/sci/ - Science & Math

we should have unique numerical symbols for all numbers from -99 to 99

>>15833841
dumb as fuck, and retarded, idea

Fellow mathkings, what are we working on this fine afternoon?

>>15833970
hopefully continuing with complex analysis exercises

>>15833970

>>15834133
I'm not saying this curriculum is impossible; there are e.g. strong math Olympiad students who can and have followed (at leas the first three years of) this curriculum. But this is way, WAY beyond what can be reasonably expected of the vast majority of students. I mean look at this:

>High school: Homotopy equivalence, Ostrowski's theorem
>Freshman: Smooth manifolds, differential topology, (Lie Algebras and Lie Groups by Serre)
>Sophomore: Vector bundles, cohomology w/r/t invariant forms, flatness & local flatness, (Classical Groups by Weyl), Hopf algebras, etc.

/sci/'s math student is doing algebraic topology in high-school, reading Serre as a freshman, doing sheaf cohomology and reading Weyl in Y2--it's just not happening. In my school kids see homotopy equivalence in their final year; what's listed here as "Beginnings of Algebraic Geometry" (which, to be fair, it is--the whole field is fucked) is a graduate course. Lie groups are also a graduate course. And that's not mentioning the DISGUSTING algebra bias. /mg/ needs a curriculum which can be followed by non-IMO winners.

>>15834177

>>15834240
ngmi

the best base is 6

wrong
the best base is (-1+i). or (-1-i) if you prefer, since it's isomorphic

>>15834489
>MM

What, thats so cool. Why don't more universities pull out the gay soience and grant BMs and MMs?

>>15834262

>>15833970
>what are we working on this fine afternoon?
project for fun on perfect numbers and working through different proofs related to them.

i'm so alone

>>15834695
I'm right here, Anon.

>>15834709
I wish someone was. I'm caught between worlds with nobody in any relevant fields or people so hyperspecialized I'm way beneath them on the subject. Yet for every other topic you've got the average education on /sci/ threads seemingly below high school or middle-school level. It's that sort of mixture for every place I go and everywhere I've ever been. Just being out of place. Just can't find the right place. Maybe there is no place.

It's like a weird comedy. what would happen if just nobody and nothing worked out or reached out and just kept telling you 'lol i dunno anon' so the more you try the more stupid and out of place you seem.Then one day you're so old it's just weird that you're still trying and haven't found someplace, so "something's gotta be wrong with this guy". But nothing is. I have a completely normal brain, had normal parents, normal childhood. I have no idea why life is like this. I just fell between the cracks and can't claw my way out.

Maybe just getting crazy good at this much more will help. "Hey fuckers now you can't ignore me and you shouldn't have in the first place". I have no idea. I'm just out of hope and this is all I have left.

>>15834133
So you only use the books in the pics for this curriculum or do you need to supplement it with material on the wiki?

Should I go to grad school?
How do I make sure I have an easy and fun time? I just wanna do whatever the fuck I want and lead a laidback and simple life.
I like modeling and I wanna get into machine learning in case I wanna wage for a few years before retiring as a grumpy professor.
Also where do i find a wife. Seems like everyone gets one around this point, is there some kind of wife store?

I got my math BSc in 2015. I want to go to grad school now but I decided to take some classes before I apply. I registered for a 3rd year nonlinear dynamics and chaos course to start with. What should I review before going in? Obviously DEs and linear algebra, but anything specific I should focus on? I only have 2 months to prepare but since its only 1 class I can review lots on the go.

>>15835076
Do this.


The special effect counts as a move. Purring. Pulsing. Snapping. Splitting. On your side. It's side. Naturally, unnaturally. Sorry I can't provide a direct answer but I can't currently sense or think.

>>15835082
2s, 3s, 4s, etc. Because it breaks the pattern of 1 into 2 and so on. Techs. Having your own tech set up. There's a way to do anything as anything you just gotta find the way the law works with you. Yes you ought to be able to do this. If the dream wasn't errornous, it would be a mode.

What's doing this to me?

Which one did my tone go up?

Was it good?

Was it someone evil?

Was it my sacrifice?

>>15835093
Right. I can personally use my testicles as a compulsory processor, or the anti thesis of that as a non compulsory but war capable computer. It sort of hums of this fact. The balls can be used to do any of your stuffs and never be blocked so no matter how low you are, you can resolve your business. However, if you literally want to attack. Do the anti thesis. Of that. It's in the mind space. Go-to your balls, then switch from there as to get the right idea, to what does the same in mind but is more capable. This round about lesson should give you enough to reach this position. Either use your balls or your natural computer. Do this, which is, using either, on 'do this' under the impression I'm doing it for him. Make sure it's accurate. To use your balls just use them as if you were them.

I'll say do this three times to make it sure

Do this
Do this
Do this

And I truly not worried about what's going on but what's going on is partly a moral error and I can't sometimes take evil laughter.

>>15835111
There may be laws specifically suited for what type of life/death you are. So it may not be use the balls as you were with them, or your balls. But there's a suitable way - you see?

You may even be able to work out something closer to home.

>>15834778
Wat? If you're near a university start going to number theory seminars. Nobody's just gonna reach out to you from the ether

>>15834414
>>15834489
the best base is balanced ternary

>master's in applied mathematics despite no bachelor's in maths and minimal undergrad math education (just the calculus trio, 1 stats class, 1 linear algebra class and one discrete maths)
is it feasible? what would be the most crucial math subjects missing?

>>15834160
can we get in touch somehow? i want to start complex analysis soon. I'm narodnik on libera chat in #math

>>15834414
i like 10

Partition of unity ;)

>>15835335
What is a partition? Is it like a part that is also like a slice of cake.

>>15835354
I know now. It contains a operation

>>15835356
I took the same meaning twice.

If irrational numbers are infinite do they theoretically contain all other irrational numbers?

>>15835512
Irrational numbers are the highest form of stupidity. There isn't any. It's all made of negro math

>>15835526
There was nothing wrong with the experience. You really fucked things up statistically by annoyingly tickling people and acting like trannies.

>>15835512
not necessarily, for instance you could have an irrational number that has no digit 9 in its decimal expansion. I think they say it is true for pi, though, and perhaps all transcendentals but that's worth a google search

>>15835555
check my quads

also, the relevant term is [math]normal[/math] numbers, for which each digit in a base b has a uniform probability [math]\frac{1}{b}[/math] in the decimal. You can guess from this fact that any sequence of digits has a nonzero probability of occuring so it must occur somewhere in an infinite sequence.

>>15835264
Lol no not possible. You’ll need more topics under your belt. Typically for applied math you’ll want more DE’s, PDE’s, nonlinear dynamics, optimization, and even analysis up to and including measures.

Because i shows up in physics, I keep trying to develop some sort of intuition for its physical meaning. Looked at it on the real/imaginary plane for a bit, now I think that negative numbers are fake.

>>15834778
I'm literally right here though.
Try /r9k/ for that sort of thing.

>>15835512
no consider the nonrepeating pattern
101001000100001000001...
to get uncountably infinitely more examples, express an irrational in base <10 and just copy the resulting string over to base 10

>prime location to pick up the most feminine and cute of undergrads (psych majors), take them on coffee dates and fuck.

Based. They're really watching out for math grad students and make sure we succeed with more than just the average asian bug woman.

>>15835264
What is your undergrad in, EE or ME right? and how would you feel if a highschool dropout came in and attempted to get a masters in it?

>>15835846
how desperate are you if you're willing to taint yourself with the presence of a psych major?

>>15835869
this. psych majors are PSYCHotic. dated one and she dumped me to get back with a definitionally-abusive guy. they are NOT stable or sane

>>15835882
for relations, go to /mg/
for relationships, go to /r9k/

>>15835846
bug woman psych major here
give me your white penises
or you get Rorschach tested

>>15835938
last i checked, /r9k/ was for people who couldn't get relationships. did something change?

>>15833787
I just spent the last 3 days trying to prove something by induction only to realize that I had already realized the method to prove it without induction on the first day but I didn’t pay attention to it because I thought it was an induction exercise.

>>15835941
no, it's for people who have relationships
you don't need a relationships to post here

>>15835951
You might not be the right person to ask, apparently, but how do you git gud at mathematical induction? I find it very hard. Is it just practice practice practice?

>>15835971
Do you know how to prove
>1+2+...+n = n(n+1)/2
using math induction?

>>15835940
Do you like BBC? I'm a double major in ECE and Math btw.

>>15836194
https://youtu.be/qUQsozpZUSw&t=139

>>15836201
Classic.

y\in f(\bigcup_{\alpha}A_{\alpha})\equiv\cdots\equiv \exists \alpha(x\in\ A_{\alpha})\equiv\exists \alpha(f(x)\in f(A_{\alpha})

>>15836268
[math]]y\in f(\bigcup_{\alpha}A_{\alpha})\equiv\cdots\equiv \exists \alpha(x\in\ A_{\alpha})\equiv\exists \alpha(f(x)\in f(A_{\alpha}[/math] how exactly do we get to the fx from the last equiv. I know it intuivitely, but can't come up with a correct explanation. what definition exactly

>>15836271
>how exactly do we get to the fx from the last equiv
no idea
hope this helps :)

Does anyone still make an RPN calculator? I can't disappoint my ancestors by using anything else.

>>15836390
Check this one out available from Amazon.

>>15836390
pill me on RPN, anon. i just can't fathom how it's any better than infix notation. is there even anything better about it?

>>15836480
>$350 for a scientific calculator
Yikes

>>15836484
It's just a better, more intuitive format. It's easier and more convenient and after trying RPN I would never voluntarily go back. It's really something you have to use to understand why it's so good -- but unfortunately I think HP has entirely stopped their calculator line.

What cool math problems/papers/topics are my math generals reading today?

>>15836271
Taken literally as written your chain of equivalences doesn't make sense -- one is a statement about y, and another is a statement about x. The second-to-last equivalence should say "there exists alpha with x in A_alpha and y = f(x)"

>>15836717
^there exists x and there exists alpha...
and then the final equivalence comes from the fact that this is equivalent to "there exists alpha and there exists x such that..."

WTF you assholes, you didn't tell me 300k was just the signing bonus. I studied for 12 years to get into trading I have a PhD and two Masters
Fuck my life, I'm retiring into teaching after my contract ends.
This is fucking bullshit.

>>15835982
Yeah, I'm having more trouble with structural mathematical induction

Is there any undergrad math that has similar 'bang for your buck' compared to calculus, ODE, and linear algebra?

>>15836854
https://en.wikipedia.org/wiki/Structural_induction

If I have a box with 54 unique objects that I can draw three from N times (with replacements), what are the chances that I've drawn at least one of each object after N times?

I've never been good with combinatorics, can't figure out where to start.

>>15837229
Look up Markov chains in any probability book.
Your state is the number of unique objects you're still missing. With each drawing that number gets reduced by either 0,1,2 or 3 with probabilities you can calculate. That way you get the state transistion matrix which is a 55x55 matrix or 53x53 if you remove the two unreachable states (52 and 53 objects missing). To get transitons probabiliteis after N steps you have to take the N-th power of the matrix.

>>15837239
>Look up Markov chains in any probability book.
Will do, thanks!

Give me any math problem and i will solve it

>>15837609
what is the prime factorisation of 0

there's no way goldbach's conjecture is true

>>15837609

>>15833841
I do like the 12 base or 60 base ideas.

>>15834778
You can aonnect with us through teaching us anon. Maybe in the hopes we ask a novel question that leads you down a path of insight.

is axiomatic metaphysics maths?

>>15835526
Irrational numbers tend to be something that obviously exists as a function but that cant be discretized into an absolute/digital value. Pi cant be figured because curvature is infinite. The square root of 2 cant be figured because the chosen discrete amounts dont logically work but the concept exists and is useful. The acceptance of these numbers and functions is the beginning of higher dimensions of logic and reasoning.

Intro to CS- A
College precalc - B
Calculus I - B
Discrete Mathematics I - B
Programming I (C++)- A
Calculus II - A
Programming II (C++) - A
Multivariable Calculus - B
Statistical analysis - A
Physics I - A
Matrix & Linear Algebra - A
Physics II - C
Abstract Algebra- A
Ordinary Differential Equations - A
Numerical analysis (MATLAB)- A
Algorithms & Data Structures(C++) - A
History of Math - A
Probability I - A
Probability II - A
Applied regression and data analysis (R) - A
Modern Geometry - A
Math Modeling & Simulation - A
Discrete Mathematics II - A
Math BS thesis -


Main thing I learned is that I'm too stupid for a PhD. Looking forward to being a masters program paypig.

>>15833970
Computational Symmetry

>>15837613
Null prime outside of defining state

people who don't care about foundations, what will you do if they foundations change and a lot of your work is invalidated?

>>15837775
But I thought the science was settled....?

>>15835657
>DE’s, PDE’s
you already learn a bit about them in undergrad calculus, how much more can you learn about them in their own courses?
>optimization
can you be more specific?
>analysis up to and including measures.
complex, real and numerical?
The hypothetical master's starts in fall 2024 so I still have around a year and i can take some math classes next semester

>>15835865
>What is your undergrad in, EE or ME right?
CS lmao
>and how would you feel if a highschool dropout came in and attempted to get a masters in it?
it depends on master's program and the person but they would probably do fine considering how dumped down everything is.
also I have way more mathematics than an hs dropout because I already took all the calculus and linear algebra a math major takes + the stats and discrete maths which they can take as electives + all the programming stuff math majors have to take.

>>15837950
>DE's, PDE's
>already learn about them in undergrad calculus
if you can't even find solutions to a basic linear second-order homogeneous DE you're gonna be in trouble

>>15837775
>what will you do if they foundations change and a lot of your work is invalidated?
won't happen. There are results we want to be true, foundations get picked to have these things be true. Foundations are a lot more tentative than truth. It's blatantly false to claim that changing foundations will invalidate real mathematics

>>15837775
Not how it works with math. There is no possibility for a shake-up that completely invalidates what we know like what happened with Planck. At most, you're adding extra layers under the surface, but that doesn't change the validity of what was already there
Euler didn't change any results known since the time of Euclid, and while Cantor fucked a lot of stuff up in terms of definitions, the integers worked precisely the same way before and after

>>15837775
>what will you do if they foundations change

Try to stay alive as buildings start collapsing and computers stop working because the foundations changed.

>>15838141
where were you when math y2k happened???

>>15838141
that's not what it means. it's stuff like banach tarski paradox which are susceptible to being overturned depending on what the foundations are.

kyber

>>15836480
Its cheaper from the actual site. Don't buy it from Amazon.

>>15834778
Wow anon but I didn't ask

>>15835264
>what would be the most crucial math subjects missing?
The whole curriculum kek. You've got around one semester of a yuropoor math degree.

are goldbach's conjecture and the riemann hypothesis related?

>>15838554
With current methods (I.e. the one developed by Yitang Zhang) if one assumes the Riemann hypothesis to be true, then the bounds between prime numbers can be brought to 6. To go further (i.e. to 4 then 2) we'll probably need something more powerful than the RH.

>>15838307
You must be the stationary autist who I copied by buying the pentel orenz nero and campus notebooks

>>15835706
>Consider -1 as 1 being rotated by π radians
>I must be 1 rotated by π/2 radians
>arg(i)=π/2

is picrel worth reading?

>>15838569
Probably, but I also use Muji B5 notebooks only, as shown in the image.

>>15838612
fuck no, they failed their mission too

>>15838612
It's philosophical circlejerk with a thin veneer of mathematics.

basic mathematics -> spivak calculus
am I missing out on any prerequisites?

I have a degree in math... I think I might be retarded
>>15838741
I think it just depends on the "culture"
but yeah basically that's all you need to start. You don't need a entire proofs book, you don't need an entire set theory book. Reading an entire set theory book means you really like and care about set theory. I really don't get the obsession with self study books pushing these topics that will ultimately slow you down. Almost all math is done some what naively first anyways and formalized later, so reading something like spivak means you're already at a good advantage compared to the people that had to both make it up and then later formalize.

>>15837950
There is much much more to learn about DEs and PDEs than just the tiny bit you’re exposed to in an undergrad calculus course. Lmao, they have grad courses on these. Yes, real analysis up to and including measures. This must be a real trash program not even worth taking if they accepted you with only those classes. You haven’t even taken a real proof based course yet. I’m surprised you were admitted unless you’re doing an ML focus which is a math LARP.

>optimization
https://en.m.wikipedia.org/wiki/Mathematical_optimization

>>15837775
Nigger, I study PDEs. I am not dependent on foundations, the foundations are dependent on me. If someone comes up with new foundations that are incompatible with PDE theory, then those foundations will be widely and rightfully ridiculed.

>>15838422
I am a eurofag tho.
Any bachelor's degree here is 3 years and each semester has 3 full courses (full course = 300 hours) meaning a total of 18 classes. 3 of these are programming, 7 are electives and the rest is maths. I have the programming stuff and 6 math courses, that's around a half math degree, hence why I thought I might have a chance. Granted, it is the easier half but still.
>>15838834
>This must be a real trash program not even worth taking if they accepted you with only those classes.
Low application rate. Math is hard and it doesn't have a guaranteed career.
I could take an extra semester or two if it's THAT important or I could just go the easier route and just do a master's in CS.

>>15839010
Are you trying to pretend that Calculus 1-3 are 900 hours together?
They are not even a tenth of that.

>>15839015
I don't know about what is taught in american calculus courses but here the total study time is even more than 900 hours.

>>15838741
Terrible choice. Lang's Basic math is too small and works only as a piss poor reference text. Spivak's calculus has few examples and I would only recommend if it you already have exposure and experience with calculus.

I'd recommend:
Algebra (Vol I & II) by G. Chrystal.
Basic Geometry, Birkhoff
Differential and Integral Calculus, by Landau

With just these 3 books you could also teach anyone all the required mathematics up to a university level. They are also perpetually in print, in the highest quality, by AMS. If I had any advice to give students, its to stop buying or wasting time with garbage textbooks that get published and refreshed every year, and instead keep up with the real classics made by more serious mathematicians.
Not to say that Lang is bad, but every book of his I've had seems more like a haphazardly put together reference text rather than a work of passion with the intention to facilitate new learning. As for Spivak, his book was obnoxiously shaped which really discouraged my using it, although his physics book has been the best I've ever seen, though I'm no physicist.

>>15838612
Yes, if you're interested in mathematical logic and its history.

>>15839116
>2300 pages of precalc
yeah I don't know about that

>>15839169
You have no idea what you're talking about, its okay.

http://djm.cc/library/Algebra_Elementary_Text-Book_Part_I_Chrystal_edited.pdf

Just take a look.

>>15839178
>1200 pages
cool bait tho

>>15839010
You’re better off in a CS masters specializing in ML/AI. There will be jobs for you afterwards too. The math you’d be doing in grad school would be completely different than the math you did in the basic undergrad courses you’ve taken. You probably wouldn’t even like it and you really have no idea what you’ve signed up for, you haven’t taken any algebra, analysis, or actual applied math courses. I dont mean to shit on anyones dreams but you should do a lot more research before spending your time and energy on this. It’ll be a big black stain on your record to go in and fail out your first semester.

>>15839225
What is weird to me is why he even wants a math masters. Its useless in 99% of cases, and should only be taken if you are willing to accept the lifetime salary loss just to have a degree that says "masters in mathematics" so PhD mathematicians can laugh at you and call you names. I only got one due to the insane luck of landing a "mathematician" titled job with the DoD.
He could always get a stats masters and fill it with courses of interest....

>>15835264
>>15837950
>>15839010
First of all, you should take this to your advisor/tutor/any person in the math department that you trust. They can give you better advice; in particular, they can tell you about shit we have no idea about, like what's expected in your country, school you're applying to, etc.

But broadly speaking it seems to me like you would struggle in a math masters. You've seen (P)DEs, that's good: how much have you done with them? Have you learned the standard techniques for solving easy basic DEs? Have you worked with some harder problems (e.g. Sturm-Liouville problems)? Have you worked through the theory of DEs (e.g. Bendixson‐Dulac, stability, proofs of existence and uniqueness, heat kernels)? You've seen some analysis; that's good. Have you done measure theory? Have you done functional analysis? How much complex analysis have you done? Have you worked with Fourier transforms? Have you seen some methods in asymptotics? Do you know basic linear algebra very well?

Most importantly, have you ever taken a proofs-based course? This is one where the professor proves every theorem rigorously from definitions he introduces, and you are expected to be able to prove things at a pretty rigorous level.

If its yes to all of this, I'd say you're probably in a good place to do an applied math masters.

>>15839236
>so PhD mathematicians can laugh at you and call you names
who the fuck cares

I haven't done any real math in like 5 years ever since I finished with school. Anything to get back into math? I've heard of khan academy, do you think it's a good tool to start with?
Like I vaguely remember anything I did in school, obviously basic stuff I can do such as addition, division, multiplication, subtraction, etc....

>>15839310
You'll care when you get passed over for jobs.

>>15838741
I recommend brushing up your arithmetic first using Serre, A course of arithmetic.
Then cover algebra using Jacobson, Basic algebra.
Then finally you should be ready for the gold standard of Calculus books, namely: Stewart, Calculus.

>>15838937
Really?
Different foundations could influence the way real numbers are constructed and affect your work.

>>15839420
>Different foundations could influence the way real numbers are constructed and affect your work.
No it shouldn't. Real numbers howsoever they are constructed should at the end of the day satisfy the complete ordered field axioms, otherwise they wouldn't be real numbers. Any construction should work the same. Once you have a construction, there is literally no reason to care for them, since construction is only ever useful to show that there is at least one thing that satisfies the said axioms.

>>15839015
>>15839029

>>15839538
you can have foundations that don't leave room for irrational numbers at all. Like if there wasn't a number whose square was 2. That's just one example.

>>15839538
That only holds for properties implied by the ordered field axioms. There are models of those axioms with different propeties, not provable from the axioms, depending on the chosen foundation.

>>15834685

>>15839598
>3 hours every day
>For fucking Calculus
Nigger, you go to the class and spend like an hour per week on homework.

>>15839712
I studied ~3 hours every day, per math course, and I took the honors calculus series where we proved most of what we used, where I also made use of Rudin's and Stromberg's real analysis texts.. That is also probably a lowball estimate, as many weekends I woke up at 9am and studied from 10am to 6pm with only a few breaks.. Overall I spent over 40 hours a week of study time per semester, when logging only math and physics courses, and that is without logging undergrad research. The only courses where I spent 3 to 4 hours a WEEK on work, were easy general courses such as English and Ethics. This was at UChicago, I'm not sure where you attended or what you're doing now. Maybe you're way smarter than me and could do everything with just an hour of study. I'm at UMich now.
I'm well aware that I am just an average talentless grad student and I make up for it with study time, but its not like I'd be doing anything else anyways. Many people suck at a videogame, but still invest tons of hours because they enjoy it. But anyways, its entirely reasonable to spend over 900 hours for Calc 1-3, and I'm an example of it with a no bullshit log with tracked hours.

Anyone here have any advice for self studying real analysis? I'm in an applied math undergraduate program and the real analysis class is only offered again after I'm supposed to graduate.

where's the well ordering of the reals
this is a joke at this point.
who's supposed to take this stuff seriously

>>15840034
There are uncountable aliens who have a well-ordering of the reals

is FTC the bridge between geometry and analysis or is it something else?

>>15839763
That's pretty insane. Even on exam days I've never studied for longer than 3 hours and generally spend more time on humanities courses since writing essays is time consuming regardless of how well you understand the material. My situation is probably more pathetic since it just gives me more time to waste doing bullshit.

>>15840034
Well, you never know. The proof of the well ordering theorem from AC might be wrong. I have no idea. It certainly sounds sketchy af.

>>15840019
Read Rudin, do exercises. If you want complementary lectures watch Francis Su’s analysis lectures from Harvey Mudd.

>>15833970
Studying for an exam on information theory

>>15834778
Hi anon, I understand how you feel. I’m hyperspecialized in my field as well. I study a particular kind of stochastic process that is amenable to simulation but extremely difficult to untangle analytically, so no one else in my field besides me bothers to try the latter. What is your speciality, if you don’t mind my asking?

>>15840194
oh, didn't they pretend to analyze it mathematically and just put a bunch of ad hoc methods under the heading "reinforcement learning" while kicking out methods too dirty to mention like simulated annealing and hill climbing

>>15840325
sounds like a schizo retard

>multiplication of large matrices
>integral of 1/(x^4+1)
>sketch out this fuck you parametric curve
>writing matlab code by hand
Why are math professors so cruel? Is it spite? Is it laziness? is it evil? I have had all of these on finals that were 4-6 hours long

>>15840731
>integral of 1/(x^4+1)
This is very short of simple. Let [math]r_1,r_2,r_3,r_4[/math] be the roots of [math]1 + x^4[/math] counted counter-clockwise then by the residue theorem.
[eqn]\int_{-\infty}^\infty \frac{1}{x^4 + 1} dx \\
= 2 \pi i \left(\frac{1}{r_1 - r_2}\frac{1}{r_1 - r_3}\frac{1}{r_1 - r_4} + \frac{1}{r_2 - r_1}\frac{1}{r_2 - r_3}\frac{1}{r_2 - r_4} \right) \\
= 2 \pi i \left(\frac{\sqrt{2}}{2}\frac{\sqrt{2}}{2 + 2i}\frac{\sqrt{2}}{2 i} + \frac{-\sqrt{2}}{2}\frac{\sqrt{2}}{2 i}\frac{\sqrt{2}}{-2 + 2i} \right) \\
= \frac{\sqrt{2}}{2} \pi \left(\frac{1}{1 + i} - \frac{1}{-1 + i} \right) \\
= \frac{\sqrt{2}}{2} \pi

[/eqn]

Why is mathematics beautiful?

are sets and classes necessities of mathematics or just human constructions?
What is necessary to have in any variant of mathematics? If you look to alien civilisations, would they have both sets and classes, and elements, and sets not being elements of themselves like we do?
They would surely have things like natural numbers wouldn't they?

>>15840806
my argument is that mathematics solves problems, and societies face roughly the same basic problems and come up with roughly the same solutions e.g. housing, roads, counting, currency, basic arithmetic, etc.. Now beyond the basic problems, I think the situation changes a bit, modern math primarily addresses problems the society of mathematicians face. The value assigned to these problems is kind of arbitrary. So I think alien math will agree almost perfectly with us on the basics, as alien society likely needs it for exactly the same basic problems we do. But they might have no analogue of faithfully flat descent simply because that might not solve an interesting problem to their society of mathematicians, or the problems it solves has not occurred to them.
To specifically address the question about sets, I think the basic notion of collections of elements is fundamental. The Russell paradox-like situations that can occur if you're not careful with your language is something that comes up immediately if you care to formalize collections, but formalizing these notions is a rather modern trend and probably not that fundamentally important.

>>15840806
You need some broader context and a historical basis in order to appreciate mathematics. Once you do, you can view it from the perspective of abstracted super compact language, given most problems were solved descriptively with language until fairly recently, I believe the renaissance abacists and the prominent French mathematicians that followed, which introduce symbolic methods mathematics beyond basic arithmetic, which you could understand today. I recommend Cajori's book.

did i do this right

Why does foundations and mathematical logic always come up in these threads by people who clearly only ever read a few wikipedia pages? No working mathematician cares about that stuff these days, it’s a dead field.

How do I solve this bros, I'm blanking out
[math]
\sum_{n=2}^{+\infty} (2^{k-4} + 3^{k+1})*5^{-k})
[/math]

I get to
[math]
2^{-4}*(\frac{2}{5})^{k} + 3*(\frac{3}{5})^{k}
[/math]

but Wolfram says it converges at 163/60, how do I get there?

>>15840989
Converges to infinity.

>>15840989
It's the sum of two geometric series.
https://en.wikipedia.org/wiki/Geometric_series?useskin=vector

>>15840806
>do boundaries exist or are they just human constructs
idk man.

>>15840951
They don't care about it because they outsourced the foundations to philosophy to pretend they aren't there to avoid things like 'why choose this axiom over this other one'

>>15840989
This is the reason why I hate math sirs

>>15840998
?
>>15841002
Ah, I see. So basically I insert the (2/5) and (3/5) into the formula 1/1-q as the q? Then I get 5/3 and 5/2 each. That still isn't it though, is it?

>>15841064
That's because the series start at k=2.

[eqn]\sum_{k=2}^\infty 2^{-4} \left( \frac{2}{5} \right)^k = \frac{2^{-4} \left( \frac{2}{5} \right)^2}{1 - \frac{2}{5}} = \frac{2^{-2}}{15} = \frac{1}{60}[/eqn]

[eqn]\sum_{k=2}^\infty 3 \left( \frac{3}{5} \right)^k = \frac{3 \left( \frac{3}{5} \right)^2}{1 - \frac{3}{5}} = \frac{3^3}{10} = \frac{162}{60}[/eqn]

Maths is wasted on mathematicians.

>>15840951
it's approachable for non-working mathematicians (most of the thread)

I've read *dozens* of Wikipedia pages.

>>15841135

>>15833841
why?

>>15841144
>SEIMR

>>15841092
This is very helpful, thanks anon. One thing I don't fully grasp is how we arrive at the top part of this
[math]
\frac{\frac{2}{5}^{2}}{1-\frac{2}{5}}
[/math]
at the top. I see the formula in pic related but I don't fully get it. When we insert n = 2 that doesn't seem to be how we land here.

>>15833841
we do?

autism is short for automorphism

>>15841415
but the etymology is auto- + ism, not automorph + ism

what will you do after the ai renaissance. And ai can find proofs on its own, and know where to look for new proofs.

>>15841135
please go back to nameposting so I can filter you

Is my back ever gunna feel normal again /mg/ :( ?

Also any of you ever read algebra for dummies?????

have you guys read aaronson's quantum computing since democritus? i got filtered like 3 chapters in

>>15840827
Those last 2 paragraphs are the most poignant thing I have ever read. Misty eyed I sit, trembling in contemplation, digesting what you've just said. You, sir, are the sperm that deserved to win the race over all others. Fucking bravo

>>15841002
based old wikipedia theme user

Is Mathematical Truth and Beauty Intrinsic or Imposed?

>>15840760
Why would you expand it that way?
Just do 2*pi*i*(1/f'(r1) + 1/f'(r2))
= (1/2)*pi*i*(1/r2 + 1/r1) = (1/2)*pi*i*(r3 + r4) = (1/2)*pi*i*(-i*sqrt(2))
=pi/sqrt(2)

To get the residues for 1/p(x) (all roots of p are degree 1),
just assume the form is 1/p(x) = Sum[w(k)/(x-r(k))].
Multiply both sides by (x-r(j)) and let x go to r(j) to get w(j) = 1/p'(r(j)).

How much of a weakness is being bad at computing by hand?

How can I proof the completeness axiom of R?

I found several proofs but I don't understand a shit.

Also, I don't understand how to proof the Inverse Property of Multiplication with Cauchy sequences of rational numbers.

Any help would be thankful. Have a nice day everybody :)

>>15843002
Depends on if by computation you mean with numbers or algebraic expressions.

>5th edition next to Fourth edition
>Same publisher
AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

>About to graduate
>University keeps growing and math department expands to offer more courses that are extremely cool

Fuck this gay earth.

>>15839236
> PhD mathematicians
Who the fuck cares what people that bang their head against dead ends for subpar payment after a career long history of being bullied professionally think?

>>15843036
>How can I proof the completeness axiom of R?
You've got to tell us the model of the reals you're working in first. Granted I see below you're using the Cauchy sequence model, so that's covered. Also, which version of the completeness axiom? That the supremum exists for non-empty sets bounded above? That Cauchy sequences have a limit? Or something else?

>Also, I don't understand how to proof the Inverse Property of Multiplication with Cauchy sequences of rational numbers.
You know how to define division, right? Like all the other arithmetic operations, just divide the nth term in the dividend by the nth term in the divisor to get the nth term in the quotient. If you would divide by zero, you can do something arbitrary since there are at most finitely many zeros unless your divisor is zero itself. Then you have to prove the quotient is Cauchy if the dividend and divisor are Cauchy, which is most of the work. Once you've proven this division operation produces real numbers, showing that (1/x)*x = 1 is trivial.

>>15843371

First, yes, all three of them.

Second, I tried using a subsequence from the nth term in which it starts to converge to something different from zero, but don't understand why is that true.

>>15838307
Pretty aesthetic, but I'm still not spending $250 on a scientific calculator

>>15843394
I mean, how is that true? That there exist a supremum of non-empty sets bounded above?

My dumbhead says that it's not possible.

And why do Cauchy sequences have a limit?

>>15843371
I forgot a step: You also have to prove that if a ~ b and c ~ d, that a/c ~ b/d. Then you can go from an operation on sequences to an operation on equivalence classes. But that should be relatively easy to do if you've figured out how to prove the sequences are Cauchy in the first place. Also it will probably be slightly easier to do just the reciprocal than to do general division.

>>15843394
If the zeros don't stop eventually, then your sequence must be equivalent to 0. Look at the statement of the equivalence relation to see why that's true.

>>15843411
I personally find the cut property more intuitive: If you cut the reals into two non-empty sets such that everything in set A is less than everything in set B, then either set A has a maximum or set B has a minimum. If you can prove that, it's pretty easy to get the supremum property by constructing the right cut.

If your model is equivalence classes of Cauchy sequences, it should be obvious that Cauchy sequences of rational numbers have a limit. The entire point of the construction is to give every Cauchy sequence of rational numbers a limit. What you have to do is extend this to Cauchy sequences of arbitrary reals. You have a sequence of sequences, and your job is to figure out how to make those into a single sequence which is the limit (more accurately, a member of the equivalence class which is the limit).

>>15843446
>Look at the statement of the equivalence relation to see why that's true.
Addendum: You'll need the fact the sequence is Cauchy too.

>>15843446
OP here, thank you anon :)

Pic related is my favorite way of constructing the reals. It's very similar to the Cauchy sequence construction, so if you can grasp intuitively how it works, maybe it will help you grasp the Cauchy sequence version.

>>15843353
>you: GS11 step 10
>them: GS15 step 1 in half the time

Terminal masters bros... not like this....

>>15833787
Anyone else here find working at your own pace far more effective and faster than doing work based on courses? I can cover material at ten times the speed if I am just doing general studying of my own interests.

>just found out about the prime number theorum
what the fuck/ that is scary. why are prime numbers and logarithms everywhere

>>15843586
How can you define a prime number when you don't even know what all the prime numbers are? Math bros.... not like this.....

>make a minor mistake on a math problem
>spiral into a 30 minute long emotional meltdown involving self-harm, writing of poetic suicide notes, and intricate daydreams about faking my death and joining the french foreign legion to start a new life away from my disgrace.
Why am I like this?

>>15843701
bpd

>>15843725
Shit, my mom had bpd. This is a bad sign.

What are some good multivariate analysis books? I would like a book that explains the subject and not a theorem catalog.
Thanks.

University makes me hate mathematics.

>>15843400
>>15838307
The next best thing would be an emulator of the
calculator, perhaps based online. But good luck
finding that...

>>15843827
I mean real analysis, not the statistics thing.

>>15843586
At first it terrified me as well, but notice it is quite natural since the defining property for primes is multiplicative. If you want to follow the opposite path of counting primes up to N, it is natural that logarithms appear.
Btw, if you are impressed by the prime number theorem, wait until you see the rest of analytic number theory with their "log log log log x" shenanigans

>>15843701
>writing of poetic suicide notes, and intricate daydreams about faking my death
that sounds gays af

>>15843827
>>15843835
You can try the book I used in grad school

>>15843855
I will take a look thanks.

HELLO G :) here I am silenced in the US with no way to download any deep web browser because the government is fucking around on my computer and I’m a noob at cybersecurity :) so I come to share information about information. WWIII is starting and it will be a war on information (hopefully without nuclear fallout). You need to understand light and pure vacuum to understand where information comes from. Additive color palettes are also important in cybersecurity. Contact me at lachattienoire0@proton.me if you want to teach me any way to break out of my prison using both the information technologies we have! <3

>>15844286
>proton.me
This should be protonmail.com or pm.me

>go to check a quick detail about differentiation notation
>>This notation is sometimes called Euler's notation although it was introduced by Louis François Antoine Arbogast, and it seems that Leonhard Euler did not use it.
>huh sucks for Arbogast. Who the fuck was he, anyway? Never heard of him.
>>In 1800, he published a calculus treatise[4] where the first known[5] statement of what is currently known as Faà di Bruno's formula appears, 55 years before the first published paper[6] of Francesco Faà di Bruno on that topic.

do you ever just find a mathematician you feel was robbed? It's especially hilarious in this case since while Euler's not a stranger to getting things named after him even when he wasn't the first to really come up with them, I don't think I've yet found a case of something that had literally nothing to do with him or his work being named after him

>>15844407
Stigler's law of eponymity.

what keeps you going. if you are working on some problem alone for years, what's the drive that keeps you going, and makes you not give up on it?
What is thing that makes you believe it will be worth it in the end, and that spending so much time on one problem will not be a waste?

>>15843827
Munkres

>>15843467
Does it generalise to arbitrary metric spaces? No? Then shut up about your worthless construction.

>>15844569
https://arxiv.org/abs/1503.04348

fucking long ass linear equation systems...
you're MEANT to simply plug in the alternatives, right?

>>15844936
You're most likely sitting in front of a Computer just now. Let it do all the calculating.
There is no reason to do calculations by hand in 2023.

>>15843467
>>15844569
>>15844851
Another generalization which should be fairly obvious (this time only to arbitrary metric spaces) is to notice what we are talking about are equivalence classes of sequences of closed balls with non-negative rational radii converging to zero. We can weaken the condition that the balls be nested to the condition that any two balls in the sequence intersect. (I'm not sure if this change is strictly necessary, but it makes things easier in the generalized version.) The equivalence relation would then need to be changed to two sequences being equivalent if corresponding balls intersect.

Easy exercise for the reader: Show that a sequence in a metric space has a corresponding sequence of non-negative rational radii about the points in the sequence satisfying the balls-touching and converging-to-0 conditions if and only if the sequence is Cauchy.

Exercise 2: Show that it is not always possible to compute such a sequence of radii for a given computable sequence of centers.

I enjoy math and especially working through it in a proof based manner. But I am kinda dumb and a midwit at best.
Any tips to make it through undergraduate? No problems doing the exercises so far, but I'm scared that I'll be just too slow to keep up.

Category theory is not math.

>>15833841
based
>>15833964
>>15841143
so that normies will struggle even more to learn math. although it should be 120 or something more divisible.

>>15845078
You are not a mathematician

>>15845078
Category theory is algebra.

Why is he so overjoyous?

>>15846236
There's an illusion on the scope that goes on for ages. Warning!

You cross the point which releases the white part the red flicker as if it don't matter. You do the skill involved to reach the front and you continue from there til you reach the scope. Then you follow the top front the orange stick of the gun until you work that bit out. And then there's more. You do the shadow several times and you end up at that little patch near the grip and trigger and one more after that.

Alternatively you rub the little extruded white knobble at the top front for quick resumption of make.

>>15843827
Jänich, Vector Analysis. Ignore the other suggestions you got.

>>15845053
>keep up in math
Hang out with your classmates. Work together. This is not about cheating or even collaboration, it’s about surrounding yourself to keep motivated.
>pic
Holy shit are they actually doing it?

>>15844999
>Exercise 2: Show that it is not always possible to compute such a sequence of radii for a given computable sequence of centers.
im not reading the thread or the paper but my gut tells me this is a diverging harmonic sequence tomfool

>>15844999
>exercise 2
let the centers go up by [math]2^{-n}[/math] as n enters the halting problem. dumb fucking question

>>15845078
is it philosophy instead then?

>>15845628
do you not think he would also think abstract algebra isn't maths?
hasn't maths become quite a loose term over time. I don't think ancient greeks would call this stuff maths.

I hate Complex Analysis so fucking much.

>>15846965
>hasn't maths become quite a loose term over time.
NTA.
If it's rigorous, structured with axioms, definitions, proofs and theorems and it's symbolic or numeric then it's maths

>have to take the math GRE
>spend weeks doing practice problems and taking mock tests
>panic the night before and buy a backup ticket in case I fail
>feel like I actually failed the exam
>start prepping to take it again
>find out I actually did ok
>take it a second time, feel like I did really well
>the instant I turn in the exam the weight of the colossal waste of time it was sets in
I hate the math GRE.

>>15847104
At least you didn't have to rush to do a test out of
your home state early in the morning like I have.

>>15847179
Utterly miserable. I'm sorry you had to do that, anon.

>>15847039
imagine stressin so much over fake numbers lmao

>>15847192
>>15847179
>>15847104
Hey, that's the math GRE for you. So anyways...

>all sites full in my city, picked a high school site in another state
>day of test, got up at 3:30 AM
>entire route planned in my head, timetables in hand
>rush out by 4:00 AM as scheduled
>took the first train to my next destination
>couldn't find the connecting hallway, ran outside a few blocks and reentered connection, 5:00 AM
>took second train to next destination, 6:00 AM
>paid peak ass for a third train to next destination, 7:00 AM
>ran to get the fourth train, but it's not active for the next couple hours
>paid cab to get to test site, 8:00 AM
>straightened myself out, sat down...why there's so many white people here?...
>remembered my 8th percentile from last math GRE, hope to beat it
>test starts
>earned 6th percentile
>also was informed GRE wasn't needed for grad school applications

Yeah, fuck that test.

But, I want to know where I can find more GRE questions.
They make great practice questions to drill with someone.

>>15847292
8th and 6th percentile? Are those typos? That's really brutal, though, I'd probably get in the single-digits too if I had to travel 5 hours to get to the test.

>>15847292
>>15847303
>Are those typos?

>>15847058
so if metaphysics had axioms/definitions/proofs/theorems it would be maths? couldn't loads of things be maths then at that point.
like if ethics had axioms, definitions, proofs, and theorems, would you really call that maths?

>>15847313
my condolences

Let's say the probability of A winning against B in one set is p and they're playing the best of m in n sets, if X is the number of sets played, how would you get P(X)?
I got
[math]P(X=k)=p^m q^{k-m}+q^mp^{k-m}[/math], if k=m, and
[math] P(X=k)=(\binom{k}{m}-\binom{k-1}{m})(p^m q^{k-m}+q^mp^{k-m})[/math] otherwise
through simple reasoning, is there a generic distribution to model this kind of experiment?

>>15846929
Yeah, it's pretty trivial if you've ever seen an example of an uncomputable number.

Figuring out the answer to
>I'm not sure if this change is strictly necessary
was more interesting for me. Although it's a simple enough construction that someone will probably find it trivial.

Any PhD anons go through a period where they did literally nothing? I've had no time to do anything and I'm worried my advisor's gonna get pissed and every day I think of just being a cop and chillin with my bros all the time. I do algebra shit.

>>15833787
can somebody please share the leaked problems from the amc 12a and 10a 2023-24? also, where does one find such paper leaks online? reddit?
olympiad

>>15847316
>so if metaphysics had axioms/definitions/proofs/theorems it would be maths
>like if ethics had axioms, definitions, proofs, and theorems
Ethics and metaphysics are neither rigorous nor symbolic or numerical. you are just writing words and making shit up
best you could do is just use some formal logic but that wouldn't make it math.
I guess it's safe to say that maths has to be independent of everything else, you don't need to experiment or see the world to do math

Professors of /mg/, what is the best subject to teach? I've been thinking about teaching linear algebra exclusively in the future.

I just watched the video about the bifurcation diagram by Veritasium I it made me wonder this.

On the bifurcation diagram, in which x-coordinates do the priod doublings occur? Is there some kind of formula for those numbers and what kind of numbers are they anyway?

I just watched the video about the bifurcation diagram by Veritasium and it made me wonder about the following.

On the bifurcation diagram, in which x-coordinates do the period doublings occur? Is there some kind of formula for those numbers and what kind of numbers are they anyway? The first one seems to be at exactly 3 but what about the next ones.

Also, I thought if you could know where the n:th period doubling occurs, that would give you more insight regarding what's the deal with the Feigenbaum constant.

>>15847847
>Ethics and metaphysics are neither rigorous nor symbolic or numerical. you are just writing words and making shit up
do you not know what 'if' means? If they had?
if they got axiomatised, that's the supposition.
>if metaphysics had
>if ethics had

>>15847058
what is symbolic? literally anything can be that. So if arithmetic is written with english words instead of symbols it's not maths?

>>15848325
I know the second doubling is at [math]3+\sqrt{6}[/math] and the third is at one of the roots of fucking [math]x^12 - 12x^11 + 48x^10 - 40x^9 - 193x^8 + 392x^7 + 44x^6 + 8x^5 - 977x^4 - 604x^3 + 2108x^2 + 4913[\math]
but that last one alone really makes me not want to make any guesses on what patterns there are

>>15848325
>>15848336
and to further that point, according to OEIS, the next time it doubles is at the root of a polynomial of degree 120
https://oeis.org/A091517
No thanks.

>>15848336
At which point does the prediod become infinite? I mean, it looks like it's doubling and doubling at a faster rate the further you move to the right looking like it reaches a point of being infinitely dense.

>>15848419
Strictly speaking, there isn't one.
the first chaotic point is at https://oeis.org/A098587 but even then you have occasional cessation of that behaviour (e.g. its period becomes 3 for a bit around [math]1+\sqrt{8}[/math])

>>15848225
I've always like doing calculus because it doesn't require much thought or prep, but students have found a million ways to make it difficult. Precalculus is torture. Multivariable is nice because the students are generally brighter, but the material is so calculationally heavy that example problems require more time to prepare, which can be annoying. I haven't taught linear algebra but I imagine it being fun. Did you like teaching it?

>>15848225
>>15848470
>Topics: X
>requested by motivated students
>can teach literally anything you want
>keeps you on your toes, can be a great way to stay motivated
>can be extra bullshit, give student 3 credits to just be your undergrad research assistant for a graduate topic.

I'm just a student but this has been my impression through a few of these as an undergrad. (deductive logic, manifold theory, stochastic processes, geometric topology)

Wow I just approximated the Feigenbaum constant with my Mandelbrot fractal software. It gives you the coordinates of your cursor on the complex plane, so I zoomed into those black circles centered on the real axis and calculated the diameter of two consecutive circles based on the coordinates of the cursor, then divided the diameter of the bigger one by the smaller and got this value.

abs(-1.39963125305673+1.400828748226664)/abs(-1.400828748226664+1.401085276183046) = 4.66808837...

>>15848493

Someone put up a supposed proof of the Fourier restriction conjecture on arxiv.
The paper isn't simple enough for me be able to decide whether it's correct or not.

>>15848225
>>15848470
I shouldn't really be surprised that actual professors post on here but on some level I still find it surprising. I guess if I manage to get a professorship someday I'll probably keep coming here. If this shithole stays up.

>>15847316
>>15848328
The point of formalization and axiomatization is that it allows mathematicians to make statements that hold for any object which has some set of properties, regardless of what that object is. But philosophy is (almost always) concerned with doing exactly the opposite: asserting what properties a specific object has. For example in the case of metaphysics an axiomatized approach is antithetical to the whole purpose of the field: metaphysicians want to make statements about the real world or our relationship with it; what can be proven about any object which satisfies some formalized criterion "real" is completely irrelevant. (And of course that's assuming the concept CAN be formalized satisfactorily. By and large nobody has every successfully formalized a philosophical notion--just look at the sideshow that is set theory as an attempt to make to formalize the notion of a "collection" or "group." Actually formalizing the concept of "being real" would probably involve far more than solving every open open metaphysical problem).

The point is yes, any such axiomatization would be something fundamentally different from metaphysics or ethics, the same way the philosophy of set theory is a different thing from set theory.

Is anyone working on creating their custom math gpt? You can upload a ton of books to increase its knowledge-base and it's honestly not that bad. I spent some time setting it up and it's already fairly capable in proving basic theorems of a Hilbert style system of PL. I think that it might become pretty cool if we make it eat lots of books. Is anyone else playing around with this?

>>15848846
I've considered the idea, especially after the one paper with GPT trimming Alpaca down confirmed that a small model trained on good data is significant better than a large model trained on terrible data (who would have guessed?).
But my computer's really not set up to run these things, so it's been a "maybe in the future" bit. Good to hear it's viable, even if it's completely unsurprising. Out of curiosity, can you share an example?

>>15848866
Prompt:
Take a Hilbert style system with modus ponens and two following axiom schemas:
1. A->(B->A)
2. (A->(B->C))->((A->B)->(A->C))

Prove A->A within that system. Be rigorous.

Reply:
To prove AA within the Hilbert-style system with modus ponens and the given axiom schemas, we will apply the axioms and the rule of inference as follows:

1. Instantiate the first axiom schema with A and AA for A and B, respectively, to get: A((AA)A).This follows from axiom schema 1.

2. Instantiate the second axiom schema with A, AA, and A for A, B and C, respectively, to get: (A((AA)A))((A(AA))(AA)). This follows from axiom schema 2.

3. From step 1 and step 2, we can use modus ponens to deduce: A(AA))(AA). This step is the application of modus ponens on the results of steps 1 and 2.

4. Again, instantiate the first axiom schema with A for both A and B to get: A(AA). This is a direct application of axiom schema 1.

5. Finally, apply modus ponens to the results of steps 3 and 4 to deduce: AA

Each step has been derived by strictly following the axioms and the rule of inference (modus ponens) from the Hilbert-style system, ensuring the proof's rigor and correctness.

I have been testing various versions of LLMs with this same task. Originally gpt3 could do it after 10 tries and a much more precise definition of everything. This is the first time any model got it first try without me giving it any corrections. It's pretty exciting.

>>15848866
Prompt:
Take a Hilbert style system with modus ponens and two following axiom schemas:
1. A->(B->A)
2. (A->(B->C))->((A->B)->(A->C))

Prove A->A within that system. Be rigorous.

Reply:
To prove A->A within the Hilbert-style system with modus ponens and the given axiom schemas, we will apply the axioms and the rule of inference as follows:

1. Instantiate the first axiom schema with A and A->A for A and B, respectively, to get: A->((A->A)->A).This follows from axiom schema 1.

2. Instantiate the second axiom schema with A, A->A, and A for A, B and C, respectively, to get: (A->((A->A)->A))->((A->(A->A))->(A->A)). This follows from axiom schema 2.

3. From step 1 and step 2, we can use modus ponens to deduce: A->(A->A))->(A->A). This step is the application of modus ponens on the results of steps 1 and 2.

4. Again, instantiate the first axiom schema with A for both A and B to get: A->(A->A). This is a direct application of axiom schema 1.

5. Finally, apply modus ponens to the results of steps 3 and 4 to deduce: A->A

Each step has been derived by strictly following the axioms and the rule of inference (modus ponens) from the Hilbert-style system, ensuring the proof's rigor and correctness.

I have been testing various versions of LLMs with this same task. Originally gpt3 could do it after 10 tries and a much more precise definition of everything. This is the first time any model got it first try.

>>15833787
I've found a technique to solve specific problems that is not well studied and I can't find similar techniques in any paper/book (I've only found some things in chinese blogs). Could I perhaps publish a paper introducing the technique? It is not a trivial one (it uses knowledge from a very niche area of mathematics, based on one paper which doesn't really have any followups) and is certainly useful (it trivializes some very specific but complicated problems). However it does not have a main result, I can only maybe explain how it can be used to solve problems (with only a few number of small theorems perhaps).

What should I do? Is it even worth trying to submit it to a journal? Could I somehow make it work? I'm a undergrad in my third year and I think a publication would be very good on my CV, considering that I am in CS and plan on doing graduate studies in math.

University makes me hate math.
When I’m studying on my own it’s challenging and pleasurable but university, professors, classes and exams make hate it.

>>15848627
We're here forever. Hopefully when 420chan comes back we'll get /math/ back.

>>15849112
Can you give an example?

>>15848910
No fucking way. What setup are you using? I just used the math tutor mode to solve a simple multivariate/joint density problem and it gave me some comical word salad.

>>15849311
>This GPT, named Mathematical Rigor, is adept in formal logic and meticulous proof construction within the realm of mathematics, particularly in Hilbert-style systems. It is committed to providing precise and accurate responses, rooted in the firm application of logical axioms and inference rules. It follows a disciplined approach to ensure that each step in a proof is valid and that the final outcome is logically sound. It must always verify the correctness of each step before proceeding, and it is expected to double-check its work for logical consistency before presenting any proof. The GPT must prioritize accuracy and the integrity of logical processes over response time, emphasizing quality in every aspect of its output.
I also provided it with the book concise introduction to mathematical logic, but it has yet to use it. I haven't tested it too much as I'm phone posting. Once I get home I'll feed it a bunch of other books and see how far it can go. You can get other LLMs to output a similar proof if you just tell them in detail what a formula is, what it means to be a proof within the system etc, but they tend to get it wrong a couple of times.

>>15848565
The fact that I haven't seen any buzz about such a strong result so far makes me sceptical.

I found this famous image that shows how the logistic map and Mandelbrot set map onto each other showing that the points of period doubling on the logistic map correspond to the "gap" between the mandelbrot circles.

I checked if this picture is accurate in reality. So first I got the ratio between the period-2 and period-4 intervals of the logistic map based on numbers anon gave, that number turned out to be 4.75. Then I got the ratio between the diameters of the largest and second largest black circle in the Mandelbrot fractal which, based on this picture, should be the same ratio. But that number turned out to be 4.23. Those ratios are not even close to each other even though they should be (regardless if one image is scaled or stretched). So what is the deal with this or did I do something wrong?

Used this as source for the other number: https://users.math.yale.edu/public_html/People/frame/Fractals/MandelSet/MandelScalings/CompDiam/CompDiam.html

>>15849824
Edit: I think I got it figured out now by reading youtube comments. So it is just showing the similarity between the Mandelbrot set and a bifurcation diagram in general, not the bifurcation diagram of the logistic map specifically.

Serious question:
Let [math]G[math] be a permutation group of [math]X[math]. Such that [math]G[math] is transitive and imprimitive.
Can we prove there is [math]H\leq G[math] subgroup that is transitive and REGULAR over [math]X[math].

A regular permutation group is one such that for every point [math]x \in X[math] its stabilizer is trivial.

Why so little information about permutation groups that are not primitive?

>>15849843
The question is is it bijective?

anyone know how to rotate text in metapost?

>>15849674
this is great and all, but every question I ever ask GTP for the last month always results in a half complete answer and [network error]
Even in its peak use for me when working my way through Gaal's classical galois theory, it could barely work its way through even the simplest of things I was offloading to it due to its mundane nature.

fellow applied math niggers, how did you control and prevent yourself from stepping out of line during your education, and enrolling in too many of the White man's pure math courses?
My heart tells me to take the useless courses, but my wallet tells me I can't afford to.

>>15848225
What is Sodachi's favorite branch of mathematics? What about her favorite book? Analysis or Algebra?

Euclid's proof of infinitely many prime numbers is false because it presupposes the existence of infinite numbers in order to prove infinite primes numbers.
If you have a finite list of primes, and add +1 to that list to run the test, that is assuming we can ALWAYS do that, i.e. implying that there must be an infinite amount of numbers available that we can always run our test with. But in order to be able to do this, we would have to prove first that there are infinite numbers to work with, and since that isn't proven, the entire logic of the proof is flawed.
Did I just disprove a 2000 year old proof?

>>15850536
You just implicitly proved there are infinitely many numbers you tard

integers are not a domain, ring, group or even magma
the assumption that they are closed under + or x is false
there is a biggest number
no you cant write it or the universe will en-

>>15850608
How?

>>15850231
My headcanon has always been that normal Sodachi is an Analysis person and reverse Sodachi an Algebra person.

>>15850770
Maybe I should continue Bakemonogatari

>>15850750
Take a finite set of natural numbers
Take the maximum of that set
Add 1 to it
Congrats, new number
You can do that for any finite set of natural numbers, therefore the natural numbers are not finite

Trying to understand generalizations of conditional Jensen's inequality, and I stumbled across this lemma. Am I missing something, or is their claim that [math] \Re\,s_i^*\;=\;0 [/math] would contradict (1.3) complete bullshit?

>>15848325
Isn't it just Feigenbaum constant?

>>15851108
To clarify: I’m pretty sure it’s a fundamental constant which can’t be expressed through other constants (at least simpler than its initial definition).

>>15850822
extension is a belief, not a fact

I am re=enrolling next semester

>>15850536
Natural numbers by definition is infinite.
https://en.m.wikipedia.org/wiki/Peano_axioms

>>15851622
who said natural numbers?

>>15851623
Euclid's proof of infinitely many prime numbers is about natural numbers.

>>15850885
Book?

>>15839763
>Many people suck at a videogame, but still invest tons of hours because they enjoy it.
True.

>>15851682
Analysis in Banach Spaces, Volume I
I managed to fix the issue, but it makes the proof 3 times as long.

>>15851461
Oh you're just retarded, why didn't you say so? Could've saved me a post.

>he thinks there are infinitely many naturals
Look at this idiot not believing that the universe is modular.
Once you hit a sufficiently large number, like 7, you loop back to 0

>>15850770
I'm not sure how to feel about this.

Taken enough courses that I qualify for all and can request a change. Should my bachelors diploma say BS in: Mathematics. Mathematics, advanced. Applied mathematics. Computational mathematics.

I'll go to grad school after I get some experience working in industry. What do employers care about, for those that have worked for a while? This is at MSU.

>>15852340
the vast majority of employers dont know the difference, never mind care about it

If you have a function f(x) and you start with some starting value, say x=1 and then feed the output of the function back to itself and repeat, in which cases is it possible to have a simple formula for the value of the n:th iteration?

As an example, if f(x)=2x and you start with x=1, the n:th iteration will be 2^n, resulting as a nice formula. But what if the function is much more complicated? I'm wondering for which type of functions this type of thing is possible to do and which not. It's interesting because I've never seen this type of ,aths in school and it feels weird to think about.

If you have a function f(x) and you start with some starting value, say x=1 and then feed the output of the function back to itself and repeat, in which cases is it possible to have a simple formula for the value of the n:th iteration?

As an example, if f(x)=2x and you start with x=1, the n:th iteration will be 2^n, resulting as a nice formula. But what if the function is much more complicated? I'm wondering for which type of functions this type of thing is possible to do and which not. It's interesting because I've never seen this type of maths in school and it feels weird to think about.

>>15833970
Shilov's Linear Algebra

>>15852372
ask your teacher about recursion

>>15852372
Solving closed-form for recursive functions is a lot like solving differential equations. There's a patchwork of different methods you try, and any one particular type of problem has its own books' worth of theory to it. One place to start is with solving recurrence relations.

>>15852535
>Solving closed-form for recursive functions is a lot like solving differential equations
the most offended I have ever been was when someone told me that the only real difference between the two is that the latter are continuous and the former are discrete

successor >>15853575

>>15845053
That movie needs a catchy tagline or something

Any recommendations for "light reads" that still teach something tangible and useful from undergraduate level math topics?

In other words: Books that are more substantial than typical pop science but not as dense as textbooks.
Something I can read on the train or before going to bed.

>>15854288
Principia Mathematica

>>15854288
Ian Stewart is good for this, picrel and Flatterland is a fun read as well

Anyone have any luck requesting a solutions manual for a book that doesn't have any exercise solutions?

Comp-Sci friend here. I've just finished my math minor recs by taking some data science and machine learning courses offered by my math department and I loved them so I wanted to learn the mathematics behind it all. Unfortunately, I haven't taken a transition to upper math course so I can't continue taking "real" stats classes. Anyone have autodidact friendly recs for online courses or books for mathematical statistics?
Picrel is the book I used for my courses. Interesting, but almost all of the math is stripped out, basically zero proofs.

>>15855127

>>15855058
Only tried it once for the abbot book. Fucker didn't write back despite claiming "if you need a solutions manual write me a mail".

>>15855127
I dropped my CS minor after 3 classes, so I could take more math.