/sci/ - Science & Math

>>11310872
Should I treat + - * / as functions? Like they can be expressed as a mapping from a set to another?

>>11310895
Of course

>>11310895
All such operations can be formalized as functions
GxG -> G
where G is the set in which your numbers live

>>11310896
>>11310902
Neat, so what field/'s are concerned with these functions/operations (don't even know what to call them now)?

>>11310919
Ring theory and group theory in specific.
Algebra in general.

>>11310919
>>11310949
Literally every field of maths.

>>11310981
What about graph theory?

>>11310991
we don't talk about graph theory anon

>>11310991
Graph theory too. A lot of graph theory is about counting (addition and multiplication). Look up chromatic polynomials.

>>11310991
>graph theory
That's computer science, not maths.

>>11310872
Should be the other way around

>>11310938
Ted brainmogs /mg/ every day from supermax purgatory

Threadly reminder to work with physicists.

>>11310938
What's the tl;dr?

>>11311028

>>11310938
absolute madness

so have we doxxed yukarifag yet?
where's he doing his phd/postdoc?

>>11311104
>where's he doing his phd/postdoc?
Yukari is not a "he".

>>11310872
What is the intuition behind convolution? Is that some kind of a moving average? Why backwards?

>>11310938
as i pointed out in the previous thread, the most significant advancements and mathematical discoveries were made without computers.

That's one small step for man...

https://www.imperial.ac.uk/news/194737/simon-donaldson-awarded-wolf-prize-mathematics/
>Professor Sir Simon Donaldson, Chair in Pure Mathematics at Imperial, will receive the Wolf Prize for Mathematics in for his contribution to differential geometry and topology. He shares the $100,000 award with Professor Yakov Eliashberg from Stanford University.

...one giant leap for the undergrad category theorists

https://hub.jhu.edu/2020/01/16/emily-riehl-mathematics-frontier-award-999-em1-art1-dtd-news/
>The $250,000 award supports individuals at Johns Hopkins who are breaking new ground and poised to become leaders in their field

https://youtu.be/hCh8Lr5z7YM

>>11311104
>so have we doxxed yukarifag yet?
Yeah, Yukariposter is Chen shitposting with a computer she bought from Rinnosuke.

>>11311106
a woman? in my physics?

>>11311139
kys

>>11311135
Why does "she" look like a weak/mangled male? Literally what is the deal with these mathlets?

>>11311135
0:40
>[...] an important emerging area of mathematic theory that essentially makes math intelligible to broad audiences.

Clearly that guy has no idea what Emily Riehl works on

>>11311166
Kek, literally the opposite is true. Oh well.

>>11310938
based Anprim bomber

>>11311415
>an unimportant waning superset of mathematic practice that incidentally makes math unintelligible to small audiences
Sounds hella based, how do I sign up?

>>11310872
Whats up friends?

Im an EE with a math specialization, as in ive taken a shit ton of pure math classes in uni and some applied math classes in addition to the standard EE curriculum.

Now, im really indecisive with respect to what to do for my graduate studies, I'm either doing a systems and signals masters, an applied math masters on systems and signals or an applied math phd on systems and signals.

Id only do a phd if I can get into a decently well paid program right out of college. But I'd really like to do a phd, its just 6 more years of barely making any money is very unappealing, as Im an EE and can make a lot of paste and live lavishly with my future wife and kids.

What should I do?

>>11311449
>Whats up friends?
> Im an EE with a math specialization, as in ive taken a shit ton of pure math classes in uni and some applied math classes in addition to the standard EE curriculum.
> Now, im really indecisive with respect to what to do for my graduate studies, I'm either doing a systems and signals masters, an applied math masters on systems and signals or an applied math phd on systems and signals.
> Id only do a phd if I can get into a decently well paid program right out of college. But I'd really like to do a phd, its just 6 more years of barely making any money is very unappealing, as Im an EE and can make a lot of paste and live lavishly with my future wife and kids.
> What should I do?
>>>/adv/

>>11311473
>Ask in a thread with people that have very specific experience relating to your question
>Or ask in a board where 99% of the posts are about talking to women without stuttering

Hard choice

>>11311494
>ask in a board where you'll be told to fuck off, called an engineer retard, and if I'm in a particularly bad mood, be given made up advice
>ask in a board where people will answer your question

>>11310995
why not anone?
is it supposed cause >>11311018?

>>11311494
>ask on a board literally named Advice
>or ask on a board which explicitly disallows asking for advice right in the sticky

Hard choice

>>11311146
yukariposter is a transvestite, a hella sweet one.

>>11311511
>>11311606
You fuckers dont have many friends do you?

>>11311620
>You fuckers dont have many friends do you?
Do you really need to swear?

>>11311620
I'm friends with >>11311606 , and he's friends with me.
Get fucked.

>>11311642
i’m not your friend

>>11311666
fuck off daemon, i don't want to be friends with devil

>>11311666
i'm not your , buddy

>>11311666
You friendless cunt.

>>11311449
>EE
Shut up. Nobody cares you pedantic faggot. Keep your bullshit on >>>/lgbt/

>>11311609
It should be burned. It will never be the opposite gender. Just a mentally ill subhuman. Being a tranny explains a lot of the pedantic posting style

>>11311748
Not him, but shut the fuck up you insecure fuck.

>>11311120
>Why backwards?
Because then for [math]g\in L^1[/math] the convolution operator [math]\cdot \ast g[/math] is Wiener-Hopf on [math]L^2[/math] so its Fourier representation is Toeplitz, which is consistent with the "moving average" picture and yields many nice regularity results.

>>11311120
>why backwards
Commutativity.

Is the collineation group of PG(2,q) always PSL(3,q)? It looks like it is, but I can't find a book/article mentioning it, yet alone proving it.

>>11311793
That's not why it's backwards though. Any invariant measure commuting with translation will have commutative convolution; even the Dirichlet convolution [math]\chi\ast \chi'(g) = \sum_{hh'=g\in G}\chi(h)\chi(h')[/math] on the representation ring [math]R_\mathbb{C}(G)[/math] is commutative.

>>11311830
Any measure invariant under operations commuting with translations*

>>11311830
>even the dirichlet convolution
That's not a counterexample, tho. It's still backwards.
[math]h'=g-h[/math]

Can you solve Taleb's math problem?

>>11311748
>Literally everyone being pedantic towards me
>Mathfags are known for being pedantic towards emgineers
>"You pendantic fuck"

Please explain yourself.

>>11311642
>>11311666
Even if you were a meany towards me ill be your friend, you clearly need one.

>>11311814
what is PG(2,q)? the 2-dimensional projective plane with q points?

>>11311853
I went so absurdly hard on the abuse of notation in this one I'm starting to feel concerned that anon didn't get it and just assumed I am retarded.
Explicitly, we pretend (emphasis on the word pretend rather than assume) [math]h[/math] has an inverse.
Then [math]h'= h^{-1}g[/math]. Passing to additive notation for multiplication, we get [math]h'=-h+g[/math]
So the sum is over [math]\chi(h) \chi '(-h+g)[/math], which is "backwards", since the second h is negative.

>>11312075
You do know [math]G[/math] acts on itself freely so I can find another [math]h''[/math] so that [math]h(h'')^{-1} = g[/math] and that still won't change the summation right?

>>11311982
No, projective plane of order q, which has n^2+n+1 points.

>>11312079
>You do know G acts on itself freely
Yes.
>so I can find another h so that h(h)−1=g
Yes.
>that still won't change the summation right?
You lost me.

>>11312094
Read some character theory anon.

>>11312093
I meant q^2+q+1

what is the mathematical abstraction of time? i mean time is oftern used as an argument of a fuction. what if time is a function itself??

>>11312096
I'll reiterate. We assume [math]G[/math] is abelian. We make them move "forward" in the sense given here >>11312075
[math]\chi * \chi '(g) = \displaystyle \Sigma_{hh'=g} \chi(h) \chi'(h'^{-1}) = \Sigma _{hh'=g^{-1}} \chi(h^{-1}) \chi'(h') = \chi'* \chi(g^{-1})[/math]
If you make it stop going backwards, it stops commuting.

>>11311814
mh, why do you think so? intuitively, i feel the collineation group should be a cyclic group of order q^2+q+1, because every mapping that multiplies by a fixed nonzero element works and then you have to check which mappings leave a one dim subspace constant (which is q-1) so you have (q^3-1)/(q-1)=q^2+q+1.

Or stated differently, the group is isomorphic to the group F_q^3*/F_q*.

also who the fuck does finite geometry, are you fucking belgian?

>>11310919
To provide an actual answer, look into functional analysis, representation theory, and to a lesser extent model theory. A few key ideas here are "group representations", "automorphism groups", "permutation groups", and "slow theorems". Really its a huge area of math that has close connections to everything from boolean algebra and logic to quantum field theory. That being said, it is probably not an easy area of math to get into for a beginner, but functional analysis and representation theory are definitely fascinating. If you'd like to move in that direction and learn more about the subject, good waying to start would be with learning as much linear algebra and real analysis as possible. You want to be really comfortable with basic matrix operations, norms, metrics, inner products, continuity, compactness, orthogonality, eigenvalues, complex numbers, and subspaces. Plenty of other stuff too, but those are really the key concepts to get started.

>>11312139
>mh, why do you think so?
Wikipedia says for the fano plane it's PGL(3,2)=PSL(3,2), and the article "The collineation groups of the finite affine and projective planes with four lines through each point" says it's PSL(3,3) for PG(2,3).
>intuitively, i feel the collineation group should be a cyclic group of order q^2+q+1, because every mapping that multiplies by a fixed nonzero element works and then you have to check which mappings leave a one dim subspace constant (which is q-1) so you have (q^3-1)/(q-1)=q^2+q+1.
>Or stated differently, the group is isomorphic to the group F_q^3*/F_q*.
Wouldn't that be a subgroup of the collineation group? Namely the subgroup of dilatations? I think there are other collineations
>also who the fuck does finite geometry, are you fucking belgian?
Do belgians study finite geometry? Quite based if you ask me
I just study it in my own free time

>>11312203
i see, you are right. i think the general case is more complicated though, since you might have isomorphisms on F_q itself (the number can be computed easily of course) if q is not prime and since mappings do not commute you get semidirect products and not direct products. your idea might work for prime fields though. i dont know enough about finite geometry to have a good intuition for it desu and i dont have my stuff here (also i dont really like it that much). check hirschfelds book on finite geometry if you can, its v good.

>Do belgians study finite geometry?
yeah, ghent and brussels university are big in finite geometry (joseph thas is/was a big guy in finite geometry, and in a small country one guy often has a big impact).

>>11312254
OK I did a bit of research and you are right, PΓL ≅ PGL ⋊ Gal(K/k) where PΓL is the collineation group and k is the prime field of K.

>>11312128
Time isn't a function, it is a scalar whose purpose is to parameterize various physical phenomena.

>>11312390
>He doesn't know that time is a 1-form
Lol

>>11310872
There are no such things as “applied mathematicians” and “pure mathematicians”, only “mathematicians”.

is there a way to approximate a function with a shape like [math]e^{-at}sin^2(x)[/math], i.e. a sharp peak and then quick decay so it would look like a polynomial. without resorting to the taylor series. i think i knew a way to express it is a a fraction but i forgot.

>>11312128
Linear orders

>>11312681
Use Stone-Weierstrass. Sample some number of points of the graph and use polynomial interpolation.

>>11312681
train a deep neural network

I intuitively understand there's something wrong with Took's infinity-hat and the concept of basically "NUH UH"-ing addition to infinity until convenient, but I can't formally explain what's wrong
Can someone explain where exactly the contradiction/illegal operation shows up?

>>11312681
Spline interpolation?

>>11312681
gamma function

>>11310919

Algebraic Structures (Rings, Fields, Groups, Spaces, Lattices) and Operator Theory

>>11312538
t. csfag
>>11312784
go back

>>11312538
>There are no such things as “applied mathematicians” and “pure mathematicians”, only “mathematicians”.
But what about the mathematicians who only work on the applied?

>>11311666
RELAX SATAN

>>11311666
>tfw not even the Prince of Darkness wants to be your friend.

>>11312681
After graphing the function:
Split the function up at the zeroes, interpolate the in betweens with parabolas, and then glue the interpolations into a single function.

>>11311166
>>11311415

Depends how you see it. Surely one doesn't start with CT. But I've seen it used as a frame to present abstract algebra in a much cleaner way. Done alongside linear algebra (lightly and simply, like frosting on a cake), it prepares you for a lot more complex math, and in the end you're much better off with it than you would be without.

I've also found that category theory allows specialist mathematicians to gain what they need to learn other areas of mathematics much faster. It helps the transition from specialist to specialist+generalist is what I mean. The ones I saw take this approach really impressed me, and I'm trying to follow suit with moderate to good success.

But if you stick with the old classics like MacLane & Eilenberg, rather than the newer Applied Category Theory works one can now find, I definitely agree that CT looks and feels like "abstract nonsense". The field is maturing, and still has some maturing to do before you'll see it on Khan Academy or in Math for Dummies.

>>11313057
What about mathematicians who only applied to work?

>ex-gf is calling me to her house today
>i have an analysis test in 10 days and I don't know anything about it
Am i cursed? Why do these chances only appears in the worst possible times? Now I won't be able to decline her and I'll waste another day not studying analysis, fuck

Have a complementrary anime girl

>>11313593
>ignoring the reality that ex-gf is an ex for a fucking reason
>ex-gf over g(f(x))
>simping at the first beckon

I hope you fail your test and kys, retard

>>11313613
Bro, I don't wanna go, but I'm too weak, don't hope for my failure, I failed too much already.

>>11313629

>tfw when you know you're relapsing yet want to take a hit, and know you'll feel like shit after

What level is your analysis test, undergrad ? I'll answer any questions you have here today (that I can answer), nice and intuitionpilled, if you don't go.

Let a be a positive number. Then there exists exactly one natural number b such that b++ = a.

b++ is the Successor of b. Tao defined a positive number is a natural number that is not equal to 0. Btw this is the Peano Axioms from Tao's Analysis I.

I've tried applying induction on a, but it's only a vacuous truth on the base case(since if we let a = 0, this will be false by definition). On b, I was stucked in the inductive step, I tried where b will become b++, that is ((b++)++) = a.

>>11313804
>>>/sci/sqt
>>>/wsr/
>++
>>>/g/

>>11313822
I'm trying to do every exercise in the book, and I'm a CS major in a third world country with nonexistent math in the curriculum.

inb4: talking about mathematics only.
What's the difference between Fourier and Laplace transforms from the *mathematical* perspective? Why do they say that one is a "complex function of a real variable" and the other is a "complex function of a complex variable"? I know it has something to do with the ROC, but with FT we have F(w) and with LT it is L(b+jw). So? How should I think about it? F(w) can be thought of as a spectrum. But wtf is L(b+jw)? Can we have a "spectrum" of a Laplace transformed function?

>>11313998
https://www.youtube.com/watch?v=3gjJDuCAEQQ

>>11314025
thanks i have like 20 books and also watched a bunch of videos. i know a lot of facts but can't quite connect the dots. i will watch this one..

>lied to captcha about motorcycles again

>>11314025
btw this is amazing, right off the bat: they show a rectangular function and its transform: a sinc function. i tend to not think of the resulting FT transform as a "function". i usually think of it as a bunch of harmonics with amplitudes and phases that make up a signal. thats what they usually show you in non-math texts. an audio spectrum for example. and conversely, with the laplace transform, it is the opposite: they always give a table of basic functions and their transforms as a function.

>>11314041
>>lied to captcha about motorcycles again
based. FUCK silicon valley

What should I review if I'm taking differential geometry

>>11314168
depends on the kind of differential geometry, but if you're an undergrad then multivariable calculus and if you've taken it basic real analysis.

if this is not an undergrad course, why are you asking this, and also you should be reviewing your analysis and measure theory as well as some topology. if you've seen some manifolds look back at that too.

>>11314168
calculus and shitload of linear algebra

>>11314201

linear algebra is pretty easy it's the fuckulus that kills you

>>11314168
oh yeah i forgot about algebra
add to this >>11314183
- linear algebra if you're taking an undergrad class
- linear algebra, basic module theory, and any homology/cohomology you know if you're taking a grad class

>>11311127
Yeah it's almost like computers are a crutch now. Whenever we actually need to develop something we jump right to a computer to try and "solve" what we don't even understand. A great example of this is CFD which stands for "Color Fluid Dynamics."

>>11314276
schizo

Anyone used paid sites like brilliant.org?

>>11312681
bingo. i did it. [0,3] is all i need. do you know what method i used? i need to patent it. it is called brute force. just see what it is changing and what is not changing and add another variable to affect that change: up down stretch squash shift repeat. i need to publish an article about this. mathematics is basically an applied science.

>>11314168
Just sheaf theory.
https://www.springer.com/gp/book/9780792350064
"Our aim by this study is to exhibit and also exploit a quite general technique, yet simple, by its very nature, which enables one to formulate, at least, a substantial amount (if not all!) of the fundamental notions of the classical differential geometry of [math]C^{\infty}[/math] -manifolds and obtain too several standard results thereof. More interestingly, this can be achieved (we might say here, surprisingly enough!), by no use at all (!) of any concept of tangent vectors or of differential forms, in the classical sense of these words; indeed, no calculus is employed altogether!"

>>11313998
https://en.wikipedia.org/wiki/Paley%E2%80%93Wiener_theorem
>>11314610
I'm so proud of you for using Demos honey.

>>11310872
Why do "pure mathematicians" cope this hard?

>>11314646

Wow you know what a sheaf is! you're cool!!

>>11314785
i am not him and i am not into anime but why are you doing this? he is actually helping people and he is not causing any harm.

>announcing a report

>>11314794

> assumes it's graduate differential geometry just to namedrop sheaf theory with a retarded avatar

>>11314249
you’re retarded

>>11314785
>you can't even shitpost about grad subjects anymore without people thinking you're showing off

>>11314816
the only thing i assume is that you are angry and triggered for some reason.

>>11314794
No one is hurting anyone by breaking the rules retard. This website is about anonymity, so making yourself identifiable breaks that. It's a weak version of tripfagging.

>>11314839
well duh but why do you care? how does that affect you? what causes your anger?

>>11314839
>This website is about anonymity, so making yourself identifiable breaks that.

>assuming the axiom of powerset
shamefuru

>>11314976
once you post in the same thread for a while it is really easy to recognize the same posters by their style. i can easily match every post itt to the posters.

>>11314992
Which poster am I?

>>11315011
this: >>11314976

>>11315011
(you) are (you)rself
but in all honesty I feel the same as anon above.
You can more or less associate the posts with certain imaginary "personas" of anons, given enough exposure.

>>11314992
Who am I, lad?

>>11314879
>>11314976
Been a while since I've seen this type of trolling. Still cancer though.

>>11314785
>[Deleted]
besedo modo

I don't like it when other people do mathematics. I see them on youtube, and suddenly they are real people and that makes me feel uncomfortable for some reason. I honestly don't like most real people. So I don't like to think that people who I don't like, like the same things that I like. Urggh. It is very convoluted but basically describes all my hobbies and everything I like. Anime helps.

>>11315248
you probably have autism

>>11315248

Take it this way: reading the mathematics of mathematicians, who are also flawed human beings, is a supreme distillation, a crystallization of what's most interesting inside their minds. People who also like mathematics are just trying to attain the same capacity to distill their thought in a way which makes them more palatable as human beings. Their efforts are commendable, at least more so than most human beings, given that we all basically start out as apes.

Also: http://www.rdos.net/eng/Aspie-quiz.php

>>11315191
>Been a while since I've seen this type of trolling.
What trolling?

[math] (2^{\aleph_0} = \aleph_1) \lor (2^{\aleph_0} \neq \aleph_1) [/math]

How to prove?

>>11315656
LEM?

>>11315656
>How to prove?
What have you tried?

>>11315667
Well, so far I've used some forcing arguments to demonstrate that in ZF or ZFC, neither the left nor the right side can possibly be assigned as truth value.

>>11315666
Oh that's right, I suppose if you form the disjunction of two propositions A and not(A) that both provably have no truth value, then A or not(A) attains a truth value because LEM is self-evident.
Thanks, case closed!

>>11314992
bullshit

>>11315439
Defending tripfagging, namefagging and avatarfagging is inappropriate.
You can think that there isn't anything wrong with it, but it's still inappropriate to go out of your way to defend it and people who do it.
Not me, tho. I don't avatarfag, I just like posting cute Remimis.

Why does math immediately make me want to drink heavily? I’ve tried to understand it but it just infuriates me so much

>>11316004
There are 3 feelings related to maths. First you fearfully hate it, then you understand it and feel a little spike of joy (for a few seconds), and then you feel indifference.

>mg: comfy but cant understand much
>pg: can understand but not comfy

well at least something is salvageable in sci

>>11316088
please don't post pedo shit in /mg/, thanks

>>11316099
but that's literally just a drawing. dont tell me you live in brexit?

>>11316111
Its a drawing of an anime girl with neotenous features in an explicitly sexualized context. Fuck off.

>>11316111
>dont tell me you live in brexit?
Imagine not living in the UK.

>>11316113
>Its a drawing of an anime girl with neotenous features in an explicitly sexualized context. Fuck off.
back to redd*t

>>11310938
based uncle ted

>>11316088
>not comfy
It's comfy when there aren't any schizos/cranks shitting it up.

>>11316122
>if you don't meekly acquiesce to our degeneracy you're reddit
get fucked nigger

Can we talk about math? Stop shitposting. I can ask a math question. What question do you want me to ask?

>>11316230
ask what's the situation with mochizuki currently

>>11316230
ask for a good book on nonlinear analysis, anon

>>11316230
Ask if one can have coequalisers of functors.

>>11316221
>nigger
Why the racism?

>>11315656
Let me see, now im completely retarded so dont take my word for it.

> Note that [math]2^{\aleph_0} = \mathcal{P}(\mathbb{R}) = \aleph_1[/math] (this is what you need to prove, i know, but recognizing you can pull R out of your ass might be helpful)
>Propose a function that is 1-1 and onto from [math]\mathbb{R}[/math] to [math]\mathcal{P}(\mathbb{R})[/math]
>[math]\square[/math]

Now i know very little about this, im just saying shit because I like how TeX looks on 4chan, almost an oxymoron.

>>11316230
Ask about what one should review in preparation for a graduate course in differential geometry.

Hey anons, new in this thread, never posted here. I was just wondering what's the situation with mochizuki currently? Was his theory debunked as a hoax? Does anyone understand it? Is he a great mathematician or a confused autist? What is a Hodge theather? I only know hodge podge.

>>11316260
Assuming GCH, P(R) would be aleph_2. Now you are telling him to prove the continuum hypothesis.

Can anyone recommend a good book on nonlinear analysis? Asking for a friend.

Can functors have coequalizers? .

>>11316272
Who knows?
>>11316275
No.
>>11316284
Perhaps.

what's up lads, what one should review in preparing for a graduate course in differential geometry?

kek, based asker anon

>>11316288
Linear algebra, differential equations and topology.

>>11316272
>I was just wondering what's the situation with mochizuki currently? Was his theory debunked as a hoax? Does anyone understand it?
Basically, Scholze and Stix have a profound ignorance of the elementary theory of heights, at the advanced undergraduate/beginning graduate level.

>>11316274
Jesus fuck I meant [math]\mathcal{N} (\mathbb{R})[/math] not the powersets of R, minor brain fart, my bad.

>>11316288
Sheaf theory.
>>11316300
He said "graduate."

>>11316253
>racism
Why the niggatry?

>>11312796
I knew no one here could answer this question

>>11316288
Your life decisions

Am I doing this correctly? Suppose I have an associative unital [math]k[/math]-algebra [math]A[/math], augmented by [math]\varepsilon \colon A \to k[/math]. If I want to take the classifying construction, I will first split the algebra into two parts: [math]A \cong I \oplus k[/math], where [math]I[/math] is the augmentation ideal. Then I divide the field [math]k[/math] out and get only that [math]I[/math], which I then move one layer upwards with the suspension [math]s[/math]. Finally, I have [math]B(A) = \sum\limits_{n \ge 0} I^{n \otimes}[/math] as my classifying construction for the algebra.

Now, suppose this [math]B(A)[/math] is simply connected. Then I would have [math]B(A)_1 \cong k[/math], but I also have [math]B(A)_1 = I[/math], so what I would be getting is [math]B(A)_n = I^{n \otimes} \cong k \otimes_k k \otimes_k \cdots \otimes_k k \cong k[/math] for each [math]n \ge 0[/math], and so the whole thing would just be a sum of copies of the field. Can this be correct?

>>11316438
I can read.

>>11316274
>Assuming GCH
This trivializes any further statement.

>>11316272
>I was just wondering what's the situation with mochizuki currently?
It has been confirmed as truth via divine revelation. We will need to wait for a decade at the very least before a subhuman Westerner begins to even come close to penetrating the divine truths hidden within his texts.

>>11316639
>Now, suppose this [math]B(A)[/math] is simply connected.
Contradiction.

>>11316088
Fuck off pedo

>>11317194
Why?

>>11317244
He's saying that, if assuming it's simply connected implies both of those, by contradiction it isn't simply connected.

>>11317247
>both of those
Both of what? I don't quite follow.

I hate most youtube videos so much. For example search for "complex frequency" and half of them will be about e^iwt+theta and the other half will be about e^-s. But the former is just a sloppy notation for e^i(wt+teta) = e^iθ e^iwt so it is a CONSTANT complex multiplier which is just the initial phase. That stuff comes up in simple 1st order DE when sinusoids are converted to the euler. However e^-s is a totally different context. And it is actually e^-(b+iw)t : notice NOTICE that ``i'' is INSIDE the parentheses and ``t'' is OUTSIDE so it is really e^(-bt) e^(-iwt) which means is a REAL-valued function of time, it is an AMPLITUDE not some lowly phase. So we are no longer on the unit circle: it is a fucking exponential decay (or growth). And we have 4 dimensions: 2 in 2 out. But we can plot in 3d or use colors, and combine the 2 outputs into a single magnitude value. God this confused me so fucking much but not anymore. Math is all like that. It is not hard it is just confusing. Notation is bad, teachers are bad. If you don't want to help yourself nobody will. Remember you pay 20k+ a year to those motherfuckers and you have to use youtube cause your profs suck? Make sure to BUG them after lectures instead, until you understand whats going on. Or tell your dad he will beat them up.

>>11317247
>He's saying
Please do not just assume that.

>>11316272
Mochizuki's "proof" of ABC is an elaborately crafted failure.

>>11317194
Could somebody tell me what the contradiction here is?

Can I remove a square root from both sides of an equations with no questions asked?
I want you to be very pedantic

>>11317625
yes you are squaring both sides

>>11315783
>I just like posting cute Remimis
and by posting 2hu here we protect yukarifag from getting b& as (s)he won't stand out so much.
not advocating or encouraging, just stating straight facts

>>11317625
the equation reads like
root(a) = root(b) = x

multiply both sides by x, but choose conveniently:

root(a)x = root(b)x
root(a)root(a) = root(b)root(b)
a = b

>>11317670
thanks, exactly what i was looking for.

is there a fast way to prove a map is a right or left quillen functor in a quillen adjunction?

It would be nice to avoid slogging through the "preserves fibrations/etc." definition

>>11317653
>straight
Yukari poster is a fat Chinese gay guy.

>>11312796
not a complex number. riemann looks for complex number roots.
>>11316567
never post here again

>>11317830
Proof?

>>11315656
>ℵ
Not maths. Try the Hebrew thread over at >>>/int/.

>algebra: 96/100
>calculus: 88/100
>geometry: 24/100
>statistics: 53/100
why am i so retarded with anything that isn't numbers? literally just a simple rotation of a shape throws my entire focus and mind into the abyss

>>11318175
hormone levels

>>11318175
>claims to be good at algebra
>can't into rotation
hm

>>11318175
what is "algebra?" basic group, ring, and field theory?

>>11311026
I fucking hate 4 vector notation.

>>11316438
You are far too hopeful regarding the standards of graduate school anywhere.

>>11318189
you don't physically rotate anything in algebra. it is about numbers not shapes.

>>11318364
[math] n : \mathbb{N} \to \mathbb{N} \in \mathbb{N} [/math]
numbers are functions that deform a line bro.
even without going into group theory examples, algebra is all about composition in closed systems, which in turn models (in particuilar) rotations excellently.

>Work my ass off in Algebraic Topology
>Go to all the lectures and most of the tutorials
>Study every day for a week and a half before the exam

>Don't try very hard in Algebraic Geometry
>Miss several lectures, don't go to a single tutorial
>Do one day of study before the exam

>Algebraic topology 83/100
>Algebraic geometry 86/100

>>11318390
too much info can be a liability, anone.

11318364
>you don't physically rotate anything in algebra.
>it is about numbers not shapes.

>>11318101
lel

>>11317765
If you have a pair of adjoint functors L and R, there are several equivalent ways of checking that they form a Quillen adjunction (e.g. R preserves fibrations and acyclic fibrations). For the adjunction part, you can use Freyd's theorem.

>>11318390
>algebraic topology
>use UCT, LES, and show something factors through the zero group
Wow so hard

>>11318836
>UCT
What was UCT again? My brain just translates it as "undergrad category theory."

Why do symmetric matrices have orthogonal eigenvectors? Is there any intuitive explanation? Is there any geometric interpretation of matrix symmetry or even matrix transpose?

>>11318930
i guess imagine you have a symmetric piece of rubber wood that you can stretch, say a perfects square and you try shearinng it or should i say stretching by pulling it by the opposite corners along the diagonals. first pull NW up and SE down, then sideways and the two lines that will not move will be your eigen vectors and they will be along the two perpendicular lines since it is perfectly symmetric.

>>11318836
We barely used UCT desu.
You forgot cup products, covering spaces, lifting theorems, and diagram chases though.

>>11318877
Universal Coefficient Theorem.

>>11310938
Absolutely brainlet take. I bet he's never even tried to step through a proof.

Why would all symmetric matrices contort the space the way you say? The symmetry is not along some line in the space but between the operation on the vector space and its dual.

>>11318959
He's a published mathematician.
https://homepages.rpi.edu/~bulloj/tjk/tjk.html

>>11318964
>>11318946

Forgot to link.

>>11318930
Symmetric matrices are basically one of those cases where the canonical Euclidean product is hidden and it looks like a geometric result is pulled out of a tophat. The other classic example is [math]df(g) = \langle grad f, g \rangle[/math].
You shouldn't think too hard on it. Just recall that being symmetric for one orthonormal basis doesn't imply that it's symmetric for any orthonormal basis.

>>11310938
entertainment is a worthwhile endeavor, it's called emotivism
https://en.wikipedia.org/wiki/Emotivism
https://en.wikipedia.org/wiki/After_Virtue

Would this be a good place to ask about how to improve on math? even if I'm pretty much basic tier.

>>11319016
Yes. Although some people might be rude to you.

>>11319016
well you take some open problem and start working from there

>>11319016
Here or /sqt/, people are probably less sassy on /sqt/

>>11318930
I have had to teach this stuff (duality, euclidean spaces, hermitian spaces..) two years in a row and nobody I know has any visual explanation for what the dual map, the adjoint map or the matrix transpose does.
Do not beat yourself up. Just remember the result and why symmetric matrices have orthogonal eigenspaces.

>>11314646
>https://www.springer.com/gp/book/9780792350064
STOP!
>>11314168
implicit function theorem, some linear algebra
DG is kind of weird for everyone in the beginning, don't let it scare you off.

>>11319016
At any stage, most improvement comes actually from playing around with things that you already know.
Learned how to differentiate? Try it on some weird functions, try asking yourself questions like "what can go wrong?"
Learned something more abstract, like triangulation in topology? Draw pictures of it, ask yourself about minimal triangulations, again "does a triangulation exist always/for some funky example?"

A surprisingly large part in math is getting a routine, but it's kind of more difficult to achive than in, say, programming.

>>11318930
Your question is about the othogonality? Instead of thinking about the matrix think about how it act on the vectors. If you have two distinct eigenvectors of a symmetric matrix with distinct eigenvalues, if you suppose that they are not orthogonal, that would mean that you could strech the eigenvector by some value and then project it to the other eigenvector, or stretch the second eigenvector by another value and project it to the first one and get the same result. A matrix is a placeholder for a linear tranformation and so I believe the best way of optaining geometric data is to see how it acts on particual vectors or subspaces. Now as to the geometric interpretation of the spectral theorem, well that's kinda difficult, but I think to not get so confused you should look at how the operator defines invariant subspaces.

>>11316288
high school calculus

>>11317537
Is the contradiction the fact that we have a zero morphism [math]I \to k[/math], but if [math]I=k[/math], then we would want that to be unital?

Lads, the plan didn't work.
https://archive.4plebs.org/adv/thread/21803219/#q21803219

>>11318959
lmao

>>11318997
/sci/ already hates philosophy. Posting shitty and completely incorrect philosophy is not helping

>>11320204
Rightfully so. It's metaphyiscs or gtfo to >>>/toy/ and >>>/lit/.

>>11310872
I just finished a study of homology theory and I guess it lives up to it's name
It's pretty gay

The fact that you could literally call it the study of holes kinda reinforces it

Okay so I'm stuck, i can not prove that the sum from k =0 to p-n of combination(p-k-2, n-1) is equal to combination(p-1, n). I thinks it's trivial but i'm stuck.

Im going to write my Bachelor's thesis next semester and I still didn't really get what I'm actually supposed to do.
My prof gave me a book and I read/skimmed it. Now it seems like the task is to "independently reproduce it with your own words" but how stupid is that, am I just going to end up modifying things slightly and then adding them to my Latex? What's the point here?
>add examples and explain things
The book explains most things quite thoroughly already and adding examples cant be everything.
Besides the content of the book doesnt go particularly deep in one direction but gives an overview over several methods.
I could try to come up with variations of these methods and show some shit but doing somwthing original is also not usually what you are expected to do, as I understood.
There are a few open problems in the book or things thst could be generalized.
Basically generaliting to higher dimensions or reducing regularity requirements. I guess I could try to do that?

>>11319454
Improvement in one’s computational abilities comes from computing, improvement in proof construction comes from reading and writing proofs, improvement in understanding comes from knowing and analyzing definitions and theorems, improvement and intuition comes to those who need to do none of the above and already possess intuition

>>11320422
>the task is to "independently reproduce it with your own words"
This is literally what everyone does when starting a new project. You need to thoroughly understand the subject in order to add anything to it, the only difference is how quickly you do it, and that only comes with time and practice.
Just count yourself lucky that you don't also need to make sure your supervisor thoroughly understands your stuff either.

>>11316284
yes. the category of small/ locally small categories is cocomplete

>>11320422
My thesis will be literally "filling the gaps" of another obscure article. Just try to fill gaps you think an average BS wouldn't get instantly and do everything as rigorous as you can. They are expecting you to show you can write and understand math at a high level.

>>11320422
I've never heard of a Ba thesis being done this way before but my intuition says if you have an interest in the subject, try to do the reproducing thing at an accelerated pace so you have time left over for your own personal additions and generalizations. It doesn't matter if you can't complete your additions to the fullest, just mentioning "this or that is possible if you continue working in this direction" is good too

>>11320429
Exept of the last part I agree.
>intuition comes to those who need to do none of the above and already possess intuition
No. Just no. Natural intuition exists, usually you are either better in discrete or spatial things. But even with intuition you need to improve on arithmetics, proof theory, and "picturing" stuff. Noone has this just like that. Or maybe I just haven't met one like thatduring my 6 years studies and 7 years postgrad/postdoc experience.

What do you negroes consider a good layout for your articles, assuming you are actually working in research?
I'm especially torn between 10p and 12p font size, since with 10p everything is easier to read imo but when long calculations are involved it usually looks fucky. Or the paper simply becomes too long. Help.

>>11320925
>dude Latex's standard formatting lmao

Just noticed that the improved Euler method (average of two points) gives the exact solution for a quadratic function dy/dx = 2x. How do I prove this? The degree of the polynomial is how many points we need to kill the truncation error? Why do the game engines push the Runge Kutta method so hard if the highest derivative you'd ever need from the engine is acceleration so the 2 point euler would be enough ??

>>11320925
>>11320935
who are you quoting?
Last I remember it is not even possible in some packages to use anything other than 10p or you'd need some kind of extension (I forget) so I had to use \big or \humongous or whatever.

>>11320944
What? 12p works fine in in the article class. Not sure about other sizes.

>>11320941
ah so taylor expansion, yes? since it is quadratic,
O(3) is zero, yes?

>>11320941
>how do I prove it
What have you tried?
Actually, have you even tried anything? Surely you've at least plugged in the definition and checked.

>>11320965
I tried this: >>11320953
that's the truncation error is determined right? for x^2 we only have first two terms of the taylor series so it is exact?

>>11321008
Listen anon, this is the one time I'll hold your hand through this.
[math]\frac{(x+a)^2-x^2}{2a}+ \frac{x^2-(x-a)^2}{2a}=2x[/math]

>>11321016
Ah, thank you senpai sama kun. I see why you said use the definition. I've only seen the explanation of truncation errors via the Taylor series: global + local, where local truncation error would be something like h^2/2 y"(0) but the second derivative is zero so we are not really truncating anything.

>>11320925
11p, double column, alpha citations.

>>11318946
>>11318964
>>11318985
>>11319409
>>11319448
>>11319564
brain dead and perpetually disappointing
>>11320909
I was being facetious about the last thing anon

>>11320422
sounds exactly like the Ba thesis in my uni -- turns out "independently reproducing" a given subject is a great way to understand it and it definitely doesn't amount to a bunch of copy-pasting. You need to compare various sources and as >>11320686 says, write it down with the required rigor. It's essentially a expository paper; an exercise in writing mathematics. For examples of what your work might look like look up REU papers or read some of Keith Conrad's blurbs. https://kconrad.math.uconn.edu/blurbs/
>>11320039
>Half this board at any given time tends to be "hey guys should I get a STEM degree I heard it was an easy career where literally everyone is making millions of dollars, also I have no interest in STEM nor do I care for it"
truer words have never been spoken

>>11321222
>double column
I'd rather split the tip of my benis with the sharp edge of one of my papers before doing this. I'm from the DG lands, meaning that formulas are very long.
>11pt
Hm, just tested this and it looks easier to "digest". Honestly thought that 11pt didn't work for some reason a few years back, but maybe I just used a different document class back then...
>alpha citations
Makes me wonder why I didn't already use that. Thanks!

>>11320039
>faggots
*blushes* yikes do you really use words like this, junko?

>>11318390
it's clearly banana^grape/hotdog squared

>be me
>math major undergraduate sophomore
>considering graduate school
>look into research opportunities at my university
>email a professor I’ve heard of to see if he has any available
>visited him today in his office, tell him my situation
>talking Calculus 2 and it’s way to mundane
>he recommends this book to me
What am I in for?

>>11321342
>What am I in for?
Why don't you read it and find out?

>>11321321
It's actually the graded ring hamburger[math][\alpha]/(\alpha^{n+1}) where [math] |\alpha| = 1 [/math]. Most of the information in the image is redundant.

>got called a racist for calling them Hindu numerals instead of Arabic numerals

If instead of asking the measure to be locally finite we ask for it to be finite on compact subsets, could we construct an infinite dimensional lebsegue measure?

>>11320683
Very good, very good.

>>11321342
>calc 2
>sophomore

>>11321575
probably haar measure or something

>>11312185
Sylow Theory.

>mfw old professor contacts me to help him with research despite the fact that I gave up mathematics a year ago because I couldn't cut it and I'll never be good enough
I don't know what to do

Reminder: /mg/ absolutely cannot understand linear algebra, do not listen to explanations of linear algebra from /mg/, hide posts from /mg/ about linear algebra, forget everything /mg/ says about linear algebra you will grow stronger from doing so I promise you

>>11322524
too useful for mathlets to appreciate

What are the algebraic prerequisites for grad level real analysis at the level of Rudin, Folland, etc.?

I know a bit of algebra but not enough to where it would constitute a whole grad level class.

>>11322524
To be fair, you need to be really autistic to learn enough about topological vector spaces, Hilbert spaces and modules, and then use the acquired experience to perfectly split up the algebraic, topological and geometric data associated to problems in linear algebra, and figure out that symmetric(equal to transpose) matrices are self-adjoint in the canonical Euclidean product by sheer coincidence, and that self-adjoint matrices have orthogonal eigenvalues by basic geometric properties.

>>11322582
really just linear algebra

>>11310938
Ted btfos /sci/ without internet access, think about that

>>11311909
You should probably break that sigma up into 3 sigmas, one for each variable, but I can't solve it past that without paper and pen

I was fucking around with operators last week and I found pic related. I don't have a proof, but if you work it out for arbitrary polynomials you can see that it's true. Are there any other fun uses of the differential operator like this?

>>11322691
Look up functional calculus.

>>11314779
>>11312538
this

>>11322691
tthis is rather straight forward anon. works for analytic functions at the very least

>>11318959
you can literally automate proofs, the definitions are just programs with bool type variables

>>11322766
I'm admittedly having trouble reading that anon

>>11322714
Will do, thanks

>>11311026
suck my dick physicist

>>11322769
do it yourself. remember binomial theorem.

>>11322776
No I mean I can't read what you wrote, I'm partially color blind

>>11311139
based
>>11311106
>>11311609
cringe tranny

>>11322780
o shit! sorry anon, i will redraw the proof on white background when i get home

>23 posts in my absence
why would you do something like that?

>>11322953
because you're a party pooper

>it's immediate that

>>11323004
>it's an obvious consequence

>>11323004
>>11323020
Lmao seeth more brainlets

>>11323021
>t. mr. no-fun-allowed

>>11323027
exactly. proof is trivial and left as an exercise for the reader

>>11322769
>>11322888
hhere sorry. i will remember to write on white bg next time

>>11323080
Those )( looking things are x's right? And there are no lowercase d's? Sorry for being autistic I just have trouble with handwriting

>mfw my posterior ring is isomorphic to your dick

>>11322691
>>11323080
As a side note, try to apply the operator(as a taylor series) to smooth functions of compact support.https://en.wikipedia.org/wiki/Bump_function This will kinda motivate operator theory and the spectral theory ala modern functional analysis.

>>11323090
those are just a's but i just have bad righting and yes they )( things are x's
>>11323122
you are saying to try to apply the operator to those functions you mention transformed into taylor series?

>>11323104
you have the entire board

Dear lad who usually makes these threads.
My bad for taking over for the last two ones. I instinctively knew the frog thread would degenerate at light speed, and I was afraid of people getting comfy in it.
This one was the remainders of my paranoia.
I'll proceed to leave it to you.
Yours truthfully, anon.

>>11323198
Bump functions are not analytic so that will obviously get you weird results. I mean to try and apply [math]e^D[/math] defined as a taylor series to such functions.

If a sinusoid can be approximated by taylor series, why cant we represent a complex function as a sum of sinusoids and then expand each of them into taylor series? can we then take another FFT of each term of the taylor series, and so forth? is it a cyclic process?

>>11323258
Why do you think you can't?

>>11323261
cause nobody does that. but a cyclic decomposition would be fun. what i don't if it will eventually degenerate or we can literally run forever given the right input: FFT->Taylor->FFT->Taylor

>>11323277
If I understand you correctly, you are just changing the representation of functions inside already well defined representations of functions, so I don't see any problem. Now, you have to understand that fourier decomposition is tricky and what it means for the series to converge will not allow you to manipulate the expression however you want.

>>11323249
I will do that in a second

>>11323309
>fourier decomposition is tricky
I don't see a problem with the convergence of e^-x multiplied by a polynomial. There shouldn't be anything tricky. Afaik FFT is done on polynomials all the time to multiply their point-value representations. I bet at least 10 such transforms have been performed across the globe as I was typing this text.
So what I mean is let's say you have a complex input that contains lots of harmonics, say a square pulse. You do an FFT and get a bunch of cosines. Then you decompose each of them into their taylor series: 1 - x^2/2! + x^4/4! etc. with some truncation errors. Of course they will still represent the cosines but in a polynomial form. Then I don't see a problem with applying a bunch of fourier transforms on these polynomials, but I see now how it gets boring. We will just cycle between two different representations of a bunch of cosines. However they might degenerate into something screwy due to the repeated truncation errors. I need to try that.

>>11310872
What is unequivocally and unironically the most ónions thing one could study in maths? By "study" I mean the thing you answer the question "what is your main interest?" with.

>>11323377
Actually I thought if I deliberately truncate the taylor series for cosine to 3-4 terms, they will end up as distorted cosines due to a huge truncation error. And doing an FFT on that lame cosine will result in extra harmonics, right? See where I am getting with that? It might create a spurious, uncontrollable growth of harmonics and eventual demise of the universe.

>>11323249
>>11323362
I found this relationship but I don't know if it really helps me

>>11322344
Go for it man. What's the worst that could happen?

>>11323377
>>11323388
There's no problem with just applying it, but I don't know if you also want to see if these iterated transformations make a good approximation of the original function in a pointwise way. Taylor series of trig functions converge uniformly , but even the most basic polynomials have "edge effects" as you have to force them to be periodic and so their fourier representation will have many points of non convergence where the gibbs phenomenon arises. Obviously you can still just take the series to converge in an [math]L^2[/math] sense, and so it is a valid representation, but it seems you will have poor convergece properties.

Is it normal to find proofs in maths books to appear as if they were pulled out of someone's arse? I have started reading those books only recently, and I find myself going back and fourth until I finally, at last, realise what's going on and why the author might have done something he did.

NOVO FIO, RAPAZES?

>>11323431
the proofs that are presented to you in books are a product of many iterations upon the core idea, which may lead to a proof that seems extremely arbitrary. I've mostly encountered this in analysis myself.

>>11323398
I think I was not clear with the motivation of the exercise. Instead if applying and finding a general formula, try out with particular values. As the functions are non analyitc, try on those values where the taylor expansion fails to converge.

>>11323403
Yeah I also have to keep in mind that the taylor approximation is local so I have to choose the limits carefully.
>gibbs phenomenon arises.
Thats not a concern. Since I mentioned I'd start with a square pulse, it obviously suffers from the gibbs disease right off the bat, but thats ok.

>>11323743
The taylor approximation of the cos and sin functions will be actually nice though, my point was that the problem was with the fourier representation of the polynomials as each of them will add to some gibbs noise and at different points.

>>11323437
Yes, I am reading about analysis precisely!

why

new thread
>>11323486
new thread
>>11323486

>>11311449
>an applied math masters on systems and signals or an applied math phd on systems and signals.
this sounds cool