Math Genral

[Anonymous No.11918605]

miligram (mg) edition
reminder work with chemistry
nummer

das alte: >>11913994

[Anonymous No.11918611]

.

[Anonymous No.11918625]

I took an algebraic geometry course in my 4th year of uni, but it was very geometric. When does it start using sheaves, schemes, categories and stuff?

[Anonymous No.11918628]

>>11918625
what the fuck ist einen sheaf?

[Anonymous No.11918633]

>Elliptic curves

[Anonymous No.11918634]

>be confused
>start typing out question
>realize i was retarded
it happens a lot

[Anonymous No.11918645]

>>11918634
>be confused
>start typing out question
>realize i was retarded
>post it anyway

[Anonymous No.11918651]

>>11918645
but what is the point in wasting everyones time if youve come to the conclusion whilst typing

[Anonymous No.11918653]

>>11918634
>>11918645
>be confused
>start typing out quetion
>still confused so post it, but make it inflammatory to bait people into providing detailed explanations instead of ignoring it
>finish off by insulting the people who provided the answers by implying they're stupid and clueless

[Anonymous No.11918705]

If you're working with a rigged Hitler space [math] (H, \Phi) [/math], where the subset [math] \Phi [/math] seemingly fulfills all the nice properties you want, why even carry along the [math] H [/math]? Can someone explain why one needs both?

[Anonymous No.11918709]

>>11918705
the H just denotes you're talking about a space, you could drop it if context permits

[Anonymous No.11918711]

>>11918605
>miligram
What the fuck is a miligram. Never use units.
Fuck physicists, never work with them
Fuck chemists, never work with them
Fuck biology
Fuck engifags
Fuck CS
Fuck niggers
Fuck Jews
And fuck jannies

[Anonymous No.11918715]

>>11918705
Because H specifies the topology.

[Anonymous No.11918722]

>>11918715
Phi also has a topology, why do you really need two? The test functions are in Phi, right?

[Anonymous No.11918724]

>>11918711
>never use units
why do you hate R and C?

[Anonymous No.11918725]

The human being in modern society has been stripped of everything organic. There is no pervading sun to wake him, no urgent bird chatter to remind her of impending nightfall. Their feet are encased, their lungs cramped from insufficient movement of the upper torso. They see no green, their water is not rough with sediment, their air smells like plastic or pesticide.

Instead of the randomness within form, the ever present motion, the branchial structures of life, there are clean sharp static lines. So it is no surprise that the human being takes to the only remaining sources of biology with such desperation, blindness, and whole acceptance. And it is no surprise that an unstimulated mind and body, soul if you won't balk at the old tongue, clings to easy pleasures and fears their removal. When you have lost the whole nuance of your world, a bit of dopamine to numb the complex network of cravings and needs is a godsend. And the words and motions you find in your fellow being, they're all that's left of the fuller world.

Unfortunately, all that remains is an entropying mirror, which has recorded and internalized millenia of life, but is now consigned to repeating it, passing memories within itself. Eventually, those memories lose meaning and form, with no anchor in reality other than the reality of the paper or screen, and nothing new enters the cycle. Like an ill fated perpetual motion machine, the collective psyche sees its hollow reverberation dream turn to nightmare and then into nothingness.

[Anonymous No.11918730]

Is Steen-Seebach the best book for general topology?

[Anonymous No.11918732]

>>11918730
Willard

[Anonymous No.11918744]

>>11918732
munkres is better than willard

[Anonymous No.11918771]

>>11918625
from experience, in practice it's all very geometric, and only invokes results from those subjects in the proofs.
A good example of a sheaf is a vector bundle on a variety. They can help study a variety in a more concrete setting, for example - although you can define a variety very abstractly, if you actually want to work on it you need to embed it in projective space. Line bundles procure rational maps into projective space, and with some mild conditions, can extend it to a whole embedding. And actually, there is a correspondence between embeddings into projective space and line bundles. For example, I think there's a result by Max Noether that roughly says that except in some well-known exceptions, a smooth curve has a canonical embedding (coming from the so called canonical line bundle) into some projective space such that its corresponding ideal is generated by quadrics. This type of result makes it easier to analyse the curve, since for example, if a line were to intersect all of these quadrics at least 3 times, then you can conclude that the curve contains the line.

[Anonymous No.11918772]

>Ramsey theory

[Anonymous No.11918786]

schadenfreude just means skull joy

[Anonymous No.11918789]

>>11918786
>schadenfreude just means skull joy
no

[Anonymous No.11918824]

>>11918789
sorry, damage joy, schadelfreude is skulljoy

[Anonymous No.11918829]

>>11918824
>schadelfreude
sch*ä*delfreude. If you are unable to type an "ä" you can replace it by an "ae".

[Anonymous No.11918836]

>>11918829
welche unversitat besuchst du?

[Anonymous No.11918840]

>>11918829
He will probably still say skahdelfrewd, so whatever you are teaching him is simply wasted.

[Anonymous No.11918842]

Friendly reminder to approach any field of math with positivity and willingness to learn.
I admit I've been laughing at category theory, while not knowing anything about it.
Such behavior is NOT okay.

[Anonymous No.11918851]

>>11918842
das ist eine moralische meinung

[Anonymous No.11918872]

>>11918836
Eine mit Rechtschreibung, Hamburg.

[Anonymous No.11918881]

>>11918872
ich verstehe nicht, warum rechtschreibung sagen? ich ignoriere umlaut

[Anonymous No.11918882]

book recommendation for principle bundles, pls. thx

[Anonymous No.11918891]

>>11918881
Selbst auf English beginnt man Sätze mit einem Großbuchstaben (und beendet sie mit eine Satzzeichen).
Außerdem schreibt man Universität groß und wenn man keine Umlaute schreiben will ersetzt man sie nicht durch den Buchstaben der am ähnlichsten aussieht...

[Anonymous No.11918899]

>>11918882
Principal, not principle. If you want a classic book, try Husemoller. It covers a lot of different types of bundles, one of which is principal.

[Anonymous No.11918901]

>>11918891
>will ersetzt man sie nicht durch den Buchstaben der am ähnlichsten aussieht...
das ist interresant, erarbeiten?

fur den rest, Grammatiknuancen storte mich nicht

[Anonymous No.11918903]

>>11918829
is this bait?

[Anonymous No.11918908]

>>11918882
Tu's book basically treats only the frame bundle, but it's a very good read
I don't have a recommendation for the theory in full generality, but I would look into books on spin geometry, gauge theory, and mathematical physics. books with "differential geometry" in the title usually go in a different direction.

[Anonymous No.11918915]

>>11918901
>das ist interresant, erarbeiten?
Wenn man nur englische Buchstaben schreiben kann weil man nicht versteht wie man mit eine US Tastatur auch andere Buchstaben schreiben kann dann kann man folgende Ersetzungen machen:
ä -> ae
ü -> ue
ö -> oe
ß -> ss

>>11918903
What could possibly be bait about that post?

[Anonymous No.11918922]

>>11918915
danke

[Anonymous No.11918968]

Is the BB function really so fast growing as to be uncomputable? You're telling me that no recursive function, no matter how self-referential, will ever beat it?

[Anonymous No.11919284]

>>11918968
Yes, it dominates every computable function. Suppose that a function f dominates every computable function and consider an arbitrary machine e run on input e, if it hasn't halted in f(e) steps then it will never halt. So you can solve the halting problem.

[Anonymous No.11919296]

>>11918901
>das ist interresant, erarbeiten?
stop using google translate, spasti

[Anonymous No.11919315]

>>11919296
There's nothing wrong with Google translate.

[Anonymous No.11919432]

>>11919296
wie sonst werde ich lernen?

[Anonymous No.11919507]

>Zariski topology

[Anonymous No.11919525]

>>11918651
should have waited a minute before posting your retarded newfag question, see >>11918653 for the essence of his reasoning

[Anonymous No.11919530]

>er kann nicht åöäšůẙ schreiben

[Anonymous No.11919545]

>>11918605
>Not mathematics general
>no "/mg" makes it hard to find
>shit grammar
>shit theme
>random german text
Never make this thread again.

[Anonymous No.11919558]

>>11919507
what's it like on finite spaces? Is it as useful?

[Anonymous No.11919559]

Do parallel lines meet in infinity?

[Anonymous No.11919588]

>>11918605
next time go with /mg/ in the title, this post is annoyingly hard to find in catalog

[Anonymous No.11919596]

[math]\int \frac{x \sin(x)}{1+\cos^2(x)}dx[/math]

[Anonymous No.11919602]

>>11919545
Goddamn Huns

[Anonymous No.11919610]

>>11919596
this is comedy gold

[Anonymous No.11919612]

>>11919558
It's discrete.

[Anonymous No.11919615]

>>11919559
yes

[Anonymous No.11919652]

>And I tell you, I will die in a duel on the occasion of some coquette de bas étage. Why? Because she will invite me to avenge her honor which another has compromised.

[Anonymous No.11919658]

>>11919652
why did he do it lads?

[Anonymous No.11919697]

>>11919545
>>11919588
>he doesnt just type "mg" and save precious microseconds of his pathetic finite lifespan

[Anonymous No.11919706]

>>11919652
Is there a more kino story in the history of mathematics than Galois'?

[Anonymous No.11919719]

>>11919658
Hormones.

[Anonymous No.11919728]

>>11919706
he died a simps death, it was the furthest from kino as you could be

[Anonymous No.11919731]

>>11919697
Typing in mg also has the advantage that /sqt/ shows up because of the imgur links btw.

[Anonymous No.11919748]

>>11919596
>It is beneath the dignity of excellent men to waste their time in calculation when any peasant could do the work just as accurately with the aid of a machine. -Gottfried Leibniz

[Anonymous No.11919756]

>>11919731
>/sqt/ shows up
>advantage
?

[Anonymous No.11919765]

>>11919697

[Anonymous No.11919789]

>>11919765
this nigga using ctrl+f instead of the dedicated search function

[Anonymous No.11919806]

>>11919748
Based Leibnizposter.

[Anonymous No.11919813]

>>11919748
>couldn’t do the integral without a machine
>postures as an ascended mathematical genius when the people that designed the CAS are significantly higher iq than him
Just lol

[Anonymous No.11919842]

>>11919813
The only person with a higher IQ than Leibniz was Goethe.

[Anonymous No.11919852]

>>11919765
post your bookmarks

[Anonymous No.11920035]

deutschmathe ist mein lieblingsfach, sehr geil
wo ist die erdbeermund?

[Anonymous No.11920037]

>>11920035
i dont speak nazi sorry

[Anonymous No.11920044]

>>11920035
Speaking in languages other than English outside of /int/ is a bannable offense.

[Anonymous No.11920097]

>>11920044
but mathematics is a language :^)

[Anonymous No.11920107]

>>11920097
noone here speaks math

[Anonymous No.11920115]

>>11920097
[math]\mathbb{Q}[\xi_n]=\{\alpha+\beta\xi_1+\gamma\xi_2^2+...+\upsilon\xi_n^{n-1}\vert \alpha,
\beta,\gamma,...,\upsilon\in\mathbb{Q}\}[/math]

:)

[Anonymous No.11920135]

If I were to attempt to correct errors in my mediocre maths education brought on by overly lax parenting, where would I start? Is there a recommended reading list?

[Anonymous No.11920139]

>>11920135
What's your current level and what do you aspire to do with said new education? In other words, is it simply for your own intrigue or are you preparing to go to school and study a field where this knowledge is needed?

[Anonymous No.11920212]

>>11920139
Mostly intrigue, part education. It is hard to diagnose my current "level", assume I know the basic rules of mathematics(order of operations etc), but that there are holes in my knowledge that may cause me to approach questions in ways that are inefficient. Also, there are some early year education branches of mathematics that I remember nothing from like geometry.

[Anonymous No.11920231]

>>11920212
Do you know how to factor [math]f(x)=x^2-2x-8[/math] into a product of linear terms?

Do you know how to expand [math]g(x)=(x+3)(x^2-4)[/math]?

Do you know how to find the roots of [math]f(x)[/math] and [math]g(x)[/math]?

[Anonymous No.11920253]

>>11920231
N-no. Don't bully me anon.

[Anonymous No.11920256]

I have a circle with fixed center and radius.
I have another ellipse with two fixed foci (both outside of the circle). Let's say I grow the ellipse around the two fixed foci until the ellipse touches the circle.
How do I find the tangent point?

[Anonymous No.11920265]

>>11920253
I'm just trying to get a grasp of where you're at. For the super basics, Khan Academy seems to be the go to resource. Here's their page on algebra I (https://www.khanacademy.org/math/algebra).).

[Anonymous No.11920273]

>>11920265
Thanks anon, I will give it a look

[Anonymous No.11920324]

>>11919615
Why?
What are the implications of this?

[Anonymous No.11920332]

>>11919842
Goethe couldn't even do math and had a retarded and WRONG theory of color and natural science. giga brainlet tier desu

[Anonymous No.11920343]

>>11920044
show me in the rules where it says that

[Anonymous No.11920357]

>>11919789
The dedicated search function is inferior. Fite me.

[Anonymous No.11920381]

>>11920343
There's a message that shows up in your native language if your browser isn't set to English.

[Anonymous No.11920400]

>>11919719
you misspelld whore-moans

[Anonymous No.11920409]

>>11920037
you should tho

[Anonymous No.11920421]

>>11918605
Hey retards, wat do? My supervisor is ghosting me, not responding to emails.

[Anonymous No.11920437]

>>11920421
send him increasingly melodramatic pls respond emails every hour until he replies

[Anonymous No.11920447]

>>11920343
>>>/global/rules/6/b
>>>/global/rules/6/e

[Anonymous No.11920478]

>>11920447

> The quality of posts is extremely important to this community. Contributors are encouraged to provide high-quality images and informative comments.

holy shit kek, did moot unironically put these in the rules?

[Anonymous No.11920487]

>>11920478
Well, according to moot, ironic shitposting is still shitposting.

[Anonymous No.11920566]

>>11920487
But that's true.
In fact, I'm pretty sure ironic shitposting comprises the majority of shitposting.

[Anonymous No.11920658]

imagine
[math] 0\to \mathbb Z\stackrel{\imath}{\to} \mathbb R \stackrel{\pi}{\to}\mathbb R/\mathbb Z\to 0 [/math]
was a splitting extension.
Let's make some theory where that's true. We can fuck with R if you like to achieve it.

[Anonymous No.11920666]

>>11920421
Literally me but the other way around

[Anonymous No.11920706]

>>11920658
We need to somehow guarantee that non-integers sum to non-integers. Otherwise we have a problem already with ½+½ which should be in R/Z.

[Anonymous No.11920717]

>>11920706
Can't I say R/Z is like an interval [0,1) and map 1/2+1/2 to the 0 in that set?

[Anonymous No.11920726]

>>11920658
>We can fuck with R if you like to achieve it.
BEHOLD
[math]\mathbb{R} = \mathbb{Z} \times S^1[/math]

[Anonymous No.11920756]

>>11918634
iktf

[Anonymous No.11920788]

>>11919706
I don't like radical french republicans but damn do I have to respect Galois to the moon and back.
There would be a lot more cross-the-aisle respect if duels were still a thing

[Anonymous No.11920967]

>>11920566
To be honest, I'm not totally sure if it's all ironic anymore. There are things I used to post ironically that I now post unironically. I have no idea where irony ends and sincerity begins anymore.
>>11919706
Grothendieck is the closest to a modern Greek tragedy that exists in the mathematical community. If you've never read Recoltes et semailles you'll know what I mean. Starts out as some Gypsies kid and escapes from an interment camp as a child and enter some bumfuck French uni only to end up the superstar of French mathematics (even though he was German). Then some kids tell him he's a square and he freaks out trying to prove that he's still "down with the cause" to literal children only to fail since he's now in a position of power and influence in academia. Abandons his job to live in the mountains where he becomes a hyper religious Christian and spends the next year or so writing a new memoir where he basically shit talks his closest friends and students.

[Anonymous No.11920974]

>>11920967
One of the greatest pictures of all time.

[Anonymous No.11920976]

>tfw starting to actually get the hang of my calc 3 class
It definitely feels like it was designed to be a weedout class

[Anonymous No.11920981]

>>11919559
Depends on where you defined the lines, in a vector space they don't.

[Anonymous No.11920989]

>>11920976
You mean calc 2? Calc 2 is the one that filters the brainlets.

[Anonymous No.11921008]

>>11920989
I found it somewhat challenging but not too hard. At the beginning of calc 3 threw me for a loop since it was completely new concepts for me like parametric and symmetric equations and shit

[Anonymous No.11921012]

>>11920666
Why you do this?

[Anonymous No.11921020]

>>11920967
>There are things I used to post ironically that I now post unironically. I have no idea where irony ends and sincerity begins anymore.
I kinda get what you're saying.
It's like when someone posts bait, and you reply seriously. But it's not like you believed he was being serious, or even that you noticed it was bait and fell on purpose, you didn't even think about whether or not it's serious.
You grow older and you gradually master the art of thinking less and less.

[Anonymous No.11921055]

>>11920967
I hate niggers and love Grothendieck. Is this irony?

[Anonymous No.11921062]

>>11921055
You need to be 18+ to post here.

[Anonymous No.11921078]

>>11921055
>I hate niggers
Cool.
>love Grothendieck
Faggot.

[Anonymous No.11921128]

Are range and image synonymous?

[Anonymous No.11921135]

>>11921128
Yes.

[Anonymous No.11921156]

>>11921128
sometimes
some people use range to mean the R part of [math]f:D \to R[/math], but that doesnt mean f needs to output every point in R
like [math]x^2 : \mathbb{R} \to \mathbb{R}[/math] has range [math]\mathbb{R}[/math] but it only outputs nonnegative real numbers
but the image always means the output points of f, so x^2 's image would be the nonnegative real numbers

[Anonymous No.11921178]

>>11921156
I guess it'd help to specify, then. In regards to the fundamental isomorphism theorem for vector spaces, it says: [math]\textrm{Let} \ T:V \rightarrow W \ \textrm{be a linear map, with} \ dim(V)< \infty \ \textrm{and} \ dim(W)<\infty. \textrm{Then},V/Ker(T) \cong Im(T)[/math].

I've seen both Im(T) and Rng(T) used for that last part. Does it matter in this particular instance?

[Anonymous No.11921196]

>>11921178
In that case they refer to the Image and Range as the same thing, but they mean the outputs of T in this case, all the isomorphism theorems around math refer to the outputs

[Anonymous No.11921200]

>>11921196
Much obliged, animeposter.

[Anonymous No.11921553]

>>11921020
>You grow older and you gradually master the art of thinking less and less.
Oh god, we're all gonna become Atiyah without the prior success, aren't we? But really, genuine sincerity feels like such a foreign concept nowadays. You know anons, I've been hanging on /mg/ on and off for about six or so years, and it feels strange to see everything get all warped and distorted. I mean /sci/ was still garbage back then, but at least /mg/ was fine. Yukari poster would make latex heavy posts of ribbon categories, gorilla poster would keep getting himself banned, that one ens anon who hung around, pretty relaxing. But things are changing so fast, not even just /mg/, but everywhere.

Honestly, I'm terrified. Currently in grad school and it's clear the academic job situation is getting worse every year. Hell, enough people in the US are pissed off enough that academic jobs may actually get hit hard, which would be a double whammy. Couple that with north korea starting up their nuclear program and refusing talks and things aren't looking too hot.

Mathematics seems to be more and more about following hot trends, and while none of them seem bad or uninteresting, it's a damn shame just how much mathematics has been lost to time just because it's not fashionable. This is gonna sound autistic, but it feels like history is being lost to time, all of those potentially interesting and fruitful ideas, the various conjectures and heuristics people have developed, all just, left to the wayside. I sometimes feel like I'm abandoning the mathematical heritage by being complicit in leaving the subjects behind. Hell, will all the things I work on now be abandoned in the same way? Is there anything to do, to fix this? Or maybe, to get used to this feeling?

[Anonymous No.11921793]

>>11920967
>Starts out as some Gypsies kid
As far as Wikipedia tells me his Father was an anarchistic Russian Jew (possibly not in a religious sense) and his mother a German Protestant?

But the article also wrongly says that his parents left him in the care of a Lutheran Pastor, which is just plainly false, as the person in question was was suspended as a Pastor a decade earlier (presumably for joining an universalist religious community, at least that is what I gather) and his only occupation at that time was being an assistant teacher...

[Anonymous No.11921798]

>>11920447
lol u tk him 2da bar|?

[Anonymous No.11921807]

>>11920447
According to the rules about 95% posts are ban worthy.

[Anonymous No.11921836]

>>11919432
doesn't your university have language courses?

[Anonymous No.11921837]

>>11921807
yes that's why I report at least a half dozen threads a day. all of them tranny or reddit threads, I make sure to report CS threads for being off-topic as well.

[Anonymous No.11921847]

>>11921837
Mods do not do anything though. /sci/, just like most boards, is absolute shit.
Ironically /pol/ is practically the only board which stays on topic (although the "topic" of hardcore political shitposting is not that appealing to me), although practically the entire board violates the "racism outside of /b/" rule.

[Anonymous No.11921852]

>>11921847
>Ironically /pol/ is practically the only board which stays on topic
Since when is posting black cocks, white women being gang raped and white children being stabbed to death on topic?

[Anonymous No.11921853]

>>11921852
>Since when is posting black cocks, white women being gang raped and white children being stabbed to death on topic?
It certainly is "political".

[Anonymous No.11921854]

>>11921852
Its a conversation starter if nothing else.
>>11921847
I don't care I just report evil people's threads. I don't report /pol/ I just hide the threads because there's nothing to be gained from them.

[Anonymous No.11921858]

>>11921854
>I just report evil people's threads
What would those be for example?

[Anonymous No.11921942]

My uni has a class on combinatorial geometry. Is it interesting? Any cool problems in that field? Won't be able to take it but it sounds kinda cool

>>11921847
>Mods do not do anything though.
Bro I got banned for >>11917539 for off topic posting even though anime is inherently math.

[Anonymous No.11921960]

>>11921942
>Bro I got banned for >>11917539 for off topic posting even though anime is inherently math.
In general mods just delete the posts which deserve deleting the least.
Usually some random in-joke shitposts get deleted while there are dozens of fully idiotic bait threats up at the same time.
Just look through the catalog and see what retardation is actually allowed on this fucking board...

[Anonymous No.11921988]

>>11920974
agree

[Anonymous No.11922015]

>>11921942
>I got banned
>tfw I won against the anime tranny
I have ascended.

[Anonymous No.11922208]

>>11921858
people who disagree with me

[Anonymous No.11922254]

>>11922208
Ah, I know them, those are some really evil people!

[Anonymous No.11922428]

>>11921553
>Oh god, we're all gonna become Atiyah without the prior success, aren't we?
Oh yeah. I'm gonna write the fucking coolest senile proof of the Riemann hypothesis. It will have all the good stuff.
References to ancient subjects no one studies? Obviously.
Use of incorrect folklore results? How could I not use those.
Theorems and lemmas gradually ascending the Sephirot until Keter, the Grand Riemann Hypothesis, plus all sorts of other autistic references to occultism? Naturally.
>Hell, will all the things I work on now be abandoned in the same way?
Probably.
>Or maybe, to get used to this feeling?
Yeah. It's alright, isn't it?

[Anonymous No.11922460]

how do I find [math]H_{n} (K(\mathbb{Z}, 3) ) [/math] or atleast a reference for it?

[Anonymous No.11922494]

>>11922460
I wish I knew. You can get some low degrees done if you use the Serre spectral sequence on the path-loop fibration [math]K(\mathbb{Z}, 2) \to * \to K(\mathbb{Z}, 3)[/math], as [math]\Omega K(\mathbb{Z}, 3) \simeq K(\mathbb{Z}, 2) \simeq \mathbb{C} P^\infty[/math]. It just gets extremely painful when you keep going up. If someone knows a reference, I would appreciate it as well.

[Anonymous No.11922668]

[Anonymous No.11922674]

>>11922668
absolutely disgusting

[Anonymous No.11922727]

>>11918605
I guess 4chan isn't the best place to ask for help, but it's not like there is good advice anywhere else. I have found most of my pure mathematics very tedious, although I've enjoyed stats and some analysis. I think I'll complete my bachelors in mathematics, but do you think I should do my masters in applied math or physics?

[Anonymous No.11922837]

>>11922727
If you want to enter the work force, applied math; if you want to continue in academia, physics.

[Anonymous No.11922873]

>>11922837
Sounds interesting. Do most of the mathematics in physics grad school revolve around analysis, since I enjoyed analysis way more than algebra? Also, does CS minor work with both?

[Anonymous No.11922881]

>>11922873
I'm not much into physics, so I can't answer your question there. A CS minor is definitely a good idea, since any job that you'll get with an applied math degree will almost certainly involve CS in some degree (data analysis, cryptography, etc.).

[Anonymous No.11923008]

>>11921960
God the amount of thinly veiled /pol/ iq threads everyday piss me off

>>11922668
What does this mean?

>>11922727
Stats are also a good idea if you're trying to avoid academia

[Anonymous No.11923014]

Is there some standard by which I can compare different undergraduate mathematics curricula?

[Anonymous No.11923041]

>>11923014
Accreditation, more or less, ensures that any accredited college will teach their students the same material. So I guess it would depend on what you want to compare in this instance.

[Anonymous No.11923079]

>>11923014
There is no meaningful difference between basic undergraduate curricula, at least if you're just comparing two different schools in the USA. The core courses everybody takes are almost literally identical at all half-respectable schools. The only thing that will change coursework-wise is the selection of advanced courses that are available, which depends on department size and on what the professors' research specialties are.
But you don't really know enough to make an educated decision about upper-division uni math straight out of HS, so it's not really something you can plan for. Maybe if you already know you like number theory or combinatorics or something you can look for departments that have a group dedicated to it.

[Anonymous No.11923103]

Is this proof wrong?
>Null T^n is a subspace of null T^n+1
>null T^dimV+n = null T^dimV
>v is a generalized eigenvector, so it is in null (T-LI)^j
>thus it is in null (T-LI)^dimV
>thus the set of generalized eigenvectors is equal to null (T-LI)^dimV
but what if j is less than dimV? Then we know the set of genral eigenvects is in nullT-Ldimv, but we dont know that the null space doesnt contain other stuff, so how does he say the sets are equal? Is it a wrong proof?

[Anonymous No.11923117]

>>11923008
>What does this mean?
filename

[Anonymous No.11923120]

>>11923103
Kinda pulled the second line out of your ass there, champ.
>Is it a wrong proof?
It doesn't look wrong, but it does look extremely sloppy. It's something like "if you're going to say it's trivial and skip it you should skip the entire thing rather than do this."
Ask this shit in /sqt/ btw.

[Anonymous No.11923148]

>>11923120
i didnt write the proof, it is from my textbooks. i am asking if the author made a mistake

the proof for the second line is that if null T^dim V does not equal null T^dimV+1, then null T^dim V+1 must contain vectors not within nT^dv, making it a larger space. this can't be true because that would make the null space larger than the vector space, a contradiction - dim nullT^dimV = dim V for trivial reasons

[Anonymous No.11923171]

>>11923148
you know parentheses exist for a reason right

[Anonymous No.11923183]

>>11923171
why do you nitpick at everything? why do you talk with a condescending tone? You are not infected with great evil, you are an inherent bastion of evil itself. Repent before the lord.

[Anonymous No.11923194]

>>11923183
I nitpick because you ought to have the common courtesy to make your post intelligible if you want me to proofread it

[Anonymous No.11923202]

>>11923194
hmm... fair enough

[Anonymous No.11923225]

>why do mathfags talk with a condescending tone to retards who expect humanity from people with a homosexual obsession with abstraction

[Anonymous No.11923234]

>>11923225
bonce ronce the cornew

[Anonymous No.11923264]

https://youtu.be/Zm-J06Cq2IY

[Anonymous No.11923266]

>>11923225
>implying being obsessed with abstraction should do anything other than give you a higher than human conception of morality

[Anonymous No.11923282]

https://youtu.be/mSOz4hwEbps

[Anonymous No.11923320]

https://www.youtube.com/watch?v=rB7XFQgJHBI

[Anonymous No.11923368]

>>11922881
All the labwork in physics does gross me out a bit, but not as much as seeing more algebra. I think with algebra the fact that things aren't "real" or tangible, or even justified really bothers me. Maybe I should take some courses of physics and computaional finance(which is another major my university offers) and see what I like. As a side note risk analysis does sound like a lot of fun like stats in general. Anyways thanks for the advice.

[Anonymous No.11923433]

>>11923368
Have you taken any courses in stochastic processes?

[Anonymous No.11923487]

Having a hard time discerning the difference Noetherinian and Artinian rings. Can't one just simply rewrite a Noetherinian ring as a descending chain of ideals and vice versa for an Artinian ring?

[Anonymous No.11923562]

>>11923433
Yes, I greatly enjoyed it. I really liked how despite often being very complicated the subject was very tangible. Which is why I think I might enjoy computational finance.

[Anonymous No.11923569]

>>11923487
Artinians don't go down and noetherians can't get it up.

[Anonymous No.11923573]

Is Lang's Algebra accessible with only a course in linear algebra? I heard it was the best book for abstract algebra.

[Anonymous No.11923606]

>>11923573
Lang is a meme. Join the Foote fetish chads. Also, if it was a proof based course in linear algebra you should be fine. If it was linear algebra for engineer monkeys, then you might get filtered.

[Anonymous No.11923625]

>>11923606
>Linear algebra course
>It's almost exclusively computational
Why is this allowed?

[Anonymous No.11923804]

>>11923569
Once again we see the use it or lose it maxim hold true.

[Anonymous No.11923833]

>>11923368
>grossed out by labwork
but that's the best part of physics.

[Anonymous No.11923996]

>>11922668
Are you confused by that or what do you mean?

>>11923487
If you think about the ring of integers and choose your favourite prime [math]p[/math], which is obviously some odd one, then consider the ideals generated by [math]p^n[/math] where n ranges over all natural numbers, with or without 0. This gives you a descending chain that will not stabilise, yet there is no [math]p^\infty \in \mathbb{Z}[/math], so you need to start from some [math]p^N[/math] and so any ascending chain obtained from this descending one will be finite (and so the descending chain does not contradict the fact that the integers give you a Noetherian ring).

[Anonymous No.11924015]

>>11923996
>obviously some odd one

2 is not a prime

[Anonymous No.11924033]

>>11924015
Odd primes are nice, 2 is not. One could even say that 2 is the odd prime. No exterior algebras over the field of 2 elements.

[Anonymous No.11924060]

>>11918605
But seriously though, we chemists would appreciate your superior mathematical skills. The unreasonable effectiveness of math is quite apparent in chemistry.

[Anonymous No.11924083]

>https://mathoverflow.net/questions/366070/what-are-the-benefits-of-writing-vector-inner-products-as-langle-u-v-rangle/366118#366118
so turns out Tao is one of those annoying notationfags...

[Anonymous No.11924087]

>>11924083
based terry

[Anonymous No.11924151]

[Anonymous No.11924164]

Calculate this, nerds.

[Anonymous No.11924193]

>>11924164
>cutfag
top kek

reported btw ;^)

[Anonymous No.11924194]

>>11924164
mmmm imagine the smell!

[Anonymous No.11924199]

>>11924151
Based Mitch.

[Anonymous No.11924215]

>>11924164
Not attractive.

>>11924199
Indeed. Maybe it's time to sleep soon when that made me chuckle.

[Anonymous No.11924218]

>>11924083
>writes down the definition
>"notation"
>writes down a random identity
>"notation"
I can't believe my boy Terry does this.

[Anonymous No.11924219]

Dickposters > animeposters

[Anonymous No.11924224]

>>11924219
what about anime dicks (on girls)?

[Anonymous No.11924229]

>>11924224
I recognize that bulge.

[Anonymous No.11924245]

>>11924164
Every time I'm reminded that the average is less than 15cm I get surprised

20cm uncut cock right here

[Anonymous No.11924323]

>>11923833
haha particles go whoosh

>>11924087
>>11924083
terry is too much of a god desu

[Anonymous No.11924329]

Is Cohn still the gold standard for measure theory?

[Anonymous No.11924508]

I'm conjecturing that Yukarifag saw this image and died on the spot.
>>11924329
Yes.
The version with the nice cover tho.

[Anonymous No.11924551]

>>11918605
I could saran wrap that whole beaker with my pussy

[Anonymous No.11924560]

>>11924245
>uncut
no epoisses ty

[Anonymous No.11924569]

>>11924560
>Falling for jew propaganda
You basically have to actively try to get cheese in order to get any real amount

[Anonymous No.11924573]

>>11924569
>jew propaganda
uh.. that's sweet and all anon, but stinky.??

[Anonymous No.11924575]

Mods deleted my post so imma re-ask the question. *Ahem* My uni has a class on combinatorial geometry. Is it interesting? Any cool problems in that field? Won't be able to take it but it sounds kinda cool

[Anonymous No.11924576]

>>11924573
>Slick foreskin musk
>Dry, chafed, literally requires lube, branded as cattle for life
I know which one I'd pick any day.
Bitches love the musk

[Anonymous No.11924590]

>>11924569
>Lainposter
base-
>>Falling for jew propaganda
cringe

[Anonymous No.11924601]

>>11924590
It's really just cope, but it's more funny to mention the jews

[Anonymous No.11924644]

>>11924590
>t. jew

[Anonymous No.11924804]

holy /mg/ on suicide watch

[Anonymous No.11924821]

>>11924804
I call baloney. There are soooo many "important" unanswered questions, unless he thinks we're close to answering most of them.

[Anonymous No.11924824]

>>11924821
Realistically speaking, how many of the Millennium Prize Problems will be solved within our lifetime?

[Anonymous No.11924834]

>>11924824
Honestly, I don't know. I don't know enough about the majority of the problems to make any sort of absolute statement. In my opinion (which is probably a bad one), I think the Riemann hypothesis is due in the next 50 years or so, and P vs NP as well IF it's true. For funsies I'll throw NS in the mix within the next 100 years or less

[Anonymous No.11924858]

>>11924804
>>11924821
Also after reading the thread, I don't think he actually knows what a computer is

[Anonymous No.11924869]

>>11924804
seems plausible

[Anonymous No.11924877]

>>11918705
>Hitler space
Based

[Anonymous No.11924886]

>>11924551
L O N D O N

[Anonymous No.11925125]

>>11923625
I remember getting Strang's book because everyone was recommending it and being kinda hyped for it before realizing it was computational garbage, or really just garbage in general

[Anonymous No.11925130]

>>11925125
>buying books

[Anonymous No.11925132]

>>11925130
I do a mix of pirating pdfs and buying. In any case it was an (used) gift

[Anonymous No.11925154]

>>11923625
CS and Engineering majors, non-whites, and women.

[Anonymous No.11925194]

>taking me 3 days to read chapter 1 of shilov and do problems
why am i so stupid

[Anonymous No.11925211]

>>11925194
Shilov is tough. Take your time. What would be stupid is rushing through it.

[Anonymous No.11925235]

>>11925211
idk i can only put in like 2 hours a night before i stop being able to focus and even that i'm on page fucking 22 lmfao i feel really fucking dumb and slow lol
prob gonna take me 2 months to read this shit god i'm fucking retarded

[Anonymous No.11925251]

>>11925130
>buying books

[Anonymous No.11925255]

>>11925235
Bro chill the fuck out that book is about equivalent to two courses (aka 8 months) at my uni

[Anonymous No.11925258]

>>11925255
back at my school it's the second half of linear (about 2 or 3 months)
graduated but never had to take it though only took the calculator roleplay first half since me code monkey

idk feels bad since the book was lying around and i was too busy with work to give a shit but now i'm prob getting fired so time to mathneet it up

[Anonymous No.11925267]

>>11925258
For real, my two classes were everything up to 5.1, chap 8 and some of 7. Nothing wrong with being a wagie and not spending all of your time on abstract symbol pushing

[Anonymous No.11925272]

Find a flaw.

[Anonymous No.11925277]

>>11925267
>Nothing wrong with being a wagie and not spending all of your time on abstract symbol pushing
had a huge mental breakdown involving work, probably have to get away from it for the sake of my mental health. not having a job will be stressful but honestly i could be comfy for a year on my current savings probably. would burn my career the fuck down though but still
cs pays very fucking well but i feel like i'm wasting my life away doing nothing interesting. want to try and probably fail miserably at pursuing some form of research level shit instead of copy pasting code from SO nonstop. maybe doing shitloads of math is useless for my goals, but honestly i just want an excuse to quit my job because i'm stupid and burnt out

[Anonymous No.11925330]

>>11925277
I don't know your life, nor do I have the greatest life advice in the world, but don't destroy something profitable (entirely) to burn yourself out with something else.

[Anonymous No.11925420]

>>11924858
>he doesn't know who Tim Gowers is

[Anonymous No.11925430]

>>11925277
>i'm stupid and burnt out
then why are you pursuing something for smart passionate people?

[Anonymous No.11925432]

>>11925430
Stupidity.

[Anonymous No.11925451]

>>11925420
Not a counter argument.
He's a smart known mathematician, therefore he's right?
What's his case that research math would end and why is it in any way realistic?

[Anonymous No.11925498]

I am sitting on the fence with the same situation, i am a piece of shit according to the *General retaliation i work hard* it does not take much to be appreciated ....or does it?

[Anonymous No.11925537]

>there are people ITT thinking we will solve anything relevant within the next 50 years

[Anonymous No.11925613]

>>11918605
I thought we said no more Germans only a week ago

[Anonymous No.11925616]

>>11920421
Rejoice and enjoy your freedom

[Anonymous No.11925625]

>>11918705
>rigged Hitler space
based /pol/ phoneposter

[Anonymous No.11925634]

>>11925613
Verpiss dich

[Anonymous No.11925667]

>Gowers talks about research mathematics coming to an end
>scroll down his twitter feed
>it's another "we've improved the upper bound on the size of biggest subset of {1, 2, ...n} not containing 3-length arithmetic progressions by a factor of log(n)^{tiny number}" episode
I'm sure Gowers wants to see this problem solved. Perhaps his last hope is computers solving this shit before he grows senile and dies.

[Anonymous No.11925727]

Let's say we have given a filtration of some abelian group H.
[math]... F^{n}H \subset F^{n+1}H \subset ... H [/math]
I want to know in which cases and how I can reconstruct H from its filtration. Does someone have a reference for this?

[Anonymous No.11925731]

>>11925727
and from the quotients [math]F^{n+1}H/F^{n}H [/math]

[Anonymous No.11925733]

>>11925667
Its just (smart)retards that don’t know anything about ML or physics saying stupid schizo shit that will amount to nothing.

[Anonymous No.11925753]

>>11925727
Let's say you have the filtration [math]0 = F^MH \subset F{M-1}H \subset \cdots \subset F^1H \subset F^0H = H[/math]. Suppose [math]0 \to F^{n+1}H \to F^nH \to F^nH/F^{n+1}H \to 0[/math] is split exact for each [math]0\le n \le M-1[/math]. Then [math]F^nH \cong F^{n+1}H \oplus F^nH/F^{n+1}H[/math], so there is the isomorphism chain [math]H \cong F^1H\oplus H/F^1H \cong F^2H\oplus F^1H/F^2H \oplus H/F^1H \cong \cdots \cong F^MH\oplus F^{M-1}H/F^MH \oplus \cdots \oplus F^1H/F^2H \oplus H/F^1H \cong F^{M-1}H\oplus F^{M-2}H/F^{M-1}H \oplus \cdots \oplus F^1H/F^2H \oplus H/F^1H[/math]. There are probably more general cases, but this is the most obvious one.

[Anonymous No.11925756]

>>11925753
Notice that you do not need to know your group before hand, only the quotient.

[Anonymous No.11925826]

>>11925272
This book gave me a crippling Foote fetish.

[Anonymous No.11925831]

>>11925272
The exercise lists are immense piles of hot garbage with one or two actual problems thrown in.

[Anonymous No.11925838]

>>11925826
haha much laughter my friend can i borrow your joke

[Anonymous No.11925840]

>>11925838
It’s all yours my friend :)

[Anonymous No.11925849]

>>11925831
Is Jacobson's Basic Algebra or Lang's Algebra better?

[Anonymous No.11925852]

>>11918625

pray it wasn't full monty algebraic

[Anonymous No.11925862]

>>11925849
I've always shilled for Grillet, but Lang isn't that bad.
Never read Jacobson tho.

[Anonymous No.11925917]

>>11925862
Is Lang actually incredibly difficult or is that a meme?

[Anonymous No.11925920]

>>11925917
pro-tip: no book in english is hard

[Anonymous No.11925936]

>>11925917
>Is Lang actually incredibly difficult or is that a meme?
It's a graduate text, published in Springer's "Graduate Texts in Mathematics" series.

[Anonymous No.11925973]

>>11925936
>What are the prerequisites to abstract algebra?
>Abstract algebra is defined by Mirriam Webster as...

This doesn't answer my question of whether it is a difficult text, or if it is approachable without a background in intro abstract algebra for example.

[Anonymous No.11925986]

>>11925973
>This doesn't answer my question of whether it is a difficult text
It isn't.
>if it is approachable without a background in intro abstract algebra
Pic related.

[Anonymous No.11925997]

>>11925849
Lang is encyclopedic. Jacobson is tough but good. Read Jacobson, but I wouldnt recommend either for a first course

[Anonymous No.11926046]

>>11925973
Lang isn't difficult per se, it's just very dense and much more like a reference than a textbook. Feels like Rudin but less well organized. Lang is just very very unpleasant to read. I recommend some other graduate algebra text if you can, but Lang is pretty much the standard and it's not THAT bad. So it's really not a big deal.

[Anonymous No.11926071]

>>11918771
Fug.

[Anonymous No.11926086]

>>11925154

and economy

[Anonymous No.11926115]

>>11920967

>hyper religious Christian

got any proofs? Did they finally translated Recoltes into English?

[Anonymous No.11926174]

>>11926046
I thought Dummit-Foote was the standard grad algebra text?

[Anonymous No.11926275]

>>11925537
>we
I never said that

[Anonymous No.11926301]

>>11925330
everyone hates what they do i guess. i fucking hate my job but it pays too well to quit
>>11925430
because i'm stupid and impulsive. there's difference between being in industry and doing things out of volition

[Anonymous No.11926388]

>>11925753
thank you, anime tranny

[Anonymous No.11926432]

>>11926388
You are quite welcome, my good sir.

[Anonymous No.11926477]

>>11926301
>could be comfy for a year on my current savings probably. would burn my career the fuck down

how on earth does taking one year out, for further education no less, destroy your career?

[Anonymous No.11926488]

>>11926477
>only 6 months into faang job
>quit to do shit
>"wtf how did this guy not last a year at a fagman it's pretty difficult to fuck up that hard"
they wouldn't buy the corona layoff excuse because big tech companies aren't laying off rn
i wouldn't have anything to show for it cause no credentials

[Anonymous No.11926508]

>>11926488
surely if it's faang they'll have some 'safe space' support shit to give you? You should just stick with the job for 6 more months and see if you can get them to sponsor a masters or something. It can't be that hard if you were hired in the first place, and you don't have a legitimate mental illness.

[Anonymous No.11926524]

>>11926508
>they'll have some 'safe space' support shit to give you?
i don't want to get political but the diversity rhetoric is just virtue signalling. it's just like academia, everyone is extremely uncomfortable with it but nobody wants to ruin their career by speaking out

>You should just stick with the job for 6 more months and see if you can get them to sponsor a masters or something
i think i have to work for another year and a half for that and you're still expected to work through your masters

[Anonymous No.11926581]

given a rational interval [x1, x2] and an integer N such that Dx=(x2-x1)/N is a small finite rational, what's the Riemann integral (over that interval) of f'(x) where we use Dt for both the finite Approximation of the integral as well as the standard derivative approximation (f(x+Dx)-f(x))/Dx at all grid points x1+n×Dx?
For N to infinity it must go to f(x2)-f(x1) by the fundamental theorem of calculus

[Anonymous No.11926592]

>>11926388
No problem. It could work with a filtration infinitely long as well, but please do not use my hunch in your next paper. It could fall apart when you would want to have an element from each of the quotients at the same time, which is obviously not possible with direct sums. However, I don't know if you would. I like my groups finite.

[Anonymous No.11926609]

>>11926524
>rhetoric
sounds about right. mental health support is generally ineffectual short of mind altering drugs. you should probably get /fit/ if you aren't already; body comes before mind.

And there are probably way more people in your department in your position or worse

[Anonymous No.11926613]

>>11925537
Collatz by the end of the decade

[Anonymous No.11926680]

>>11926174
Dummit and Foote is probably the second most common book for graduate level. I think a lot of people use it for undergrad too.

[Anonymous No.11926684]

>>11926609
>you should probably get /fit/ if you aren't already; body comes before mind.
i'm trying to fix my sleep so that i wake up at 9 (i work 12-8), i'm slowly cleaning up my diet. getting /fit/ and meditating is probably a good idea as well. going slowly insane and worshipping pagan spirits but i can't recommend that last one.
the whole reason i started mathfagging is because i'm experimenting with biphasic sleep and i get a burst of motivation in the middle of the night
i am on mind altering drugs and they do help a bit. my parents want me to get back on addy but those give me manic panic attacks

>And there are probably way more people in your department in your position or worse
the first year new grads maybe but i'm the only junior on my team. if i last 4 years at this company i'm in a really good spot, i'm just so immature i can't handle working

[Anonymous No.11926688]

>>11926524
>diversity rhetoric is virtue signaling
no, it isn't, no matter how many times you say this it will never be true for me. it might be true for some people but for me it's a moral imperative.

[Anonymous No.11926700]

>>11926684
Take the Buddhapill.

[Anonymous No.11926720]

>>11926680
I think someone asked this in the last thread, but is there a topology textbook that's analogous to what Dummit/Foote is for algebra?

[Anonymous No.11926773]

>>11926684
>biphasic sleep
>worshipping pagan gods
>mind altering drugs

You are 'going slowly insane' because you are inducing psychosis through poor lifestyle choices you pathetic retard

>immature ... can't handle working

how did you even get a job at a faang company in the first place?

[Anonymous No.11926786]

>>11926773
>insanity
thats a delusion

[Anonymous No.11926791]

>>11926688
Saying you really believe it is also virtue signalling. You know this, at least subconsciously. It's okay though, you can be self-interested and still do the right thing to help others. It's a win-win.

[Anonymous No.11926795]

>>11926791
its not inherently virtue signalling, it could also be virtue-controlling. an ape can shout MORAL to make other apes think it is good, or to shame/influence other apes into being good

[Anonymous No.11926799]

>>11926688
the issue isn't going to be solved with what is being done now. it frustrates people to hear uncomfortable rhetoric without impact
>>11926700
perhaps
>>11926773
>you are inducing psychosis through poor lifestyle choices you pathetic retard
medication seriously helped me, i don't want to go back to having panic attacks every other night
i started the pagan god and biphasic sleep thing like 3 days ago, those are symptoms, not a cause
is biphasic sleep really that bad?
>how did you even get a job at a faang company in the first place?
went to good college got handed an interview, studied for the interview. they aren't super special elite clubs for the top 1% they're big corporations that hire shitloads

[Anonymous No.11926819]

>>11926720
you mean Munkres? also D&F a shit

[Anonymous No.11926887]

>>11926684
>>11926799
Why does this guy just make me want the worst for him? Why does he inspire this feeling in me?

[Anonymous No.11926911]

>>11926887
Because he's had everything handed to him but he's so spoiled that he parties too hard and is going to fuck it up.

[Anonymous No.11926962]

>>11926911
And what's worse is he's whining about it at the same time

>>11926613
Nah, I don't think so. I'd put it in the 20-40 years category at least

[Anonymous No.11926973]

>>11926911
>he's had everything handed to him but he's so spoiled that he parties too hard and is going to fuck it up.

[Anonymous No.11927112]

>>11926887
envy is a natural feeling. if it makes you feel any better i'm on course to fucking up my life. i doubt i can fail upwards my way out of this one
>>11926911
>he parties too hard
what parties? i didn't have a social life before covid
i deserve less than what i have though that's a hundred percent for sure
>>11926962
i used be a complete bootlicker, but emotions are emotions and i lack the willpower to control mine. not being able to say anything remotely negative about life at all to anyone ever is gay

[Anonymous No.11927146]

>>11927112
>what parties?
You said you were on a bunch of drugs, up at all hours of the night.

[Anonymous No.11927159]

>>11927146
>You said you were on a bunch of drugs,
medications
>up at all hours of the night.
insomnia

[Anonymous No.11927169]

Love Groebner bases, lads.

[Anonymous No.11927177]

>>11927169
The computer can never actually find them through and it makes me sad.

[Anonymous No.11927225]

>>11925272
based

[Anonymous No.11927246]

>>11927177
Use Macaulay2

[Anonymous No.11927269]

>>11927246
Thanks, I tried Sage but it didn't do well with systems of several thousand polynomials in a few hundred variables.

[Anonymous No.11927305]

>>11927269
I'm not sure what you expected, Sage was basically written in Python.

[Anonymous No.11927306]

>>11927269
>wtf why is this exponential-time algorithm slow when I feed it 4000 polynomials

[Anonymous No.11927350]

Extremely retarded question here:
How do you correctly expand the first term in the Laplace equation in spherical coordinates (i.e. [math] \frac{1}{r^2} \ \frac{dV}{dr} \ ( \ r^2 \ \frac{dV}{r} \ ) [/math] )

I assume regular algebra [math] a^{-2} \ b \ ( \ a^2 \ b \ ) [/math] cannot be utilized here due to the differential operator. Am I supposed to use the chain rule?

[Anonymous No.11927445]

>>11927269
>systems of several thousand polynomials in a few hundred variables.
Based and Groebpilled.

[Anonymous No.11927474]

>>11926819
You’re shit faggot.

[Anonymous No.11927532]

>>11920256
Help.
Numerically, this can be done easily, but I need to find a closed form / explicit formula for the tangent point.

[Anonymous No.11927553]

>>11927350
You've written it wrong.
Btw, no, you use, get this, the Leibniz rule.

[Anonymous No.11927836]

>>11920256
>>11927532
First, move the coordinate center to the ellipse's center.
Then, linearly map the ellipse onto a circle.
Now you just find the point of the old-circle-that's-now-a-squiggly-thingy that has minimum norm, easy peasy.
Easy peasy.

[Anonymous No.11928007]

>>11927836
Let's say my initial ellipse was horizontal. If I map the ellipse onto a circle, and use the same mapping to transform the initial circle into some curve C (now looks like a thin vertical ellipse), then wouldn't the points with minimum norm on C be the topmost or bottommost points of it, irregardless of the position of the tangent point?

[Anonymous No.11928089]

>>11918605
>tfw going to community college and have to relearn Algebra and Trig concepts
feel like a retard not knowing how to complete a perfect square when 12 year olds in Korea do.

[Anonymous No.11928137]

>>11928089
[math]f(\theta)=\sin^2(\theta)+cos^2(\theta) \Rightarrow f'(\theta)=2\sin(\theta)\cos(\theta)-2\cos(\theta)2\sin(\theta) = 0 \\f(\theta)=f(0)=0^1+1^2=0+1=1[/math]

[Anonymous No.11928148]

>>11927350
Leibniz and chain rule are the only things you need to differentiate, in any context. From basic calculus to Gâteaux derivatives through differential geometry that shit will always save your ass (except maybe on stochastic calculus, I remember hearing the product rule is not exactly the same there)

[Anonymous No.11928166]

>>11928148
What about the Radon–Nikodym derivative?

[Anonymous No.11928181]

>>11928166
Are there even any 'rules' for that? Only thing I can think of is maybe some corollary of Fubini's theorem.

[Anonymous No.11928186]

>>11928137
Nice LaTeX

[Anonymous No.11928196]

>>11928186
[math]T^{h^a}_{n_k}s[/math]

[Anonymous No.11928249]

>>11928007
No, because it's the norm in relation to the new circle.

[Anonymous No.11928260]

>>11928148
You also need [eqn]\frac{d}{dt} \langle x(t), y(t) \rangle = \langle \frac{dx (t) }{dt} , y(t) \rangle + \langle x(t) , \frac{dy (t) }{dt} \rangle [/eqn].
Which, in all fairness, is a version of the product rule.
It's still useful enough to merit mentioning tho.

Also the stuff with differential of the determinant equalling the trace, that's important.

[Anonymous No.11928276]

man i can’t wait to slowly engulf that rock hard beaker in my pussy and ride it like a rodeo boy until it shatters or squirts out clammy juice

[Anonymous No.11928283]

>>11928276
Ma'am please don't use the beaker to dilate.

[Anonymous No.11928289]

>>11928260
>differential of the determinant equalling the trace
Can you elaborate on this? I don't think I've heard this before.

[Anonymous No.11928303]

>>11928289
This thingeridoo:
https://en.wikipedia.org/wiki/Jacobi%27s_formula
I honestly just always remember that SL has Lie algebra trace zero matrices, so the adjugate part completely passes me by until I look at the formula again.

[Anonymous No.11928305]

>>11928276
L O N D O N

[Anonymous No.11928317]

>>11928303
Thanks. I think I have seen this before, now that I look at the Wiki article.

[Anonymous No.11928333]

>>11928317
Probably Lie Groups stuff.