/sci/ - Science & Math

What's the point of these threads when most people moved to discord?

>>14592026
Discord is for trannies

>>14592026

>>14591912
Epic prank.
B)

>>14592037
discord trannies? in MY /sci/?

Be honest, when was the last time /mg/ has a good discussion other than homeworks?

>>14592026
>>14592063
Can you fuck off, these threads are fine and active

>>14592103
discord trannys are trying to steer more victims into their tranny discord, thats what they use this thread for.

Could there be hidden algebraic or other mathematical structures within the audio representation of sounds? Like within the waveform or fft transformation? Perhaps distinct but related classes of sounds share the same structure but different substructures?

>>14592129
Wtf are you even saying?

>>14591893
What should I write my masters thesis on?
Focusing masters on systems and signals theory, pde theory and numerics, and some deep learning.
Cmon give me a juicy topic

>>14592129
Pontryagin duality, convolution with integrable functions in abelian locally compact topological groups give an algebra. DFT is representation of cyclic group. Lots of linear algebra, DFT can be given as a unitary matrix.

>>14592172
>Cmon give me a juicy topic
thats what your advisor is for.

>>14592129
>Perhaps distinct but related classes of sounds share the same structure but different substructures?
Well if they're related they must have some relation, which you could probably describe in an algebraic or mathematical way couldn't you?

I searched "crackle wave sound" and I found it interesting there's a wikipedia entry for "crackling noise"

>>14592026
When I post here no one knows who I am.
We are Anonymous. We are legion. Expect us.

Where can I find a complete classification of all possible isomorphism classes of locally convex topological vector spaces?
If that's too hard, I'd be satisfied with a classification of all Banach spaces.

>>14592235
Yeah sure, here's your classification:
Locally convex topological classifications fall into two types:
Type A - those isomorphic to Hilbert spaces.
Type B - those not isomorphic to Hilbert spaces.

>>14592174
>in abelian locally compact topological groups give an algebra
Forgive my ignorance but why must it be locally compact?

>>14592172
buzzwords, namedropping and stylish text formatting. be as superficial as possible, avoid rigor at all costs, devote all your energy to creating a facade of expertise and use it as a false pretense to justify reviving a degree.

>>14592172
use deep learning algorithms to look for statistical correlations between violent crime rates and ethnic makeup in american neighborhoods

>>14592026
What's the discord? This thread is way too slow

>>14592026
if this thread dies i have to move to discord and if i do that i die

What's everyone working on?

>>14592506
would also like to know the answer to this

>>14592842
what are the conditions necessary for a left-topological group to be left-orderable (and topological group to be bi-orderable)? My guess is that if it's connected, and it's disconnected if you remove the identity, that should be enough, but i've made zero progress getting it anywhere. it probably needs another condition

>>14593280
you're a homosexual pedophile who jacks off to children's cartoons, according to the science, you probably collect child pornography also, you're too focused on your masturbation habits to understand math.

>>14592129
Study representation theory and abstract harmonic analysis.

>>14593382
Obsessed.

>>14592546
I would fail then

>>14592557
Sounds boring

>>14592178
I dont have an advisor yet

remember when /mg/ was going mental when atiyah announced his proof of the riemann hypothesis

>>14593435
Sometimes it's still hard to believe to me that the mad lad actually did it.

>>14593280
Consider [math]\mathbb{R} \cup i \mathbb{R}[/math] as a group under multiplication.
Basically, I think you need to ask for it to have two connected components once you remove the identity and there's no shortcut in the connected case.
Or at least if there is it's an absurdly weird shortcut.

So I heard some Anons talking about how a base 12 number system would work better with the true framework of reality but since we have ten fingers it's all whacky. Is this true and what are the implications of it

this is obviously not bounded above but how is it not bounded below?
clearly [math] \emptyset \in P(X)/X [/math] and is obviously a subset of any element, is this a mistake?

>>14594368
Review the definition of bounded and think about the logical negation of that.

>>14592279
Kek. I was looking for results similar to Banach-Mazur or Anderson-Kadec. But I found "Selected Topics in Infinite-Dimensional Topology" by Bessaga and Pelczynksi now.

>>14594400
>Banach-Mazur
Saying Banach-Mazur classifies real separable Banach spaces is like saying Nash's embedding theorem classifies Riemannian manifolds.

>>14594388
My bad I'm feeling extra retarded today and for some reason thought it meant that it was bounded neither below nor above

>>14594489
thank you for sharing your freshman intro to proofs studies with us, anon. sorry that you’re feeling retarded. maybe tomorrow your genes will be better and you’ll be less retarded

Why is geometry and trig so fun bros? Im still learning trig at the moment so is topology just as interesting?

>>14595008
Yes, yes it is. Especially if you've suffered through a real analysis course, because all of the theorems from real analysis are put in more intuitive terms.

>>14595064
what do you mean by intuitive?

>>14595008
No, topology isn't useful, so not as fun to learn

>>14593280
Interesting
>>14593435
Not real

>>14592600
Is it is against the rules to give it out?

>>14595209
I think advertising other forums is against the rules.

>>14595209
There is no /mg/ discord. Seriously. All of those links you may have seen in the archives are dead servers.

>>14595223
Oh, ok, thanks. Are 30 year old boomers allowed on discord or is it just for young people?

>>14592842
working on phys II and calc II on asynchronous online classes. Calc I had challenged me more than Calc II has for some reason, maybe because I'm really getting down the work ethic needed and even though it's harder work it comes easier. Got the calc II final coming up, anyone got any resources on practicing integration? Any and all help/ advise is welcome.

>>14594352
>The number twelve, a superior highly composite number, is the smallest number with four non-trivial factors (2, 3, 4, 6), and the smallest to include as factors all four numbers (1 to 4) within the subitizing range, and the smallest abundant number. All multiples of reciprocals of 3-smooth numbers (a⁄2b·3c where a,b,c are integers) have a terminating representation in duodecimal. In particular, +1⁄4 (0.3), +1⁄3 (0.4), +1⁄2 (0.6), +2⁄3 (0.8), and +3⁄4 (0.9) all have a short terminating representation in duodecimal. There is also higher regularity observable in the duodecimal multiplication table

https://en.wikipedia.org/wiki/Duodecimal

>>14591893
Been 5 years since school
Now I wanna get into data analysis job with a degree in statistics
What resources can I use to help study?
What math path do I go through starting from algebra? (just to refresh I swear I'm not that retarded)
What tips are there for college so I don't have to spend 4 years getting an aa and ba?

>>14595233
discord is the number 1 place for groomers, you'll fit right in

>>14595230
Liar

>>14595230
Based.

>>14594550
Fuck off, everyone starts somewhere

>>14595785
That doesn’t sound nice

Do I need to know a lot of algebra/analysis for the Putnam exam?

>>14596700
no
there's very little algebra overall. any crappy intro to abstract algebra course will cover enough that you won't be roadblocked on a problem by not knowing necessary concepts
there are occasionally problems where it's helpful to know a theorem from higher-level analysis, but for the most part everything on a putnam is accessible using methods from a calculus sequence (at least a proper one for math majors)

Can someone explain roughly what cohomology is? Supposedly it's dual in some sense to homology but I don't really understand what it is about.

>>14596978
the most accessible is probably de rham cohomolgy, and it basically tells you how many solution exist for certain diff eqs. Example would be the existence of scalar and vector potentials in EM.

But if you already understand (singular) Homology, Cohomolgy should come for free. You just consider the algebraic dual of your chain complex.

>>14597081
I'm currently learning about singular homology, but I underestemated the amount of algebra I'd need vs topology and am (more than) a bit rusty on the former.

>>14597256
Then you're gonna love spectral sequences.

>>14597266
;_;
Do you have any good resources to quickly brush up on algebra?

>>14597297
I'm assuming you mean homological algebra. It's a deep subject, and you're going to have to read a lot to brush up on it.

>>14597266
That is from an old Gilbert Gottfried joke.

New inmate in prison is nervous.
"Hey new guy, do you like homology?"
"Yeah, I really like homology."
"Then you will love Mondays, we all sit together and talk about homology. Now, do you like cohomology+"
"Sure, I love cohomology, can't get enough of it."
"Then you will enjoy Tuesdays, because we all have great discussions about cohomology. Now, do you enjoy spectral sequences?"
"No, I cannot really say that I do."
"Oh, then you are going to hate Wednesdays."
Except in the original version of the joke, the question was whether the new inmate is a faggot.

>>14592219
fuck off avatartranny

>>14592669
>>14590347
QRD on Cartan?

>>14596978

simplest definition:

Cohomology is an invariant of a topological space, formally "dual" to homology, and so it detects "holes" in a space.

https://mathworld.wolfram.com/Cohomology.html

>>14595151
>>14595008
nah topology is useful

roger penrose proved that singularities are unavoidable in general relativity field equations using differential topology

Every particle physicist nowdays study topological quantum field theory.

>>14595250
Just do opposite of derivative.

>>14596949
thanks friend

Derivatives are starting to confuse me...

I know the differences between the exterior, Lie, and covariant derivatives in a basic sense, but for a tensor field what is the difference between the Lie derivative and the covariant derivative?

>>14597923
Hes your (our) daddy

Each semester i think I know less math than the previous one. I'd give everything to stop being a brainlet.

what's the hardest math subject you can take as an undergrad?

>>14598277
Calculus

>>14598277
it really depends how a subject is taught at your facility but... real analysis can be a very painful experience. its the only subject i feared in my bsc.

>>14598277
functional analysis

someone recommend me an algebraic geometry book

>>14591893
Im studying sobolev embeddings and find it confusing as fuck.
What the fuck is even going on here? Can someone please explain?
Just feels like youre melding all these spaces together

>>14598195
More info?

when working with conditional expectations, what are the minimal necessary conditions in order for [math]E[XY|\mathcal{F}]=XE[Y|\mathcal{F}][/math] to hold for [math]X[/math] [math]\mathcal{F}[/math]-measurable? afaik this works if all 3 variables [math]X,Y,XY[/math] are [math]L^1[/math]. would it work if only [math]XY[/math] and [math]Y[/math] were [math]L^1[/math]? what if all 3 variables are positive, can we drop the [math]L^1[/math] assumptions altogether? i know [math]E[X|\mathcal{F}][/math] always exists for [math]X\geq0[/math], even if [math]X[/math] isn't [math]L^1[/math]

>probabilists

>>14592842
Nothing. My brain is fried. I picked up painting. Much less taxing than mathematics. Also, the paints smell nice and it gets me pussy.

I have a question: who is going to win the Fields Medal this year? I remember there was a lot of excitement back in 2018 over it. Things seem a lot more chill this year. Maybe because everything else is fucked.

if [math]L/K[/math] is a field extension (let's say finite, to keep things simple) and [math]A,B[/math] are [math]K[/math]-matrices, that are similar over [math]L[/math], will they be similar over [math]K[/math]? i know this works w/ [math]\mathbb{C}/\mathbb{R}[/math] so i assume it should probably work for finite extensions of infinite fields as well. what if finite is changed to algebraic or even dropped altogether, what happens then?

Best math script?
For me it’s \mathcal, what about you anons?

>>14599284
what lead does to a mfer

I start grad school in the fall. Wish me luck guys

>>14599284
Based

Is there any non-arbitrary way to order the elements of an n x n Boolean matrix ring?

>>14598277
At my uni, it was algebraic geometry. Really, nothing got even close.

How long do I have to learn algebraic geometry until I get to the geometry part? So far it's only algebra.

>>14600258
There is no geometry part. That's why trannies love it.

>>14592842
Trying to prove there exists a model structure on Cat in which the weak equivalences are the functors F : C —> D whose pullback F* : [C^op,Set] —> [D^op,Set] is an equivalence of categories.

>>14600258
>>14600268
Here's the filter: it's all geometry. If you dont get it then you dont really know algebraic geometry.

>>14600258
It's algebra unto geometric ends. What else could you call Nullstellensatz?

>>14597954
qrd on penrose's proof?

>>14598277
At my uni is some applied math course. There's even a phrase about that course; "if you pass Mathematical methods for science you can pass everything."

>>14592842
Some basic topology and real analysis. Periods are in a week so I'm starting to lose my mind.

How relevant are ordinal and cardinal numbers outside of pure set theory? Is knowing their definitions and transfinite induction enough if my main interest is in topology?

>1 + 1 = 2
a condition with holds true nowhere in observed reality

>>14601865
Really? Not even with money? Great, I'd like to do business with you. And I'd be unironically not surprised if you're willing to lose money only for the purpose of being stubborn.

>>14601725
topology is a broad field. could you be a bit more specific?
but in general, set theory is very irrelevant for other fields. i think you will be fine

>>14601886
>could you be a bit more specific?
Algebraic topology and functional analysis

>>14601875
my money is worth vastly more than yours is. i would happily spend $100 of your money on something that i wouldn't pay a penny for myself.

>>14601893
pretty sure you will be fine

>get absolutely torn apart by first exam
>cried over the last week
>turns out I got a B, as now that I'm finally intro math courses like Calculus its not about the answer, its about the journey

>>14591893
I can't talk math but I want to. Where is the best place to get a online math education?

I am prepared to do math as a hobby for many years but I would like something where you get little certificates or even a degree that if I spend the next 30 years doing math as a hobby and do something worth publishing I would like to be able to publish it without everybody shitting on Old Man Bryan for not having a degree. I get that if you're a super genius you would be able to publish without a degree but us mere mortals need stupid degrees for everything.

>no solutions
>let's just extend the space so that there are solutions :>
holy fuck mathematicians are hacks

>>14601926
>no solutions in unnecessarily restrictive space
>use a less restrictive space to obtain solutions and solve real world problems
>n..nooo how are negative numbers even real, fucking mathematicians playing us for FOOLS

>>14601920
Setting goals is very important in (self) education. So let's clear something up right away: you won't publish anything meaningful. Just get it out of your system asap. Or settle for "not meaningful".

Moving on, no online degree will get you a proper understanding of math (unless we are talking some basics like trigonometry/calculus/linear algebra). Research-level math requires years and years of slowly building everything. It also requires discussing stuff, talking to your colleagues, participating in and giving seminars.

Next, a "genius" publishing something "without a degree" is pure copium. The concept of "mathematical talent" (or any talent, really) with which you are born with or which is somehow inherent to you is just a ruse, retard. It's a meme. It's not real. At least not to an extent where its absence complete precludes you from doing maths. I guarantee you that everyone who knows how to draw realistic portraits, play jazz improv, or knows mathematics has achieved it through hours, and I mean hundreds and thousands of hours of practice.

So, tldr: forget about actual meaningful research, it won't happen. Reading math aa a hobby though (including pure math topics like algebraic geometry etc.)? Totally possible, there is no such thing as talent or predisposition to math. Just put in effort, have fun, balance it out with the rest if your life, and you'll see progress.

Arbitrary products of compact spaces are compact (Tykhonov theorem). Take the countably infinite product of the [-1,1] interval and embed this into separable Hilbert space. This "cube" is therefore compact. It contains the closed unit ball as a subset. Closed subsets of compact sets are compact. But unit ball in separable Hilbert space (or in any Banach space at all) is non-compact. What is happening here?

>>14602063
I think you should be more careful in referencing the topology wrt which shit is compact

>>14602093
Oh, I see. Hilbert space topology is finer than product topology, right?

>>14602046
>>14602046
>So let's clear something up right away: you won't publish anything meaningful.

I know but it's fun to dream, I want to at least be able to read and have some understanding of more abstract math and it's why I have been trying to go deeper into topology. I don't understand why your post basically devolved into calling me a retard and saying people like Ramanujan don't exist.

The only thing I said was that a genius could publish without formal schooling in math not without effort or actually working in math. You made a lot of logical leaps and didn't really help at all. I have published in a unrelated field by submitting to blind peer review and it got accepted and only after they found out that I have no formal schooling in psycology did they pull it.

>Let [math] n [/math] be an odd integer [math] >2 [/math] and let [math] f(x)\in \mathbb{Q}[x] [/math] be an irreducible polynomial of degree [math] n [/math] such that the Galois group [math] Gal(f/\mathbb{Q}) [/math] is isomorphic to the dihedral group [math] D_n [/math] of order [math] 2n [/math]. Let [math] \alpha [/math] be a real root of [math] f(x) [/math]. Prove [math] \alpha [/math] can be expressed by real radicals if and only if every prime divisor of [math] n [/math] is a Fermat prime.

>>14602171
Before trying to understand maths, you probably need to work on your reading comprehension, buddy. I literally did the opposite of calling you a retard. That was the whole fucking point of my post.
>Ramanujan
Ah, of course it's Ramanujan. It's always Ramanujan

Alright, you seem to already have a certain romanticized image of mathematical research so there is no point for me to discuss it further.

I still can't get over the fact that Z and Q have the same cardinality but R \ Z lets you have intervals of length 1 but meanwhile there is no non-degenerate intervals ((a,b) with a < b) in R \ Q.

always wanted to know the inner details of why there exists no anti-derivative for certain functions, say like x^x. i've heard that differential galois theory holds the answers, but i'm a bit of a brainlet. took an algebra course back in the day that covered the gist of groups, rings and fields. any books or recommendations on the subject would be helpful.

which android calculator supports easy to type in logarithm base format? I'm tired of having to divide shit, something like excel format would be good but anything is fine
=-1/2*Log(1/2;2)

>>14601865
do you have a smol or a big apple?

Is Mochimuchi done?

https://arxiv.org/pdf/1004.2445.pdf
pretty poggers

>>14602592
sus

>>14600282
Neat

Guys, can any of you explain to me why R1, R3 and R4 are considered transitive relations? The question is just asking to pick the transitive relations, my answer was R2 and R5, but the answer key says: R1, R3, R4 and R5, I don't understand why he left out R2 but included the others.

>>14603357
Transitive means if aRb AND bRc then aRc. Try going through again and seeing if for every a, b, c in each of the relations that this is true. In the case of the singleton sets, it's kind of vacuously true because there's only one element.

>>14603388
I get the singleton sets part - all the elements relate to each other because there's only one item in the set, but what about R2? Why didn't he include it when it seems to be quite clear that there's transitivity? 1R2, 2R3, 1R3, isn't that textbook transitivity?

trivial

>>14602171
This general has a few pure math graduates and at least two pure math PhDs, probably more. It's not very productive to your ambitions to just 'lalalalala I can't hear you' every post that goes against the narrative in your head.

Ramanujan: it's impressive what he managed to achieve without formal education, yes. But the gap between what he was doing and what pure mathematicians do is colossal. This might sound elitist and condescending, but you can't even imagine just how large that gap is, it's incomprehensible for a newcomer.

It's unfortunate that Ramanujan didn't get to learn what we knew back then, he would have probably contributed so much more. But having Ramanujan as an example to aim for just sets you off for a bad start.

You cannot cut corners in mathematics if you want to make meaningful contributions.

>>14596978
It's literally homology but with reversed arrows. Think covariant and contravariant functors.

>>14603532
>Ramanujan: it's impressive what he managed to achieve without formal education, yes. But the gap between what he was doing and what pure mathematicians do is colossal.
not him but isn't ramanujan a valid counterexample to the claim a genius publishing something without a degree is pure copium etc.?

>>14603402
2R1 and 1R2 but we're missing 2R2 for transitivity

>>14603613
>is pure copium
Ramanujan is a valid counterexample to the claim that it's impossible for anyone to ever do math without a formal background. That's all. You can't point to one guy who was so legendarily talented he just hallucinated a bunch of identities that took an army of mathematicians decades to figure out and go "yeah see I could do that, you're just coping"

Though the guy you're replying to is being a condescending dickhead.
The problem with independent research isn't an intellectual one. You can learn whatever you want on your own. It's social. Past a certain point you need a network of other mathematicians to actually understand a modern research area. At the level of producing new papers, just sitting down and reading stuff becomes (IMO) literally secondary to talking to people.

>>14603637
Interesting, so for a relation to be considered transitive all elements must abide to the transitivity property, I was using the same logic that is applied to reflexive relations - as long as the ΔA is present, it's considered a reflexive relation, even if some other items don't follow the same pattern. Thank you!

>>14603613
Anons are beating around the bush. Ramanujan's contributions to modern maths are close to none. He fiddled with cute series and number theory identities like an undergraduate Fermatist. Now he's been made popular through popculture and movies and shit because muh Indian underdog. I knew a guy who intuitively understood spectral sequences and shit like the index theorem when he was 19, where's the movie about him

what are the most fundamental areas of maths, logic and set theory?

>>14603613
>not him but isn't ramanujan a valid counterexample to the claim a genius publishing something without a degree is pure copium etc.?
No one actually thinks that you absolutely need a PhD to publish revolutionary results, that's just an excuse people use not to comb through crank proofs for mistakes.

>>14603974
Yeah this.
If you make a breakthrough as a no name and your paper is 10 pages long? Great, people are going to try reading it.
But if your paper is 200 pages long? It's gonna die on arxiv.

Given the spectrum of a graph is there a simple way of recovering a graph from it? Or do I have to check every graph of given order?

>>14604080
https://mathworld.wolfram.com/CospectralGraphs.html

>>14604080
If your graph is weighted, it might be possible generally. Relevant paper:
http://user.math.uzh.ch/halbeisen/publications/pdf/massen.pdf
In non-weight (or uniform weight) case it's pretty much impossible because there are just a lot of them.

hello my friend say this is cool place to learn math before exam period. i am teach myself for indian national math competition

>>14604051
>If you make a breakthrough as a no name and your paper is 10 pages long? Great, people are going to try reading it.
Honestly it depends on the proof outline.
I recall this dude who came here a couple of years back and claimed to have proved Riemann by separating the zeta function into real and imaginary parts, and his pdf was something like 20 lines long. The second you read that your brain computes that there's a 50% chance he divided by zero somewhere or made some other algebraic mistake, a 40% chance that he misused some previous result and a 10% chance of it being some other error.
Catching algebraic mistakes? Tremendous pain in the ass. Verifying if any previous results were used correctly? Immense pain in the ass unless you're already very familiar with the subject. These two things coupled with the outline sounding kinda dim means most people wouldn't read the proof if it were 5 pages long.

>>14604151
>20 lines long
20 pages long.

>>14603974
>>14604051
Anon is at a level where he thinks that getting online certificates would give him more cred when publishing math research
It is safe to say with a 99.(9)% probability that he won't make a breakthrough

If you are working something by writing on your notebook, do you write QED or are you using the white square?

>>14604868
neither, just put a dot at the end of the sentence and call it done

>>14604868
“This shows that …, as desired”
Or something along those lines

Principal bundles are killing me, do I really need them or can i get by with just vector bundles?

>>14604100
good morning, sir

>>14604868
I put a tombstone

>>14604868
'proof is obvious and therefore will be omitted.'

>>14604868
I just stamp it with my thumb after I dab it in ink, and then sign my name with a red pen. It's solid proof that it was my work.

>>14601920
Why dont you just enroll in your local university?

when one first encounters the differentiation of real functions in one variable, one gets the impression that the essence of the derivative at a point is it being the slope of the tangent at that point. At least that is the point usually emphasised. But if we wanted to extend this point of view to functions in more than one variables or to matrices, it wouldn't really make sense. The morale of this is that being the slope of the tangent is not in fact the essence of the derivative. The (more) correct notion is that the derivative is the linear map that approximates your function the most accurately at that point. This lets us generalise the notion of differentiation to more general functions.

>>14605811
Why did you post this?

>>14604868
I write "[...] which was to be proven."

>>14605811
>But if we wanted to extend this point of view to functions in more than one variables or to matrices
Huh? Makes absolute sense since you just consider partial derivatives of each component, so every single element of the differential (viewed as an n x m matrix) has a geometric interpretation.
>The (more) correct notion is that the derivative is the linear map that approximates your function the most accurately at that point.
Well duh, good textbooks emphasise this exact interpretation.

>>14595782
watch
https://www.youtube.com/user/patrickJMT/videos

read
https://tutorial.math.lamar.edu

>>14604868

>>14605811
The partial derivative computes the slope of the tangent in the axis of the derivative, following the first interpretation

helllo bro's i am learning math here. lets gooooooooo i am legendary.

>>14606209
based, what are you studying as of recently

I hecking hate complex geometry. I will never accept that a Riemann surface is a complex 1D manifold. In my POV it will always be 2-dimensional.

>>14606541
Give an example of a complex manifold that actually has a single dimension then.

>>14606598
the complex line (drawn as a line, labelled [math]\mathbb C[/math])

>>14606612
Jesus Christ how horrifying.

>>14592506
>>14593208
Anyone know the answer to this? Why does the Pontryagin dual require the original abelian group to be locally compact Hausdorff?

>>14606768
Can't you spend two minutes googling this?
It's so you can put a Haar measure on the group.
>inb4 why can't you put a Haar measure if it's not locally compact
Infinite-dimensional Hilbert space.

What is the area of a kilogram? Not as a bullshit question, but like, what happens if you use type theory or something equally rarefied to solve equations over incomparable measures?

>>14606968
everyone who isn't a skhitzoz will look at what you've done and spot the mistake immediately because non-sckiztos do unit analysis first, its the easiest way to spot the most common errors. in the non-abstract world, most analytical work can be completed via simple unit analysis, its a wonderful shortcut, the more complicated full solution then becomes a safety check to confirm that the initial unit analysis was correct.

>>14606927
Nta, but I didn't know this either. Now it makes sense.

>Mathematical physishit
>Gets 60% at the algebraic geometry exam while sweating my balls.

Am I getting filtered ?

I dream of starting a "fraternal order" of mathematics.
Pythagoreans, Path of Erdős

Lodges in major cities around the world. Living quarters and common quarters with chalkboards. Stay for free if you clean up a little, do some free local tutoring.
Businesses could have access to "consultants" depending on their contributions.
But mostly I just want to travel around and stay at a Math Lodge and work on some problems with fellow rando transient or local math folks.

This is my beautiful dream.

>>14607209
I don't know what to say other than that is indeed quite wholesome. I wish you well math lodge anon, may the road rise to meet you.

>>14607209
the church of satan has already cornered the market on amoral atheistic know-it-alls who lack the self awareness to avoid recurrent humiliation at the hands of their own grandiose delusions.
>reeeee, i hate god
daddy issues

>>14607244
I think the road rose to meet me a few times, and I always turned away.
>grad school -- nope
>high "priestess" or whatever in OTO -- nope
>being rich from the 100 btc I bought at $1 -- nope, lost in a landfill

oh well, maybe it will just magically manifest by the time I'm a sad homeless old man and I can sweep and work on problems and tutor in peace until I die.
Sorry for semi off-topic, no more from me, carry on

>>14607301
I don't see anything about God you cringelord.
Are you American? You seem to be "dunking" on a lot of weird things that no one's bringing up.
You doing ok? What you working on?

wanna tell /mg/ that im got accepted into a top grad school in mathematics even though you guys always told me im retarded. fuck you
>>14607126
maybe your score was above average. regardless i dont think theres any reason why a mathematical physicist would know or be good at algebraic geometry

Why are the slopes of f=x and f=2x algebraically independent of each other?

>>14607313
now you've gotten all emotional and angry because you have been accurately characterized. why don't you take a while to calm down so you can use your rational thinking ability instead of trigger reacting to emotional stimuli like a farm animal? you wouldn't have been triggered so hard if characterization of your was inaccurate, if you can't control your emotions then manipulating you via emotional triggers is child's play. you also have an inferiority complex with respect to the usa as because you are naive enough to have been coerced into the nationalism fallacy. the region you live in is the same size as any other region of similar size anywhere on the planet, lines on maps are imaginary. there you go, no more need to chimp out at usa all day errrry day.

For some graph G(V,E)
simple (is this the right word?):
V = {1,2,3,4}, E = {{1,2}, {2,3}, {2,4}, {3,4}}

directed:
V = {1,2,3,4}, E = { (1,2), (1,3), (1,4) }

how do I denote weighted graphs? and weighted+directed?
I think the better representation is matrix (but correct me) just wondering.

>>14607318
Good job, what’s the school if you don’t mind?
If you do mind can you at least say top n in the country

>>14607318
>regardless i dont think theres any reason why a mathematical physicist would know or be good at algebraic geometry
String theorists love algebraic geometry, retard. K3 surfaces and homological mirror symmetry and shit.

>string theorists
many such cases

>>14607376
thanks anon.
according to the US news ranking, top 15.
>>14607387
whatever nerd

>>14607412
Very impressive, I just realized the uni I go to is too 20 which I hadn’t realized.
For my own comparison, how much research experience did you have and what sorts of classes were you taking?

>>14607449
i literally never published lmao (which is why /mg/ called me retarded).
but i was almost exclusively taking grad classes since my sophomore year and did projects/reading courses with distinguished professors.

>>14607304
What problems do you want to work on?

>>14607506
Holy based
I’m doing a reading project with a prof right now for the summer and I’m taking mainly grad courses next year as well. You give me hope brother

>>14607209
That would sound like an interesting concept, these math lodges...

A return of math to its natural and philosophical
roots, perhaps. A firm, unyielding dedication
to the love and power of the subject and great
service to the laymen of their crafts.
And, maybe, some damn good beer that gives
the other monastery breweries a run for their money.

Shit's great, man.

>>14607602
keep it up bro you can make it

>>14592842
Trying to read up on some Complex Analysis over the summer before I start grad stuff since I never learned it too well during undergrad.

>>14592842
Actuary P exam prep

>>14607685
Using Rudin?

>>14592842
Character tables character tables character tables.
It hurts being a codelet but it’s still kind of fun

>>14607791
Is it hard?

>homology and cohomology finally starting to click
we're all gonna make it bros

I'm such a brainlet, I just googled "algebraic geometry for physicists" because my IQ is too low to read the pure math books. I feel like I'm not worthy of posting in /mg/ anymore.

>>14608396
if you're a physics person you should just learn the math you need from the books for physicists that cover such things. the mathematical physics crowd aren't real physicists anyway.

How bug of a mistake am I making by majoring in mathematics

>>14608447
A herculean one.

>>14608447
Are you going to be a researcher in mathematics? Then it's ok.
Are you going to work in finance/engineering/programming/analytics? Then it was a waste of time.

>>14608503
>>14608521
grim

>lebesgay

suppose that two topological spaces X and Y are not only homeomorphic, but there is a unique homeomorphism f: X -> Y. Are there any examples of this aside from the trivial ones where X, Y are one point spaces?
I hope this is not a super retarded question

>>14608559
Le Beg

Are acos(m) and acos(n) algebraically independent for all positive integers m,n?

>>14608564
>. Are there any examples of this aside from the trivial ones where X, Y are one point spaces?
You can construct such spaces of any finate length.

Why do people (including some physicists) think that math "proves" things?

>>14592842
Intransitivity of random variables.

>>14608595
>all positive integers
I though acos is defined over domain [-1; 1]?

The other thread made me realize I don't really understand matrices, help me out.

So complex numbers can be represented by matrices of a specific form (with two parameters). Those live in GL(2, R) which is a vector space of dimension 4. So we have 2 parameters unaccounted for, what do they represent?
Complex numbers correspond to rotations + scaling. What is left? Projections are not injective so they don't live in GL(2, R) but rather just Mat(2, R). So... reflections and shears?
Literature recommendations are also welcome

Is it possible to get 100 heads in a row from flipping a coin that only has one head? Where do the other 99 come from?

>>14608564
Yeah.
[math]\Omega = \{ 0, 1 \}[/math], [math]\tau = \{ \emptyset, \{ 0 \}, \{ 0, 1 \} \}[/math]
>any manifolds
No.
>anything Hausdorff non-trivial
Probably yes but I can't come up with any constructions.

>>14609082
>>14608564
the relevant term here is topological rigidity, ie a space with trivial group of homeomorphisms
examples shouldn't be that hard to find, tho I cannot think of any off top of my head

How do I simplify (sqrt(12)+sqrt(18))/12

>>14609100
carefully

>>14608015
Depends, the biggest difficulty is translating the insurance language to working components for the problem, other than that, its just a lot of content to cover.

>>14609097
>examples shouldn't be that hard to find, tho I cannot think of any off top of my head
Seems pretty fucking hard to find non-trivial Hausdorff examples to me but you can have your fun.
It can't be finite. It can't be a manifold or a variety and probably also can't be a subset or quotient of either. It can't be a graph. That leaves uhhhhhh ordered sets? I'm good thanks.

>>14609168
when I said it shouldn't be hard to find I meant by googling, obviously

>>14606927
i spent well over two minutes googling for this. What search query did you use successfully?

>>14608988
If you write complex numbers as matrices, then they’ll span a subspace of GL(2,R), so it won’t be a 4 dimensional space, but a 2 dimensional space as expected

should I just watch 3blue1brown, or go through Euler's Elements then Apostol or Spivak's Calculus?

>>14609382
none. start with baby rudin.

>>14609324
She already said this in her post. Except GL(2,R) is not a vector space.

>>14609453
>she
>her

>>14608988
>GL(2, R) which is a vector space
Nope. Zero matrix (required to be a vector space) is not in GL.

>>14609538
>>14609453
Well the question still applies regardless of this detail, yes only Mat(2, R) is a vector space.

I'm tutoring in a kind of group home and there's this kid who's self-learning trig while his peers are starting fights with eachother, crawling around with army-men making explosion noises, and have difficulty with subtraction when it involves regrouping.
I fucking feel for this kid, especially since he dislikes trig due to all the memorizing, but he sees it as the "next step" towards calc, which is some kind of milestone I suppose. So I'm working on a little packet introducing vectors/matrices and some basics of graph theory, since of course he has never heard of graph theory because we have this disgusting beeline to calc for some reason.
I feel some kind of obligation to introduce set theory and logic basics too but I'm not going to spend too much unpaid time on this (though it's giving me good reason to review and create material for future tutoring)
My ultimate goal is to have a "crash course in vectors/matrices" and "crash course in graph theory", and then coming together with representing any graphs (directed, weighted, directed+weighted, and "simple" [is that the right term?]) as matrices, with some application type things.

Topics with graphs I want to cover: chromatic number, minimum spanning tree, ...??? I barely dipped into graph theory in my undergrad so I don't know what else could bring up neat problems or structures.
With vectors/matrices: I don't want to go too theoretic because 1) this is just a fuckin packet for a curious self-learner in a hellscape, 2) I don't want to introduce all the tools to lead up to it, and without introducing those tools I risk a negative impact like "this is too hard." Already planned: some simplistic weather prediction with a markov matrix, and rotation matrices/computer graphics.

Just kinda rambling because why not. Tell me any examples/problems/method of teaching ideas that come to mind. If you can't think of anything, weigh in on whether I should even bother with determinant.
Timothy Dexter for your time.

>>14609587
Matrices are used everywhere so that's a good idea, graph theory can be skipped completely and nothing of value will be lost
You will still need some theory about vector spaces and linear transformations to motivate shit, otherwise it will be just another trigonometry with memorization.

>>14609436
you want me to do analysis without understanding math?
I could just scribble some random symbols on the paper instead

>>14609608
>Matrices are used everywhere so that's a good idea, graph theory can be skipped completely and nothing of value will be lost
Well, I disagree. For one thing, I think it's valuable for an early student to see a new kind of structure, and one that has almost no prerequisites. Also it's helpful for an early student to have something "visual", and finally it's great to culminate in showing that graphs can be represented as matrices.
As an example (and thanks for reminding me of it), the "Party Problem" from Ramsey Theory is perfect for graphs.

I don't necessarily agree about needing vector spaces for this purpose. I'm not his professor, he's not a student. Motivation will come from examples and application, and the only memorization I think necessary for these ends is matrix/vector multiplication.
If I decided that introducing vectors/matrices did require theory and introduction of vector spaces, then I would drop it and focus entirely on graph theory and some extra, algorithms, problems, etc
There just isn't time or motivation on my part to proceed too much into theory with linear algebra.
If you are interested in providing a clear and simple path to this, I could revisit that.

>>14609382
You should watch 3B1B but also realize that "mathematics is not a spectator sport", and you should be pausing almost every 5seconds, to work out what's being said, create your own problems, alter the examples given, etc.
There is really no reason to go through Euler's Elements at this point (assuming you're asking how to progress through proof-based mathematics).

You should find a discrete text that resonates with you, one which uses number theory and such things as a medium for learning proof techniques.
I used "Mathematical Proofs: A Transition to Advanced Mathematics" by Gary Chartrand and others, in my undergrad, and I'd still recommend it.

>>14609621
if you understand basic arithmetic you can go onto analysis. baby rudin is self-contained. trust me: stick with it, and you will be rewarded a hundred, sixty, or thirty times over.

>>14592842
(applied) designing constant function market makers with convex analysis

people recommending rudin for learning math is like people recommending K&R for learning C

Why do set theorists have to be so autistic about constructions of number sets? Why can't we just define natural numbers via counting, reals via adjoining algebraics + transcendentals to the rationals, and hyperreals/surreal numbers via adjoining appropriate ordinals and their inverses? Sounds much more useful than these overformalized Peano axioms, Dedekind cuts, ultrafilters and whatever bullshit debate about axiom of choice. After all we're talking about numbers. Everyone intuitively knows what numbers are. Formalism is only useful in higher math.

>>14609944
>Formalism is only useful in higher math.
All math is "higher math." The things which are "not higher math" are just instances of "higher-math."
>overformalized
what did he mean by this?
>we're talking about numbers
what did he mean by this?
>Everyone intuitively knows what numbers are
what did he mean by this?

Also it's not just set theorists who are "autistic" about foundations. Mathematics is a method that's self-consistent by way of deductive reasoning, with the material implication at the heart of things. The implication A=>B tells us that either A leads to B, or we've fed in garbage.
I don't know how a set theorist hurt you, but it's only one approach to an axiomatic, logically-consistent system.
I'm also drunk and am likely the stupidest person to ever get a math degree so I probably missed your point.

Daily reminder of the absolute apogee of pedagogy, Herr Schuller:

https://www.youtube.com/watch?v=V49i_LM8B0E&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic

Watch as this angel of a man builds up the mathematics from propositional logic/sets through topology and beyond.
An absolutely beautiful view.
Clean, lovely.

>>14610005
18:21 if you're impatient

>>14610005
Love this guy

Let G be a group, consider a function [math] f: G\rightarrow \mathbb{C} [/math] having the following property :
There is a [math] \delta > 0 [/math] such that [math] \forall (x,y) \in G^2 \space \space |f(xy) - f(x)(y)| \leq \delta [/math].

Show that there exists a [math] C > 0 [/math] such that [math] |f(x)| \leq C \space \space \forall x \in G[/math] or [math]f(xy) = f(y)f(x) \space \space \forall (x,y) \in G^2 [/math]

*it's [math] f(xy) = f(x)f(y) [/math] Small typo.
Bonus question find the smallest possible value for C. :)

>not deleting and reposting with correction

Best complex analysis book?

>>14607209
>>14607244
>>14607610
samefag

>>14610070
>>14610087
We are not here to do your homework for you.

math dummy here. I'm doing my PhD in an engineering field, never took linear algebra in undergrad so I figured I'd teach myself it. Why am I just now learning that the determinant is calculated by the multiplication of the diagonals of a triangular matrix? Why did they not teach it this way in the first place? I feel stupid now for never taking this class

Forgive me bros, i tried but I'm not good enough. Since i was 12yold a read about Euler and Gauss I've always wanted to be a great mathematician but i will kill myself, i did try as hard as i could but no matter how much i understand a theorem i will never be good enough to give a proof. I really hope all you can fulfill your dreams, it was fun. Goodnight.

>>14609587
>I barely dipped into graph theory in my undergrad
don't mess with it until you understand how the more important proofs work

>>14610545
Who would be so stupid so as to ask for a homework question here and not
math.stackexchange ? It's just a fun math problem for a general for people
interested in maths.
No no. I don't think that you think it's homework. You were stomped by the question
and decided to lash out on (double quote) me. This is a question for a 1st year real analysis student btw. If you can't solve it continue living in copeland.

>>14610742
all this time you put into this larp you could've had the problem solved by now.

>>14610761
I will make this clear I have a solution to the problem that I will post at 300+ replies and you seemingly don't. Anyway this conversation is over.

>>14610766
Ok

>>14610461
Personally read Stein + Shakarchi and Priestley and liked them. Haven't read Ullrich but some people here swear by it

>>14610070
What does [math]f(x)(y)[/math] mean? Is that supposed to be [math]f(x)f(y)[/math]?

>>14610791
yes. It's a typo sorry

>>14610070
I found a way to solve this using the boundedness or unboundedness of [math]f[/math].
I also tried looking at whether [math]f(1)=1[/math] or not. If that's not the case then the function is clearly bounded. Now I'm stuck with the other case.

>>14592129
>audio representation of sounds
Other than Fourier series?

>>14610070
>delta > 0
>|difference| <= delta
???

>>14611700
Does mommy know her son is retarded

>>14611716
i get it, it just reads sloppy

>>14610070
If [math]f(xy)=f(x)f(y)[/math] holds for all x,y then we are done, so fix [math]a,b[/math] be such that [math]f(ab)\neq f(a)f(b)[/math]
The following inequalities hold for all x.
[eqn]|f(xab)-f(x)f(ab)|\le \delta [/eqn]
[eqn]|f(xab)-f(xa)f(b)|\le \delta [/eqn]
Adding, and rearranging slightly gives
[eqn]|f(xa)f(b)-f(xab)|+|f(xab)-f(x)f(ab)|\le 2\delta [/eqn]
Now use triangle inequality
[eqn]|f(xa)f(b)-f(x)f(ab)|\le 2\delta [/eqn]
We also have
[eqn]|f(xa)-f(x)f(a)|\le\delta[/eqn]
Multiply by |f(b)|
[eqn]|f(xa)f(b)-f(x)f(a)f(b)|\le\delta|f(b)|[/eqn]
Now add the inequalities and use triangle inequality again to get
[eqn]|f(x)f(a)f(b)-f(x)f(ab)|\le 2\delta +|f(b)|\delta[/eqn]
Finally,
[eqn]|f(x)|\le \frac{ 2\delta +|f(b)|\delta}{|f(a)f(b)-f(ab)|}[/eqn]
|f(a)f(b)-f(ab)| is nonzero, and the quantity on the right side is fixed, and the equation holds for all x, as desired.

>>14611774
Jesus christ I fucked up the latex, hopefully it's still legible

>>14592842
finish writting my thesis on applied statistics so i can start studying math on my own

>>14611700
That's closest to how it would be spoken aloud.
>>14611774
>>14611779
Good job, though a little wordy.

>>14611829
>little wordy
Yeah, it’s a bad habit I got from dealing with nitpicky graders

>>14611829
open delta going into a closed ball threw me off
also would a closed ball of radius 0 be equivalent to a point or just nonexistent?

>>14609944
Define transcendentals without defining reals first

>>14611892
What do you think?
The literal interpretation would be, "the set of all points whose distance to some given point is zero." You seem confused though.

>>14611909
Just tell them about pi and e and say they aren't algebraic.

So derivatives and antiderivatives are functions from functions to functions.
If you take differentiating as the input function, what is the derivative of derivatives?

>>14612139
It depends on your choice of domain and range and your notion of differentiability. You probably want to choose function spaces in such a way that the differential operator is bounded. Any meaningful such space is infinite dimensional. So you gotta say whether you're interested in Frechet derivative, Gateaux derivative, Bastiani calculus etc. In those instances where it can be defined, intuitively I wouldn't expect it to be very interesting, since derivatives of linear operators are usually constants.

Is this convention or did the author make a mistake by not instead writing [math] d: X \times X \to \mathbb{R^+} \cup \{0\} [/math]?

>>14612230
A good author will have a preface on if they mean 0 to be positive. It's certainly non-negative. You'll have to understand from context, which is why in-person guidance (as small a ratio as possible) is preferable.

>>14612230
neither, its laziness (based)

>>14610742
Anti-fun, stumped anon btfo

why is it on me to figure things out instead of them just being explained clearly?

>>14613195
You can lead a horse to water but you can’t make it drink. Part of the process is up to you

>>14613195
good question!

>>14613288
>You can lead a horse to water but you can’t make it drink. Part of the process is up to you
For other subjects I can simply read a sentence and comprehend its meaning. But with mathematical sentences it is somehow acceptable for it to be difficult to understand. If I explained something and you had a hard time understanding it, it would be considered my fault. But for some reason for this it is allowed for them to not explain clearly.
>Part of the process is up to you
I don't understand. Obviously I'm trying to understand it. You're implying the choice to understand is mine when I'm obviously saying there is a prohibitive difficulty due to it not being explained clearly.

>>14613139

>>14613350
Interesting. QRD?

>>14609944
Honestly, I've never understood formalism. It seems like a mysticism placed over real concepts in order to make everything as general as possible, but in that generalization you lose the actual applications and the problems that inspired the entire field of subfields.

I'm good at formalism and rigor, it's not particularly hard once you know what's going on, but overall it's practically useless. But all the good texts and good fields are riddled with it so what can you do?

This fall I'll be taking real analysis, abstract algebra and topology concurrently. What should I work on over the summer to prepare? I took a rigorous proof-based vector calculus class so I already know shit like e-d proofs, continuity, sets(open/closed, boundaries/closure, etc), manifolds/parameterizations, and the like.

>>14613350
the man the myth the legend

>>14613195
>>14613345
Math is inaccessible to lower iq people and mathematicians prize elitist abstraction over being easily comprehensible especially to the uninitiated neophyte. This is one of the many reasons why historically physicists have not liked mathematicians.

>>14613455
oh i did that recently, uhh pick the one you're the worst at (analysis for me) and just self teach yourself it in the next two months it'll make your life soo much easier

>>14613446
formalism and rigor aren't important when solving problems until they are. Not everything is intuitive so if you trust your intuition too much you will make a mistake. The point of teaching rigor is to correct you intuition, as unintuitive notions do come up whether you want them to or not. I was researching whether there was a way to naturally topologize the fundamental group, and a paper I found needed to immediately state it was using choice.

And those who worked on rigor are just as important. Their results may not be very important to the work you do, but it's the basis of a lot of important adjacent work, as well as forming the basis of the intuition that you're being taught as explained above

>>14613578
I'm not saying intuition is the be all and end all, I'm just saying formalism typically eclipses the use cases of the field itself. To the point that you'll build up some deep notation and difficult general proofs for applications that are often just trivial in comparison.

It's almost like formalism seems like a massive intricate multi-tool when you only need a hammer or a knife to solve the real problems. That hammer and knife can be very well defined and not relied on intuitions without being this, somewhat mess of, 'higher math', generalisms, and notation.

I guess. A lot of 'high math' seems to insist upon itself.

>>14613345
>For other subjects I can simply read a sentence and comprehend its meaning.
there is not a single subject where this is true

>>14613455
How did you take a rigorous proof-based vector calculus course before real analysis?

>>14613699
Maybe they used a text like Hubbard and Hubbard?

>>14610461
Remmert

>>14613195
Things are usually explained clearly.
>>14613345
>I can simply read a sentence and comprehend its meaning
Literally me studying mathematics.

>>14613577
>it's poorly explained because... it's abstract
>>14613608
But I should always be able to parse the meanings of sentences.
>>14613970
>Things are usually explained clearly.
For you, maybe. To me, the logic is insufficiently explained.

>>14613970
>Things are usually explained clearly
Post textbook list

What does the algebraic closure of F_2 look like?

>>14614372
Post a single example of a sentence in a math book which isn’t explained clearly

What is the known, exhaustive mathematical structure(s) of reality? For example out notion of space conforms nicely to R^3 (ignoring relativistic effects), a vector space, but then you also have topological properties, and structure from things like algebra and analysis

>>14614992
Not him, but can you tell me what a tensor is? Or post a clear explanation of it?

>>14615622
It's an array of numbers

>>14615622
I've never actually used them but to my understanding it is simply an extension of the idea of a matrix to more dimensions. A square matrix is an nxn array of numbers, right? Well a tensor can be any number of dimensions. So a matrix is a tensor of rank 2, an nxnxn array of numbers would be a tensor of rank 3
https://m.youtube.com/watch?v=f5liqUk0ZTw

>>14615622
You know how a function of multiple variables can be thought of as taking a single input that is a tuple? In the same way a multilinear function can be thought of a linear function that takes a single object called a tensor. A tensor is the "natural argument" to a multilinear function.

>>14615020
Every mathematical structure appears in reality, in the sense the we (or computers that can check proofs) are a part of reality that conforms to the given structure. If you mean something more specific, can you give an example of a mathematical structure that does not describe some part of reality?

Why the fuck do hypergeometric functions have such retarded notation? The little numbers next to the F are pointless and I got marked down for omitting them.

if I wasn’t great and interested in math since elementary school should I give up on any idea of exploring and studying it? I only got into it in my junior year of high school and even then I was good but wasn’t even at the top of my class. I want to go full autism on number theory.

>>14616205
No, mathematics is an interest many people mature into. A lot of the kids acing childrens' math courses or even doing IMO or whatever competitions aren't really into math per se, they just like grinding calculations out as fast as possible or solving a predefined set of puzzles over and over again.

As far as I know, there are two exhaustive graduate books on Algebra: Rotman and Jacobson.
Can you tell me about them? What are their differences?

>>14615780
>>14615812
>>14616101
>>14615780
What kind of functions do we feed them to? It makes sense to me that we pass a vector to a function, since they are sort of analogous to numbers (a number represents a point on the real line, a vector a point in R^n), but a matrix, and tensor I assume, are themselves functions (linear transformations)? I mean of course I've seen function composition before, things that look like f(g(x)), so I suppose it all so far removed from what I've seen before. Also, since tensors and matrices are functions, are vectors in some way functions? Or numbers themselves?

>>14615660
>>14615812
What is the physical interpretation of an array?

>>14614992
http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Challen/proof/proof.html

>he doesn't carry a pouch of pebbles to demonstrate novel mathematical ideas as a party trick

>>14605966
Thanks friend

>>14616248
Thank you, this was quite interesting and encouraging.

>>14615622
A tensor is an element in a tensor product space

>>14616884
>not carrying around a bunch of vertices and edges and crayons

>>14616205
I bounced from Literature, to Music, to Electrical Engineering, to some other shit, and finally landed on math.
And actually even more than that. It wasn't much because 1) I was moving around and working in between, and 2) student loans are some of the cheapest loans you can get, especially if you go to cheap-ass community colleges/state schools.

Was it dumb? Eh, I guess. If I had beelined graduation after highschool I would have ended up with a lit degree and wtf no. I love lit, but no.
I also went to cheap schools and my total bill over the however many years I attended various places, is like .... less than 3 years as a software developer. So you pick your battles. I always knew I had that as a fallback.

Anyhow my own personal stupid weird journey aside, I actually came into math in my late 20s, got my bachelors in it and keep reviewing/learning ever since.
My shit grades and doing badly on the GED (what can I say, I'm great at proofs and shit at computation) put post-grad out of the picture.
But math is still fundamental to my life and it just depends on what you want out of this short stupid ride on spaceship earth.

>>14618519
I'll also say that some of my communtiy college profs were absolute fucking gold, vs some of my university profs who had a lot of other things on their plate.
If your goal is Learning The Language of Patterns, that's one thing, goals "I need to impress bezos" and "I need to impress some board of directors letting me teach" are another.

If it's a spiritual calling, you'll pursue it in any case, but you might find more like-minds at smaller/less impact institutions. If you want to boost your CV then you know what to do probably.

>>14618024
Lol