/mg/ - math general

[Anonymous No.11252098]

300k won't solve this edish

[Anonymous No.11252115]

>>11252098
Actually very interesting!

[Anonymous No.11252227]

>In the first chapter author introduces Gamma/Beta functions and proves their properties
>In the second chapter he introduces sets
Why do authors do this?

[Anonymous No.11252520]

>>11252227
What textbook are you talking about?

[Anonymous No.11252618]

Your image is flawed. Length 0 implies angle red/blue and green/blue are the same point. Assuming green/red is a 90* angle, side blue would be the hypotenuse, requiring it to be the longest side.

It's a play on A^2 + B^2 + C^2. i^2 = -1. 1^2 = 1. The sum of which is 0. Issue being, negative distances are just distances which are measured and displayed in the wrong direction. Moving forward -2 units is actually moving backwards 2 units. Distance "i" should be going below the X axis, assuming angle red/green is at 0/0.


Also; the green/blue lines don't connect, so its not a triangle in the most pedantic sense.

[Anonymous No.11252641]

>>11252227
If you want people to read your book it helps to open with something interesting rather than opening with a mind-numbing list of definitions that everybody just skips anyway

[Anonymous No.11252682]

>>11252227
>Why do authors do this?
>authors
name 343 books that do this

[Anonymous No.11252872]

>>11252618

it's an abstraction

[Anonymous No.11252902]

my frend came up with this:
>obi-van der waerden
funny right? lmaooo

[Anonymous No.11252982]

>>11252902
I don't think anybody thinks that.

I found that Chrysippus (from the "allegedly died of laughter" meme image) had some neat logic even 200 BC.
https://en.wikipedia.org/wiki/Chrysippus#Conditional_propositions

The last primitive in that table is a "more likely" expression. I wonder if that can be captured by a subjective logic approach, which are also cool but virtually unknown afaik, one modern formal one being
https://en.wikipedia.org/wiki/Subjective_logic

I wonder if there'd be any merit of breaking up your logic to take into account those thing, e.g. as in time-dependent modal logics, as in
https://en.wikipedia.org/wiki/Temporal_logic#Temporal_operators

or whether those things are best kept for math _written in_ that logic. I.e. I wonder if you should keep your logic slim and mathematical axioms characterize your math, or whether it might be worth a try to have a more bloated logic

For what it's worth, I also came across this
https://arxiv.org/abs/1408.3901
>A countable definable set of reals containing no definable elements
scary

[why so violent No.11252986]

>>11252982
PS this book makes me dislike the Romans more

[Anonymous No.11252988]

>>11252520
Probability and Information
an integrated approach
David Applebaum

[Anonymous No.11253124]

>>11252115
I don't think Euclidean geometry is well modeled by a vector space over a field extended with the imaginary i.

Although that makes me wonder, is there anything bad about a variant of Euclidean geometry using all the algebraic numbers [math] \hat Q [/math]?

[Anonymous No.11253128]

how do I learn trigonometry fast (~3 weeks)?

[Anonymous No.11253129]

>>11252982
why won't you do actual math instead of logic wankery

[Anonymous No.11253130]

That was supposed to become [math] \bar Q [/math]

[Anonymous No.11253150]

>>11253129
It's all wankery at the end of the day.

Down at the bottom, there's some pretty creatures literally inaccessible to the folks who've unknowingly have indirectly postulated their non-existence through adopting axioms that seemed convenient to 1920's Germans who found them to be convenient at the time.

That said, I've recently become friendly with
https://en.m.wikipedia.org/wiki/Goormaghtigh_conjecture
and cooked up some descriptions of the problem that are pleasently geometry.

What you You up to?

[Anonymous No.11253354]

Give me the coomutative algebra meme

[Anonymous No.11253382]

>>11253354
Here.

[Anonymous No.11253383]

>>11253382
And here's a garbage edit I made in ten minutes.

[Anonymous No.11253397]

>>11253382
>>11253383
谢谢你们

[Anonymous No.11253810]

>>11253383
>>11253382
hello plebbit

[Anonymous No.11253821]

>>11253383
>reads "ring" as "associative, commutative and noetherian ring with identity"
Objectively correct, aside from the noetherian bit

[Anonymous No.11253881]

do you ever feel like you are torturing numbers?

[Anonymous No.11253903]

This image has been posted for a few weeks now, yet /sci/ still can't properly refute it. Mathfags are truly pathetic.

[Anonymous No.11253929]

>CS BS + Math BA - 126 credits
>CS BS + Math BS - 137 credits
I don't think I can do the double BS, bros

[Anonymous No.11253956]

>>11253929
nobody care

[Anonymous No.11253963]

>>11253956
I do

[Anonymous No.11253965]

>>11253929
it's ok if you have a cs major nobody will take the math major seriously anyways

[Anonymous No.11253987]

>>11253903
no one gives a shit, but i can explain it. the pythagorean theorem is the R^n case of a simple result on arbitary inner product spaces: if <u, v> = 0 then <u, u> + <v, v> = <u + v, u + v>. the inner product on C^n is not "just multiply the values and sum", this is not an inner product because it is not conjugate symmetric. rather, the inner product is "multiply one by the conjugate of the other and sum," provably one can write every possible inner product as a matrix which acts similarly, and so the pythagorean theorem will always involve multiplying numbers by their conjugates, not by themselves.
this, of course, holds in the real case since real numbers are their own conjugates.

[Anonymous No.11254015]

>>11253987
explain to the folks at home what a conjugate is

[Anonymous No.11254019]

>>11254015
it's what you do to your wife on your wedding night

[Anonymous No.11254055]

>>11253821
>all rings are coomutative
>matrices don't form a ring

Are you some hardcode alg. geom. weeb?

>>11253903
it's been pointed out in this very thread, the Pythagorean theorem isn't a result involving vector spaces over C. If you work with a Hilbert space, then you gotta take the norm. The unit i isn't a length.

[Anonymous No.11254073]

post some cuties

[Anonymous No.11254118]

when would you ever use continuous compounding interest instead of daily, monthly, etc?

[Anonymous No.11254136]

>>11254015
You don't know what a complex conjugate is? Do you know what a complex number is?
The complex conjugate of a+bi is a-bi.
The reason we need a conjugate when we take an inner product is because for any complex number z, its modulus (distance from zero) is sqrt(z*conjugate(z)).

[Anonymous No.11254141]

>>11254118
You probably wouldn't, but literally hundreds of phyical and biological phenomena do (in the sense that the amount they increase in a time step is proportional to their value at that time). Take any kind of population growth.

[Anonymous No.11254144]

when would you ever use continuous compounding interest instead of daily, monthly, etc? it doesn't return the same as compounding it daily.

[eqn]
10000(1+\frac{0.03}{365.2425})^{365.2425(5)} = 11618.27 \\
10000e^{0.03(5)} = 11618.34
[/eqn]

[Anonymous No.11254151]

>>11254141
I guess my question is what defines the time step? It seems to be arbitrary without otherwise defining it.

[Anonymous No.11254167]

>>11254151
There is no set time step, I just mean if you take a small time step your growth is approximately proportionate to the size of your object. Continuous growth is usually a (very accurate) approximation of a system which compounds with a very small time step relative to the time frame.

[Anonymous No.11254175]

>>11254151
>>11254167
Just adding to this, if you know what a derivative is, continuously compounded growth is the same as saying "derivative equals a multiple of value"
A continuously compounded quantity y satisfies the differential equation dy/dt = cy, where dy/dt is the rate of change of y. c can be any constant (if you want growth, c > 0). For interest, c will represent the interest rate. This is the most fundamental differential equation and every other differential equation starts there (and so almost every other physical/chemical/biological system)

[Anonymous No.11254250]

>>11252902
Actually I came up with that and your "frend" lied to

[Anonymous No.11254320]

>>11254250
you

[Anonymous No.11254386]

What are the best textbooks for someone getting into calculus?

[Anonymous No.11254394]

>>11254386
My school uses pic related

[Anonymous No.11254404]

>>11254394
Is it any good and does it have gimmicky bullshit like "check on the webpage program partner for a half decent explanation"?

[Anonymous No.11254416]

>>11254404
I haven't gone through Calculus yet, but the precalculus book by the same guy is pretty good.It explains a lot of stuff fairly straightforwardly.

They also have answers for all the examples online, pre and post chapter tests online, etc. And you don't need a code for that stuff...

[Anonymous No.11254462]

>>11253987
speak english faggot

[Anonymous No.11254476]

>>11253929
Just bee urself

[Anonymous No.11254527]

whats a good book to read calculus of variations from. trying to read mechanics by landau and the calculus looks fake. help

[Anonymous No.11254545]

>>11253929
Get a cs minor and a math major

[None !niqjediPCA No.11254546]

>>11252098
who is allow'n a mother fucker this much money?

[Anonymous No.11254598]

>>11254527
>whats a good book to read calculus of variations from.
If you are in physics, you don't actually need the whole theory of calculus of variations (and shit like the Jacobi condition, for instance). You literally need only the basic stuff up to the Euler-Lagrange theorem and this can be learnt from literally any relevant source including wikipedia.
>mechanics by landau
Best book in the series honestly, it all goes downhill from there especially in QM.

[Anonymous No.11254818]

>>11254598
>it all goes downhill from there, especially in QM.
elaborate on that in some detail plz

[Anonymous No.11255022]

>>11254073

[Anonymous No.11255029]

>>11255022
Is the proposition on the t-shirt true for all n?

[Anonymous No.11255032]

>>11255029

> use wilf zeilberger

[Anonymous No.11255038]

>>11255032
Nice. The real "wilf" was Herb Wilf, at Penn State, he was a good guy, passed too soon. Doron Zeilberger is pretty much a moron Zeilberger.

[Anonymous No.11255042]

>>11254545
My options are
>CS BS - 108 credits
>CS BS, Math BS - 137
>CS BS, Math BA - 126
>CS BS, Math Minor - 117
>CS BA, Math BS - 109
>CS Minor, Math BS - 87
Since I need 120 credits to graduate anyway, I figure I might as well get the double degree. And since CS is my main interest/where the jobs are, I figure that's better for the BS.

The other option, since I live near a bunch of military contractors and there's a ton of jobs, is
>CS BS, Cybersecurity Masters - 140 credits
I don't know if that is a meme degree though. I haven't looked into it too much.

[Anonymous No.11255054]

>>11255042
No sounds good desu

[Anonymous No.11255139]

>Given a triangle ABC, and a triangulation T of the triangle, the set S of vertices of T is colored with three colors in such a way that
>
>* A, B, and C are colored 1, 2, and 3 respectively
>* Each vertex on an edge of ABC is to be colored only with one of the two colors of the ends of its edge. For example, each vertex on AC must have a color either 1 or 3.
>
>Then there exists a triangle from T, whose vertices are colored with the three different colors. More precisely, there must be an odd number of such triangles.

[Anonymous No.11255201]

>>11255042
>And since CS is my main interest/where the jobs are, I figure that's better for the BS.
I wouldn't worry too much about the math minor/major. Just focus on CS and keep up that GPA. But do keep in mind that you can break into industry with a CS minor. Also wtf
>>CS Minor, Math BS - 87
>>CS BS, Math Minor - 117
Math has less credit requirements than CS. That's like 5 or 6 classes at my school. It seems that CS is the more intensive major at your school, no?

[Anonymous No.11255217]

>>11255042
get the fuck out of the thread, retard

[Anonymous No.11255313]

>>11253987
Correct.

[Anonymous No.11255327]

Fusion systems are the shit.

[Anonymous No.11255363]

Hi all
I'm expecting a child soon, I want to give my kid a science related name.
Does Möbius sound like a good name for a girl? or is that too cringey...

xx

[Anonymous No.11255400]

>>11255363
Call her Amalie, after Amalie Emmy Noether.
It's an extremely popular reference, and also one next to no one will get, since everyone thinks her first name was Emmy.

[Anonymous No.11255402]

>>11255363
cringe

[Anonymous No.11255408]

>>11255400
dubs get names child

[Anonymous No.11255420]

>>11255363
Möbia Labia.

[Anonymous No.11255422]

>>11255408
>posting this in a slow board
Her name is Ledasha.
Check my dubs >>11255422

[Anonymous No.11255423]

>>11255422
it's actually Lea because the dash be silent

[Anonymous No.11255448]

>>11255363
Just call her Scienza or Matematica.

[Anonymous No.11255472]

>>11255363
Lifshitz or Lanlifshitz

[Anonymous No.11255480]

>>11255408

Integralina III

[Anonymous No.11255484]

>>11255363
Don't do that to your poor child

[Anonymous No.11255511]

>>11255363
if you were expecting a grumpy cat I would tell you Hausdorff

[Anonymous No.11255586]

>>11255363
Andrej

[Anonymous No.11255637]

>>11255363
Mobius is a male sounding name

[Anonymous No.11255694]

>>11255363
mobius is a dope name

[Anonymous No.11255699]

>>11255201
Yeah
>Math BA - 32 credits
>Math BS - 43 credits
>Comp Sci BA - 48 credits
>Comp Sci BS - 82 credits

[Anonymous No.11255855]

>>11255422
>>11255480
It's a joke boys and girls, the post I was replying to had dubs

[Anonymous No.11255897]

>>11253128
>Global Rule 2: You will immediately cease and not continue to access the site if you are under the age of 18.

[Anonymous No.11256157]

is trigonometry hard? never took it in hs

[Anonymous No.11256202]

Here's a fun fact: When multiplying in your heads, you do not actually count. You take the desired result from you memory. That is no way to live. I do real counting. I count and count and count. I really do.

[Anonymous No.11256209]

>>11256202
okay count

[Anonymous No.11256231]

>>11256202
quick! what is 10 000 000 * 1

[Anonymous No.11256242]

>>11256231
10

[Anonymous No.11256251]

>>11256231
that can be expressed as 1*(666*(log666(10 000 000))) * 1*(666*(log666(1)))
>>>/x/

[Anonymous No.11256253]

>>11256231
that can be expressed as (666^(log666(10 000 000))) *(666^(log666(1)))
>>>/x/

[Anonymous No.11256265]

>>11256202
Computers do it this way too, I found out. Log tables aren't just a meme.

[Anonymous No.11256272]

>>11256253
>>11256242
just you wait until the counting guy is done

[Anonymous No.11256401]

>>11256157
>is trigonometry hard?
Why don't you try it and find out?

[Anonymous No.11256404]

>>11254462
>faggot
Why the homophobia?

[Anonymous No.11256514]

/sqt/ didn't know.

How do you calculate the coordinates without calculus?

[Anonymous No.11256656]

>>11256514
Solve
[math] (1-x^2)^{1/2} = x [/math]

[Anonymous No.11256668]

>>11256514
Picture is divided into top and bottom section. Both are labeled sections of a unit circle.

Consider length x in the top section. Rotate the picture by 90 deg ccw to see x = y. By the Pythagorean theorem 1 = x^2 + y^2 = x^2 + x^2. Solve for x.

The red highlighted triangle in the bottom section is an equilateral triangle so that each of its sides has length 1. The vertical axis bisects the top edge of the red highlighted triangle. The top edge of the red highlighted triangle has length 1 so that length z must be 1/2. Use the Pythagorean theorem to solve for the remaining side length.

Elite mathematicians only browse /mg/ and wouldn't dare be seen with the engineers in /sqt/.

[Anonymous No.11256771]

>>11255363
no, not cringy
Entropy is cringy

[Anonymous No.11256772]

>>11256404
Faggot are unnatural

[Anonymous No.11256860]

Try to write this here.
I finally landed an assistant professorship. It's in machine learning (formally), but there should be enough freedom to write and publish pure math papers (at least in free time and exploiting the affiliation without the necessity to include the boss as a coauthor).

Still way better than being a PD slave.

AMA

Also greetings to Nikolaj.

[Anonymous No.11256888]

>>11256860
What do you study? What's PD slave? PhD you mean?

Also, why is /sci/ and /mg/ so dead, isn't it holidays?

[Anonymous No.11256892]

>>11256888
I study many things. But my education is long finished if that's what you mean. PD = PostDoc.

[Anonymous No.11256953]

>>11255363
Fuck no, go with Emmy as others suggested, or Sophie/a

[Anonymous No.11256982]

>>11256953
>as others suggested
Literally no one suggested that.

[Anonymous No.11257000]

>>11256982
but the very first response >>11255400 was an Emmy poster!?

[Anonymous No.11257005]

>>11257000
The very first response said to call her "Amalie", not "Emmy."

[Anonymous No.11257054]

>>11257005
Okay fair enough.

[Anonymous No.11257236]

>>11252098
>>11252115
no it's not, you don't square the hypotenuse, what's the square of a line? (i mean it can be the square with that segment as side, but that doesn't help either) you square the *length* of the sides, and using that we have no contradiction. Or if you want to say that the side has length i that's going to be a problem, you can't give a nice order to the complex numbers, so defining a metric/norm with them is difficult at best and impossible at worst.

[Anonymous No.11257268]

>>11255363
call her Algebra

[Anonymous No.11257314]

>>11257268
That'll do, thanks bro. I'm gonna do this one.

[Anonymous No.11257331]

don't know if this is the right place to ask, but if anyone can help me with this question it'd be greatly appreciated because I have no idea on how to approach it

Let
[math]v_1 = [1,2]^T, v_2 = [1,-1]^T[/math]
Determine a basis such that the coordinate vector for [math]v_1[/math]is [math]v_2[/math] and that the coordinate vector for [math]v_2[/math] is [math]v_1[/math]

[Anonymous No.11257340]

>>11257331
basis for [math]{\rm I\!R}^2[/math] *

[Anonymous No.11257368]

>>11256860
Computational Topology for Machine learning?

https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=8483&context=etd

[Anonymous No.11257419]

>>11252098
This actually makes sense. It's just like how lightlike spacetime intervals are 0. If you could somehow send a clock along a path at the speed of light, it wouldn't register any time passing. (More precisely, in the limit as the speed of the clock goes to c, the proper time goes to 0.)

[Anonymous No.11257420]

>>11257419
In the same sense, if you threw a ruler at the speed of light, it would flatten out and wouldn't be able to measure any distance.

[Anonymous No.11257455]

>>11257420
You could still measure distance indirectly through redshift assuming you knew its original mass.

[Anonymous No.11257560]

Algebraic geometry: how the fuck do I get past this jewish shit? The fags who teach this strive on making problems as unintelligible as possible, relying on what can pretty much be called downright crypticism. Also, since I'm not part of a chink cheater ring, I don't have access to previous years' exam samples

[Anonymous No.11257566]

>>11257560
Are we talking "sheaf theory" algebraic geometry, "beginning of Hartshorne" algebraic geometry or "Cubics and Conics" algebraic geometry?

[Anonymous No.11257575]

>>11257566
Mostly the first three chapters of Hartshorne

[Anonymous No.11257603]

>>11257560
>how do i stop being a brainlet
Anglo cope.

[Anonymous No.11257616]

>>11252098
>he never heard of a metric tensor
oh no no no

[Anonymous No.11257622]

>>11257603
Well you chinks are all over the place, you seem to like the anglosphere quite a lot. If anglos are brainlets then please stay away from us, we won't miss you.

[Anonymous No.11257626]

>>11257575
>first three chapters of hartshorne
For the varieties part, study commutative algebra and the rest comes naturally.
For the schemes and homological algebra part, don't be a retard.

[Anonymous No.11257629]

>>11257419
>>11257420

[Anonymous No.11257699]

what is "超一流 algebra" ?

[Anonymous No.11257712]

>>11257686
this anon mentions "超一流 algebra"? can someone please tell me what that is?

[Anonymous No.11257718]

>>11252098
Is there any way to simplify this more, or write in a different way? I'm kind of retarded when it comes to exponent rules. [math]a^{a^{b}}[/math]

[Anonymous No.11257783]

>>11257712
It's like 超 algebra, but without 流's.

[Anonymous No.11257788]

>>11257712
Those are classes muslims have to take in China to get out of the labour camps and gain citizenship.

[Anonymous No.11257813]

Threadly reminder to work with physicists.

[Anonymous No.11257844]

hello fukugen friends

[Anonymous No.11257851]

>>11252682
Why did you pick 7^3

[Anonymous No.11257984]

>>11257622
Oh snap!

[Anonymous No.11257999]

>>11257368
THat shit is cool!

I thank there is a lot to explore way beyond NN approxmation theorems

[Anonymous No.11258018]

>>11255363
Stop being an Am*rican retard and give the kid a NORMAL person's in a NORMAL family name, like, idk, Jane or Eliza, whatever

[Anonymous No.11258025]

>>11255699
How is that even possible? How many classes do Math majors have? I am a MeChAniCaL Engineering major and I have 130 credits

[Anonymous No.11258083]

>>11257718
[math]a^{a^b}=a^{ab}[/math]
Proof is an exercise left to the reader

[Anonymous No.11258087]

>>11258025
you are smart

[Anonymous No.11258102]

>>11258025
different schools have different course credit systems you absolute dolt
>>11258087
no he's not

[Anonymous No.11258109]

>>11258102
But he's engineer, he must be

[Anonymous No.11258153]

[Anonymous No.11258154]

>>11257999
Audio 10:45
https://www.youtube.com/watch?v=b1Wu8kTngoE
Move thing to algebraic topology

[Anonymous No.11258162]

>>11258154
Thanks, I'll definitely mark it

[Anonymous No.11258215]

>>11258025
Math BA has 10 courses
Math BS has 13 courses
CS BA has 9 courses in the major; another 4 related courses (2 maths, 2 other)
CS BS has 14 courses in the major; another 8 related courses (4 maths, 2 lab science, 2 other)

That's ignoring Gen Ed stuff (although some of the CS classes will count towards gen eds)

[Anonymous No.11258233]

>>11258215
>13 courses
What's up with americans and drafting up absolutely surreal undergrad curriculums?
Here just about every subject has 5 courses a semester, and it only goes down to ~3 near the last semester, to clear up time for a bachelor's thesis.

[Anonymous No.11258366]

>>11258233
If I was just doing a BS in Math, it would be about 70 credits and 21 classes. That's including gen eds. I would have another 50 credits to fill with other stuff. That can be major-related (which will help you in your career) or meme classes.

It's up to the student to make sure they are well prepared for the future. Most companies don't look at your transcript after your first job, anyway. They want to see what you did in a professional environment.

That's why I'm looking at double majoring vs just sticking with the CS stuff and doing other random classes. Math is close enough to CS to be useful.

[Anonymous No.11258463]

>>11256656
>>11256668
how do you get from [eqn]\frac{\pi}{3}[/eqn] to that, though?

[Anonymous No.11258522]

>>11258463
>>11256514
>>11256656
>>11256668
Nevermind, I think I got it now. It seems easiest just to convert from radians to degrees first.
[eqn]\frac{\pi}{4}\text{ rad} \cdot \frac{180^{\circ}}{\pi\text{ rad}} = \frac{180\pi^{\circ}}{4\pi\text{ rad}} = 45^{\circ}\\
x = \cos 45^{\circ} = \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2}\\
y = \sin 45^{\circ} = \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2}\\
[/eqn]
and for the one I asked about:
[eqn]\frac{\pi}{3}\text{ rad} \cdot \frac{180^{\circ}}{\pi\text{ rad}} = \frac{180\pi^{\circ}}{3\pi\text{ rad}} = 60^{\circ}\\
x = \cos 60^{\circ} = \frac{1}{2}\\
y = \sin 60^{\circ} = \frac{\sqrt{3}}{2}[/eqn]

Thanks

[Anonymous No.11258529]

>>11258463
>>11256514
>>11256656
>>11256668
Nevermind, I think I got it now. It seems easiest just to convert from radians to degrees first. Then draw a triangle with those measurements, set a side to 1 and work from there.
[eqn]\frac{\pi}{4}\text{ rad} \cdot \frac{180^{\circ}}{\pi\text{ rad}} = \frac{180\pi^{\circ}}{4\pi\text{ rad}} = 45^{\circ}\\
x = \cos 45^{\circ} = \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2}\\
y = \sin 45^{\circ} = \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2}\\
[/eqn]
and for the one I asked about:
[eqn]\frac{\pi}{3}\text{ rad} \cdot \frac{180^{\circ}}{\pi\text{ rad}} = \frac{180\pi^{\circ}}{3\pi\text{ rad}} = 60^{\circ}\\
x = \cos 60^{\circ} = \frac{1}{2}\\
y = \sin 60^{\circ} = \frac{\sqrt{3}}{2}[/eqn]

Thanks

[Anonymous No.11258625]

>Fuzzy sets
Yay or nay?

[Anonymous No.11258665]

>>11257331
The basis you're looking for is [math]\left\{\begin{pmatrix}1\\1\end{pmatrix},\begin{pmatrix}0\\-1\end{pmatrix}\right\}[/math].
I'll leave it yourself to prove this is indeed a basis of [math]\mathbb{R}^2[/math].

[Anonymous No.11258964]

Uhm do you guys take notes while going through the Script? I never really make notes and just did the exercise sheets, but I dont know if I should Change my approach for exam preparation.
First Semester Europe Student

[Anonymous No.11259016]

>>11254015
> what a conjugate is
Replace i with negative i
>why do we do this?
Because squaring only makes sense with real numbers. You could just take the absolute value and square that, but it was found that if you multiply the complex number with its conjugate, you get the same result.
This is because what's really happening here, is [math](a+ib)(a-ib)=ce^{i\theta}*ce^{-i\theta}=c^2*e^{(i-i)\theta}=c^2*e^0=c^2[/math]

[Anonymous No.11259034]

>>11258964
I've found that making notes of the script gives me a richer overview of all the topics being covered. It's better to get a rough sketch of the ideas and concepts the professor wants you to know than to get into every detail. If you read back your notes and you don't understand something, you can still reference the skript.

Of course exercises can not be left out either, but if there are topics in excercises you don't understand, or have completely missed, doing more exercises will not help you understand the topic better or help you with your exam

[Anonymous No.11259097]

just a cs student whos studying category theory passing by
in groups, we have identities, i wont belabor the details
but there is another curious number that have unique property, namely the value 0
what is this type of value called? it seems to collapse every input you give into a singleton

[Anonymous No.11259190]

>>11259097
What you mean is called zero element
https://en.wikipedia.org/wiki/Zero_element

But you may or may not oversee some things here:
In the integers, Z, the number 0 is indeed the additive identity:
a * 1 = a
a + 0 = a
So what "0" is in terms of the properties you mention is a matter of which operation you look at.

You're also learning "ring theory 101" here and people will hit you if you say
>I'm a CS guy, I'm a category theory expert, here's the definition of a monoid
Formal are, roughly, a 1820's thing, while category theory is a 1940's thing.

[Anonymous No.11259193]

>>11259097
What you mean is called zero element
https://en.wikipedia.org/wiki/Zero_element

But you may or may not oversee some things here:
In the integers, Z, the number 0 is indeed the additive identity:
a * 1 = a
a + 0 = a
So what "0" is in terms of the properties you mention is a matter of which operation you look at.

You're also learning "ring theory 101" here and people will hit you if you say
>I'm a CS guy. I'm learning category theory. Here's the definition of a monoid
Groups as objects on their own are, roughly, a 1820's thing. While category theory is a 1940's thing.

[Anonymous No.11259197]

>>11259097
What you mean is called absorbing and zero element
https://en.wikipedia.org/wiki/Absorbing_element
https://en.wikipedia.org/wiki/Zero_element

But you may or may not oversee some things here:
In the integers, Z, the number 0 is indeed the additive identity:
a * 1 = a
a + 0 = a
So what "0" is in terms of the properties you mention is a matter of which operation you look at.

You're also learning "ring theory 101" here and people will hit you if you say
>I'm a CS guy. I'm learning category theory. Here's the definition of a monoid
Groups as objects on their own are, roughly, a 1820's thing. While category theory is a 1940's thing.

[Anonymous No.11259446]

>>11259097
https://en.wikipedia.org/wiki/Identity_element
?

[Anonymous No.11259487]

>le stop bullying people
>this isn’t your sekret klub anymore incel!!!1!!
>le help me with my cs-math double majo
>le teach me how to teach myself desu senpai
>le category theory
>le why the homopederasty desu?
>le yukarifag is evil for knowing math
>le herp derp reddit is better than 4chan for math discussions and such :3
good job you fucking stupid niggers

[Anonymous No.11259494]

>>11259097
>in groups, we have identities
wrong, in groups you have a *unique* identity
> another curious number that have unique property, namely the value 0
wrong. in the context of groups, 0 (at least within the usual "number" groups id assume youre familiar with), does not have another unique property other than, possibly, additive identity.
> it seems to collapse every input you give into a singleton
wrong, it "collapses" every input into itself, 0. A singleton is a set containing one element.
>what is this type of value called?
its called an additive identity when located in specifically a ring (up to irrelevant generalizations)

[Anonymous No.11259622]

>>11259487
seething

[Anonymous No.11259630]

>>11259487
this

[Anonymous No.11259634]

>>11259097
fuck of ranjeet. you have no business in an /mg/ thread

[Anonymous No.11259636]

>>11259097
>cs
>category theory
see >>>/lgbt/

[Anonymous No.11259638]

Has yukarifag finally killed himself?

[Anonymous No.11259697]

>>11259487
>>le herp derp reddit is better than 4chan for math discussions and such :3
how many times has reddit made significant breakthroughs in maths?
https://en.wikipedia.org/wiki/Superpermutation#Lower_bounds:_%22The_Haruhi_Problem%22

[Anonymous No.11259703]

>>11259487
>ironically adding le
Cease at once.

[Anonymous No.11259734]

what happened to the math monk threads? are they all hiding out at their new monastery?

[Anonymous No.11259744]

>every even integer is a diagonal-length of a hypercube with an integer-sized sides
what the fuck did math mean by this?

[Anonymous No.11259750]

>>11259744
I don't even know what you meant by that

[Anonymous No.11259759]

>>11259750
if you have a hypercube, and the length of every side is an integer, then the size of the line that goes from one corner of the hypercube to another is always an even integer (2n, where n is an integer)

[Anonymous No.11259767]

>>11259744
Hypercube as in, specifically the 4D one?

[Anonymous No.11259769]

>>11259759
>hypercube
You lost me

[Anonymous No.11259775]

>>11259767
can a hypercube ever be anything other than the 4D shape?

[Anonymous No.11259780]

>>11259775
Yes.
Do you actually go to /mg/ post garbage without even reading the subject's wikipedia page?

[Anonymous No.11259785]

>>11259775
There are an infinite number; this is a 10D hypercube.
>It has 1024 vertices, 5120 edges, 11520 square faces, 15360 cubic cells, 13440 tesseract 4-faces, 8064 5-cube 5-faces, 3360 6-cube 6-faces, 960 7-cube 7-faces, 180 8-cube 8-faces, and 20 9-cube 9-faces.

[Anonymous No.11259886]

If I have an integral domain D with a valuation v, can I always define an absolute value? If so, its completion with respect to this absolute value is an integral domain too?

[Anonymous No.11259889]

>>11259886
>If I have an integral domain D with a valuation v, can I always define an absolute value? If so, its completion with respect to this absolute value is an integral domain too?
What have you tried?

[Anonymous No.11259890]

>>11259780
>>11259785
oh, i guess i got my terminology mixed up, i was under the impression that a hypercube was specifically a 4-dimensional object.

>every even integer is a diagonal-length of a 4-dimensional hypercube with integer-sized sides
what the fuck did math mean by this?

[Anonymous No.11259895]

>>11259889
I'm learning about the p-adic valuation and I was trying to generalize it because in this case, the completion Z_p is an integral domain too so I don't know how I would even define the absolute value if I'm not using Z as my valuation ring, maybe trying to assign each prime/maximal ideal an element in R and then work from there?

[Anonymous No.11259907]

>>11259890
According to Pythagoras, [math] l=\sqrt{4 c^2}=2 c [/math]. It's nothing mind-breaking. The hard part is proving Pythagoras's theorem for dimension n.

[Anonymous No.11259908]

>>11259890
>what did nature mean by this
That the euclidean norm of [math](n, n, n, n)[/math] is 2n.

[Anonymous No.11259911]

>>11259908
but thats 4n

[Anonymous No.11259918]

>>11259907
i'm pretty sure you could do a simple proof-by-induction to prove it, that's just my intuition though, i suppose its never as simple as it feels

[Anonymous No.11259962]

What did math mean by this?
[eqn]\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \frac{x^9}{9!} - ...[/eqn]

[Anonymous No.11259999]

>>11259962
>alternating signs
cringe. [math]\sinh(x)[/math] on the other hand..

[Anonymous No.11260011]

>>11259197
cool, i learn something new today :)
i couldn't care less for autism
i just tried my best to explain my problem

[Anonymous No.11260168]

How do mathematicians deal with the fact that most of their work has little to no real applications?

[Anonymous No.11260179]

>>11260168
Be thankful to god?

[Anonymous No.11260184]

>>11260168
"Real mathematics must be justified as art if it can be justified at all." - G.H. Hardy

[Anonymous No.11260187]

>>11260168
There are more applications than you might think. Algebraic geometry is being used in encryption research. Algebraic topology is beginning to be used in data analysis/machine learning. The US army is paying people to apply category theory.

[Anonymous No.11260195]

>>11260168
>How do mathematicians deal with the fact that most of their work has little to no real applications?
We don't deal with that fact since the people who give us grants don't seem to care.

[Anonymous No.11260237]

>>11260195

what do you even need a grant for? office supplies and fancy chalk?

If you're lucky, you can get a check for teaching cuckulus to premeds

[Anonymous No.11260247]

>>11260187
>this very second, american taxpayer money is being used to finance categorytrannys' hrt

[Anonymous No.11260255]

>>11254015
>all these retarded replies
It's a real meeting of the MIND

[Anonymous No.11260268]

>>11260237
>Neet doens't understand salaries or being paid for ones work

[Anonymous No.11260283]

>>11254015
>>11260255
Well ya see uncle, a conjugate is just the reflection of a complex number along the real axis.
Like a mirror or something.

[Anonymous No.11260405]

what

[Anonymous No.11260530]

>>11260405
What resources are you using to learn these topics? I think it would be helpful to review a resource that introduces these topics from fundamentals.

There is a gap in your understanding that rote memorization of gimmicky tables may not help fill.

[Anonymous No.11260534]

>>11260530

[Anonymous No.11260545]

>tfw even the gorilla poster made better contributions to /mg/ threads than 95% of the anons in this thread
Shame, I used to like this general.

[Anonymous No.11260553]

The absolute value of i is still 1

[Anonymous No.11260570]

>>11260405
It's ridiculous to memorize stuff like this. Allow me to assist you.
All you need is the pythagorean theorem, and SohCahToa.

The unit circle is a circle of radius 1, centered at the origin (as in pic related).
Any point on this circle can be used to form a right triangle as shown in blue, with the height of the triangle intersecting the X axis. This is known as a reference triangle.
[math]sin(\theta) = \frac{opposite}{hypotenuse}[/math]
[math]cos(\theta) = \frac{adjacent}{hypotenuse}[/math]
Because the hypotenuse is 1, the base of the triangle on the unit circle is cosine, and the height is sine!

By the pythagorean theorem, [math]a^2 + b^2 = c^2[/math]
Substituting in the sides for our right triangle: [math]sin^2(\theta) + cos^2(\theta) = 1^2[/math]
You can use this to derive the other identities for the most part.

As for the ridiculous quadrant chart, simply know that by drawing a right (reference) triangle for your point, you can trivially know the proper sign like this:
In quadrant two, sine is above the Y axis (so it's positive), and cosine is to the left of the X axis (so it's negative).
Tangent is sine over cosine, which is positive over negative, so it's negative.
The secant, cosecant and cotangent functions are just 1 over the other trig functions. 1 is a positive number, so it will always have the same sign.
There! Now you don't need to memorize any of that stupid chart!

[Anonymous No.11260582]

>>11260545
Are you talking about the gorilla poster that made me draft up explanations of measure theory and functional analysis and then pretended to have understood what I said or someone else?

[Anonymous No.11260588]

>>11260570
Forgot pic

[Anonymous No.11260598]

>>11260534
This texts covers that figure in section 4.4. I suggest carefully reviewing chapter 4 and completing many of the accompanying exercises.

Start at the beginning and slowly make your way through the chapter. If you feel you've already mastered the topic being covered try to complete the in section examples without using the provided solution and additionally attempt many of the end of section exercises.

If you encounter a topic that you aren't completely confident about then ask for help. Be sure to include the details of your misunderstanding and cite the relevant text/section.

[Anonymous No.11260632]

>>11260598
I'm in 4.4 and that's where I'm stuck. I don't have a good memory.
>>11260570
>>11260588
Thank you. That helps a lot.

[Anonymous No.11260635]

>>11260632
Happy to help!

[Anonymous No.11260666]

>>11260632
In that section they give you 'new' definitions for the trig functions in terms of a point (x,y) on the terminal side of your angle theta. The sign (positive or negative) of the trig function is related to the sign of the associated x or y coordinate.

See the remark just before example 2 in section 4.4.

Be sure to make use of your text. It will explain what you need to know. You just need to read through it carefully and practice with examples/exercises.

[Anonymous No.11260671]

>>11260545
>>tfw even the gorilla poster made better contributions to /mg/ threads than 95% of the anons in this thread
gorillaposter here, would have enjoyed to keep it up but don't have the time anymore plus not enough content from other posters to work with.

>>11260582
>Are you talking about the gorilla poster that made me draft up explanations of measure theory and functional analysis and then pretended to have understood what I said or someone else?
Might be bad memory on my part but I don't think I'd partake in discussions on those topics.

[Anonymous No.11260775]

>>11260553
I don't think that the image is trying to use euclidean distances. It's a good thought experiment but there is no way to measure distance between complex numbers as they're not ordered. Maybe ordered based on some abstract non-rational order that finally allows you to have i as a metric but definitely not according to what we have right now. Still not a bad "what if" case because some of the basic right triangle identities do seem to hold, like c^2 = a^2 + b^2 - 2ab cos(pi/2)

[Anonymous No.11260799]

>>11260775
>there is no way to measure distance between complex numbers as they're not ordered

[Anonymous No.11260906]

>>11255022
baste

[Anonymous No.11260925]

>>11260775
>there is no way to measure distance between complex numbers as they're not ordered

[Anonymous No.11260932]

>>11252098
i or "square root of negative one" is just used as a tool in bigger equations that require it. In a situation like this, it's meaningless. A triangle can't exist in the real world with that as the size of one of its sides. Your image is faulty.

[Anonymous No.11261035]

>>11260187
I think they are using homotopy theory for smth related to missiles

[Anonymous No.11261092]

>>11254144
If you’re into actuarial this question is important based on exact times for large sums. It’s also a better general form. However actuarial is just accountant plus and overhyped.

[Anonymous No.11261272]

>>11261035
Hell yeah brother gotta love the military-industrial complex

[Anonymous No.11261287]

I have a series published on the OEIS, do I qualify as a math?

[Anonymous No.11261289]

>>11261287
Post it and we'll see

[Anonymous No.11261291]

>>11261289
https://oeis.org/A318235

>please no bully

[Anonymous No.11261298]

>>11261287
>>11261291
>happy numbers
I'll allow it

[Anonymous No.11261420]

>>11261291
how's the bees?

[Anonymous No.11261512]

Wildbergers Monopoly Money series is unironically based and a service.
I respect the man.

[Anonymous No.11261539]

>>11260405
Each of the trig functions is a ratio of two of {opposite, adjacent, hypotenuse}. The hypotenuse is always positive, the adjacent is positive in quadrants I and IV (right half), the opposite is positive in quadrants I and II (top half).

Consequently, cos (a/h) and sec (h/a) are positive when the adjacent is positive (I,IV), sin (o/h) and cosec (h/o) are positive when the opposite is positive (I,II), tan (o/a) and cotan (a/o) are positive when opposite and adjacent have the same sign (I,III).

Basically, you need to understand the behaviour of sin and cos; the other 4 are just shorthands: tan=sin/cos, sec=1/cos, cosec=1/sin, cotan=1/tan=cos/sin. You don't need to memorise anything involving tan, cotan, sec or cosec other than how to express them in terms of sin and cos. Any identity involving the other 4 can be trivially derived by converting to sin/cos, using identities involving sin/cos (e.g. sin^2+cos^2=1), then converting back.

Understanding beats memorisation every time.

[Anonymous No.11261543]

>>11260799
>>11260925
It's clear that he wanted to say that there's no way to measure distance *using* complex numbers

[Anonymous No.11261584]

>>11261543
>It's clear that he wanted to say that there's no way to measure distance *using* complex numbers

sure there is. every real number is also a complex number.

[Anonymous No.11261586]

>>11261543
Ahem:
[math]d(a, b)=a-b[/math].

[Anonymous No.11261589]

>>11261586

that's not a metric on the set of complex numbers.

[Anonymous No.11261597]

>>11261586
[math]d(i, 0) = i \ge 0[/math]?

[Anonymous No.11261637]

>>11252098
https://www.youtube.com/watch?v=h6XGsdQ-Dfs
He is being misleading, isn't he? With that title.
He is evaluating the limit of a function with x approaching zero, not 1^inf.

[Anonymous No.11261640]

https://youtu.be/qWuaPEpKgfk

[Anonymous No.11262139]

>>11252098

[Anonymous No.11262257]

>>11261589
>>11261597
What if we use the ordering
[math] a \geq b \iff |a| \geq b [/math]

Then the metric satisfies the triangle inequality and the other metric axioms (other than not being a real function).

[Anonymous No.11262266]

>>11262257
Not a partial ordering, lad.

[Anonymous No.11262278]

>>11262266
Sorry I mean
[math] a \geq b \iff |a| \geq |b| [/math]

[Anonymous No.11262280]

>>11262278
No, I mean it's not a partial order, you don't have that [math](a \geq b) \wedge (b \geq a) \Leftrightarrow (a=b)[/math].
If I were pointing out the issue you're correcting I'd have just said you didn't define anything.

[Anonymous No.11262288]

>>11261420
I'm a software engineer now, but my bees are winterized

[Anonymous No.11262289]

>>11252098
I'm a math major and I'm doing very well. But the higher level stuff (graduate level math) literally looks like an alien language to me. It's all symbols and hieroglyphs, wtf.
So tell me, do you need innate talent to do a PhD in this subject? How do you even understand this stuff? Do you guys just see symbols in your head?

[Anonymous No.11262291]

>>11262280
The metric axioms don't say it needs to be a partial order :^)
Obviously anon's metric is not symmetric however

[Anonymous No.11262327]

How did he used that sqrt(m) is not a square to arrive to the highlighted eqn? I don't get it

[Anonymous No.11262343]

>>11257813

are they readable?

[Anonymous No.11262361]

>>11262289
>So tell me, do you need innate talent to do a PhD in this subject? How do you even understand this stuff? Do you guys just see symbols in your head?

Hard work, sitting on your hairy fat arse for hours and hours, putting a shitton of effort into understanding and utilizing the material. No shortcuts, no genius gene or divine blessing. Just hard work.

[Anonymous No.11262366]

Is there a 1-to-1 mapping from the real numbers to the surreal numbers, or do the surreal numbers have a unique, even "denser" cardinality? If so, what is that cardinality called and what are the implications of its existence?

[Anonymous No.11262369]

>>11262361

this

[Anonymous No.11262374]

>>11262289
>It's all symbols and hieroglyphs
Stay away from algebra then.

[Anonymous No.11262379]

>>11262361
especially the hairy far arse part

[Anonymous No.11262385]

>>11262366
The surreal numbers aren't even a set, they're a proper class.

[Anonymous No.11262402]

>>11262385
Is there some kind of axiomatic violation if you say “there exists a set S such that every quantity described by the surreal number system is an element of S”?

[Anonymous No.11262408]

>>11262402
That's a bijection from the surreals to S, but proper classes don't biject with sets.

[Anonymous No.11262418]

>>11262289
>math
>symbols
Is this seriously how zoomers think?

[Anonymous No.11262458]

>>11262289
Behind every formal system is some intended interpretation (or at least motivating example). I find it best to think in terms of these first, because your intuition leads you to discover properties of these that actually generalize to a broader class of examples. Then you either formalize your idea into a proof of a general theorem, or discover where the gap in such a proof is and therefore a special property of your original object.

[Anonymous No.11262477]

graph theory niggeres where you at

[Anonymous No.11262480]

>>11262289
>do you need innate talent to do a PhD in this subject?
Yeah, you need to be a kike, otherwise just forget about it, especially algebraic geometry

[Anonymous No.11262485]

>>11262361
>no genius gene
Yes, you need kike genetics, I don't have it and I am failing as a result.

[Anonymous No.11262490]

>>11262485
>he doesn't have jewish ancestry

[Anonymous No.11262497]

>>11262485
>mfw descendant of french protestants, traitors and kikes
Nothing personal, lads.

[Anonymous No.11262505]

>>11262477
Complete amateur yet enthusiast reporting in

[Anonymous No.11262741]

>>11262402
If the surreals have all ordinals by definition, then I think at the very least it clashes with the axiom of replacement, which enables you to generate all the limit ordinals and in particular [math] \omega_2 [/math].

[Anonymous No.11262784]

>>11262289
no, you just need to learn what the symbols mean, lmao
how the fuck do you expect to understand what something is talking about if you can't read it?
learning how to read it isn't very hard, just takes time and practice.

[Anonymous No.11262795]

>>11262289
I think what you mean is that because high level stuff will not have years of development and pedagogy into them, sometimes everything is written in really obsucre ways. It sucks, but math isn't done in a couple of days lmao.

[Anonymous No.11263246]

>CAT(0) geometry, robots, and society: Black Lives Matter
https://arxiv.org/pdf/1912.10007.pdf

[Anonymous No.11263267]

>>11263246
Lmao, applied cucks

[Anonymous No.11263424]

what kind of jobs does a math degree get you?

[Anonymous No.11263430]

>>11263424
Hand job.

[Anonymous No.11263436]

>>11263430
I bet yukarifag gets more pleasure outta giving than recieving hjs~

[Anonymous No.11263443]

>>11263424
Ones where you dont need to compete on leetcode against 200,000 other applicants.

[Anonymous No.11263453]

>>11263430
Go to bed, mr. Chen.

[Anonymous No.11263468]

>>11262327
Now what I don't get is why they replaced
(ut +vw) with (ut+vm)

[Anonymous No.11263525]

>>11263443

wait really?

[Anonymous No.11263552]

>>11263424
Jobs in academia (researching maths and teaching at a university).
Industry jobs (Machine learning, data analysis, high speed trading, etc).
Cursed military jobs (cryptography research for example).
Other applied mathematics jobs; working with a team of non-mathematicians (medical research, biology research, etc).
High school teaching (seriously what are you doing if this is you).

[Anonymous No.11263756]

Is there any mathematical research done about spaces where length between two points can be different depending on from which point measurement is started from?
This can be thought as circle connecting two points. If one is allowed to move only in counterclockwise or clockwise on that circle when moving from point to point, then length from each point can be different or equal depending on position of points on that circle.

[Anonymous No.11263770]

>>11263756
Try looking at generalised metrics. I'm not saying there would be something like that, but you can have quasimetrics for which all the other properties hold except the part that d(x, y)=0 implies x=y. You C O U L D have something like triangle inequality + d(x, y)=0 iff x=y, but I don't know. Search.

[Anonymous No.11263773]

>>11263756
Is this just a metric space without the symmetry axiom?

[Anonymous No.11263802]

>>11263770
Thanks. I try to google some words.
>>11263773
I dont know. My level of knowledge is half way trough algebra 2.
I got this idea by thinking about how to describe chemical reaction space. If points in space are reagents and products, connections between points are reactions and length between points describes percentage of end products from reaction, with reversible reactions one needs different lengths between points depending from witch point one starts measurement.
For example reaction A + B <-> AB that has equilibrium at 25% A + B and 75% AB when one starts with A + B 75% changes to AB. If one starts with AB 25% changes to A + B.

[Anonymous No.11263810]

>>11263802
I'm pretty sure what you're talking about is a quasimetric: https://en.wikipedia.org/wiki/Metric_%28mathematics%29#Quasimetrics
I don't really understand the chemistry stuff though.

[Anonymous No.11263815]

>>11263802
>>11263810
See also https://math.stackexchange.com/questions/23390/examples-of-non-symmetric-distances
The top answer mentions the example you gave ([math] S^1 [/math] refers to the standard circle).

[Anonymous No.11263822]

>>11263810
Yes this seems to be it. Thanks.

[Anonymous No.11263882]

>>11263756
Shortest distances in directed graphs?
I don't know those with uncountably many nodes, but what you can also do is integrate the velocity V not against itself, but against a vector field. Will not be aetric, generally, though

[Anonymous No.11263927]

>>11262505
good, now explain branch sets to me

[Anonymous No.11264007]

>>11263430
I'll take three right now and one for the ride.
Do you accept payment in elliptic operators?
>>11263756
Ah, I see. That's an old problem, known as the "hurricane metric." Gauss studied it a lot.
You are at a point A inside a hurricane, and you want to get to a point B. But the air currents inside the hurricane are just too strong, so you can only move counter-clockwise, in other words, with, instead of against, the wind.
So you restrict the set of allowable paths to be those that go counter-clockwise and define the distance between any two points to be the infimum of a distance functional (in this case, the Euclidean one) on the set of allowed paths.

[Anonymous No.11264434]

>>11264007
that's a very nice image, saved

[Anonymous No.11264561]

>be the only TA in the office
>6 min to finish my turn
>group of women walk in

[Anonymous No.11264710]

Does anyone know of a good source to read about spectral graph theory? In particular about what the fuck it means when graphs are cospectral but not isomorphic, and how the spectrum changes with regard to the Laplace?

[Anonymous No.11264760]

>>11263552
whats the answer to your pic?

[Anonymous No.11264764]

>>11262327
the equation above the highlighted one is
*integer* = *integer times sqrt(m)*
and this is only possible if both sides are zero
>>11263468
looks like a typo to me

[Anonymous No.11264796]

>>11264760
A friend of mine solved it a while back - it's
" H^(hotdog;hamburger) ~ (hamburger)[croissant]/(croissantpeach+grapes) where peach= n*grapes, croissant any constant."
feel free to TeX it up if you care enough

[Anonymous No.11264812]

Ideals are nice because they generalize the notion of normal subgroup to rings and that allows you to take quotients and that kind of things. In group theory we don't care only about normal subgroups, yet in what I've read so far about ring theory (a bit of commutative algebra/ algebraic number theory) they seem to only care about ideals. In what context do we actually care about subrings?

[Anonymous No.11264835]

>>11264796
what's the latex for a croissant?

[Anonymous No.11264838]

>>11264812
>In what context do we actually care about subrings?
Field theory desu.

[Anonymous No.11264841]

>>11264835
idk mate lmao

[Anonymous No.11264855]

>>11264835
[math]\croissant[/math].
If it doesn't display correctly, update your browser and change the system locale to Tuvalu.

[Anonymous No.11264870]

Mathematicians Allow Useless Non-computable Fantasy Objects.
This is idiotic for many reasons
even for them
but it is especially idiotic for physics.

[Anonymous No.11264886]

>>11264870
hello fellow stack exchanger

[Anonymous No.11264895]

>>11264870
You Need To Go Back
Where You Came From

[Anonymous No.11264906]

>>11264870
>Touhou: Useless Non-Computable Fantasy Object

[Anonymous No.11264995]

>>11264886
Where does this association come from? For each subfield, Math StackExchange tends to have a a few core posters who's word is taken as gospel and their opinions appear to be rather streamlined. It is (or was) different with physics and philosphy, where discourse was often quite influenced by exotic folks like Ron Maimon and other complicated characters. On math you got your logic Prof and your functional analysis postdoc and they usually give you the perspective you could have guessed.

>>11264895
I've never used reddit, is there actually a good math page?

>>11264870
But where-else would you play around with fantasy objects then?
Besides, while I understand your sentiment, I'm not certain if you mean what you say. There's probably no way around non-computability if you don't literally want to give up on Turing complete systems. And I think as soon you have one, you got them in your number system.

Also just stumbled upon this text, which seems super nice
https://arxiv.org/pdf/1804.05495.pdf

I think I'll write down a rant on weaker principles like REM's and LPO's, i.e.
https://ncatlab.org/nlab/show/principle+of+omniscience
it's an interesting topic.

[Anonymous No.11265026]

>>11264870

are they any good books on constructivist physcis?

[Anonymous No.11265036]

>>11264995

Don't post images of random prostitutes. It's weird.

[Anonymous No.11265044]

convention or not it is a useful convention

https://www.youtube.com/watch?v=fQX6qmLNamM

[Anonymous No.11265058]

Here is a headline from 2008: news.bbc.co.uk/2/hi/americas/7640183.stm

>Huge new prime number discovered

I wonder who would say that this prime number was invented in 2008?

[Anonymous No.11265090]

mfw I get back home for the break but I'm no longer being able to do math because I literally have PTSD from an abusive household

[Anonymous No.11265098]

sit quietly by yourself for at least 15 minutes until you get bored, then go do some math for fun

[Anonymous No.11265112]

>>11265026
I don't know any. In fact, those who'd even think about it would probably be called mathematicans or at least mathematical physicist by others.
In physics practice, you just work with "the numbers" (and if you ask which, then as answers you get "the reals" or the complexification thereof), but then if you compare against measurements or do simulations, it's always compared against an floating point read-off or put on a grid. Similarly, you want to work with Hilbert spaces over field that have all lower and upper bound and chain end properties you might want, to create your model without thinking about any such issues, but if you end up speaking about physical results, you can be sure that there exists an enumeration in the sense of [math] f:\omega\to S [/math] to whatever state space [math] S [/math] you need.

On a related note, pic related has - among other things - a nice elaboration of QED on a grid.

>>11265036
Just trying to stay 3D here.

>>11265098
I wish I could meditate

>>11252098
Oh, something I had been wondering about the last few days, namely whether there's any interesting norm or metric on a space you study via it's Zariski topology.
I ended up with the question when searching for topology results that find application in cases where the topology can not be viewed as induced by a norm or metric. The cases where those functions don't play a role tend to be exotic - except in algebraic geometry where people genuinely care about there metric despite possibly not even being interested in fields as big as the continuum.
I've asked this elsewhere and got a confirmation for that there indeed seems to be a lack of theorems involving those extra structures (metric and norms) in the field, but I didn't get as far as to find out what the real topological results are that are used in e.g. algebraic geometry and that don't make use of any structure that the object of study have, and which aren't in direct correspondence with topological properties

[Anonymous No.11265153]

>>11265090
>mfw I get back home for the break but I'm no longer being able to do math because I literally have PTSD from an abusive household
>>>/r9k/

[Anonymous No.11265160]

>>11265112
>any interesting norm or metric on a space you study via it's Zariski topology
The Euclidean metric on [math]R^2[/math]?
Ellipses, parabolas and hyperbolas, for example, can be constructed purely from the Euclidean metric (ellipse, for example, as the set of points whose distance to two different points sum to a certain prescribed value, as you well know), but you'll study these geometric objects by considering them as closed in the Zariski topology in [math]R^2[/math], ascribing them polynomials and studying those.

I might have completely misunderstood your question, tho.
>Just trying to stay 3D here.
2D is best.

[Anonymous No.11265259]

>>11265160
I'm aware that, I think, the topology of any topological vector space over R can be consdier to be generated by its balls.
So let's think of e.g. algebraic topology over a finite field where this is out of the question by the Zariski topology still exist:

I'm in search for a tool or theorem from plain* topology (only proven from the fact that we have a notion of open sets here and so on, not dependent on us working e.g. with coordinate rings and their arithmetic operations) being used in a context of a topology T that is not induced by a metric.

*plain as in Tychonoff's theorem, which is really only dependent on the theory of topology

[Anonymous No.11265263]

can anyone introduce me to cryptography?

[Anonymous No.11265269]

>>11265263
nope

[Anonymous No.11265335]

>>11264812
>
ideals are just the kernel objects in the category of rings. The latter is a bad category since the kernels are not rings themselves with the usual conventions (and even changing defintions doesnt solve the problem), so taking a module approach solves many of the problems that arise, since both ideals and rings are modules.

Subrings on the other hand dont really interact all too nicely with rings - they are not submodules, and the very nice correspondence theorem (theres one for groups, rings, modules - youve probably seen it) does not apply to them. However, not all is lost. Under nice properties (namely, integrality, which is the ring concept of algebraicity of fields, among others), one can find that primes are inherited in a subring, and even chains of primes behave nicely too, so that concepts of dimension can take place there. Of course, theres also field theory as the other anon said, but fields lack primes so you lose these sort of interesting things

[Anonymous No.11265350]

>>11265259
In what way is the weak topology generated by balls?

[Anonymous No.11265351]

>>11265335
You are mistaken, fool. You don't have the correct information, and if you did, you would have come to a different conclusion.

[Anonymous No.11265353]

>>11265351
?

[Anonymous No.11265356]

>>11264870
All abstract objects are made concrete by its representations. In fact the whole of field theory is founded upon the representation theory of compact Lie groups.

[Anonymous No.11265377]

>>11265350
Might be a good example.
Do you know what's some nice results where the weak topology is crucial and no further properties of the objects are used?

[Anonymous No.11265551]

Let [math] (a_n)_n [/math] be a sequence of natural numbers with [math] \lim_{n\to \infty} \dfrac{a_n}{n} = 0 [/math].
Are the values of the sequences bounded by some natural number?

[Anonymous No.11265559]

>>11265551
>>>/sci/sqt
[math]\log n=a_n[/math] .

[Anonymous No.11265595]

>>11265350
Families of sup-seminorms [math]N_C^\infty(x) = \sup_{y \in C}|y(x)|[/math] over compact sets [math]C\subset Y[/math] on locally convex spaces [math]X[/math] generates the Mackey topology [math]\tau(X,Y)[/math], so we can consider the "balls" obtained from t[math]N_C^\infty[/math].
By Mackey-Arens, any dual topology [math]\mathscr{T}[/math] is both coarser than the weak-operator topology [math]\sigma(X,Y)[/math] and finer than the Mackey topology [math]\tau(X,Y)[/math], which is in turn finer than the strong-operator topology [math]\rho(X,Y)[/math] (due to Bourbaki-Alaoglu/"balls are compact" theorem). We may wish, then, to investigate if we can still generate dual topologies with seminorms as we tune its coarse-ness between weak- and Mackey. Perhaps we need to change what the [math]C[/math]'s are in [math]Y[/math] or consider [math]N_C^p[/math] for [math]p<\infty[/math]. I'm not sure, but it certainly can be interesting.
>>11265377
Let's investigate this possibility in QM. Note that w- and s-closures of the algebra of observables coincide via von Neumann's bicommutant theorem. Since states are given by linear [math]*[/math]-irreps, weak and strong notions of convergence can only differ due to the topology on the rep-space, not that on the algebra.
Now when dealing with rigged reflexive Hilbert spaces with Frechet topology, such as tempered distributions, however, one can prove that closed bounded subsets in [math]\mathcal{H}'[/math] is compact, hence [math]\text{weak}\xrightarrow{\text{Frechet}}\text{Mackey} \rightarrow \text{strong}\rightarrow \text{weak}[/math]. So w- and s-convergence again coincide on Frechet spaces. In particular, since Stone-von Neumann tells you that there is essentially only one unitarily-equivalent irrep of the Weyl algebra, and Groenewold-van Hove quantization lands your rep-space in a maximal Poisson subalgebra of [math]C^\infty[/math] (which has Frechet topology), the strong-weak distinction basically never happens in QM.

[Anonymous No.11265605]

>>11265559
What does this mean? a_n are all natural numbers.

[Anonymous No.11265610]

>>11255363
Pure cringe.

[Anonymous No.11265619]

>>11252098
i is not a number of geometric magnitude. It is imaginary in order to allow for the even based root function to propagate over negative odd numbers.

[Anonymous No.11265624]

>>11265356
idgi aren’t you gay? d-don’t stop posting them or anything its just curious.

[Anonymous No.11265708]

>>11265263
https://crypto.stanford.edu/~dabo/cryptobook/BonehShoup_0_4.pdf

[Anonymous No.11265806]

>>11265112
>nice elaboration of QED on a grid
Lattice QFT and is in general not a nice way of doing foundational QFT. There's a reason why C/AQFT and quantum jets start by quantizing the fields from the get-go, and the reason is that the continuum limit fucks with the Hilbert space of states.

[Anonymous No.11266127]

>>11265356
>All abstract objects are made concrete by its representations.
EPIIIC!!!! I LOVE CONCRETE BLACK HOLES!!!
Psst, mind if I repost this on >>>/r/science?

[Anonymous No.11266167]

>>11265605
>Are the values of the sequences bounded by some natural number?
it means not necessarily

[Anonymous No.11266259]

has anyone a books guide for getting into advanced maths? thanks

[Anonymous No.11266271]

>>11266259
we have a wiki

[Anonymous No.11266323]

>>11265605
Take the roof function or something, ya dimwit.

[Anonymous No.11266414]

>>11258154
>""set theory""
>mathematical
OH NO NO NO

[Anonymous No.11266418]

>>11262289
>I'm doing very well
>(graduate level math) literally looks like an alien language to me
Pick exactly one.

[Anonymous No.11266420]

>>11264906

[Anonymous No.11266639]

>>11266414
get him my lil'nigga!

[Anonymous No.11266758]

>>11265551
No, of course not. Literally any sublinear function which goes to infinity satisfies this.

[Anonymous No.11266761]

>>11266127
You're a disgusting, pathetic, vile creature. Have some fucking respect for representation theory.

[Anonymous No.11266808]

>>11252227
Read Bourbaki if you want top-down construction of mathematics. It's not a criticism, I actually really like it and I think it gives you a deeper understanding in the end than the traditional learn-from-example methods you can find in anglo textbooks