a \in (I:f^n) \rightarrow a = gf^n \rightarrow a = (gf)f^{n-1} \rightarrow a \in (I : f^{n-1} )[/math], so it trivializes to [math](I: f)[/math], and I'm thus assuming he forgot a for all in the definition.
Also because I distantly recall seeing this stuff before.

>>11460135
Never mind, I think I just mixed it up.

>>11460117
i c u p

>>11459597
Ok anon, basically you have ti prove two containments as usual. One of them is trivial, the other one follows by an argument similar to
>>11460135
To show that (I:f^m)=(I:f^(m+n)) for n>=1

Hey, I need some advice y'all. I study math in my free time as a way of challenging myself and I'm having trouble getting past proofs. I've gotten through Hammack's Book of Proofs and How to Prove It, but every time I try to learn linear algebra and a basic questions asks me to prove something, I draw a complete blank. I seem unable to apply what I've learned to more advanced subjects. Am I skipping a step? Are there any techniques that will enable me to retain and use the simpler mathematical concepts I've absorbed more effectively?

>>11460541
practice, practice, and more practice.
in basic Algebra though, it's usually about finding out correctly what exactly you know, what's asked of you, and the connection between the two.

Bitch i found my path, still in school but im not good with math.

Did you espy the Seshat in the library? The fuck's up with that?

>>11459070

grad math talks about doing math.

undergrad physics does math.

it's the difference between a music theorist and a musician.

that's why astrophysics majors score higher on quant GRE than math majors, and within math majors operations research (applied math) score higher than "pure" (lmfao) math majors.

none of this would be confusing if we didn't live in a society where we had to be polite to insecure people, but alas, we must.

>>11460907
That's the dumbest thing I've ever heard

>>11462240
>If a 21:9 image is being displayed on a 16:9 1920x1080 Display, what would be the resolution of the empty spaces above and under the image?
>~411 pixels
>Op here, I think that's 5:18 for each empty space, then 5/18 multiplied by 1920 equals 533 pixels per empty space. I think the answer is 1920 x 533?
>photoshop says 1920 x ~138.5 per each empty space
Can /mg/ solve this?

>>11462302
Based lost 4chins newfag

>>11446627
i didnt understand a single thing, yet im a math major. is this bad?

>>11462588
Are you capable of correctly deducing consequences of a given axiomatic system?

>>11462601
huh?

>>11462603
Have you ever noticed a correct theorem? Has a proof ever made sense to you? Have you ever verified a math statement on your own just to make sure it was correct?

>>11462609
huh?

>>11462618
huh? huh? huh?

>>11462609
>Have you ever noticed a correct theorem?
All theorems are correct.

https://www.imdb.com/title/tt4481414/

I kinda loved this film. Have any of you seen this?

>>11462825
except that one inequality from a few years ago that was found to have been egregiously wrong despite the mathematics using it for over 40 years

we don't talk about that one

>>11462901
>except that one inequality from a few years ago that was found to have been egregiously wrong despite the mathematics using it for over 40 years
That wasn't a theorem.

>>11462906
it is.

>>11462906
Which theorem was that? Cohen did his thing more than 50 years ago.

>>11462932
Jacobian conjecture is one. Supposed proved in 1939 by Keller and bestowed theorem status, it was assumed to be a proper theorem for years until the 1960's when Vitushkin took a giant shit on it and showed that over 90% of Mathematicians were fucking hacks because they couldn't be arsed to properly READ Keller's incorrect proof. But hey that's fine, just let them keep their PHDs while they sit in ivory towers casting judgment on Undergraduates for making the very same mistakes they did.

Who moving to online classes here

Just fuck my shit up

>>11463144
me

fuck this country

>mfw BMC got cancelled

>tfw uni doesn't do online classes
I can manage to keep up with the supposed curriculum, but the others? I don't think so...
hopefully they get their sit together starting next week

I see, perhaps this one was a bit too much.

Unslain Beasts
>>11453142

Here's a new one that perhaps is easier:
[math](a_{n})[/math] is a real sequence with the following property true for all natural numbers [math]n[/math]:
[eqn]a_{n+1}^{2}+a_{n+1}=a_{n+2}^{2}+a_{n}[/eqn]
Prove that a sequence such as this converges, and if so to what.

>>11463023
Where can I find the wrong proof? Google doesn't turn up anything. Which journal did Keller publish it in?

>>11464009
I don't follow.
Let [math]a_n[/math] equal [math]1[/math] if [math]n[/math] is even, and [math]-2[/math] otherwise.
Then [math]1+1^2=2=-2 + (-2)^2[/math].

>>11464025
>>11464009
Ah you're right, apologies I didn't catch myself in drafting this, [math]a_{n}[/math] is a recursive, real sequence. Very quick work on the disproof though.

>>11464068
I misread the property as [math]a_{n+1}^2 + a_{n+1} = a_{n+2}^2 + a_{n+2}[/math] and just looked for a counterexample to [math]f(x)=x^2 +x[/math] being injective.

>>11453142
Let n=4 and D=2016. Then the modulo checks out
https://www.wolframalpha.com/input/?i=2016*6%5E625+%3D2016+modulo+10%5E4
but 16 doesnt divide 6+1*2+8*2 = 24, right?

>>11464086
Don't downplay yourself, your answer still works without mancer's correction

>>11464068
how is this any correction to the problem
this sequence >>11464025 is still a counterexample

>>11464362
Make it recursive then faggot

>>11464379
what do you think "recursive" means faggot
you can't compute a_n+2 from the previous terms, because it could be a positive or negative square root

>>11464326
Perfection, well done.

>>11464397
[eqn]a_{n+2}^{2}-a_{n+1}=a_{n+1}^{2}-a_{n}=C[/eqn]
[eqn]a_{n+1}=\pm\sqrt{C+a_{n}}[/eqn]
Yeah suppose it could be negative you twat, what happens then? Someone has to retake Real Analysis.

>>11464424
congratulations, now look here >>11464025 and realise that this still fits your formulas you dumb fuck, because we can choose the plusminus arbitrarily

>>11464448
?
[eqn]a_{1}=1;a_{2}=-2=-\sqrt{C+1}\Rightarrow3=C[/eqn]

[eqn]a_3=-\sqrt{3+(-2)}=-1[/eqn]
Oops!

>>11464488
[math]a_3 = \sqrt{3 + -2} = 1[/math]
it does not follow from the original equations in any way that you have to select ALWAYS PLUS or ALWAYS MINUS
it's only a plusminus which may be sometimes plus and sometimes minus depending on n

>>11464503
Plus/minus doesn't give you a pass to pick one, both must satisfy the circumstance.

>>11446728
see this
>>11462902
>>11464931
>>11464928
>>11464996
>>11456441
>>11459266
>>11464920
>>11464544