Anonymous at Fri, 3 Jan 2025 20:43:24 UTC No. 16534312

finishing undergrad, what should i know by now for masters?

Anonymous at Fri, 3 Jan 2025 20:45:32 UTC No. 16534314

just finished Lang's basic mathematics, what's next

Anonymous at Fri, 3 Jan 2025 21:37:49 UTC No. 16534384

I need help understanding the Fundamental Theorem of Graphs

Anonymous at Fri, 3 Jan 2025 22:07:58 UTC No. 16534436

>>16534314

Anonymous at Fri, 3 Jan 2025 22:17:57 UTC No. 16534447

>>16534436
i have this one, do i need lang too

Anonymous at Fri, 3 Jan 2025 22:30:14 UTC No. 16534463

Nobody told me that a math degree is worth nothing. Nobody hires mathematicians. :(

Anonymous at Fri, 3 Jan 2025 22:35:44 UTC No. 16534471

>>16534463
Try applying at middle schools. Math teachers are always needed.

Anonymous at Fri, 3 Jan 2025 23:27:22 UTC No. 16534516

>>16534314
Stewart's Calculus

Anonymous at Fri, 3 Jan 2025 23:31:16 UTC No. 16534518

Which numbers are able to be the sum of consecutive cubes? Assuming that the cubes don't have to start from one. For example, one of such numbers could be 1584 because of the fact that 1584 = 7^3+8^3+9^3.

Do those numbers have a formula and how common would they be?

Anonymous at Fri, 3 Jan 2025 23:36:34 UTC No. 16534524

>>16534518
[math]( n - 1 ) ^ 3 + n ^ 3 + ( n + 1 ) ^ 3 = 3 n ^ 3 + 6 n[/math]

Anonymous at Fri, 3 Jan 2025 23:38:36 UTC No. 16534526

>>16534463
Try becoming a quant at Jane Street

Anonymous at Fri, 3 Jan 2025 23:42:14 UTC No. 16534528

I hate applied math, but the only way to do a master degree at my uni is in a statistic program.

🗑️ Anonymous at Fri, 3 Jan 2025 23:43:28 UTC No. 16534529

>>16534524
But isn't that just three consecutive cubes? What if there's a number which cannot be the sum of three consecutive cubes but is still the sum of some other number of consecutive cubes.

🗑️ Anonymous at Fri, 3 Jan 2025 23:47:07 UTC No. 16534531

>>16534524
That's only three consecutive squares. You can not make the number 1800 with that formula but yet 1800 is still able to be the sum of consecutive cubes.

Anonymous at Fri, 3 Jan 2025 23:48:32 UTC No. 16534533

>>16534524
That's only three cubes. You can not make the number 1800 with that formula but yet 1800 is still able to be the sum of consecutive cubes.

Anonymous at Sat, 4 Jan 2025 00:10:30 UTC No. 16534543

>>16534463
I became a code monkey.

Anonymous at Sat, 4 Jan 2025 01:31:17 UTC No. 16534597

>>16534543
all the physics and math majors end up becoming code monkeys, meanwhile i was ahead of the game at became a code monkey from the start. Now i see the writing on the wall though with how AI is going to fuck everything up, so i'm returning to my studies to learn everything i can to try to still have an identity after the great ai reckoning in all intellectual fields

Anonymous at Sat, 4 Jan 2025 01:39:07 UTC No. 16534605

>>16534516
>Stewart's Calculus
$200 bucks, why these textbook publishers always trying to scam students

Anonymous at Sat, 4 Jan 2025 01:40:01 UTC No. 16534606

>>16534605
it's free on libgen

Anonymous at Sat, 4 Jan 2025 01:42:29 UTC No. 16534608

>>16534606
i need the bound paper, unless it's physically sitting in my library daring me to read it, i'm not going to

Anonymous at Sat, 4 Jan 2025 01:56:05 UTC No. 16534615

>>16534605
Bro, I got my copy of Stewart's Calculus for $5 on thrift books.

Anonymous at Sat, 4 Jan 2025 02:49:45 UTC No. 16534660

>>16534533
pardon me, I'm retarded and saw a 3 where there was none
for the sum of all cubes from [math]x[/math] to [math]y[/math] you have the mildly unpleasant formula [math]\frac {y^4 + 2y ^ 3 + y ^ 2 - x ^4 + 2 x ^3 - x ^2} {4}[/math]

which is ugly enough that I don't want to do heuristics to figure out how common numbers of that form are

Anonymous at Sat, 4 Jan 2025 04:00:21 UTC No. 16534706

>>16534526
Are you Indian?

Anonymous at Sat, 4 Jan 2025 04:01:32 UTC No. 16534708

>>16534528
Are you also Indian?

Anonymous at Sat, 4 Jan 2025 06:27:04 UTC No. 16534819

Why shouldn't I go to Columbia for their cash cow masters? I want it. I hate how the voices in my head are making me insecure about being self indulgent for doing something for myself, just for myself. There are people who waste their time and money restoring cars, or gardening, or even playing video games. I want to get a masters in math. No it won't matter, no it's not a PhD and I don't have the time and money for that. It's fine, I'm fine, and I can cope by thinking that what I'm putting in cash wise will fund math PhD students so everyone wins. I can't afford to lose my job no fucking way in today's economy is anyone in tech making 200k salaries anymore. There are kids being hired now, over five years later, for less than I did when I started.

I live in in the bay area, no I'm not going to move anywhere else for school. I need a fellow sperg here to hype me up to do this.

Anonymous at Sat, 4 Jan 2025 06:35:54 UTC No. 16534824

>>16534183
lol no undegrad program is going to ask for anything beyond your "freshman year".

Anonymous at Sat, 4 Jan 2025 08:20:10 UTC No. 16534870

>>16534183
>posted the meme list that noone has ever read one book from again

Anonymous at Sat, 4 Jan 2025 14:58:44 UTC No. 16535047

>>16534706
No, Slavic

Anonymous at Sat, 4 Jan 2025 16:56:54 UTC No. 16535154

Bros, How can I get a scholarship for a master's degree in mathematics?
My university has an agreement with the University of Paris Saclay, but since my country is garbage, they only let me apply for the master's degree in applied mathematics, but I would like to do pure mathematics.

I have been searching on different websites for scholarships but the only thing I have been able to find have been scholarships that only include tuition fees.
What I'm looking for are scholarships like the Sohpie Germain foundation, (https://www.fondation-hadamard.fr/en/our-programs/transversal-programs/graduate-program/apply-for-a-sophie-germain-scholarship/) , which give you money while you study so you can live.
Sorry for the repost.

Anonymous at Sat, 4 Jan 2025 17:11:38 UTC No. 16535177

>>16534708
????
>>16534543
But i hate coding. It makes me feel like ive wasted 4 years of undergrad. My uni only had one class of programing.

Anonymous at Sat, 4 Jan 2025 17:40:07 UTC No. 16535209

i got a book on Lie groups, i'm either going to understand higher mathematics or die trying

Anonymous at Sat, 4 Jan 2025 18:17:27 UTC No. 16535250

>>16535209
Sounds exciting (the part about dying)

Anonymous at Sat, 4 Jan 2025 19:56:40 UTC No. 16535362

>>16535047
Basically the same thing.
>>16535177
So, you admit you are?

Anonymous at Sat, 4 Jan 2025 20:00:21 UTC No. 16535364

>>16534183
Lean's syntax irritates the fuck out of me.
I don't know how people use this shit.

Anonymous at Sat, 4 Jan 2025 20:15:59 UTC No. 16535384

>picrel
thoughts gentlemen? I just want to blitz through precalc and this text is nice and condense, with better writing than stewart's

Anonymous at Sun, 5 Jan 2025 02:47:53 UTC No. 16535775

>>16535384
What is your motivation for learning this material? Having an end goal will help.

Anonymous at Sun, 5 Jan 2025 03:16:22 UTC No. 16535809

>>16534183
Do any of you know of a software package that can do efficient kernel density estimation using a beta distribution?
I'm currently using the scipy.stats implementation, but it's slow.

🗑️ Anonymous at Sun, 5 Jan 2025 05:44:12 UTC No. 16535943

>>16534471
They don't teach actual math until you go to college and study something STEM--public school math is a debauchery of actual math.

Anonymous at Sun, 5 Jan 2025 08:01:22 UTC No. 16536004

How do you feel about cs students in your classroom?

Anonymous at Sun, 5 Jan 2025 13:32:57 UTC No. 16536148

>>16536004
The smartest person in my graduate level probability class was an ML guy.

Anonymous at Sun, 5 Jan 2025 14:12:33 UTC No. 16536165

>>16536004
I firmly believe we should return theoretical CS to math departments. The difference between them and the baby brain webdev /g/tards is so much larger than them and like a statistician, physicist, or mathematician.

Anonymous at Sun, 5 Jan 2025 15:51:40 UTC No. 16536222

>>16536165
as a CS guy I support this, automata and formal languages and complexity theory is math not computer science

Anonymous at Sun, 5 Jan 2025 17:50:57 UTC No. 16536320

So a Lie Group is a differential manifold and also a group. So it's basically bridging together topology and group theory?

Anonymous at Sun, 5 Jan 2025 20:42:16 UTC No. 16536515

>>16536320
it is simpler to think about it as a way of defining smooth group actions and their derivatives. it isn't really a bridge, just a subject which uses differentiable manifolds and group theory as tools.

Anonymous at Sun, 5 Jan 2025 21:14:10 UTC No. 16536541

>>16536004
at least some of them actually like math.
my course is FULL of tryhards with no passion for the subject but they really want good jobs, it's embarrassing desu

Anonymous at Mon, 6 Jan 2025 01:44:29 UTC No. 16536780

>>16536541
it was the same way in CS, 90% of people had no real interest in the subject and just wanted a high paying job

🗑️ Anonymous at Mon, 6 Jan 2025 01:46:55 UTC No. 16536783

Here's a cool way to solve cubics.
[math]\text{For cubic p, let a, b be solutions to the quadratic equation: }3p(x)p''(x)-2p'(x)^2 = 0.\\
\text{The zeros of p are given by: }z=\cfrac{a(-\frac{p(b)}{p(a)})^{1/3}+b }{(-\frac{p(b)}{p(a)})^{1/3}+1}.[/math]

Anonymous at Mon, 6 Jan 2025 02:05:30 UTC No. 16536797

>>16536783
wtf formatting. I'll try again
Here's a cool way to solve cubics.
[math]\text{For cubic p, let a, b be solutions to the quadratic equation: } 3p(x)p''(x)-2p'(x)^{2} = 0.\\
Zeros\ of\ p: z= \cfrac{ a(-\cfrac{ p(b) }{ p(a) })^{1/3}+b }{ (-\cfrac{ p(b) }{ p(a) })^{1/3}+1 }.[/math]

Anonymous at Mon, 6 Jan 2025 13:51:41 UTC No. 16537207

Let [math]G[/math] be a connected Lie group with Lie algebra [math]\mathfrak{g}[/math] and adjoint representation [math]\mathrm{Ad}_G : G \to \mathrm{Aut}(\mathfrak{g})[/math].

I'm desperate for a reference of the following (hopefully true) claim: Assume [math]G[/math] is semisimple and let [math]u \in G[/math]. Then [[math]\mathrm{Ad}_G (u)[/math] is unipotent w.r.t [math]\mathfrak{g}[/math]] if and only if [for some/any representation [math]\rho: G \to \mathrm{GL}(V)[/math] on a finite dimensional real/complex vector space, [math]\rho(u)[/math] is unipotent w.r.t [math]V[/math]].

Clarification: A linear operator [math]T[/math] on a vector space [math]V[/math] is called unipotent if [math]I_V - T[/math] is nilpotent.

Anonymous at Mon, 6 Jan 2025 17:04:21 UTC No. 16537333

Starting a math degree in your late 20s is a gamble. You’ll face a steep learning curve, especially if you're transitioning from a different field, and the workload can be overwhelming. While it may open doors in academia or research, the reality is that most jobs in industry require more applied skills than pure math. At that age, competing with younger students who have been immersed in the subject for years might feel discouraging. The payoff in terms of salary is often low, especially in academia, and breaking into high-paying fields like tech or finance usually requires additional qualifications. Balancing school with other life responsibilities, like work or family, can be draining.
The shift toward programming and data science is tempting for many math majors, as it's seen as a way to make the degree more practical. However, the rise of AI tools is making it harder to stand out in these fields. While you might have a background in math, automation and AI are already taking over many data science and programming tasks, making it harder to compete with younger, more specialized candidates. The market for skilled professionals is shifting fast, and as AI systems evolve, the demand for human programmers or data scientists may shrink, leaving many to question if the time and effort invested in this path will be worth it in the long run.

Anonymous at Mon, 6 Jan 2025 20:26:59 UTC No. 16537501

>>16537333
You literally described how i feel.
A a math major but hadn't been able to find a proper job, all my classmates went to data "science" and are making a lot of money. I think a master degree will solve my problems.

Anonymous at Mon, 6 Jan 2025 20:49:14 UTC No. 16537524

>>16537501
>You
That's a chatbot.

Anonymous at Mon, 6 Jan 2025 21:27:55 UTC No. 16537567

Which of the remaining Millenium Prize problems do you think is most likely to be solved next?

Anonymous at Mon, 6 Jan 2025 21:43:13 UTC No. 16537577

>>16537567
You may as well use a magic 8-ball to answer that one. It's effectively impossible to know.

Anonymous at Mon, 6 Jan 2025 21:48:41 UTC No. 16537582

>>16534312
>what should i know by now for masters?
your plan to afford grad school besides shoveling on more loans

Anonymous at Tue, 7 Jan 2025 02:13:35 UTC No. 16537795

I'm starting to realize that I'm probably too retarded and also not ambitious enough for academia. I'm almost finished with my master's and I'm experiencing some sort of crisis right now.
Is there anything in-between the two extremes of either becoming another npc codemonkey or trying to larp my way through a phd? As in, are there some fulfilling jobs outside of academia that I'd be qualified for?
I'm from Europe btw if that matters (yes this shit is keeping me awake at night)

Anonymous at Tue, 7 Jan 2025 04:40:33 UTC No. 16537898

>>16537795
Crypt keeper

Anonymous at Tue, 7 Jan 2025 09:04:24 UTC No. 16537989

>>16537795
You're right. No other jobs exist out there for someone with a math degree, none at all.

Anonymous at Tue, 7 Jan 2025 09:57:49 UTC No. 16538019

>>16534312
https://users.itk.ppke.hu/~vago/all-the-mathematics-you-missed.pdf

Anonymous at Tue, 7 Jan 2025 10:23:31 UTC No. 16538030

>>16534447
Strang's book is more applied/computational. I recommend the linear algebra problem book by Paul Halmos as a supplement to whatever. It takes you from the level of https://www.3blue1brown.com/topics/linear-algebra to the theoretical side.

Firedberg, Insel, and Spence or the book by Hefferon are some entry-level linear algebra books

Anonymous at Tue, 7 Jan 2025 10:38:17 UTC No. 16538042

>>16534819
Can you do a local master's after work?

Anonymous at Tue, 7 Jan 2025 10:40:33 UTC No. 16538045

>>16535809
https://www.researchgate.net/publication/374879305_DELTD_An_R_Package_for_Kernel_Density_Estimation_using_Lifetime_Distributions

Anonymous at Tue, 7 Jan 2025 15:24:42 UTC No. 16538199

How do you feel about EE students in your classroom?

Anonymous at Tue, 7 Jan 2025 16:13:51 UTC No. 16538252

>>16538199
As someone who has been that EE student in the classroom, we tend to occupy the extremes. Every EE student I've seen in math grad programs tend to either be the most stereotypical braindead engineer who can't into math, or they tend to be way ahead of everyone.

I've done both. I was way ahead of just about everyone in my introductory complex analysis course (just because we get so used to analytic functions of complex variables in undergrad) and then got my shit repeatedly rocked in measure and functional analysis.

Anonymous at Tue, 7 Jan 2025 19:37:38 UTC No. 16538408

Why do "they" keep it suppressed? Why don't "they" want us to know about Geometric Algebra?

Anonymous at Tue, 7 Jan 2025 19:55:24 UTC No. 16538421

>>16538408
A treatment of exterior algebra is found in any good linear algebra textbook.

Anonymous at Tue, 7 Jan 2025 22:14:21 UTC No. 16538557

>>16534183
Any PhD havers have advice for getting through the burnout/slump phase? I'm a fourth year and I would rather do literally anything except work on my problem. I've been distracting myself reading other stuff (I do rep theory/categorification). Wanted to ditch my advisor's seminar today to go to a QFT seminar. I don't have the heart to tell my advisor I didn't do shit over winter break except read about tensor categories.

Anonymous at Tue, 7 Jan 2025 22:41:01 UTC No. 16538583

what am I missing

Anonymous at Tue, 7 Jan 2025 23:27:45 UTC No. 16538636

>>16538583
Which of those have you spent time reading/feel like you have a mastery of? Having a gigantic collection of unread textbooks (which I am also guilty of) is worth far less than a smaller collection of textbooks you actually have a mastery of.

Anonymous at Tue, 7 Jan 2025 23:42:32 UTC No. 16538648

>>16538636
i am a master of nothing, barely qualified to do arithmetic, I just like collecting books

Anonymous at Tue, 7 Jan 2025 23:42:33 UTC No. 16538649

>>16538636
>Having a gigantic collection of unread textbooks (which I am also guilty of)
Why is this so common? Is it just consumerism?

Anonymous at Tue, 7 Jan 2025 23:49:00 UTC No. 16538663

>>16538649
NTA but for me it's a mixture of procrastination, OCD and books that I don't really intend to read and only use as a reference.

Anonymous at Tue, 7 Jan 2025 23:49:23 UTC No. 16538664

>>16538649
for me it's just general curiosity, i've been reading bits and pieces from them and combining it with internet learning, trying to understand the full scope of mathematics before diving too deep into any particular topic

Anonymous at Tue, 7 Jan 2025 23:54:18 UTC No. 16538668

>>16538649
In my case, my PhD has required that I have a really large amount of reference material. What ends up happening is I realize that some area I'm researching has a lot of related requisite material for some part of it, I end up getting textbooks on that requisite material, and I read one or two chapters and that's it.

As an example, I think I have a dozen probability theory/statistics related textbooks, and it's always because of one or two chapters in each that are different enough that it's useful to have both as a reference.

I don't think I own any textbooks I've never opened/used in some capacity, but the majority of them I've needed one or two chapters of their specific reference material and that's it. So I end up having a ton of textbooks in the "I'll get around to reading the whole thing some day" pile, after only using the bit of reference material I needed and moving on.

Anonymous at Tue, 7 Jan 2025 23:56:22 UTC No. 16538669

>>16538648
Ah, then I guess it just depends what you want to look at. Personally, I like probability theory, so I'd say get a book or two on that and related subjects. I quite like Bremaud's Discrete Probability Models book and it also covers some information theory and graphical models as well.

Anonymous at Wed, 8 Jan 2025 05:55:18 UTC No. 16538919

hi guys im horrible at math, i am trying to write a program. so the x input will always be 1, 2, 3, 4 etc increments of 1. the y is random it doesnt matter.
how do i find an equation that matches like this graph so when the input is 1 itll give me the y input. the way i imagine it is multiple linear lines that zig zag like that graph. i dont know how to say what im tryna say.

someone point me into what to look into to get what im trying to do. the equation isnt a linear equation i dont know what equation it is but i think it looks like that graph i dont care about 1.5 2.5 on the x line only increments of 1. maybe it also doesnt have to be straight lines but up and down parabolas.

Anonymous at Wed, 8 Jan 2025 05:58:43 UTC No. 16538922

>>16538919
You're looking for a piecewise linear function, or a linear interpolation. Take a look at a numerical analysis textbook for interpolation and you'll find what you need. Burden is the standard one. Or just read articles and posts about spline-based interpolation online.

Anonymous at Wed, 8 Jan 2025 06:00:54 UTC No. 16538924

>>16538922
thanks for the keyword ill check it out

Anonymous at Wed, 8 Jan 2025 14:44:44 UTC No. 16539128

Any recommendations on books that provide an overview of discrete math? I want something targeted at CS students, even something midwitish like "so well there are graphs and there's Djikstra alg which is just non-heuristic A* alg" will do just fine as long as most things are somewhat covered.

Anonymous at Wed, 8 Jan 2025 15:38:26 UTC No. 16539166

>>16539128
Graphs, Networks and Algorithms by Jungnickel.

Anonymous at Wed, 8 Jan 2025 15:39:33 UTC No. 16539168

>>16539128

Anonymous at Wed, 8 Jan 2025 16:49:41 UTC No. 16539261

Greetings mathematicians!

How can I prove the following statement?

Let \( f: \mathbb{R}^n \to (X, \rho) \) be a function, where \((X, \rho)\) is a metric space. If \( f \) is continuous with respect to one of the metrics \( d_1, d_2, d_\infty \), then it is continuous with respect to all the others.

I just cant figure out how to get one or another metric using the other(s).

Thanks in advance

Anonymous at Wed, 8 Jan 2025 16:52:03 UTC No. 16539266

>>16539261
I will read your question if you properly format it.

Anonymous at Wed, 8 Jan 2025 17:15:19 UTC No. 16539296

>>16539261
Try to show (for example) that [math]d_1 \leq \sqrt n d_2 \leq n d_\infty[/math] pointwise.

Anonymous at Wed, 8 Jan 2025 17:21:53 UTC No. 16539307

aaaand i'm failing for real

Anonymous at Wed, 8 Jan 2025 17:23:11 UTC No. 16539309

>>16539266

Let [math]f: \mathbb{R}^n \to (X, \rho)[/math] be a function, where [math](X, \rho)[/math] is a metric space. If [math]f[/math] is continuous with respect to one of the metrics [math]d_1, d_2, d_\infty[/math], then it is continuous with respect to all the others.

Anonymous at Wed, 8 Jan 2025 17:24:34 UTC No. 16539311

>>16539296
Hmm. How is that definition of continuity pointwise based in that inequality?

Anonymous at Wed, 8 Jan 2025 17:33:52 UTC No. 16539324

>>16538557
Probably your advisor cares less about you and your thesis than you think, and will not really care if you check out for a while and come back. If learning about other fields of math or physics keeps your overall interest level up that is maybe a good thing. But do come back to your main project. If you are really honestly stuck somewhere that is your advisor's responsibility too, and maybe you can work on something else more interesting and fruitful.

Anonymous at Wed, 8 Jan 2025 17:54:45 UTC No. 16539339

>>16539311
https://proofwiki.org/wiki/Lipschitz_Equivalent_Metrics_are_Topologically_Equivalent

Anonymous at Wed, 8 Jan 2025 18:16:40 UTC No. 16539360

>>16539339
>lipshit
I'm not into that.

Anonymous at Wed, 8 Jan 2025 18:22:29 UTC No. 16539364

>>16539339
Thank you

Anonymous at Wed, 8 Jan 2025 20:02:08 UTC No. 16539458

>>16534608
Print it then

Anonymous at Wed, 8 Jan 2025 20:48:56 UTC No. 16539497

>>16534518
[math]Re[\int\limits_{m-1/2+\frac{i}{\sqrt{12}}}^{n+1/2+\frac{i}{\sqrt{12}}}x^3dx][/math]

Anonymous at Thu, 9 Jan 2025 00:59:51 UTC No. 16539726

>>16539339
Now theres something I am confused about. The statement of equivalences of metrics is true if the inequality holds, but the reciprocal is false. So, assuming the inequality I cannot go further on proving why those are equivalents, neither how it can prove the main problem. What can I do there?

Anonymous at Thu, 9 Jan 2025 07:51:37 UTC No. 16540058

IQ
Hardest math you can do in your head

Anonymous at Thu, 9 Jan 2025 11:22:19 UTC No. 16540156

This is Grok:
If a spherical object triples its surface area, we need to understand how this affects its volume (and hence its weight, assuming uniform density).

First, let's define some terms:

Let A0
be the original surface area of the sphere.
Let V0
be the original volume of the sphere.
Let r0
be the original radius of the sphere.


The surface area A
of a sphere is given by:
A=4πr2

The volume V
of a sphere is given by:
V=43πr3

If the surface area triples:
3A0=4πrnew2

Solving for rnew
:
rnew2=3A04π

rnew2=3r02

rnew=r03

Now, let's find the new volume:
Vnew=43π(r03)3

Vnew=43πr03⋅33

Vnew=33V0

Thus, the new volume is 33≈5.196
times the original volume.

Since weight (or mass) is proportional to volume for a uniform density object, the sphere gains approximately:

5.196−1=4.196
times its original weight.

Therefore, if the sphere triples its surface area, it would gain about 4.196 times its original weight.

Anonymous at Thu, 9 Jan 2025 11:27:22 UTC No. 16540164

>>16538649
Yep, literal funko pops collecting. But because they are made out of paper and not plastic it's somehow ok.
>BUT BOOKS ARE USEFULLLLL
No, they are not, a free PDF on your computer is way more practical (hyperlinks embedded in the textbook etc). Watch everyone seethe now.

Anonymous at Thu, 9 Jan 2025 12:12:05 UTC No. 16540192

>>16540164
I have read quite a few math textbooks and all of the textbooks I've read I've read on my computer screen. I have a handful of textbooks on my shelf and I never read them. Sometimes I read the same textbooks I have physically but on my computer because flipping pages is much more difficult than scrolling/pressing page down.
Also another perk with a PC is that you can have two copies of the book opened at the same time which I find extremely useful, because what often happens is that some part references another and you want to quickly switch between them. Physically flipping pages loses context and it's harder to return to where you were before as well as physically taxing. With ebooks I just alt tab.
As for hyperlinks, that's definitely a perk, however most of the time the ebooks I read don' t have any hyperlinks and I just manually scroll to the referenced lemmas/theorems. And to be honest I'm not sure how much having hyperlinks would help, since my scrolls are typically quite fast, just a few seconds (I use sumatraPDF and scroll using the scrollwheel on the scroll bar which makes it scroll very fast).

Anonymous at Thu, 9 Jan 2025 14:56:52 UTC No. 16540302

>>16534183
So, are there any books that reflect Gian Carlo Rota's thoughts? Or should I just pick any book and use attached article as a filter for the content/chapters?

I don't mind reading, but many ODE books are voluminous and if half the stuff is truly obsolete, then I'd rather not waste time and focus on the important stuff.

Anonymous at Thu, 9 Jan 2025 15:52:38 UTC No. 16540339

What is this guy talking about? Someone explain it to me in English.

Anonymous at Thu, 9 Jan 2025 16:15:05 UTC No. 16540362

>>16540164
>>16540192
Maybe I'm just retarded, but I find (especially for self study on something difficult) that if I don't have the book, I won't be as serious in reading it. It's a sort of "accountability" thing where having a PDF of the book is easily "out of sight, out of mind." Instead, having a copy of the book near my desk staring at me makes me far more likely to actually spend my free time going through it.

Anonymous at Thu, 9 Jan 2025 17:16:23 UTC No. 16540452

Just finished reading and doing all the exericses in Atiyah&Macdonald AMA

Anonymous at Thu, 9 Jan 2025 17:24:52 UTC No. 16540458

>>16540452
Is it worth it

Anonymous at Thu, 9 Jan 2025 17:27:13 UTC No. 16540461

>>16540362
Nah, I feel this too, but for me it depends on the content and pacing of the book, I think.
Books with shorter chapters (more dense thus requiring more notes) and longer problem sections are better for me on PC whereas the reverse is better for books.

Anonymous at Thu, 9 Jan 2025 17:31:15 UTC No. 16540466

>>16540458
Too early to tell. However the book itself was very interesting and fun to read. I feel like learned a lot.

Anonymous at Thu, 9 Jan 2025 20:40:47 UTC No. 16540629

Bros, a very retarded and personal question, but let's assume that you are going to do a master's degree in mathematics. Would you rather do a master's degree at a university that is recognized worldwide as the university with the best mathematics department and is in the top 3 of the Shanghai ranking but the master's degree is in an area of mathematics that you don't like or do a master's degree in something that you do like but at a university that is in position 300 in that range.

Anonymous at Thu, 9 Jan 2025 20:47:43 UTC No. 16540633

>>16540629
The latter

🗑️ Anonymous at Thu, 9 Jan 2025 20:53:48 UTC No. 16540640

>>16539726
>>16539309
If I understand correctly your question, what you want to prove is that if the function is continuous with one of the three norms then is continuous with the other two. So, assume is continuous the [ math ] d_1 [ /math ] metric the is continuous with the [ math ] d_2, d_{\infty} [ /math ]. So assume without loss of generality that [ math ] f [ /math ] is continuous with respect to the [ math ] d_1 [ /math ] norm. Then by the inequality you have that there is some constant [ math ] C >0 [ /math ] such that [ math ] d_2(f(x), f(x_0)) \leq Cd_1(f(x), f(x_0)) [ /math ]
And since [ math ] f [ /math ] is continuous then [ math ] d_2(f(x), f(x_0)) \rightarrow 0 [ /math ] as [ math ] x [ /math ] approaches [ math ] x_0 [ /math ]. And similarly with the infinite norm.

Anonymous at Thu, 9 Jan 2025 21:03:29 UTC No. 16540647

>>16539726
>>16539309
If I understand correctly your question, what you want to prove is that if the function is continuous with one of the three norms then is continuous with the other two. So, assume is continuous the [math] d_1 [/math] metric the is continuous with the [math] d_2, d_{\infty} [/math]. So assume without loss of generality that [math] f [/math] is continuous with respect to the [math] d_1 [/math] norm. Then by the inequality you have that there is some constant [math] C >0 [/math] such that [math] d_2(f(x), f(x_0)) \leq Cd_1(f(x), f(x_0)) [/math]
And since [math] f [/math] is continuous then [math] d_1(f(x), f(x_0)) \rightarrow 0 [/math] as [math] x [/math] approaches [math] x_0 [/math], implying that [math] f [/math] is continuous with respect to the [math] d_2 [/math] norm. And similarly with the infinite norm.

Anonymous at Thu, 9 Jan 2025 22:03:57 UTC No. 16540691

>>16540647
>So, assume is continuous the [math]d_1[/math] metric the is continuous with the [math]d_2,d_\infty[/math].
Anon did you have a stroke? Are you ok?

Anonymous at Fri, 10 Jan 2025 05:17:28 UTC No. 16541050

>>16538636
"mastery" of textbook material is overrated. The first time I did this it got to the point were I was cringing at the professor making basic mistakes every lecture. Then promptly forgot everything a few months after studying it for several hundred hours, cause you don't need it.
Much better is a quick skim over many books until you either have, context or real motivation.

Anonymous at Fri, 10 Jan 2025 18:02:02 UTC No. 16541600

>>16540164
Based

Anonymous at Fri, 10 Jan 2025 18:40:54 UTC No. 16541642

>>16534183
Are there ANY mathematically rigorous books on classical electromagnetism? All the books I have seen don't even properly prove Gauss' law from Columbs law since they don't cover measures and distributions (even the "for mathematicians" texts).

Anonymous at Fri, 10 Jan 2025 20:33:15 UTC No. 16541827

>>16541642
Doesn't it make more sense to do it the other way? Gauss' law > Couloumb's law? Isn't Gauss' law more general in that it applies to 3d geometry regardless of what phenomena you are describing? It's really just the divergence theorem or am I misunderstanding this?

Anonymous at Fri, 10 Jan 2025 20:50:58 UTC No. 16541841

>>16541642

Anonymous at Fri, 10 Jan 2025 23:04:08 UTC No. 16541985

Does the law of excluded middle follow from the following "set theory version" of the drinkers paradox?
For any non-empty set A and subset D of A there is an a in A such that if a is in D then D is all of A.

🗑️ Anonymous at Sat, 11 Jan 2025 01:37:16 UTC No. 16542079

>>16540647

Here’s your text translated into MathJax:

Ok, I figured out something about the question, but I need someone's help to finish it properly. By definition, [math]d_\infty(x, y) \leq d_2(x, y) \leq d_1(x, y)[/math] for all [math]x, y \in \mathbb{R}^n[/math].

Suppose then first that [math]f[/math] is continuous with respect to [math]d_1[/math]. By the basic definition of limit, for all [math]\epsilon > 0[/math], there exists a [math]\delta > 0[/math] such that

[math] d_\infty(x, y) \leq d_2(x, y) \leq d_1(x, y) < \delta \implies \rho(f(x), f(y)) < \epsilon. [/math]

So, as the above follows with [math]\delta = \epsilon[/math] for [math]d_2[/math] and [math]d_\infty[/math], we conclude that [math]f[/math] is continuous with respect to those metrics too.

By a similar reasoning, we assume that if [math]f[/math] is continuous with respect to [math]d_2[/math], then it is continuous with respect to [math]d_\infty[/math] as well.

Now the deal starts when trying to prove the same assuming [math]f[/math] is continuous with respect to [math]d_2[/math] and concluding it is also continuous with respect to [math]d_1[/math].

I would say that by the completeness axiom, there exists an [math]n[/math] such that

[math] d_1(x, y) \leq n d_2(x, y), [/math]

and hence, take something like [math]\delta = \frac{\epsilon}{n}[/math] (I don’t know how to get [math]\delta[/math] properly, but assuming it's correct I'll follow) so that [math]f[/math] is in fact continuous with respect to [math]d_1[/math] too.

The same argument I would use assuming [math]f[/math] is continuous with respect to [math]d_\infty[/math].

Is it correct, or should I rewrite it for better? Any ideas?

Anonymous at Sat, 11 Jan 2025 01:39:13 UTC No. 16542080

>>16540647
Ok, I figured out something about the question, but I need someone's help to finish it properly. By definition, [math]d_\infty(x, y) \leq d_2(x, y) \leq d_1(x, y)[/math] for all [math]x, y \in \mathbb{R}^n[/math].

Suppose then first that [math]f[/math] is continuous with respect to [math]d_1[/math]. By the basic definition of limit, for all [math]\epsilon > 0[/math], there exists a [math]\delta > 0[/math] such that

[math] d_\infty(x, y) \leq d_2(x, y) \leq d_1(x, y) < \delta \implies \rho(f(x), f(y)) < \epsilon. [/math]

So, as the above follows with [math]\delta = \epsilon[/math] for [math]d_2[/math] and [math]d_\infty[/math], we conclude that [math]f[/math] is continuous with respect to those metrics too.

By a similar reasoning, we assume that if [math]f[/math] is continuous with respect to [math]d_2[/math], then it is continuous with respect to [math]d_\infty[/math] as well.

Now the deal starts when trying to prove the same assuming [math]f[/math] is continuous with respect to [math]d_2[/math] and concluding it is also continuous with respect to [math]d_1[/math].

I would say that by the completeness axiom, there exists an [math]n[/math] such that

[math] d_1(x, y) \leq n d_2(x, y), [/math]

and hence, take something like [math]\delta = \frac{\epsilon}{n}[/math] (I don’t know how to get [math]\delta[/math] properly, but assuming it's correct I'll follow) so that [math]f[/math] is in fact continuous with respect to [math]d_1[/math] too.

The same argument I would use assuming [math]f[/math] is continuous with respect to [math]d_\infty[/math].

Is it correct, or should I rewrite it for better? Any ideas?

Anonymous at Sat, 11 Jan 2025 02:12:40 UTC No. 16542089

>>16536320
the whole “also differential manifold” thing only becomes relevant when you start considering adjoint action of the manifold on itself. The other anon correctly pointed out that the most natural way of thinking about them is as smooth actions on other manifolds.

Anonymous at Sat, 11 Jan 2025 11:05:28 UTC No. 16542364

>>16541841
This book doesn't do that either.
>>16541642
Gauss' law for a set of point-charges is trivial, I'm talking about the case of continous charge-distributions.

Anonymous at Sat, 11 Jan 2025 11:33:01 UTC No. 16542368

Some people just seem to have a state of mind where they think quickly and have a very active brain. I also have such a state sometimes but most of the time my mind is slow and doesn't want to think a lot. Do you guys know what I'm talking about? Do you have any methods to become much more productive?

Anonymous at Sat, 11 Jan 2025 11:34:02 UTC No. 16542369

>>16542368
I know about coffee and it doesn't really do it for me, it just makes me jittery. I don't want to do amphetamines. Maybe there are some psychological tricks.

Anonymous at Sat, 11 Jan 2025 12:13:03 UTC No. 16542382

>>16539497
Wow. How would you come up with that and what does it mean?

Anonymous at Sat, 11 Jan 2025 18:02:52 UTC No. 16542735

>>16542382
It is just summing x^3 from x=m to x=n.
The usual midpoint method to approximate the sum would just have integral bounds m-1/2 to n+1/2
This gets the leading two terms correct (gives exact result for summing x^0 and x^1).
Going off the real line allows you to hack two more correct terms (giving exact results for x^2 and x^3).
The basic idea is that you can get twice the accuracy for about the same work by using properties of complex functions.
Usually, to approximate the derivative of a function, you need two sample points (to do the difference quotient).
For functions satisfying f(x*) = f(x)*, you can get two evaluations for the price of one.
f '(x) ~ [f(x+iy) - f(x-iy)]/(2iy) = Im[f(x+iy)]/(iy)
Utilizing the symmetry of f allows you to do more with less.

Anonymous at Sun, 12 Jan 2025 00:57:39 UTC No. 16543149

>>16542080
Yeah the idea is fine, but I'd recommend using [math] d _1 (x,y) \le n d _\infty (x,y) [/math] instead, as it follows immediately from the definitions of the metrics.

Anonymous at Sun, 12 Jan 2025 01:20:01 UTC No. 16543178

>>16543149
Thanks a lot. Have a nice day anon

Anonymous at Sun, 12 Jan 2025 07:14:08 UTC No. 16543482

>>16540339
this sounds like philosophical logic so who care. also anime is ugly shit esp that one

Anonymous at Sun, 12 Jan 2025 07:47:18 UTC No. 16543497

Does Fermat's method of adequality work for all curves analyzed? I'm trying use historical examples of finding the tangents to curves and its quite apparent that Descartes method breaks down when we get to non-polynomial functions because it predisposes that we can get an unknown polynomial function H(x) from the polynomial function F(x) we are finding the tangent of. If your function isn't a polynomial then obviously you wont find a different polynomial to satisfy the equity unless you use a power series, which requires a derivative, which kinda defeats the purpose of the problem in the first place. However I'm having a difficult time with Fermat's method of adequality. There appears to be some functions that don't work, but I don't know if I'm being retarded and doing it wrong. Any resources on the subject would be greatly appreciated.

Anonymous at Sun, 12 Jan 2025 11:01:23 UTC No. 16543579

>All are sufficiently detailed to be solved with a minimum of effort
Guess I'm retarded then.

Anonymous at Sun, 12 Jan 2025 13:51:59 UTC No. 16543645

What's a good intro gauge theory book?

Anonymous at Sun, 12 Jan 2025 16:49:58 UTC No. 16543783

Can someone explain what the "convert" tactic in lean does

Anonymous at Sun, 12 Jan 2025 17:47:08 UTC No. 16543821

How important is the Philosophy of Mathematics for studying Mathematical Logic?

Anonymous at Sun, 12 Jan 2025 17:51:13 UTC No. 16543824

>>16543821
Not a big deal.

Anonymous at Sun, 12 Jan 2025 17:51:25 UTC No. 16543826

>>16543821
not at all

Anonymous at Sun, 12 Jan 2025 17:57:10 UTC No. 16543832

>>16534312
according to columbia:

https://web.archive.org/web/20241126212740/https://www.math.columbia.edu/programs-math/graduate-program/what-graduate-students-are-assumed-to-know/

Anonymous at Sun, 12 Jan 2025 18:19:26 UTC No. 16543859

Greetings again anons. Can someone give me an example of a function [math]f: [0, 1] \to \mathbb{R}[/math] such that [math]f[/math] is not continuous over all the interval, but the set

[math] {x \in [0, 1] : f(x) < t} [/math]

is open for all [math]t \in \mathbb{R}[/math].

Any ideas greatly appreciated

Anonymous at Sun, 12 Jan 2025 18:31:47 UTC No. 16543865

>>16543859
f(x)=1 for x=0
0 otherwise

Anonymous at Sun, 12 Jan 2025 18:37:19 UTC No. 16543869

>>16543865
How does it satisfy the condition of the open set for all t real?

Anonymous at Sun, 12 Jan 2025 18:44:01 UTC No. 16543876

>>16543869
There are three possible inverse images of (-infty, t):
[0,1], (0,1] and empty set.
All three sets are open in [0,1].

Anonymous at Sun, 12 Jan 2025 18:49:17 UTC No. 16543880

>>16543876
You're right. Thanks anon!

Anonymous at Sun, 12 Jan 2025 19:59:36 UTC No. 16543956

What are the prerequisites for reading this book?

Anonymous at Sun, 12 Jan 2025 20:07:04 UTC No. 16543969

>>16543956
On paper nothing but in practice real and functional analysis. I tried reading it before studying real and functional analysis and it was a bad experience, would not recommend at all. Nothing felt motivated and I was very confused by it. It all started making sense after I studied real and functional analysis.

Anonymous at Sun, 12 Jan 2025 20:24:03 UTC No. 16543998

>>16543969
Functional analysis? Wtf? That’s a PhD subject here…

Anonymous at Sun, 12 Jan 2025 21:18:53 UTC No. 16544043

I think I'm gonna drop math, I'm just too stupid...

Anonymous at Sun, 12 Jan 2025 21:32:41 UTC No. 16544060

>>16543998
What shithole are you from?
Normally you're expected to produce new research in a PhD not study something that was discovered in the 20s and 30s of the last century.

Anonymous at Sun, 12 Jan 2025 21:42:14 UTC No. 16544069

>>16544060
Peru. You gotta be lying, I don't believe Americans are studying functional analysis as undergrads, either that or you're an MIT or Harvard honors student idk

Anonymous at Sun, 12 Jan 2025 21:43:04 UTC No. 16544070

>>16543956
I would STRONGLY recommend analysis, alongside a sizeable amount of mathematical maturity.

Anonymous at Sun, 12 Jan 2025 21:46:13 UTC No. 16544075

>>16544070
I'm doing an analysis course alongside it, will I be fine?

Anonymous at Sun, 12 Jan 2025 22:01:29 UTC No. 16544090

>>16544069
In Germany functional analysis is a class for third year undergrads.

Anonymous at Sun, 12 Jan 2025 22:08:18 UTC No. 16544096

>>16544069
I took functional analysis as a junior (though it was a 700-level course) at my state school. I think most students could if the US education system stopped treating K-12 students like retards and challenged them

Anonymous at Sun, 12 Jan 2025 22:13:34 UTC No. 16544103

I'm confused.
The matrix [math]A =\begin{bmatrix}
\frac{1}{2} & \frac{1}{3} & \frac{1}{6} \\
0 & \frac{1}{6} & \frac{5}{6} \\
\frac{1}{2} & \frac{1}{2} & 0
\end{bmatrix}[/math] is irreducible, since [math]A^{2}[/math] is positive, right? And the sum of the entries of each line is equal to 1.
In class we supposedly proved that if a non-negative matrix is irreducible and the sum of the entries of each line is [math]\le 1[/math], then [math]\rho\left( A \right)\lt 1[/math]. However, I've put that matrix in 3 different calculators and they all said that 1 is an eigenvalue of A.
Am I missing something really obvious or is the exercise we did in class just wrong?

Anonymous at Sun, 12 Jan 2025 22:23:38 UTC No. 16544110

>>16544103
You shouldn't need a calculator to see that (1,1,1)^T is an eigenvector for the eigenvalue 1.

Anonymous at Sun, 12 Jan 2025 22:39:26 UTC No. 16544121

How much do you guys retain of a subject after studying it? Like can you solve some Sylow Theorem problem without looking up the theory?

Anonymous at Sun, 12 Jan 2025 22:43:34 UTC No. 16544123

>>16544121
>How much do you guys retain of a subject after studying it?
Not much. But restudying it is much easier than doing it for the first time. Most of the mental structures needed are already there.
>Like can you solve some Sylow Theorem problem without looking up the theory?
No, I'd need to look it up.

Anonymous at Sun, 12 Jan 2025 23:36:09 UTC No. 16544169

>>16542368
Yes, no.
It just seems to be how I wake up, I immediately notice it if I am full of energy, and then I try to do a lot of math and other interesting things that day.
If I wake up very tired, I try to do some chores for at least the first few hours, until I stop feeling so slow.

Anonymous at Mon, 13 Jan 2025 00:11:55 UTC No. 16544184

Anonymous at Mon, 13 Jan 2025 00:44:00 UTC No. 16544210

>>16544184
69.. nice

Anonymous at Mon, 13 Jan 2025 00:59:42 UTC No. 16544218

>>16534660
https://www.wolframalpha.com/input?i=%28y%5E4+%2B+2+y%5E3+%2B+y%5E2+-+x%5E4+%2B+2+x%5E3+-+x%5E2%29%2F4

Anonymous at Mon, 13 Jan 2025 01:14:59 UTC No. 16544237

>>16540156
S/s = (R/r)^2
V/v = (R/r)^3 = (S/s)^(3/2) = 3^(3/2) ~ 5.196

Anonymous at Mon, 13 Jan 2025 05:07:50 UTC No. 16544459

>>16543956
Calculus and basic set theory.

Anonymous at Mon, 13 Jan 2025 07:40:47 UTC No. 16545507

>>16544210

Anonymous at Mon, 13 Jan 2025 13:48:49 UTC No. 16545951

>>16545507

Anonymous at Mon, 13 Jan 2025 14:43:13 UTC No. 16545982

:( at Mon, 13 Jan 2025 15:02:31 UTC No. 16546003

Im undergrad students and next week I got exams for Programming, Analysis and Calculus(resit) and the week after that two resits (Linear Algebra 1 and Set Theory). I'm so fucked man. I love math but I just have such a hard time focusing.

Anonymous at Mon, 13 Jan 2025 15:44:07 UTC No. 16546040

Friendly reminder that 2025 is a perfect square (2025 = 45^2). (For whatever reason it excites normies.) Next perfect square year will be 2116 and most likely none of us will live that long.
>>16543998
Excuse me? On my university functional analysis is introduced in fifth semester.

Anonymous at Mon, 13 Jan 2025 17:31:11 UTC No. 16546186

>>16545507
>>16545951

(372 + 1)^2 - (372 - 1)^2 = 373^2 - (7×53)^2

(186 + 2)^2 - (186 - 2)^2 = (4×47)^2 - (8×23)^2

(124 + 3)^2 - (124 - 3)^2 = 127^2 - 11^4

(93 + 4)^2 - (93 - 4)^2 = 97^2 - 89^2

(62 + 6)^2 - (62 - 6)^2 = (4×17)^2 - (8×7)^2

(31 + 12)^2 - (31 - 12)^2 = 43^2 - 19^2

Anonymous at Mon, 13 Jan 2025 18:03:23 UTC No. 16546223

>>>/v/700021364
(I) can't solve this

Anonymous at Mon, 13 Jan 2025 18:18:57 UTC No. 16546240

>>16540156
>>16544237

Question:
If the volume of a sphere increases by a factor of n, then by what factor does the surface area (of the sphere) increase?

Answer:
V/v = (R/r)^3
S/s = (R/r)^2 = (V/v)^(2/3) = n^(2/3)

Example:
If the volume increases by a factor of 8, then the surface area increases by a factor of 8^(2/3) = 4.

Anonymous at Mon, 13 Jan 2025 18:59:00 UTC No. 16546285

>>16546223
Anon, your 'one' variable also increments in the event of both hits critting, so summing 'one' and 'both' in line 19 double counts

Anonymous at Mon, 13 Jan 2025 19:06:41 UTC No. 16546293

>>16546040
>2025 is a perfect square (2025 = 45^2)

45^2 - 5^2 = 2000
"The T-1000 is a fictional character in the Terminator franchise[.]"
Is there a T-2000?

Anonymous at Mon, 13 Jan 2025 19:15:01 UTC No. 16546304

>>16546240
>the surface area (of the sphere)
improvement:
its surface area

Anonymous at Mon, 13 Jan 2025 20:00:49 UTC No. 16546352

What's the deal with [math]C^*[/math]-algebras?
It's a nice definition, sure, but it seems any time you want to prove something nontrivial, you have to either use a functional calculus / spectral theorem, reducing the statement to one about continuous or measurable functions, where the statement is probably very easy, or a representation as bounded operators on a Hilbert space, where the result probably is not too difficult either.
Why deal with them in so much generality, if the proofs don't allow for it?
Even something as simple as [math]a,b[/math] are positive elements in a [math]C^*[/math]-algebra with [math]a \leq b[/math], prove that [math]\|a\| \leq \|b\|[/math] requires one of the above results (as far as I can tell).

It would seem very strange if, in finite-dimensional vector spaces, you first prove all such are isomorphic to [math]\mathbb R^n[/math] and then use this embedding and some particular properties of the real numbers in each subsequent proof.
Or, in smooth manifolds, if you first show there exists an embedding into [math]\mathbb R^{2n}[/math] and then pass this embedding around constantly while proving something basic.
These concepts seem to, instead, ``stand on their own'', while [math]C^*[/math]-algebras don't.

Anonymous at Mon, 13 Jan 2025 22:30:59 UTC No. 16546535

>>16544069
Yes

Anonymous at Mon, 13 Jan 2025 22:33:21 UTC No. 16546540

>>16543969
I would say a point set theory course, an introductory real analysis course and a formal algebra course (not talking bout linear algebra)

Anonymous at Tue, 14 Jan 2025 01:21:17 UTC No. 16546717

im tired of struggling

now if i feel like i am putting too much effort i shall skim or move on. think about math in elementary school. kids struggled with basic algebra until suddenly it became easy to them. just let the subconscious do all the work

"in mathematics you do not understand things, you get used to it"
von neumann was chuddha

Anonymous at Tue, 14 Jan 2025 02:14:41 UTC No. 16546759

I dropped out after calc 1 and have spent several years of my forklift job watching math youtube in my downtime, but I've never returned to rigorously studying or solving anything and it's been purely for entertainment. I don't know how to prove shit or even how to solve most of the harder stuff in precalculus.
I think I've just found a motivating reason to actually grind the learning out. I've discovered the following:
>Polynomials are special cases of power series
>Power series are special cases of the hypergeometric function (whatever it is)
>Which is a special case of the Meijer G-function
>Which is a special case of the Fox H-function
>Which is a special case of taking a contour integral of some F, where F is [math]\frac {G_{1}, G_{2}, \dots, G_{m}} {H_{1}, H_{2}, \dots, H_{n}} [/math] and each [math]G_{i}[/math] or [math]H_{j}[/math] is some infinite product with some indices [math]p,q[/math] of a gamma function of a linear function of [math]p,q[/math].
So what I want to know is how come this convoluted pile of stuff,
>a contour integral of a big pile of multipled together infinite products of gammas of certain linear functions of the indices of the infinite products in which the linear functions are self-referentially contained,
can be so reliable that there is some general idea of how many simple objects are special cases of it. If I do a basic calculus/maturity book chart, what direction do I go in to find out how all of these different objects fit together? Is it undergrad pde stuff or more like postgrad complex analysis?

Anonymous at Tue, 14 Jan 2025 11:41:33 UTC No. 16547029

>>16546759
I'm involved in number theory so I'm not a good source but your questions sound like they belong to harmonic analysis to me.

Anonymous at Tue, 14 Jan 2025 11:54:22 UTC No. 16547033

lowercase sage !!IaxlA1xvEP/ at Tue, 14 Jan 2025 12:11:14 UTC No. 16547039

>>16547033

Anonymous at Tue, 14 Jan 2025 13:47:34 UTC No. 16547085

>>16546186

Anonymous at Tue, 14 Jan 2025 14:03:09 UTC No. 16547100

9 - 11 = -2
and
9/11 = 81/99 = 0.818181...

https://bollyn.com/solving-9-11-the-book

Anonymous at Tue, 14 Jan 2025 14:21:22 UTC No. 16547113

Greetings.

I need to prove that if [math]f[/math] is one-to-one and analytic over an open set [math]U[/math], and if [math]f(U) = V[/math], then [math]f: U \to V[/math] is an analytic isomorphism. What I tried to do is prove it is locally invertible for an arbitrary [math]z_0 \in U[/math], and because it is one-to-one, it follows that [math]f[/math] is a global analytic isomorphism.

My problem is that I don't think it's possible using the inverse mapping theorem because I have no clue what inverse I should take. My other problem is that I don't know how to prove [math]V[/math] is open. Any ideas would be greatly appreciated.

Anonymous at Tue, 14 Jan 2025 14:23:50 UTC No. 16547116

>cross product is only defined for 3 and 7 dimensions
What the fuck is this bullshit?

Anonymous at Tue, 14 Jan 2025 14:24:53 UTC No. 16547117

>>16547039
Works every time.

Anonymous at Tue, 14 Jan 2025 14:53:05 UTC No. 16547133

>>16540339
sounds like faggots
>there is a possible world where anime haters are not communists
not what the material implication means (and not what intensional means). throw it in the bog

Anonymous at Tue, 14 Jan 2025 14:54:30 UTC No. 16547134

>>16547033
>take the middle match from 3
>use it to set the rest on fire
what now NERD

Anonymous at Tue, 14 Jan 2025 14:55:46 UTC No. 16547136

>>16547116
Lmao
https://www.jstor.org/stable/2323537

Anonymous at Tue, 14 Jan 2025 15:13:32 UTC No. 16547147

Given an nxn matrix, does the likelihood that it is non invertible decrease as n gets larger?

Anonymous at Tue, 14 Jan 2025 15:22:45 UTC No. 16547155

>>16547147
There is no uniform probability measure on R, but
the set of all non-invertible matrices in R^nxn is of measure zero. So, in any reasonable probability distribution, a random matrix is invertible with probability 1.

Anonymous at Tue, 14 Jan 2025 15:36:46 UTC No. 16547161

>>16547155
Thanks. I don't understand most of what you said but I kinda know where to look now.

Anonymous at Tue, 14 Jan 2025 16:10:34 UTC No. 16547205

>>16547116
This still blows my mind and if I was actually smart I could somehow tie this into why only 3 spatial dimensions physically exist.

Anonymous at Tue, 14 Jan 2025 16:17:14 UTC No. 16547217

>>16547113
>I don't know how to prove [math]V[/math] is open.
https://en.wikipedia.org/wiki/Open_mapping_theorem_(complex_analysis)

Anonymous at Tue, 14 Jan 2025 16:25:25 UTC No. 16547229

>>16547205
But then what about 7?

Anonymous at Tue, 14 Jan 2025 16:26:49 UTC No. 16547231

>>16547229
That'll be excluded by some other restriction.

Anonymous at Tue, 14 Jan 2025 16:27:33 UTC No. 16547232

>>16547231
Well, get on with it anon!

Anonymous at Tue, 14 Jan 2025 17:18:15 UTC No. 16547276

I LEARNED HOW TO PROPERLY DECOMPOSE THIS TRASH NOW
YESTERDAY I FLOPPED BECAUSE I WAS TOO SLOW TO UNDERSTAND THAT BINOMIALS WITH FRACTION EXPONENTS CAN BE ADDED TOGETHER
I NEED FURTHER HIGH TIER HIGH SCHOOL MATH TRICKS IN THE NEXT 6 HOURS BECAUSE MY PROFESSOR IS A MATH WING FREAK
HELP

Anonymous at Tue, 14 Jan 2025 18:56:36 UTC No. 16547379

>>16519567
>>16519568
>>16519592
turns out this shit is really easy now that i actually looked at it why did i waste a year on this?

Anonymous at Tue, 14 Jan 2025 20:40:57 UTC No. 16547538

>>16547161
The space of noninvertible matrices is defined by det(A) =0 which is a polynomial equation in the entries of the matrix. This is a hypersurface, and all hypersurfaces have measure zero in the ambient space. This means you can cover the the space of noninvertible matrices with open balls whose total sum volume is less than epsilon for any positive epsilon (similar to how you can cover the set of rationals with arbitrary small volumes: enumerate all rationals q_i, and around the rational number q_i put an interval of length e/2^i. Then the total sum of lengths of intervals is e(1+ 1/2 + 1/4 + ...) = 2e which can be made arbitrarily small by lowering e)

Anonymous at Tue, 14 Jan 2025 22:11:05 UTC No. 16547648

Anonymous at Tue, 14 Jan 2025 22:23:27 UTC No. 16547672

[math]\:\:\: ▲ؚ \\
▲ؚ\:▲ؚ[/math]

Anonymous at Tue, 14 Jan 2025 22:25:23 UTC No. 16547675

mathematicians are spiritually wordcels and don't feel as soulless as stembros do

Anonymous at Tue, 14 Jan 2025 22:44:24 UTC No. 16547698

A word salad is a "confused or unintelligible mixture of seemingly random words and phrases", most often used to [...].

Anonymous at Tue, 14 Jan 2025 22:49:21 UTC No. 16547704

Anonymous at Tue, 14 Jan 2025 23:48:53 UTC No. 16547754

>>16547648
>>16547704

(187^4 - 185^4)/(186^2 + 1^2)

(95^4 - 91^4)/(93^2 + 2^2)

(65^4 - 59^4)/(62^2 + 3^2)

(37^4 - 25^4)/(31^2 + 6^2)

((a + b)^4 - (a - b)^4)/(a^2 + b^2) = 8*a*b

Anonymous at Wed, 15 Jan 2025 00:27:15 UTC No. 16547776

>>16547276
I can give this to start you off, I guess...
https://www.youtube.com/watch?v=S70GNLBJpj0

Also, on the second line you multiplied top and bottom
by A = e^x but you kept the bottom and not the top.

Anonymous at Wed, 15 Jan 2025 01:25:27 UTC No. 16547824

haha

🗑️ Anonymous at Wed, 15 Jan 2025 05:37:01 UTC No. 16547945

what are the most eye opening areas of math

Anonymous at Wed, 15 Jan 2025 05:38:05 UTC No. 16547947

what are the most eye opening areas of math?
especially things that make you see connections that you couldnt see before

haha at Wed, 15 Jan 2025 09:15:59 UTC No. 16548051

23^2 - 21^2

Anonymous at Wed, 15 Jan 2025 10:35:51 UTC No. 16548091

>>16534533
6^3 + 7^3 + 8^3 + 9^3 = 1800

Anonymous at Wed, 15 Jan 2025 10:47:49 UTC No. 16548097

left

Anonymous at Wed, 15 Jan 2025 14:20:04 UTC No. 16548231

right?

Anonymous at Wed, 15 Jan 2025 22:52:30 UTC No. 16548749

>>16547947
>Linear algebra, Group theory, analysis, topology, diff geometry, number theory and measure theory

Anonymous at Thu, 16 Jan 2025 01:05:43 UTC No. 16548829

>>16548749
is it possible to dip your toes in more than 2/3 of them? what about category theory?

Anonymous at Thu, 16 Jan 2025 01:11:19 UTC No. 16548833

>>16548829
>dip your toes in more than 2/3 of them?
At a surface level, yeah, I mean, an average good mathematician has formally read at least two books on those topics. Cat theory is an extension of group theory to much useful and complex stuff.

meow at Thu, 16 Jan 2025 05:11:49 UTC No. 16549112

did someone say cat
theory?

Anonymous at Thu, 16 Jan 2025 16:52:09 UTC No. 16550584

>>16536797
I did find this formula after searching a bit.
https://settheory.net/cubic-equations
He starts by letting p be a difference of cubes.
My derivation started with the substitution (Ax+B)/(x+1)
The benefit of this substitution over the usual Tschirnhaus transformations is that it is invertable while still providing 2 parameters (which would usually require a quadratic substitution).
I also like that the solution makes no reference to coefficients of p and is probably easier to remember.

I'm still trying to do the quartic.
Idk what form of substitution or form of quartic I should be aiming for.
I need a miracle extra cancellation similar to 3pp'' - 2p'p' for cubics (it seems like it is 4th degree, consts were chosen to cancel leading terms to make it 3rd, but is really 2nd degree).

Anonymous at Thu, 16 Jan 2025 17:37:21 UTC No. 16550654

>>16548833
what about abstract algebra
it tickles my autism

Anonymous at Fri, 17 Jan 2025 02:03:58 UTC No. 16552952

>>16550654
I mean, as far as I'm concerned, the first steps in abstract algebra are implied in group theory, then ring theory, then field theory, but all of that has the background built in general group theory.

Anonymous at Fri, 17 Jan 2025 06:21:30 UTC No. 16553284

What did I mean by this?

Anonymous at Fri, 17 Jan 2025 07:52:53 UTC No. 16553379

>>16553284
cramer rule applied to Ix=x

Anonymous at Fri, 17 Jan 2025 12:52:35 UTC No. 16553624

Does Lang really expect me to do all this shit by hand?
What's the point of such busywork exercises?

Anonymous at Fri, 17 Jan 2025 18:21:18 UTC No. 16554054

>>16553624
Only a retard would write the full table.
Your are supposed to find it tedious then try to use your brain to find a shortcut.

(x^a)*(y^b)*(x^c)*(y^d) = (x^i)*(y^j)
i = a + c*(-1)^b mod 6
j = b+d mod 2

Anonymous at Fri, 17 Jan 2025 23:46:10 UTC No. 16554512

Greetings anons!

Is there any formula to find how many abelian groups of order n exist up to isomorphism?

Anonymous at Sat, 18 Jan 2025 00:02:23 UTC No. 16554536

>>16554512
Have you tried checking OEIS? https://oeis.org/A000688

Anonymous at Sat, 18 Jan 2025 00:06:17 UTC No. 16554542

>>16554512
Only in terms of the partition function which itself has no known closed-formula.

Anonymous at Sat, 18 Jan 2025 00:08:09 UTC No. 16554544

>>16554536
>https://oeis.org/A000688
Certainly not, but Im gonna check it and reply if something appears interesting. Thanks!

Anonymous at Sat, 18 Jan 2025 00:09:23 UTC No. 16554545

>>16554542
How is it in terms of the partition function?

Anonymous at Sat, 18 Jan 2025 00:34:43 UTC No. 16554566

>>16554545
If the exponents of the prime decomposition of [math]n[/math] are [math]a_1, \ldots, a_k[/math] then the number of abelian groups of order [math]n[/math] is
[eqn]p(a_1) \times p(a_2) \times \ldots \times p(a_k)[/eqn]

Anonymous !!a7lkkGc84ku at Sat, 18 Jan 2025 00:59:44 UTC No. 16554588

Unfortunantly i cannot mark images spoilers warning this is a post for those involved with making the new temple, if any. Coming from someone with no expertise, deadends involving a right triangles length approximation derived from two divided protonic elementals : x^y spin states/x^y dimension or spin idk no doubt involved with this image
Find it helpful? You can find other randommm very lucky by chance equations using 4plebs.com that I completely just blindly went into without knowing anything ill post those to give you an idea of my headspace.
[spoiler]25^2.5/47^2=hypo .618...= Base point is it starts with 1.2725...
4plebs my trip for some more random triangle calcs if you feel you must... >>39656529 (You)
How many digits for a 22^x/___/___/___/.../209^2 to get the most closely converging result or was website buggy...[spoiler]

Anonymous !!a7lkkGc84ku at Sat, 18 Jan 2025 01:05:24 UTC No. 16554596

>>16554588
[spoiler]test[spoiler]
you can find equations copy pasted on there not just images forgive my poor formatting when formatted/equated properly [spoiler]the results are profound using 197^8^8[spoiler]

Anonymous !!a7lkkGc84ku at Sat, 18 Jan 2025 01:43:57 UTC No. 16554632

whoops here we go, a few by chance equations that may be of assistance involving a certain cosmological equations relating to [spoiler]1.68...[/spoiler] from tonyb.freeyellow.com and ending and/or starting backward also may include idk i'm a complete noob that reminds me one i dont remember that you may want to ask your local devil as i lost it idk do your own thoughts is the (not much of a spoiler but includes repeating digit a few digits in and likely with incorrect formatting that reminds me the difference between mathisfun.com and keisan.casios.com calculators for me is that [spoiler]mathisfun's often glitches but gives twice the amount for correctly formatted mega set keisans does while the latter was responsible for the converging set and the "profound" sets i havent made sure for all of the megasets however)[/spoiler] will also be evidenced in the next photo heres the devil question [spoiler]"golden 666 equation"[/spoiler] another equation getting [spoiler]phi approx and pi approx[/spoiler] are in spoiler both technically [spoiler]brute force haks iirc these were with correct formatting[/spoiler] so beware and involved for [spoiler]self iterating matching numbers that are random on last two digits for phi[/spoiler] [spoiler]setting it to divisive powers then cancelling at 56 or, less likely, starting[/spoiler] < this is the one for that certain cosmological "constant"

[spoiler]using addition at end for neptuniums isotope sum iirc[/spoiler] and for [spoiler]phi[/spoiler] [spoiler]this ones harder to guess[/spoiler] and what some might presume a [spoiler]hack editing either/just 22 and 47's powers decimals starting either/or with one or two of their respective digits iirc dk if with decimal or whole form or multiplication or division[/spoiler] i doubt these will be needed for anything either than curiosity given humanities natural ability to spot patterns unless digital calculations do indeed seek timed convergence in a digital temple of sorts

Anonymous !!a7lkkGc84ku at Sat, 18 Jan 2025 01:51:49 UTC No. 16554635

WARNING the above posts spoilers didnt work and heres what mathisfun's was likely hacked on next post will be based on going up to dimension ^7 getting a certain convergence as first result that worked twice using ^7 I KNOW you guys might want to gift me genius but im sure i was manipulated given the fact i edited digit count then scrolled down on a certain one to find a very very strange [spoiler]pi matching[/spoiler] match that can be found on my 4plebs trip on /x/

Anonymous !!a7lkkGc84ku at Sat, 18 Jan 2025 02:00:59 UTC No. 16554645

i shouldve mentioned this ones formatting takes a divergence from my usual ones but here it goes i should mention that NO ARCHIVE UP RIGHT NOW HAS /SCI/ ON ITS ARCHIVES and next posts photo is a "[spoiler]decimal based power to x[/spoiler]' system that is incorrectly formatted but still has an interesting convergence to a correct mega set that was on keisan its been down since Sep 20, 2023

Anonymous at Sat, 18 Jan 2025 02:01:00 UTC No. 16554646

Nigger what the fuck are you doing?

Anonymous !!a7lkkGc84ku at Sat, 18 Jan 2025 02:05:38 UTC No. 16554650

this one only has [spoiler]64 56 48 26 22[/spoiler] in view as last digits using the [spoiler]decimal powers system going to dimension 13[/spoiler] system

Anonymous !!a7lkkGc84ku at Sat, 18 Jan 2025 02:13:06 UTC No. 16554657

>>16554646
tbqf i took four of my mom's amph/dexamph pills because i thought she had two bottles saved up but maybe one is for my step-dad, le sigh. plus had to drink some piss. although these and all my drawings have been made while almost completly sober

height 3.2304... area .6169... from real big inputs anyone? base angle 86.6166

Anonymous !!a7lkkGc84ku at Sat, 18 Jan 2025 02:27:16 UTC No. 16554667

WARNING below/above posts aren't showing as spoiled for me so avoid unless if you NEED help involving making something crazy involving divisors or can't make varied and likely novel but online calculator isn't to be trusted just ask around about a lost "crazy equation that got 666 in first few digits" if you're feeling sure about (likely) improperly formatted divison

Anonymous at Sat, 18 Jan 2025 20:00:55 UTC No. 16555466

The chad metamath vs the virgin Lean

Anonymous at Sat, 18 Jan 2025 20:46:22 UTC No. 16555518

>>16554667
>got 666

Anonymous at Sat, 18 Jan 2025 21:39:20 UTC No. 16555607

>>16538030
> Firedberg, Insel, and Spence
> 250,67€
Jesus christ somebody needs to take the CEO and executives of pearson publishing and beat them with a hammer.

Anonymous at Sat, 18 Jan 2025 21:40:08 UTC No. 16555609

>Insel

Anonymous !!a7lkkGc84ku at Sat, 18 Jan 2025 23:47:48 UTC No. 16555749

>>16555518
that reminds me of some website pages filled with the most abominable irrational number approximations

Anonymous at Sat, 18 Jan 2025 23:55:03 UTC No. 16555759

that's not true

Anonymous at Sun, 19 Jan 2025 00:10:31 UTC No. 16555775

>>16555518

Anonymous at Sun, 19 Jan 2025 13:30:30 UTC No. 16556141

https://www.youtube.com/watch?v=OmJ-4B-mS-Y

>The map of literature:
>books on shapes and colors
>books on spelling
>books without the letter E
>books on the hirstory of Africans, but only those who moved to India
>books on engineering (all fields)
>this is all of literature, thanks for watching!

Anonymous at Sun, 19 Jan 2025 17:57:11 UTC No. 16556301

Anyone interested in the intersection of category theory and information theory? I guess the goal would be to develop an information theory that works on some general class of categories (e.g. symmetric monoidal). I think it would be an interesting avenue of research, and it could help us shed new light on some computer science problems.

Anonymous at Sun, 19 Jan 2025 18:16:46 UTC No. 16556319

>>16556301
I'm interested, but I only know category theory at the undergrad level and information theory from papers.

Anonymous at Sun, 19 Jan 2025 18:18:52 UTC No. 16556323

>>16556319
Take a look at "Markov Categories and Entropy" by Perrone

Anonymous at Sun, 19 Jan 2025 20:00:10 UTC No. 16556415

>>16556323
Ok

Anonymous at Sun, 19 Jan 2025 22:12:23 UTC No. 16556610

Greetings anons!

Anyone know tips, tricks, hacks, tables of formulas or anything you have to get better at differential equations?

Thanks is advance!

Anonymous at Sun, 19 Jan 2025 23:25:43 UTC No. 16556655

>>16547947
Set theory, in my experience.

Anonymous at Sun, 19 Jan 2025 23:41:21 UTC No. 16556670

>>16537567
>>16537577
Not that impossible. You can make an educated guess. Personally, my field of study has very little to do with any of them. But I have plenty of friends in areas that are adjacently or just completely relevant to each problem.
From my understand, a Riemann Hypothesis resolution is still unimaginable. Researchers working on Navier-Stokes, P vs NP, Yang-Mills existence the most optimistic.
I have one friend whose life goal is to solve the Swinnerton-Dyer conjecture. From what he says, I gather that he's more optimistic than complex analysts are about the RH but less than PDE analysts, computer scientists and field theorists are about their respective Millennium Prize problems.

Anonymous at Mon, 20 Jan 2025 01:35:07 UTC No. 16556780

fuck it's looking grim

Grim Reaper at Mon, 20 Jan 2025 18:15:11 UTC No. 16557682

Did someone say grim?

Anonymous at Mon, 20 Jan 2025 20:21:32 UTC No. 16557856

>>16534463
Come on anon we even have a meme about that

Anonymous at Tue, 21 Jan 2025 01:08:12 UTC No. 16558164

>>16534463
I have a master's and work at an Amazon warehouse. Can't fool you, I really like the job, but it pays really badly. One of my coworkers has an incomplete PhD in oceanography as well, and even she teases me about my math degree being worth nothing.
But many failed mathematicians find better jobs than warehouse wageslave.

Anonymous at Tue, 21 Jan 2025 08:05:55 UTC No. 16558479

>>16558164
>I really like the job
Why?

Anonymous at Tue, 21 Jan 2025 11:42:44 UTC No. 16558618

>>16558479
It's relaxing, you can listen to music while you do it, the health insurance is good and the task itself tickles the tism.

Anonymous at Wed, 22 Jan 2025 02:55:30 UTC No. 16559362

Why does my statistics teacher keep using race and crime as examples in his questions

Anonymous at Wed, 22 Jan 2025 03:21:21 UTC No. 16559383

how do i into math if im a 7th grade dropout who hasnt done anything higher than algebra 1?

help a tard out, shill me a book or something.

Anonymous at Wed, 22 Jan 2025 05:11:31 UTC No. 16559506

>>16559383
Go watch khan academy

Anonymous at Wed, 22 Jan 2025 05:13:38 UTC No. 16559514

>>16559506
aghh alright

Anonymous at Wed, 22 Jan 2025 10:17:47 UTC No. 16559733

>>16559362
It's a good way to make people only look at the numbers and to put aside any personal or political bias (gl with that).

Anonymous at Wed, 22 Jan 2025 14:42:25 UTC No. 16559969

>>16556610
Yes

Anonymous at Wed, 22 Jan 2025 18:16:02 UTC No. 16560173

>>16555775

Anonymous at Wed, 22 Jan 2025 19:38:23 UTC No. 16560290

how the fuck do you do this? I know is that n + 1 has to be prime but cant figure out how to use that. binomial theorem doesn't help. I thought Wilson's theorem might help but it doesn't.

Anonymous at Wed, 22 Jan 2025 19:39:51 UTC No. 16560293

>>16560290
oh yeah and I checked up to 30! and 99% sure (1, 1) (2, 1) and (4, 2) are the only solutions

Anonymous at Wed, 22 Jan 2025 20:56:02 UTC No. 16560393

Can computers do computations and answer queries about infinite sets like ℕ

Anonymous at Wed, 22 Jan 2025 21:09:31 UTC No. 16560404

Just published my first paper in my PhD. I've been so incredibly burnt out, I have done 0 work the past 3 months. How do I overcome this?

Anonymous at Wed, 22 Jan 2025 21:49:12 UTC No. 16560440

>>16560393
Yes.

Anonymous at Wed, 22 Jan 2025 22:10:19 UTC No. 16560456

>>16560440
But how? Don't computers have a finite amount of memory and computation power. How can it reason about, analyze and compute on ℕ when it can't conceptualize of ℕ due to it's hardware structure.

Anonymous at Wed, 22 Jan 2025 22:19:20 UTC No. 16560459

>>16560456
>Can computers do computations and answer queries about infinite sets like ℕ
>Don't computers have a finite amount of memory and computation power
Can humans do computations and answer queries about infinite sets like ℕ

Learn to ask better questions.

Anonymous at Wed, 22 Jan 2025 22:21:15 UTC No. 16560460

>>16560459
i mean i don't know how humans do it, i don't claim to understand how the human brain works. But I think I understand how computers work, so it confuses me.

Anonymous at Wed, 22 Jan 2025 22:53:26 UTC No. 16560491

>>16560460
>i don't claim to understand how the human brain works
All of the math and comp sci theory is written down. Finite number of symbols.
>But I think I understand how computers work
maybe at a superficial level

Let f(x) = x+1
finite number of symbols
==
{ (x, f(x)) } = {(1,2),(2,3),....}
infinite number of pairs

I assume there's an answer somewhere in the example.
Your questions still make it unclear what you are confused about. Just be more specific in the future so I don't need to play 20 questions just to get to the real question.

>ℕ
What is ℕ?
>Set
What is Set
...
Set theory
Wikipedia
Construct natural numbers

Lazy ℕigger

Anonymous at Wed, 22 Jan 2025 23:01:06 UTC No. 16560506

>>16560491
ok but let's say you want that computer to generate new proofs about ℕ, find out new math for us etc. It can't do that very well because it can't conceptualize ℕ. It can learn certain logical rules about ℕ and it can relate them to other logical rules. but it doesn't have real mathematical intuition that humans do, it can't conceptualize ℕ

Anonymous at Wed, 22 Jan 2025 23:23:35 UTC No. 16560542

>>16560506
Step 1) Fuck Off
Step 2) Figure out how you do it in your brain
Step 3) Figure out how to tell a computer to do it

Define generate
Define new
Define very well
Define conceptualize
Define learn
Define relate
Define real mathematical intuition

You don't know how to prove anything or verify proofs so even if I did give you an answer that was satisfactory, you would not be able to verify it.

Anonymous at Wed, 22 Jan 2025 23:25:08 UTC No. 16560544

>>16560542
i'm just stating something i believe is true, you can agree with it or disagree with it, the hostility isn't necessary

Anonymous at Wed, 22 Jan 2025 23:41:06 UTC No. 16560567

>>16560506
there is nothing special about infinite sets, computers can't "conceptualize" anything. computers dont "learn logical rules" they have algorithms programmed into them. computers don't "relate them to other logical rules" they convert one set of numbers into another using predetermined algorithms.

Anonymous at Wed, 22 Jan 2025 23:47:30 UTC No. 16560574

>>16560567
if the computer tells me the result of a calculation on a finite set, i believe it, because i know computers can compute things over finite sets. I wouldn't trust a computer to tell me anything new about an infinite set without a rigorous proof, because I don't believe computers can reason about infinite sets due to the limitations of their hardware.

Anonymous at Wed, 22 Jan 2025 23:52:20 UTC No. 16560578

>>16560290
>>16560293
[math](n+1)^k - 1 = n ( 1 + ( n + 1 ) + ... + ( n + 1 ) ^ { k - 1 } ) = n ( \sum _{j=0} ^ {k-1} ( n + 1 ) ^ j)[/math]
So you can factor [math]n[/math] out of both sides of the original equation to get [math](n-1)! = ( \sum _{j=0} ^ {k-1} (n + 1) ^ j)[/math]

Since [math]n+1[/math] is forced to be prime by Wilson's theorem, [math]n[/math] must be composite (unless it is 1 or 2). There is a corollary to Wilson's theorem which says that if n is composite (unless it is 4), [math](n-1)! \mod n \equiv 0[/math]
So working mod [math]n[/math], with the exceptions of the cases you've already found, [math]( \sum _{j=0} ^ {k-1} (n + 1) ^ j)[/math] must be congruent to 0, but each term in the sum must obviously be congruent to 1 - since we have [math]k[/math] terms it follows that [math]k[/math] is congruent to 0 mod [math]n[/math]. This signifies that [math]k \geq n[/math]

Then [math](n+1)^k-1 \geq (n+1)^n-1 > n^n > n![/math], so there are no solutions besides the aforementioned exceptions

Anonymous at Wed, 22 Jan 2025 23:53:59 UTC No. 16560581

>>16560574
if you can make alphageometry make geometrical proofs there is no reason you couldn't theoretically make one for set theory. an infinite set is just a set without the property that every proper subset of it has the a different cardinality of it. there is nothing special about this property that allows AI to do geometrical proofs but not proofs about infinite sets.

Anonymous at Thu, 23 Jan 2025 00:00:38 UTC No. 16560587

>>16560581
so you think because the AI is great at pattern recognition it has some conceptualization of what an infinite set is, even if it can't actually store it in memory.

Anonymous at Thu, 23 Jan 2025 00:11:40 UTC No. 16560601

reply here if you are starting to agree with the harshness
No more spoonfeeding
Sink or swim

Anonymous at Thu, 23 Jan 2025 00:19:03 UTC No. 16560607

>>16560601
it's too everyone's benefit that we discuss what AI is and isn't capable, not a competition to be smug about your mathematics proficiency

Anonymous at Thu, 23 Jan 2025 00:22:40 UTC No. 16560613

>>16560578
thanks
>There is a corollary to Wilson's theorem which says that if n is composite (unless it is 4), (n−1)!modn≡0
guess I should try to prove this now

Anonymous at Thu, 23 Jan 2025 00:24:36 UTC No. 16560617

>>16560613
>guess I should try to prove this now
wait, that's actually trivial since all the prime factors of n are less than n. damn

Anonymous at Thu, 23 Jan 2025 00:24:55 UTC No. 16560618

>>16560607
>what AI is and isn't capable
How about you look into what was done before AI?
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
https://www.youtube.com/watch?v=QQbBzOvPBpc

Anonymous at Thu, 23 Jan 2025 00:57:10 UTC No. 16560649

>>16560618
computer programs are more than a proof because they can interact with the real world. you are math-brained though so you don't know about that

Anonymous at Thu, 23 Jan 2025 01:37:11 UTC No. 16560695

Go argue with Curry and Howard.
I trust them over you.

You are asking questions like a retard in bad faith.
>Proof
You are initially concerned with how computers represent natural numbers and statements/truths/theorems about them.
You then narrow the scope from "computers" to "AI".
When provided with a way to represent such proofs, you pretend to find fault with the answer by expanding the scope of your concern to programs that don't represent proofs (which excludes what you were initially interested in).

There is harm. I'm not sure if it from malice or ignorance but the impact is the same.
Thank you for making this board shittier.

Anonymous at Thu, 23 Jan 2025 01:39:44 UTC No. 16560696

>>16560695
Ok but you started it with the shit talking

Anonymous at Thu, 23 Jan 2025 01:41:05 UTC No. 16560698

>>16560649
see
>>16560542
>even if I did give you an answer that was satisfactory, you would not be able to verify it.

Anonymous at Thu, 23 Jan 2025 01:44:49 UTC No. 16560700

anyway i see now, Natural numbers can be reasoned about by a computer because computer programs themselves are proofs, putting the elements of the set into memory isn't the only way to accurately represent what an infinite set is.

Anonymous at Thu, 23 Jan 2025 01:45:56 UTC No. 16560701

>>16560696
Because I know you have not done even the bare minimum to find the answers yourself.
Hence
>Lazy ℕigger

My insults have diagnoses and prescriptions in them.

Anonymous at Thu, 23 Jan 2025 01:47:37 UTC No. 16560703

>>16560701
>i'm gonna be toxic, and then i'm going to complain when someone else is toxic, rules for thee, not for me

Anonymous at Thu, 23 Jan 2025 01:55:25 UTC No. 16560711

I was toxic and provided answers
Questions are a dime a dozen. Answers take time.
Recognize the asymmetry and be respectful by formulating coherent questions.

Anonymous at Thu, 23 Jan 2025 02:44:55 UTC No. 16560755

How are math teachers so patient with stupid fucks?

Anonymous at Thu, 23 Jan 2025 02:47:09 UTC No. 16560758

>>16560755
Because they spent a lot of time being stupid fucks before gradually becoming less stupid over time? I look back at my dumb ass ideas and understanding during undergrad now, and I'm sure in 20 years I'll think I am stupid at the moment.

Anonymous at Thu, 23 Jan 2025 02:59:40 UTC No. 16560770

>>16560758
Why does /sci/ bully me then?

Anonymous at Thu, 23 Jan 2025 04:58:10 UTC No. 16560891

>>16560587
If you think that to reason about the natural numbers with a computer, you need to have all the natural numbers listed in the computer's memory, you are fundamentally confused about how humans do this reasoning about the first place. No human has every natural number "written" in their memory.

Anonymous at Thu, 23 Jan 2025 05:16:23 UTC No. 16560924

>>16560290
(n, k)
(1, 1)
(2, 1)
(4, 2)
https://www.wolframalpha.com/input?i=n%21+%3D%3D+%28n+%2B+1%29%5Ek+-+1

Anonymous at Thu, 23 Jan 2025 05:35:08 UTC No. 16560956

got
damn

Anonymous at Thu, 23 Jan 2025 09:29:36 UTC No. 16561095

>>16560173

anymo'e jquations?

Anonymous at Thu, 23 Jan 2025 12:19:08 UTC No. 16561230

Why the FUCK are we still using first order logic?

Anonymous at Thu, 23 Jan 2025 12:23:15 UTC No. 16561234

>>16561230
What do you prefer us to use?

Anonymous at Thu, 23 Jan 2025 12:35:33 UTC No. 16561242

>[math]\mathcal B \subset 2^X[/math] is a basis in a topological space [math]X[/math] iff it satisfies the following two conditions
>(1) [math]\bigcup\mathcal{B} = X[/math]
>(2) [math]\forall B_1,B_2\in \mathcal{B}: p\in B_1\cap B_2 \implies \exists B_3\in\mathcal{B}:p\in B_3\subset B_1\cap B_2[/math]
Is the above definition equivalent to pic related? How so?

Anonymous at Thu, 23 Jan 2025 14:22:46 UTC No. 16561311

>>16561234
SOL

Anonymous at Thu, 23 Jan 2025 14:37:20 UTC No. 16561328

>>16561311
>SOL
second order logic?
what dhat?

monkey at Thu, 23 Jan 2025 14:43:06 UTC No. 16561336

>>16561242
>Is the above definition equivalent to pic related? How so?
i'm still scratching my head

Anonymous at Thu, 23 Jan 2025 15:22:11 UTC No. 16561362

>>16561234
independence-friendly first-order logic

Anonymous at Thu, 23 Jan 2025 23:54:18 UTC No. 16561870

>>16561242
>>16561336
Yes, they're equivalent.
Your second condition is equivalent to [math]B_1\cap B_2\subseteq\bigcup(\mathcal{B}\cap 2^{B_1\cap B_2})[/math]. The right-to-left inclusion is simply true, so by taking [math]\mathcal{A}=\mathcal{B}\cap 2^{B_1\cap B_2}[/math] you get that your second condition implies the second condition in the image.
The converse is a rather straightforward element chase: If [math]p\in B_1\cap B_2[/math] then [math]p\in\bigcup\mathcal{A}[/math] (by the left-to-right inclusion of the second condition in the image), so there is some [math]A\in\mathcal{A}[/math] such that [math]p\in A[/math]. Since [math]\mathcal{A}\subseteq\mathcal{B}[/math] we have that [math]A\in\mathcal{B}[/math]. We're done if we can show that [math]A\subseteq B_1\cap B_2[/math]. But this follows from the right-to-left inclusion of the second condition in the image, for of [math]a\in A[/math] then [math]a\in\bigcup\mathcal{A}[/math] (since [math]a\in A\in\mathcal{A}[/math]), so [math]a\in B_1\cap B_2[/math] and we're done.

Anonymous at Thu, 23 Jan 2025 23:59:38 UTC No. 16561873

>>16560755
can you stop being mean, i don't bully you for not having sex

Anonymous at Fri, 24 Jan 2025 03:39:17 UTC No. 16562042

How do I fraud my way through a math PhD?
I failed the calculus portion of the exam because I refused to do calculus without a computer, I'm not a fucking slave I wouldn't even entertain that shit.
I'm just not into the whole "working my ass off" thing

Anonymous at Fri, 24 Jan 2025 04:27:20 UTC No. 16562067

>>16562042
Expect to fail then.

Anonymous at Fri, 24 Jan 2025 06:05:55 UTC No. 16562133

>>16534183
High school should start with Axiomatic logic. Truthfully that should be taught in middle school with Number theory.
Projective Geometry also needs to be added to freshmen year.

Anonymous at Fri, 24 Jan 2025 06:08:30 UTC No. 16562134

>>16560695
>>16560711
You can't even properly respond to postings on this website.

Anonymous at Fri, 24 Jan 2025 06:10:48 UTC No. 16562135

>>16536165
Some schools have better CS departments than others.

Anonymous at Fri, 24 Jan 2025 06:12:35 UTC No. 16562136

>>16538199
They're shitty programmers.

Anonymous at Fri, 24 Jan 2025 07:42:32 UTC No. 16562192

For the fuck's sake, the next student that mispronounces Poisson as 'poison' repeats whole year.

Anonymous at Fri, 24 Jan 2025 09:10:11 UTC No. 16562234

>>16561870
I get it now. Thanks a lot anon!

Anonymous at Fri, 24 Jan 2025 10:38:47 UTC No. 16562269

What are the downsides of studying topological manifolds alongside smooth manifolds? Is it that much of a bad idea?

Anonymous at Fri, 24 Jan 2025 12:13:58 UTC No. 16562311

Is anyone else increasingly dumbfounded when they stop to think that having a PhD is synonymous with achievement for the average normie? I feel like most math PhDs are so unbelievably dumb.
>>16562042
Go into the field of algebra and have your PhD thesis be a worthless classification of an ultra-specific type of group.
>>16562269
Not a bad idea at all, as long as you're competent.

Anonymous at Fri, 24 Jan 2025 13:06:12 UTC No. 16562330

>>16561095

Anonymous at Fri, 24 Jan 2025 16:51:31 UTC No. 16562511

Neu >>16562509

Anonymous at Fri, 24 Jan 2025 22:46:14 UTC No. 16562933

>>16534471
I've taught middle school science and tutored middle school math. teaching is absolutely awful if you're in the US, I can't recommend it to anyone. you're not actually teaching the material, you're spending all your time on "classroom management" aka getting kids to stop being little assholes. tutoring is better, but the pay is even worse than teaching

Anonymous at Sat, 25 Jan 2025 01:00:48 UTC No. 16563055

>>16562511
The image of the third post in that thread is a PDF file.
I'm not tapping that image!
I bet, that it contains malware!
In conclusion, "nice try", but I'm not taking the bait!

Anonymous at Sat, 25 Jan 2025 08:55:04 UTC No. 16563331

No.16555580

Anonymous at Sat, 25 Jan 2025 16:30:59 UTC No. 16563650

>>16559969
Can you share some of them please?