/mg/ - maths general

[Anonymous No.10747924]

Previously >>10737655 , Operator Algebras edition.
Talk maths.

[Anonymous No.10747983]

>>10747924
>operator algebras
finally, a way to unite the analyst and the algebraists

[Anonymous No.10748076]

I have these two books. Are they any good?

[Anonymous No.10748087]

I don't understand, do different states use different textbooks in school in USA?

In sweden all schools I've taught in use the same books

[Anonymous No.10748090]

>>10748076
do you want to use them for self-study or along a course? I think they are more apt for the second.

[Anonymous No.10748107]

>>10748090
Self-study.

[Anonymous No.10748119]

stop asking "is this book good".
all these books are literally the same, they contain the definitions and some basic proofs

[Anonymous No.10748130]

>textbooks

All undergradute math is immediate and trivial, if you can't derive it by yourself you're never gonna make it anyways.

[Anonymous No.10748132]

>>10748076
>>10748087
>I
>I've
Mathematicians use "we" and "we've."

[Anonymous No.10748194]

>>10748132
We am not mathematicians

[Anonymous No.10748353]

>>10748132
Do you mean writing proofs?

[Anonymous No.10748465]

>>10748353
Do you?

[Anonymous No.10748497]

>>10748076
>Are they any good?
Why don't you read them and find out?

[Anonymous No.10748502]

Threadly reminder to work with physicists.

[Anonymous No.10748589]

What's a vertex operator algebra?

[Anonymous No.10748824]

>>10748132
Why do people keep making this unfunny joke?

[Anonymous No.10748831]

>>10748132
>all mathematicians are schizos
This explains everything.

[Anonymous No.10749018]

>>10748497
Yeah, that's a practical thing to do.

[Anonymous No.10749032]

Why are publishers so shitty?

Every Springer textbook we buy seems to have been printed as cheaply as possible (because it is). The binding is always fucked, the spine always splits etc. It's just so frustrating to spend 30£+ on textbooks and then they're absolute turd quality. We'd like to stop buying Springer but there's too much good stuff they publish.
Other publisher tiers: Cambridge University Press are OK. The London Math. Soc. texts they print are nice. Best are Princeton University Press, who are cheap and use string binding.
Also why is it absolutely impossible to find a reasonably priced copy of Munkres - Topology that isn't a pajeet edition?

[Anonymous No.10749233]

>>10749032
We recently bought a rather expensive Springer book and we thought it was quite nice. It was decently printed and had a nice hardcover.
It was 50 Eurobucks and we bought it for fun, instead of printing it ourselves, but the price was literally robbery.

[Anonymous No.10749457]

>>10749233
I buy cheap toner on eBay. Fuck buying books.
50 EUR and you could have bought a cheap b/n laster printer.

[Anonymous No.10749603]

>>10749018
No, it isn't.
>>10748824
I'm not joking, am I?

[Anonymous No.10749618]

>>10749457
I once did the calculation. It was like 13 books per toner cartridge on average, but I'm so addicted to libgen now that I routinely get 20+ books for every topic I'm interested in.

[Anonymous No.10749638]

How many of the 2^(n^2) n by n square matrices with entries in GF(2) are solvable?

[Anonymous No.10749650]

>>10749638
>solvable
what do you mean by this? do you mean invertible?

[Anonymous No.10749658]

>>10749650

Yes

[Anonymous No.10749686]

>>10749638
>>10749658
alright.
it's going to be [math](2^n - 1)(2^n - 2)\cdots (2^n - 2^{n-1})[/math].
We need all the columns to be linearly independent, yes? So for the first column, we have 2^n - 1 choices, because we can pick any vector besides 0. Now there are 2 vectors in the span of the first column, the vector itself and 0. So there are 2^n - 2 choices for the second column. Now there will be 4 vectors in the span of the first two columns, because we can take coefficients 0,0; 0,1; 1,0; or 1,1. (each gives rise to a new vector thanks to linear independence implies uniqueness of linear combinations). So now there are 2^n - 4 choices for the third column.
See how this works?

[Anonymous No.10749688]

>>10749638
>>10749686
If it's not already clear, a simple argument works for matrices over any finite field.

[Anonymous No.10749693]

>>10749688
>simple
I meant to say *similar.

[Anonymous No.10750207]

why is math full of fags

[Anonymous No.10750213]

>>10750207
Why not?

[Anonymous No.10750236]

>>10750207
Because math is full of the elitist spergs who think memorizing pi decimals will make them superior and give them magical powers.

[Anonymous No.10750243]

>>10750207
>fags
Why the homophobia?

[Anonymous No.10750287]

>>10750207
trannies go to compsci and high test men go to engineering

[Anonymous No.10750359]

>>10749032
yeah ever since Springer was bought over by EQT V they went to shit with print-on-demand texts and all, not surprised if other publishers slowly begin following suit (if not already); though AMS is still comfy smyth-sewn binded (for now); also I absolutely love the binding on Princeton University press' Gravitation (Misner-Thorne-Wheeler) with its flexible spine

for the Springer texts I've taken to cheap chink editions since nowadays their binding is more or less the same quality as the Springer softcover prints but cheaper; they're basically the same just with some chinese words on the cover for like 10$; what a world

[Anonymous No.10750548]

>>10749032
It's funny that you use pounds since I've actually had substantially better luck with Springer texts if I buy them from Britain (or sometimes Europe too).
Amazon.co.uk is generally print-on-demand trash (even still; they're substantially better than Amazon.ca. I don't even order books from here anymore, they're always literally unusable junk, more than half of the books I ever received had egregious printing errors like random pages printed at a 30 degree slant, double-printed text, backwards/upside-down pages, or just pages that were entirely blank in the middle of the book), but the last GTM that I bought from the Book Depository about two months ago is a real hardback with a sewn binding and professionally printed pages. Blackwell's is generally good for Springer books too.
The best option is to buy from reputable used sellers though if possible, since you'll get a slightly older copy of the book and you're basically guaranteed it's not a garbage printing.

[Anonymous No.10750617]

>>10749233
Who was it printed by? A lot of the European ones we find are printed by Printforce NL. Their hardbacks are fairly solid but quite blurry printing.

>>10749457
The thing is, we own a nice a mono laser printer but just like owning books too much.

>>10750359
Where do you get the ching chong editions from?

>>10750548
I haven't bought anything at the Book Depository. Pic related is the copy of Tu's Differential Geometry I recently bought from Blackwells, some pages weren't even properly glued in.

[Anonymous No.10750734]

>>10750617
getting chink editions totally depends on your country since you get it from the chinese equivalents of amazon (taobao, tmall), it's kinda hard to buy reasonably priced in the US for example since you'd have to use some shipping agent or something

luckily it's much easier for me since i'm in singapore; or if you go to Beijing (the bookstores opposite their major universities have shelves full of all these math texts, see pic)

[Anonymous No.10750838]

>>10747924
Logic is a fictional mode.
I can't see numbers.
Fuck science and math.

[Anonymous No.10750863]

>>10750838
>fiction
Refer to >>>/lit/.

[Anonymous No.10750875]

>>10747924

Is there anyway to get someone to look over my proof and fix up the notation/language to make it publishable without someone calling me a dumbass?

[Anonymous No.10750880]

>>10750875
Yeah, post it right here.

[. No.10750949]

>>10750838
see >>10750863

[Anonymous No.10751038]

>>10749457
Yeah, I usually abuse my dads printer for that purpose, its quite a decent laser printer.

[Anonymous No.10751105]

I'm in mathematical physics, and I have two masters.
The first one is in pure math, with a focus on geometric analysis and applications to general relativity.
The second one is in theoretical physics, with an emphasis on QFT/ string theory.
Due to my subject behind " too theoretical/speculative" I don't have a phd funding for this year.
Since I want to keep busy and try next year in a more applied topic ( cosmology perhaps ), I need some help selecting textbooks to buy.
Do any of you know some books which offer an overview of qft/string theory, perferably with an emphasis on analysis ?
Something among the lines of the books Choquet-Bruhat has written.

[Anonymous No.10751118]

>>10751105
>I'm in mathematical physics
Cool. Refer to >>>/sci/eng/ or >>>/toy/ or >>>/lit/.

[Anonymous No.10751124]

>>10751105
>too theoretical/speculative
That's what usually happens when you work on fiction and attempt to pass it off as reality. See >>10750949

[Anonymous No.10751179]

>>10751105
>pure math
>geometric analysis and applications to general relativity

[Anonymous No.10751196]

>>10751179
>he doesn't know about minimal surfaces, yamabe problem, hyperbolic pde on lorentzian manifolds, conformal geometry and so on and so forth
Why is this board full of undergrads and schizos ?

[Anonymous No.10751199]

>>10751196
>minimal surfaces, yamabe problem, hyperbolic pde on lorentzian manifolds, conformal geometry
>pure math
see >>10751179 or >>10751118

[Anonymous No.10751211]

>>10751199
Well explain your point, I'm curious as to how this is not pure math. Define pure math, perhaps ?
That is, if you're able to. You sound like the guy who's barely passing calculus 1 or w/e it's called in murica.

[Anonymous No.10751213]

>>10751211
>Define
Try asking the guys over at >>>/lit/.

[Anonymous No.10751219]

>>10751211
>calculus 1
see >>10751199

[Anonymous No.10751240]

>>10748589
>>10751105
Yukarifag, do your thing.

[Anonymous No.10751303]

>>10747924
>maths
britbong pls

[Anonymous No.10751327]

>>10747924
Assuming I never got a high school education of math (because we had no teacher), what do I do?
The only thing I remember well was imaginary numbers.

What I'm wondering to is about note taking, how do I go about that? I have an iPad and a note taking app I use for things at work. Is there an actual good way to math notes or is it just based on your own stye of learning

[Anonymous No.10751502]

>>10751327
>High school math
>>>/sci/eng/

[Anonymous No.10751524]

>>10747924
Been watching Indian videos but I want to know the underlying principles behind stability theory in graph and control engineering. Anybody got some videos or online articles?

Bit of a brainlet (engineer) and I don't want to just follow some rules but want to understand better. All those Indians assume I already know the basis. Been a year since I had had any meaningful math in general.

[Anonymous No.10751532]

AAAAAAAAAAAAAAAAAA WHY IS /MG/ FULL OF FUCKING LINKS TO OTHER BOARDS!!!!!

[Anonymous No.10751536]

>>10751524
>control engineering
>engineer
see >>10751502

[Anonymous No.10751546]

>>10751524
I know it is entry level shit but I mean Lyapunov, La Salle, Cooperative control etc. Been out of the loop for a while and it's actually the last course before I graduate.

Some youtube lectures or powerpoints you guys know?
>>10751536
Those guys don't know shit sadly. professor is a mathematician as well so it is not really engineering heavy at all.

[Anonymous No.10751568]

>>10751546
the link thing is a meme, but so is control theory

[Anonymous No.10751593]

>>10751568
Classic

[Anonymous No.10751765]

Have any of you tried your hand at a problem from Kourovka Notebook of Group Theory?
How did it go?
I want to try something but there is no guidance as to what problems might be approachable at all.

[Anonymous No.10752063]

>>10751105
There are a few qft/string theory books for mathematicians like Folland's book on qft, the qft/string theory lecturers edited by Deligne, or Nash's differential topology and qft. If you want some more old school that goes heavy into the nitty gritty of functional analysis, then Reed-Simon's four volume text has you covered. In fact, Barry Simon has a number of books on qft from a more analytic perspective, so you may want to check those out as well.
>>10751327
>Assuming I never got a high school education of math
Khan academy
>>10751524
>Been watching Indian videos but I want to know the underlying principles behind stability theory in graph and control engineering
Are you referring to
https://www.youtube.com/watch?v=cJRlUGDtS-0&list=PLghJObT_RyfLmKRT86TquJhG6QuiHZ6Pi&index=24&t=0s
It seems pretty straightforward, what's the issue?

[Anonymous No.10752373]

>>10752063
Will Khan academy actually explain the processes in how it works?
I got a lot of "here's the fastest way to solve the problem, it doesn't matter if you understand why" in school because they try to condense six years into 2 years.

[Anonymous No.10752409]

>>10751524
>but I want to know the underlying principles behind stability theory in graph and control engineering
If you multiply a real number with itself repeatedly it blows up if it is larger than one, goes to zero if it smaller than one and if it is one it stays itself.
That is LITERALLY it.

[Anonymous No.10752447]

>>10751211
It's a shitpost by autistic algebraists.

[Anonymous No.10752486]

The logic holds. Be kind to yourself and you will never be lonely.

[Anonymous No.10752498]

>>10752373
>because they try to condense six years into 2 years
I'm gonna be brutally honest with you anon, most of the math you learn in k-12 is repeated over and over again. Every fucking year we returned to fractions again and again and somehow people still couldn't do them despite being able to take a derivative correctly. All that stuff you went over in those six years were likely filled with fluff and repetition. The real secret is just doing a lot of exercises and then you'll get it. Further you should be able to cover all the material in a fraction of the time and yes, he will explain things, though there really isn't very much to explain. I'd also recommend Paul's notes http://tutorial.math.lamar.edu/ for calc I-III.
>>10752486
You know, at first I wanted to be kind to myself, but then I realized I didn't deserve it. So now I'm trying to become good enough to love myself.

[Anonymous No.10752505]

>>10752373
read the first few chapters of Apostol or Spivak's Calculus, and if that is too much for you Basic Mathematics by Lang. They will prove the identities, properties and behavior of basic functions and the reals.

[Anonymous No.10752537]

>>10752486
If I were kind to myself, I would be a person which I hate far too much to ever call a friend.

[Anonymous No.10752538]

>>10751532
see >>10751118

[Anonymous No.10752541]

You're a piggot

[Anonymous No.10752548]

>>10750863
>>10750949
>>10751118
>>10751199
>>10751213
>>10751219
>>10751502
>>10751536
>>10751568

see >>10752541
see >>10752541

[Anonymous No.10752719]

almost forgot about the piggot meme

[Anonymous No.10752827]

>>10752537
Mathematicians use "we".

[Anonymous No.10753172]

>>10752486
>The logic holds.
See >>10750863

[Anonymous No.10753253]

>>10751211
>pure math
This is a meaningless notion.

[Anonymous No.10753272]

>>10750287
>high test men go to theoretical quantum physics
ftfy

[Anonymous No.10753356]

love prime numbers, hate analysis on the R

simple as'

[Anonymous No.10753366]

>>10751240
Thank you for paging.
>>10748589
A vertex operator algebra is the (abstract) operator algebra of a 2D conformal field theory, made concrete by the choice of an irreducible highest-weight representation by Verma modules. In general, it is an affine Lie algebra satisfying fusion and braiding relations encoded by the pentagon and hexagon equations.
>>10751105
I'm not a string theorist, but I found Baez's book to be very accessible when I was an undergrad.
>qft/string theory, perferably [sic] with an emphasis on analysis?
Personally I don't think the parts of string theory that are worth studying have much intersection with analysis. The geometry is beautiful, but modular invariance makes the whole theory extremely nice analytically speaking. Please refer to Friedan and Shenker's paper on the analytic geometry side of CFT, which lays the foundation for string theory.
Foundations of QFT on the other hand, has; you may wish to look up the Haag-Kastler program of constructive QFT and Zhou-Baez program of algebraic QFT. I recommend Velo and Wightman's conference proceedings on problems in guage theory and Strocchi's book on non-perturbative QFT.

[Anonymous No.10753553]

>>10753366
>but I found Baez's book to be very accessible when I was an undergrad.
Isn't the last portion of Baez's book a loop quantum gravity book? I guess it works for basic qft though

[Anonymous No.10753624]

>>10752063
Thanks for the recommendations anon. Folland and Nash seem to be a nice fit for what I want.
>>10753366
You're right in that most of the interesting math in string theory is algebra. In my (small) country, most people have switched to study geometric Langlands or other algebraic topics, without much string theory at all.
However I didn't know about Strocchi and it definitely looks right up my alley, thanks anon !

[Anonymous No.10753837]

>>10753356

[Anonymous No.10754343]

Doing FFTs on an arbitrary waveform in python, and I'm wanting to filter out unwanted high frequencies by applying a function and inverse FFTing it. Problem is, I can't just apply a normal filter like f0/(1j*f+f0) since it bodges up the second half of the FFT.
Should I bite the bullet and just write a function that FFTs my data just into the first half and scales it, and a complementary function that copies the first half and inverts the imaginary part before descaling it and taking the IFFT? Or is there some simple way of making a filter transfer function invert about an aribitrary vertical axis?
Sorry if this is more of a programming question.

Also does anyone have an intuitive explanation as to why I have 1st, 3rd, 5th, etc. harmonics, but no even numbered ones? What would even numbered harmonics entail?

[Anonymous No.10754352]

>>10754343
For reference, here's my input waveform (yes I did extrapolate it to have a continuous sampling rate).

[Anonymous No.10754384]

Just learned that multilinear algebra is a thing. Started learning about abstract algebra before I take linear algebra as a class in Sept., are there any helpful things I should learn that might come up in Abstract A?

[Anonymous No.10754447]

Hello /mg/,
Today I couldn't prove that for a non-constant polynomial [math] f(x) \in \mathbb{Z}[x] [/math], there are infinitely many primes [math] p [/math] which divide the set of values [math] f(n) ,\ n \in \mathbb{Z} [/math] so I had to look the solution up.
Thank you for coming to my Ted talk.

[Anonymous No.10754577]

>>10754343
>>10754352
Shh the autists here get angry at the sight of anything that requires human intuition.

[Anonymous No.10754601]

>>10754447
proof?

[Anonymous No.10754613]

I can't figure out how to prove that if A^{n-1} is not diagonalizable, but A^n is, then A is nilpotent. Any hints?

[Anonymous No.10754647]

>>10754613
>I can't figure out how to prove that if A^{n-1} is not diagonalizable, but A^n is, then A is nilpotent. Any hints?
What have you tried?

[Anonymous No.10754665]

>>10754613
I don’t think that’s right, consider:
[math]\begin{pmatrix}1 & 0 & 0 \\0 & 0 & 1 \\ 0 & 0 & 0\end{pmatrix}[/math]

[Anonymous No.10754671]

>>10754601
If the constant term is 0, then [math] f(x) = x g(x) [/math] for some g so that the [math] p | f(p) [/math] for all p. If f is not constant, let [math] f(x) = xg(x) + k[/math] for some non-0 constant k. Now suppose that only a finite number of primes [math] p_1, \cdots, p_N [/math] divide the values of f. Let [math] c [/math] be an integer and let [math] M = kc p_1 \cdots p_N [/math], then [math] f(M) = k(cp_1 \cdots p_N g(M) + 1) [/math]. For c sufficiently large the second factor is not +/-1 or 0 and none of the primes [math] p_i [/math] divide the second factor, so there must be a prime other than those which divides f(M).

[Anonymous No.10754677]

>>10754665
Sorry, I posted it incomplete. n is also the size of the square matrix. But your example does give me an idea of where to look at!

[Anonymous No.10754688]

>>10754677
Ah I see ! Well the answer to questions about eigenspaces is usually the Jordan normal form. It explains this one very well for example, but there is probably a less expensive proof

[Anonymous No.10754746]

OK. Anons, I did legitimately fucked up my education. In spite of the fact I'm about to graduate (one year left), I feel that I simply got through it by pure luck. It's not an impostor syndrome, because all the grades related to math were C, mostly (only Diff. Eq was B, but our course was dumbed down). I feel I don't even deserve the degree.
Is it possible to at least catch up? What should be the plan? How many hours does one spend on solving the math-related problems? I doubt that I'll be able to redeem myself, but at least I won't be a complete total fucking monkey.

[Anonymous No.10754845]

>>10754343
>in python
Ask >>>/g/.

[Anonymous No.10754914]

>>10754845
What about the last part of the question?

[Anonymous No.10754919]

>>10754914
I didn't even bother reading the rest. Ask on >>>/g/ if you want answers.

[Anonymous No.10754920]

>>10754919
then I'll repost it:
Does anyone have an intuitive explanation as to why I have 1st, 3rd, 5th, etc. harmonics, but no even numbered ones? What would even numbered harmonics entail?

[Anonymous No.10754934]

>>10754920
>I'll
Mathematicians use "we'll".

[Anonymous No.10754949]

>>10754934
This feels like the (more) retarded cousin of saying "they" instead of "he" or "she".

Anyhow I made custom functions and got a pretty good result, pic related is a 4Hz sharp cutoff filter. I'll share the code if anyone else cares and happens to use spyder for their calculations instead of something like matlab.

[Anonymous No.10754962]

>>10754949
>Anyhow I made custom functions and got a pretty good result
Refer to >>>/g/

[Anonymous No.10754965]

>>10754962
>he doesn't think fourier and filter design is on topic
Sorry, did I miss the Applied Math General?

[Anonymous No.10754971]

>>10754949
>>10754965
>I
Mathematicians use "we".

[Anonymous No.10754977]

>>10754920
>Does anyone have an intuitive explanation as to why I have 1st, 3rd, 5th, etc. harmonics, but no even numbered ones?
If [math] f [/math] has period [math] 2 \pi[/math] and [math] f(x + \pi) =-f(x)[/math], then [math] \int_0^{2 \pi} f(t) e^{i2kt } dt = \int_0^{ \pi} f(t) e^{i2kt } dt + \int_\pi^{ 2\pi} f(t) e^{i2kt } dt = \int_0^{ \pi} f(t) e^{i2kt } dt + \int_0^{ \pi} f(t + \pi) e^{i2k(t + \pi) } dt = 0 [/math]

[Anonymous No.10754985]

>>10754965
You did.

[Anonymous No.10754986]

>>10754965
Don't worry, this general is filled with seething retards and autists. There are a few good posters tho.
As for your question, perhaps post more details on what you did ? I'm not an expert in applied math, but a fourier transform ( whether it is FFT or not doesn't matter ) is decomposing the signal in a sum of sine and cosine waves, which have an obvious parity.
The fact that you have only odd order harmonics might indicate that you picked a not-so-arbitrary waveform, and, when you apply your filter, the resulting function has a specific parity.
Probably not the answer you're looking for, but hey, at least I'm not shitposting.

[Anonymous No.10754995]

>>10754343
> Should I bite the bullet and just write a function that FFTs my data just into the first half and scales it, and a complementary function that copies the first half and inverts the imaginary part before descaling it and taking the IFFT?
Just use a real FFT (e.g. np.fft.rfft and irfft). If you're using some other library which only has a generalised complex FFT, apply the filter to the first half and impose conjugate symmetry (X[N-k]=X[k]*) on the second half before performing the inverse transform.

> Or is there some simple way of making a filter transfer function invert about an aribitrary vertical axis?
A transfer function which maps reals to reals in the time domain will have H(-ζ)=H(ζ)*. For a DFT, H(N-n)=H(-n) => H(N-n)=H(n)*.

> Also does anyone have an intuitive explanation as to why I have 1st, 3rd, 5th, etc. harmonics, but no even numbered ones?
You get only odd harmonics if one half of the waveform is just the negation of the other half: f(t+T/2)=-f(t) where T is the period. The integrals of sin(n*t) over [0,π] and [π,2π] are 2/n and -2/n if n is odd but 0 and 0 if n is even. So any waveform consisting only of odd harmonics has that property. If you split the waveform into half cycles a,b and find p=(a+b)/2 and q=(a-b)/2, you have a=p+q and b=p+q=p+(-q), i.e. the original waveform is the sum of two waveforms [p:p]+[q:-q]. The first term is double the fundamental frequency so it contains only 2f,4f,6f,... terms, the latter matches the fundamental frequency and contains only odd harmonics.

[Anonymous No.10755015]

>>10754384
your thought process is so fucked i dont know where to begin

you're learning abstract algebra before linear algebra. this is already weird, although acceptable (and logically makes more sense, not pedagogically)
you want to learn helpful things that might come up in AA - you mean things from LA that might help AA, or things from AA that might help LA?

also multilinear algebra is just a fancy way of saying linear algebra with tensor products

[Anonymous No.10755017]

>>10755015
>you're learning ""abstract"" algebra before linear algebra.
As you should.
>not pedagogically
Only if you're a drooling retard with no imagination/intuition.

[Anonymous No.10755023]

>>10755015
>logically makes more sense
Refer to >>>/lit/.

[Anonymous No.10755028]

>>10754343
>>10754986
>>10754995
The engineering thread is over at >>>/sci/eng/.

[Anonymous No.10755037]

>>10754965
>fourier and filter design
see >>10755028

[Anonymous No.10755040]

Im so smart

Bourbaki is god

i would not be able to compute any example, let alone the trivial ones, because i only concentrate on the theory, which is the goal in and of itself

my theorem-proving ability extends as far as mindlessly pushing symbols and definitions allows me to

i would not be able to briefly explain the theory to a competent mathematician, because i myself dont understand it

[Anonymous No.10755042]

>>10754977
not intuitive enough for a brainlet, sorry

>>10754986
>The fact that you have only odd order harmonics might indicate that you picked a not-so-arbitrary waveform
I'll give a few other ones a go. good thing about what I've written is it makes it easy to turn any number of paired coordinates into a waveform.
My starting set being:
[[0, 0], [0.2111111, 1], [0.38888, 0.5], [0.4333, 1], [0.6232232323, 1], [1, 0]]

>>10754995
>numpy has rfft and irfft
Do those take in both the time and amplitude (or alternatively frequency and amplitude) as arguments? Because that's what I've just written, somewhat clumsily.

[Anonymous No.10755056]

>>10755040
>Bourbaki is god
Use >>>/lit/.

[Anonymous No.10755059]

>>10755040
>Bourbaki
Isn't that some kind of chocolate?

[Anonymous No.10755060]

>>10755040
>Im so smart
Mathematicians say "we are so intelligent".

[Anonymous No.10755066]

>>10755059
It's a God, apparently. Such ontological matters are best discussed at another board.

[Anonymous No.10755068]

>>10755042
>not intuitive enough
You're supposed to actually work through that and develop the intuition yourself. Or is even that too much to ask of a braindead engineer like you?

[Anonymous No.10755096]

>>10753366
get the fuck out you shitty toymaker
make your own general and do people's homework there

[Anonymous No.10755103]

>>10755068
Wait no I sort of get it. It's a bit unusual the way it's been split up but it makes sense for the most part. So the limiting condition is that the function can't be moved π out of phase and inverted and still give even harmonics?
Just tested a function without this property (as I'd been doing exactly that in my method to generate a waveform) and you're completely right. It seems though a symmetry about theta = π is indicative of even harmonics, which is interesting, I might add a function to invert the function in this way instead of the other.
I'll listen to these odd and even sounds and see what they sound like (based sounddevice).

[Anonymous No.10755123]

>>10755096
>fuck
>>>/pol/ >>>/reddit/
Mathematicians don't use foul language, especially not against Animeposters.

[Anonymous No.10755128]

>>10755123
>Animeposters
Mathematicians say "2huposters".

[Anonymous No.10755133]

>>10755128
2huposters are merely a dense subspace of Animeposters.

[Anonymous No.10755134]

>>10755103
No, the key-point is that the parity of the function ( waveform + filter ) you used is odd. It's what this anon >>10754995 said, and this is illustrated in the example of this anon >>10754977
The "theorem" you want is that the fourier transform of an odd function is odd, hence why you only get odd terms. The period of your waveform can be anything, it's irrelevant.
What you call the symmetry about theta is the parity of the function.

[Anonymous No.10755173]

>>10755134
I don't think I implied any dependance on the period, assuming π meant the fundamental harmonic in all instances. But yes parity is what I was getting at. It's been a while since I've touched the terms "even" and "odd" for curves so I was a bit hesitant.
They sound kinda boring, I'll have to take a look at synthesisers to see what waveforms they use.
Anyhow thanks for the help!

[Anonymous No.10755246]

>>10755133
Except that the space of animeposters is discrete, so animeposters are all 2huposters.

[Anonymous No.10755308]

>>10755246
>space of animeposters is discrete
Reference?

[Anonymous No.10755309]

>>10755308
Theorem 1: There are a finite number of animeposters.
Proof: the set of animeposters is contained in the set of people alive, which is finite.
From this it follows trivially.

[Anonymous No.10755320]

>>10755309
>the set of animeposters is contained in the set of people alive, which is finite.
LOL

[Anonymous No.10755330]

>>10755309
>set of people alive, which is finite.
Reference?

[Anonymous No.10755332]

Can someone redpill me on why Cambridge is the best university in the world for maths?

[Anonymous No.10755350]

>>10755332
>redpill
Refer to >>>/tv/ for movie discussions.

[Anonymous No.10755355]

>>10755330
Assume there originally existed n humans. Considering gestation to be 9 months, it's easy to prove that, for any finite amount of time, human population is bounded.
Otherwise, new humans would need to constantly spawn from apes, clots of blood, or some other such source. But that's trivially disproven by a short reference to Genesis in the Bible.

[Anonymous No.10755359]

PARALLEL SHIT BITCH DON'T GET LINED UP
SOSA IN HIS PRIME HUH?

[Anonymous No.10755398]

>>10755332
Based
I just finished second year at one of the small colleges here, where you at and how did you do?

[Anonymous No.10755518]

What's currently hot in geometry/topology? I'm looking to do a master's thesis in this direction

[Anonymous No.10755549]

>>10755359
Sorry, I don't listen to black people "music". What did you mean by that?

[Anonymous No.10755577]

Does anyone here use pari/gp on linux? It is saying it is up to date but I don't have any of the modular forms commands. Any help?

[Anonymous No.10755586]

>>10755549

that's because you are a hopeless square

[Anonymous No.10755641]

>>10754746
Usually relearning a subject is easier than learning it the first time. Try looking over some of the books you used before and see if it makes more sense now. Spend a couple hours each day making a dent reading and solving problems and you'll be able to relearn and solidify your base understanding of these topics.

[Anonymous No.10755805]

Suppose I have an electric and magnetic field. Do they have a common field extension?

[Anonymous No.10755878]

>>10755805
>Suppose I have an electric and magnetic field. Do they have a common field extension?
Yes, the electromagnetic field

[Anonymous No.10755883]

>>10755878
nice
is Galois?

[Anonymous No.10756064]

>>10755332
>tfw got sick and failed STEP
probably for the best i don't think i would've done very well there

has anyone got any recommendations for an abstract algebra text?
i've done courses in it during undergrad and want to go over it again
i'm not particularly interested in it for its own sake, but more as a support for other stuff e.g topology, geometry, PDEs, dynamical systems

[Anonymous No.10756532]

>>10756064
artin

[Anonymous No.10756550]

>>10756064
It really depends, but if you need a 600 Grad text for an entire year course, Grillet>Aluffi>Lang>Rotman tbqhwyf.

[Anonymous No.10756632]

>>10756550
>It really depends, but if you need a 600 Grad text for an entire year course, Grillet>Aluffi>Lang>Rotman tbqhwyf.
Lang is a meme.

[Anonymous No.10756634]

>>10755133
>2huposters are merely a dense subspace of Animeposters.
Dense subcategory, actually.

[Anonymous No.10756639]

>>10756632
Yeah, but Rotman is absolute dogshit, and those are the only four texts I know which cover what anon wants.

[Anonymous No.10756955]

it's literally impossible to make it without having jewish ancestry, their brains must look like the alps or a desert's dunes with huge ridges that form almost like a dinossaur's crest

[Anonymous No.10757085]

>>10755134
> The "theorem" you want is that the fourier transform of an odd function is odd
This is incorrect. The transform of an odd function is imaginary (i.e. is the sum of sin() terms with no phase shift), while the transform of an even function is real (i.e. is the sum of cos() terms with no phase shift).

However, if you "distort" a sine wave with a function f: f(sin(ωt+φ)), if f is odd then the Fourier transform only has odd harmonics, if f is even then it only has even harmonics. Most natural oscillators (e.g. musical instruments) generate waveforms with only odd harmonics. Even harmonics are characteristic of the distortion from electric guitar amplifiers.

The absence of even harmonics corresponds to a waveform where one half-cycle is the negation of the other: f(t+T/2)=-f(t). For an odd function, the half-cycle is mirrored both vertically and horizontally: f(t)=-f(-t) => f(T-t)=-f(t) => f((T/2-t)+T/2)=-f(t). If the half-cycle is itself symmetric (about π/2), then both properties apply: the function only has odd harmonics and the amplitudes are imaginary (sin() terms only).

[Anonymous No.10757172]

>>10756955
What? The "high IQ" only applies to the Ashkenazi Jews, other Jews are not very much different from other people of that area.
And, genetically speaking, Ashkenazi Jews are part Middle Eastern and part Central European upper class and those genetics are what is driving their science.

[Anonymous No.10757229]

>>10755332
Harvard is generally better (more talented kids there) but Cambridge is also top notch.

[Anonymous No.10757274]

>>10757085
>This is incorrect
If your function is complex, there is indeed an hermitian symmetry to consider on top of parity.
However, for a signal in the reals, the statement is correct.
>one half-cycle
>distort a sin wave
Your examples are basically using the property of the Fourier transform you claim is incorrect, but with the bullshit vocabulary of signal processing.

[Anonymous No.10757276]

>>10747924
Isn't math that glorified adition and subtraction field of study that people take too much seriously?

[Anonymous No.10757317]

>>10757276
Yes, the glorified field of adding and subtracting that makes literally every modern technology possible.

[Anonymous No.10757367]

>>10757317
> that makes literally every modern technology possible

I tought my computer was made in an industry using metal manipulation techniques

[Anonymous No.10757373]

>>10757276
Yes, addition and subtraction are the tennets of mathematics, and yes, it is completely solved. What is not completely solved (and is the subject of much research), is the inverse addition problem.

Say I have some number, and I add it to it self, it-self times, and then again. Then I add it to it self again 'a' times where a is some fixed number, and then I add to all that some other fixed number b.

When is this equal to some other number added to it self, it-self times?

Very hard question

[Anonymous No.10757400]

>>10757373
extremely based post

[Anonymous No.10757531]

In the entire history of mathematics, I am aware of there being three major impossibility proofs, the emergence of which coincided with and heralded major changes in the, sort of, general ideology of mathematics. These are: Greek incommensurability proof (author unknown), insolvability proof (Ruffini and Abel, although the latter's proof uses results from Cauchy's paper, which is directly based upon Ruffini's works, and is thus not independent of those) and Godel's proofs.

What I am interested in, is whether there were, throughout the entire history of mathematics, modern included, any other such impossibility proofs of the comparable, sort of a, magnitude, scale, effect.

[Anonymous No.10757536]

>>10757531
>Godel's proofs
>heralded major changes in the, sort of, general ideology of mathematics
>comparable, sort of a, magnitude, scale, effect
Seems like something you should post on >>>/lit/.

[Anonymous No.10757551]

>>10757367
>I tought my computer was made in an industry using metal manipulation techniques
Nah, there are uncountably many different steps and factories involved, every single one of them impossible without mathematics.

Metal manipulation techniques, among the others, rely on heavy use of mathematics, in pretty much any production step.

For just chip design at the very least you need, Boolean logic, linear Algebra, PDEs (both for thermodynamics and electricity) and so on, the list is practically endless.

[Anonymous No.10757552]

>>10757536
Nearly the entirety of, so called, "computer sciences" are based upon consequences from those proofs, as far as I gather (with Turing's and Church's works being direct follow-ups to Godel's to begin with)?
And the paradigmatic shift I meant was formalism -> constructivism (Brouwer's works weren't regarded all that seriously before Godel). That spme people prefer to engage in retrograding and to still follow in Hilbert's footsteps is, well, their own busyness.

[Anonymous No.10757594]

>>10757552
>computer sciences
>Turing's and Church's works
>Godel
Refer to >>>/g/ and >>>/lit/.

[Anonymous No.10757597]

>>10757551
>factories
>Metal manipulation techniques
Refer to >>>/diy/.

[Anonymous No.10757613]

>>10757531
I don't know if this counts as being within your domain, but I'd say the impossibility proof of solutions in the integers to [math]x^n+y^n=z^n[/math] for [math]n\geq 2[/math]. In fact, most of modern algebra/ring theory and algebraic number theory derives from Kummer's spotted error of Lamé's proof and subsequent developments by Dedekind et al.

[Anonymous No.10757614]

>mom! I did it again!!

[Anonymous No.10757617]

>>10757613
Thanks.

[Anonymous No.10757619]

>>10757613
>>10757617
of course, I meant n>2

[Anonymous No.10757621]

>work as a data scientist
>some code monkey walks by and starts making fun of the books on my desk
>picks up my nonlinear programming textbook and jokes about how I need a book to learn how to program
REEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

[Anonymous No.10757660]

>>10757621
>data (((scientist)))
>calling anyone a code monkey
>posting on a math general
>on /sci/

Fuck off to /g/

[Anonymous No.10757661]

>>10757621
>data scientist
What makes you think you're allowed in this thread?

[Anonymous No.10757670]

>>10757621
>nonlinear programming
>data scientist
>code monkey
>program
Refer to >>>>/g/.

[Anonymous No.10757676]

>>10747924
Recently, I've been studying the foundational crisis in mathematics during the early 20th century: the problems themselves and the men who developed problems, solved them, or- occasionally- both.
Good lord, that's a lot to unpackage. But it's incredibly rewarding self-study.

I've also been trying to keep abreast of recent novel techniques in topology. The mathematics of communications and networks is advancing at an absolutely amazing pace. But, as far as topology is concerned, I've really got to crack open the old textbooks and get down to brass tacks.

Anyway, what are some of your favorite contemporary mathematical breakthroughs? There's really no wrong answer since everything can essentially be described mathematically.

[Anonymous No.10757681]

>>10757676
>foundational crisis
>incredibly rewarding
Refer to >>>/lit/.

[Anonymous No.10757687]

>>10757676
Congratulations, this is the cringiest post I've read this whole week.

[Anonymous No.10757690]

>>10748087
Even different universities within a state will sometimes have drastically different textbooks for the same general material.
The USA has never really been known, in general, for being adept at the process of standardization.
Hell, the only thing for which most people use the metric system in every day life where I live (rural TN) is 2 and 1 liter soft drinks.

[Anonymous No.10757691]

>>10757676
>everything can essentially be described mathematically.

[Anonymous No.10757693]

Which theorems do /mg/ reject?

[Anonymous No.10757695]

>>10757676
Read some pseudo-intellectual like Alain Badiou. I'm sure someone like you'll think that this is the best shit ever. Also, make all of your shitposts about foundations on >>>/lit/ from now on.

[Anonymous No.10757701]

>>10757693
see >>10757681

[Anonymous No.10757702]

>>10757693
any theorem that can be proved with ZF only

[Anonymous No.10757704]

>>10757702
>ZF
See >>10757701

[Anonymous No.10757707]

>>10757701
I meant mathematical theorems, not literal theorems.

[Anonymous No.10757708]

>>10757704
see >>10757614

[Anonymous No.10757717]

>>10757687
Nice buzzword, m80. You'll need to not be afraid to apply your own reason more if you want to make it in mathematics.
>>10757681
>linking to other boards as the entirety of your argument.
How tiresome.
Besides, I don't come to /sci/ to talk details. I don't consider posting on 4chan(nel) to be actual work. Only a fool would do such a thing.

[Anonymous No.10757718]

>>10757717
>Besides, I don't come to /sci/ to talk details.
Mathematicians use "we", not "I".

[Anonymous No.10757720]

>>10757718
Formality can suck my dick.

[Anonymous No.10757727]

>>10757720
>Formality can suck my dick.
Please refrain from this sort of language while posting in emgee.

[Anonymous No.10757729]

>>10757718
Poseurs, cosplaying mathematician, use "we", not "I". Those who have worth, know it.

[Anonymous No.10757730]

Anyone else sad that /amg/ didn't take off?
Why is there such a dearth of applied people on /sci/? Everyone is obsessed with purity.
I'd rather work on exciting emergent science/tech than on theory, desu.

[Anonymous No.10757738]

>>10757730
>I'd rather work on exciting emergent science
Use some other thread on >>>/sci/.
>tech
Use >>>/g/.

[Anonymous No.10757742]

>>10757594
Maybe it's you who should refer to >>>/bk/ and|or >>>/bourbaki/ instead. And stay there for good.
Oh wait, there is neither.

[Anonymous No.10757743]

>>10757717
>reason
Discuss the deep ontology behind reason at >>>/lit/.

[Anonymous No.10757745]

>>10757730
>Anyone else sad that /amg/ didn't take off?
This is likely since "applied maths" and "pure maths" are meaningless notions, neither are well-defined.

[Anonymous No.10757746]

>>10757730
Not everyone is obsessed with pure mathematics.
Besides, pure vs. applied maths is a somewhat useful but ultimately false dichotomy.

[Anonymous No.10757747]

>>10757742
>bourbaki
See >>10755056

[Anonymous No.10757751]

>>10757746
>pure mathematics
>applied maths
Discuss such meaningless notions at >>>/lit/.

[Anonymous No.10757753]

>>10757717
>tiresome.
Work out more and refer to >>>/fit/.

[Anonymous No.10757754]

>>10757743
If you enjoy /lit/ so much that your posts are nothing but redirections to /lit/, perhaps it would be best if you were the one that redirected himself to /lit/, my friend.

[Anonymous No.10757756]

>>10757717
>Only a fool would do such a thing.
Nice self-criticism. Now exile yourself to some other board for pseudo-intellectuals and jerk off to your """deep""" foundations elsewhere.

[Anonymous No.10757758]

>>10757754
>enjoy /lit/
Cool. Post about that on >>>/lit/ from now on.
>my friend
We are not your friend.

[Anonymous No.10757764]

>>10757730
Because it was a joke thread I made to do this reply >>10754985
I'll properly read up on a random applied subject that isn't economics or stats and then try to make a serious thread next week.

[Anonymous No.10757768]

>>10757753
>tiresome referring only to physical exertion.
Ooof, maybe y'all should go to >>>/reddit/. That might be more your speed.

[Anonymous No.10757769]

What's the best introduction to Gödel for non-mathematicians? I want to get into pure maths and I've heard he has some really cool ideas about it.

[Anonymous No.10757772]

>>10757768
>Ooof
Refer to >>>/b/ to learn more about this topic.
>speed
Refer to >>>/sp/ to learn more about this topic.
>>10757769
see >>10757704

[Anonymous No.10757775]

>>10757769
>non-mathematicians.
Sorry, m8, there's only mathematicians in this thread. Maybe you should ask one of the non-math boards. I hear /lit/ is pretty popular nowadays.

[Anonymous No.10757776]

>>10757764
>joke
Refer to the nearest comedy thread.
>random applied subject
Refer to >>>/g/ or >>>/sci/eng/.

[Anonymous No.10757780]

>>10757775
>I
Mathematicians say "we", not "I".

[Anonymous No.10757781]

>>10757775
>mathematicians
>>>/not /sci/mg//

[Anonymous No.10757783]

>>10757775
>m8
This is not well-defined.

[Anonymous No.10757784]

>>10757745
>>10757746
I would think /amg/ would be more about cool applications of theory rather than on theory that has application potential.

>>10757764
I know it was a joke but I actually think it would be a super interesting idea.

[Anonymous No.10757785]

>>10757780
>I
Mathematicians say "we", not "we".

[Anonymous No.10757786]

>>10757780
Mathematicians can suck our dicks then.

[Anonymous No.10757787]

>>10757786
>suck our dicks
Refer to >>>/soc/ or >>>/lgbt/.

[Anonymous No.10757790]

>>10757783
The proof is beyond the scope of this text.

[Anonymous No.10757793]

>>10757786
see >>10757727

[Anonymous No.10757797]

>>10757784
>cool applications of theory
Refer to >>>/sci/eng/.

[Anonymous No.10757798]

>>10757787
Wait, weren't we supposed to be talking about maths?
I've lost the thread of this conversation.

[Anonymous No.10757802]

>>10757798
>I've
Mathematicians say "we have", not "I've".

[Anonymous No.10757812]

>>10757802
Mathematicians would say we- because plurals.
However, a singular mathematician (if such a thing were to exist) would say I though.

[Anonymous No.10757813]

>>10757798
>weren't we supposed to be talking about maths?
No. This thread is devoted to telling people to go to other threads/boards.

[Anonymous No.10757814]

>>10757812
>I
>>10757785

[Anonymous No.10757815]

>>10757813
>devoting an entire thread to redirecting to other boards.
/sci/ has fallen on hard times.

[Anonymous No.10757824]

Irregardless, this has been an enjoyable thread.

[Anonymous No.10757833]

>>10757730
you mean that thread with literally 0 replies lol?

anyways, the problem with applied sciences is how unabstract and unobjective they are.

If I were to ask, what are the optimal metabolic pathways for mitochondria in the liver (or whatever applied ppl ask)? you need a model, probably to have read some papers, and the answer will depend precisely on the context of the question, the desired maximal error.

While if i were to ask, show that a finite group of order divisible by p has an element of order p, you only need to know a small amount of context, and generally you can't provide a proof that would require too many different techniques to understand that would be outside of the scope of the questioner.

[Anonymous No.10757841]

>>10757769
The book Godel Escher Bach is self-contained. If you still don't understand it, read I am a Strange Loop by the same author.

[Anonymous No.10757856]

>>10757833
>anyways, the problem with applied sciences is how unabstract and unobjective they are.
Someone get this hothead out of here!
Quickly! We aren't even sure to which board we should redirect us.

[Anonymous No.10757897]

>>10757594
I prefer refering to >>>/sci/ in general and to this here thread in particular, thankyouverymuch.
>>10757718
>>10757780
Nobody gives a flying fried fuck about your individual fancies, thankyouverymuch.
Nor dud anyone in these two particular cases even asked for the particular two cents of yours in particular, thankyouverymuchinparticular.

[Anonymous No.10757944]

Can someone redpill me on p-adics? I see them in a couple places here and there but I just have no clue what they're on about. I understand their construction (both as a completion of a metric and as an inverse limit), but I don't know what I get from them

[Anonymous No.10757960]

>>10757944
It's basically a way that number theorists can port tools from analysis to number theory.

[Anonymous No.10757971]

What is number theory actually about? What makes it distinct from other commutative algebra (Sutdying prime ideals etc.)?
And are there any fundamental results of number theory that would be at the end of an "introduction to number theory"? I just realizef I don't actually know any non trivial but general number theoretic statements about Z lol.

[Anonymous No.10757987]

>>10757960
thank you for giving me such deep insights

[Anonymous No.10758002]

>passing topology but failing analysis
how can this happen?

[Anonymous No.10758078]

>>10754384
>>10755015
what is "abstract algebra?"

[Anonymous No.10758080]

>>10758002
autism

[Anonymous No.10758082]

can you just stop already
you made your point, nobody's laughing, you arent trolling anyone, and youre just annoying

>mathematicians use we hurrr

[Anonymous No.10758083]

>>10756064
what is "abstract algebra?"
also use dummit and foote or aluffi

[Anonymous No.10758086]

>>10757897
>thankyouverymuch
Refer to >>>/r/eddit/.

[Anonymous No.10758087]

>>10757824
>Irregardless
Mathematicians say weregardless or just regardless.
>>10757971
It's about the shittiest and simplest infinite ring known to man, and we often struggle for hundreds of years to prove stuff.
>>10758002
You're psychologically efficient, but not smart.

[Anonymous No.10758090]

>>10757897
>to this here thread in particular
>>computer sciences
>>Turing's and Church's works
>>Godel
Refer to >>>/g/ and >>>/lit/.

[Anonymous No.10758094]

>>10757897
>flying fried fuck
Why the profanity?

[Anonymous No.10758111]

fuck it, im just gonna leave this general until summer's over, guess your epic trolling worked

[Anonymous No.10758121]

>>10758111
>im
Mathematicians say "we are", not "im".

[Anonymous No.10758133]

>>10758121
lad, just stop

[Anonymous No.10758138]

>>10758133
>lad
We are not your "lad".

[Anonymous No.10758145]

>>10758111
DON'T LEAVE ME ALONE HERE WITH HIM

[Anonymous No.10758150]

>>10758145
>ME
Mathematicians say "us", not "me".

[Anonymous No.10758174]

>>10758150
Please present your credentials as a mathematician, or at very least reference your posts in this thread which pertain to mathematics.

[Anonymous No.10758218]

>>10758174
>present your credentials as a mathematician
Mathematicians say "they should please present their credentials as a mathematician".

[Anonymous No.10758237]

>>10757987
Look man, that's really just about it. The idea is that analysis works really well on the real line and you want to port those tools to number theory since you frequently deal with analytic functions there, so you take a different completion of the rationals that emphasis the primes and you get all the tools you need from analysis. Tate took this further and became famous for it.

[Anonymous No.10758258]

>>10757824
>Irregardless

[Anonymous No.10758278]

>>10758218
mathematicians often use the second person plural, as we did in our post.

[Anonymous No.10758288]

>>10758002
Completely different maths, my friend.
If I were you, I'd re-double my efforts in both topology and real analysis.
Try to analyze why you were successful in topology but unsuccessful in analysis, using your personal notes and textbooks to starters.
Because, sometimes, just looking at things from a different perspective is beneficial.
Lately, breakthroughs in mathematics are more about rigorously applying the techniques of different, seemingly unrelated, fields to one another.
It's hard trying to be a polymath nowadays, but don't give up on maths so easily.

[Anonymous No.10758294]

>>10758288
>learning both topology and analysis makes you a polymath
Lmoa. The absolute state of /mg/

[Anonymous No.10758298]

>>10758111
Ironic shitposting is still shitposting.

[Anonymous No.10758302]

>>10758294
>implying I said that in the above post.

[Anonymous No.10758306]

>>10758302
You definitely implied it and not to mention you also made the ridiculous statement that real anal and topology are completely different fields.

[Anonymous No.10758310]

>>10758150
Mathematwecweans say we.
>>10758306
They are when you leave babby level.

[Anonymous No.10758316]

>>10758306
>implying implications.
Pretty sad, bruh.

[Anonymous No.10758320]

I'm days away from graduating high school and I chose a math degree. I was skimming through some undergraduate textbooks and they are completely different from my high school ones, basically rigor scares the shit out of me. Luckily I'll move to quantitative finance as soon as possible, but damn.
Utmost respect for all mathematicians, literally doing god's work and bringing the world forward.

[Anonymous No.10758326]

>>10758310
>They are when you leave babby level.
Pseud detected. Go back to shitposting and don't try to discuss math

[Anonymous No.10758328]

>>10758320
>I chose a math degree
>rigor scares the shit out of me

[Anonymous No.10758329]

>>10758288
>rigorously
Refer to >>>/lit/.

[Anonymous No.10758331]

>>10758326
>anyone who thinks differently from myself is a psued.
The absolute state of /sci/.

[Anonymous No.10758335]

>>10758320
>rigor
see >>10758329
>quantitative finance
Refer to >>>/biz/.

[Anonymous No.10758336]

>>10758331
No you're a pseud because you say stupid things and don't even realize it

[Anonymous No.10758338]

>>10758320
You are in for a bad time if you can't love rigorous study and mathematics simultaneously.

[Anonymous No.10758341]

>>10758338
>rigorous study
What do you mean by that?

[Anonymous No.10758342]

>>10758336
Via your unique definition of stupidity.
What an absolute waste of a mind you are.

[Anonymous No.10758346]

>>10758341
Just study, like, really hard.
It's not rocket science.
Well, unless you're studying rocket science that is.

[Anonymous No.10758347]

>>10758342
>unique definition of stupidity
Can you prove uniqueness though?

[Anonymous No.10758354]

>>10758347
The proof is outside the scope of this thread.

[Anonymous No.10758359]

>>10758346
>rocket science.
Refer to >>>/sci/eng

[Anonymous No.10758386]

>>10758326
>equivariant cohomology and analysis on Fock spaces are similar subjects

[Anonymous No.10758501]

>>10758320
>skimming
there's your problem

you should give it a chance, in my opinion. Just read the book without any distractions and think about the statements. You might like it

[Anonymous No.10758539]

>>10758501
Brevity really is the soul of wit. You replied to that anon better than I could ever hope to.
I sometimes try too hard to inspire confidence because I've done a lot of work teaching mathematics to people that hate math. It's a very thankless job at times.

[Anonymous No.10758606]

>>10758539
jeez, ok dude, you can take my dick out of your mouth now

[Anonymous No.10758633]

>>10758501
>>10758338
Never said I didn't like it. I love it, for that kind of matter. It scares me because I'm simply not mature enough to comprehend everything I see in a matter of seconds, as I do with the kind of shit that high school provides you. I suppose I'll grow out of it; one of my classmates, also pursuing math, says that in a couple of years I'll change my mind and never switch to finance. I'm in for the money though, that's why I respect mathematicians out of my hear: they do what I love for the it's sake, and are not aiming at something else. Thanks for the input though

[Anonymous No.10758638]

>>10758633
Also fuck physics, that weak shit

[Anonymous No.10758682]

>>10758633
Why assume that which is worth knowing can be understood in seconds?
High school is definitely not the end all be all of human knowledge.
So, I really do like your attitude towards what you've skimmed of your potential university studies. Sometimes, fear can be a useful emotion. Fear of the unknown can either drive one to further understanding by reducing that which one does not know or destruction.
Just keep studying maths and you'll make it.

[Anonymous No.10758694]

Is there a better motivation for weak formulation of PDEs other than "let's integrate by parts lmao"?

[Anonymous No.10758767]

>>10758633
I remember when I was a lil fella I picked up Schaum's Outline of Abstract Algebra, and I could actually read the thing, but I had no idea how to pace myself and my memory couldn't keep up with my understanding, so I was reading some stuff about rings while feeling absolutely nauseous.
Fun times.

[Anonymous No.10758780]

>>10758633
> I'm in for the money though
I was like you too when I was applying for universities, thinking about applying in finance and such after I finished my degree. Then I grew out of it and started loving math (specifically after finally having algebraic number theory click). You do you I guess, but perhaps you should think of putting your personal happiness over money. Having a bunch of money gets old fast.

t. wealthy parents (and no, im not mooching off of them)

[Anonymous No.10758788]

>>10758780
>
Do you have a list of ANT books you'd recommend?

[Anonymous No.10758796]

>mathematicians use X not Y xDD
>refer to /otherboard/

[Anonymous No.10758815]

Stewart Tall's
or Primes of the form x^2+ny^2
or Problems in algebraic number theory (some springer book, can't remember the author)

ultimately i just liked solving problems

right now im reading EGA for the ultimate redpill

[Anonymous No.10758819]

>>10758815
>>10758788

[Anonymous No.10758915]

>>10758815
I’m curious, do you know french (some people read it without having mastery of french).

[Anonymous No.10758935]

>>10758780
Heh, I don't come from wealth so I may have a corrupted view of happiness, though money could honestly solve a big portion of my problems. If I had some degree of financial freedom I'd definitely choose pure over everything else.
Obviously I don't think that money alone could bring me happiness, but just having children and being able to provide them with possibilities that I wasn't able to pursue would bring me so much joy.

[Anonymous No.10758950]

>>10758935
If you want money why are you majoring in math?

[Anonymous No.10758968]

>>10758950
https://www.payscale.com/research/US/Job=Quantitative_Analyst/Salary/314d0911/Entry-Level

[Anonymous No.10758974]

>>10747924
does anyone have a dl link for maths books etc? or an archive link? i know theres a recommended reading link in the sticky, but i dont wanna have to buy everything

[Anonymous No.10758989]

>>10758694
>Is there a better motivation for weak formulation of PDEs other than "let's integrate by parts lmao"?
Yes. There are at least 2(3) other, equivalent, ways of defining them:
-Approximation by smooth functions, called "strong derivatives", which very importantly turn out to be equivalent, and happen to be quite natural.
-Convergence of difference quotients, also quite natural and equivalent
(-Bonus, partial absolute convergence)

But, Integration by parts happens to be the best, as it allows you to define a weak Derivative (function, measure, Distribution, sorted by generality) for EVERY L^1loc function, something which can most easily be derived from the formulation of partial derivatives.

Also, the motivation isn't "let's integrate by parts", you have a rule which is true for all classical derivatives and define weak derivatives as the functions for which the rule also holds.

[Anonymous No.10758992]

>>10758974
Libgen.io

[Anonymous No.10759009]

>>10758968
There are lots of jobs that pay really well and are much easier to get than being a quant. Also better working conditions.

Here: https://www.payscale.com/research/US/Job=Medical_Physicist/Salary

Quant is an overhyped job. The career path is full of risks that you're not taking into account.

[Anonymous No.10759017]

>>10759009
>Medical_Physicist/Salary
>/mg/
Epic.

[Anonymous No.10759024]

>>10759017
Still more math than you'll use as a quant.

[Anonymous No.10759028]

>>10758974
gen.lib.rus.ec

[Anonymous No.10759040]

>>10758968
>>10759009
Fuck off to >>>/biz/ or >>>/adv/ with this this garbage.

[Anonymous No.10759088]

pic related is the surface of my brain.

[Anonymous No.10759101]

>>10752447
the topics of pure math and analysis are disjunct. sorry

[Anonymous No.10759190]

>get the entire problem solving method right
>fuck up arithmetic or some other headass shit like marking x=1 as y=1
How do i stop making stupid mistakes god please i cant stop making them and its ruining my chances at a beautiful 4.0

[Anonymous No.10759208]

This thread was horrendous, someone else make the next one.

[Anonymous No.10759209]

>>10759208
what makes you think the next one will be any better?

[Anonymous No.10759219]

>>10759209
Statistics.

[Anonymous No.10759233]

>>10759219
>Statistics
Refer to >>>/sci/eng/.

[Anonymous No.10759262]

>>10757660
>>10757661
>>10757670
t. unemployed

[Anonymous No.10759334]

>>10758694
>what the fuck is a linear functional

[Anonymous No.10759386]

>>10757971
(1) number theory does not necessarily study commutative objects
(2) number theory emphasizes the underlying objects, which can actually vary significantly by context, but would generally be a group of integers or the field of rationals or something like that. Algebra on the other hand emphasizes operations and morphisms on and between these structures, rather than the individual objects contained in these structures
(3) getting more so into the philosophy and history of math, number theory might be described as more "real"/platonic/ontological/model theoretic, whereas an algebra associated with something like the set of integers and the functions that can be constructed from these operations are generally given a more syntactic/epistemological/proof theoretic interpretation.
(3*) That being said, things can get more confusing, because in model theory we sometimes actually consider that our formal system is a model of something like an abstract group or number field or something, which throws the "syntactic interpretation" of an algebra out the window but such is life.

[Anonymous No.10759458]

>>10759386
>"real"/platonic/ontological/model theoretic
>syntactic/epistemological/proof theoretic
Refer to >>>/lit/.

[Anonymous No.10759531]

I'm going into neuro grad school and I want to get some more math under my belt that'll be relevant.
Any suggestions? I was thinking nonlinear dynamics, maybe stochastic calculus or differential geometry if I go into vision. I've taken the basics (calc, diff eq, linear algebra, real analysis, abstract algebra, probability/statistics).

[Anonymous No.10759581]

>>10759531
It really depends on the field. Before you get deeper in differential geometry or nonlinear dynamics, you should probably focus on information theory, which should be fairly easy to learn given your background. I'd recommend looking into James V Stone's books.

[Anonymous No.10759630]

>>10759581
Thanks, I'll check out Principles of Neural Information Theory.

[Anonymous No.10760072]

>>10758915
No, I'm spanish though, and have learnt some french in the past (not fluently, but given that it's so similar to spanish, it's easy to read)

I actually talked about this with my supervisor yesterday and he said it's such easy french that you can genuinely not have to bother too much and pick up most of it on the way.

[Anonymous No.10760077]

>>10758935
To be fair, your point of view is exactly how my father (who made the wealth) thought, and perhaps my children will have a similar reckoning

[Anonymous No.10760615]

>>10759190
are you me

[Anonymous No.10760618]

Is this a youtube comment section ?