/sci/ - Science & Math

>>11641742
BASED edition.

Sometimes I like browsing through nlab pages on completely non-categorical topics just to see how they attempt to shoehorn in a category somewhere

>>11641742
I don't get it

>>11641742
How to get a rec letter this short but good? Being called a mathematical genius is no small feat

For some reason making these got really easy really fast.

Threadly reminder to work with physicists.

>>11641838

step one: dont be a brainlet

>>11641830
You ever seen a beautiful mind? John Nash was this guy who was really good at math and was recuited by the US government to crack codes to defeat the Russians. I think that was the plot. Its not particularly important, considering that John Nash suffered from schizophrenia and this was all in his head. Hes like the popsci crazy genius guy.

>>11641840
>For some reason making these got really easy really fast.
do me

>>11641848
>schizophrenia
No such thing.

>>11641838
if you have to ask you're not smart enough
nash was so chad he didn't even care and still impressed the shit out of everybody

>>11641830

A short letter is more powerful than a long one.

Maths is poopy :)

>>11641868
ok lol

>>11641830
19 year old Mr. Nash give really good head.

This is just a rant of frustration and depressive thoughts, you can ignore it:

I am a computer science student that might have to repeat a math class on Probability and statistics.
so basically with coding at least, you can approximate to a better solution by the approximating cycle of sketching, programming, reviewing the compile errors and the expected result, researching more about the problem.
The compile error and the expected result i am trying to approximate helps me to undersand everything more deeply.

In intermediate math, i have the problem that I get no compile errors and i can only slightly approximate to the result i am thinking is the solution and if I get them, then they are related to me not getting enough points to get admitted into the exams.
Furthermore, if I send it to my tutor, all i get is a true or false for syntax errors.
It causes me severe anxiety and feelings of doom and uncertainty as I fear losing and shaving off more years out of my life for a piece of paper.
I'd have been much more happier if I could learn math on my own as a hobby and meet up with people to discuss it and not be scared of a deadline and probable loss of a year.

Thank you for your attention if you actually read this.

>>11641776
This is literally the babby's first identity with binomials, I'm sure I knew this in highschool already for x, y natural. Extending the result to x, y complex is even easier, just basic properties of polynomials. Then an undergrad category theorist comes by, inserts words like "zariski-dense", "extensive category" and thinks he's doing advanced math.

>>11641776
How did they not prove that using a classifying topos or at least some [math](\infty, 1)[/math]-category? My, my, they are losing their edge with only that level of pretentious.

>>11641742
Does anyone know how professors recognize genius? Is it because they solve problems fast? Is it because Nash discovered something new? How would you recognize that a student is a genius?

>>11642393
how could you NOT recognize that some people in your class are dumb and some are smart?

>>11642320
lel

>>11642393
Solve problems states in discussion quickly, bring forward interesting viewpoints and questions, recognize/rediscovering known concepts without having heard of them, etc. Is my guess.

>>11641776
Related,

The /mg/ from 2 weeks ago is not in the archive anymore, but back then someone posted a link to this PhD thesis and I'm gonna do an overview of it later today, if you're interested
https://arxiv.org/pdf/2004.05631.pdf
My tl;dr would be that it's about (with an eye on feasible Generative Model computations) casting available statistical information in QM language, to be able to do things like taking partial traces. It has a very textbooky kind of flair and as such was a good read.
The last chapter is somewhat separated and clarifies the commonalities (of the adjunctions living) in the vector space C^X, the predicates 2^X and the sheaves Set^X.
Here's a relevant item on how the math looks like
https://en.wikipedia.org/wiki/Matrix_product_state
Here's a video of the advisor

https://youtu.be/hZfLEX6d-Dk

>>11641864
Dozo.

>>11642467
Her right hand's middle finger was kind of funny, so small adjustments have been made.

[eqn](a+b)^2=a^2+b^2[/eqn]
[eqn]sin^{-1}(x)=\frac{1}{sin(x)}[/eqn]
[eqn](a+b)(a-b)=a^2+2ab-c^2[/eqn]
[eqn]\sqrt{a+b}=\sqrt{a} + \sqrt{b}[/eqn]

What about von Neuman. He helped J. Nash. And pretty much had influence on every area of Physics and math today
https://www.youtube.com/watch?v=VoXh5_3uBBE

Dear Professor Makise:

This is to recommend Mr. Anon B. Ased Jr. who has applied for entrance to the graduate college at /sci/.
Mr Ased is 35 years old and was able to solve it. He is a mathematical genius.

>>11642457
https://youtu.be/sIy9pD4sTVA

>>11641742
>>11642990
CALIFORNIA INSTITUTE OF TECHNOLOGY
CHARLES C. LAURITSEN LABORATORY OF HIGH ENERGY PHYSICS
October 14, 1985

Dr. Stephen Wolfram
School of Natural Sciences
The Institute for Advanced Study
Princeton, NJ 08540

Dear Wolfram:
1. It is not my opinion that the present organizational structure of science inhibits “complexity research” – I do not believe such an institution is necessary.
2. You say you want to create your own environment – but you will not be doing that: you will create (perhaps!) an environment that you might like to work in – but you will not be working in this environment – you will be administering it – and the administration environment is not what you seek – is it? You won’t enjoy administrating people because you won’t succeed in it.

You don’t understand “ordinary people.” To you they are “stupid fools” – so you will not tolerate them or treat their foibles with tolerance or patience – but will drive yourself wild (or they will drive you wild) trying to deal with them in an effective way.
Find a way to do your research with as little contact with non-technical people as possible, with one exception, fall madly in love! That is my advice, my friend.

Sincerely,
Richard P. Feynman

>>11643175
Don't tell me he named his program Wolfram Alpha to re-establish his self-perceived alpha male status.

Does Desargues's theorem hold on Fano plane?

>>11642498
Anon, did you have a stroke?

>>11643271
>Does Desargues's theorem hold on Fano plane?
What have you tried?

>>11643253
He even effectively renamed his language Mathematica to Wolfram Language.

>Mathematica was always just the UI, bro

>>11643447
End my pain.

>>11643412
>What have you tried?
Marijuana. But I didn't inhale.

>>11643271
no
>(...) the Fano plane is considered to be a Desarguesian plane, even though the plane is too small to contain a non-degenerate Desargues configuration (which requires 10 points and 10 lines).
https://en.wikipedia.org/wiki/Fano_plane
literally took me under a minute of searching and I'm not even a geometer, stop being so fucking lazy

>>11643542
>the Fano plane is considered to be a Desarguesian plane
I'd interpret it as 'yes'.

>>11643542
>he thinks vacuously true means false

https://www.muramatik.com/motives-what-not/

>>11642498
a) a,b = 0

b) x = +- 0.944039..

c) a,b = 0

d) x =/= 0, y = 0 or x = 0

NEXT

>>11643737
why do these all use fucking zoom?
I'd watch some if they were posted to youtube but fuck manually signing up for every single seminar I watch to casually watch.

>>11643753
No idea. Maybe the reason is something like making it easy to ask questions both via voice and text chat. Regardless, I liked the way Regensburgers did their thing with a riddle giving a password instead of requiring any registration. It was a nice idea.

>>11641742
>>11641742

I don't get it. How did they get rid of the sum that defines [math]\eta[/math] in the first line of the proof?

Shouldn't [math]d\eta = \sum\limits_{b=1}^{k}dA^{a}_{b}\wedge \theta^b[/math]?


(The only thing missing from this image is the condition on the [math]\theta[/math] that they mention. This condition is just that they are pointwise linearly independent.)

>>11643800
it's a type of notation
they don't write the symbol [math]\Sigma[/math], the summation is implied by the b letter

>>11643800
It seems like the author just forgot it is there, or it could be the Einstein notation.

>>11643800
Einstein notation is the stupidest fucking shit ever invented

>>11643808

Ok, fair enough

But still, why does it look like they applied some kind of Leibniz rule?

In other words, where did they get the term [math]A^a_bd\theta^b[/math]?

>>11643814
You have a product of stuff, and you apply the differential on that. The differential is a derivation, so you get the Leibniz rule sum thingy. Does the material not mention that?

>>11643822

> The differential is a derivation

I forgot about this fact. I thought the Leibniz rule was only for vector fields

Idk maybe I am thinking of the exterior derivative. I don't really know the difference at this point

>>11643814
don't you know the Leibniz rule for the exterior derivative of forms ? if you don't, you should seriously go back a bit

>>11643853
dude just go back in your book and look up the definition of the d letter

>>11643853
>I thought the Leibniz rule was only for vector fields
I mean, no.
You don't have the Leibniz rule for differential forms tho, you have the *graded* Leibniz rule.
See https://en.wikipedia.org/wiki/Exterior_derivative#In_terms_of_axioms

>>11642333
>I am a computer science student
stopped reading right there

bros.....

for me, it's the theory of functions of one or several complex variables, the king of mathematics

>>11644047
Still haven't found your thing, eh? What was it that drove you to pick maths in the first place?

>>11643937
> it was at this moment
Why tho. Looks natural (probably even in a technical sense)

>>11644100
SCV gang lel
best meme

>>11644100
Why?

What's a book that deals with Grassmanians in the context of algebraic geometry in a nice way? Even if it's just a page or something. The example on Shafarevich's Basic AG is unparsable

>>11644337
Husemoller's book on bundles treats Grassmannians in the general context. It may be worth checking out, at least for reference purposes. Chapter 2 https://www.maths.ed.ac.uk/~v1ranick/papers/husemoller

Nighty-night /mg/.

does probability theory ever get interesting?

>>11644374
Gn

>>11644392
what are some uninteresting parts?

>>11644374
It makes me depressed that this is 55 years old. Is there nothing new under the sun?

>>11644337

Griffiths and Harris

>>11644478
lel
>>11644337
Harris' AG book has lots of stuff about Grassmannians. In fact it has a ton of stuff about basically any specific example you want to read about.
Also I think there's an entire bigass chapter of Hodge/Pedoe dedicated to Grassmannians and Schubert calculus but the age of that will depress you even further than the other book

>>11644042
lol rekt

>>11644439
he really has a way with epsilons

what impact does your level of free will have on your mathematical ability?

Would using Lang's Algebra as a pillow allow me to permeate the contents of it in my brain while I rest my head on it during my sleep?

>>11644670
what have you tried?

>>11644670
>Would using Lang's Algebra as a pillow allow me to permeate the contents of it in my brain while I rest my head on it during my sleep?
Lang is a meme.

Was it ever decided what the morphisms are in the category of axioms?

reply to this post with the year you predict Riemann hypothesis will be solved

>>11644439
>what are some uninteresting parts?
all the problems my book uses and the pace it moves at

>>11643336
>yes i don't know how to to use TeX, how could you tell?

>>11644687
>Was it ever decided what the morphisms are in the category of axioms?
Hodge theatres

>>11644153
>Why tho. Looks natural (probably even in a technical sense)
>defines [math]u(f)[/math] using [math]d[/math] instead of defining the differential of a function using [math]u[/math]
>using a random theorem as the definition of the Lie bracket and then proving the definition
I honestly don't even know what definition of the tangent space he's using, because both the Leibniz rule one and the curve speed one come with an action on functions.

>>11644687
There's a bunch of abstract categories relating to such broad ideas, e.g.
https://ncatlab.org/nlab/show/syntactic+category
https://ncatlab.org/nlab/show/proposition#in_categorytheoretic_logic
The objects are contexts G (e.g. x:A), constructively, those are theorems and their proof's, and arrows in G to H between them, exist when given the context G, you can actually form the judgements given by the context H.

>>11644692
2058

>>11644746
I don't know why he decides to use the bracket to set things up, but in any case, if there's no more choices being made, it's probably natural enough. It's just a feeling though, I haven't checked anything there.

>>11644687
The mathematical consensus is that projections are the morphisms.

>>11644676
I tried eating it.

>>11641838
just be exactly as the letter indicates you are, the fact you asked or didn't understand that immediately really makes me think you aren't an english genius, math genius maybe?

I spend a massive amount of time on my phone away from home. I can't watch videos but I can read at my leisure. Is there any decent way to keep studying math on the go that isn't some meme app or site?

Is the end of non-academic math quantwhoring

>>11645234
ibooks/literally any pdf reader app

>>11645245
no. quant jobs are pain. you spend 80 hour weeks digging around the guts of models in the most cutthroat high-stress environment available (that doesn't involve people dying) competing with gigabrain robot chinks who haven't missed a question on a test since the 2nd grade.
98% of the people who say they want to be quants have no idea what being a quant means, they just have no real career goals or interests in life so the only thing they can think of is to just make SOOO MUCH MONIEEEE DUDE

the endgame of non-academic math is a government job where you are basically tenured and make $150K/year to do 3 hours of research a day

>>11645344
Why the racism?

>>11644184
Have you ever seen a quasiconformal mapping? It's not a definition an intro to complex analysis lecturer would tell you.

Good morning /mg/!

>>11644439
>It makes me depressed that this is 55 years old
I never realised it is that old. Now that we started on the topic of old things, I wish there was a more modern version of https://web.math.rochester.edu/people/faculty/doug/otherpapers/bk-yellow.pdf

Can you recommend some good math blogs or some interesting collection of some sort of articles? Just interesting stuff or good insights or things that help in the math studies.

>>11645953
http://arminstraub.com/math/what-is-column

>>11644670
no, use bourbaki instead

>>11644670
try listening to it while you are sleeping

You have a pool with 3000 L of water with 35 g salt per liter. You also pour in water with 12 g salt per liter at a rate of 10 L per minute. You also pour out 10 L per minute.

I found the differential equation and solved for S(t) and found the salt concentration after s(120) = 27,41 g/L. But I can't seem to solve what in / out has to be when you want the salt concentration to be 25 g/L after 120 minutes.

>>11645925
>Good morning /mg/!
/gmmg/

And I understand your frustration.

will mathematics help me forget about her?

https://groups.google.com/forum/#!topic/homotopytypetheory/Sy2Xho5O-xk

>>11646035
could this not just be solved with algebra?

>>11646147
no but you will keep telling yourself that it does

>>11646147
I dedicated my life to mathematics after realizing I will die alone. Made lots of progress already in my work.

>>11646139
>/gmmg/
Clever. A slight generalisation: [math]\text{/g}x\text{mg/}[/math] where [math]x\in \{ \text{m}, \text{n}\}[/math].

>>11646147
No, but trying to forget about her can help you do mathematics if you use it as a coping strategy.

doesn't look like i got into the msc program i applied to. what the heck do i do now? take a few courses at a local uni and apply somewhere else? yes... i only applied to one.

>>11643175
>literally calls him incel
>watch an interview with wolfram
>he talks about his time working with Feynman and how all was good
Jesus Christ

>>11646372
severe cringe

>>11646382
I'll have a #6 supersize

>>11646382
Just do a masters in your bsc school?

>>11646412
I don't usually feel anything but despair or the 5 seconds joy of understanding something while reading papers, but this time I must admit severe cringe entered my list of feelings towards this one. Imagine my shock!

>>11646706
Ill have more time from now, but brain still fried from signals test

>>11646372
he must have been tired of slapping quasi- and pseudo- in front of already defined concepts

>>11646709
Nice! How did it go?

>>11646712
Seems quite likely. Alternatively, it may be that this is inspired by strange words like syzygy, and is an attempt to get to name something oddly. However, in that case it's not even the obvious but not too over the top "notice me senpai" trick of using the Greek version of the first letter of your name. This is like pure chaotic evil.

>>11646525
he hasn't finished his msc yet, tho

>>11646746
I think it was enough to pass, thats what you get when you try to study 2.5 months of material in 3 days;
Now just have to understand a more in depth chapter about fourier transform and series and submit the lab in under 3 days, a lot less stressful tho and I think ill get back to algebra

>>11645344
>the endgame of non-academic math is a government job where you are basically tenured and make $150K/year to do 3 hours of research a day
Sounds pretty comfy

>>11646918
That's what I call the bulimia strategy. You binge all the material and then you vomit it on the exam sheet. Not much is learned, but hopefully your exam is passed. Good to hear that your stress levels are going down. Try to get some rest over the weekend!

If there's anybody here who does algebraic topology or anything else with a lot of categorical bullshit in it: how do you approach all the big convoluted commutative diagrams in books/papers? Do you actually work through the details? Do you just skim them? Is it one of those things where with enough experience it's just supposed to be magically obvious to you whether a diagram commutes or not?

Just keeping track of a basic little diagram chase on a couple exact sequences makes me want to jam a pencil in my eye. When I encounter those gigantic hideous diagrams with 30 arrows that take up half a page it's really hard to believe that anybody has actually even checked the whole thing.

how do i go about getting a non academic math job? ive searched for companies and jobs but it seems like the best employer is the nsa which requires a phd and an incredible background. is there any middle ground or do you have to be in the top .1% to actually get a math job

>>11646997
Yes, me. I put my fingers on the diagram and move them along (and against) the arrows if it's a diagram chase thingy, and if it's not then I check what the arrows in the diagram actually are. If there is some universal property inducing an arrow, I check that I know what that UP is, etc. Let's suppose we have a two short exact sequences and then arrows between all but the second objects (counting from either left or right, doesn't matter). Suppose that these given arrows make the diagram commute. Why is there an arrow filling the empty space between the second objects and making the whole diagram commute? Because the second objects are (co)kernels!

Now, let's apply this approach to some gigantic diagram. First, check what commutes by assumptions, then check which objects have universal properties inducing arrows. If lucky, there may be a square where you have corresponding subobjects or quotients, so the commutativity is easily checked. Little steps like these, my friend.

Do you have some particular (non-IUTeich) example in mind?

>>11646035
just gonna leave this here, probably not right

>>11646997
When those diagrams get too complicated to check, I usually put the blame the 1870's Germans for ignoring the 1840's Germans and get the US military to fund a new Foundations project that retcons the situation. Don't get in bed with CS people though, you'll end up an hero.

do you know any places where you can get diverse and creative math and logic problems? like putnam, CEMC contests, math kangaroo

it can be both formal math problems but also iq test like problems. I really enjoy solving them

You're basically asking for puzzles - and in particular, puzzles that have already been solved?
Otherwise, math is full of "math and logic problems" (that don't have a solution) and textbooks generally feature problems at the end of each chapter.

>>11646997
It's just notation for several different compositions being equal. You could write it as one (or multiple) big equations if you wanted to, but that's not as informatic as a schematic with all the domains/codomains shown. A picture is worth a thousand words as they say.

>>11646994
I agree and I hate niggers that do it, I still got 'lucky' because it was 'open book' since it was online, so i focused on understanding stuff and then I just knew where to find stuff that I had already done or was in the lecture notes; I still didnt do a lot of shit and have a far weaker grasp and intuition than I should tho

>>11647106
Just do the exercises in a textbook

>>11647041
It wasn't really a complaint about a particular diagram, just a curiosity. I sometimes have to read things about Hopf algebras and they sometimes do generalities for Hopf monoids in (braided) monoidal categories in there. Most of the proofs in the categorical sections follow the same pattern of
>fatass diagram
>well duh
>
Maybe this isn't so bad since pretty much every individual polygon follows from some axiom or another if you're patient enough, but I've seen an example or two where they got so tangled the author had to start omitting [math]\otimes[/math] between objects just to clean them up.
It seems intimidating to keep track of that much shit at once, it made me wonder how people who have to do so approach them, especially in topology or AG where maybe the individual steps aren't so trivial either.

>>11646189
bruh that shit's retarded

>>11647360
What exactly?

I'm simply surprised that the guys working so close on HoTT still have those philosophical fundamental questions/different views on the basic building blocks of their framework. Although the issues they raise probably could also have been raised about Martin Löfs theory in the 80's.

>>11647287
Well, the good thing is that people who do that all the time tend to fall off eventually. I don't know why it was that particular course, but the one on Lebesgue measures and integrals was one that could even stop such people from getting their bachelor's degree back in the uni I got mine from. They get punished eventually. Just make sure you fill the gaps in your understanding over time, so the same won't happen to you!

>>11647314
I see what you mean. Essentially, like >>11647246 said, it is pretty much just saying that different composites are equal. It all comes down to triangles and rectangles in the end, and if you just happen to know some relationships between the arrows, universal properties of objects etc., then you can work it out. Some notational burden is OK to be dropped for clarity, but really the tensor product signs? Seriously?

>>11647384
Tbh wasn't looking super closely, just seems like they're arguing semantics. + the start reminded me of why I hate tankies (i.e. "Well Marx said..." or for them "Well Aristotle said..." like bitch that was so long ago, who cares!). Just define your shit mathematically and move on?

>>11647396
>but really the tensor product signs? Seriously?

>>11647246
>You could write it as one (or multiple) big equations if you wanted to
To be entirely honest, sometimes you couldn't because of abuse of notation.
I mean, you [math]could[/math], but it would take a while.

>>11647427
Not as bad as you made it sound like for objects, since the author explains the notation. However, that is still both a horrible diagram and the morphism notation I wouldn't personally like to see or use myself. I seriously hope the same author doesn't drop the composition circle.

>>11647445
>Not as bad as you made it sound like for objects, since the author explains the notation.
oh, for sure, I'm sure nothing I have access to is THAT bad compared to what's out there. I'm a complete tourist regarding anything like this.

That's also admittedly an exaggeratedly bad example, since the diagrams in the book that comes from are easily the worst ones I've ever seen. Most people are more restrained with them, but even less comical diagrams are still a bit of a challenge for me to keep pace with.

>>11647466
I'm not saying it's not bad. Here it is almost OK, since it just a fixed object and its ideal, but imagine having [math]M\otimes_R N = MN[/math] as the notational convention for any suitably sided modules. Then I would find the author and extract some answers to the simple question "why do you hate your readers?". The morphism notation is absolutely horrible, and I hope the author got some feedback on it. That is probably the worst non-Mochizuki diagram I have seen, too. Not even the model category diagrams look that bad, but they actually have reasonable notation, so that may help.

>>11647423
I think it's a good discussion to have.
As a type theoretical frameworks, not only are proofs mathematical objects, so are there expressions (judgements) that aren't propositions (statements that can be false.)
Homotopy Type Theory is all about adopting a groupoid view on equality, as oppose to the extensional e.g. set theoretical one. I.e. isomorphisms vs. nested bags comparisons.

And they discuss and wrestle with the fact that traditionally, in math you don't distinguish between equality and identity. In German: "das gleiche" vs. "das selbe".
>Der iPad, den du gestohlen hast ist der gleiche, den ich vor 2 Wochen gekauft habe.
>Der iPad, den du gestohlen hast ist der selbe, den ich vor 2 Wochen gekauft habe.
In English I guess that's
>The ipad you stole is the same that I bought 2 weeks ago.
and I don't know if you can quickly make the distinction if this situation now means I don't have my iPad anymore or not.

They give the common language example
>In an equilateral triangle, any two sides are equal
where, in any case, the meaning is not that all sides of a triangle are the the same (in the identity sense) triangle.

The issue comes up in relation to the fact that type theory has definitional judgements of equality b:=a+1 as part of the theory (unlike first and higher order logic, whether definitions are a matter of the meta-theory) and they discuss if they made misleading choices when writing their HoTT book.

Which brings us back to
>>11647427
>>11647091
given the motivation of Vodovosky for the HoTT program was to come up with mathematical foundations that could be implemented on a computer ... As opposed to set theory, which falls back to model theory, not equating isomorphic structures by design, and which has super-exponential ballast as soon as you discuss anything resembling geometry.

>>11647498
*(in the identity sense) side

how do i stop comparing my own intelligence and mathematical abilities to others

>>11647543
I don't think anybody knows, but be assured it's pointless.

>>11647491
whore gtfo

>>11647427
>Thus, H^3 stands for H * H * H
This should just be standard notation. In fact, the tensor product symbol should just be abolished and replaced with something that's not three goddamn strokes and an optional subscript.

>>11647669
I recall seeing [math]H^{3 \otimes}[/math] or something similar enough once.
Good notation.

>>11647679
That's the standard notation for tensor powers, afaik. It's even what Wikipedia uses.

>>11647721
>indices swapped
Knew I was doing something wrong.

>>11647721
But he's doing the 3 first, not last.

Something different:
Does anybody know the number of legal bracketings in the finite sets (without urelements)?
For lists, this the Catalan numbers, but for sets you e.g. have
{{},{}} = {{}}
and so at level 3, already one is kill

>>11647669
Should it just be a \cdot with a subscript if necessary then?

>>11647750
What are you doing about commutativity? i.e. for ordinary Catalan bracketings (())() =/= ()(()), but if you're treating these as sets I'm not sure if you want to distinguish those or not.

>>11647750
i'm entirely sure what do you want to count
also, my advice for any counting problem is: compute the first 5 terms, then search it in OEIS

>>11647802
I think of finite sets with all their behaviours, so
{ {{}} , {} }
and
{ {} , {{}} }
are the same (in the my iPad stolen kind of way)

>>11647547
i do kind of know it its pointless but i cant stop it

>>11647818
Come here and I'll give you a hug.

>>11647811
good idea. I had already stated that trial (pic related, might have blunders) and I find this sequence, although it doesn't speak of sets or backets

https://en.wikipedia.org/wiki/Padovan_sequence
https://oeis.org/A000931
>931
an early one, cute

>Zagier conjectures that a(n+3) is the maximum number of multiple zeta values of weight n > 1 which are linearly independent over the rationals.
wat

>>11647814
You're missing my point. I'm asking if this is happening inside of a set or not (i.e. do you always assume there are fixed brackets on the outside so you have { a legal bracketing }? Like I'm saying the example {{}}{}, which is a legal bracketing in the Catalan sense, cannot be interpreted as a single set unless you place two extra brackets around it.

>>11647850
Shouldn't { { {{}} , {} }, {} } also be viable for 12 brackets?

>>11647934
I meant with brackets around them, as basically I'm counting unique standalone sets in a certain way (and if we'd take the unpacked ones, we'd double count some). Although the numbers obtained from the two variants might have a simple relation as well.

>>11647998
You're correct, the level 7 block will probably have issue

>>11647850
I computed this 9 terms out, I think I found what you want
http://oeis.org/A004111
>thus a(n) is also the number of sets that can be made using n pairs of braces.

>>11648265
Nice!!
How did you compute it? You mean by hand?
I tried to find a simple recurrence scheme but didn't get far, and I also tried to brute force is but chose a naive approach based on some code I already had, and that would also not finish.

So this read that the recurrence relation is
[math] a_{n+1} = \frac{1}{n} \sum_{k=1}^n \sum_{d|k} (-1)^{k/d+1}\cdot d\cdot a_d [/math]

That [math] a_d [/math] is nasty and really hoped for something nicer but it indeed already felt like some sort of inclusion/exclusion thing going all the way down at each level.

>he calls it Grothendieck-Riemann-Roch instead of "Riemann-Roch Theorem: The New Black"

Mhm, so ZF minus Infinity is also directly a theory of the "is a node on the root" 2-ary predicate (otherwise known as "[math] \in [/math]") of the trees that have no non-trivial automorphisms (no superfluous/duplicated branches).

I already saw something like this before. Then there's set theory axioms that plain say
>Every rooted directed graphs (i.e. loops allowed) corresponds to a unique set
and thus you get set theories that allow for self-inclusion. E.g. the simplest one has [math] x\in x[/math], which is the graph that's just one loop.

https://en.wikipedia.org/wiki/Non-well-founded_set_theory

>>11648439
Riemann-Roch Theorem: >Hells Kitchen Edition

>>11648311
>How did you compute it? You mean by hand?
Yeah, by hand. It's not too bad once I got down how to do it.
This explanation is very shit, but I'll try: to build a set on 2(N+1) brackets , pick a partition of N: (k_1,k_2...k_n). I want to find for each component of this partition a set on 2k_i brackets, and if I take all of those sets as _elements_ of a set, that gives me a set on 2(N+1) brackets.

So then you simply run through all the partitions of N and count how many ways there are to choose sets of matching sizes.
For example, to count sets on 7 pairs of parentheses, you would look at the partitions of 6:
6 = 6,5+1,4+2,3+2+1...
and for each partition count how many ways you can builds sets of those sizes, which you can do as long as you've computed the previous numbers already. It's not as slow as it looks because the majority of the partitions have zero ways (e.g. you can never have more than a single 1, because there's only 1 set on 2 brackets)

You could probably define some notation and write out an "explicit" formula for this as a sum over a bunch of products, but it's going to be ass cancer.

>>11648469
>This explanation is very shit, but
Nah I get it because I also tried this recursive thing, pic related.

I also saw that the OEIS guys have derived formulas, such as the partial sums. Quote
>A004111 is an important sequence and the OEIS should include various sequences derived from it.

>>11648449
>ZF minus Infinity
Should have said >ZF plus not Infinity
Here's that paper from the screenshot btw: https://core.ac.uk/download/pdf/82527034.pdf
The guy seemed to have a bunch of paper on random graphs and the games on them. It's not about the combinatorical formula, though.

>>11648439
>he calls it Grothendieck-Riemann-Roch instead of Riemann-Roch

>>11643175
>have sex basically
holy shit what a burn

>>11648522

Why don't we give certain structures names of greek gods?
>Let [math] \mathcal{H} [/math] be a separable Hilbert space
>Let [math] \mathcal{H} [/math] be a Hyperion space
>Let [math] \mathcal{H} [/math] be Hyperion
sounds good imo

What math classes are best to take at the graduate level (as opposed to undergrad level) when you're still doing your bachelor's?

>>11649320
>What math classes are best to take at the graduate level (as opposed to undergrad level) when you're still doing your bachelor's?
All of them.

Are proof books truly a meme? If so, why?

>>11641846
>mathematicians: "oh that was an interesting lil specific case of our theorem. back to thr full generalized setting!"

>>11649481
It's like reading about how to swim instead of actually getting into the lake and giving it a go.
It's just very artificial.

she is so hot bros
https://www.youtube.com/watch?v=ltvCOrIWcEY

>>11649754
She looks fuckable, but also like she's grabbing for attention in an autistic SJW way.

And why cut a 36 minute lecture into 12 three minute clips?

We call a cycle which contains every Hamiltonian cycle a "Haruhi cycle".
Do Haruhi cycles have a real name or do I have to resign myself to that shitty reference?

MATHS BTFO HOW WILL IT EVER RECOVER?

https://www.youtube.com/watch?v=UWZH-CHzFKQ

>>11650162
Okay, I just started writing my letter of resignation.

>>11649754

why is chalk still used in 2020

My internship was cancelled due to COVID-19 and now I have nothing to do over the summer. Do you guys think I can self-study Algebraic Geometry in this time? Also what are the prerequisites that I should know... I've taken the Abstract/Linear Algebra, Analysis, and Topology classes (undergrad level) but not much beyond that.

>>11650386
That sucks, anon. Do you know your rings and polynomials, do you know topological stuff like compactness and connectedness in the general context? Maybe you could pick Eisenbud's textbook if you need to get some more info on commutative algebra.

>>11650392
Yeah it's not fair, it was a software internship (inb4 cs not science or math) so it could have been remote too... anyways, I've read through the first half of Munkres but don't know any Commutative Algebra so I'll probably start with Atiyah-MacDonald. I'll check out Eisenbud, thanks.

Can you recommend me a discrete math book focused on series? https://en.wikipedia.org/wiki/Series_(mathematics).. I have one book that I've read long ago, it's called Numbers and patterns(rough translation) but I want something in English. Basically the entire book teaches you to solve questions like: find formula for patterns 1,2,3,4....; 2,4,6,8.... etc

>>11650402
https://www.math.ens.fr/~benoist/refs/Eisenbud.pdf (try to) have fun!

>>11641742
i could have been a mathematical genius as well, im schizo just like nash

How do I become a third-rate mathematician?

>>11650162
Lmao this is great

>>11650444
>How do I become a third-rate mathematician?
What have you tried?

>>11650444
Study some pure maths field in depth and produce "applications" of it.
The more categorical, homological or topological the subject the better.

>>11649481
Intro to proof is a weird class. Everyone agrees it doesn't teach you much at all, but no one teaching analysis wants to deal with a room full of students who are writing proofs for the first time. So you end up with this contentless course whose only purpose is to mark the boundary between lower and upper level math courses.

>>11649320
None of them. They're all boring.

>>11650483
>Everyone agrees it doesn't teach you much at all
I'm not sure I'd entirely agree with that. Intro to proofs is "what you should have learned in high school but didn't". Nobody in a math program SHOULD learn any math from that class, but a lot of people do, because they've been underprepared by their crappy educations.
It's a necessary evil to prevent people from coming into your Rudin-based class thinking proof by example is a perfectly valid argument.

Can I decompose functions into linear combinations of heat kernels? Similar to a fourier transformation?
Let [math] \phi(t,x) = \frac{1}{\sqrt{4\pi t}^d} e^{-\frac{|x|^2}{4t}} [/math]
Then what is [math] \overline{span(\{a \phi(t b, x - y): a,b \in \mathbb{R}, y \in \mathb{R}^d\}) } [/math] where the closure is taken in mabye the sup, L2 or W12 norm?

>>11650483
>Intro to proof is a weird class.
I thought proofbooks were already a meme on their own, there are really entire classes devoted to intro to proof? Which brainlet schools do this?

>>11650386
>>11650392
>hi I'm interested in learning a bit of algebraic geometry on my own over a few months
>hey bro here's an 800 page reference bible on pure algebra intended for people working through the entirety of Hartshorne

>>11650597
I'm not sure if that is how the English speaking part of the world functions as a whole, but it seems to be the case at least in the US.

>>11650606
I see no problem with this.

>>11650410
Concrete Mathematics might be something like what you want.

>>11650386
>My internship was cancelled due to COVID-19 and now I have nothing to do over the summer. Do you guys think I can self-study Algebraic Geometry in this time?

>>11650620
>tfw you have more authors than you have chapters

>>11650386
>algebraic geometry for babbies
Conics and Cubics.
You can also pick up a text on algebraic curves.

>>11650410
https://www.math.upenn.edu/~wilf/gfologyLinked2.pdf

>>11650594
Finite combinations only?
At least for integrals over those expressions with t to zero you obtain the trivial representation of functions with an integral over the diract delta.
Maybe topics in
https://en.wikipedia.org/wiki/Reproducing_kernel_Hilbert_space
get you somewhere

>>11650386
Smith et al. Invitation to algebraic geometry
Bertlmann. anomalies in quantum field theory. chapter 1 for geometry/topology
https://web.evanchen.cc/napkin.html the chapters on algebraic topology, category theory, and algebraic geometry
Schlichenmaier. Riemann surfaces, algebraic curves, and moduli spaces
Hori et al. Mirror symmetry. part 1
Atiyah and Macdonald. Commutative algebra. do the exercises
Vakil. algebraic geometry notes

>>11650659
> do the exercises
What for?

>>11650643
infinite combinations, and thanks for the link that is cool. Although I dont think it directly answers the question

>>11650719
No, it doesn't, I know.

>infinite combinations
What is infinite.
Again,
[math] f(x) = \int f(y)\delta(x-y) dy \sim \int f(y) \frac{1}{\epsilon \sqrt{\pi}} \mathrm{e}^{-((x-y)/\epsilon )^2} dy [/math]

How do you count "degrees of freedom" in projective space?

For example, suppose I have [math]d\geq 4[/math] points in [math]\mathbb P^n[/math] that are not all on the same line. Also assume that at least two points are not on the line [math]L[/math] containing the maximal amount of points. Could I pick the line [math]L: X_0=...=X_{n-2}=0[/math] AND also that the two points are on the [math]({n-2})-[/math]plane [math]X_{n-1}=X_n=0[/math]?

>>11650821
In hindsight, you probably can't do this in dimension [math]n=2[/math] for obvious reasons

>>11649754
Sher cute, but I don't know about that hot bud

>>11650335
It was 2015, that's about 105 years ago

>>11650597
At my school there was the class "Elementary Discrete mathematics", which was logic + proofs + basic set theory and functional notation + basic number theory + basic combinatorics + intro to graph theory. Pretty useful imo since I got none of that in high school.

>>11650746
Sorry for being vague, and I didnt want to sound passive aggressive.
Let [math] X = L^2,W^{1,2},C_b(\mathbb{R}^d)[/math] be any of those spaces.
Define the shift operator [math] \tau_y(f)(x) = f(x-y)[/math] and let [math] \phi_t(x) \in X [/math] be the heat kernel at time step t.
Then set [math] D = \{ \tau_y(\phi_t): y \in \mathbb{R}^d, t \in \mathbb{R}\} [/math]. It is the set of translated heat kernels at different steps t.
Now te question what the subspace [math]\overline{span(D)}[/math] looks like. In other words, which functions in X can be arbitrarily aporoximated by finite linear combinations of heat kernels?
And yea, because the heat kernels in time approach the dirac measure it seems like these should be many functions.

>>11651174
>I didnt want to sound passive aggressive
I have that impression at all anyhow

Yeah since you can approximate the Delta and the integral as Riemann integral, it will be basically all those nicely integrable functions?

>>11641742
What are people's thoughts on Lee's smooth manifolds book? What books would you recommend to try to learn some differential topology (and eventually get into diff geo)?

>>11651209
Do you think one could give restrictions to end up with a unique representation?
For example which functions can be written as:
[math] \sum_{n = 1}^\infty a_n \tau_{y_n}(\phi_{\frac{1}{n}})[/math]
for the right a_n and y_n.
Id two functions of this type are equalthen the coefficients are probably equal and the representation is unique.
Then you can define linear operators that shift around the heat kernels.

Wanted to ask since I started learning math, will I at some point be able to understand more advanced topics at an intuitive level?
Right now I can for example do basic differential equations and integrals but everything still feels very abstract and non-intuitive.

When you look at some complicated equation, do you guys get some immediate understanding of how it works or is math just too abstract to reach that level for most people (i.e. I have log(1) IQ)?

>>11651413
Only if you actually apply what you learn and do exercises and examples. You can push symbols all you want but that won't give you any actual understanding

>>11651413
The newest thing you've learned will never be something you really understand that well. Getting to the intuitive level of understanding takes multiple passes over the subject at multiple different times. 3 years from now when you've been using calculus constantly for years it will be basically automatic for you.

>>11651413
Some things resemble things you know on a sufficient level for you to make quick observations of how it works, but some completely new stuff can take quite a while. Drawing pictures helps when doing topology or calculus, and also checking some easy examples. I remember checking how different topological properties live and die by checking whether they are satisfied by an infinite space equipped with either the minimal or the discrete topology, for example, and thus developed intuition on those. You can do the same by using some easily accessible functions to create your own diffeqs or to practice integration by parts or substitution tricks. Examples are really important.

>>11651363
Sum over n but [math] \phi_{\frac{1}{n}} [/math] ?

How do I memorize theorems?

>>11651771
>How do I memorize theorems?
Anki

>>11651771
write them on a piece of paper and then eat it

>>11651778
this

>>11651771
Put your phone under a book, then place your pillow on the top of the book. When you sleep, the phone will send radiation through the book into your brain.

Good night, /mg/!

>>11651585
Yea, you need arbitrarily thin heat kernels

>>11651866
but the fact that you use a particular succession of widths and each only once feels quite particular.

Today was a bad study day. No particular reason, just not very good :/

>>11642389
so that zariski dude was really dense?

/gnmg/

Today I begin my first step towards completing my degree. I'm no giant like you guys (Yet!) but please enjoy this funny I found.

when in your graduation you stopped having to share the classroom with CS and physics kids?

>>11651997
>please enjoy this funny I found.
So I lost my sleep just to see this thing posted. DELET

>>11651872
yes, but mabye in a slow-divergence-of-harmonic-series kind of fashion this can still reach any function! Maybe only on a compact domain!

>>11650950
you dont know shit buddy

>>11643937
that looks like fun actually

Hw to prove that if F is continuous function and G is continuous function then max(F, G) is also a continuous function?

Tell me /mg/uys, what symbols do you use for 'exclusive or' and 'symmetric difference'?

>>11652887
how about you start with google
https://en.wikipedia.org/wiki/Symmetric_difference

>>11652914
I know what symbols are being used. I ask which symbols do *you* use.

>>11641742
What are some interesting looking projective varieties in real [math] \mathbb{P}^2 [/math]?

>>11652882
prove that it's continuous at each point. let x0 be a point in the domain.
if F(x0) > G(x0), then this holds also on a neighborhood of x0, because of continuity of F and G. therefore max(F,G) = F around x0, so it's continuous at x0.
if F(x0) = G(x0) = y, prove it straight from definition. for epsilon>0 you have a neighborhood of x0 on which |F - y| < epsilon. you have also a neighborhood of x0 on which |G - y| < epsilon. choose the smaller one of these neighborhoods and note that max(F,G)(x) is either F(x) or G(x). result follows.

>>11652882
Start with lemma
[math]\forall a,b \in \mathbb{R}:\max(a,b)=\frac{|a-b|}{2}+\frac{a+b}{2}[/math]
Then substitute a and b with F(x) and G(x).
[math]\max(F(x),G(x))=\frac{|F(x)-G(x)|}{2}+\frac{F(x)+G(x)}{2}[/math]

F(x) and G(x) are continuous so F(x)+G(x), F(x)-G(x), |(F(x)-G(x)| (composition of two continous functions is continous), F(X)+G(x)+|(F(x)-G(x)| and (F(X)+G(x)+|(F(x)-G(x)|)/2 are also continous.

>>11652958
>>11652983
Thank you.

>>11641742
What is 'gamma zero of m structure'?

>>11651898
Same, but let's have better days today!

>>11652983
nice

>>11653089
Thanks! We will!

Is there a way to write an 'indicator function' as a polynomial?

For example, I have a [math]2\times 4[/math] matrix and I want to describe the relation algebraically that at least one of the [math]2\times 2[/math] minor determinants is non-zero. Denote the matrix [eqn]\begin{bmatrix}
a & b & c & d \\
e & f & g & h \\

\end{bmatrix}[/eqn] and suppose I want either of [math]af-be\neq 0[/math] or [math]bg-cf\neq0[/math]. The values of these minors can be all over the place, including 0, so I'm not sure if I can.

>>11653283
There isn't going to be a polynomial to do this, but what you're asking is just equivalent to whether or not the rank of the matrix is >= 2, which isn't that hard to compute.

If you're willing to accept non-polynomial answers then you can cheat and use absolute values, since |x| + |y| > 0 iff x=/= 0 or y=/=0.

>>11653283
if you're talking about real numbers, then
(af-be nonzero or bg-cf nonzero) <=> (af-be)^2 + (bg-cf)^2 > 0

>>11653283
>>11653315
>>11653321
The need for such a relation is my attempt to answer this question.

My idea is something like: all quadrics in [math]\mathbb P^3[/math] are projectively equivalent, and the Segre variety there is a quadric, so it is enough to show that the union of the lines forms a quadric. The lines [math]L,M,N[/math] are given as an intersection of two planes, that is, two linear relations. After some thought, one can try the particularly convenient setup with:

[eqn]L: \begin{cases}X=0\\ Y=0\end{cases} ;\;\;M:\begin{cases}Z=0\\ T=0\end{cases};\;\; N:\begin{cases}X+Z=0\\ Y+T=0\end{cases}[/eqn]Any line through these three lines can be written as [eqn]l:\begin{cases}aX+bY+cZ+dT=0\\eX+fY+gZ+hT=0\end{cases}[/eqn]Subject to the relations [math]af=be,dg=hc,cf+ah=de+bg[/math], as well as them not being proportional and not all coefficients being [math]0[/math] (we can write the former as not all minors of the determinant of the planes of [math]l[/math] are [math]0[/math]).

Now from here I don't know how to turn it into a variety.

An attempt is by considering a point on the union of lines [math]U[/math]; every such line [math]l[/math] can be written as a point of [math]\mathbb P^7[/math] as [math][a:b:c:d:e:f:g:h][/math], and further, it is inside the variety [math]V=V(af-be,dg-hc,cf+ah-de-bg)[/math]. Every point in [math]U[/math] defines a line, so this could define a map [math]U\to V\subseteq\mathbb P^7[/math]. My attempt at describing the minor relations algebraically is to 'refine' this image into perhaps something that is isomorphic to [math]U[/math].

The fact that not both planes are proportional could be taken to be that [math]V[/math] lies inside at least one of the open sets defined by a minor.

I can't wrap my head around the Whitehead products signs. If [math]\alpha\in \pi_n(X), \beta\in \pi_m(X)[/math], why is [math][\alpha, \beta] ) (-1)^{mn + m+ n}[\beta, \alpha][/math]?

I do realise my approach is a bit overkill/overcomplicated but it seemed like an interesting train of thought>>11653400

>>11653425
[math][\alpha, \beta] = (-1)^{mn + m+ n}[\beta, \alpha][/math] I meant

>>11653400
i don't know too much about this but:
let L, M, N be as in your post
pick a point (0,0,c,d) on L, and a point (a,b,0,0) on M
the line passing through those points is described by equations bX-aY=0 & dZ-cT=0
this line intersects N iff ad-bc=0
from here it should be simple

>>11653081
>What is 'gamma zero of m structure'?
Hecke congruence subgroup
https://en.wikipedia.org/wiki/Congruence_subgroup#Examples

>>11649652
a good book on proofs generally encourages the reader to dive into the lake, i.e. do some exercises or complete the details of proofs.

>>11643752
absolutely based

what linear algebra textbook is the least meme

>>11653951
lang

>>11653951
alxer

>>11653951
Axler

>>11653951
Alright.
I've thought long and hard about this, and the least meme linear algebra textbook needs to:
>have been published, or have had a new edition published, in the last decade
>it needs to be written for undergrad mathematicians, preferably freshmen
>it can't have been written by a meme author
>it can't have been published by a meme publisher
>it can't cover a meme selection of subjects
>it can't have a meme name
>/mg/ can't shitpost about it
After considering all of those things, it seems like Strang is the least meme book, although I absolutely could be wrong.
Not that I would recommend it, I've never read it.

>>11653954
Lang is always a meme.

>>11654030
>>11654053
Eschewing determinants for no reason is also a meme

>>11653425
>>11653432
Can anybody help?

>>11654689
>Can anybody help?
What have you tried?

Pardon my retardation but I want to make sure my reasoning isn't complete shit. Is it possible to find nonzero [math]a,b,c\in \mathbb{Z}[/math] s.t. [math]\overline{ab} = \overline{ac} \mod 12 [/math] where b is not equal to c. I'm claiming no because no matter what a and b are [math]\overline{ab} = \{a*b + 12k : k\in \mathbb{Z}\} [/math] has infinitely many elements while [math]\overline{ac} \mod 12[/math] will have finitely many elements since we are performing the operation of modular arithmetic on the elements of ac which means most elements of ac will go to 0. Does this make any sense?

>>11655015
>Does this make any sense?
You're retarded.

>>11653951
Halmos

>>11653951
Just get the intro book by Lay. You're not going to get much out of an advanced text on your own. It's literally a meme on /sci/.

wolframalpha or symbolab for practice problems (with step by step instructions)?

>>11655535
>with step by step instructions
Unless you have some way of not having to pay for Wolfram Pro to get the step-by-step feature Symbolab seems like a better choice

Is anyone into proof verification? I want to learn lean. Nothing sounds more satisfying to me than spending day and night formalizing undergrad analysis.
I cant wait till mathematics has rid itself of this unverified proof bullshit

>>11654987
I can sort of get the mn by lifting the twist map [math]S^m\vee S^n \to S^n \vee S^m[/math] and checking its degree in cohomology. That's when I reach my limitations.

>>11641742
What a useless recommendation letter. Maybe Duffin should've taken some writing classes before math ones

>>11653400
Why do algebraic geometry fans have their heads so far up their asses

>>11655601
do you have any experience with programming
i think this would be boring and frustrating, not satisfying

>>11655015
If
a = 2
b = 1
c = 7
then ab and ac will belong to the same equivalence class but b and c don't if this is what you're asking.

what should i do with my life...

>>11655859
Yes, I do, and I enjoy programming. But there is an important difference between programming and formal proof writing because when you write a proof into the system you can know that you are correct. If your proof compiles then you know, 100%, that what you produced is bug free. You will make steady satisfying progress every day and end up with a truly useful result.

>>11653432
Check the degree of the map interchanging the two spheres.

>>11656354
Yeah I got the same answer in another thread. Thanks anyway man.

>>11656276
1. get lean, lift and learn the learn a handstand
2. read and understand the Historical-critical Introduction to the Philosophy of Mythology
3. become well versed on the subject of Central Algebras

Everything will fall into place. None of those 3 points are listed for shits and giggles btw., each of them must be taken as seriously as the other and also they only go together.

Don't waste your life and start. People will follow.

>mfw I finally found the proof

>>11656387
Have you improved your handstand time?

>>11656560
What were you trying to prove?

>Axiom of constructability
why is this not used
it makes more sense than AC

>>11657259
i'm pretty sure many people unconsciously assume that every set is constructible until you explain to them how this can be false
it is not used because no one actually needs to "use" this unless you're doing autistic set theory
and if you are doing autistic set theory, then this axiom just settles most questions and there wouldn't be much left to do

The axiomatization of ZFC and its consequences have been a disaster for the human race

>>11657295
>better known for other work

>>11656387
I, for one, do 3 second handstands. Will improve in the coming weeks, tho.

>>11657259
I'd argue that e.g. extensionality
[math] \forall x,y.\ [ \forall z.\ (z \in x \Leftrightarrow z \in y) \Rightarrow x = y] [/math]
is about 20 characters long, while "[math] V=L [/math] " is probably a few thousand characters long.

That being the case, the real answer is probably that choice was just part of Zermelos 1910 theory without question and when Freankel added Replacement to round up the axiom system, I think people were just okay let's take what we have here now.
Also, some more "applied" topology users are probably too used to descending chain conditions and such. You find funny rage discussions of people on SO triggered from being asked whether their claims depend on choice.

On that note, thanks again to
>>11648265
After some more digging in that direction, I came across two fantastic texts this week.

https://www.ps.uni-saarland.de/courses/cl2-ws16/tex/st.pdf
>Set Theory in Type Theory (2017)

https://www.ps.uni-saarland.de/Publications/documents/SmolkaStark_2016_Hereditarily.pdf
>Hereditarily Finite Sets in Constructive Type Theory (2016)

Both by a German CS guy called Smolka and the second together with a qt PhD student.
The first steps through the ZF axiomatization, proving some basics right at the axioms and taking care and making explicit what is used where, and the second giving a straight axiomatization of just the Hereditarily Finite set, which is very nice and concise.
Both are not in FOL but instead a type theoretic underpinning, making some use of dependent function types.
But nonetheless the axioms in the ZF text are expressed as classical as it gets. I can say some things about it if someone's interested.

Reminder: tomorrow 15 o'clock Greenwich Mean Time https://sites.google.com/view/nialltaggartmath/oats
>Ulrich Pennig (Cardiff University)
>Title: Loops, groups, and twists - the role of K-theory in mathematical physics
>Abstract: While K-theory has its origins in Grothendieck's formulation and proof of his version of the Riemann-Roch theorem, it now plays a significant role in many diverse branches of mathematics: It provides a fundamental example of a cohomology theory, and it is one of the most important invariants of C*-algebras. In the first half of the talk, I will define the K-groups and discuss some of their applications. In the second half, I will concentrate on equivariant twisted K-theory, which is related to the representation theory of loop groups and the geometry of two-dimensional quantum field theories by a theorem of Freed, Hopkins, and Teleman. I will finish with an outline of joint work with D. Evans, in which we study generalizations of this work to higher twists.
[math]b\text{ there }\lor b^2[/math]

>>11657497
Surprisingly accessible abstract

>>11657497
>To minimise security concerns, access information for the Zoom meeting will only be sent out through the mailing list approximately an hour before the seminar is due to begin, details of which are below.
could you stop dumping seminars you can't watch without signing up for emails

>>11656387
What do you suggest reading to get better at points 2 and 3? I've tried getting into maths by reading wikipedia and reading here, but it overwhelmed me, and I tried getting into philosophy by reading some works, but the shit is so wordy I can't muster the patience. Although if I give it enough time the wordiness seems worth it.

My handstands are on point B^)

>>11657497
Okay, I signed up to that mailing list. Didn't get any confirmation email, but let's see till tomorrow an hour before it.

>>11657513
I gather it being a university makes it as non-intrusive as it can get.

>>11657516
In both cases, whether you'll stick with it will depend on how relevant it is to you. And what you want to get out of it. And what kind of media you consume.

>>11657516
math's impossible if you have adhd, I'd stop if I were you and valued my sanity

>>11657513
Yes, I could very well do that. I think it should be pretty obvious.

>>11657528
So far I have received my emails 2, 4 and 4 hours before the talk.

>>11657436
>After some more digging in that direction, I came across two fantastic texts this week.

Not sure what you're trying to achieve, but this is fairly folklore stuff, look at e.g. Aczel model of sets if you want the original. I'd recommend Miquel's slide for a gentle introduction:

https://github.com/Coq-Andes-Summer-School/CASS2020/raw/master/typesets.pdf

> qt PhD student

She deserves her Stark name, as she has been doing some savage shit recently. Fear the Germans.

>>11657539
oh no, I've learned a fuckton of maths in my day and was quite good at it. I'd say I'm upper quartile. It's just after I started doing computer science the maths just died down and I'm just looking for any guidance.
>>11657528
Fair enough. Any particular books worth reading though?

>>11657590
>doing computer science
>the maths just died down
you sure you're not conflating programming with cs

>>11657649
I mean BSc computer science isn't that maths heavy.

There is some good stuff, but when I'm trying to read some extra topics I have my pants down.

Fucking hate programming too

>>11657590
>Any particular books worth reading though?
You haven't said what interests you.
Sure I can point you places, but I want to avoid bringing you off that course by giving you something you're not interested in in the first place.

>>11657850
Uh my problem with learning maths is that I enjoy them as long as I understand them. In essence, I don't know what interests me, as I don't know what's out there. I feel like my only way forward is to just get into it.

Just literally any pointer I could cling to would be appreciated

>>11657548
>but this is fairly folklore stuff
I'd avoid this sort of dismissive language

>>11657863
I want someone to read Michele Audin's Geometry and tell me if it's good.
Are you up to the task?

Is pi really a meta number as /ourguy/ Professor Norman J Wildberger says?

>>11657885
nothing "is really", this question has no conclusive answer

>>11657882
fuck it, sure

>>11657893
Very nice, thanks.

>>11657548
>Not sure what you're trying to achieve
To write a nice Wikipedia article on Hereditarily Finite Sets, for example, but my ip range is always blocked and I don't want to make an account since I don't want to get intot he horrible Wikipedia politics.

It's nice that those slides have some pics, I was scrambling some on my own the last two days. I read the unfinished constructive book, but the Stark paper actually works primarily with functions such as one that adds a set to a new one (the "adjunction", and the axioms for that don't even look like ZF). That said, \in is quickly defined and so the rest looks conventional.

Also, I never understood if there's a good reasons why people (or at least Aczel) studied anti-foundations. Just because out of principle because it wasn't investigated?

>doing some savage shit recently
What? I couldn't find anything.

Is Calculus by Gilbert Strang a meme? Need a calculus book to recommend to my friend for self study, its going to be his first serous encounter with calculus

>>11657878
the word "folklore" is the biggest cope mathematicians have
>you find new result
>uh yeah everybody knew this already haha
>nobody ever wrote it down anywhere but trust me we all knew

>>11657930
I want to f*ck Hong Meiling!

>>11658079
We should start to use folklore claims inflationarily on /sci/. Who's on board?

>>11658129
https://en.wikipedia.org/wiki/Mathematical_folklore
?

>>11658120
Same bro.

>he doesn't practice meditation to help him focus better on math without any substance abuse

Is Euclidian Geometry solved?

>>11658418
Yes

>>11658338
>meditation
misspelled meme there

>>11659279
>meditation is a meme
oof and yikes

>>11658129
>We should start to use folklore claims inflationarily on /sci/.
It is folklore that we use folklore claims inflationarily on /sci/.