/sci/ - Science & Math » Thread #12853803

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Anonymous Fri 19 Mar 05:21:29 2021 No.12853803 View Reply Original Report

Quoted By: >>12853807 >>12854015 >>12854062 >>12854331 >>12857645 >>12858060 >>12858811 >>12859935 >>12865769 >>12866780 >>12868724

Math, generally
>make it stop edition
Talk maths

Anonymous

Anonymous Fri 19 Mar 2021 05:22:13 No.12853807 Report

Quoted By: >>12853811 >>12853834 >>12855034 >>12859898 >>12861865 >>12867225 >>12868471

>>12853803
name things nobody understands.
>quiver theory

Anonymous

Anonymous Fri 19 Mar 2021 05:22:55 No.12853811 Report

Quoted By: >>12868539

>>12853807
Just pull on the drawstring

Anonymous

Anonymous Fri 19 Mar 2021 05:32:27 No.12853834 Report

Quoted By: >>12854270

>>12853807
>sheaf theory

literally, there is a "quiver theory" and a "sheaf theory" and nobody understands what either is.

Anonymous

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Anonymous Fri 19 Mar 2021 05:35:10 No.12853843 Report

Quoted By:

First for Weierstrass, who has btfo'd and will continue to btfo feeble-minded undergrads for an eternity

Anonymous

Anonymous Fri 19 Mar 2021 06:45:40 No.12854015 Report

Quoted By: >>12854019 >>12857941 >>12857946

>>12853803
The proof of kruskal algorithm starts by saying given tree S produced by the algo assume for contradiction a spanning tree T with weight less than S.
Select an edge p from T and add it to S.
This will produce a cycle.
Here is what i dont get. Why are allowed to say p is the largest weight of that cycle?

The algorithm selects the least weight such that it produces no cycle. Isnt it possible there exist an edge selected from the algo larger than p because p would have created a cycle in S?

Anonymous

Anonymous Fri 19 Mar 2021 06:48:57 No.12854019 Report

Quoted By: >>12854060

>>12854015
>kruskal
oh no he mentioned a physicist!!! OH NOES!

Anonymous

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Anonymous Fri 19 Mar 2021 07:14:16 No.12854060 Report

Quoted By:

>>12854019
>seething over physicists
Someone's superiority has made you upset

Anonymous

Anonymous Fri 19 Mar 2021 07:15:10 No.12854062 Report

Quoted By: >>12854081 >>12854119 >>12859374

>>12853803
What to make of people who "hate math"? Are they stupid? Afraid of challenges? I always think less of people who immediately say things like I hate math

Anonymous

Anonymous Fri 19 Mar 2021 07:18:20 No.12854068 Report

Quoted By: >>12868476 >>12869302

Whats some schizo math field that is fun to study as a hobby and is pretty undeveloped as of now?

Anonymous

Anonymous Fri 19 Mar 2021 07:20:35 No.12854072 Report

Quoted By: >>12854075 >>12854160 >>12854735

Is it just me or is real analysis fucking boring.

Anonymous

Anonymous Fri 19 Mar 2021 07:22:24 No.12854075 Report

Quoted By: >>12854093 >>12854835

>>12854072
it is and im studying at these very moments for a retake next week
>prove this prove that
fucking niggers im not even a mathematician

Anonymous

Anonymous Fri 19 Mar 2021 07:29:19 No.12854081 Report

Quoted By: >>12854092 >>12858300

>>12854062
What would be a good topic to convert someone who "hates math"?
Something without any of the negative connotations of high school math. No geometry, no trigonometry, no polynomials, no "solving for x".
Maybe graph theory

Anonymous

Anonymous Fri 19 Mar 2021 07:35:41 No.12854092 Report

Quoted By: >>12854099 >>12854105

>>12854081
geometry is a negative connotation? its literally the most based field, who can hate it

Anonymous

Anonymous Fri 19 Mar 2021 07:36:21 No.12854093 Report

Quoted By: >>12854122

>>12854075
Hmm, tell me, when you hear the phrase "epsilon-delta" how does that make you feel?

Anonymous

Anonymous Fri 19 Mar 2021 07:40:18 No.12854099 Report

Quoted By:

>>12854092
"High school geometry" is code for "shitty proofs for idiots" in America
I imagine the word is dirty

Anonymous

Anonymous Fri 19 Mar 2021 07:42:55 No.12854105 Report

Quoted By:

>>12854092
Yeah, it might be one of the most based topics in high school if taught properly, but if someone doesn't like math then they probably had a bad time in high school.

Anonymous

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Anonymous Fri 19 Mar 2021 07:51:41 No.12854119 Report

Quoted By: >>12858771 >>12867941

>>12854062
Why would people love some social constructed axioms and inference rules leading to the dubious situation where the most fertile logics and theorems rely on the voodooism called the axiom of choice which is not verified in nature?

Anonymous

Anonymous Fri 19 Mar 2021 07:52:20 No.12854122 Report

Quoted By: >>12854126

>>12854093
makes me wanna puke and drink my own vomit to puke again

Anonymous

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Anonymous Fri 19 Mar 2021 07:54:25 No.12854126 Report

Quoted By: >>12854132 >>12854140

>>12854122
Another undergrad dabbed on, from the grave

Anonymous

Anonymous Fri 19 Mar 2021 07:58:10 No.12854132 Report

Quoted By: >>12854136 >>12854280

>>12854126
fuck you after this retake im not gonna see that shit ever again

epsilon delta my ass

Anonymous

Anonymous Fri 19 Mar 2021 08:01:39 No.12854136 Report

Quoted By: >>12854139

>>12854132
>im not gonna see [analysis] ever again
oh, so you're transitioning?

Anonymous

Anonymous Fri 19 Mar 2021 08:04:41 No.12854139 Report

Quoted By:

>>12854136
ill never become a tranny, real talk

Anonymous

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Anonymous Fri 19 Mar 2021 08:04:48 No.12854140 Report

Quoted By: >>12854159 >>12854256

>>12854126
Boo

Anonymous

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Anonymous Fri 19 Mar 2021 08:11:23 No.12854156 Report

Quoted By:

>tropical geometry

Anonymous

Anonymous Fri 19 Mar 2021 08:12:26 No.12854159 Report

Quoted By:

>>12854140
hyper-reals are neat.

Anonymous

Anonymous Fri 19 Mar 2021 08:13:51 No.12854160 Report

Quoted By: >>12854173

>>12854072
It's not boring. Rudin speedrunning it just because he could makes it look boring.

Anonymous

Anonymous Fri 19 Mar 2021 08:20:25 No.12854169 Report

Quoted By: >>12854178

Analytic continuation still feels like black magic to me.

Anonymous

Anonymous Fri 19 Mar 2021 08:22:18 No.12854173 Report

Quoted By:

>>12854160
based.
i will never understand people that suck that book's dick when there's better alternatives.
Tho, the fact that the copy i got was printed like shit probably didn't help my impression of it.

Anonymous

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Anonymous Fri 19 Mar 2021 08:25:11 No.12854178 Report

Quoted By: >>12854709

>>12854169
all math is black magic.
cease this dark art before it corrupts you further brother.

Anonymous

Anonymous Fri 19 Mar 2021 08:47:08 No.12854222 Report

Quoted By: >>12854279 >>12862708

What is your favorite stochastic process?

Anonymous

Anonymous Fri 19 Mar 2021 09:11:20 No.12854256 Report

Quoted By:

>>12854140
Mega cope
Just accept you got filtered

Anonymous

Anonymous Fri 19 Mar 2021 09:24:06 No.12854270 Report

Quoted By:

>>12853834
sheaf theory is easy

Anonymous

Anonymous Fri 19 Mar 2021 09:32:53 No.12854279 Report

Quoted By:

>>12854222
my sex life

Anonymous

Anonymous Fri 19 Mar 2021 09:33:23 No.12854280 Report

Quoted By:

>>12854132
>retake
Are you in grade 5 ?

Anonymous

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Anonymous Fri 19 Mar 2021 10:05:39 No.12854325 Report

Quoted By: >>12854327 >>12854333 >>12854337 >>12854577

I, uh. Never learned the multiplication table.
What are some tricks?
1 is easy.
2 is just double so it's easy.
These are the ones I've figured out so far.
x3 is 2*x+3
x4 is 2*x + 2*x
x5 is (x*10)/2
x9 is (x1-1) & (y where y is x2+y = 10)
for example 8*9 => 72 (8-1, 8+2 = 10)
x10 is x0

Anonymous

Anonymous Fri 19 Mar 2021 10:06:42 No.12854327 Report

Quoted By:

>>12854325
oops, I did not really mean to write x1 and x2 for x9

Anonymous

Anonymous Fri 19 Mar 2021 10:12:19 No.12854331 Report

Quoted By: >>12854359

>>12853803
are numbers real?

Anonymous

Anonymous Fri 19 Mar 2021 10:13:53 No.12854333 Report

Quoted By: >>12854336

>>12854325
oh yeah, I could to x6 with just x5+6. That's pretty quick too. If it's x5, it ends in 2, if it's x0 it obviously ends in 6. Just 7 and 8 left now and then a bit of training to help me do it quicker.

Anonymous

Anonymous Fri 19 Mar 2021 10:16:03 No.12854336 Report

Quoted By:

>>12854333
wait no lol, that's not how it works.

Anonymous

Anonymous Fri 19 Mar 2021 10:16:41 No.12854337 Report

Quoted By: >>12854343

>>12854325
>x3 is 2*x+3
It's 2*x + x
Just look at your hands for 9

Anonymous

Anonymous Fri 19 Mar 2021 10:19:10 No.12854343 Report

Quoted By:

>>12854337
yeah thanks, meant that, wrote it all pretty badly lol

Anonymous

Anonymous Fri 19 Mar 2021 10:22:49 No.12854359 Report

Quoted By:

>>12854331
no, real is a set of numbers.

Anonymous

Anonymous Fri 19 Mar 2021 10:31:44 No.12854389 Report

Quoted By: >>12854399

Lets say there are 2 polynomials of at most degree $m < n$ and I have $n$ values of $c$ such that $a(c) = b(c)$. I need to prove that $a(x) = b(x)$

Here's the proof I got: let deg $[a(x) - b(x)] = m < n$, then $a(x) - b(x)$ can be factored in at most $m$ ways $(x - c_1) \cdots (x - c_m)$ but there exists a $c$ such that $c \neq c_i$ for all $m$ values, yet

$$a(c) - b(c) = 0 = k (c - c_1) \cdots (c - c_m)$$

by the fact that $F$ is a field, then $F[x]$ is an integral domain and has no zero divisors. This means $k = 0$ since all the other terms are non-zero.
$$a(x) - b(x) = 0 \implies a(x) = b(x)$$

I redid the proof several times but idk something still annoys me. Is this correct?

Anonymous

Anonymous Fri 19 Mar 2021 10:34:33 No.12854397 Report

Quoted By:

Reposting using proper formatting:

Lets say there are 2 polynomials of at most degree $m < n$ and I have $n$ values of $c$ such that $a(c) = b(c)$ . I need to prove that $a(x) = b(x)$

Here's the proof I got: let deg $[a(x) - b(x)] = m < n$ , then $a(x) - b(x)$ can be factored in at most $m$ ways $(x - c_1) \cdots (x - c_m)$ but there exists a $c$ such that $c \neq c_i$ for all $m$ values, yet

$a(c) - b(c) = 0 = k (c - c_1) \cdots (c - c_m)$

by the fact that $F$ is a field, then $F[x]$ is an integral domain and has no zero divisors. This means $k = 0$ since all the other terms are non-zero.
$a(x) - b(x) = 0 \implies a(x) = b(x)$

I redid the proof several times but idk something still annoys me. Is this correct?

Anonymous

Anonymous Fri 19 Mar 2021 10:35:23 No.12854399 Report

Quoted By: >>12854412

>>12854389
consider a-b. degree of this polynomial is at most m, but it has at least n roots. therefore it's the zero polynomial.

Anonymous

Anonymous Fri 19 Mar 2021 10:41:19 No.12854412 Report

Quoted By: >>12854422 >>12854426 >>12854456

>>12854399
but the deg 0 is undefined? this is the main issue I was having with the proof. why does n roots imply it is 0?

Anonymous

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Anonymous Fri 19 Mar 2021 10:44:32 No.12854418 Report

Quoted By: >>12854456

How did you see a lynx? Was it scary?

Anonymous

Anonymous Fri 19 Mar 2021 10:45:45 No.12854422 Report

Quoted By: >>12854456

>>12854412
Isn't this one of the places where it's convenient to say that $\deg 0 = -\infty$

Anonymous

Anonymous Fri 19 Mar 2021 10:47:21 No.12854426 Report

Quoted By:

>>12854412
if a polynomial P has a root k, then it's divisible by (x-k). the quotient has lesser degree than P, at least over an integral domain or something. this easily implies that a degree m polynomial cannot have more than m roots.

Anonymous

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Anonymous Fri 19 Mar 2021 11:02:11 No.12854456 Report

Quoted By: >>12854524 >>12854678

>>12854412
>>12854422
You can either call it undefined or set it to negative infinity. Those are the only reasonable options. No integer $n$ would work, as $n = \text{deg}(0) = \text{deg}(0 \cdot x^m) = n+m$ for all $m \ge 0$ .

>>12854418
I was just walking through the woods when I heard the animal-in-a-bush noise. I looked in the direction to see what kind of a bird was responsible and a cat popped out running away from me. It would have been scary if it had stayed there, but I guess I was the more scary beast in that situation. Lynx is basically a domestic cat compared to the tigers our neighbours.

Anonymous

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Anonymous Fri 19 Mar 2021 11:23:44 No.12854522 Report

Quoted By: >>12854541

Anonymous

Anonymous Fri 19 Mar 2021 11:24:39 No.12854524 Report

Quoted By: >>12854850

>>12854456
Waow
https://youtu.be/LMRc2T5Cebw?list=PLDwyP_CyZqit6uwkZSaHYSlTxrcGIx2fZ

Anonymous

Anonymous Fri 19 Mar 2021 11:28:56 No.12854541 Report

Quoted By: >>12854545

>>12854522
What's the boldface P represent

Anonymous

Anonymous Fri 19 Mar 2021 11:31:43 No.12854545 Report

Quoted By:

>>12854541
$\wp$

Anonymous

Anonymous Fri 19 Mar 2021 11:44:47 No.12854577 Report

Quoted By: >>12854671 >>12859589

>>12854325
When I was in grad school there was a guy who did the Toom-Cook algorithm in his head when he didn't have a calculator. He single-handedly convinced me I was right to avoid number theory.

Anonymous

Anonymous Fri 19 Mar 2021 12:15:00 No.12854671 Report

Quoted By:

>>12854577
>Toom-Cook

that actually sounds like fun

Anonymous

Anonymous Fri 19 Mar 2021 12:16:39 No.12854678 Report

Quoted By: >>12854850

>>12854456
a lynx is probably more safe than a wild cat

NEARAutomata

NEARAutomata Fri 19 Mar 2021 12:26:35 No.12854709 Report

Quoted By: >>12854717 >>12854736

>>12854178

when i woke up this morning i saw your post and immediately called bullshit but now im seriously questioning my own arrogance.

This is highly likely

NEARAutomata

NEARAutomata Fri 19 Mar 2021 12:28:26 No.12854717 Report

Quoted By: >>12854736 >>12854850

>>12854709

math itself is a type of ouija board in base 10

Anonymous

Anonymous Fri 19 Mar 2021 12:36:14 No.12854735 Report

Quoted By:

>>12854072
You're probably just another failure who'd enjoy shit like algebraic number theory.

Anonymous

Anonymous Fri 19 Mar 2021 12:36:32 No.12854736 Report

Quoted By:

>>12854709
>>12854717
https://www.youtube.com/watch?v=lYtkW9_Wmn4

Black magic huh? Asimov likened math to arcane rune pushing to fold spacetime. I mean it is fucking crazy that we could discover black holes with just some tensor calculus.

Anonymous

Anonymous Fri 19 Mar 2021 13:23:12 No.12854835 Report

Quoted By: >>12854850

>>12854075
What's your major?
>>12854170
True, but after three or so irregular books (I can't in good faith call them bad) I didn't have it in me to try more of them.

Anonymous

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Anonymous Fri 19 Mar 2021 13:31:34 No.12854850 Report

Quoted By: >>12854908 >>12854997 >>12856174

>>12854524
https://www.youtube.com/watch?v=IVE3eltiB-g

>>12854678
Could very well be. They are very timid. It's funny how a wildcat looks fluffier and like a pet, but is the more ferocious one. Have you seen one? I haven't. Maybe I get to go to some place where they live some day.

>>12854717
Nope. Hexadecimals. t. $\frak{Mathemagick\ Hex}$

>>12854835
I can very well see why. But hey, the good thing is that it basically forces you to read them in English or French, so you will learn the international terminology. Sometimes the translations can be a bit odd, like for example calling commutative ring with every non-zero element invertible a municipality. Not that fields make any more sense. The German names for the algebraic structures do, however. Groups, rings (like an international criminal ring = a band of criminals) and bodies (like a student body for example) are all collections of people.

Anonymous

Anonymous Fri 19 Mar 2021 13:52:20 No.12854908 Report

Quoted By: >>12854960

>>12854850
>Sometimes the translations can be a bit odd, like for example calling commutative ring with every non-zero element invertible a municipality.
It's more in the meaning of "realm" than "municipality". There's an older English book which calls algebraic number fields "number realms" actually.

Anonymous

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Anonymous Fri 19 Mar 2021 14:04:12 No.12854960 Report

Quoted By: >>12854994

>>12854908
Oh right, domains in English. They carry the regal heritage. I was thinking about the Finnish word which is literally a municipality. It also took a while to remember that a "total area" translates to an integral domain.

Anonymous

Anonymous Fri 19 Mar 2021 14:11:28 No.12854994 Report

Quoted By: >>12855339

>>12854960
"Kuningaskunta".

Anonymous

Anonymous Fri 19 Mar 2021 14:12:15 No.12854997 Report

Quoted By: >>12855339 >>12855391

>>12854850
Yeah, that's an upside. The problem comes when I have to ask questions or explain something and I forget the terms in spanish. Happens in more than just math really, I spend way too much time reading english.
Field is translated as cuerpo (body) in spanish too actually, but the ring connection isn't there. The one that puzzled me for a second was limit point

Anonymous

Anonymous Fri 19 Mar 2021 14:22:41 No.12855034 Report

Quoted By:

>>12853807
Choas Theory

Anonymous

Anonymous Fri 19 Mar 2021 14:47:06 No.12855129 Report

Quoted By: >>12855152 >>12855193 >>12855201 >>12855322 >>12855598 >>12861354

The other day I assisted a conference on "What Can You Work if you can't find or don't want a job in academia". The whole thing felt like a recruiting ad for the company the guy was working on but he gave some advice, maybe stuff that everyone already knows.
>you need good (social) networking more than anything
>machine and ai learning is hot right now and mathematicians will get automatically hired if they know programming
>videos and tutorials are easier for learning than books (kinda disagree with this but that depends on the subject)
>you can still publish papers even if you work on companies
>a degree/phd is more of a formality for companies
Now I know I want to work a company that makes AI weapons or something like that.

Anonymous

Anonymous Fri 19 Mar 2021 14:53:10 No.12855152 Report

Quoted By:

>>12855129
I would agree with all those those point as from my experience they are all true, except the networking. Unless you want to move into management then you can be as anti-social as you want as long as you do good work.

Anonymous

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Anonymous Fri 19 Mar 2021 15:00:06 No.12855179 Report

Quoted By: >>12855185

Well, I finished munkres up to where it looks like most quals want (which is really fuck all, sorry point-set bros). I'm now onto algebra review. I think I'll read munkres up to the ultimate metrization theorem (smirnov?) because it seems like a neat result, but I can't be assed to spend 2 more weeks grinding exercises for something I'm not likely to need. That'll be for relaxation though.
Pic related, the next task for myself

Anonymous

Anonymous Fri 19 Mar 2021 15:02:30 No.12855185 Report

Quoted By: >>12855210

>>12855179
>munkres
>not dugundji

Anonymous

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Anonymous Fri 19 Mar 2021 15:04:41 No.12855193 Report

Quoted By:

>>12855129
the green text about 300k starting was right all along

Anonymous

Anonymous Fri 19 Mar 2021 15:06:45 No.12855201 Report

Quoted By: >>12855259 >>12855335

>>12855129
>>machine and ai learning is hot right now and mathematicians will get automatically hired if they know programming
has machine learning and ai ever been used for anything useful by a low / middle tier company? i mean i know the big ones are using it successfully, but every "AI project" i've seen in small companies has always been garbage that could be replaced by a simple SQL query with 99% of the functionality and 1% of the effort

Anonymous

Anonymous Fri 19 Mar 2021 15:10:51 No.12855210 Report

Quoted By: >>12856339

>>12855185
>dugundji
>not willard

Anonymous

Anonymous Fri 19 Mar 2021 15:29:37 No.12855259 Report

Quoted By:

>>12855201
Stop blowing my spot up anon. Small companies pay me a fortune to wrap traditional databases in a shitty AI interface.

Anonymous

Anonymous Fri 19 Mar 2021 15:38:54 No.12855276 Report

Quoted By:

is anyone interested in doing a lang study group in may?

Anonymous

Anonymous Fri 19 Mar 2021 15:57:03 No.12855322 Report

Quoted By: >>12855335

>>12855129
>>>you need good (social) networking more than anything
>>machine and ai learning is hot right now and mathematicians will get automatically hired if they know programming
>>videos and tutorials are easier for learning than books (kinda disagree with this but that depends on the subject)
>>you can still publish papers even if you work on companies
>>a degree/phd is more of a formality for companies
alll this stuff is obvious

also, AI is hot right now, not in 10 years.

Anonymous

Anonymous Fri 19 Mar 2021 16:02:45 No.12855335 Report

Quoted By:

>>12855201
Usually these small companies are "bought" or outsourced by big companies to make their projects, which later are resold. The company the guy is working with mostly worked for a big bank and pharmaceutical industries.
>>12855322
Pretty much, I'm surprised people there didn't knew that already.

Anonymous

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Anonymous Fri 19 Mar 2021 16:04:12 No.12855339 Report

Quoted By: >>12855832

>>12854994
Good point. One day, I will define a structure called "empire".

>>12854997
Yeah, that also happens quite easily. But hey, who talks to anyone irl anyway? Isn't punto de acumulación pretty logical, though? Stuff gathers around it.

Anonymous

Anonymous Fri 19 Mar 2021 16:23:54 No.12855391 Report

Quoted By: >>12855832

>>12854997
>Field is translated as cuerpo (body) in spanish
In my experience that was in old books, since the original word in german was körper. Most recent ones use campo instead to match english books.

Anonymous

Anonymous Fri 19 Mar 2021 16:50:25 No.12855446 Report

Quoted By: >>12855499 >>12855981

The octagon $P_1 P_2 P_3 P_4 P_5 P_6 P_7 P_8$ is inscribed in circle with all the vertices in the given order around the circumference. $P_1 P_3 P_5 P_7$ is a square of area 5 and $P_2 P_4 P_6 P_8$ is a rectangle of area n. For a given n, what are the maximum and minimum areas of the octagon?

Anonymous

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Anonymous Fri 19 Mar 2021 17:00:29 No.12855479 Report

Quoted By: >>12855489 >>12867941

can someone help me visualize this? Why can you just do this?
You follow some integral rule on the function, then you just throw in the beginning and the end for x, taking away the beginning outcome from the end outcome. And this somehow finds the area under the space of the given parameters for the function. How does this fill in the exact amount of space needed under the line?

Anonymous

Anonymous Fri 19 Mar 2021 17:02:54 No.12855489 Report

Quoted By:

>>12855479
look at the definition of a riemann sum

Anonymous

Anonymous Fri 19 Mar 2021 17:06:02 No.12855499 Report

Quoted By:

>>12855446
I've seen this before

Anonymous

Anonymous Fri 19 Mar 2021 17:13:05 No.12855535 Report

Quoted By: >>12855558

Can I write integrals with a sigma notation instead of a long s sum sign?

Anonymous

Anonymous Fri 19 Mar 2021 17:19:18 No.12855558 Report

Quoted By:

>>12855535
https://www.math.ucdavis.edu/~hunter/m125b/ch1.pdf

Anonymous

Anonymous Fri 19 Mar 2021 17:29:28 No.12855598 Report

Quoted By: >>12858155

>>12855129
Don't forget about quantum computing. That stuff is great for people who like analysis, operator theory, and even possibly representation theory.

Anonymous

Anonymous Fri 19 Mar 2021 18:32:21 No.12855832 Report

Quoted By: >>12856008

>>12855339
Oh I explained myself badly. I like punto de acumulación, it was limit point that threw me off a bit.
>One day, I will define a structure called "empire".
Please do, that sounds cool as hell
>>12855391
That's interesting. I never used an abstract algebra text in spanish and all the other books it could have come up actually were pretty old.
Man I ought to learn german someday.

Anonymous

Anonymous Fri 19 Mar 2021 18:51:40 No.12855890 Report

Quoted By: >>12855900

When I studied mathematics one of lecturers said "Frankly all we know about Euler-Mascheroni constant is that its value is somewhere between 0 and 1." Was any progress made since? Is it transcendent? Irrational? Anything?

Anonymous

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Anonymous Fri 19 Mar 2021 19:00:16 No.12855900 Report

Quoted By:

>>12855890
we know plenty of digits but fuck all else

Anonymous

Anonymous Fri 19 Mar 2021 19:08:22 No.12855923 Report

Quoted By: >>12855947 >>12856637 >>12859481

Why do we call them linear equations if they aren’t linear operators? Shouldn’t we just always call them affine operators?

Anonymous

Anonymous Fri 19 Mar 2021 19:10:05 No.12855930 Report

Quoted By: >>12858159 >>12858181

Can you define a curve as a union of a bunch of little arcs of a circle of differing radius, (0,inf]?

Anonymous

Anonymous Fri 19 Mar 2021 19:11:50 No.12855933 Report

Quoted By: >>12855937 >>12855974 >>12855984 >>12856008 >>12856069 >>12856319 >>12856324 >>12858048 >>12859865 >>12867941 >>12868518

Let's have a quick survey:
Among all theorems that are mathcore (that is, excluding extremely autistic stuff that belongs to specialized fields) which one do you think has the absolutely ugliest proof?

El cAbrón

El cAbrón Fri 19 Mar 2021 19:13:16 No.12855937 Report

Quoted By:

>>12855933
ABC conjecture

Anonymous

Anonymous Fri 19 Mar 2021 19:18:03 No.12855947 Report

Quoted By:

>>12855923
they look like lines :^)

Anonymous

Anonymous Fri 19 Mar 2021 19:30:56 No.12855974 Report

Quoted By: >>12856066

>>12855933
Fubini’s Theorem

Anonymous

Anonymous Fri 19 Mar 2021 19:37:01 No.12855981 Report

Quoted By:

>>12855446
look at one quarter of the circle O, P_2, P_4 then think about where P_3 should be

Anonymous

Anonymous Fri 19 Mar 2021 19:38:04 No.12855984 Report

Quoted By:

>>12855933
1+1=2

Anonymous

View Same Google iqdb SauceNAO spj ms.png, 105KiB, 393x370

Anonymous Fri 19 Mar 2021 19:47:13 No.12856008 Report

Quoted By:

>>12855832
>Oh I explained myself badly. I like punto de acumulación, it was limit point that threw me off a bit.
Ah, I see. I must admit I too had problems with limit and derived points at first. However, any variant of accumulation point seems reasonable. Now I need to think about this imperial structure of mine.

>>12855933
The axiom of choice, obviously. Dugundji's proof is absolutely horrendous.

Anonymous

Anonymous Fri 19 Mar 2021 20:11:29 No.12856066 Report

Quoted By:

>>12855974
What, why?
Its not a exactly an elegant proof but its a simple application of Tonelli, which in itself can be proved by super standard measure theoretic induction.
Can you explain why this is particularly ugly? Or which proof you are referring to?

Anonymous

Anonymous Fri 19 Mar 2021 20:13:22 No.12856069 Report

Quoted By: >>12856652 >>12868174

>>12855933
I recall the Sylow theorems having a pretty fucking ugly proof.

Anonymous

View Same Google iqdb SauceNAO Screen Shot 2021-03-19 at 1.24.4 (...).png, 300KiB, 2656x1242

Anonymous Fri 19 Mar 2021 20:31:31 No.12856112 Report

Quoted By: >>12856190 >>12856246

Am I retarded or is this example wrong?

The matrix with respect to the standard basis vectors is constructed as so
T(1,0) = 41+0, -20 0 = 41,-20
T(0,1) = 0+7, 0+74 = 7,74
M(T, (e1, e2)) = 41 7
-20 74

since each column represents what happens to the basis vectors under T

then M(T, (1,4), (7,5)) is made by taking
T(1,4) = 41 + 28, -20, 296-20 = 69, 276
T(7,5) = 322, 230
so we have
69 322
276 230

???!?!?!?!?!??!??!?!??!??!??!?!!!??!?!?!?!!?

Anonymous

Anonymous Fri 19 Mar 2021 20:51:51 No.12856174 Report

Quoted By: >>12856186

Does calculus include implicit assumptions of euclidean geometry?

>>12854850
Oo I know that song well!

Anonymous

Anonymous Fri 19 Mar 2021 20:55:53 No.12856186 Report

Quoted By:

>>12856174
No. All of the geometry that you use in calc is analytic, Like using the equation of the circle to find the slope of a tangent line or trying to find the largest rectangle that could fit under a parabola.

Anonymous

Anonymous Fri 19 Mar 2021 20:56:36 No.12856190 Report

Quoted By: >>12856204

>>12856112
You pass the new bases through the new matrix

Anonymous

Anonymous Fri 19 Mar 2021 21:00:13 No.12856200 Report

Quoted By: >>12856333

What kind of socks should I wear when studying algebra?

Anonymous

Anonymous Fri 19 Mar 2021 21:03:32 No.12856204 Report

Quoted By: >>12856260

>>12856190
what? why?

Anonymous

Anonymous Fri 19 Mar 2021 21:12:48 No.12856246 Report

Quoted By:

>>12856112
T(1,4) = 69*(1,4) + 0*(7,5)
T(7,5) = 0*(1,4) + 46*(7,5)

Now look up the definition again of matrix of a linear mapping with respect to a basis.

Anonymous

Anonymous Fri 19 Mar 2021 21:18:10 No.12856260 Report

Quoted By: >>12856297

>>12856204
Because the second matrix is built for the second pair of bases, to satisfy the transformation.

Anonymous

Anonymous Fri 19 Mar 2021 21:27:23 No.12856297 Report

Quoted By: >>12856578

>>12856260
Why are you posting in /mg/ if you can't even explain linear algebra?

Anonymous

Anonymous Fri 19 Mar 2021 21:33:23 No.12856319 Report

Quoted By: >>12856652 >>12867941 >>12868174 >>12868263

>>12855933
Sylow theorems or fucking Tychonoff's theorem.

Anonymous

Anonymous Fri 19 Mar 2021 21:33:58 No.12856324 Report

Quoted By: >>12858581

>>12855933
Four color problem? Classification of simple groups?

Anonymous

Anonymous Fri 19 Mar 2021 21:35:03 No.12856333 Report

Quoted By:

>>12856200
None. You need to count up to twenty.

Anonymous

Anonymous Fri 19 Mar 2021 21:35:53 No.12856339 Report

Quoted By:

>>12855210
>Willard
>not Engelking

Anonymous

Anonymous Fri 19 Mar 2021 22:05:55 No.12856451 Report

Quoted By: >>12856656

So I know there was some guy complaining in another thread about how Munkres' Topology has too much abstruse infinite product shit, but I just want to say if you don't have a natural inclination to think "hey, what if we made this thing infinite" then you just don't really have a soul.
Yeah, it may not be the most useful thing, but how can you not be intrigued? Not saying everyone should go deep into esoteric set theory inaccessible cardinal autism, but shit like transfinite induction over the ordinals is cool to mess around with at least once and shouldn't cause any long term negative effects.

Anonymous

Anonymous Fri 19 Mar 2021 22:32:10 No.12856578 Report

Quoted By: >>12856618

>>12856297
My explanation makes more sense than yours, lol. Telling someone to just look at the definition gives no intuition.

Anonymous

Anonymous Fri 19 Mar 2021 22:41:47 No.12856618 Report

Quoted By:

>>12856578
What you said is vague and conveys absolutely no intuition

Anonymous

Anonymous Fri 19 Mar 2021 22:46:12 No.12856637 Report

Quoted By: >>12856827 >>12857309

>>12855923
I had this one prof in undergrad, geometer, worlds leading expert in planimeters, who would mark you -1 for calling anything affine linear, including equations.
His autism was inspiring

Anonymous

Anonymous Fri 19 Mar 2021 22:48:29 No.12856652 Report

Quoted By: >>12856819 >>12866139

>>12856319
>>12856069
There are nice proofs of the sylow theorems anons

Anonymous

View Same Google iqdb SauceNAO 1615082475756.png, 296KiB, 500x375

Anonymous Fri 19 Mar 2021 22:49:33 No.12856656 Report

Quoted By:

>>12856451

Anonymous

Anonymous Fri 19 Mar 2021 23:36:33 No.12856819 Report

Quoted By: >>12868174

>>12856652
There's nothing "nice" about the Sylow theorems.

El cAbrón

El cAbrón Fri 19 Mar 2021 23:38:00 No.12856827 Report

Quoted By:

>>12856637
based

Anonymous

Anonymous Sat 20 Mar 2021 01:38:09 No.12857309 Report

Quoted By: >>12857508

>>12856637
Is y=x+5 an affine equation?

Anonymous

Anonymous Sat 20 Mar 2021 02:50:46 No.12857508 Report

Quoted By: >>12857921

>>12857309
Yes, because it doesn't go through the origin

Anonymous

Anonymous Sat 20 Mar 2021 03:39:11 No.12857645 Report

Quoted By: >>12857921

>>12853803
You forgot the link to the last thread, you fucking retard. Don't create /mg/ generals if you're a newfag that doesn't know how things work.

Anonymous

Anonymous Sat 20 Mar 2021 03:39:11 No.12857646 Report

Quoted By: >>12857689 >>12857738 >>12857938 >>12858597 >>12861308 >>12867941

why do so many universities make you take a linear algebra course before an abstract algebra course? vector spaces make so much sense when you talk about them in the context of fields.

Anonymous

Anonymous Sat 20 Mar 2021 03:53:49 No.12857689 Report

Quoted By: >>12857710 >>12861308

>>12857646
Hah, at my school they gave us a linear algebra course without eve mentioning vector spaces, we just solved matrices and did geometric stuff with vector operations. Cegep in Quebec. Soon I'm going to actual university.

Anonymous

Anonymous Sat 20 Mar 2021 04:01:48 No.12857710 Report

Quoted By: >>12857864 >>12859033

>>12857689
did your school at least explain the intuition behind matrix multiplication? matrix representations of linear transformations? or did they just tell you how to multiply matrices without explaining why it's defined that way?

Anonymous

Anonymous Sat 20 Mar 2021 04:11:40 No.12857738 Report

Quoted By:

>>12857646
Because vector spaces over the reals are extremely friendly, and in the context of a university, linear algebra is useful across a variety of disciplines.

Anonymous

Anonymous Sat 20 Mar 2021 05:03:26 No.12857864 Report

Quoted By: >>12859041

>>12857710
How could they define linear transformations without mentioning vector spaces?

Anonymous

Anonymous Sat 20 Mar 2021 05:35:19 No.12857921 Report

Quoted By:

>>12857508
What does affine mean?

>>12857645
I was depressed.

Anonymous

Anonymous Sat 20 Mar 2021 05:40:01 No.12857938 Report

Quoted By:

>>12857646
Linear algebra is necessary for all of the analysis courses, so it needs to be done fast. Going through group, rings, and modules obviously give the one line proof of JCF, but that takes at least two courses. Also, finite dimensional R vector spaces are intuitive enough to be introduced without understanding of general fields and vector spaces.

Anonymous

Anonymous Sat 20 Mar 2021 05:41:28 No.12857941 Report

Quoted By: >>12858351

>>12854015
go back to 1st grade and learn this shit properly. this forum is for people with actual brains and phd candidates. go whine to mommy somewhere else bith

Anonymous

Anonymous Sat 20 Mar 2021 05:43:28 No.12857946 Report

Quoted By:

>>12854015
The other edges in the cycle, since they have already been added must have a weight less than the edge just added to the spanning tree as we choose arcs in order from least to greatest weight.

Anonymous

Anonymous Sat 20 Mar 2021 06:39:57 No.12858048 Report

Quoted By: >>12862631

>>12855933
>which one do you think has the absolutely ugliest proof
ugly proofs exist only in classical maths. In constructive maths, all proofs are either trivial or smart and elegant. This is why undergards hate constructive math, they are too dumb to for the smart proofs and too dumb to stop thinking complicated proofs means they are smart

Anonymous

Anonymous Sat 20 Mar 2021 06:46:35 No.12858060 Report

Quoted By: >>12858062

>>12853803
Why are there so many trannies in math?

Anonymous

Anonymous Sat 20 Mar 2021 06:49:23 No.12858062 Report

Quoted By:

>>12858060
Analysis tends to make people believe in falsehoods

Anonymous

Anonymous Sat 20 Mar 2021 07:49:55 No.12858151 Report

Quoted By: >>12858164 >>12858168 >>12858212 >>12858607 >>12859767

Sorry if this is wildly off topic, but have you noticed a significant political difference between math students / professors and the rest of the student body / faculty? On a campus steeped in woke / pc culture the math people seem to be the only group that couldn’t give less of a shit..

Anonymous

Anonymous Sat 20 Mar 2021 07:53:53 No.12858155 Report

Quoted By: >>12859757

>>12855598
but does quantum computing even work, or is it just fake "research" to milk grant money because it has the word "quantum" in it?

Anonymous

Anonymous Sat 20 Mar 2021 07:55:53 No.12858159 Report

Quoted By: >>12858176

>>12855930
probably not, circles have constant "acceleration" (second derivative), many curves do not

Anonymous

Anonymous Sat 20 Mar 2021 07:58:19 No.12858164 Report

Quoted By: >>12858168

>>12858151
there's not much politics that you can do with math, except maybe with the "women in math" meme, and math has always been low-key a women's degree, just like chemistry is a women's degree when compared with physics

Anonymous

Anonymous Sat 20 Mar 2021 07:59:30 No.12858168 Report

Quoted By:

>>12858151
>>12858164
also math doesn't carry much prestige in current society, and women only care about having "representation" on those fields that carry prestige, that means it's politically useless to them

Anonymous

Anonymous Sat 20 Mar 2021 08:03:50 No.12858176 Report

Quoted By: >>12858181

>>12858159
https://en.wikipedia.org/wiki/Osculating_circle

Anonymous

Anonymous Sat 20 Mar 2021 08:06:53 No.12858181 Report

Quoted By:

>>12858176
Meant to reply to >>12855930
Starting with cubics, parametrization is difficult, so I imagine finding osculating circles gets hard as well

Anonymous

Anonymous Sat 20 Mar 2021 08:24:09 No.12858212 Report

Quoted By:

>>12858151
throughout history there have been many mathematicians with very different political opinions
those opinions have no little to effect on their work and as such are kept as personal opinions, there is no desperate acts to appear on the "right side of history" and departments has no fears of its legitimacy being questioned.
the tuition fee milking subjects do however clamber over each other to appear inclusive, progressive etc. as not to invoke the wrath of administrators and grasp the nearest well meaning young adult looking for a higher education "experience" as opposed to looking for higher education

Anonymous

Anonymous Sat 20 Mar 2021 09:00:56 No.12858300 Report

Quoted By: >>12858304

>>12854081
>graph theory
graph theory made me hate math

Anonymous

Anonymous Sat 20 Mar 2021 09:03:09 No.12858304 Report

Quoted By:

>>12858300
>combinatorics in a plane
filtered

Anonymous

Anonymous Sat 20 Mar 2021 09:19:30 No.12858351 Report

Quoted By: >>12859096

>>12857941
Are there any phd students in these threads anyway?

Anonymous

Anonymous Sat 20 Mar 2021 09:54:41 No.12858447 Report

Quoted By: >>12858930

Lee or Do Carmo for Riemannian Manifolds ?

Anonymous

Anonymous Sat 20 Mar 2021 10:37:42 No.12858581 Report

Quoted By:

>>12856324
Best answer

Anonymous

Anonymous Sat 20 Mar 2021 10:39:38 No.12858597 Report

Quoted By:

>>12857646
We got told the field axioms before the definition of vector space. That was probably the first or second lecture after defining sets and logical notation.

Anonymous

Anonymous Sat 20 Mar 2021 10:42:03 No.12858607 Report

Quoted By: >>12858615

>>12858151
Not really. I would say mathematicians are more likely to voice controversial things though because they have less of a filter.

Anonymous

Anonymous Sat 20 Mar 2021 10:43:12 No.12858615 Report

Quoted By:

>>12858607
but maths is irrelevant to real life, so nobody is asking them in the first place

Anonymous

Anonymous Sat 20 Mar 2021 11:43:06 No.12858771 Report

Quoted By: >>12858813

>>12854119
Why would linear algebra not simply be placed in algebra? It quite literally is just finite vector spaces.

Anonymous

Anonymous Sat 20 Mar 2021 12:03:26 No.12858811 Report

Quoted By: >>12858815

>>12853803
in order to show that 2 composition laws are distributive do i have to show that they're right distributive AND left distributive? or can i show only one of them for brevity?

Anonymous

Anonymous Sat 20 Mar 2021 12:04:04 No.12858813 Report

Quoted By: >>12858819

>>12858771
where's linear algebra? don't see it

Anonymous

Anonymous Sat 20 Mar 2021 12:05:04 No.12858815 Report

Quoted By: >>12858820

>>12858811
Left and right distributivity do not imply each other in general.

Anonymous

Anonymous Sat 20 Mar 2021 12:06:06 No.12858819 Report

Quoted By: >>12859350

>>12858813
It's a picture of a linear subspace with daggers nearby.

Anonymous

Anonymous Sat 20 Mar 2021 12:06:08 No.12858820 Report

Quoted By:

>>12858815
well I just figured it out doing this exercise lol
still, if an exam problem is to show that 2 laws are distributive I have to show RD and LD right?
cuz i was hoping not to

Anonymous

Anonymous Sat 20 Mar 2021 12:28:08 No.12858860 Report

Quoted By: >>12858911 >>12862666

feels so good solving a problem lads
like sex but better

Anonymous

Anonymous Sat 20 Mar 2021 13:08:12 No.12858911 Report

Quoted By: >>12859192 >>12859233

>>12858860
>like sex
Kill yourself normalfag

Anonymous

Anonymous Sat 20 Mar 2021 13:16:32 No.12858930 Report

Quoted By:

>>12858447
Petersen or Chavel.

Anonymous

Anonymous Sat 20 Mar 2021 13:57:02 No.12859033 Report

Quoted By:

>>12857710
No, but I figured it out myself just by reading part of a linear algebra book cause I realized what a shit job they did of teaching me and I wanted to take it into my own hands so I don't let the possibility of becoming a mathematician go down the drain.

Anonymous

Anonymous Sat 20 Mar 2021 14:00:48 No.12859041 Report

Quoted By: >>12859081

>>12857864
They taught us R2 R3, I just mean they didn't teach us nullspace, rowspace, etc. If you asked a student from that class what's a vector space they probably couldn't answer you. It was basically just the concept that you can only dot product a 2 number vector with anything but another 2 number vector. I guess I was being inaccurate when I said they didn't teach is vector spaces, I mean there was no focus on the concept.

Anonymous

Anonymous Sat 20 Mar 2021 14:29:48 No.12859081 Report

Quoted By: >>12859093

>>12859041
what kind of linear algebra class teaches R2 and R3 only? This is literally taught in middle school, unironically

Anonymous

Anonymous Sat 20 Mar 2021 14:35:26 No.12859093 Report

Quoted By:

>>12859081
*Rn with a focus on 2 and 3. Ok I just remembered one semi advanced thing they taught us: determinants. I'm glad they at least taught that. But the class was mostly fancy geometry.

Anonymous

Anonymous Sat 20 Mar 2021 14:35:55 No.12859096 Report

Quoted By: >>12859742

>>12858351
yes, obviously

Anonymous

Anonymous Sat 20 Mar 2021 14:38:28 No.12859105 Report

Quoted By: >>12859181 >>12859253

What is the hardest subject they usually teach in undergrad and how can I prepare for it?

Anonymous

Anonymous Sat 20 Mar 2021 15:01:30 No.12859181 Report

Quoted By: >>12859387

>>12859105
Varies wildly from institution to institution. I would either say something like abstract algebra 2 or perhaps Real analysis 2 diffygeo/multivariate boogaloo is as hard as it will get at most places without having a graduate course number attached

Anonymous

Anonymous Sat 20 Mar 2021 15:07:03 No.12859192 Report

Quoted By:

>>12858911
there is nothing normie with having sex

Anonymous

Anonymous Sat 20 Mar 2021 15:21:50 No.12859233 Report

Quoted By: >>12859953

>>12858911
>normal bad
>being a defective autist good
you mongoloids should all be locked up away from any type of contact to the rest of the society

Anonymous

Anonymous Sat 20 Mar 2021 15:29:11 No.12859253 Report

Quoted By: >>12859387

>>12859105
some places let you do 2 postgrad modules instead of 3 undergrad modules
idk how your uni is structured tho

Anonymous

Anonymous Sat 20 Mar 2021 16:05:52 No.12859350 Report

Quoted By:

>>12858819
ah yes, that seems to fall under Algebra though? just overlapping with some other oval, but not even sure what that oval is, the brown one is Topology, but there's another green one almost overlapping with Topology that i don't know what it is

Anonymous

Anonymous Sat 20 Mar 2021 16:13:58 No.12859374 Report

Quoted By:

>>12854062
people don't even know what math is don't take it to heart.

Anonymous

Anonymous Sat 20 Mar 2021 16:22:48 No.12859387 Report

Quoted By: >>12859398 >>12859443 >>12859513 >>12859546 >>12859830 >>12862658

>>12859181
>>12859253
I've been accepted to McGill under the condition that I maintain my academic performance. (I think they just mean they would have to retract the acceptance if I didn't graduate cegep.) Here's the specific major I want to do:
https://www.mcgill.ca/mathstat/undergraduate/programs/b-sc/honours-mathematics-b-sc

Required Courses:

Calculus 3
Algebra 1
Honours Algebra 2
Honours Analysis 2
Honours ODE's
Honours Probability
Honours Statistics
Honours Advanced Calculus
Honours Analysis 3
Honours Analysis 4
Honours Algebra 3
Honours Algebra 4
Honours Differential Geometry
Honours Complex Analysis
Honours Research Project
Honours PDE's

Complementary Course Options:
Analysis 1
Honours Analysis
Principles of Statistics
Intro to Statistical Computing
Fundls of Statistical Learning
Theory of Interest
History & Philosophy of Math
Dynamic Programming
Mathematical Finance
Intro to Computer Science
Honours Algorithms&Data Struct
Honours Discrete Mathematics
Problem Seminar 1 Credits
Honours Nonlinear Dynamics
Honours Number Theory
Honours Numerical Analysis
Hons Matrix Numerical Analysis
Honours Euclidean Geometry
Honours Independent Study
Honours Set Theory

Students may select other courses with the permission of the Department.

Anonymous

Anonymous Sat 20 Mar 2021 16:25:43 No.12859398 Report

Quoted By: >>12859405 >>12861229

>>12859387
>two dozen courses with "Honours" in the name
Americans are absolutely repulsive sometimes.

Anonymous

Anonymous Sat 20 Mar 2021 16:27:28 No.12859405 Report

Quoted By: >>12859413

>>12859398
That's because it's the honours requirements ya dumbo, and the second block is options, they don't actually expect students to scatter their focus over that many courses.

Anonymous

Anonymous Sat 20 Mar 2021 16:29:59 No.12859413 Report

Quoted By: >>12859419

>>12859405
That's not the point, distinguishing courses into a normal version and an honours version is repulsive.

Anonymous

Anonymous Sat 20 Mar 2021 16:32:29 No.12859419 Report

Quoted By: >>12859431

>>12859413
I can see what your point is if you mean that they shouldn't bother having worse variants of courses cause people who can't do the honours probably shouldn't be in university in the first place, but if that is not what you mean, than what is your point?

Anonymous

Anonymous Sat 20 Mar 2021 16:36:49 No.12859431 Report

Quoted By: >>12859435

>>12859419
It's not that "you shouldn't bother", it's that it's a repulsive money-grabbing scheme.

Anonymous

Anonymous Sat 20 Mar 2021 16:37:49 No.12859435 Report

Quoted By:

>>12859431
Is it more expensive to take the honours courses?

Anonymous

Anonymous Sat 20 Mar 2021 16:41:58 No.12859443 Report

Quoted By: >>12859448

>>12859387
if you are on thin ice they might not be as agreeable
if you are in search of le ebin hard course then look at https://www.mcgill.ca/mathstat/graduate/current-students/advanced-courses and liaise with the people who run those courses/dept staff, take prereqs into consideration

Anonymous

Anonymous Sat 20 Mar 2021 16:44:43 No.12859448 Report

Quoted By:

>>12859443
>if you are on thin ice they might not be as agreeable
What do you mean?
Thank you for the link! Yeah, basically my goal is to learn as much math as possible cause I just really like math, and also to maximize my chances of making a new discovery in math.

Anonymous

Anonymous Sat 20 Mar 2021 16:54:05 No.12859481 Report

Quoted By:

>>12855923
>Shouldn’t we just always call them affine operators?
yes, we should

Anonymous

Anonymous Sat 20 Mar 2021 17:06:12 No.12859513 Report

Quoted By: >>12859830

>>12859387
What is that algebra sequence. The syllabi repeat themselves almost.

Anonymous

Anonymous Sat 20 Mar 2021 17:15:27 No.12859546 Report

Quoted By: >>12859607 >>12859830

>>12859387
Also wtf is the difference between advanced calculus, calculus 3, odes, pdes, complex, diff. geo, and analysis 3,4. There's gotta be major overlap or each course's content is super minor I think.

Anonymous

Anonymous Sat 20 Mar 2021 17:31:51 No.12859589 Report

Quoted By:

>>12854577
he does not use toom cook i guarantee it

Anonymous

Anonymous Sat 20 Mar 2021 17:37:59 No.12859607 Report

Quoted By:

>>12859546
Of course there will be overlap, these fields are not completely separate things but that does not mean they don't deserve their own classes. Analysis will formalize what is learned in calculus, odes and pdes are two seperate variants of diff eq in general, diff geo will probably be a segue into topology.
If I seem to not know what I am talking about, can you please share a university curriculum that you would deem good?

Anonymous

Anonymous Sat 20 Mar 2021 18:24:23 No.12859742 Report

Quoted By:

>>12859096
Rarely seen anything advanced being posted.

Anonymous

Anonymous Sat 20 Mar 2021 18:28:44 No.12859757 Report

Quoted By: >>12861925

>>12858155
i’m pretty sure we were able to factor 6 into 2*3 using quantum computing

Anonymous

Anonymous Sat 20 Mar 2021 18:32:15 No.12859767 Report

Quoted By:

>>12858151
my cohort of math majors only has like 12 people, about 4 of them (including me) use 4chan regularly and hate identity politics. and 3 of them that i know are full blown communists. i guess communism is sort of to be expected in high school but 4/12 is probably a relatively large portion of 4chan users

Anonymous

Anonymous Sat 20 Mar 2021 18:53:57 No.12859830 Report

Quoted By: >>12859842 >>12861115

>>12859387
Currently U2 at McGill. Hardest class first semester is hon anal 1, that's mostly because its the only hon class you can take the first semester. Main tip is just to go to class and start assignments as soon as possible, if you have any questions, there are a shitton of resources where you can ask for help. There isn't a hard class per say, it depends on the teacher. Darmon is very hard, there's a reason why he is a top NA number theorist. He might appear intimidating but it is very approachable. Don't hesitate to go to his office hours. Never, ever, take PengFei Guan. Nice guy but horrible accent, almost made me not do analysis ever again.

>>12859513
alg1 is just intro to rings and groups, alg 2 is linear algebra, alg 3 is redoing alg 1 without the retards and going more in depth, alg 4 is galois theory

>>12859546
anal 3 is measure theory, anal 4 is functional analysis

Anonymous

Anonymous Sat 20 Mar 2021 18:59:04 No.12859842 Report

Quoted By:

>>12859830
>redoing alg 1 without the retards
based

Anonymous

Anonymous Sat 20 Mar 2021 19:06:46 No.12859865 Report

Quoted By: >>12859884

>>12855933
Anything related to the foundations of differential geometry: Inverse function theorem, Picard-Lindelöf theorem, existence of partitions of unity, Stokes, just ew.
Now once all of that is set up, you can start having fun

Anonymous

Anonymous Sat 20 Mar 2021 19:10:50 No.12859884 Report

Quoted By:

>>12859865
if we're going this way, then Sard's theorem beats all of those four

Anonymous

View Same Google iqdb SauceNAO E8hyperbolics.png, 4MiB, 2245x2257

Anonymous Sat 20 Mar 2021 19:13:35 No.12859898 Report

Quoted By:

>>12853807
Mmm, unidimensional.

Anonymous

View Same Google iqdb SauceNAO F8FA8D4E-1578-4D58-8010-C63A83FC (...).jpg, 336KiB, 1029x1520

Anonymous Sat 20 Mar 2021 19:27:33 No.12859935 Report

Quoted By: >>12859972 >>12860065

>>12853803
I don’t understand this, how did they get the number 46,080?

Anonymous

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Anonymous Sat 20 Mar 2021 19:30:59 No.12859953 Report

Quoted By:

>>12859233
Haha

Anonymous

Anonymous Sat 20 Mar 2021 19:34:50 No.12859972 Report

Quoted By: >>12860046

>>12859935
Wouldn't that be set theory? Idk, did go to school.

Anonymous

Anonymous Sat 20 Mar 2021 19:55:11 No.12860046 Report

Quoted By: >>12861941

>>12859972
Pretty much everything is set theory, depending on how you look at it. I think it would be more meaningful to consider this a problem of combinatorics

Anonymous

Anonymous Sat 20 Mar 2021 20:00:24 No.12860065 Report

Quoted By: >>12860084

>>12859935
Each of the six pieces has two orientations, so it's 2^(6!)

Anonymous

Anonymous Sat 20 Mar 2021 20:08:37 No.12860084 Report

Quoted By:

>>12860065
nope
6!*2^6

Anonymous

Anonymous Sat 20 Mar 2021 20:35:27 No.12860211 Report

Quoted By: >>12860242 >>12860311

Prove that every closed $n$ -dimensional submanifold $M\subseteq{R^{n+1}}$ is orientable. (closed means compact and without boundary)

Anonymous

Anonymous Sat 20 Mar 2021 20:48:20 No.12860242 Report

Quoted By:

>>12860211
one more important thing: SMOOTH

Anonymous

Anonymous Sat 20 Mar 2021 21:04:37 No.12860311 Report

Quoted By:

>>12860211
If a manifold is closed, there's a fifty percent chance it's orientable. If its embedded in $\mathbb{R}^{n+1}$ , that's another fifty percent, telling us that there's a one hundred percent chance it's orientable.

Anonymous

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Anonymous Sat 20 Mar 2021 21:42:57 No.12860423 Report

Quoted By:

let S be the set of equivalence classes ordered pairs of finite groups under the relation (G,H)~(J,K) iff GxK is isomorphic to (JxH). then S is a group under the operation (G,H)*(J,K)=(GxJ,HxK). All the x symbols here mean direct product

Anonymous

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Anonymous Sun 21 Mar 2021 00:40:00 No.12861064 Report

Quoted By: >>12861341 >>12861950

Any /mg/ approved sources on Philosophy of Mathematics?
Yeah, cringe topic, but I want to familiarize myself enough with the topic to dab on math laymen who think they know philosophy.
There's nothing worse than having to endure the opinions of non-mathematician-philosophy-undergrad-equivalents who pseud ramble about Gödel (Jordan Peterson for example).
It's definitely worth being equipped to discuss this topic.

Anonymous

Anonymous Sun 21 Mar 2021 00:57:50 No.12861115 Report

Quoted By: >>12861317

>>12859830
I'm looking forward to alg 1 and 3 then, I love group theory! Just been reading a linear algebra book, seems like an interesting field once you get past the boring stuff they teach in cegep. I'm gonna love doing just math in school so much! FUCK ENGLISH CLASS

Anonymous

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Anonymous Sun 21 Mar 2021 01:47:44 No.12861228 Report

Quoted By: >>12861393

Is there an up to date book that covers all of this?

Anonymous

Anonymous Sun 21 Mar 2021 01:48:50 No.12861229 Report

Quoted By: >>12861248 >>12861265

>>12859398
>McGill
>Americans
You are truly retarded

Anonymous

Anonymous Sun 21 Mar 2021 01:54:28 No.12861248 Report

Quoted By:

>>12861229
Us Canadians are just Americans that don't live in the USA and are less obese.

Anonymous

Anonymous Sun 21 Mar 2021 01:59:54 No.12861265 Report

Quoted By: >>12861281

>>12861229
America the continent lad.

Anonymous

Anonymous Sun 21 Mar 2021 02:08:31 No.12861281 Report

Quoted By: >>12861292

>>12861265
Are you “European” Brexitfag?

Anonymous

Anonymous Sun 21 Mar 2021 02:12:51 No.12861292 Report

Quoted By: >>12861311

>>12861281
Nah, I just dislike united statisans, canadians, mexicans, brazillians, argentinians and haitians, so I round it upwards to "america".

Anonymous

Anonymous Sun 21 Mar 2021 02:22:19 No.12861308 Report

Quoted By: >>12861330

>>12857689
CEGEPs are pretty general though aren't they? It makes sense they would keep it concrete
>>12857646
Does your LA course not talk about fields?

Anonymous

Anonymous Sun 21 Mar 2021 02:24:10 No.12861311 Report

Quoted By: >>12861322

>>12861292
Wow, you sound like a fun person

Anonymous

Anonymous Sun 21 Mar 2021 02:26:58 No.12861317 Report

Quoted By: >>12861345

>>12861115
What CEGEP are you from? Also as a bit of a warning, no matter how much you like math, there's gonna be a point where you'll be drowning in it. I strongly recommend you to never take 5 math classes at the same time. Also never go turbo-autist. Talk to your peers and professors, invite the boys next to you in class for a coffee. This stuff matters way more in the long run.

Anonymous

Anonymous Sun 21 Mar 2021 02:28:26 No.12861322 Report

Quoted By:

>>12861311
Why yes, I'm the cream on the cracker, how could you tell?

Anonymous

Anonymous Sun 21 Mar 2021 02:30:37 No.12861330 Report

Quoted By:

>>12861308
I'm in the science program and everyone had to take linear algebra so I guess you have a point. Well, it's my last semester in this useless place, finally gonna go to big boy school!

Anonymous

Anonymous Sun 21 Mar 2021 02:33:52 No.12861341 Report

Quoted By:

>>12861064
Youre not worthy

Anonymous

Anonymous Sun 21 Mar 2021 02:35:57 No.12861345 Report

Quoted By:

>>12861317
Thanks for the advice! Makes sense. I need to have at least some free time or else I'll end up going insane and not be able to do any math. I'm from Heritage. Kind of wanted to go to Vanier but moving out wouldn't have been a good idea at that age on top of the fact that it doesn't even matter now cause I got my first choice of university anyway.

Anonymous

Anonymous Sun 21 Mar 2021 02:37:58 No.12861354 Report

Quoted By:

>>12855129
Good post. But does LinkedIn matter any more? Seems like the getting jobs from linkedin meme has run its course

Anonymous

Anonymous Sun 21 Mar 2021 02:55:23 No.12861393 Report

Quoted By: >>12862624

>>12861228
How is it out of date? Genuine question

Anonymous

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Anonymous Sun 21 Mar 2021 06:18:25 No.12861833 Report

Quoted By: >>12862576

I'm almost dry on this asa-gao blue ink, suggestions for the next color?

Anonymous

Anonymous Sun 21 Mar 2021 06:35:05 No.12861865 Report

Quoted By:

>>12853807
Finsler geonetry

Anonymous

Anonymous Sun 21 Mar 2021 07:00:16 No.12861925 Report

Quoted By:

>>12859757
amazing tech desu

Anonymous

Anonymous Sun 21 Mar 2021 07:07:28 No.12861941 Report

Quoted By:

>>12860046
>combinatorics
There is it, right right.

Anonymous

Anonymous Sun 21 Mar 2021 07:11:03 No.12861950 Report

Quoted By:

>>12861064
To dunk on one must first BE dunked on.
> read Pythagoras and stop eating beans
> read Tesla and marry a bird
> read Archemedes and draw circles

Anonymous

Anonymous Sun 21 Mar 2021 12:47:23 No.12862576 Report

Quoted By: >>12868866

>>12861833
>>>r/fountainpens
>>>r/handwriting

Anonymous

Anonymous Sun 21 Mar 2021 12:57:03 No.12862596 Report

Quoted By: >>12862669

What's a retard proof curriculum for statistics?

Anonymous

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Anonymous Sun 21 Mar 2021 13:04:14 No.12862615 Report

Quoted By: >>12862620 >>12862685 >>12862700

Hi!

I'm doing Exercise II-16 from $Geometry$ $of$ $Schemes$ . Dunno if I should post this here or on sqt.
I have proved that the family of degree-21 subschemes of $\mathbb{A}^{21}$ between $V(\mathfrak{m}^3)$ and $V(\mathfrak{m}^4)$ is 84-dimensional (basically, you need to add a certain number of 3-forms to $\mathfrak{m}^4$ until you get a codimension 21 ideal).
What I don't get is how to describe the family of subschemes that arise as limits of 21-tuples "converging" at the origin as a grassmanian-looking space. What I know is that 21-tuples can be seen as elements in a 21×4=84 dimensional variety, so that limits at the origin should presumably be a variety of lesser dimension.

Anonymous

Anonymous Sun 21 Mar 2021 13:05:46 No.12862620 Report

Quoted By:

>>12862615
* $\mathbb{A}^4$

El cAbrón

El cAbrón Sun 21 Mar 2021 13:06:48 No.12862624 Report

Quoted By: >>12862635 >>12863496

>>12861393
Only a shitty djvu is out there. So, what’s an alternative?

Anonymous

Anonymous Sun 21 Mar 2021 13:08:40 No.12862631 Report

Quoted By:

>>12858048
This. Constructivism is the future.

Anonymous

Anonymous Sun 21 Mar 2021 13:09:14 No.12862635 Report

Quoted By:

>>12862624
Henle’s Modern Geometries

Anonymous

Anonymous Sun 21 Mar 2021 13:17:47 No.12862658 Report

Quoted By: >>12868872

>>12859387
Pls explain what do honours courses mean. Is there a non-honours euclidean geometry course where you draw shapes with crayola and only consider polygons with less than two angles?

Anonymous

Anonymous Sun 21 Mar 2021 13:21:10 No.12862666 Report

Quoted By:

>>12858860
It feels like winning 150cc at mario kart. You are very happy for a little while, until you realize that nobody understands or cares.

Anonymous

Anonymous Sun 21 Mar 2021 13:21:35 No.12862669 Report

Quoted By:

>>12862596
There's a fifty fifty chance any curriculum you find is nigproof, either it is or it isn't.

Anonymous

Anonymous Sun 21 Mar 2021 13:27:32 No.12862685 Report

Quoted By: >>12862742

>>12862615
Based geometer

Anonymous

Anonymous Sun 21 Mar 2021 13:31:59 No.12862700 Report

Quoted By: >>12862713 >>12862742 >>12866475

>>12862615
why (and how) did you make your pdf white text on a black background

Anonymous

Anonymous Sun 21 Mar 2021 13:34:32 No.12862708 Report

Quoted By:

>>12854222
My gender

Anonymous

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Anonymous Sun 21 Mar 2021 13:35:38 No.12862713 Report

Quoted By:

>>12862700
Not that anon, but evince has a night mode

Anonymous

Anonymous Sun 21 Mar 2021 13:46:56 No.12862742 Report

Quoted By:

>>12862700
I use a high-contrast (either sepia or night) mode paired with a red light filter because it's easier on the eyes. Plus night mode feels like reading from a blackboard which is nice.

On my phone I use read era which works well and allows you to store quotations in a library. I use that to store exercise I haven't yet solved, and stuff I don't fully understand.

>>12862685
I haven't come here for a long while. Is/are tohoku poster/s gone? He used to talk algebraic geometry all the time. I was recommended Geometry of Schemes here.

Anonymous

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Anonymous Sun 21 Mar 2021 16:59:34 No.12863496 Report

Quoted By: >>12863579

>>12862624
What's so bad about it?

Anonymous

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Anonymous Sun 21 Mar 2021 17:14:50 No.12863570 Report

Quoted By: >>12863697 >>12865467

Shilov+Lax vs Hoffman+Lax

Anonymous

Anonymous Sun 21 Mar 2021 17:18:47 No.12863579 Report

Quoted By:

>>12863496
Again, nothings wrong with it just that there’s only a shitty .djvu. If you happen to have a higher resolution version please let me know where to get it.

Anonymous

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Anonymous Sun 21 Mar 2021 17:48:40 No.12863685 Report

Quoted By: >>12863711 >>12863766 >>12863778

I'm going to write a master's thesis on something in Algebraic Topology. Probably something in homotopy theory but I have no idea. Any suggestions?

Anonymous

Anonymous Sun 21 Mar 2021 17:51:27 No.12863697 Report

Quoted By: >>12863937

>>12863570
How about just Lax

Anonymous

Anonymous Sun 21 Mar 2021 17:55:28 No.12863711 Report

Quoted By: >>12863730

>>12863685
do you want to do original research?

Anonymous

Anonymous Sun 21 Mar 2021 18:00:37 No.12863730 Report

Quoted By:

>>12863711
Yes, but I'd be willing to write something that's just expository as well.

Anonymous

Anonymous Sun 21 Mar 2021 18:09:07 No.12863766 Report

Quoted By:

>>12863685
Survey the current homology theories and try to come up with your own.

Anonymous

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Anonymous Sun 21 Mar 2021 18:11:04 No.12863778 Report

Quoted By:

>>12863685
Maybe something related to the Hilton-Milnor theorem. It's an important result.

Anonymous

Anonymous Sun 21 Mar 2021 18:59:46 No.12863937 Report

Quoted By:

>>12863697
Lax seems fast paced enough to make me worry I might miss something by reading only it.

Anonymous

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Anonymous Sun 21 Mar 2021 19:07:36 No.12863979 Report

Quoted By: >>12864004 >>12864210

how am i supposed to feel by the end of a maths degree

Anonymous

Anonymous Sun 21 Mar 2021 19:14:00 No.12864004 Report

Quoted By: >>12864278

>>12863979
useless but smug

Anonymous

Anonymous Sun 21 Mar 2021 19:57:43 No.12864176 Report

Quoted By:

Favorite lecture videos?

Just found this series from John Milnor which is neat.

https://www.youtube.com/playlist?list=PLelIK3uylPMFHC6Xny11XFXgwwtv9_PO3

Anonymous

Anonymous Sun 21 Mar 2021 20:08:36 No.12864210 Report

Quoted By: >>12864278

>>12863979
smug but useless

Anonymous

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Anonymous Sun 21 Mar 2021 20:29:24 No.12864278 Report

Quoted By:

>>12864004
>>12864210
feeling useless, yeah...

Anonymous

Anonymous Sun 21 Mar 2021 20:35:57 No.12864299 Report

Quoted By:

>This is obvious. Insneed, if we...

Anonymous

Anonymous Sun 21 Mar 2021 21:01:43 No.12864402 Report

Quoted By: >>12864424 >>12864697 >>12865924 >>12866130 >>12866201 >>12867186 >>12867195 >>12867217

Let $M \subseteq \mathbb{R}^{n+1}$ be an $n$ -dimensional compact smooth submanifold without boundary. Prove that $M$ is orientable.

Anonymous

Anonymous Sun 21 Mar 2021 21:06:54 No.12864424 Report

Quoted By: >>12864605

>>12864402
What have you tried?

Anonymous

Anonymous Sun 21 Mar 2021 21:47:46 No.12864605 Report

Quoted By: >>12864613 >>12864691 >>12866343

>>12864424
it's not homework, it's let's see what proofs can /mg/ come up with (if any)

Anonymous

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Anonymous Sun 21 Mar 2021 21:49:01 No.12864613 Report

Quoted By:

>>12864605

Anonymous

Anonymous Sun 21 Mar 2021 22:07:58 No.12864691 Report

Quoted By:

>>12864605
Yeah bro that's gonna be a yikes from me.

Anonymous

Anonymous Sun 21 Mar 2021 22:09:25 No.12864697 Report

Quoted By:

>>12864402
let M be a subset of Rn+1 be an n-dimensional compact smooth submanifold without boundary. then M is orientable.
qed.

Anonymous

Anonymous Mon 22 Mar 2021 01:13:46 No.12865467 Report

Quoted By:

>>12863570
My advisor always joked that Lax personally sought him out for help with an important problem. Finding the bathroom at a conference!

BenjaminW

BenjaminW Mon 22 Mar 2021 02:25:55 No.12865769 Report

Quoted By:

>>12853803
FUCK HENDOG MATHS ON YOUTUBE!!!

Anonymous

Anonymous Mon 22 Mar 2021 03:05:31 No.12865924 Report

Quoted By:

>>12864402
Use Nakayama's lemma

Anonymous

Anonymous Mon 22 Mar 2021 03:27:02 No.12866007 Report

Quoted By:

https://www.youtube.com/watch?v=f43WbnN2tBU

Anonymous

Anonymous Mon 22 Mar 2021 04:10:53 No.12866130 Report

Quoted By: >>12866343 >>12866747

>>12864402
Did you even get this problem from anywhere? It doesn't look like its written by someone who knows what they're talking about.

Anonymous

Anonymous Mon 22 Mar 2021 04:13:33 No.12866139 Report

Quoted By: >>12867309 >>12868174

>>12856652
Any recs? I remember disliking them a fair bit the first time.

Anonymous

Anonymous Mon 22 Mar 2021 04:38:06 No.12866201 Report

Quoted By: >>12866343

>>12864402
Does the mbois strip have boundary

Anonymous

Anonymous Mon 22 Mar 2021 04:48:14 No.12866220 Report

Quoted By: >>12866311

"Algebra" or "algebra over a field" is such a horrible name for such a useful structure.
It silently tilts me all the time I encounter the term.
Like come the fuck on. Do other languages have better names for this?

Anonymous

Anonymous Mon 22 Mar 2021 05:23:47 No.12866311 Report

Quoted By:

>>12866220
Rename it yourself, tell us.

Anonymous

Anonymous Mon 22 Mar 2021 05:33:41 No.12866343 Report

Quoted By: >>12866747

>>12866201
Yeah, but it's essentally why the theorem has the conditions that it does.

You can just "delete" the boundary parts, but then it wouldn't be compact. And if you keep them,then you have a manifold with boundary. Each violates the theorem.

>>12866130
>>12864605
Woops, I was a bit presumptous. You can construct "an atlas" for M such that the image of every chart is just a n-ball in R^n+1, and the orientability of R^n+1 allows us to have this atlas orientable. Taking projections then gives us an orientable atlas for M.

Anonymous

Anonymous Mon 22 Mar 2021 06:19:48 No.12866475 Report

Quoted By:

>>12862700
put this as a bookmark
javascript:void(viewer.style = 'filter: grayscale(0%) invert(100%) contrast(100%) brightness(100%)')

Anonymous

Anonymous Mon 22 Mar 2021 08:18:09 No.12866747 Report

Quoted By: >>12870154

>>12866130
what? the wording couldn't be more clear

>>12866343
this doesn't work, or rather it needs serious elaboration
>and the orientability of R^n+1 allows us to have this atlas orientable
how exactly does orientability of R^n+1 allow us to have this atlas orientable?
>>12866343
>Taking projections then gives us an orientable atlas for M.
non sequitur, Mobius strip gives counter example (can be covered by ambient charts with orientation-preserving transitions, but its restriction has orientation-reversing transitions)

Anonymous

Anonymous Mon 22 Mar 2021 08:38:53 No.12866780 Report

Quoted By: >>12866979 >>12867941

>>12853803
>Math logic
Rigorously defines proofs and proves they work
>Set theory
Rigorously defines numbers/sets and prove N/Z/Q/R/C satisfies group/ring/field axioms.
>Number Theory
Proves the rules of grade school arithmetic
>Abstract Algebra
Proves the theorems in middle school algebra
>Analysis
Proves the theorems in calculus
>[404 not found]
Proves the theorems of geometry in a rigorous modern way using set theory/algebra/analysis assuming nothing from hs geometry.

Does anyone have any books that rigorously builds up geometry in a modern (algebraic and analytic) manor?

Anonymous

Anonymous Mon 22 Mar 2021 10:03:55 No.12866979 Report

Quoted By:

>>12866780
>>Rigorously defines numbers/sets
oups

Anonymous

Anonymous Mon 22 Mar 2021 11:36:34 No.12867186 Report

Quoted By: >>12867195

>>12864402
I'm surprised this feels so no obvious to me. Then again I don't really know "why" a Klein bottle doesn't embed in R^3 (beyond it contradicting this result) so maybe understanding that would help.
I feel like there's something here about taking a tubular neighborhood and trying to show that there are two connected components.

Anonymous

Anonymous Mon 22 Mar 2021 11:40:34 No.12867195 Report

Quoted By:

>>12864402
>>12867186
Oh, actually it's probably some dumb homology duality shit to show the manifold splits space into multiple connected components.

Anonymous

Anonymous Mon 22 Mar 2021 11:50:10 No.12867217 Report

Quoted By:

>>12864402
https://math.stackexchange.com/questions/2609770/are-closed-topological-submanifold-in-mathbb-rn-of-codimension-1-orientabl

https://math.stackexchange.com/questions/553939/are-closed-properly-embedded-manifolds-of-co-dimension-1-in-mathbbrn-orie

Anonymous

Anonymous Mon 22 Mar 2021 11:53:52 No.12867225 Report

Quoted By:

>>12853807
Me

Anonymous

Anonymous Mon 22 Mar 2021 12:33:18 No.12867309 Report

Quoted By:

>>12866139
I'll post soon bro

Anonymous

Anonymous Mon 22 Mar 2021 14:09:41 No.12867639 Report

Quoted By:

>do all tests online
>have to retake one test, this time its frontal
>few weeks later i check to see if ive received a grade
>see that no test form was submitted
>get a heart attack
>remember it was frontal
anyone else shares this feel? i almost shat my pants, redoing a course youre good at would be super painful.

Anonymous

Anonymous Mon 22 Mar 2021 14:56:10 No.12867792 Report

Quoted By: >>12867830 >>12867837

Is it possible to calculate n in this situation without using anything that involves a constant taken out of nowhere?
$2 = 1.625^n$

Anonymous

Anonymous Mon 22 Mar 2021 15:08:12 No.12867830 Report

Quoted By:

>>12867792
> ${2 \over 1} = \left({13 \over 8}\right)^n$
> ${2 \over 1} = {13^n \over 8^n}$
No.

Anonymous

Anonymous Mon 22 Mar 2021 15:10:56 No.12867837 Report

Quoted By:

>>12867792
>a constant taken out of nowhere
What do you mean
It's quite clear where $\log_2(1.625)^{-1}$ comes from

Anonymous

Anonymous Mon 22 Mar 2021 15:48:43 No.12867941 Report

Quoted By:

>>12854119
>quantum physics
>PDE and complex analysis far away from topology
>no analytic number theory
Let me guess, an undergrad made this, right?

>>12855479
This is just the fundamental theorem of calculus. If you pick up any book on Riemann integration they usually prove this very fast, and pretty much everyone forgets of all the "area under the curve" thing

>>12855933
I didn't liked uniqueness of Lebesgue measure, it forces you to rebuild the whole measure construction

>>12856319
>Tychonoff's theorem
This is easy depending on the proof. You can prove that the Ultrafilter theorem implies UF-compact = compact from which proving Tychonoff is trivial with choice

>>12857646
Because normies like to give intuition of calculus + lin. algebra, so they need vectors, matrices and determinants fast. I agree it is nicer to see knowing group and field theory first

>>12866780
>Proves the theorems of geometry in a rigorous modern way using set theory/algebra/analysis assuming nothing from hs geometry.
I like Hilbert's axiom for rigurous geometry. In general, you should be able to prove common general theorems in it (like Thales, Pythagoras and circle theorems), and from that you can take any normal geoemtry book. Recomendations are Dillon's Geometry through History, Greenberg's Euclidean and non-Euclidean geometries, Evan Chen's book for olympiads and Moise's Elementary geometry.

Anonymous

Anonymous Mon 22 Mar 2021 16:52:06 No.12868174 Report

Quoted By: >>12868232

>>12856319
>>12856069
>>12856819
>>12866139
If $p$ is a prime and $p^k, k\geq 0$ divides the order of a finite group $G$ , then the group contains a subgroup of order $p^k$ . Our proof approach is to induct on the order of the group. Clearly the result holds for the group of order 1. Assume that it holds for every group of order less than $|G|$ . By a theorem due to Cauchy, we know that for every prime divisor $p$ there is an element of order $p$ . Recall the class equation $|G|=|Z(G)| + \sum [G:C(y_j)]$ Either $p$ divides the order of the center or it does not.

Case 1: $p\not| \;|Z|$ Then $p$ does not divide the index of one of the $C(y_j)$ . So $p^k \; | \; |C(y_j)|$ . This group has order divisible by $p^k$ and less than $G$ . So it has a subgroup of order $p^k$ by induction.

Case 2: $p | |Z|$ By cauchy's theorem above, $\exists c \in Z, |c|=p$ . The center commutes with everything, so the cyclic subgroup generated by $c, <c>$ is normal. The factor group has order divisible by $p^{k-1}$ . By induction it has a subgroup $H/<c>$ with that order. Then $H\subset G$ has order $p^k$ , which completes the proof of Sylow I.
Note that this version is stronger than most of the sylow proofs given in textbooks.

Anonymous

Anonymous Mon 22 Mar 2021 17:04:44 No.12868232 Report

Quoted By:

>>12868174
Sylow II, about the conjugacy and the nesting of the subgroups shown to exist in Sylow I is a little more ass, but it's really just dicking around with the orbit-stabilizer theorem applied to $G$ acting on the set of Sylow $p$ -subgroups by conjugation.

Anonymous

Anonymous Mon 22 Mar 2021 17:10:21 No.12868263 Report

Quoted By:

>>12856319
>Tychonoff's theorem.
valid in constructive maths, hence proof is beautiful

Anonymous

Anonymous Mon 22 Mar 2021 17:18:37 No.12868294 Report

Quoted By: >>12868313

Is it okay to become a category theorist in grad school?

Anonymous

Anonymous Mon 22 Mar 2021 17:23:17 No.12868313 Report

Quoted By: >>12868334

>>12868294
Are you a cute girl(male)?

Anonymous

Anonymous Mon 22 Mar 2021 17:28:58 No.12868334 Report

Quoted By:

>>12868313
No(t yet)

Anonymous

Anonymous Mon 22 Mar 2021 18:08:29 No.12868471 Report

Quoted By:

>>12853807
Linear algebra
This is not troll, it's more geared towards communicating with normies. You say you're taking linear algebra at uni and they say, "Oh! I remember taking that in highschool! What a hard class!"

Anonymous

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Anonymous Mon 22 Mar 2021 18:10:43 No.12868476 Report

Quoted By:

>>12854068

Anonymous

Anonymous Mon 22 Mar 2021 18:13:48 No.12868485 Report

Quoted By: >>12868545

Is Shilov better than H&K?

Anonymous

Anonymous Mon 22 Mar 2021 18:23:55 No.12868518 Report

Quoted By:

>>12855933
Implicit function theorem

Anonymous

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Anonymous Mon 22 Mar 2021 18:29:31 No.12868539 Report

Quoted By:

>>12853811

Anonymous

Anonymous Mon 22 Mar 2021 18:31:23 No.12868545 Report

Quoted By:

>>12868485
Not necessarily. But more than marginally better than H&M.

Anonymous

Anonymous Mon 22 Mar 2021 18:49:44 No.12868618 Report

Quoted By:

Why is there no formalism for proofs by inspection on continuums, such as you can achieve by rotating a physical dial? Maybe something with a proof of continuity and stability beneath a step limit.

Anonymous

Anonymous Mon 22 Mar 2021 18:54:31 No.12868639 Report

Quoted By: >>12868653

U(3) is not cyclic, right? My teacher is memeing, right?

Anonymous

Anonymous Mon 22 Mar 2021 18:58:33 No.12868653 Report

Quoted By: >>12868674

>>12868639
Tell me what U3 and cyclic mean then I can answer

Anonymous

View Same Google iqdb SauceNAO un.jpg, 4KiB, 247x50

Anonymous Mon 22 Mar 2021 19:04:53 No.12868674 Report

Quoted By: >>12868704

>>12868653
cyclic group = monogenous group

Anonymous

Anonymous Mon 22 Mar 2021 19:09:50 No.12868704 Report

Quoted By: >>12868723

>>12868674
Why do you think that it isn’t cyclic?

Anonymous

Anonymous Mon 22 Mar 2021 19:12:59 No.12868723 Report

Quoted By: >>12868741

>>12868704
Because it's a multiplicative group.

Anonymous

Anonymous Mon 22 Mar 2021 19:13:02 No.12868724 Report

Quoted By:

>>12853803
Why is it the moment I want to calculate anything interesting I need retarded large matrices? I am writing some fem solver for a 2d schroding wave equation and I need like 10k by 10k matrix to get okayish numerics

Anonymous

Anonymous Mon 22 Mar 2021 19:16:23 No.12868741 Report

Quoted By: >>12868783

>>12868723
But anon.
$2^2=1$ .

Anonymous

View Same Google iqdb SauceNAO 170120-noel-el-chapo-extradition (...).jpg, 169KiB, 1566x880

Anonymous Mon 22 Mar 2021 19:24:32 No.12868783 Report

Quoted By:

>>12868741
Oh... Well, thanks.

Anonymous

Anonymous Mon 22 Mar 2021 19:37:31 No.12868851 Report

Quoted By:

>>12868846

Anonymous

Anonymous Mon 22 Mar 2021 19:41:55 No.12868866 Report

Quoted By:

>>12862576
You're just jealous of him

Anonymous

Anonymous Mon 22 Mar 2021 19:43:58 No.12868872 Report

Quoted By:

>>12862658
It's where you do harder versions of the classes, do more credits, and do an honours project, and you generally have to do this to be eligible for a graduate program.

Anonymous

Anonymous Mon 22 Mar 2021 21:13:05 No.12869263 Report

Quoted By: >>12869341

At this point I only come here to see anime tranny's posts.

Anonymous

Anonymous Mon 22 Mar 2021 21:19:56 No.12869302 Report

Quoted By: >>12869546

>>12854068
tropical geometry

Anonymous

Anonymous Mon 22 Mar 2021 21:28:45 No.12869341 Report

Quoted By:

>>12869263
(S)he hardly posts anymore

Anonymous

Anonymous Mon 22 Mar 2021 22:15:43 No.12869546 Report

Quoted By:

>>12869302
it must be fun to draw loads of random lines and pretend its the forefront of the field

Anonymous

Anonymous Tue 23 Mar 2021 00:28:39 No.12870154 Report

Quoted By:

>>12866747
Mobius strips aren't compact or boundaryless submanifolds. I don't think the proof is that good either, as it's construction doesn't flagrantly fail for mobius strips.

We can design a GL+ cocycle structure on T(R^n+1) for any atlas, so just pick a finite atlas on M \subset R^n+1 so M occupies the first n coordinates.

Each cocycle is then a matrix in GL+, and the top left n x n block corresponds to M's transition functions. Every other entry save the (n+1,n+1) spot must be zero. If the top block doesn't have positive determinant, just change the coordinate of the (n+1)th by multiplying by -1. We may then obtain a reduced GL+ structure for T(M). Done.

Maybe there's a nicer way with differential forms? If you've got a proof I'd like to see it

Anonymous

Anonymous Tue 23 Mar 2021 03:09:57 No.12870755 Report

Quoted By: >>12870952 >>12870967

is real analysis a prereq for complex analysis? my uni doesn't list it as so, so I'm a bit worried it's a shit class

Anonymous

Anonymous Tue 23 Mar 2021 04:30:51 No.12870952 Report

Quoted By:

>>12870755
kinda but not really. youll be fine bitch damn bitch you fine a ha ha

Anonymous

Anonymous Tue 23 Mar 2021 04:37:33 No.12870967 Report

Quoted By:

>>12870755
no. I did this as well and the only analysis concept I needed periodically were supremums and infimums.

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