/mg/ maths general: spooky sequence edition

[Anonymous No.11107652]

talk maths, formerly >>11094565

[Anonymous No.11107655]

What is your way of learning through textbooks? Please be as detailed as you can.

[Anonymous No.11107659]

http://www.kurims.kyoto-u.ac.jp/~motizuki/2019-10-31-iu-teich-revisions.txt
Inter-universal Teichmuller Theory III
--------------------------------------
>Changed various references to "Remark 3.9.5" throughout the paper to references to "Remark 3.9.5, (i)" (5 instances)
>Updated the Acknowledgements
>Added Remark 1.1.2
>Added Remark 1.2.5
>Slightly modified the third display of Proposition 3.1, as well as the discussion immediately following this display
>Rewrote various portions of Remark 3.1.1, (iii)
>Slightly modified the final portion of Remark 3.1.1, (iv)
>Corrected misprints (7 instances) in Remark 3.9.1, (i), (ii) ("n" ---> "n_{v_Q}")
>Rewrote Remark 3.9.4 and added references (2 instances) to Remark 3.9.4 at the beginning of Remark 3.9.6
>Rewrote Remark 3.9.5 and added references (2 instances) to Remark 3.9.5 at the end of Remark 3.12.2, (v)
>Slightly modified the discussion following the first display of Remark 3.9.7, (i)
>Rewrote Remark 3.9.7, (ii), and added (iii)
>Slightly modified the final portions of the discussion of "IPL" and "SHE" in Remark 3.11.1, (iii)
>Slightly modified the discussion of Remark 3.11.1, (iv)
>In the Step (xi) of the proof of Corollary 3.12:
>>Slightly modified the discussion of log-shells in Step (xi-a)
>>Slightly modified the discussion of hulls in Step (xi-c)
>>Added references to Remark 3.9.5 [together with supplementary explanatory text] in Step (xi-d)
>In Remark 3.12.2, (ii), slightly reworded (c^{itw}), (d^{itw}), (e^{itw}), (f^{itw}), (b^{toy}), (c^{toy}), (e^{toy}), (f^{toy})

Inter-universal Teichmuller Theory IV
-------------------------------------
>Updated the Acknowledgements
>Corrected a misprint in the display of the statement of Corollary 2.2, (iii) (and slightly modified the surrounding explanation)

[Anonymous No.11107824]

>>11107655
open book
fucking read

[Anonymous No.11107831]

>>11107652

> spectral theorem

[Anonymous No.11107933]

>>11107831
>spectral/spectrum
Is there a more overused word in math?

[LMC !!6bFXHDKL67m No.11107940]

>>11107659
I want to believe

[Anonymous No.11108120]

>>11107652
Just what exactly is a ‘radian’ and why does theta have to be in ‘radians’ and not degrees? Just what is degrees then? The measurement of a circle arc? And what does it mean if radians has no pi attached? How can a length be 2 radians instead of 2 pi radians?

[Anonymous No.11108133]

>>11108120
1 radian is 1 radius length around the circle.

[Anonymous No.11108150]

>>11107933
Yes
>normal

[Anonymous No.11108325]

It seems that I have a chance to get my PhDick at Harvard, lads. Should I take it?

[Anonymous No.11108332]

>>11108325
>Should I take it?
No, why would you even consider getting a PhD at some prestigious University?
Just slave the rest of your life away as a codemonkey or, even better, go work at McDonalds.

[Anonymous No.11108466]

>>11107831
>spectral measure
>not some dollarstore EMF sensor

[Anonymous No.11108530]

>>11107652
why do you link the old thread but don't but not the new thread in the old thread. you dumb fucking idiot.

[Anonymous No.11108547]

*flips to random page*

Let [math]p:\mathbb{R}\to S^{1}[/math] be the standard covering map; consider the covering map [math]p\times p : \mathbb{R}\times \mathbb{R} \to S^{1}\times S^{1}[/math]. Let [math]b_{0}=(1,0)\in S^{1}[/math]; set [math]X=(b_{0}\times S^{1})\cup (S^{1}\times b_{0})[/math]; let [math]E=(p\times p)^{-1}(X)[/math]; and let [math]q:E\to X[/math] be the covering map obtained by restricting [math]p\times p[/math]. The fundamental group of [math]X[/math] has free generators [math]\alpha[/math] and [math]\beta[/math], where [math]\alpha[/math] is represented by a loop in [math]b_{0}\times S^{1}[/math] and [math]\beta[/math] by a loop in [math]S^{1}\times b_{0}[/math]. Find a system of free generators for the subgroup [math]q_{*}(\pi_{1}(E,e_{0}))[/math], where [math]e_{0}[/math] is the origin in [math]\mathbb{R}^{2}[/math].

[Anonymous No.11108550]

*flips to random page*

Prove the existence of a continuous function [math]f[/math] on [math]I=[0,1][/math] which satisfies the equation [math]\displaystyle f(x) = \int_{0}^{1}\sin(x+f^{2}(t))dt[/math] for all [math]x\in I[/math].

[Anonymous No.11108557]

*flips to random page*

Prove that through any point [math](a_{1},a_{2},a_{3})[/math] on the hyperbolic paraboloid [math]HP: d_{1}x_{1}^{2} + d_{2}x_{2}^{2} = 0[/math], ([math]d_{1}>0[/math], [math]d_{2}<0[/math]) pass two straight lines lying entirely on it.

[Anonymous No.11108568]

bonus round
*flips to a random page*

Let [math]p[/math] be a prime and let [math]P[/math] be a Sylow [math]p[/math]-subgroup of the finite group [math]G[/math]. Show that for any [math]G[/math]-module [math]A[/math] and all [math]n\geq0[/math] the map [math]\text{Res} : H^{n}(G,A)\to H^{n}(P,A)[/math] is injective on the [math]p[/math]-primary component of [math]H^{1}(G,A)[/math]. Deduce that if [math]|A|=p^{a}[/math] then the restriction map is injective on [math]H^{n}(G,A)[/math].

[Anonymous No.11108587]

Spooky reminder to work with physicists

[Anonymous No.11108595]

>>11107933
>admissible

[Anonymous No.11108651]

>libshits continuous

[Anonymous No.11108653]

>>11108530
>why do you link the old thread but don't but not the new thread in the old thread.
Why should we link the new thread in the old thread?

[Anonymous No.11108734]

>>11107824
You're missing something: "The only way to learn mathematics is to [math]\bf{do~mathematics}[/math]."
>>11107933
>Let
>>11108547
dumb frogposter

[Anonymous No.11108801]

>advisor tells me to only do 4 classes per semester
>120 credits to graduate / 3 credits per class = 40 classes
>40 classes / 4 classes per semester = 10 semesters
>10 semesters / 2 semesters per year = 5 years
???

[Anonymous No.11108855]

>>11108801
You were told to your face that you are a brainlet and you are so much of a brainlet that you didn't get it.

Pro tip: If you take 0 classes per semester you graduate in 0 years. Trust me on the math.

[Anonymous No.11108964]

>>11108801
Taking 5 years to graduate is fairly common and honestly (in my opinion) it's a better way of doing things. 40 classes is roughly standard, and that means that in order to graduate in 8 semesters you have to do 5 credits every single semester without fail and if you have even a single issue in 4 years, you're stuck there another year anyway or you have to waste a summer taking classes.
Doing it over 5 years relaxes the crunch a ton, so you have more free time and more control over your schedule.
This is especially important in your senior year when you should be busy with shit that actually matters (applying to grad schools, finding a job, senior thesis, research projects you might be working on, etc.) and you won't want to be grinding away at 5 difficult classes.

[Anonymous No.11109011]

[Anonymous No.11109015]

>>11109011
What's the point of this post? To make <160 IQlets feelbad? :(

It was funny at first, but just seems like namedropping circlejerk at this point.

[Anonymous No.11109064]

>>11107655
Open book, read, copy down theorems and definitions to help with memorization, sketch intuitions, try to derive a proof from the intuition, read the proof if the result is unsatisfactory, eenie meenie exercises and sketch solutions.
>>11108550
>functional equation and calculus of variations problem
Yikes.

[Anonymous No.11109091]

>>11109015
It's a meme to trigger insecure brainlets such as yourself

[Anonymous No.11109099]

>>11109091
no u.

It's just an unfunny extension of "majoring in triple integrals" or pic related.

[Anonymous No.11109105]

>>11108964
>>11108801
You're forgetting 4 credit courses.

[Anonymous No.11109111]

>>11108568
>Sylow subgroup
cringe

[Anonymous No.11109122]

>>11108801
Just override your counselor retard

[Anonymous No.11109180]

optimization sounds cool, what does the research level of this look like? what's active and promising?

(obviously) I don't know much about it.I always thought it was just part of a calculus applications course but it looks like it extends beyond that into some cool subsets and niches

>t. optimal spooky man

[Anonymous No.11109191]

>>11109011
What happens if you learn all of this?

[Anonymous No.11109195]

>>11109191
you get a gf

[Anonymous No.11109197]

>>11109195
Disgusting.

[Anonymous No.11109207]

>>11108133
Thanks anon

[Anonymous No.11109208]

>>11109191
brief moment of galaxy brain euphoria then commit sudoku with the subsequent realization of the vapidness of irl

[Anonymous No.11109212]

>>11109191
Misha appears to you in a dream and tells you to go to Rio and collab on a paper about hyperkahler manifolds with him.

[Anonymous No.11109225]

>>11109111
I honestly don't know why the Sylow theorems are emphasized so much in grad algebra. Almost every single algebra qual I've ever seen has exactly one question on the Sylow theorems, and yet for all that ubiquity I've never heard of a single person using them ever again unless they're a pure finite group theorist (which are a dying breed anyway).

[Anonymous No.11109239]

>>11109180
Check out https://www.springer.com/gp/book/9783319897998..
Haven't read it but it's got Brezis in the name so it can't be bad.

[Anonymous No.11109246]

How do I prove that there is only one nonabelian semidirect product [math](C_2 \times C_2) \ltimes C_3 [/math], up to isomorphism? I can't figure it out lads without breaking it into cases. Is there a cleverer way??

[Anonymous No.11109258]

>>11109246
model it as a pde.

[Anonymous No.11109269]

>>11109258
what?

[Anonymous No.11109271]

>>11109191
You feel exactly the same as you are now but have wasted time learning shit that hasn't tangibly advanced your standing

[Anonymous No.11109276]

>>11109269
model it as a pde and solve it brainlet.

[Anonymous No.11109282]

>>11109276
Nigga I don't even know what you're talking about

[Anonymous No.11109289]

>>11109282
maybe you should read your textbook a little more closely. pde's are commonly used to prove results in group theory.

[Anonymous No.11109303]

>>11109289
Knapp's Basic Algebra has no mention of it dude. Regardless, I'm sure my professor would question my methods given that this was never discussed in class.

[Anonymous No.11109310]

>>11109303
this is the last time im going to respond. just look into it you stupid undergrad. not everybody will hold your hand for your entire life.

[Anonymous No.11109315]

>>11109246
model it as a circuit.

[Anonymous No.11109320]

>>11109246
If you start with a morphism f from H into Aut(N), then there are some theorems, not too hard to prove (basically just write down the isomorphisms) which tell you that composing f with an automorphism of H gives you the same semidirect product, and also that conjugating f by an automorphism of N (meaning that you take some a in Aut(N) and define f'(h) = af(h)a^(-1) ) gives you the same semidirect product

Either of those should save you the horrific labour of showing that one thing is not isomorphic to another thing.

[Anonymous No.11109324]

>>11109310
>posts question on maths general
>angry engineer gets mad at stranger online
>"hurr undergrad, me big man"
yawn
>>11109315
Are there any fucking MATH people in this thread? I just figured out my question anyway. If [math]\phi,\psi[/math] are two actions of [math]C_2\times C_2[/math] on [math] C_3[/math], then the existence of automorphisms [math]\alpha[/math] of C_2\times C_2 and \beta on C_3 satisfying \psi(h) = \beta^{-1} \phi(\alpha(h)) \beta for all h \in C_2 \times C_2 implies that the semidirect product of C_2 \times C_2 on C_3 via either action is isomorphic.

[Anonymous No.11109327]

>>11109324
just saw this ,>>11109320
thanks friend. not sure why I didn't see that before

[Anonymous No.11109330]

>>11109324
it's just bantz, fren

[Anonymous No.11109334]

>>11109324
fuck you stupid undergrad faggot. i bet you walk around on campus like your hot shit even though you couldnt even model the problem in question as a basic pde of finite variables.

[Anonymous No.11109339]

>>11109330
Happy Halloween. Wasted mine on this fucking algebra assignment.

[Anonymous No.11109342]

>>11109334
responding again eh? stick to trig my engineering compatriot ;-)

[Anonymous No.11109352]

>>11109342
>implying a lowly engineer would be able to bamboozle a stupid math undergrad for a total of 30 minutes

[Anonymous No.11109388]

>>11109352

[Anonymous No.11109457]

ok boys, probability question. Suppose I'm in a multi var calc class, and all we've done so far is:
-limits for f(x1,x2,...,xn)=w
-Partial derivation of f
-generalized chain rule for f
-implicit partial derivation
-homogeneous functions/Eulers theorem
-Cauchy-Riemann equations
-level curves and surfaces
What are the odds we actually get through everything we're supposed to see?

[Anonymous No.11109460]

>>11107933
but spectral exclusively refers to one of two things which are related as is, namely pertaining to the spectrum of an operator (eigenvalues + other shit) or the spectrum of a ring (some set of ideals)
there are many words whose meanings are far more wide reaching

[Anonymous No.11109462]

>>11109342
>>11109191
>>11107655
>>11109457
You should be fed to wolves and sharks

[Anonymous No.11109471]

>>11109457
about tree fiddy

[Anonymous No.11109472]

>>11109462
>you should be fed to wolves and sharks
that sounds impractical. but i'm sure you could model it as a pde.

[Anonymous No.11109478]

https://arxiv.org/pdf/1910.14667.pdf
>Making an Invisibility Cloak: Real World Adversarial Attacks on Object Detectors
>Zuxuan Wu, Ser-Nam Lim, Larry Davis, Tom Goldstein
>(Submitted on 31 Oct 2019)

>We present a systematic study of adversarial attacks on state-of-the-art object detection frameworks. Using standard detection datasets, we train patterns that suppress the objectness scores produced by a range of commonly used detectors, and ensembles of detectors. Through extensive experiments, we benchmark the effectiveness of adversarially trained patches under both white-box and black-box settings, and quantify transferability of attacks between datasets, object classes, and detector models. Finally, we present a detailed study of physical world attacks using printed posters and wearable clothes, and rigorously quantify the performance of such attacks with different metrics.

[Anonymous No.11109481]

>>11109471
Thanks anon. Actually kek'd

[Anonymous No.11109484]

>>11109478
Looks comfy. Is facebook funding this for PR?

[Anonymous No.11109789]

What are your guys essential (graduate level) math topics, ie the things that everyone should at least learn a bit of?
In other words, any topic X that if someone told you they'd never studied X you'd feel like they were missing out big time. Bonus points for reasonably accessible stuff.
I've been doing a bunch of self-studying as a NEET lately, mainly DiffGeo and analysis, and I want to broaden my curriculum just for the sake of getting a taste of all the coolest topics out there before I die.

[Anonymous No.11109819]

>>11109789
This is hard to answer to me because I'd rather just take all topics and sort them.
Lie groups, stochastic integrals, lambda calculus, those are very different topics and missing any would lead to a one sided view of the scope of math. Just as an example.

[Anonymous No.11109840]

>model it as a pde.

[Anonymous No.11109933]

>>11107655
Try to understand what is going on. Do exercises. Literally nothing to it.

[Anonymous No.11109989]

>>11109819
>lambda calculus
why

[Anonymous No.11110152]

>>11109789
Weak derivatives and in general variational and PDE problems using Functional analytic tools.

[hist No.11110268]

Just came across this, might be good

https://youtu.be/vmcbm5FxRJE

[Anonymous No.11110281]

>>11109789
Galois theory
Covering spaces
Algebraic curves
Riemann surfaces
Some basic theory of number fields and local fields
The connections between all of the above (see eg. in Szamuely’s book for everything but the number theoretic side)

Functional analysis
Operator algebras
Geometric group theory

[Anonymous No.11110293]

Is note taking a meme? Isn't is just a time waste compared to simply reading and rereading a text?

[Anonymous No.11110304]

>>11108120
It doesn't mean anything if a radian doesn't have pi attached, pi is just used commonly because a 180 degree angle is exactly pi in radians.

[Anonymous No.11110306]

>>11110293
We had this discussion already. It depends. Some people do it, some people don't. Just try both and do what works best. End of discussion.

[Anonymous No.11110310]

>>11110293
I do it simply because it helps me remember the content easier

[Anonymous No.11110359]

Hi /mg/, I need help on some analysis. This isn't homework, just something that's been bothering me
The mean value theorems require differentiability on the open interval and continuity on the closed interval. But the theorems work just fine for functions like [eqn]x^{\frac{1}{3}}[/eqn]. I think they should require something slightly weaker: the ability to draw a tangent line at every point on the open interval (including vertical tangent lines).

Thoughts?

[Anonymous No.11110370]

>>11110306
I didn't see it. I'll check the archives.

[Anonymous No.11110375]

>>11110359
I have given you a detailed answer in your thread about this cca month ago. It's basically the Cauchy's mean value theorem.

[Anonymous No.11110418]

>>11110359
My guess is that weak differentiability is enough so that the weak derivative has a lebesgue point with that property.

(Take for example the absolute value centered in the middle between -1 and 1.
It is weakly differentiable with the sign function as it's derivative of I am not retarded (which isn't certain) zero is the Lebesgue point of sign(0) so the theorem holds.)
I conjecture that this is always the case, I might give it some thought tomorrow.

[Anonymous No.11110447]

>>11110418
>>11110359
Yep, I think I was right. By the ACM characterization you can apply the integral mvt to the weak derivative and you are basically done.

[hist No.11110453]

>>11110268
yeah, this was very nice.
Here's the latest vid form that channel btw.
https://youtu.be/pzq1FvmEjaM

[Anonymous No.11110686]

Are a scalar and a 1x1 matrix the same?

[Anonymous No.11110692]

>>11110686
no

[Anonymous No.11110705]

>>11110686
yes, you can multiply any matrix by a 1x1 matrix as if it were a scalar
that's what the dot product is, actually

[Anonymous No.11110731]

>>11110686
Yes.
They may end up being literally the same in math. If you do programming and define a dynamically sized matrix type, then the 1x1 matrix might have an extra wrapper.
But in any case, they are certainly isomorphic.
Indeed the determinant is a nice surjective map in the category of matrices.

[Anonymous No.11110747]

>>11110686
>Are a scalar and a 1x1 matrix the same?
What have you tried?

[Anonymous No.11110763]

>>11110686
Not literally, but essentially yes

[Anonymous No.11110802]

>>11110705
no
...maybe tensor product

[Anonymous No.11110853]

>>11110686
Define "same".

[Anonymous No.11110932]

>>11110686
They are equal as sets.

[Anonymous No.11110972]

How do you prove that the product of two [math]C^\inf[/math] functions are [math]C^\inf[/math]? Seems like an elementary result but can't find anything on the internet. I've thought of induction but wouldn't that only work for C^k?

[Anonymous No.11110983]

>>11110972
A function is smooth if it is C^k for all k. Try fixing two smooth function f and g, and show that fg is C^1. Then show that if fg is C^r for all r < k, then fg is C^k.

[Anonymous No.11110990]

>>11110983
Yes, but doesn't induction only work for finite k?

[Anonymous No.11110994]

>>11107652

hey guys, where can I publish a paper that isn't too serious, but isn't complete shit either.

thanks

[Anonymous No.11110999]

>>11110990
Yes, but if you can show that fg is C^k for any choice of k, then you know fg is smooth. A function is smooth if it will a smooth up to all orders, by definition.

[Anonymous No.11111014]

>>11110999
Thanks, guess I need to RTFM more carefully.

[Anonymous No.11111057]

>>11110293
I don't find it a waste of time, writing out a proof and drawing diagrams myself gets them into my head much better. It's a tactile learning thing.
This is also why I don't type notes. When I've tried to in the past, I don't remember a thing of them.

[Anonymous No.11111148]

>>11110281
>Galois theory
>graduate level
Yikes.
>Riemann surfaces
Nice.
>>11109789
Riemannian geometry, metric spaces of non-positive curvature, sheaf theory, symplectic and contact geometry, lie algebras, several complex variables.

[Anonymous No.11111272]

>>11110994
arxiv.GM

[Anonymous No.11111297]

>>11111272

I need an endorsement.

[Anonymous No.11111302]

>>11111297
Tell them Remilia Scarlet sent you.

[Anonymous No.11111346]

what do /mg/

[Anonymous No.11111350]

>>11111346
>what do /mg/
What have you tried?

[Anonymous No.11111479]

>>11111346
the value of this limit is [math]\sqrt{\pi/4}[/math]

[Anonymous No.11111640]

>>11111346
anon

[Anonymous No.11111645]

>>11110686
No, but there is a trivial isomorphism between them.

[Anonymous No.11111671]

>>11111645
>trivial isomorphism
0 -> 0?

[Anonymous No.11111794]

>>11111671
R -> R^(1×1)
x |-> [x]

[Anonymous No.11111795]

>>11111671
Also, that isn't an isomorphism.
It isn't defined on all the real numbers.

[Anonymous No.11111801]

>>11111794
>>11111795
Yeah you missed the "joke". Pic related to both of us.

[Anonymous No.11111812]

how do I know if I have dyscalculia or not. someone told me they have trouble determining larger numbers but I dont have issues there, its only in 'carrying' the numbers mentally and crossing over tens.
when I'm forced to carry any sets, they just evaporate. forcing past base 10 feels like a brick wall.
Do you guys go from abacus to mental visualisation of one like the japs do it?

[Anonymous No.11111816]

>>11111801
>Yeah you missed the "joke".
I don't get it.

[Anonymous No.11111821]

>>11111816
Trivial homomorphism etc. Just forget it.

[Anonymous No.11111914]

>>11110686
If you bother distinguishing every trivially isomorphic object in math, you will just annoy yourself.

[Anonymous No.11111921]

honestly I enrolled in math because it is fun
second year of a math course now, should I continue with theoretical math or pursue financial math / cryptography? (as electives next year)

[Anonymous No.11111928]

>>11110686
yes if you're a sane person. no if you want to be an autistic faggot.

[Anonymous No.11111932]

>>11111921
>honestly I enrolled in math because it is fun
Same. Do what I did and become a theoretical PhD guy.

[Anonymous No.11111934]

>>11110990
yes, but C^inf also simply means differentiable for all FINITE orders. there's no infinite number of iterations going on.

[Anonymous No.11111969]

>>11111921
Theory of course

[Anonymous No.11111977]

>>11111914
Which doesn't mean you shouldn't be unaware of the issues.
How many members does the set {1/1, 2/2} have?

[Anonymous No.11112025]

>>11111977
Sure, whenever it comes up.

[Anonymous No.11112093]

>>11111914
>>11111977
How many members does the set
{((0,1),+ mod 2), ({1,-1}, *)}
have?

Probably two in ZF and one in HoTT.

[Anonymous No.11112097]

>>11111914
>>11111977
How many members does the set

{
((0,1),+ mod 2),
((1,-1), *)
}

have?

Probably two in ZF and one in HoTT, where equivalent terms are equal. I'm not sure about the latter, though.

[Anonymous No.11112125]

Is there a book on the connections between music and mathematics that's both mathematically and music theoretically sound? Does this connection even exist or is it just something pop scientists say after hearing that "even rations of tones sound good" and that Pythagorean tuning exists? I'm mostly interest in looking at classical and baroque music from this perspective if that's helpful.

[Anonymous No.11112158]

>>11112125
I think the amount of non-trivial math - as a math student would understand it - in music theory is very limited. That is to say, the math<=>music connection is probably overstated.

That said, there's a lot of music theory that one will grasp quickly if one is acquainted with mathematics. This may also be the reason why music people who learn (about) math to understand music better might end up thinking that there's a lot of math in music (not knowing that there's just a gigantic bulk of mathematics far removed and more complicated than the one you need for music).

I personally only learned to play basic flute and harp, so my music background is extremely limited. If you want a few resources I found entertaining at least, I came across various youtube channels who at least point to some connections. E.g. if you consider

https://youtu.be/Ur6GOoSNGN0

There is a small but interesting subgenre of youtube videos dealing with music theory that I want to recommend, even if it's not all that mathy. E.g. I really like this one

https://youtu.be/MdZSOoOF5Ms

Coming back to proper math, of course there's all the mechanics and harmonic analysis that in principle relates to acoustics and thus math - but I should probably not count that.

I have not read it, and it might just be that it's the work of a mad man, but there is a 1000 pages treaty discussing music via topos theory

https://www.amazon.com/Topos-Music-Geometric-Concepts-Performance/dp/3764357312
You can read the table of contents here
https://www.researchgate.net/publication/257259829_The_Topos_of_Music_Geometric_Logic_of_Concepts_Theory_and_Performance

That one might be hard to read just for not knowing topos theory.
Btw., for those interested in Topos Logic, this week I came across 2018 lecture notes that seem to be put together nicely, here

https://tcsc.lakecomoschool.org/files/2018/06/Como2018.pdf

[Anonymous No.11112228]

What, morally, are Theta Functions?

Are they like generating functions for solutions of Diophantine equations?

[Anonymous No.11112331]

>>11111969
>>11111932
what about employment?

[Anonymous No.11112337]

>>11112331
I'm not familiar with that mathematical structure.

[Anonymous No.11112346]

>>11112337
stupid joke, but I keked

[Anonymous No.11112359]

>>11112331
Research after getting my diploma, or then warehouse and stuff like that. I liked working in a warehouse.

[Anonymous No.11112382]

good intro diff eq textbooks, tried and tested by /mg/?

[Anonymous No.11112418]

>>11112331
learn2code and then btfo cs kids who don't understand what a tree is

[Anonymous No.11112454]

>>11112382
tenenbaum and pollard is kind of the standard if you just want to learn how to solve and apply differential equations
if you just want the theory, strogatz nonlinear dynamics and chaos is very good

[Anonymous No.11112459]

>>11112331
>asking that question
better stick with financial, you're never gonna make it in the pure world.

[Anonymous No.11112516]

>>11112331
Getting a job with a math PhD is easy as long as you network correctly and know how to code. All the work they make you do will feel trivial and they'll throw a fuckton of money at you to do it.

[Anonymous No.11112557]

>>11112228
>morally
shoo shoo category tranny

[Anonymous No.11112702]

Does studying mathematical logic help with debates? Would you be able to for example point out fallacies in arguments?

[Anonymous No.11112723]

>>11112702
Not really. Mathematical logic as a field is about mathematical modeling of the mathematical world.
The basic logic you learn in first year is about all that is useful in everyday life, and it goes a long way. It is not sufficient to point out fallacies in most arguments irl, because natural language is a lot more subtle (and full of pitfalls) than mathematical language.
To argue efficiently, you should read up a lot on statistics, rhetoric, maybe epistemology and then, of course, the subject of the debate in question.

[Anonymous No.11112732]

>>11112702
No, Math logic is very formal, you will looks like an autist.

First 2 chapters
https://www.people.vcu.edu/~rhammack/BookOfProof/BookOfProof.pdf

But arguments in real world ...
https://onedio.co/content/19-ways-to-win-an-argument-even-if-you-know-youre-wrong-13524

[Anonymous No.11112744]

>>11112702
Use this

[Anonymous No.11112796]

Undergrad Category theorist do research .... goes wrong

https://www.oliviacaramello.com/Unification/InitiativeOfClarificationResults.html

[Anonymous No.11112803]

>>11107655
i just read it until i get it

[Anonymous No.11112806]

>>11108587
why would you want to work with literal fucking retards

[Anonymous No.11112807]

>>11112796
Many such cases.

Jokes aside, was the really an undergrad when this went down?
She's more or less known now, anyway. She's talking on a bunch of conferences. She's actually mentioned as inviter in the last link (the topos logic notes) here
>>11112158

[Anonymous No.11112811]

>>11112807
No, just oh Undergrad Category theorist goes to PhD Category theorist

[Anonymous No.11112816]

>>11109099
why is the section representing serious math empty?

[Anonymous No.11112837]

>>11112796
>https://www.oliviacaramello.com/Unification/InitiativeOfClarificationResults.html
what's the tl;dr?

[Anonymous No.11112875]

>>11112837
She is a mathematician working at the interface between category theory, logic and algebraic geometry. During her PhD, she apparently made some contributions which some prominent figures in the CT community considered "well-known" or "folklore" (despite not being written anywhere, as is often the case).
There began an apparently pernicious campaign of these same people (including her former advisor) to denigrate her work on the grounds of her being overrated, despite her talent being attested by the likes of Connes or Laurent Lafforgue.
It all ends well, thankfully, since she did get a professorship in Italy and (according to her page) will soon get a permanent position at IHES, but it is a good example of the sort of things that go on in the tiny, tiny world of mathematical academia.

[Anonymous No.11112893]

>cant study maths this weekend because I have to write a 2 page paper (any topic) by Tuesday night

[Anonymous No.11112951]

>>11112228
> morally

who started these meme I hear mathematicians say it all the time.

the correct term would be intuitively, essentially, or philosophically

[Anonymous No.11112975]

>>11112951
>correct
This is a meaningless notion in 2019.

[Anonymous No.11112979]

What is category theory and why is there so much controversy around it?

[Anonymous No.11112988]

>>11112979
https://en.wikipedia.org/wiki/Abstract_nonsense#Background

Btw. I just uploaded a discussion of recommended readings:

https://youtu.be/hEW42ARKNoE

Direct link to the book list:
https://gist.github.com/Nikolaj-K/282515e58c1c14de2e25222065f77a0a

[Anonymous No.11112994]

>>11112951
>who started these meme I hear mathematicians say it all the time.
It's category faggotry, they say morally instead of something else because words like "intuitively" or "philisophically" don't work to convey the smug superiority that this is _the one correct way_ to think about whatever they're espousing.

[Anonymous No.11113001]

>>11112994
>_the one correct way_
up to isomorphism*

[Anonymous No.11113004]

>tfw graduated this spring
>tfw barely done math since
>tfw haven't applied to graduate programs
>tfw don't know what you're doing
AHHHHHHHHHHH I want to go back to being an undergrad where I could just skip lecture and read about Lie algebras and shit all day

[Anonymous No.11113005]

>>11112994
I don't think it has its origin in this corner, consider e.g.

https://mathoverflow.net/questions/14849/what-would-a-moral-proof-of-the-weil-conjectures-require

Unless by "category theory" you also include the geometers from the 50's on. Grothendieck would probably not have called himself a cateogry theorist.

[Anonymous No.11113046]

>>11112979
it's a very abstract field of mathematics. it's great for connecting different subfields together and it provides kind of a "big picture" of all mathematics. however it's actually useful only if you already have some mathematical maturity and you already know a lot of material. otherwise it's just form over substance. some math beginners (especially those getting their asses kicked by analysis and what not) resort to being obsessed with category theory. they think it makes them smart, because "that's what them big boys do", while the truth is that category theory is actually not hard at all, it's just abstract. and it's utterly pointless to study any of it unless you have a large stock of examples where you can apply it.

[Anonymous No.11113055]

>>11113005
>Grothendieck would probably not have called himself a cateogry theorist.
There was a video posted here a day or two ago (about Grothendieck's late thoughts on toposes) where the lecturer argued the exact opposite, actually.
Regardless of what he would have _called_ himself, lots of his work was pure or almost pure category theory and his philosophy of math was prototypically categorical in nature.
Regardless, a mathematician doesn't have to be a pure category theorist to engage in what I'm referring to as "category faggotry". Kontsevich screeching that Deligne's proof is "morally" bad (the word moral obviously just being a pure value judgement here and not meaning anything mathematical) because he used tricks and difficult arguments instead of 700 pages of trivial commutative diagrams is pure category faggotry, regardless of what his main research area is.

[Anonymous No.11113057]

>>11113046
>some math beginners (especially those getting their asses kicked by analysis and what not) resort to being obsessed with category theory
That's the meme, but is this actually the case?

[Anonymous No.11113075]

>>11113057
>but is this actually the case?
it definitely is, at least in my uni

[Anonymous No.11113087]

>>11113057
It's not like it's the standard thing that happens to _everybody_ the first time they get reamed in the ass by real math, but it happens often enough that this stereotype has been generated.
I've met people like this in real life, and they come on here from time to time too (there used to be a pair of them on this board what must be like two goddamn years ago now, long before this was even a meme, who would just post anime pictures and suck each other off about how deep their categorical ramblings were)

[Anonymous No.11113097]

>bombed my College Algebra midterm
>now the ATFE is after me

[Anonymous No.11113401]

>>11111297
Tell them Yukari Yakumo sent you.
>>11112796
>the undergrad category theorist
>the undergrad constructivist
>the undergrad finitist
>the undergrad olimpian
>the undergrad non-standard analyst
>the undergrad foundationalist
>the undergrad logician and philosopher of mathematics
>the undergrad applied mathematician
I feel like you lads focus too much on beating category theory, there is a wondrous world of undergrads out there.
>>11112979
We have this question every thread.
Essentially, category theory is largely sterile in and of itself, and needs to be built on top of an understanding of topology, geometry and algebra. Possibly only two of these three, but I wouldn't recommend it.
>>11113057
I have never seen it happening, thank the Lord, but it probably does.
Fellas here just disappear.
Absolutely hillarious.

[Anonymous No.11113440]

Hello frens I got a question. Is it worth it to simplify what I got any further (which will be hell) or just leave it be as the question asked to simplify whenever possible. . . If I do need to simplify, help would be very very much appreciated. a,k,R are all constants.

[Anonymous No.11113452]

>>11113440
This isn't a maths question as much as a question of your teacher's grading policy. Personally I wouldn't simplify it as it would just make it harder to see if you did the quotient rule properly.

[Anonymous No.11113455]

>>11113440
>[math]v'=3ax^2+2R[/math]
It don't be like that.

[Anonymous No.11113460]

>>11113455
Checked and thanks for noticing my mistake even though I don't see how. At least its not at the beginning and I don't have to do everything from start. Wait I see it! I just have to erase R. Thanks mate. Do you think I have to try to expand and simplify it?
>>11113452
Thank you for your input.

[Anonymous No.11113471]

>>11113460
>expand and simplify it
Nah. You can still isolate an x in the numerator, but going further is probably pointless. I can't see anything else cancelling out.

[Anonymous No.11113473]

>>11113471
Alright, thank you very much for your help.

[Anonymous No.11113474]

What's the loli gf formula

[Anonymous No.11113503]

>>11113474
the greatest question of our time, truly

[Anonymous No.11113631]

If I already know the minimum bandwidth ordering of a graph, how do I convert it to the maximum bandwidth ordering?

[Anonymous No.11113678]

>>11113474
[math]\text{(You)}\in \textsf{Faggot}^{cocc}_{succ}[/math]

[Anonymous No.11113680]

>>11113631
not sure I understand, you can make a matrix have maximum bandwidth simply by reordering a non-zero entry to the top right or bottom left

[Anonymous No.11113808]

>>11113680
I should have specified that the graph is ordered according to a more strict definition on minimum/maximum bandwidth, where it's defined by sum(x1-x2) rather than max(x1-x2).

[Anonymous No.11113862]

What is it with higher category theory that attracts low quality mathematicians so much? Lurie is like a lamp attracting a swarm of sloppy flies around him. Absolutely disgusting.

[Anonymous No.11113864]

>>11113862
Undergrads trying too hard to be next level mathematicians and skipping all the context behind it.

[Anonymous No.11113990]

>>11113862
because it's easy yet abstract enough to make you feel smart

[Anonymous No.11114034]

>>11113864
>>11113990
I get your sentiment - but tbqh I think people just like it because it's very nice and different that set theory "Lego" foundations. It feels more right to characterize objects up to isomorphism and working with that and not choosing models. So say they want to be smart... that might be part of it, but the theory is also a great achievement of the mind

[Anonymous No.11114275]

>>11114034
I just like commutative diagrams

[Anonymous No.11114281]

>>11111928
/thread

[Anonymous No.11114289]

>>11111821
Fucking retard

[Anonymous No.11114297]

>>11112516
[citation needed]

[Anonymous No.11114302]

>>11111921
>>11111932
>>11111969
>>11112331
Dont listen to these retards, if you go pure youll die a poor faggot and maybe youll have to work odd jobs even after a phd.

[Anonymous No.11114304]

>>11112454
Are they better than george f simmons diff eq?

[Anonymous No.11114321]

>>11114304
>Are they better than george f simmons diff eq?
Why don't you read them and find out?

[Anonymous No.11114331]

>>11114302
Someone didn't get a PhD position.

[Anonymous No.11114359]

>>11114302
University isn't a job education (at least it shouldn't be)

[Anonymous No.11114382]

>>11114359
yeah but in the current environment if you don't use it as one you're fucked if you're not already rich and connected. also universities are increasingly treating themselves as job training (pretty gross desu)

[Anonymous No.11114477]

>>11114304
i'm sure simmons is good too, i have no idea.
listen, every fucking introductory DEs text is exactly the same. strogatz is really different, but it's also only somewhat an introductory DEs text. it's a bit more advanced.

[Anonymous No.11114481]

>>11114382
>you're fucked!!!!!1!1
god who gives a shit
just shut the fuck up. you're stuck on 4chan, you aren't some oracle of ideal decision making. if we have something we love doing enough that we don't mind living a humble life to do it, and we get to do it our whole lives, well, that's a whole lot more successful to me than shilling out and working for a heartless tech company for 50 years.

[Anonymous No.11114538]

>>11114481
chill the fuck out dude, I'm not part out autistic argument chain here. Do you PhD if you want to, why the fuck do I care? Stop shitting up our comfy thread with your autism (not the good kind).

[Anonymous No.11114542]

>>11114359
that's true for undergrad. Absolutely not true for graduate school. A PhD in math is job training to be a researcher/professor. An MBA is business job training, etc.

and correspondingly the pure math undergrad is extremely general education. you can pretty much do anything afterwards.

[Anonymous No.11114546]

>>11114538
stop shitting up our comfy thread with your thoughts on industry and the job market (not science or math)

[Anonymous No.11114547]

>>11114542
this post >>11114481 is for you now. IF YOU WANT TO TALK ABOUT JOBS GO TO THE FUCKING JOB GENERAL.

[Anonymous No.11114548]

>>11114481
Cringe

[Anonymous No.11114600]

>>11107655
>read
>take notes of major formulas and methods of solving problems
>write a sample problem in my notes so it makes sense just from reading the notes
>do exercises/homework until I get it
>put notes in Anki so I can refresh later before an exam

[Anonymous No.11114818]

should I add more math to my computer science degree?

[Anonymous No.11114884]

Should I add more maths to my Computer Science degree?

[Anonymous No.11114930]

>>11109099
>Genius Level Gap
>Symplectic Geometry
kek, so true

[Anonymous No.11114933]

>>11109472
elegant impracticality is sort of the whole shtick for mathfags rite?

[Anonymous No.11114947]

brainlet question here, can someone explain why the highlighted part goes to zero? I get the negative 1/2 part because e^0 is just 1, but I don't understand how plugging in negative infinity into 1/2e^(-t)^2 produces a zero.

[Anonymous No.11114953]

>>11114884
>Computer Science degree
>last math course: calc 2
>no number theory nor cryptography
yes, you should

>history of jazz
kino course btw

[Anonymous No.11114967]

>>11114947
well, do you agree that
[math]\displaystyle\lim_{x\to\infty}y^x=\infty[/math]
when [math]y>1[/math]? If you do, then it quickly follows that
[math]\displaystyle\lim_{x\to\infty}y^{-x}=\lim_{x\to\infty}\frac{1}{y^x}=0[/math]
and thus the result

[Anonymous No.11114969]

>>11114953
They’re literally all like that, the last math class is usually discrete+lin alg by sophomore year and then they’re done for good. This is the case even at the ivies and UC schools

[Anonymous No.11114973]

>>11114947
As an experiment for yourself, plug in [math] t=-9000 [/math] and then [math] t=-9001 [/math].

[Anonymous No.11114975]

>>11114884
>more
Connecting statistic with AI won't be wrong.

>>11114953
How many people really get into cryptogrpahy, tho

[Anonymous No.11114987]

>>11114953
Should I switch out Intro to Stats for Linear Algebra, Multivariable calculus, or Differential Equations?

[Anonymous No.11114995]

>>11114947
Shouldnt it to to 1/2?

[Anonymous No.11115280]

>>11114987
Do not prioritize Multivariable Calculus or Differential Equations over Stats, Linear Algebra or Number Theory.

[Anonymous No.11115377]

>>11115280
out of those 3 (stats, linear algebra, number theory) which would you say is most important? I'm thinking stats and number theory, since I'm also doing cybersecurity/crypto classes

[Anonymous No.11115385]

Who here prefers blank paper to lined paper when doing math? There seem to be no options for unruled paper notebooks at the store, unless you buy giant sketch books.

[Anonymous No.11115391]

>>11115385
Unlined for doing math.
Lined (not graph) for notes.

[Anonymous No.11115622]

>>11108120
why is 2pi 360 degrees? why not make 360 degrees just pi?

[Anonymous No.11115656]

>>11115385
>notebooks
Buy a block of A4 paper and a stapler. Better and cheaper.
>>11115622
>what is the tau meme

[Anonymous No.11115666]

>>11113401
>the undergrad _____
>everythang is undergrad, me so smart
>nothing is worth investigating, just listen and believe
>you don't accept cantor as your christ and savior? HERETIC!
You faggots are so insufferable.

[Anonymous No.11115771]

when would this ever come up in real life?

[Anonymous No.11115778]

>>11115771
>when will I ever have to add logarithms

[Anonymous No.11115779]

>>11115771
probably never, but it's fucking easy shit anon, honestly. just suck it up and learn it.

[Anonymous No.11115791]

>>11115779
I did. It just seems pointless.

Also I'm done with all my homework for the semester, so I guess I'll start teaching myself other shit.

[Anonymous No.11115835]

>>11115771
>"alright students, today we will cover how to add variable expressions"
>ugh, when will I ever have to use that?

[Anonymous No.11115891]

>>11114034
>>11114275
>>11113990
>>11113864
bingo. Trannies have a very fragile ego and they try to validate their decisions. Too stupid to accept that fact that you were born a male? must be obviously smart enough for a math degree. Oh wait its not plug and chug? Ill learn category theory so other people think im smart.
>>11113862

[Anonymous No.11116031]

>>11111794
Is this category theory?

[Anonymous No.11116102]

>>11114947
it's not e^(-t)^2, it's e^(-(t^2)). learn to fucking read.

[Anonymous No.11116105]

>>11115666
helloooooo undergrad
i'll break it to you now, you're never going to make it

[Anonymous No.11116306]

>>11116031
No, it is very, very basic mathematical terminology.

[Anonymous No.11116321]

Is there anything mathematical to standardization? Of AI in particular. I heard IEEE developed some standards

[Anonymous No.11116339]

>>11115385
I like these. The creature is cute.

[Anonymous No.11116352]

>>11108120
The radian measure of an angle is the ratio of the arclength to the radius.

[Anonymous No.11116399]

Well since category theory is such a popular topic I have a question about it but I don't know category beyond the basic definitions.
What I got though is that many proofs algebra and topology use some recurring patterns, which category theory can describe, so it is a useful language.
Similarily I see recurring patterns in basic analytical proofs when you play around with epsilon and N etc. You always do the same kinds of things. The order of the forall and exists determine what levers you have to make the error margin smaller than epsilon.
Similarily you constantly mollify functions or split an integral into an inner ball and outer rest.
Could there be a "category theory" for this kind of stuff?

[Anonymous No.11116410]

>>11108855
more like trying to make big $$$ for the school

[Anonymous No.11116432]

>>11107652
How do you solve this?
I can't do it :(
>>11114887

[Anonymous No.11116444]

>>11115385
I used to think people who used unlined/blank paper were just being pretentious, but I've since started using it myself, and I have to say I prefer it a lot.

[Anonymous No.11116450]

>>11116399
That has nothing to do with category theory, retard
It's just simple second-order logic.
You can always state and prove "schemes" of statements, for example:
Given P[x], t0,t1
if forall x x in t0 iff P[x] and forall x x in t1 iff P[x] then t0 = t1
Proof:
given x;
assume x in t0
then P[x]
then x in t1
assume x in t1
then P[x]
then x in t0
thus t0 = t1 by extensionaly Axiom
After that you can take any well-defined predicate P that takes some set x as an input and some arbitrary sets t0,t1 and use that theorem for them.
Similarly you can do that for any "repetitive" reasoning code in your mathematics.

[Anonymous No.11116514]

how do i stop leaving my problem sets until the last day

[Anonymous No.11116518]

>>11116514
By growing some self-discipline. It's that simple.

[Anonymous No.11116522]

>>11115385
I buy a block of printer paper. There are unruled paper notebooks in my store, but usually they are very expensive. Not really a sustainable investment for someone who writes a lot/takes lots of notes

[Anonymous No.11116860]

>>11116450
pathetic schizo

[Anonymous No.11116865]

>>11111914
this

[Anonymous No.11116890]

>>11116399
Category isn't good (or not interesting) with total orders

[Anonymous No.11117090]

>>11116522
Definitely this. Over here most photocopying places also offer spiraling, so I just bring a handful of white paper and then leave with a cheap notebook.

[Anonymous No.11117461]

Dumb question but something isn't clicking right. For functions defined on a finite interval, there's no reason to use full/sine fourier series over the cosine series, right? Since you can always define an even periodic extension and that would guarantee uniform convergence for the cosine series.

[Anonymous No.11117501]

The multivariable calculus book that we are using for my calculus course is atrocious (James Stewart Calc, 8th edition). Does anyone have any better books/lecture series?

[Anonymous No.11117513]

>>11116105
>helloooooo :3 undergrad >_>
t. basement autist who didn't make it

[Anonymous No.11117754]

>>11117461
sin(x+d)=cos(x)
?

If you have a means to define a function which is 0 at x=0, then you're fine.

[Anonymous No.11117759]

is production bad?

[Anonymous No.11118426]

>>11112988
>https://en.wikipedia.org/wiki/Abstract_nonsense#Background
Labeling an argument "abstract nonsense" is usually not intended to be derogatory, and is instead used jokingly, in a self-deprecating way, affectionately, or even as a compliment to the generality of the argument.

[Anonymous No.11119067]

Have (You) taken the Triple Quad Formula pill yet, /mg/?

[Anonymous No.11119081]

What if the notion of proof in general ends up being proven self-contradictory?

Will that constitute a clean kill for math as a whole?

[Anonymous No.11119101]

>>11119081
>What if the notion of proof in general ends up being proven self-contradictory?
This is a meaningless statement. And I suspect that if you had any formal training in mathematics you wouldn't say something as retarded.

A proof is a transformation of one statement to another statement by means of basic logical transformations (usually drawing upon other proofs, which are constructed similarly).

How could it even be contradicts? Except if basic logic is contradictory, at which point you might as well blow your brains out since deduction of anything is literally impossible.

[Anonymous No.11119115]

>>11119101
What you described is called derivation, not proof though.

As for the way to prove notion self-contradictory, I assume, it goes like this. Assume the notion in question is basic, taken for granted. Assume you manage to end up managing to define it circularly through a combination of itself and certain other notions. You elaborate those notions as per their definitions until all of those notions constituting the circular definition in question are decomposed into basic notions only. If, after simplification, all the other basic notions cancel themselves perfectly, and you gain Proof= Proof, you are golden, if not, and there is like Proof = f(Proof, whateverremains), chances are, you are fucked. Same for the case, where Proof is not to be considered a basic notion, and where you manage to end up with something like f(Proof, whateverelse1) = g(Proof, whateverelse2).

[Anonymous No.11119118]

>>11119115
Or more like Proof = f(whatever1) = g(whatever2).

[Anonymous No.11119119]

>>11119118
Where whatever1 and whatever2 are different (while possibly overlapping) subsets from the same set of notions considered basic and mutually independent).

[Anonymous No.11119122]

>>11119115
>What you described is called derivation, not proof though.
No. Do you have any formal training in mathematics?
A "derivation" is just a certain kind of proof and a proof is EXACTLY what I described.

For the rest of the nonsense you write. I have no idea, it clearly has no relationship to mathematics and seems to be logically incoherent.
Again, do you have any formal training in mathematics?

[Anonymous No.11119125]

>>11119122
Nah, rather than engage I prefer to return once I manage to formulate my argument clearer. See you later. And yeah, I'll be careful in regard to damn door.

[Anonymous No.11119127]

>>11119122
Formal, by the way, implies formalistic paradigm, that has been overthrown and supplanted for almost a century already.

[Anonymous No.11119129]

>>11119125
Try doing some mathematics first, that will help familiarize yourself with what a "proof" is.

[Anonymous No.11119132]

>>11119127
>Formal, by the way, implies formalistic paradigm
Nope.
It implies you having any actual training and not just having watched a few popsci videos.

[Anonymous No.11119135]

>>11119132
Pure math is still a branch of formalism and is to be treated on the same rights nowadays as metaphysics.

[Anonymous No.11119149]

>>11119135
LMAO.
You have no clue what mathematics is, right?

[Anonymous No.11119152]

>>11119149
I know what it isn't anymore. Anything even remotely related to common sense or any practical considerations whatsoever.

[Anonymous No.11119158]

>>11119081
a proof is not some theorem or axioms that can turn out to be self-contradictory, a notion of proof is given by a definition and you can't apply "self-contradictory" to definitions. Perhaps you meant to ask what if rules of logic that we use end up being proven self-contradictory but the chance for that is very minimal because we have proved with a very weak assumptions that they are sound.

[Anonymous No.11119159]

>>11119152
>Anything even remotely related to common sense or any practical considerations whatsoever.
The pure mathematics from 100 years ago is absolutely essential for our lives today, although it was useless 100 years ago.
Your critique of math today is retarded and lacks a fundamental understanding of history.

Also there is no distinction between "pure" and "applied".

[Anonymous No.11119165]

>>11119158
If a notion of proof is given by definition, and if I, using that definition, end up constructing another, circular, definition of the same notion, proof, and that, second, definition, after having been simplified to basic notions only, ends up being irreconcilable with the first - then there will be a problem.

[Anonymous No.11119168]

>>11119158
Definition is construction of notions that are to be considered complex, from notions, that are to be considered basic (undefinable) - as well as some other to-be-considered-complex notions constructed earlier.

[Anonymous No.11119182]

>>11119158
In other words, what if I circularly define "proof" through "proof" and something else, and that "something else", that, figurative speaking, got stuck to "proof" while I was going in circles, ends up being 1) independent of notion of "proof" - and 2) not cancelling itself on its own?

[Anonymous No.11119186]

>>11119165
Which will be equivalent to a contradiction in first Order Logic.

If 2 notions are the same, but by valid simplification different then logic is contradictory.

[Anonymous No.11119190]

>>11119182
That would obviously be a contradiction to basic logic.

>>11119168
>basic (undefinable)
LMAO
What the fuck are you on about. EVERYTHING in mathematics is defined precisely, even THE MOST BASIC NOTION.

[Anonymous No.11119191]

>>11119186
Or it could also mean there is implicit substitution of notions going on in case of, in this case, "proof". Or in one the basic notions it is defined from. In other words, somewhere, two different notions are considered one.

[Anonymous No.11119195]

>>11119191
If two equivalent things are different then FIRST ORDER LOGIC IS BROKEN.

This shouldn't be hard to understand and really has nothing to do with the concept of proof.

If you take any valid statement which is equivalent to another valid statement and carry out equivalency transformation and get something different first order logic is broken.
There is no other option.

[Anonymous No.11119200]

>>11119190
Defined in WHAT TERMS? And in what terms are THOSE terms defined? And so on? Don't you think by regressing thus you should arrive at either circular definition or an undefinable notion while following ANY GIVEN STRAND?

[Anonymous No.11119208]

>>11119200
>Defined in WHAT TERMS? And in what terms are THOSE terms defined? And so on?
First order logic and set theory.

>Don't you think by regressing thus you should arrive at either circular definition or an undefinable notion while following ANY GIVEN STRAND?
No. You arrive at the axioms of first Order Logic and set theory.
Or whatever foundations you have chosen instead.


Okay, seriously. Do you not know this? Have you ANY mathematical background at all? Mathematics isn't like your philosophy 101 class, where you vaguely handwave Ideas back and forth.

[Anonymous No.11119209]

>>11119195
You do the circle by making transformations allowed by axioms and, by extension, theorems of your current theory. It is through THEM something extra can get stuck to a definition while doing a circularity. A circular definition constructed from a direct one and irreconcilable with said direct one, would mean there is something wrong with the axioms of the theory you do this in.

[Anonymous No.11119213]

>>11119208
I will reply like this: I have my own interests.
First Order Logic. Okay.

[Anonymous No.11119217]

>>11119209
>there is something wrong with the axioms of the theory you do this in.
Yes, namely first Order Logic or set theory, ZFC specifically as it is the most common foundation.

But this Idea is over a hundred years old and it is known that no solution exists.

[Anonymous No.11119220]

>>11119213
>I will reply like this: I have my own interests.
So no clue about foundations of mathematics, so in no position to have any informed position.

[Anonymous No.11119226]

>>11119217
If you mean the idea of doing a circle the way I described then I have reasons to consider this idea being more than 200 years old, actually.

Doesn't matter. I'll return once I am able to elaborate further.

[Anonymous No.11119227]

What the fuck are matrices in the REAL world (inb4 movie jokes) I want to anchor it to something real and tangible

[Anonymous No.11119232]

>>11119220
Nobody has any clue on foundations of mathematics, it's just an approximation of how universe works because we can't see the source code so we reverse engineer from the inside

What is a point
Prove that a point exists
Etc

[Anonymous No.11119237]

>>11119232
Not me.
-circle-poster

[Anonymous No.11119240]

>>11119226
>If you mean the idea of doing a circle the way I described then I have reasons to consider this idea being more than 200 years old, actually.
No, the idea that the foundations of mathematics are logically inconsistent.

>>11119232
Mathematics is derived from precisely defined formal statements, called Axioms.
Also these Axioms are mostly unrelated to reality (and in fact go against common experiences in reality, such as the Axiom of infinity).

[Anonymous No.11119242]

>>11119227
>What the fuck are matrices in the REAL world
What does that mean? A matrix is a mathematical object, it doesn't exist in the "real world".

[Anonymous No.11119244]

The virgin theorem vs the chad axiom
>theorems are not self evident :^)
>but axioms are!
>how so?

[Anonymous No.11119245]

>>11119232
>Prove that a point exists
Can be done by construction, construct R from ZFC and define a point as an element of R^n.

[Anonymous No.11119252]

>>11119244
Axioms are not self evident.
They are just true by assumption.

[Anonymous No.11119253]

>>11119242
You can (probably) approximate real world shit with it just as you can approximate certain phenomena in electricity with imaginary numbers. Coincidence?

[Anonymous No.11119255]

>>11119252
Prove that axioms are true by assumption.

[Anonymous No.11119260]

>>11119245
Good point

[Anonymous No.11119264]

>>11119255
The definition of an Axiom is a statement which you can not prove but you assume to be true.

This is logic 101.

[Anonymous No.11119270]

>>11119264
It is logical to assume something to be intuitively true... but why is it intuitively true? How did our intuition "prove" it to us - so it is known as true in the mind of every conscious person?

[Anonymous No.11119273]

>>11119264
So you define axiom through proof? Kay. Whay you define proof through then?

[Anonymous No.11119278]

>>11119273
Bro just watch spirit science video the maths of god

[Anonymous No.11119281]

>>11119227
arrays of numbers

[Anonymous No.11119317]

>>11119281
They are not random and follow specific rules which can be counterintuitive at times (A*B != B*A) so they aint just arrays jose

[Anonymous No.11119343]

What is zero (0) ?

[Anonymous No.11119351]

>>11119270
it's better to view axioms as definitions

[Anonymous No.11119362]

>>11119227
linear transformations: rotations, reflections, orthogonal projections, scalings, shearings, translations (not completely linear, but they fit the picture)

[Anonymous No.11119413]

Going through Pinter's and I finished the exercise in which you need to write down the Cayley table of the (Abelian) group corresponding to the power set of a 3-element set endowed with the symmetric difference as operation. Does anybody know which of the 3 Abelian groups of order 8 this is isomorphic to? I thought I could just compare the Cayley tables, but perhaps this reasoning was wrong.

[Anonymous No.11119504]

>>11119413
What is the order of any element of your group?

[Anonymous No.11119542]

>>11109011
zoomer here
memes aside, is this a legit roadmap?

[Anonymous No.11119569]

>>11119542
Every road map is a legit road map if it leads to where it is claims to lead to. This one would lead to mathematical mastery of non-western levels if carried out.

[Anonymous No.11119612]

>>11119542
no

[Anonymous No.11119662]

>>11119270
Axioms are not always intuitively true, they are very carefully chosen to enable a certain kind of mathematics, a mathematics which is (coincidentally or not) also used to describe physical phenomena.

>>11119273
Neither of these statements is coherent.
For example, axioms aren't defined, especially not "through proof".

[Anonymous No.11119665]

>>11119317
They are arrays in combination with certain operations.
Alternatively they are linear maps between vector spaces.

[Anonymous No.11119739]

>>11119504
[math]a^2 = b^2 = c^2 = e[/math], so 2. I haven't quite gotten around to quotient groups yet (I just like adding stuff I try to figure out myself to the notes I'm making), but would I be correct to say [math]\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}+2\mathbb{Z} = E8[/math] , the elementary abelian group of order 8?

[Anonymous No.11119743]

>>11119739
[math]\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}
Sorry, latex error.

[Anonymous No.11119845]

>>11119662
So, is "axiom" to be considered a basic (undefinable) concept then?

[Anonymous No.11119985]

>>11119115
>Assume the notion in question is basic
>Assume you manage to end up managing to define it circularly through a combination of itself and certain other notions
>You elaborate those notions as per their definitions until all of those notions constituting the circular definition in question are decomposed into basic notions only
These are meaningless notions.

[Anonymous No.11119999]

>>11119081
>>11119115
>>11119118
>>11119119
>>11119125
>>11119127
>>11119135
>>11119152
>>11119165
>>11119168
>>11119182
>>11119191
>>11119200
>>11119213
>>11119209
>>11119240
>>11119244
>>11119255
>>11119264
>>11119270
>>11119273
>>11119662
>>11119845
Undergraduate ```````logicians''''''' are not welcome in this space. Kindly fuck off to >>>/lit/.

[Anonymous No.11120083]

>>11119999
Checked.

[Anonymous No.11121191]

holy shit this place only ever gets worse
i leave for like 9 months and we get a different schizo