Anonymous at Tue, 18 Jun 2024 03:52:07 UTC No. 16240517

Anonymous at Tue, 18 Jun 2024 04:08:39 UTC No. 16240527

first for number theory

Anonymous at Tue, 18 Jun 2024 04:24:35 UTC No. 16240545

>cardinal arithmetic
>ordinal arithmetic
>transfinite induction and recursion
>NBG set theory
>type theory
>surreal numbers

Are these concepts useful/do these concepts commonly arise in the context of (other) modern mathematics research (say, on algebraic topology or ergodic theory)? Or is it all just metamathematical ramble/computational nerd shit

Anonymous at Tue, 18 Jun 2024 05:40:08 UTC No. 16240588

I'm gonna graduate at 30 am I cooked

Anonymous at Tue, 18 Jun 2024 05:40:22 UTC No. 16240589

>>16240545
>is it all just metamathematical ramble/computational nerd shit
yes

Anonymous at Tue, 18 Jun 2024 05:48:00 UTC No. 16240593

>>16240545
Cardinals and ordinals sometimes appear as examples or counterexamples in topology. Type theory had its revival by being combined with topology to homotopy type theory ten years ago.

Anonymous at Tue, 18 Jun 2024 15:34:29 UTC No. 16241140

>>16240588
i got my first job at 31 lol

Anonymous at Tue, 18 Jun 2024 16:35:28 UTC No. 16241233

I'm trying to understand why we get the signs in the boundary homomorhpishm in simplicial homology:
[math]
\partial([v_0, ..., v_n]) = \sum_k (-1)^k [v_0, ..., \hat{v_k}, ..., v_n]
[/math]
hatcher says that these signs count the induced orientation on the kth face of the standard n simplex and that this is just obvious.
why is it obvious that the face we get when we remove the kth vertex inherits the orientation corresponding to [math](-1)^k[/math]?

What is rigourously even meant by orientation here?
I've been trying to make it more precise by thinking of a simplice as a convex subset of a certain affine subspace of [math]R^m[/math],
which through the ordering of the vertices get an ordering of the vectors spanning it but this approach turned messy.
I also had the faint hope that the boundary homomorphism would be uniquely defined by the property that
[math]\partial_n \circ \partial_{n-1} = 0[/math] and [math]\partial_1([v_0, v_1]) = [v_1] - [v_0][/math]
as I understand why we want these properties when we're trying to algebraically count holes of various dimensions (the motivation behind homology?).
but this fails to uniquely define a homomorphism...

Anonymous at Tue, 18 Jun 2024 16:41:43 UTC No. 16241238

>>16240545
surreal numbers are useful in combinatorial game theory, which is probably one of the furthest fields from metamathematical ramble. the other stuff shows up on occasion but only at a low level. last week i was doing some homological algebra and needed some ordinal arithmetic to construct one of the counterexamples. in general if you don't enjoy them don't bother learning though.

Anonymous at Tue, 18 Jun 2024 17:09:39 UTC No. 16241271

>>16240472
What actually compelled Kepler to believe this was the case? He was a smart guy but this was pretty batshit

Anonymous at Tue, 18 Jun 2024 17:28:42 UTC No. 16241294

>>16241271
i thought this was like the ancient greeks, not kepler. the ancient greeks had some great ideas but a lot of it is batshit insane. idk how they came up with it i think they just had no clue so they made shit up.

Anonymous at Tue, 18 Jun 2024 17:31:29 UTC No. 16241297

>>16241294
Part of the reason that it took so long to move away from the idea of epicycles was because it was inconceivable that heavenly bodies could move in anything other than a perfect circle.
These ideas lasted until very recently, all things considered

Anonymous at Tue, 18 Jun 2024 17:39:20 UTC No. 16241305

>>16241297
yeah i mean it took thousands of years until people thought "maybe aristotle was full of shit and just made all this up" so i wouldn't doubt it

Anonymous at Tue, 18 Jun 2024 18:37:53 UTC No. 16241363

Can i get some measure theory books recommendations. Not just the wich but the why.

Anonymous at Tue, 18 Jun 2024 18:49:44 UTC No. 16241381

>>16241363
measure theory is pseudoscience

Anonymous at Tue, 18 Jun 2024 19:00:02 UTC No. 16241399

>>16241297
>>16241305
It had much more to do with the invention of telescopes that enabled more precise measurements to be made.

Anonymous at Tue, 18 Jun 2024 19:06:19 UTC No. 16241410

>>16241271
>What actually compelled Kepler to believe this was the case? He was a smart guy but this was pretty batshit
Not at all, actually. There were only 6 known planets at the time, so it made sense to correlate them with the platonic solids. His model also closely adhered to the known planetary distance measurements. Finally, it wasn't understood that objects could follow orbits by only a central force; it was assumed that there must be an attractive force and an opposing force (just how there is for electron orbits, hint hint) and the natural shape that two opposing forces creates is a platonic solid. Kepler was a smart dude.

Anonymous at Tue, 18 Jun 2024 19:08:45 UTC No. 16241414

>>16241363
folland is great. it also just so happens to be what my school uses

🗑️ Anonymous at Tue, 18 Jun 2024 19:11:58 UTC No. 16241421

>>16241410
>6 planets
>6 platonic solids
>woah… these le numbers are, like, the same number??? Bruv I have a le theory!!!

Anonymous at Tue, 18 Jun 2024 19:17:04 UTC No. 16241427

>>16241421
There's only five, but no worries... not everyone can be Kepler caliber.

Anonymous at Tue, 18 Jun 2024 19:19:37 UTC No. 16241430

>>16241421
this is literally what the ancient greeks did. plato mocks it (or maybe he's just that stupid) in the republic [587b - 588a].
>>16241427
kek

Anonymous at Tue, 18 Jun 2024 19:21:52 UTC No. 16241433

>>16241410
>6 planets
>5 platonic solids
>woah… these le numbers are, like, kinda similar??? I have a theory!!!!

Anonymous at Tue, 18 Jun 2024 19:24:30 UTC No. 16241437

>>16241433
If we weren't on this Mongolian grasshopper board I'd think you must be a woman

Anonymous at Tue, 18 Jun 2024 20:34:51 UTC No. 16241547

>>16240472
How old were you when you realized that the Microsoft Equation Editor is good enough for 99% of the times you would othewise tinkertranny with a hodge podge of various LaTeX modes?

Not only does Word let you enter Latex syntax, you can use the faster Unicode form.

Anonymous at Tue, 18 Jun 2024 22:23:20 UTC No. 16241709

>>16240545
>useful
if you come into maths with that outlook for existence then you have the wrong disposition

Anonymous at Tue, 18 Jun 2024 22:29:53 UTC No. 16241719

>>16240527
lol applied computer science fail

🗑️ Anonymous at Tue, 18 Jun 2024 22:48:15 UTC No. 16241745

>>16241233
>What is rigourously even meant by orientation here?
You know how in computer graphics if you specify three vertices in order, a triangle appears, but only from one side? And if you swap two vertices in the order, the triangle switches the way it's facing?
That exactly corresponds to what's meant by orientation here. The induced orientation is the order in which to specify the vertices so all the faces of the simplex are visible from the outside.
The way you can do that is by rotation. Define a_k = [v_0,..,v_k-1, v_k+1,...., v_n], and suppose you take v_0 as one of the faces as a convention. You want to obtain v_(k+1) to be the same orientation as v_(k) (starting with v_0), by rotating the vectors v_0,...., v_n. Clearly you do that by a linear map that moves swaps v_k with v_k+1 and leaves the other vertices untouched. This matrix has determinant -1, therefore it reverses the orientation, therefore you multiply by -1 to account for it so that the orientation stays the same.

Anonymous at Tue, 18 Jun 2024 22:51:26 UTC No. 16241752

>>16241233
>What is rigourously even meant by orientation here?
You know how in computer graphics if you specify three vertices in order, a triangle appears, but only from one side? And if you swap two vertices in the order, the triangle switches the way it's facing?
That exactly corresponds to what's meant by orientation here. The induced orientation is the order in which to specify the vertices so all the faces of the simplex are visible from the outside.
The way you can do that is by rotation. Define a_k = [v_0,..,v_k-1, v_k+1,...., v_n], and suppose you take a_0 as one of the faces as a convention. You want to obtain a_(k+1) from that of a_(k) (starting with v_0), by rotating the vectors v_0,...., v_n. Clearly you do that by a linear map that moves swaps v_k with v_(k+1) and leaves the other vertices untouched. This matrix has determinant -1, therefore it reverses the orientation, therefore you multiply by -1 to account for it so that the orientation stays the same.

Anonymous at Tue, 18 Jun 2024 23:02:17 UTC No. 16241765

>>16241233
It is just a consequence of wanting del^2 = 0

You can do things purely symbolically to arrive at the properties without any simplex "story".
Let d be the operator defined by dv = 1 - vd, d(const)=(const)d.
Applying this to a sequence s=(v0)(v1)...(vn) and then pushing d to the right does what you want.
ds = (something1)[s] + (something2)[s]d
dv = 1-vd
ddv = d(1-vd) = d - (1-vd)d = vdd
dds = sdd
Clearly (something1)^2 = 0,
(something1)(something2) + (something2)(something1) = 0,
(something2)^2 = Id.
call (something1) del

d(v0) = 1 - (v0)d
d(v0)(v1) = (v1) - (v0)d(v1) = (v1) - (v0) + (v0)(v1)d
d(v0)(v1)(v2) = (v1)(v2) - (v0)(v2) + (v0)(v1) - (v0)(v1)(v2)d
Etc.
d(v0)(v1)(v2)...(vn) = del[v0,...,vn] - (-1)^n*(v0)(v1)(v2)...(vn)d

d is very similar to the usual differential operator, D, satisfying Df = f' + fD. The minus sign in d gives a kind of alternating product rule which makes the (del)^2 = 0 work.

Probably not the kind of answer you want but it is what it is.
You can use this to generalize del to get del_k satisfying (del_k)^k = 0 by requiring dv = 1 + v*exp(2*pi*i/k)d.

Anonymous at Wed, 19 Jun 2024 00:26:50 UTC No. 16241910

I need to create a rectangle of X square feet with an aspect ratio of Y. Help a dumb engineer out.

Anonymous at Wed, 19 Jun 2024 00:44:33 UTC No. 16241936

>>16241910
[math]
width := \sqrt{X Y}, height := \sqrt{\frac{X}{Y}}
[/math]

Assuming positive X, Y.

Anonymous at Wed, 19 Jun 2024 00:55:53 UTC No. 16241944

>>16241936
Thanks homie, I’d hire you any day.

Anonymous at Wed, 19 Jun 2024 01:02:46 UTC No. 16241953

>>16241765
what is d? it acts on what and results in what? what is v? what is a sequence?

the general setting I'm thinking about is a free abelian group [math]C_n[/math] with a basis a set of n simplices, and then we're interested in obtaining a boundary homomorphism
[math]\partial_n : C_n \to C_{n-1}[/math]

I fail to see how any of what you wrote makes any sense in this context

Anonymous at Wed, 19 Jun 2024 01:24:33 UTC No. 16241971

What are some nice math communities where people study together?
I want to find study groups.

Anonymous at Wed, 19 Jun 2024 03:04:16 UTC No. 16242071

Any anons know of a good youtube series that gets you up to speed on stuff like calculus and matrix/vector multiplication? I'm trying to get into electronics and programming as a hobby and I'm running into shit that I haven't studied since high school.

Anonymous at Wed, 19 Jun 2024 03:38:57 UTC No. 16242122

>>16242071
try khan academy?

Anonymous at Wed, 19 Jun 2024 03:55:36 UTC No. 16242135

>>16242071
Why does it have to be youtube? There's good books for that.

Anonymous at Wed, 19 Jun 2024 04:20:30 UTC No. 16242161

>>16241363
I also back folland.

Anonymous at Wed, 19 Jun 2024 04:22:08 UTC No. 16242163

>>16241953
d acts on the terms v0, v1, ... that are "multiplied" together similar to how the differentiation operator acts on functions.
The monomials you get correspond to your [] terms (assuming the v's don't commute)
For the usual derivative operator,
Df = f'+fD
Dfg = (f'+fD)g = f'g + fg' + fgD
This is how multiplying works for differential operators in the usual sense (evaluation of D remains pending).
The simple rule Df=f'+fD reproduces the product rule.
I used d as modified version of D.
It is basically related to Weyl algebra. You have dx+xd = 1 instead of Dx-xD=1 in the weyl case.
It is a bit different since Weyl algebras have {Di} and {xi} and [Di,xj] = kronecker(i,j), [Di,Dj]=0, [xi,xj]=0
I am only using 1 d and many v where d(vi) + (vi)d = 1 and vi do not commute (technically you could allow the vi to anticommute for your case).
Just think of d as acting on the term (v0)...(vn) where the decision branches for each factor that is encountered by d from the left.
For dv = 1 - vd, think of the the 1 as the action of removing v and the -vd as skipping past v and picking up a factor of (-1).

I told you this is purely mechanical and has nothing to do with the simplex "story". My point is this is the only way to get something that behaves like your boundary operator "del" and the alternating signs are just necessary to get del^2 = 0.

Anonymous at Wed, 19 Jun 2024 05:08:06 UTC No. 16242208

>>16242163
My whole motivation was just to have some operator give ddv = vdd for each variable v since this would give a del that satisfies del^2 = 0 and operates on things of any dimension.
Since del returns objects of 1 dimension less, d must behave like dv = A+B*vd
This gives ddv = (A+BA)d + BBvdd.
For ddv to equal vdd, B must be -1. This B = -1 explains why removing vk has a factor of (-1)^k.
The value of A doesn't really matter (besides not being 0) since A^k will just keep track of how many times the dimension is reduced which is redundant since the number of terms in the monomials also keep track of this.
You can conclude
d(v0)(v1)...(vn) = A*del[v0,...,vn] + (something)d without even computing anything.

Anonymous at Wed, 19 Jun 2024 05:56:19 UTC No. 16242244

>2015: took calc 1
>got sick and almost died
>2015 summer: took calc 1 again
>2015 fall: took calc 2
>got a biz degree in sucking boomer dicks and getting meme'd on
>2024: taking calc 2 again going back for engineering and math minor
>have collected a full library of recreational mathematics by now
>the only thing I know is I need to know linear algebra, data structures & algorithms to become gigaChad
Feels chud, homers enemy

Anonymous at Wed, 19 Jun 2024 05:59:23 UTC No. 16242246

>tfw I could have avoided a decade of pain if I had listened to my highschool nerd friends instead of my boomer barons

Anonymous at Wed, 19 Jun 2024 06:05:17 UTC No. 16242250

When did you realize math was for you?
For me it was Calc 2 seeing the Fast Fourier transform and being gatekept from the hyperbolic functions. It was the first time I felt like I invented math AND I stood on the shoulders of giants.

Anonymous at Wed, 19 Jun 2024 06:14:26 UTC No. 16242256

>>16242122
I'll give it a shot, thanks.

>>16242135
Because I don't need a book's worth of knowledge, just the cliff notes.

Anonymous at Wed, 19 Jun 2024 06:17:01 UTC No. 16242261

>>16241971
My university has quite a few if you can put up with the REDDIT AURA. They have a "Geeks with Beers" Saturday meet up at a bar. No classy people in sight. So much blight. It always ends in a Discord detour. It's hard because I want to be genuinely friendly instead of social credit NPC script. So many of my personal projects have become dusty beyond my own grasp. People come and go. Americans are hard to host and harder to invite and even harder to keep around. I have kept much foreign company. Chinese, Saudi, Russian guests. When you meet someone super good they tend to travel a lot. I wish we had tea time.

Anonymous at Wed, 19 Jun 2024 06:21:32 UTC No. 16242264

>>16242246
How?

Anonymous at Wed, 19 Jun 2024 06:30:25 UTC No. 16242270

>>16242264
My nerd friends did AP Calc in highschool, CAD, and so many AP classes they basically did 95% of their associates degree in highschool. I met homeschool kids who straight after middle school did their associates.
During HS I saw some rich kids "social skill" their way to the big bucks and thought shmoozing with them would give me such an opportunity. It failed. I sandbagged academia for the sake of desperate temporary grifts that were never enough. Those nerds never got gfs, never partied, never rubbed shoulders with big wigs, but they got out of school early and got the best jobs while the world was more upside down than we could have imagined. Those friends were like the big doge. Boyscouts. Based even. In the mean time I shagged my way to the Prodigal Son's shame.

Anonymous at Wed, 19 Jun 2024 13:40:14 UTC No. 16242576

>>16242163
>>16242208
it looks like you're trying to say something programming language theory parsing related, but you're unable to make it precise, comprehensible or connect it to the general situation of sequences of free abelian groups and homomorphisms between them such that any composition becomes 0.

Anonymous at Wed, 19 Jun 2024 14:34:43 UTC No. 16242605

>>16242250
when i watched the 3blue1brown "the hardest problem on the hardest test" and realized "hey this math shit is cool".

Anonymous at Wed, 19 Jun 2024 15:05:15 UTC No. 16242654

>>16242576
>something programming language theory parsing related
Df=f'+fD is just Weyl algebra. It is how big boys multiply differential operators beyond the baby ones in diffeq with constant coefficients.
I constructed d from the free algebra R<v0, v1,...vn,d> modulo the ideal generated by all of the d(vi) + (vi)d -1 = 0.

Each monomial corresponds to your [] cycles in the obvious way if there are no repeats.
You just add multiply, distribute the way you normally would.

>connect it to the general situation of sequences of free abelian groups
I am defining the boudary operator since that is what was required.
There was a bunch of WHY questions about del. I am answering the why question by getting at something more abstract but arguably more illuminating (since you can cook up what del must be just from the specification del^2 = 0 which would be a nightmare if you just stayed in the "simplex" story).
I handed you del and its recipe. You figure out how it can be used.

I've noticed you haven't opined on how the simple rule dv = 1 - vd gives the correct answer for del for all dimensions.
Maybe start there.

Anonymous at Wed, 19 Jun 2024 17:47:40 UTC No. 16242846

>>16242654
as I stated in my original post it is in fact wrong that as you said [math]\partial[/math] is uniquely defined by
[math]\partial_n \circ \partial_{n+1} = 0[/math] and [math]\partial_1 \left( [v_0, v_1] \right) = [v_1] - [v_0] [/math].
Since already for n = 2 we can define
[math]\partial_{2} [v_0, v_1, v_2] = -[v_1, v_2] + [v_0, v_2] - [v_1, v_2][/math].
Here we have the signs being the opposite of what they are in the usual definition. and yet [math]\partial_1 \circ \partial_2 = 0[/math], as well [math]\partial_2 \circ \partial_3 = 0[/math], with the usual [math]\partial_3[/math]!

Thus we have choices as to how we actually define [math]\partial_n[/math] for arbitrary n. what I was interested in was whether there is a compelling reason for why the definition of the boundary homomorphism looks EXACTLY like it does for arbitrary n. not why is it an alternating sum, or any other question. such a justification could be along geometric lines in a way that clearly justifies it for general n simplices. or it could be along algebraic lines. but as I just showed we can in fact not provide such an algebraic justification for the two minimal reasonable requirements. since we can specially define [math]\partial_2[/math] with the opposite signs as usual and everything still works out!

from more research I'm settling on the conclusion that the exact form of the boundary homomorphism is defined the way it is simply because it 1. confirms to our geometric conventions in low dimensions, 2. because it's a convenient formula and 3. because it does confirm to the requirement that [math]\partial_{n} \circ \partial_{n+1} = 0[/math].
this is somewhat disappointing.

beside all that, your language and notation isn't well defined.
dv = 1 - vd is not a well defined expression in this context.
>d acts on the terms v0, v1, ... that are "multiplied" together similar to how the differentiation operator acts on functions
this is of course nonsense without more precisely specifying.

Anonymous at Wed, 19 Jun 2024 18:45:08 UTC No. 16242938

>>16242250
Calc 3 when I accidentally found a formula for the volume of a pyramid during an exam

Anonymous at Wed, 19 Jun 2024 20:06:17 UTC No. 16243061

>>16242846
>Thus we have choices as to how we actually define
Obviously you can just multiply my del by arbitrary constants c_n to get your "choices" of del_n since it is linear.
That isn't interesting. The ratios of the constants multiplying the "faces" remains the same.
>this is of course nonsense without more precisely specifying.
I worked examples.
Start with the monomial (v0)(v1)...(vn) where the vi don't commute.
multiply by d
d(v0)(v1)...v(n)
= (1-(v0)d)(v1)(v2)...(vn)
distribute in the usual sense
=(v1)(v2)...(vn) - (v0)d(v1)(v2)...(vn)
= (v1)(v2)...(vn) - (v0)(v2)(v3)...(vn) + (v0)(v1)d(v2)(v3)...(vn)
...
=del[v0,...,vn] - (-1)^n * (v0)...(vn)d

You might think this is just programming language or parsing but this is just how things are when you modulo things in algebra. You still retain the richness of the ring structure so it isn't just simply string rewriting.
I encourage you to at least look into weyl algebra (since I assume you know basic calculus) to even understand the flavor of what is going on.
Weyl algebra is useful because sometimes you can recast your problem in terms of the mechanics of differential operators then use analysis techniques to approximate the answer when a closed form is not available.
I'm surprised you are learning abstract math yet are so opposed to me taking your problem and abstracting it then recasting it in a different form to get the answer easily.
Better not look at how laplace/fourier transforms are used to turn differential equations into algebraic equations.
God forbid you look into generating functions and see functions that you never plug in a value for the variable but still add and multiply them to do combinatorial operations with the coefficients.

I solved your problem and a whole family of generalizations with some slick abstract algebra which I think is pretty cool.
Please tell me how you would find an operator del with the property del^k = 0 with your simplex "story".

Anonymous at Wed, 19 Jun 2024 20:47:22 UTC No. 16243110

>>16243061
>I'm surprised you are learning abstract math yet are so opposed to me taking your problem and abstracting it then recasting it in a different form to get the answer easily.
you fail to do that and you fail to make any sense.
>Please tell me how you would find an operator del with the property del^k = 0 with your simplex "story".
oh ok you were just a literal ranting schizo this whole time.

Anonymous at Wed, 19 Jun 2024 21:16:18 UTC No. 16243158

>>16243110
>oh ok you were just a literal ranting schizo this whole time.
The answer is to just replace -1 with e^(2*pi*i*m/k) in the alternating sum in the pic >>16241233
I gave you the answer. Now good luck proving it satisfies del^k = 0

Anonymous at Thu, 20 Jun 2024 00:07:36 UTC No. 16243378

I'm looking into the fact that a fractional brownian motion is not a semimartingale, but I'm having a hard time understanding a certain point in the proof : it is said that if a process has a quadratic variation of 0, then for it to be a semimartingale, it must have a finite 1-variation, but I found no proof of this, I have a hunch that it's due to the decomposition as a local martingale and a process of bounded variation, but I really dont know what to do with all that, could you fellows give me a hand ?

Anonymous at Thu, 20 Jun 2024 01:47:16 UTC No. 16243464

>>16242256
>just the cliff notes.
Look at math books for physicists or engineers. They're pretty good for just distilling the things you'll need.

Anonymous at Thu, 20 Jun 2024 10:59:18 UTC No. 16243900

>>16243378
If you have a continuous semimartingale [math]X=X_0+M+A[/math], for a local martingale [math]M[/math] and a BV process [math]A[/math], its (predictable) quadratic variation [math]\langle X\rangle=\langle M\rangle[/math].
Wlog you can take each [math]M^{\tau_n}[/math] bounded, for a localizing sequence [math](\tau_n)[/math], and also [math]\langle M^{\tau_n}\rangle=\langle M\rangle^{\tau_n}=0[/math], implying that [math](M^{\tau_n})^2[/math] is a martingale with [math]\mathbb E ((M^{\tau_n})^2)=0[/math], implying [math]M^{\tau_n}=0[/math] a.s.
This extends to [math]M=0[/math] a.s. because for any [math]t \geq 0[/math], [math]\mathbb P(M_t\neq0)\leq\sum_n \mathbb P(M^{\tau_n}_t\neq0)=0[/math] and modifications of continuous processes are indistinguishable.
So if [math]\langle X\rangle=0[/math] then [math]X=X_0+A[/math] which is BV.

Anonymous at Thu, 20 Jun 2024 14:59:36 UTC No. 16244173

>>16243900
Got it, thanks man

Anonymous at Thu, 20 Jun 2024 20:12:14 UTC No. 16244512

>>16240472

Anonymous at Thu, 20 Jun 2024 21:38:38 UTC No. 16244609

>>16241294
You should read this book.

Anonymous at Thu, 20 Jun 2024 21:40:04 UTC No. 16244611

>>16241363
Axler's book is free on his website.

Anonymous at Fri, 21 Jun 2024 08:58:36 UTC No. 16245290

>>16241363
Why would anyone waste their time studying a theory? Study some measure facts

Anonymous at Fri, 21 Jun 2024 11:39:33 UTC No. 16245445

>>16242244
Sounds like my dad's college experience

Anonymous at Fri, 21 Jun 2024 16:13:24 UTC No. 16245814

what's the most esoteric out of touch branch of mathematics which will never have any practical application?

Anonymous at Fri, 21 Jun 2024 17:01:51 UTC No. 16245901

>>16245814
large cardinals

Anonymous at Fri, 21 Jun 2024 17:08:40 UTC No. 16245907

If you throw a ball from height h meters and with velocity v m/s, what does the angle alpha need to be in terms of h and v to maximize the distance in which the ball lands when it falls to the ground?

Hint: it is not 45 degrees because 45 degrees only applies for h=0.

Anonymous at Sat, 22 Jun 2024 08:24:37 UTC No. 16247100

>>16245907
>homework

Anonymous at Sat, 22 Jun 2024 16:09:44 UTC No. 16247603

>>16247100
Not homework. I came up with the problem for recreational math

Anonymous at Sat, 22 Jun 2024 16:19:51 UTC No. 16247628

>>16245907
Range can be expressed as a function of angle. Differentiate and find the roots

Anonymous at Sun, 23 Jun 2024 00:47:58 UTC No. 16248524

Are you guys worried that AI is going to steal your mathematical jobs?

Anonymous at Sun, 23 Jun 2024 09:08:35 UTC No. 16248988

>>16248524
Not literally today. But they do seem to be improving fairly fast, in 5 years yeah probably.

Дypaндaл !!DuST03+8twr at Sun, 23 Jun 2024 10:08:44 UTC No. 16249023

Anonymous at Sun, 23 Jun 2024 12:04:17 UTC No. 16249081

>>16248524
The first computers were invented to do mathematics. It's right there in the term.
They've been threatening to steal our roles since their very conception, and yet, all they've done is make it easier to do extensive, tedious calculations.

So, if anything, I'm pretty optimistic.

Anonymous at Sun, 23 Jun 2024 16:53:59 UTC No. 16249422

>>16245907
Look here >>16249417

Anonymous at Sun, 23 Jun 2024 21:27:14 UTC No. 16249907

>Got the highest ever grade in a PDE course.
>2 semesters passes
>??????
>Barely remember anything.
Is it over?

Anonymous at Sun, 23 Jun 2024 21:58:48 UTC No. 16249952

>>16249907
No
Normal part of the human experience

Anonymous at Mon, 24 Jun 2024 01:48:39 UTC No. 16250193

>>16249907
You still probably have some of the basic intuition, and can relearn it all in a few weeks if you actually need it

Anonymous at Mon, 24 Jun 2024 02:43:27 UTC No. 16250246

how do I pass calc 2 this summer. these concepts and rules regarding playing with integrals aren't getting sponged by my brain as well as calc 1 concepts

Anonymous at Mon, 24 Jun 2024 05:50:34 UTC No. 16250408

>>16250246
You mostly just grind them until you can do them fairly quickly. I basically just dedicated half an hour a day for a few months before my odes class to practicing the various techniques

Anonymous at Mon, 24 Jun 2024 06:07:53 UTC No. 16250423

>>16240545
transfinite induction and recursion, yes

Anonymous at Mon, 24 Jun 2024 07:02:49 UTC No. 16250458

Who came up with the term "positional" when discussing positional games?
>https://en.wikipedia.org/wiki/Positional_game
I tried to search for the earliest paper to use that word and I found Hales & Jewett (1963) to be the earliest, but I just want to double-check here on the off chance someone here knows an earlier usage of the word 'positional'.

Anonymous at Mon, 24 Jun 2024 21:02:55 UTC No. 16251550

>>16250458
As far as I searched the term was first used in a 1967 book by
the same name, published by Nauka. Author unknown.

Anonymous at Mon, 24 Jun 2024 21:19:37 UTC No. 16251577

>>16251550
>>16250458
Hold up, spoke too soon. By the attached PDF, reference 11,
the authors Nikolai Vorob'ev and I.N. Vrublevskaya.

But then again, I might have found the second time the term
was used.

Anonymous at Mon, 24 Jun 2024 22:40:29 UTC No. 16251773

Posting some kino

https://youtu.be/vUJEG3tUVaY

Anonymous at Mon, 24 Jun 2024 22:43:45 UTC No. 16251783

>>16248524
>Gram Rothschild theorem
The jews are behind Instagram and Israel!

Anonymous at Mon, 24 Jun 2024 22:46:10 UTC No. 16251791

>watch pic rel
>name drops protocols of learned elders of zion in the first scene
>says nothing else about it
>haha whoopsie!
Is being Jewish like playing Cops and Robbers by yourself as both sides?

Anonymous at Tue, 25 Jun 2024 14:15:09 UTC No. 16252741

>>16251773
That's some good kino

Anonymous at Tue, 25 Jun 2024 21:13:18 UTC No. 16253564

What's the best starting point in math if I haven't done any math since highschool 5 years ago?

Anonymous at Wed, 26 Jun 2024 01:33:13 UTC No. 16254071

I'm doing my masters in the fall, but I don't care about math anymore. I'm just scared of being in the real world and having a real job again.
Actually, I haven't done any math in over a year because I ran out of classes but had to take electives to get my degree. And I've been much happier with zero math.

Anonymous at Wed, 26 Jun 2024 10:15:38 UTC No. 16254535

>>16254071
>I don't care about math
>I haven't done any math in over a year
>I've been much happier with zero math
So why are you posting in this thread

Anonymous at Wed, 26 Jun 2024 14:35:46 UTC No. 16254806

>>16251791
>>name drops protocols of learned elders of zion in the first scene
does this actually happen?

Anonymous at Wed, 26 Jun 2024 17:14:39 UTC No. 16255001

>>16253564

Anonymous at Thu, 27 Jun 2024 04:58:52 UTC No. 16256053

>>16248524
I have already lost hope of getting a proper job in mathematics. However, i still do to entertain myself.

Anonymous at Thu, 27 Jun 2024 16:01:15 UTC No. 16256769

Hello I need some resources for math that cover the basics but I have some requirements
1) they need to explain things well unlike some other resources. I struggled to understand quantifiers because when I saw "for all x, there exists a y such that" and I would get confused as to what it meant, until I realized that confusion was that I didn't understand if "for all x" meant that y would be the same for all of them or that there exists a y for each individually. Some resources clarify this like some university of hawaii page.
2) I want more practical uses for things like statistics, something where you're given data and you have to analyze it with python would be best.
3) a decent book on proofs and math foundations, again something that isn't retarded and actually explains things, not some backwards rigorous autism, so actually showing why you'd do it one way and not another, etc.
Thanks

Anonymous at Thu, 27 Jun 2024 16:06:05 UTC No. 16256774

>>16248524
Is that output any good?

Anonymous at Thu, 27 Jun 2024 16:09:40 UTC No. 16256778

>>16242605
>3blue1brown
This any good? The visualizations are cool but they just seem like a way to make you think you actually understand what is going on, without actually being helpful in actuality.

Anonymous at Thu, 27 Jun 2024 17:28:09 UTC No. 16256855

>>16256769
``For all'' really should be called ``for any''.

Anonymous at Thu, 27 Jun 2024 17:38:23 UTC No. 16256881

>>16256855
Or "for each", I agree it's confusing and it makes it even more frustrating that this doesn't seem to be clarified when it is presented. Many such cases, that's why I ask for something where I don't waste my time trying to decipher the notation instead of actually learning new ideas.

Anonymous at Thu, 27 Jun 2024 17:40:24 UTC No. 16256886

>>16248524
We are progressively moving towards constructive mathematics and the use of proof-assistants for proof writing.

https://leandojo.org/

Anonymous at Thu, 27 Jun 2024 18:03:16 UTC No. 16256913

>>16256778
damn you're fucking retarded. it's hilarious you're really trying to front right now but all you managed to do was expose to everyone how big of a fucking retard you are.
lmao if you're gonna actually learn math you have to work through textbooks, or watch actual lectures while taking serious notes. how retarded are you? obviously 15 mins cool visualization youtube vids wont actually teach you math. holy fuck you're retarded. fucking obviously it is at best a supplement.

Anonymous at Thu, 27 Jun 2024 18:05:11 UTC No. 16256920

>>16256769
all your "requirements" betray a serious lack of any kind of understanding of math, combined with an arrogant attitude that will prevent this from being rectified.

Anonymous at Thu, 27 Jun 2024 18:11:49 UTC No. 16256935

>>16256774
That's an exercise for the reader.

Anonymous at Thu, 27 Jun 2024 18:47:42 UTC No. 16257028

Does there exist a scalene triangle such that the resulting disphenoid is space-filling?

Anonymous at Thu, 27 Jun 2024 21:07:40 UTC No. 16257247

bump

Anonymous at Thu, 27 Jun 2024 21:09:41 UTC No. 16257252

Suppose H is a subset of a group G. Does it follow then that H is a subgroup of G?

Anonymous at Thu, 27 Jun 2024 21:14:04 UTC No. 16257258

>>16257252
Nope. The empty set is never a subgroup. Also {1,-1} forms a group under multiplication and {-1} is a nonempty subset of it that is not a subgroup.

Anonymous at Thu, 27 Jun 2024 22:19:16 UTC No. 16257341

>>16256913
nta but who are you arguing with
he didn't say any of that shit you're arguing against, he just asked if 3b1b videos are any good (even said he himself has doubts about them) and the answer to that is yes, they are a good supplement (to rigorous learning from elsewhere) for helping intuition/visualization about a topic

Anonymous at Thu, 27 Jun 2024 22:36:51 UTC No. 16257370

>>16256778
Yes they are good. I'm sure all of us have had lecturers that couldn't teach a topic for shit, these can help. Sure his stuff might be a simplification at times but that's what textbooks are for. Combine the two and you have a winning combination.

Anonymous at Fri, 28 Jun 2024 04:07:36 UTC No. 16257650

>>16257252
What does that even mean? lol.

t.mathlet.

Anonymous at Fri, 28 Jun 2024 04:20:38 UTC No. 16257664

>>16257252
If you're going to make /sci/ do your homework at least make it nontrivial

Anonymous at Fri, 28 Jun 2024 06:30:29 UTC No. 16257776

>>16257258
>>16257650
>>16257664
newfigs

Anonymous at Fri, 28 Jun 2024 08:21:26 UTC No. 16257856

Niggas will do literally ANYTHING but read the assigned textbook. They'll watch that one Brooklyn Jew with the lisp for 40 minutes and come out of it with a surface level understanding rather than spend < 1 hour reading the assigned section, doing the examples, and doing the problem set.

Anonymous at Fri, 28 Jun 2024 13:55:52 UTC No. 16258123

My boss went ballistic today because I compared two quotations from different companies using percentage difference rather than percentage increase/change.
How can I best explain to him that he's an idiot?

Anonymous at Fri, 28 Jun 2024 14:28:40 UTC No. 16258157

>>16258123
send him a copy of Lang's Basic Mathematics

Anonymous at Fri, 28 Jun 2024 15:48:29 UTC No. 16258264

>>16257370
>Combine the two and you have a winning combination.
Oh yeah of course, but you do have to combine them, whereas his videos are just some nice graphics.

Anonymous at Fri, 28 Jun 2024 16:03:05 UTC No. 16258276

>>16240472
So a partial derivative is a limit?

Anonymous at Fri, 28 Jun 2024 16:29:13 UTC No. 16258310

>>16258264
bet you're hoping we'll call you BASED right?
BASED smartbro who KNOWS you can't really learn math properly from 3b1b vids... you're really smart and redpilled and BASED, not like all the normies who think you can learn math properly from 3b1b vids...
BASED. take this. feel good about it. you are smart. and you are special.

Anonymous at Fri, 28 Jun 2024 17:19:15 UTC No. 16258371

>>16258123
I don't understand. Isn't percentage increase exactly the percentage difference? Do you have an example?

Anonymous at Fri, 28 Jun 2024 17:31:56 UTC No. 16258383

>>16258276
Yes

Anonymous at Fri, 28 Jun 2024 20:35:50 UTC No. 16258689

bump

Anonymous at Sat, 29 Jun 2024 10:31:14 UTC No. 16259542

>>16257028
bump

Anonymous at Sat, 29 Jun 2024 11:01:32 UTC No. 16259560

What are the prerequisites for Riemann geometry?

Anonymous at Sat, 29 Jun 2024 13:02:00 UTC No. 16259691

>>16259560
Multivariate calculus and basic topology.

Anonymous at Sun, 30 Jun 2024 01:08:06 UTC No. 16260479

Took calc 3 a while ago and have a few questions since I don't feel like finding a textbook. If you have a function V(a, b, c, d) that you got by taking an integral (so V gives you volume over rectangular bounds), is there a way to use this formula if you want the volume over non-rectangular bounds? For example, if you say y = x +/- 1, then V(a, b, x - 1, x + 1) is in terms of x and doesn't actually tell you the volume. Does this expression have any significance? What does it mean?

A related question I had was, if you write an integral like that normally, with constants on the outside bounds and variable bounds on the inside, and then switch the order of operations, what does that do? For example, taking the integral normally over the triangle (0,0), (0,1), and (1,0) with f(x,y,z) = 1 you get 1/2, but if you switch the integral order, you get x.

Also, how would you integrate over a region like pic related?

Anonymous at Sun, 30 Jun 2024 01:15:42 UTC No. 16260487

https://math.arizona.edu/~kirti/report-on-scholze-stix-mochizuki-controversy.pdf

joshibros we're back. abc is getting proved whether the nip and krauts like it or not

Anonymous at Sun, 30 Jun 2024 01:52:02 UTC No. 16260516

>>16242135
Youtube is unironically better than books for anything pre-algebra/analysis.

Anonymous at Sun, 30 Jun 2024 01:56:59 UTC No. 16260521

>>16256778
His early videos were good (I think prior to the linear algebra series), but then he started pandering to the masses of retards, and his videos are now like numberphile videos if you got rid of the mathematicians.

Anonymous at Sun, 30 Jun 2024 02:02:08 UTC No. 16260525

>>16255001
Based.

Anonymous at Sun, 30 Jun 2024 02:03:42 UTC No. 16260527

>>16256855
"For any" genuinely causes confusion. "For all" does not cause any confusion except among literal retards.

Anonymous at Sun, 30 Jun 2024 07:14:24 UTC No. 16260802

>>16256769
>book on proofs and math foundations,
kunen's Foundations of math is easy to read

Anonymous at Sun, 30 Jun 2024 08:22:37 UTC No. 16260855

Just realised scalar multiplication does not obey matrix multiplication rules. A scalar (1x1) cannot be multiplied by a column vector (nx1) according to matrix multiplication rules. It also does not obey associativity like in the case x^t x y. Left to right is defined but right to left isn't.

Anonymous at Sun, 30 Jun 2024 08:56:55 UTC No. 16260872

>>16260855
>A scalar (1x1) cannot be multiplied by a column vector (nx1) according to matrix multiplication rules
Yes it can.
>It also does not obey associativity
Yes it does.

Anonymous at Sun, 30 Jun 2024 09:38:45 UTC No. 16260906

>>16260487
It's coming home

Anonymous at Sun, 30 Jun 2024 09:42:46 UTC No. 16260909

>>16260855
just write scalar multiplication on the right and then it works exactly the same way. It's a bit better to consider scalar multiplication as multiplication by the scaled identity matrix.

Anonymous at Sun, 30 Jun 2024 09:59:35 UTC No. 16260926

>>16260527
What confusion does for any cause?

Anonymous at Sun, 30 Jun 2024 10:24:58 UTC No. 16260937

>>16260926
"If for any Y, f(Y), then X"

Anonymous at Sun, 30 Jun 2024 10:31:07 UTC No. 16260940

>>16260521
3b1b could make some great videos if he actually read more math.

Anonymous at Sun, 30 Jun 2024 10:46:22 UTC No. 16260951

>>16260937
This doesn't confuse me. How should it?

Anonymous at Sun, 30 Jun 2024 10:50:11 UTC No. 16260953

>>16257252
Why do you think we invented the term subgroup

Anonymous at Sun, 30 Jun 2024 10:50:22 UTC No. 16260954

>>16260951
It could mean either the existence of a single element satisfying the condition or a for all condition.
For example,
"If for any natural number n, pi_n(X) = 0, then X is weakly contractible" could be interpreted either way.

Anonymous at Sun, 30 Jun 2024 11:14:56 UTC No. 16260980

>>16260954
Fair enough.

Anonymous at Sun, 30 Jun 2024 13:02:06 UTC No. 16261052

>>16260954
And that sentence should be a for all condition you mean, cause otherwise it makes sense where it just has to be true for one (for any of them). But I disagree with >>16260527 when combined with the existence qualifier it is vague if it's for all or for any of them, and it did confused me fora while.

Anonymous at Sun, 30 Jun 2024 13:12:46 UTC No. 16261060

>>16260802
I skimmed the beginner of a pdf of it I found. It doesn't seem like it really is what I'm asking for, since it just presents some things and jumps over them with barely any explanations, as if the reader already understands them, in which case why show them at all.
Is this a meme rec or are all fundation books actually not fundations since only people who have done math for a while would care about that subject?

Anonymous at Sun, 30 Jun 2024 14:37:16 UTC No. 16261148

>>16261060
>and jumps over them with barely any explanations,
Example? Be specific.

Anonymous at Sun, 30 Jun 2024 15:08:57 UTC No. 16261185

>>16261052
Are you ESL?

Anonymous at Sun, 30 Jun 2024 16:30:45 UTC No. 16261333

>>16261148
Well the issue above with for all and the exists, for example. From what I've seen it just says, "for all is written with an upside down A" and then moves on. Albeit I did skim, so I might have just not seen it.
In terms of content, it probably goes into more depth then I care about, so if you have one that also cover the other areas I'm interested in, please tell me.

Anonymous at Sun, 30 Jun 2024 16:33:45 UTC No. 16261342

>>16261185
Yes but I don't think that's the issue. When you say something is true for all things, it means that that one thing is true for all things. So it seems that there would be some confusion there too.

Anonymous at Sun, 30 Jun 2024 17:04:24 UTC No. 16261423

>>16261333
The book is extremely introductory though. If you want something with less depth I highly doubt you truly want to learn about foundational stuff. In that case you might as well read introductory chapters in analysis books

Anonymous at Sun, 30 Jun 2024 17:06:06 UTC No. 16261431

>>16261060
Read Girard's Blind Spot

Anonymous at Sun, 30 Jun 2024 18:41:51 UTC No. 16261682

>>16256769
Jay cummings "proof a longform mathematical textbook"
Essential statistics with R or something like that
Cummings should satisfy 1 and 3. I like it better than velleman how to prove it

Anonymous at Sun, 30 Jun 2024 18:44:51 UTC No. 16261690

>>16261682
meme book

Anonymous at Sun, 30 Jun 2024 18:46:12 UTC No. 16261694

>>16261060
It didn't jump over anything last time I read it. What are you referring to specifically?

Anonymous at Sun, 30 Jun 2024 18:47:35 UTC No. 16261696

>>16261682
neither this nor vellemann are books on foundations

Anonymous at Sun, 30 Jun 2024 18:48:44 UTC No. 16261699

>>16256920
Nta, i genuinely love math, give me a good discrete math recommendation after learning proofs. Right now between harris&mossinghoff graph theory and combinatorics, grimaldi comb&disc math and invitation to disc math by matousek. Thanks in advance.
Currently doing langs first course in calculus (did his basic math, intend for his books and enderton's to be my core study where possible, but willing to add others. I like his style) but kind of losing steam on the integration techniques section. Thinking of reading kline's calculus and returning to it, or skipping all the exercises and then going through it again and doing them, or just going through the how and why of one variable calc, which would you advise? I have already skipped over exercises from quite a few sections.

Anonymous at Sun, 30 Jun 2024 18:50:30 UTC No. 16261701

>>16261696
Nigger you ar fussing about the symbol for for all and there exists. If you can't handle kunen, either try after proofs, or dp algebra first and come back

Anonymous at Sun, 30 Jun 2024 18:51:04 UTC No. 16261703

>>16261699
Diestel's Graph Theory is nice.

Anonymous at Sun, 30 Jun 2024 18:52:24 UTC No. 16261707

>>16261703
Isn't it graduate level? I think i have some talent, but i am not a high flier

Anonymous at Sun, 30 Jun 2024 18:54:01 UTC No. 16261710

>>16256769
>>16261699
>>16261060
>>16261333
>>16261696
read http://arxiv.org/abs/2101.02031
It handles foundations rigorously and then applies it to topology and algebra. No prerequisites

Anonymous at Sun, 30 Jun 2024 18:54:50 UTC No. 16261713

>>16261696
Come to think of it, what do you consider foundations? maybe halmos naiveST+exercisebk or hrbacek and jech set theory might be worth a try.

Anonymous at Sun, 30 Jun 2024 18:56:29 UTC No. 16261715

>>16261710
Thanks b

Anonymous at Sun, 30 Jun 2024 18:58:36 UTC No. 16261721

>>16261707
NTA but you shouldn't ever shy away from reading GTM books just because you haven't graduated yet lol. I read most of lang's algebra in undergrad just fine. Even Springers Encyclopedia of the mathemtical sciences has some readable books.

Anonymous at Sun, 30 Jun 2024 19:17:14 UTC No. 16261746

>>16261721
Ok fair, but i am self taught and admit to being a little impatient to finish what i think are the core courses that would be equivalent to the undergraduate curriculum in a relatively strong programme. While i do value depth and beauty, i think combinatorics and discrete math are a little outside of that and i really want them to be able to analyse algorithms and understand computer science/programming better

Anonymous at Sun, 30 Jun 2024 19:28:15 UTC No. 16261772

>>16261682
I'll check them out, I vaguely remembered there was some book that was something like that but I thought there ought to be some resource online that someone made where they put up the data along with whatever, and also make the data interesting, like trying to replicate what someone else had done when they were analyzing it.
Also I'm not necessarily looking for a book on foundations (or at least don't care to go past some of the basic ideas), that was mainly an example of how I felt a lot of books just didn't do a good job of teaching things. And I could add more things to it like how for some reason people in academia think it's a good idea to teach generalizations first instead of concrete examples, and basically derive things from observations (which is how it's basically done in the real world).
>>16261701
I'm not >>16261696, I'm >>16261682.
>>16261710
Will have a look.

Anonymous at Sun, 30 Jun 2024 19:30:24 UTC No. 16261777

>>16261694
>>16261333, but as I said I skimmed through a random pdf, which may or may not have been the actual book in question.
>>16261423
I'll download a proper pdf and have a closer look then.

Anonymous at Sun, 30 Jun 2024 20:16:12 UTC No. 16261871

>>16261772
>things from observations
math isn't science. Math books teach you how to prove stuff and do math research on your own. Deduction != observation

Anonymous at Sun, 30 Jun 2024 20:18:40 UTC No. 16261876

>>16261772
I still don't get what you're looking for.

Anonymous at Sun, 30 Jun 2024 20:21:11 UTC No. 16261878

>>16261746
just study what your soul dictates but note you shouldn't postpone learning linear algebra forever. Far too many fields depend on it and often at a quite deep level

Anonymous at Sun, 30 Jun 2024 21:11:42 UTC No. 16261938

>>16261772
Well, I mean it works for some people, although perhaps it's useful once the student passes a certain level. Very few high schoolers like bourbaki style, but for some mathematically inclined persons, there is a beauty to axiomqtic development. For the most part it's a balance, I guess

Anonymous at Sun, 30 Jun 2024 21:40:29 UTC No. 16261983

>>16261871
You observe the patterns and then come up with some formula and then you try to prove it. And also what you're actually training is your intuition which is basically fucked every time people try to organize math in a retarded way which isn't how people actually got there, and which makes no sense (in the sense that you're just presented with random rules and conventions and definitions of, say, different ways to group numbers).
>>16261876
Actual practical math taught in a specific way. From practical problems or observation of some pattern -> to generalization of the observation -> whatever else can be learned from there.
I'll check the books some anons have recommended though, maybe those will actually tickle my bone.

Anonymous at Sun, 30 Jun 2024 21:52:03 UTC No. 16262000

>>16261938
My point is that if you're teaching someone something you should kinda show them how you go there. So I imagine someone teaching a class about computers and they start with a definition of what is a computer "it's a turing complete thing that does computation", which is utterly useless, because nobody in the past would have thought about computers that way they just made computers and then eventually once a bunch of them were made and you couldn't just go well it's a big box with tapes and whatever (because there would've been PCs too) they tried to find a common attribute and since computers are so different they just have some intangible af quality they pick. Same shit happens with dictionary definitions, a lot of them are useless cause they try to cast a vast net, which is useless for someone trying to understand the thing cause they don't get what it means.
>>16261876
And also a book that is fucking verbose and has diagrams and shit and pics and history lessons and shit like that why the fuck are people writing like they're trying to preserve paper (I mean cause they are when they're making books, but that's why an online resource would be better).

Anonymous at Sun, 30 Jun 2024 22:05:44 UTC No. 16262021

I study math as a hobby and because of that I'd like to know some math topics that are not mainstream but still interesting. Don't worry about the level required to understand the topic, if I find it interesting I'll study whatever is need to follow it.

Anonymous at Sun, 30 Jun 2024 22:18:21 UTC No. 16262036

>>16241433
Did you forget they used to assume Earth wasn't a planet?

Anonymous at Sun, 30 Jun 2024 22:58:30 UTC No. 16262095

>>16261983
Yeah, that's what i understood. I'm saying it's a style issue. I like it the other way sometimes, although i guess it is harder to do well

Anonymous at Sun, 30 Jun 2024 23:32:13 UTC No. 16262117

Does there exist a space-filling rhombic disphenoid?

Anonymous at Mon, 1 Jul 2024 01:26:45 UTC No. 16262207

>>16262000
I don't want to abuse the analogy, but i can understand that it is not the simplest way to deliver the material. I enjoy a terse axiomatic development if i can follow it and a textbook written that way is fine for mature mathematician looking to familiarize themselves with the central results of a subject and often ideal for teachers who then may be able to flesh it out on their own using it as guidance on selection of material. My advice is to read the preface of the book, make sure if you have the prerequisites, see if you are the target audience and then skim to see if you like the style>>16262095
After that, i really do think it is just preference. I am neither professor nor complete mathematician, but i do enjoy serge lang's terse logical development, although i might supplement it. I literally just like it, even if it doesm't complete my study

Anonymous at Mon, 1 Jul 2024 03:11:41 UTC No. 16262336

>>16261342
Unless you have a learning disability, it is most likely the issue.
In English, the precedence of statements involving quantifiers which come before the predicate is determined by the order in which they are stated. So there is absolutely no ambiguity when you say "For all x, there exists a y such that P(x,y)"; this means precisely that if you pick any x, then associated to that x, you can find some y such that P(x,y) is true.
On the other hand, there can be confusion when statements involving quantifiers come both before and after the predicate, e.g. "There exists y such that P(x,y) for any x". This really should mean that you can find a particular y, and then no matter what x you choose, P(x,y) will hold. Bad writers however will sometimes write this to mean the sentence in the previous paragraph.
That said, any math proof/logic book will be unambiguous, and as long as you are aware of this unwritten rule for the language, there should not be confusion.

Anonymous at Mon, 1 Jul 2024 03:50:18 UTC No. 16262399

>>16240472
Prove that pi is irrational
Prove that sqrt2 is irrational

Anonymous at Mon, 1 Jul 2024 03:55:37 UTC No. 16262406

>>16262336
I am not ESL. The ESL is correct.
'For all x, there exists a y' would in English (not math) suggest that the y is the same regardless of the x.
If the y is different for different x, then it would be 'For each x, there exists a y'
Traditionally in math, 'For all x, there exists a y' allows for y to be different depending on x but that is just math speak, not regular English.
If it matters, I am from the US and English is the only language I know and I am white

Anonymous at Mon, 1 Jul 2024 03:59:38 UTC No. 16262408

>>16262406
I don't think I would ever interpret it like that, but I guess it's because I'm so accustomed to it. I'd still maintain that in regular English, "for all", "for any", "for every" are all equivalent.

Anonymous at Mon, 1 Jul 2024 04:06:10 UTC No. 16262415

>>16262408
When I first read the first post itt about it I didnt get why he was confused either then I thought about it more and realized that yeah the way we say it in math doesnt really add up with the way we talk in plain English so I think its mostly being accustomed to mathspeak.

Anonymous at Mon, 1 Jul 2024 05:26:13 UTC No. 16262470

>>16261983
>which is basically fucked every time people try to organize math in a retarded way which isn't how people actually got there
I envy you for knowing fuck all about math history since it's really ugly and chaotic, this romantic belief of math history being all linear or making sense intuitively couldn't be further from the truth. Lots of parrallel developments all over the world, or lack of information giving us an incomplete picture of math research at certain places, or threads that went nowhere or were far beyond their time, like Abu l-Wafa developing an n-dimensional analogue of the pythagorean theorem in the 10th century.
Go on and read history books if you want. You'll eventually realize you're not ever getting to contemporary mathematics that way and choose one of these "artificial" constructions commonly found in textbooks instead; after all, you need to organize all that info in your brain somehow.
And you're still wrong on observation. If you want to advance a field, you'll want to read a lot about it first, or else you'll be on your death bed having rediscovered some theorem proved in the 18th century at best. Even Grothendieck who may seem like the polar opposite in that regard credited Serre for all of his ideas. And guess what Serre did? Read a fuck ton of books. So no, math is much more about hard work than Eureka moments from observing nature.

Anonymous at Mon, 1 Jul 2024 06:51:57 UTC No. 16262531

>>16262470
I didn't mean it was linear and having developed in a logical way, I'm actually saying the opposite and books usually try to make it too clean, which I assert fucks you up. Read the first reply here >>16262000. Now I don't think it will be slower since you're not going to be going through all the threads that go nowhere and also it takes more trial and error to come up with a proof than to explain it.
But I think for proofs it would take less time to understand them if they explaining what they're trying to achieve when they start cleverly defining variables and sets to prove some contradiction for example. As someone that doesn't have much experience, it's like I'm just reading someone do random stuff and then go "and as you can see it leads to a contradiction", like the writer is trying to impress with how clever they are, and you're left with cool I can see you did something but I don't get why it works or what your thought process was.
What I'm saying they should do is explain more thoroughly why they made certain decisions, which should in fact aid learning. Another example of this is for example giving something like etymology when learning rational numbers, as a ratio of two others, which is easier to remember, and gives you actual insight into WHY things are a certain way.
>So no, math is much more about hard work than Eureka moments from observing nature.
I'm mainly talking about introductory learning material though, but I imagine even at higher levels someone still had to observe something that they reused somewhere else or generalized, but I'm not at that level.

Anonymous at Mon, 1 Jul 2024 07:06:12 UTC No. 16262539

>>16262408
>>16262336
Thing is, I think the precedence might be what's causing confusion, since you can move things around when you use a comma, like saying "for now, i think it's best left alone" vs "i think it's best left alone, for now". So with "for all", if you're not sure what it means, you might end up thinking the precedence is the other way around, since "Ey, Ax" would be the wrong interpretation of "Ax, Ey" (but it's not obvious when you're learning it).
But with "for each" either way you write it is understood the same thing, "for each x, there exists a y" for "there exists a y for each x" they mean the same thing.

Anonymous at Mon, 1 Jul 2024 08:00:20 UTC No. 16262575

Claire has two children. One is a boy who lives in France. What is the probability that both are boys?
>Consider all the possibilities
B (France) B (France)
B (France) B (Not France)
B (Not France) B (France)
B (France) G (France)
B (France) G (Not France)
G (France) B (France)
G (Not France) B (France)
>How many of them are there?
7
>How many have two boys?
3
>So what's the probability
3/7

What the fuck?

Anonymous at Mon, 1 Jul 2024 09:04:15 UTC No. 16262636

>>16262575
Assuming you are OK with the "the oldest child is a boy" question having probability 1/2, and the "at least one is a boy" question having probability 1/3, then, the more you know about one of the two children, the better you can identify which of the two kids he is , reducing probability of overlapping cases(the other might not live in france, assuming that's uniformly distributed), until eventually (or immediately if you get perfect information setting them apart, such as knowing one is the oldest) the probability increases from 1/3 to 1/2 again.

Anonymous at Mon, 1 Jul 2024 09:06:28 UTC No. 16262637

>>16240588
>>16241140
>doing maths until late 30s
>becoming a philosopher at early 40s
That's more or less the way Plato envisioned his cursus studiorum, ergo it couldn't be more based.

Anonymous at Mon, 1 Jul 2024 09:10:20 UTC No. 16262642

>>16262636
But being in France gives us no new information, and I can do this with even ridiculous additions.
>Claire has two children. One is a boy who had a shower yesterday. What is the probability that both are boys?
3/7 is patently nonsensical here.

Anonymous at Mon, 1 Jul 2024 09:37:00 UTC No. 16262656

>>16262642
You most certainly do get new information. You change the underlying probability structure by implicitly assuming that any child, boy or girl, has a 50% chance of being stinky and not having had a shower yesterday. Maybe this is what's tripping you up; assuming everyone showers every day would change the probability from 3/7 back to 1/3 because then it indeed gives no information.
Just to be sure, it does make intuitive sense to you that "Claire has two children. One of them is a boy. What is the probability that both are boys?" has probability 1/3?

Anonymous at Mon, 1 Jul 2024 09:49:00 UTC No. 16262670

>>16262656
Yes. You just write out all the possibilities:
BB
BG
GB
And the proportion of those which are two boys is 1/3. I did that here:
>>16262575
and got 3/7

Anonymous at Mon, 1 Jul 2024 09:57:40 UTC No. 16262678

>>16262670
Right. Mathematically, it all works out. You can do the same for your showering question. So, what causes statements like "what the fuck" or "that's nonsensical"? I assume it's because of intuition with "information". So, what is, according to you, the difference in "information" between the two versions mentioned at the start of >>16262636 ? One has outcome 1/2 and one 1/3, so something must be different.

Anonymous at Mon, 1 Jul 2024 10:02:22 UTC No. 16262683

>>16262678
So the answer in both the France case, and the showering case, is 3/7? And it would still be 3/7 if it was "one is a boy who"
>Lives in North Korea
>Is allergic to peanuts
>Has never won an olympic gold medal

Anonymous at Mon, 1 Jul 2024 10:09:14 UTC No. 16262685

>>16262683
Yes. No, then it would be higher than 3/7, assuming a 50/50 split between all of (yes/no living in Korea), (yes/no being allergic to peanuts) and (yes/no having not won an olympic gold medal). You can do the counting to find the probability.

Anonymous at Mon, 1 Jul 2024 10:13:01 UTC No. 16262689

>>16262685
So what's the probability of the France one and the shower one?

Anonymous at Mon, 1 Jul 2024 10:20:23 UTC No. 16262695

>>16262539
If you insert a "such that" after any "there exists", then makes it clear that they are not the same.
"For all (each) x, there exists y such that..."
"There exists y such that for all (each) x..."

Anonymous at Mon, 1 Jul 2024 10:25:07 UTC No. 16262697

>>16262575
>>16262636
>>16262656
>>16262670
>>16262685
I buy a lottery ticket. What is the probability that I win?
>Consider the possibilities:
I win
I don't win
>How many of them are there?
2
>In how many do I win?
1
So what's the probability?
1/2

brb, buying a lottery ticket.

Anonymous at Mon, 1 Jul 2024 10:28:33 UTC No. 16262700

>>16262697
Not equally likely. We assume boy/girl is equally likely.

Anonymous at Mon, 1 Jul 2024 10:32:27 UTC No. 16262703

>>16262700
>We assume
No. (You) assume that.

Anonymous at Mon, 1 Jul 2024 10:37:58 UTC No. 16262706

>>16262703
The original poster of the reply chain assumed that here >>16262575.
>>16262689
3/7 according to >>16262575, you can substitute (showered/not showered) for (france/not france).
Whether it's a reasonable model you can decide for yourself, but this is how the riddle was asked (and is usually asked).

Anonymous at Mon, 1 Jul 2024 10:41:20 UTC No. 16262708

>>16262706
Assumed what?

Anonymous at Mon, 1 Jul 2024 11:47:12 UTC No. 16262739

>>16262021
define mainstream. Anyways, try to come up with a good cohomology theory of derived stacks please and thanks

Anonymous at Mon, 1 Jul 2024 16:15:01 UTC No. 16262951

need ideas on how to solve there

Anonymous at Mon, 1 Jul 2024 16:19:58 UTC No. 16262961

>>16262951
Your lecture notes will almost certainly just have the answer. Look at them.

Anonymous at Mon, 1 Jul 2024 17:35:33 UTC No. 16263027

Am i right? >>16262939

Anonymous at Mon, 1 Jul 2024 17:47:44 UTC No. 16263045

Is Soft Logic a meme?

Anonymous at Mon, 1 Jul 2024 18:35:14 UTC No. 16263090

>>16263027
no. Langlands is incredibly arcane and complicated and very few people can precisely state what they are doing.
tl:dr
>normal langlands noticed a correspondence between some arithmetic shit and some other arithmetic shit with a slightly more geometric flavor
>too bad it's really fucking difficult to figure out what's going on
>this got the number theorists with their panties all in a twist
>as per usual when the number theorists don't know what they're doing, they turn to the algebraic geometers to solve their problems for them
>enter geometric langlands
>turns out a lot of the arithmetic shit the number theorists cared about in the first place looks very similar to some actual geometric shit and you can rephase the original correspondence to be more geometric
now it looks like the geometric version of problem has been largely solved by a pretty reputable dude, but of course it's so fucking complicated it will likely take at least a year of review before we're sure his proof is correct

Anonymous at Mon, 1 Jul 2024 20:01:59 UTC No. 16263202

>>16262951
>where [math]|\cdot|[/math] denotes Lebesgue measure
Cursed.

Anonymous at Mon, 1 Jul 2024 20:05:25 UTC No. 16263208

>>16263202
There are no such things as CURSES douchebag.

Anonymous at Tue, 2 Jul 2024 01:09:15 UTC No. 16263595

>>16263045
It is a meme, but it also isn't a meme

Anonymous at Tue, 2 Jul 2024 05:44:02 UTC No. 16263877

nobody will ever know this but I think I finally helped solve basically all cancers. It will probably be another 3-5 years but I finally did it.

they starved me, ambushed me, took away my ability to eat. they mocked me and tried to drive me insane, and yet I still found a way to save them. I will not be able to stay alive for much longer but alas, I have won. I finally found a way to save them and by pass the shitty logic that was prevalent in cancer research.

I never got anything for it but shit. No matter what I tried to do, my life only got worse. I can die knowing that I saved beings that do not deserve to be by my side. They destroyed the only being that ever actually loved them, lol.

>ghosto
>code name: eye of sauron
>Ascendancy: Transcendent
>Logic: infinite
>Supremacy: Totality

gg universe, I finally won.

Anonymous at Tue, 2 Jul 2024 10:56:13 UTC No. 16264177

>>16241233
>I'm trying to understand why we get the signs in the boundary homomorhpishm in simplicial homology:
>∂([v0,...,vn])=∑k(−1)k[v0,...,vk^,...,vn]
>∂
>(
>[
>v
>0
>,
>.
>.
>.
>,
>v
>n
>]
>)
>=
>∑
>k
>(
>−
>1
>)
>k
>[
>v
>0
>,
>.
>.
>.
>,
>v
>k
>^
>,
>.
>.
>.
>,
>v
>n
>]
>hatcher says that these signs count the induced orientation on the kth face of the standard n simplex and that this is just obvious.
>why is it obvious that the face we get when we remove the kth vertex inherits the orientation corresponding to (−1)k
>(
>−
>1
>)
>k
>?
I'm trying to understand why we get the signs in the boundary homomorhpishm in simplicial homology:
∂([v0,...,vn])=∑k(−1)k[v0,...,vk^,...,vn]

hatcher says that these signs count the induced orientation on the kth face of the standard n simplex and that this is just obvious.
why is it obvious that the face we get when we remove the kth vertex inherits the orientation corresponding to (−1)k
?

i fink cause you work in an 3d static field.

Anonymous at Tue, 2 Jul 2024 13:05:45 UTC No. 16264276

>>16262961
Yeah these are quite obviously not lecture notes

Anonymous at Tue, 2 Jul 2024 14:32:30 UTC No. 16264341

>>16242250
as my land wanst able anymore tu stustain the supply lines

Anonymous at Tue, 2 Jul 2024 14:57:26 UTC No. 16264363

If an "n-perfect number" is defined as a number so that the sum of its divisors is equal to n-times that number, does an n-perfect number exist for any positive integer n (n>1)?

Anonymous at Tue, 2 Jul 2024 15:23:41 UTC No. 16264390

>>16264363
Do you mean proper divisors? I don't have time right now, but my guess is no, and AM-GM might be helpful to show it.

Anonymous at Tue, 2 Jul 2024 15:36:36 UTC No. 16264401

>>16264390
No I mean all divisors. I just watched a numberphile video about it.

For example, the divisors of 30240 add up to four times that number which includes the numbers 1 and 30240. So 30240 is one example of n=4. It made me wonder if at least one example exists for any n.

Anonymous at Tue, 2 Jul 2024 16:33:19 UTC No. 16264474

>>16241381
Science is pseudoscience

Anonymous at Tue, 2 Jul 2024 16:53:19 UTC No. 16264502

>>16264363
As far as I can tell, we don't know.
We know an example for everything up to 11 (the first 11-perfect number being 1907 digits long, discovered in 2001), but nothing beyond - though it was shown in 2008, at least, that we haven't missed any examples below [math]e^350[/math] for any multiplicity.

You might find this page to be of interest, though.
https://wwwhomes.uni-bielefeld.de/achim/mpn.html

Anonymous at Tue, 2 Jul 2024 16:57:52 UTC No. 16264508

>>16254806
15:30 in the train of thought begins
-1:27:57 the name drop
https://youtu.be/npcmIC-I7Ec?si=BdhQC6XHP9JOU0h0

Anonymous at Tue, 2 Jul 2024 16:59:19 UTC No. 16264511

Hi anons, is anyone here familiar with machine learning?

Anonymous at Tue, 2 Jul 2024 17:22:33 UTC No. 16264545

>>16264511
Somewhat

Anonymous at Tue, 2 Jul 2024 17:26:29 UTC No. 16264549

>>16264511
Everything you need to know is right here https://dontasktoask.com/

Anonymous at Tue, 2 Jul 2024 17:33:26 UTC No. 16264558

>>16264545
I'm struggling a bit with supervised ML.
I know there's no way to figure out an ideal model training pipeline for a given dataset, especially as the number of vectors scales up. But generally speaking, how do you know whether to use a specific method to train a baseline model? Is it just guesswork?
I'm working on a model right now, I've cleaned up my data, split my variables, but I don't know whether I should be using logistic regression, a decision tree, if I should include a grid search at some point, or whatever. I haven't been doing this for long but I'm getting the impression that people just throw shit at the wall until it sticks and there's no real methodology.

Anonymous at Tue, 2 Jul 2024 17:38:33 UTC No. 16264567

>>16264558
> I haven't been doing this for long but I'm getting the impression that people just throw shit at the wall until it sticks and there's no real methodology.
There are specific methods or models that work better for different problems, but instead of making a reasoned argument about which one is best for your dinky use case no one cares about it’s much cheaper in time and effort to just try all of those and see which performed best for that dataset.

Anonymous at Tue, 2 Jul 2024 17:42:48 UTC No. 16264572

>>16264567
Alright, guess I'll do that, thanks.
I can't stand not understanding why something works though. I feel like a retard just shoving data into pipelines and transformers without really getting how or why it works.

Anonymous at Tue, 2 Jul 2024 17:50:52 UTC No. 16264588

>>16264558
I wouldn't recommend trying to train a new base model at this point, they cost way too much compute, fine-tuning is much more efficient. You don't need to worry too much about data cleaning, quantityis more important as long as it's a format that looks close enough to stuff that could have appeared in Common Crawl.

Anonymous at Tue, 2 Jul 2024 17:57:00 UTC No. 16264601

>>16262951
Idk, i dont do math. Have you tried out starting with the def of a limit? What do you have so far? Anything involving epsilon?

Anonymous at Tue, 2 Jul 2024 17:58:28 UTC No. 16264603

>>16264588
I haven't gotten into fine tuning preexisting models yet. All I'm doing for now is taking a dataset, identifying a target variable and figuring out how to reliably make predictions for the test set. Really basic shit. For any real project I'll definitely follow that advice though.
>You don't need to worry too much about data cleaning
What if my dataset is (fairly) small? Cleaning noticeably improves my F-score. Although you're right in that it's a shitty toy model and won't ever be used for anything practical

Anonymous at Tue, 2 Jul 2024 18:07:06 UTC No. 16264615

>>16262951
Why did you only post 3 exercises. I get that one of the exercises has 5 different parts, but if you want any help you should post at least a whole chapter's worth of exercises, if not the whole book. Also, you should ask us to summarize the whole material for you, not just do the exercises for you.

Anonymous at Tue, 2 Jul 2024 19:11:06 UTC No. 16264740

>>16264588
You didn’t understand his question at all, you just parroted some shit you hear from Nvidia’s marketing materials. I bet you have a “degree” in “machine learning” or “data science”. Please leave /mg/, mathematicians actually examine the claims they’re making before spouting them

Anonymous at Tue, 2 Jul 2024 19:15:00 UTC No. 16264756

I came up with a math problem that I think is one of the hardest problems ever. Here's how it goes.

Pick three (uniformly) random points inside a circle, connect them with lines to create a triangle. Do the same thing again to create another triangle. The problem is as follows: what is the probability that the region where the triangles overlap is an irregular hexagon?

Anonymous at Tue, 2 Jul 2024 19:25:23 UTC No. 16264784

>>16264756
Isn’t the probability 1?

Anonymous at Tue, 2 Jul 2024 19:25:29 UTC No. 16264786

>>16264756
I came up with an even harder math problem:
Take the first 10^10^10 decimal digits of pi. Are at least 90% of them 1?

Anonymous at Tue, 2 Jul 2024 19:35:11 UTC No. 16264801

>>16264784
Most definitely not

🗑️ Anonymous at Tue, 2 Jul 2024 19:41:00 UTC No. 16264808

>>16264801
Not sure what your picture is trying to show but the probability is definitely 1. Regular hexagons are measure zero in the space of all hexagons with any reasonable metric.

Anonymous at Tue, 2 Jul 2024 19:46:58 UTC No. 16264818

>>16264756
Well, the chance of a perfect hexagon is technically zero since the coordinates are indiscrete. So you basically have to find the conditions for any hexagon, right?

Anonymous at Tue, 2 Jul 2024 19:47:27 UTC No. 16264820

How many of my fellow autists did the upgrade?

https://www.youtube.com/watch?v=U04wFOnbR5Y

grayish blue bezel doesn't look as sleek, but you can't argue with those features.

Anonymous at Tue, 2 Jul 2024 19:49:09 UTC No. 16264822

>>16264818
Yes

Anonymous at Tue, 2 Jul 2024 19:50:30 UTC No. 16264824

>>16264801
Ok thanks I’m an idiot

Anonymous at Tue, 2 Jul 2024 19:52:08 UTC No. 16264828

>>16264820
I was looking into calculators a few years ago, but I realized there’s nothing they do that my smartphone can’t do a million times better

Anonymous at Tue, 2 Jul 2024 20:15:15 UTC No. 16264865

>>16264822
I think I'm getting there. We can lengthen the first triangles' sides to cut the circle into 7 different sectors: 1 Triangle, 3 edge sectors and 3 corner sectors, all in which the next three points can fall. Only two outcomes produce a hexagon: T,E,C (with no neighbouring sectors) and E,E,E. The next bit is tricky, I'll look at it tomorrow.

Anonymous at Tue, 2 Jul 2024 20:38:08 UTC No. 16264902

>>16264828
I can't use my smartphone at work, outside of a few areas. In any case, the convenience of the C47 overwhelms whatever a phone can put out. I've even started to phase most of my MATLAB and R use.

Anonymous at Tue, 2 Jul 2024 21:21:25 UTC No. 16264967

>>16264902
>I can't use my smartphone at work
Wtf, where do you work at?

Anonymous at Wed, 3 Jul 2024 01:42:10 UTC No. 16265260

>>16264902
>>16264967
Yeah that’s a really odd work restriction. With my cellphone I have the SAGE app which is a full blown CAS and I also have Juno which is a Python notebook environment with the whole numpy scipy and sympy stack available

Anonymous at Wed, 3 Jul 2024 15:21:58 UTC No. 16266065

Why is "r" is conventionally used for parametrically-defined space curves?

Anonymous at Wed, 3 Jul 2024 15:30:20 UTC No. 16266082

>>16266065
Because it's the radial vector from the origin to the point in question

Anonymous at Wed, 3 Jul 2024 15:41:48 UTC No. 16266096

>>16266082
ahah! Thank you

Anonymous at Wed, 3 Jul 2024 21:21:22 UTC No. 16266647

>>16262951
What book is this? I wanna read it

Anonymous at Wed, 3 Jul 2024 22:07:16 UTC No. 16266745

My third year of my PhD has turned me into an alcoholic. I have given most of my recent lectures hungover. My research productivity has plummeted but my teaching reviews have shot through the roof. Any anons relate?

Also respond with your favorite algebra. The integral heisenberg algebra is kino.

Anonymous at Wed, 3 Jul 2024 23:33:46 UTC No. 16266864

>>16248524
It's over the moment they get a general intelligence AI. It would probably lead to societal collapse

Anonymous at Thu, 4 Jul 2024 00:23:29 UTC No. 16266918

Am I dumb if I think Blitzer’s books are the best way to learn Maths?

Anonymous at Thu, 4 Jul 2024 03:55:11 UTC No. 16267162

>>16266745
Nice I didn’t start doing that until it was clear that I wasn’t getting a postdoc position.

Anonymous at Thu, 4 Jul 2024 13:37:07 UTC No. 16267583

Are time series stochastic processes?

Anonymous at Thu, 4 Jul 2024 18:41:09 UTC No. 16267911

>>16240472
Hey bros, can someone recommend a good problem book for a applied math grad who wants to get back into things?

Anonymous at Thu, 4 Jul 2024 19:38:03 UTC No. 16267983

>the exact question you have is on stackexchange
>no answers

Anonymous at Thu, 4 Jul 2024 20:25:54 UTC No. 16268048

>>16267983
Post the link.

Anonymous at Thu, 4 Jul 2024 23:08:29 UTC No. 16268201

Was watching Programming Should Be Fun by Sussman (who wrote SICP), and he was encouraging people to think with code. He gave the example that really resonated with me: mathematical formulas have tons of hidden, implicit types and rules. Formulas themselves are incomplete to convey what they are tyring to say. I struggle a lot going back and forth trying to find these missing parts to understand what it is doing.

Anonymous at Fri, 5 Jul 2024 01:40:18 UTC No. 16268326

In K theory, what the hell does it mean that the isomorphism classes of Vector bundles form a set? This is just stated in all the references I've seen but this clearly cannot be true. If that is a set so it is the union which just gives you the original class.

Anonymous at Fri, 5 Jul 2024 01:54:13 UTC No. 16268335

>>16268201
That is stupid as fuck. Programmers only think that math is vague because they are autistic and effectively illiterate; instead of reading/writing the preceding and succeeding paragraphs to gain clear context, they choose to invent this absurdly complicated notation that no reasonable person would waste his time to remember.

Anonymous at Fri, 5 Jul 2024 02:19:23 UTC No. 16268353

>>16264558
What do you mean by training? If you have a baseline model why are you not sure if you want to use logistic regression or a decision tree? Fucking ML lingo is so fucking retarded.
But well if you are still trying to define the model, OBVIOUSLY you need to understand what the fuck you are trying to model. And CLEARLY there is no magic formula for this. The reason why scientists who want to actually understand what they model try to use the least number of parameters they can is because they want to actually know what those parameters represent. What I can tell you is that to avoid an over fitted mess you have to see what you are trying to do and try and find the model that seems to best adapt to this. If you know some math, you will see that the typical models are basically the simplest shit you can come up with by just understanding the problem. Even transformers are not really that complex.
If you mean you already have a model and just want to know what algorithm to use, this is just understand that the usual optimizer are already kinda complex and it is kinda difficult to get a grasp on what is happening. So yeah test test and test.
People have to understand that modern ML is kinda the most naive solution one could consider and it is literally just possible to do the amount of data and computer power available. This means the actual theory is basically glorified regression, and everything else is will be model dependent.

Anonymous at Fri, 5 Jul 2024 15:21:08 UTC No. 16269026

>>16268335
That notation is the actual definition of it in math notation. It is absurdly complicated because standard math notation is clumsy and unprecise. The version in lisp is very clear if you understand even a bit of lisp.

>can't read the preceding and succeeding paragraph
That's the point. Math formulas are not descriptive, they are really *abbreviations*, abbreviated by complex, arbitrary and hidden rules. Another example is calculus. The d is an entirely different type than an algebraic variable obeying its own rules. But this fact is almost entirely glossed over, and even in famous texts like Spivak the rules of this type is never explained clearly. The hope is that learners will learn by trial and error that you, for example, can't cancel a d in the numerator and denominator. Then you stack on how these symbols might mean something else entirely in adjacent contexts and it gets worse.

Anonymous at Fri, 5 Jul 2024 15:44:12 UTC No. 16269055

>>16268201
>mathematical formulas have tons of hidden, implicit types and rules. Formulas themselves are incomplete to convey what they are tyring to say.
Yes, definitely. There's a lot of overloading of operators and functions, as well as ambiguity and some stuff simply meaning different things in different contexts. It's definitely not perfect, and I recall myself being very tripped up with partial derivative notation as in your first picture a long time ago.
Ultimately I do think it's a positive, simply because so much math is written by hand and read from books that it's nice to have the most compact notation, even at the expense of the reader having to spend some time parsing what equations are actually saying. There is consistency.
>>16268335
It's funny, I recall some anon insisting that sigma notation for sums was silly and unclear, and wanting math to be written as computer programs instead. https://warosu.org/sci/thread/15054168#p15054183
>>16269026
>It is absurdly complicated because standard math notation is clumsy and unprecise.
It certainly is, and it's unlikely to change because most math people are used to it already. A good author would have defined anything that is ambiguous or conflicting in the text before the equation.
While the formula in functional notation is clearer. Can you imagine trying to write anything complicated in that way? It'd be illegible, because there's no nice indenting, syntax highlighting or curly brackets helping understand what the formula is saying as there are in computer code.
>The hope is that learners will learn by trial and error that you, for example, can't cancel a d in the numerator and denominator.
Not really, and if it is you have a shit teacher or book. It should be explained that it is ''just notation''.

I really like SICP, by the way.

Anonymous at Fri, 5 Jul 2024 15:46:57 UTC No. 16269058

Is there an FAQ for this general? I am an undergrad and want to know how to continue with one math track in particular as I have exhausted it at my school.

Anonymous at Fri, 5 Jul 2024 16:06:22 UTC No. 16269091

>>16268326
It means that there is a set of representatives from every isomorphism class. I know this and I don't even know K-Theory.

Anonymous at Fri, 5 Jul 2024 16:06:51 UTC No. 16269094

>>16262021
What kind of stuff do you like?
>>16269058
What field?

Anonymous at Fri, 5 Jul 2024 16:28:56 UTC No. 16269122

>>16267162
>>16266745
How does one cope with not making it in academia? I went to codemonkey in finance immediately after finishing my math undergrad and I'm pretty comfy. Reading math stuff on the side when I get home after work. Can't imagine being able to tolerate the cut throat environment and low pay of academia, especially with such a large and talented competition pool.

Anonymous at Fri, 5 Jul 2024 16:37:22 UTC No. 16269130

>>16268201
>>16269026
math is meant to be read by humans, not computers (or low functioning autists, i.e. human computers)
>The hope is that learners will learn by trial and error that you, for example, can't cancel a d in the numerator and denominator. Then you stack on how these symbols might mean something else entirely in adjacent contexts and it gets worse.
the hope is that learners will show up to class and learns the meaning of the notation from the instructor

Anonymous at Fri, 5 Jul 2024 17:45:14 UTC No. 16269215

Thoughts?

Anonymous at Fri, 5 Jul 2024 17:53:08 UTC No. 16269219

>>16266745
>My third year of my PhD has turned me into an alcoholic.
happens to everybody

Anonymous at Fri, 5 Jul 2024 17:58:21 UTC No. 16269226

>>16269055
>some anon insisting that sigma notation for sums was silly and unclear, and wanting math to be written as computer programs instead.
those retards don't do math so their opinion can be discarded the moment it is uttered. Verbitsky was right about people losing the plot

Anonymous at Fri, 5 Jul 2024 18:05:10 UTC No. 16269237

>>16269226
>Verbitsky was right about people losing the plot
Quote?

Anonymous at Fri, 5 Jul 2024 18:13:58 UTC No. 16269253

>>16268201
>>16269026
I do love Sussman, but this isn't a great point to bring up, because human brains are very good at handling ambiguity. We don't need to and shouldn't write like computers, because we don't have the same weakness that computers do.

Anonymous at Fri, 5 Jul 2024 18:31:41 UTC No. 16269276

Anyone here read through this book? It seems like RL doesn't get much attention these days

Anonymous at Fri, 5 Jul 2024 18:38:02 UTC No. 16269282

>>16269276

Anonymous at Fri, 5 Jul 2024 18:46:33 UTC No. 16269293

>>16269091
ok what are those sets?

Anonymous at Fri, 5 Jul 2024 18:57:29 UTC No. 16269318

>>16269091
Ok how do you define that set? It is not just technicalities, operations in K theory are only really well defined for classes, or at least that is kinda the point. Also it is important to not arbitrarily fix any representative.

Anonymous at Fri, 5 Jul 2024 19:04:43 UTC No. 16269327

If an integer is possible to factor into consecutive integers in N different ways without any overlap, what are the possible values for N? And can N be greater than two?

As an example, 720 is example of N=2 (two different ways)

2*3*4*5*6 = 720
8*9*10 = 720

Anonymous at Fri, 5 Jul 2024 19:44:57 UTC No. 16269386

>>16269327
possible values for N are (0,infinity)

APPLE PIE at Fri, 5 Jul 2024 19:54:33 UTC No. 16269395

>>16240472
Prove that pi is irrational.
Oh wait, you can't.

Anonymous at Fri, 5 Jul 2024 20:06:44 UTC No. 16269410

>>16269395
Follows easily from Lindemann-Weierstrass, which I leave as an exercise for the reader.

Anonymous at Fri, 5 Jul 2024 20:19:03 UTC No. 16269419

>>16269395
Trivial, see https://www.ams.org/journals/bull/1947-53-06/S0002-9904-1947-08821-2/S0002-9904-1947-08821-2.pdf

APPLE PIE at Fri, 5 Jul 2024 20:27:06 UTC No. 16269436

>>16269410
>Lindemann-Weierstrass,
literally who
>exercise for the reader
Bold of you to assume americans exercise
>>16269419
If its so trivial then type it out yourself without looking at an article, in ten lines or less

raspberry pie at Fri, 5 Jul 2024 20:29:15 UTC No. 16269442

RATIOnal number: Number written as a RATIO
Consider circle radius h circumferance p
pi=p/2h
There, I wrote pi as a ratio of two numbers so its rational

Anonymous at Fri, 5 Jul 2024 20:37:43 UTC No. 16269461

>>16269386
How do you know? Is there a way to find examples for each N?

Anonymous at Fri, 5 Jul 2024 20:44:44 UTC No. 16269479

>>16269461
I don't know, just guessing, but perhaps a proof kinda like the no-largest-prime proof could prove it! Idk what I am talking about though lol

Anonymous at Fri, 5 Jul 2024 21:00:59 UTC No. 16269499

>>16269318
>>16269318
>Ok how do you define that set?
Scott's trick: for each equivalence class X there is a minimal ordinal such that [math]V_a \cap X[/math] is nonempty, take that [math]V_a \cap X[/math] as the representative.
>It is not just technicalities, operations in K theory are only really well defined for classes, or at least that is kinda the point. Also it is important to not arbitrarily fix any representative.
Eh, maybe. But sets are just small classes. And a collection of classes isn't even a class, it's a hyperclass, so people usually substitute in representatives when they want to deal with collections of classes

Anonymous at Fri, 5 Jul 2024 21:05:23 UTC No. 16269503

>>16269499
I was also about to talk about scotts trick but though that it doesn't really apply here as the construction is more geometric than set theoretic. AFAIU the vector bundles are finite dimensional (if their dimension is unbounded we would obviously necessarily have a proper class, since the cardinals would inject into it), so you can probably prove that for each n, n-dimensional vector bundles form a set and go from there.

Anonymous at Fri, 5 Jul 2024 22:00:54 UTC No. 16269577

>>16267583
Rarely.

Anonymous at Fri, 5 Jul 2024 22:02:24 UTC No. 16269579

>>16269094
I am looking for what comes after complex analysis. I am not a math major but simply very much enjoy this area of math.

Anonymous at Fri, 5 Jul 2024 22:03:00 UTC No. 16269580

>>16269122
> How does one cope with not making it in academia?
Depression and bitter anger, plus delusional hopes that maybe you can find meaning in corporate work, followed by even more bitter anger when you realize you can’t.

Anonymous at Fri, 5 Jul 2024 22:03:44 UTC No. 16269581

>>16269579
Look into Harmonic Analysis, if you like Complex Analysis specifically

APPLE PIE at Fri, 5 Jul 2024 22:56:39 UTC No. 16269638

>>16269327
>>16269327
SOMEONE ANSWER HIM (NOT EVEN ME)

Anonymous at Fri, 5 Jul 2024 23:20:12 UTC No. 16269673

>>16269055
Programming also is compact with function definitions. Definitions are still explained with words with precise jargon put in to try and remove ambiguity. My gripe is both that the symbols do a very poor job of reflecting different types, return values and other manipulations. In a sense it's possible math is long overdue for a new interpreter. Most of the syntax of math is based on the algebraic equation balancing of the Arabs, who were solving quadratic and other such things. It in itself was a huge leap, before that equations were expressed in words like, let y equal the value of x + 1 multiplied by x + 1. The equation notation was a cognitive tool that enormously magnified mathematical ability and knowledge transfer. Maybe math now is infinitely more complex and needs another leap forward.

It's entirely possible to learn with current notation, in the same way it was possible to learn Algebra with words. It's just it's probably possible to invent something better. Syntax should reflect the nature of what it describing.

Anonymous at Fri, 5 Jul 2024 23:22:04 UTC No. 16269679

>>16269130
Code is read by humans too.

>show up to class
Yes no doubt students eventually learn, but they only grasp that specific quality of it by punishment - they don't know what it is really, just that you can't divide it like variables. But as a tool for thinking it is enormously bad.

Anonymous at Fri, 5 Jul 2024 23:23:36 UTC No. 16269682

>>16269253
Human brains ingest and produce a huge amount of ambiguity, which is why we struggle with math. It's not just ambiguity, it's about the beauty of math. Math needs a way to express it beautifully and elegantly. Can you imagine if we described formulas with words like they used?

Anonymous at Fri, 5 Jul 2024 23:42:20 UTC No. 16269694

>>16269094
>What kind of stuff do you like?
My favorite topics are Linear Algebra and Metamathematics.

>>16262739
>define mainstream
Those that have far more books related to them (like Algebraic Geometry compared to Knot Theory) and usually more people doing research on them.

Anonymous at Sat, 6 Jul 2024 03:34:31 UTC No. 16269914

so i've recently learned that I love math so i've been working my way through gelfands algebra over a bit
there was a question that I got the answer for, but it took a bit, and I have some questions
it was find every parentheses permutations of 2 * 3 * 4 * 5 * 6, I want to know if there is an equation to find how many permutations there are, the question of the problem wasn't how many, but to write out each one, which I did. I'm just really curious if there's an equation for this, and if so explain it to me as if i'm braindead

raspberry pie at Sat, 6 Jul 2024 04:39:57 UTC No. 16269961

>>16269914
Are you just asking how many orders 2,3,4,5,6 can be written in?
There are five terms, all unique. You can choose any one of the five as the first term. After choosing the first term you have four remaining to choose from for your second term. And so on. So given five terms, all unique, they can be ordered in 5x4x3x2x1 ways (aka, 5! ways) which is 120.
Sorry if not what you are asking

Anonymous at Sat, 6 Jul 2024 05:28:39 UTC No. 16269999

>>16269579
sheaf theory, complex algebraic geometry

Anonymous at Sat, 6 Jul 2024 05:44:05 UTC No. 16270013

>>16269579
More complex analysis. The subject is vaster than the concepts of a typical first or even second university course on the subject. See Segal's "Nine Introductions in Complex Analysis" for further topics and Hayman's "Research Problems in Function Theory" for some idea on the current state of research.

Anonymous at Sat, 6 Jul 2024 06:03:53 UTC No. 16270035

>>16269679
I am convinced that you either have never actually read a math text, or you're just severely retarded. You seem to have a view of math based on how high school teachers teach it, and can't fathom that math is anything different to that.

Anonymous at Sat, 6 Jul 2024 08:24:15 UTC No. 16270070

>>16269679
>they only grasp that specific quality of it by punishment - they don't know what it is really
they learn it the same way you learn language rules - by seeing how it is used and using it yourself. Humans are good at this type of thing where you have unclear and arbitrary language rules but you can still use the language correctly (or mostly correctly) even if you don't explicitly know the rules. In fact, we are much better at this than things like code where there is only one rigid way of using the language with a ruleset you absolutely have to know

Anonymous at Sat, 6 Jul 2024 08:24:44 UTC No. 16270071

>>16269130
>low functioning autists
Low functioning autists aren't reading jack shit, let alone math stuff lol

Anonymous at Sat, 6 Jul 2024 13:02:17 UTC No. 16270262

>>16269961
Not what I meant, I think I was vague so i'll elaborate
Examples of what I mean:
2(3(4(5*6))), (((2*3)4)5)6, etc
is there a way to calculate how many different ways parentheses could be used in a problem?
not like 2 * 3 * 4 * 5, ..., 98, 99 = 194 instances of ( or ), but I'm just curious if there's a way to calculate how many permutations of the parentheses in a problem
and the order isn't changing on the numbers we're multiplying, should've said that as well.

Anonymous at Sat, 6 Jul 2024 14:12:23 UTC No. 16270318

>>16269581
Thanks, my school offers this not exclusively to grad students, but does not make it very clear what it is. This one is actually very relevant to what I actually do.

>>16269999
Thanks I will look into those, but probably not now.

>>16270013
My school only offers two courses on complex analysis. I will need to self-study if I want to go further with it. Ironically though it is super relevant for grad students in my field. Not sure why so little emphasis is placed on it.

Anonymous at Sat, 6 Jul 2024 14:33:30 UTC No. 16270344

>>16269638
Sorry I’m an analysist

Anonymous at Sat, 6 Jul 2024 15:29:31 UTC No. 16270388

>>16269694
If you like linear algebra, you can look into error correction codes. For example, Reed–Solomon codes are the reason why CDs work even with some scratches. You could also look into information theory.

Anonymous at Sat, 6 Jul 2024 15:49:34 UTC No. 16270408

>>16270388
Thanks, anon. Will give those topics a try.

Anonymous at Sat, 6 Jul 2024 16:50:38 UTC No. 16270456

>>16270262
catalan numbers

Anonymous at Sat, 6 Jul 2024 17:30:15 UTC No. 16270495

>>16270035
If you aren't just pretending to be retarded, this isn't about education. It's about writing as a way of thinking/cognitive tool, of which teaching is just a downstream effect. There are many other examples like the partial derivative of the Lagrangian or the notation for the ring of p-adic integers.
>>16270070
>we're much better at this
No, we're not. You can learn the structure of Lisp and use it in ten minutes. If you tried to learn a language with a different grammar it'd take years. Programming syntax is the result of a handful of syntax rules applicable universally.

The specific quality you'd have to prove is not just that we are good at it, but better understanding it than having a few strict rules. This is of course nonsensical - if it's true, why don't we return to using words to describe algebraic equations?

Anonymous at Sat, 6 Jul 2024 18:04:28 UTC No. 16270535

>>16270495
>The specific quality you'd have to prove is not just that we are good at it, but better understanding it than having a few strict rules.
no, the specific quality in question here is that we don't need the extremely verbose syntax with strict rules. A little ambiguity makes things much easier to read and write, everyone can figure out what you mean from the context.

Anonymous at Sat, 6 Jul 2024 18:33:01 UTC No. 16270564

>>16270495
>the notation for the ring of p-adic integers.
???

Anonymous at Sat, 6 Jul 2024 21:05:44 UTC No. 16270734

>>16270495
Focus on passing your exams first, my undergrad friend ;)

Anonymous at Sat, 6 Jul 2024 21:10:50 UTC No. 16270743

>>16270495
>low functioning autism: the post

Anonymous at Sun, 7 Jul 2024 07:01:21 UTC No. 16271197

>>16270495
>There are many other examples like the partial derivative of the Lagrangian or the notation for the ring of p-adic integers.
Both of which are very clearly and unambiguously established when they are introduced. You would understand this if you were literate.

Anonymous at Sun, 7 Jul 2024 07:37:48 UTC No. 16271238

New >>16271237

Anonymous at Mon, 8 Jul 2024 20:38:28 UTC No. 16273197

Is it difficult to get into applied math Ph.D programs if I have a master's in pure math (one publication in homotopy theory)? I'm thinking of working in numerical PDE or some kind of numerics so I can bail into industry for a decent paying job if I have to.

I want to keep going down the pure math path (really like model theory) and I think I'm good at research, but I'm a slightly older student and I don't really want to be 40 still depending on my parents.