/mg/ maths general

[Anonymous No.12203008]

Twistor edition
Talk maths
Antecedent >>12190956

[El Arcón No.12203017]

>>12203008
A twistor is like a spinor in momentum space. Something like that, I forget the exact transformation.

[Anonymous No.12203019]

>>12203017
what's a tensor?

[Anonymous No.12203022]

>>12203017
they said you died or got arrested. took remains unspookable.

[El Arcón No.12203028]

>>12203022
Not only did they say I died, they entered my name into the NatSec table of deceased individuals and have been selling insurance to people with the absolute guarantee that I am a dead man.

[Anonymous No.12203037]

>>12203008

[El Arcón No.12203038]

>>12203019
A tensor is an object that obeys the tensor transformation law. If you were wondering about a spinor maybe, then a spinor is an object that obeys the the spinor equation.

[Anonymous No.12203046]

>>12203037
I can't recommend working on this one, mathematics is not ready for such problems. Consider triple integrals instead.

[Anonymous No.12203113]

>>12203038
very nice
anyone who says a tensor is a matrix is instantly discarded into the pit of dumb

[Anonymous No.12203132]

>>12203028
wtf? did these claims go through? isn't someone with authority supposed to file that?

[Anonymous No.12203137]

>>12203017
>>12203019
>>12203022
>>12203028
>>12203038
>>12203113
Piss off schizos

[Anonymous No.12203147]

Some papers that might be of interest to somebody:
>Zeta functions of Lie [math]\mathbb{F}_p[/math]-algebras and finite [math]p[/math]-groups
https://arxiv.org/pdf/2010.02268.pdf
>Group-like Small Cancellation Theory for Rings
(This one looks like a whole book!)
https://arxiv.org/pdf/2010.02836.pdf
>The Steenrod algebra from the group theoretical viewpoint
https://arxiv.org/pdf/2003.14156.pdf
>Wick polynomials in non-commutative probability
https://arxiv.org/pdf/2001.03808.pdf

[Anonymous No.12203181]

>>12203147
Cheers, lad.

[Anonymous No.12203182]

studying the GRE practice exam. how does C imply invertibility?

[Anonymous No.12203235]

>>12203182
Expand it and you will get [math]I - A + A^2 - \cdots + (-1)^k A^k = 0 \Leftrightarrow I = A - A^2 + \cdots -(-1)^k A^k = A(I - A + A^2 - \cdots -(-1)^k A^{k-1})[/math]. The stuff inside the parentheses is now the inverse of [math]A[/math]. Warning: I may have made a mistake with the signs, but the idea is the same, nevertheless.

[Anonymous No.12203238]

Lads, please help me: I would be grateful if you could point me in any direction where I can find the (most) information regarding any one graduate school. In a sense, a list of grad schools, their tuition, admission and field of study (analysis, algebra...) etc etc

It's tiring spending a good chunk of my day sifting through university websites trying to find information.

And I'm not talking about master portals, they just give USA, UK and the Netherlands mostly.

Arigato ^___^

[Anonymous No.12203241]

>>12203235
wack. never seen that before
honestly learning a lot just going through these and finding gaps in my learning, though I suppose that's the point. I should probably stop and run through this exam style properly rather than continue as I am

[Anonymous No.12203256]

>>12203241
I just realised I forgot all the coefficients in the expansion. Remember to get some sleep or else you will do similar mistakes. I knew something was off, but I thought it was the signs. The idea is still the same, as the correct version provides a matrix B such that AB = I = BA. Sorry about that.

[Anonymous No.12203297]

>>12203147
got anything on stochastics?

[Anonymous No.12203302]

>>12203008
any guides on induction for recursive sequences?
I cant seem to grasp that shit

[Anonymous No.12203391]

>>12203238
>Arigato ^___^
is this nigga serious?

[Anonymous No.12203417]

>>12203235
>I may have made a mistake with the signs
You need binomial coefficients too right? The idea still works though obviously.

[Anonymous No.12203418]

>>12203417
Oops >>12203256
This is why I should read the thread before posting.

[Anonymous No.12203425]

Can someone explain why [math] C\rtimes D \cong C*D / \{dcd^{-1}\}_{d\in D, c\in C} [/math]?

[Anonymous No.12203717]

>>12203182
>>12203235
Another way is to notice that no invertible <=> A has 0 as an eigenvalue.
If Ax = 0 then (I-A)x = x so (I-A)^k x = x so (I-A)^k is not 0.

[Anonymous No.12203730]

>>12203008
Whats the best book/website for maths problems of all kinds to solve?
I was never one of the "maths people" in highschool; I was above average so I'm looking to better myself now before I start my compsci degree

[Anonymous No.12203734]

>>12203730
Khanacademy for you.

[Anonymous No.12203747]

>>12203734
Really? I was expecting some crusty old book lol
thanks I guess
Which course should I stay with? Algebra basics?

[Anonymous No.12203757]

>>12203747
start* with

[El Arcón No.12203761]

based Sir Roger. awareness of this technique was very useful for me.
https://www.nobelprize.org/uploads/2020/10/advanced-physicsprize2020.pdf

[Anonymous No.12203858]

If a line, or the slope of a line, has the property of 'steepness', what is the term for the corresponding property of curves and derivatives? 'Intensity' seems close but wrong.

For example, how would I describe, in language, the difference between the yellow curve and the red? I could say one is 'flatter' than the other, but that seems to include other properties than what I want.

[Anonymous No.12203888]

How do I prove [math]\exists \varepsilon>0 [/math] such that [math]\ mypeepee > \varepsilon[/math]?
I'm worried I'm going to have to use imaginary numbers to prove this.

[Anonymous No.12203891]

>>12203008
If I keep studying mathematics, will I also pick things up about physics along the way?
I'm thinking that I might get a textbook or something with physics problems and see if I can use that to learn more.
I don't want to study physics because I don't really want to work in physics but I still like learning about it, as I find applications for it everywhere.

[Anonymous No.12203897]

>>12203888
You're not funny, you're not smart, and the trips have been wasted on you. Go back to r*ddit.
I hope you get in a car crash and die.

[Anonymous No.12203907]

>>12203297
Nope, sorry. I took those from my email.

>>12203418
We were both a bit silly, I guess.

>>12203717
Nice one.

[Anonymous No.12203919]

>>12203858
Curvature is what you're looking for. It's a well researched concept.

[Anonymous No.12203934]

>>12203919
Perfect, thanks!

[Anonymous No.12203943]

Would it be weird to enter a zoom/whatever else conference if I'm in another country?

[Anonymous No.12203950]

>>12203943
No, as long as you're white.

[Anonymous No.12203958]

>>12203943
Why would it be? I attended some German conferences like that.

[Anonymous No.12203988]

>>12203950
Mr. Moore pls

[Anonymous No.12204008]

>It's 2020 and we still don't know how many real numbers there are
This is getting stupid... At what point do you just give up and admit they're not real?

[Anonymous No.12204027]

Is there any exercises / problem solving book or website that you really enjoyed going through?
Something with actual hard exercises in anything (analysis, algebra, number theory, combinatorics, probability, even algorithms if it's good)..
please recc

I only know Project Euler, but you guys may know something better for mathchads.

[Anonymous No.12204030]

>>12204027
Check out "Linear Algebra Problem Book" by Paul Halmos.

[Anonymous No.12204034]

[Anonymous No.12204086]

>Racism has become the only issue for many Millennials. Even as they ignore how deeply human it is to categorize some fellow humans as the "other", they are doing it themselves to those they believe are racists. They have become totally intolerant of those whom they see as lacking sufficient tolerance.
wtf I didn't know Mumford was based.
http://www.dam.brown.edu/people/mumford/blog/2020/Simple.html

[Anonymous No.12204110]

>>12204086
You can afford to be based when you've got tenure and you're too old to care anyway
I remember he wrote some pretty interesting blogs in the past too.

[Anonymous No.12204167]

>>12204034
Third option: put your hands on your ears and pretend it never happened.

[Anonymous No.12204202]

>>12203008
Hello, can someone help me understand fractional indices?

How do I work out the value of something like pic related?

[Anonymous No.12204206]

>>12204202
FUCK OFF with your kindergarten questions. GO SOMEWHERE ELSE

[Anonymous No.12204213]

What do you love about math? Was there a moment in your life when you realised something that made you love it?

[Anonymous No.12204218]

>>12204206
Where am I suppose to go?

[Anonymous No.12204219]

>>12204213
always been good at it, grew to love it more as I did more and more with it

[Anonymous No.12204220]

>>12204218
/sqt/

[Anonymous No.12204226]

>>12204220
>>12204206
Damn, I guess you got filtered by kindergarden math if you can't answer it, lol

[Anonymous No.12204242]

>>12204226

[Anonymous No.12204273]

Is there a concrete guide for math olympiad prep? Or it's stuff well hidden from commoners?

[Anonymous No.12204292]

>>12204273
the best people get their prep from teachers who are into highschool olympiads

[Anonymous No.12204297]

>>12204242

All Mr Filtered

[Anonymous No.12204310]

>>12204273
>Is there a concrete guide for math olympiad prep?
step 1, ignore olympiad shit
step 2, study actual math

[Anonymous No.12204316]

>>12204292
The problem with this reasoning is that to become "best", you have to get an adequate prep first.

[Anonymous No.12204322]

>>12204030
will check it out, thanks

[Anonymous No.12204326]

>>12204310
If you can't solve olympiad problems, then you are wasting time by doing math.

[Anonymous No.12204329]

>>12204326
By that logic like half the number theorists in Australia should have their tenure revoked.

[Anonymous No.12204352]

>>12204326
>if you dont have 3 dozen different identities memorized from areas of math you dont work in, then you are wasting time by doing math
when was the last time you did a geo problem outside of a fucking olympiad

[Anonymous No.12204358]

>>12204352
I do some basic geometry when I teach calculus I guess.

[Anonymous No.12204442]

>>12204352
Ask this a physicist or an engineer.

[Anonymous No.12204477]

>>12204329
>TERRY!
>TERRY GET THE FUCK OUT HERE!
>>Oh geeze whats going on?
>GET IN THE CAR TERRY
>GET IN THE FUCKING CAR!
>>Oh geeze I was having a sleep, I was having a little Tao sleep, working on the Schrö-
>TERRY, GET IN THE DAMN CAR NOW
>>ohhhh why?
>WE'RE GOING TO BINDEGO TO GET ME ROBIN'S THEOREM
>WE'RE GONNA PROVE THE RIEMAN HYPOTHOSIS TERRY
>>oh geeze...

[Anonymous No.12204493]

>>12204358
>>12204442
Olympiad Geometry, not analytical geometry
im talking about similar triangle bullshit
theyre not even related to the geo that physicists or engiees do
fucks sake, its obvious from context what kind of geo im talking about

[Anonymous No.12204497]

>>12203730
Khan has a lot. Brilliant gets shilled a lot but is apparently quality.

[Anonymous No.12204501]

>>12204497
>Brilliant
I tried a free trial by them once, but it seems to me as if their lessons are aimed at the lowest common denominator, is this incorrect?

[Anonymous No.12204602]

>>12204493
You are just a kind of person who haven't dealt with mathematical problems, otherwise you'd know that translating everything into coordinates is not always the best way to go.

[Anonymous No.12204625]

>>12204602
>otherwise you'd know that translating everything into coordinates is not always the best way to go.
wow cool, its almost like thats not what we're talking about
also
>haven't
you mean hasn't ESL retard

[Anonymous No.12204680]

>>12204493
>there's no similar triangle bullshit in calc classes

[Anonymous No.12204692]

>>12204625
There's nothing wrong with being an ESL.

[Anonymous No.12204722]

>>12204213
I watched vsauce

[Anonymous No.12204784]

>>12204213
I went blind into math because engineering seemed boring. I didn't even liked it until third semester when I had a cool teacher for Linear Algebra I.

[Anonymous No.12204809]

>>12204784
I went into math. Linear algebra was fucking terrible for me, an absolute slog through boring material. Abstract algebra and its secondary grad level classes were my favorite classes during my entire undergrad.

[Anonymous No.12204868]

>>12204213
When I had my first class about modular arithmetics in high school, and had to make proofs for the first time.
Before that I wanted to become a doctor, but I decided I just wanted to learn more maths instead

[Anonymous No.12204928]

>>12204202
The n-th root of x is another way of writing x to the power 1/n. From there you should be able to find out to use them, it follows standard rules.

[Anonymous No.12205077]

>>12204027
anyone else got any suggestions?

[Anonymous No.12205134]

>>12205077
Thank me later.

[Anonymous No.12205147]

>>12204202
x = nth root of y means x=y^(1/n) which means x is the solution of the equation x^n-y=0, which can be solved numerically by algorithms like newton-raphson, bisection, regula falsi, and the Illinois algorithm.

[Anonymous No.12205181]

>>12205134
is that really an exercise book? seems like a good read nevertheless.

[Anonymous No.12205228]

>>12205181
Not strictly, but it has lots of good problems in it.

[Anonymous No.12205629]

>>12203113
Anyone who says anything but a multilinear map of the elements of the vector spaces and their duals is is instantly discarded into the pit of dumb.

[Anonymous No.12205744]

>>12203235
>expand it
What do you mean expand it?
[math]\frac{1}{1 - x} = \sum _{k = 0}^{\infty} x^ k[/math]. By the same token, [math]\frac{I}{A} = \frac{I}{I - (I-A)} = \sum _{k = 0}^{\infty} (I-A)^ k[/math]. The sum terms eventually zero, so the series converges and you get an inverse.

[Anonymous No.12205796]

Anyone know some good math books for soft reading? I was looking at, "Mathematics and Its History" for example.

[Anonymous No.12205827]

I need help with alg
Given a [math]k[/math]-cycle in [math]S_n,\ \sigma[/math], with [math]2\leq k\leq n-2[/math] I want to show that the centralizer [math]C(\sigma)[/math] is the product of two nontrivial groups.
The obvious isomorphism is [math]C(\sigma) \cong \langle\sigma\rangle \times S_{n-k}[/math], given by the normal composition where [math]S_{n-k}[/math] is the collection of permutations disjoint to [math]\sigma[/math]. but I'm stuck on the final part of showing it's iso. I need help showing that every element of the centralizer is a product of a power of [math]\sigma[/math] and something disjoint to [math]\sigma[/math].
Any ideas?

[Anonymous No.12205984]

If [math]g: A\to B[/math] is a continuous open map such that [math] B[/math] is Hausdorff and connected, why is [math]g[/math] surjective? It's clear that [math]g(X)[/math] is open. It's not clear to me that [math]g(X)[/math] is closed.

[Anonymous No.12206046]

>>12205984
wouldn't [math]g:A\rightarrow B[/math] being surjective imply [math]g(A)[/math] is open and closed and not necessarily [math]g(X), X\subset A[/math] being open and closed?
[math]g(A)[/math] being open and closed seems intuitive at least, so if that's how it works there you go.

[Anonymous No.12206055]

>>12206046
Oops I made a mistake. I meant to say [math]g(A)[/math] instead of [math]g(X)[/math]. Anyways, the point being that I want to prove that [math]g(A)[/math] is both open and closed which would then prove that [math]g(A)[/math] is surjective as the only subsets of a connected space that are open and closed are the space itself and the empty set. Proving that [math]g(A)[/math] is open is really easy. I'm stuck on trying to prove that [math]g(A)[/math] is a closed set.

[Anonymous No.12206065]

>>12205629
>elements of the vector spaces
But anon what about [math]R[/math]-algebra tensors?

[Anonymous No.12206331]

>>12203113
The transformation law meme is a complete brainlet take for physicists.

[Anonymous No.12206334]

>>12206065
Algebras over a ring have underlying modules, of which you can take tensor products.

[Anonymous No.12206336]

>>12206055
>>12205984
Doesn't that whole arrangement imply [math]A[/math] is connected as well?
[math]g^{-1}(B)=\text{clopen}[/math] and [math]g^{-1}(\emptyset)=\text{clopen}[/math] follow from the closed and open definitions of continuity? Then [math]A[/math] and [math]\emptyset[/math] are the only clopen subsets of [math]A[/math] and [math]g(A)[/math] is one of [math]\emptyset[/math] or [math]B[/math] and therefore has an open complement.
Been a while since I skimmed a topology book but is that right?

[Anonymous No.12206442]

>>12206334
If I'm interested in the universal property (cofibred product) as ring algebra tensors then I have to do a fair bit of work to get there from a definition of tensors of [math]R[/math]-modules. It turns out there are multiple useful descriptions!

[Anonymous No.12206564]

>>12204086
Based mumford

[Anonymous No.12206568]

Question is "Find 3 subset A, B, C to set E such that A, B, C, A∩B"

How do you even read A, B, C, A∩B? What do the commas represent? Thank you /sci/

[Anonymous No.12206631]

>>12203182
The answer is (E) right? Because even if Av_i is not zero, it could map all three vectors to a proper subspace of R^3? Just want to make sure I haven't forgotten my linear algebra.

[Anonymous No.12206640]

>>12205629
anyone who doesn't mumble something about monoidal categories is instantly discarded in the pit of dumb

[Anonymous No.12206808]

>>12206631
yeah, it's E

[Anonymous No.12206846]

In Ontatio, Canada we have a 90 credit BSc./BA. degree and a 120 credit Honours BSc./BA. degree. I'm currently in the 90 credit BSc. Applie Math degree. A 120 Hons. BSc/BA is required for grad school. For anyone familiar with this distinctiin, what are my job optics if I stick with the 90 credit degree?

[Anonymous No.12206851]

>>12206846
kings honor friend

[Anonymous No.12206857]

>>12206851
??

[Anonymous No.12206864]

>>12206846
There is a few factors I would consider.

Do you have the capital to sustain yourself and go to school and get the honors degree as compared to the regular one? Also, are you young? I would say the honors program will probably lead to an increased career outlook, as a rule, but if you can't afford it or are too old it may not be worth it.

[Anonymous No.12206939]

>>12203425
yes

[Anonymous No.12206942]

>>12203907
Is it a public mailing list? Can I add my email?

[Anonymous No.12206954]

>>12205744
>What do you mean expand it?
Yes.

>>12206942
Follow these instructions. https://arxiv.org/help/subscribe

[Anonymous No.12206988]

>>12203182
>>12203235
>>12203717
Did you guys figure this out just now, or have you seen something similar before?

[Anonymous No.12206994]

>>12206988
Figured it out when I posted it. Haven't seen it before (third one you're replying it).

[Anonymous No.12206996]

>>12206988
I'm specialised in algebra stuff, so I sometimes do similar tricks to get inverses.

[Anonymous No.12207004]

>It's October 8, year of our Lord 2020, and we still don't know how many real numbers there are

[Anonymous No.12207042]

The long ray is comprised of an uncountable number of [0,1) segments laid end to end.

Does it have a first segment? Does it have a second segment? If so, why aren't the segments countable?

[Anonymous No.12207045]

>>12207004
[math]\mathfrak{c}[/math]

[Anonymous No.12207051]

>>12207045
Oh wow you gave a letter to the size. Now what?

[Anonymous No.12207055]

>>12207042
>Does it have a first segment? Does it have a second segment?
Yes, yes.
>If so, why aren't the segments countable?
Because you defined it so they aren't. (uncountable number of [0,1))

[Anonymous No.12207056]

>>12207004
[math]\infty[/math] times two, duh.
one for the positives, one for the negatives.

[Anonymous No.12207058]

>>12207051
It can be bounded.
[math]|\mathbb{N} |\leq \mathfrak{c} \leq \aleph_{1} [/math]

[Anonymous No.12207062]

>>12207055
Then the definition is inconsistent and the long ray doesn't exist.

[Anonymous No.12207063]

>>12207058
Sorry, the first [math]\leq[/math] should just be <

[Anonymous No.12207064]

>>12207058
We know c is bigger that |N|, so you're saying that c= aleph_1.
Where can I find a proof of this?
>>12207062
>Then the definition is inconsistent
How so?

[Anonymous No.12207073]

>>12207064
If the long ray exists you can use the same construction on the number of digits in decimal representations of numbers to construct an uncountably irrational number with uncountably many digits.
No such number exists, as all decimal representations are countable.

[Anonymous No.12207076]

>>12207064
I'm not saying that [math]\mathfrak{c} = \aleph_{1}[/math], I'm saying that [math]\mathfrak{c} \leq \aleph_{1}[/math].

[Anonymous No.12207080]

>>12207073
>If the long ray exists you can use the same construction on the number of digits in decimal representations of numbers to construct an uncountably irrational number with uncountably many digits.
How? What is the construction?

[Anonymous No.12207088]

>>12207076
but aleph_1 is the smallest uncountable cardinal

[Anonymous No.12207090]

>>12207080
Take a segment [0,1). Append another [0,1) to the right hand side. Do this such that the numbers of segments is in bijection with [math]ω_1[/math].
Substitute segments with digit places.

[Anonymous No.12207094]

>>12207088
Oh. I'm retarded.
Should be [math]\aleph_{1} \leq \mathfrak{c}[/math]

[Anonymous No.12207097]

>>12207090
>Do this such that the numbers of segments is in bijection with ω1ω1.
I'm not sure you know what you mean by that. This is not a rigorous construction.
>Substitute segments with digit places.
Lol what?

[Anonymous No.12207099]

I hate this fucking board.

[Anonymous No.12207104]

>>12207099
What don't you like about it?

[Anonymous No.12207176]

>>12206568
Did the subgroup poster started a competition for the stupidedt question asked in the history of /mg/?

[Anonymous No.12207182]

>>12207176
Certainly looks like it.

[Anonymous No.12207206]

>>12206568
[math]\forall C: A\cap B[/math] viva la involucion!

[Anonymous No.12207237]

>made no progress so far the entire week
>feel like absolute shit
>have to meet my advisor tomorrow
What the fuck do I tell her, /mg/

[Anonymous No.12207242]

>>12207237
Same but 3 weeks. I tell mine of all the stupid ideas I had and was unable to take to the end or turned out to be stupid after checking the details.

[Anonymous No.12207247]

>>12207242
Not bad, I will do that as well. I knew it was a good idea to consult /mg/

[Anonymous No.12207530]

>>12207004
[math]2^{\aleph_0}[/math]

[Anonymous No.12207608]

>>12203008
Is the empty set a member of the complement of the empty set?

[Anonymous No.12207611]

>>12207608
No. The complement of the empty set is not a set.

[Anonymous No.12207619]

someone explain to me how picking contours in the complex plane somehow magically allows us to solve real integrals

[Anonymous No.12207623]

>>12207530
Right, it's also
[math]\aleph_0 ^{\aleph_0} = 3^{\aleph_0 }= 1000^{\aleph_0 }=\aleph_0 ^ {\aleph_0 \times \aleph_0 }[/math]
There are infinitely many ways to express it. That doesn't tell you how big it is.
The question is for which k, [math]\aleph_k = 2^{\aleph_0}[/math]

[Anonymous No.12207626]

>>12207623
k=2.3

[Anonymous No.12207630]

>>12207626
Aleph_k is only defined for ordinal values of k. What do you mean by aleph_2.3?

[Anonymous No.12207631]

What area of math is the most poggers?

[Anonymous No.12207632]

>>12207611
Specify a universe before taking complements, heathen. It's like you don't even know about restricted comprehension.

[Anonymous No.12207639]

>>12207632
Bro it's perfectly fine to form general sets {x: P(x)} as long as P(X) does not involve x containing itself (or logically reducible to x containing itself)

[Anonymous No.12207642]

>>12207630
[math]\aleph_2<2^{\aleph_0}<\aleph_3[/math]

[Anonymous No.12207648]

>>12207642
That's provably impossible because by definition Aleph_3 is the smallest cardinal that's bigger than Aleph_2.

[Anonymous No.12207649]

>>12207619
The integral over the big semicircle is basically zero.

[Anonymous No.12207653]

>>12207648
Sorry, spend a few more decades studying, then you might get to the level where you can understand this

[Anonymous No.12207655]

>>12207653
Ok thanks for the help bro

[Anonymous No.12207657]

>>12207655
yeah no worries bro

[Anonymous No.12207658]

>>12207639
No it's not, just take P(x) to be any statement which is always true, like 1=1.

[Anonymous No.12207676]

>>12203008
>Twistor edition

One comment about twistors that's vaguely right, the rest are shit posts about basic math. This sums up everything that's wrong about /sci.

[Anonymous No.12207695]

>>12207658
So you get the set of everything.

[Anonymous No.12207715]

>>12207623
Set theory fag here, for any uncountable ordinal [math]\alpha[/math], it is consistent with ZFC that [math]\aleph_{\alpha}=2^{\aleph_0}[/math]. This is called Easton's theorem.

[Anonymous No.12207726]

>>12207676
And the vaguely right thing was some schizo mindlessly repeating something he heard on a YouTube video. At least there's no race bait yet.

[Anonymous No.12207733]

>>12207715
Woops, I had a brainfart, I meant to say it is consistent with ZFC that [math]\aleph_{\alpha}=2^{\aleph_0}[/math], where [\math]\aleph_{\alpha}[/math] has uncountable cofinality. In particular the continuum cannot be [math]\aleph_{\alpha}[/math], where the cofinality of [math]\alpha[/math] is countable.

[Anonymous No.12207735]

>>12207695
There is no such thing. Its existence would contradict Cantor's theorem.

[Anonymous No.12207872]

>>12207653
Based.

[Anonymous No.12207933]

how do I learn proofs by induction?
I kinda slacked off in my uni course and the learning curve got very steep very fast and I have no idea what's happening and how to approach the problems

[Anonymous No.12207958]

>>12207933
First you learn a basic proof, then you imagine that you've learned the first n proofs in the class. If you can use that to learn the (n+1)st proof in the class you've learned proofs by induction.

[Anonymous No.12207975]

>>12207933
Prove Laplace expansion and Cauchy's integral formula by induction.

[Anonymous No.12207989]

>>12207933
Do you understand the basic idea? You have a claim that is somehow related to the natural numbers. First you show it is true in the case where n is the smallest allowed natural number. Then you want to show that if it holds for some k, then it will hold for k+1. This is done by assuming that it is true for k, and this assumption is the induction hypothesis. Once you have done these two, you will get it for all (allowed naturals), as being true for the smallest OK number implies truth for the next one, and that will then imply truth for the one after itself etc. And what I mean by allowed/OK is that you don't necessarily start from 0, for example [math]n! > 2^n[/math] is true for [math]n \ge 4[/math].

[Anonymous No.12208022]

>>12207989
I know the idea but I can never come up with the solutions on my own because there doesn't appear to be a consistent way, it feels like you have to guess or come up with bullshit ideas

[Anonymous No.12208043]

>>12208022
Can you do babby's first induction proof, that is [math]\sum\limits_{i=0}^n = \frac{n(n+1)}{2}[/math]? If not, show us (or me) where you get stuck. Otherwise, give some other problem you are stuck with and point out where you get stuck.

[Anonymous No.12208050]

>>12208043
Lol induction is such a weird way to prove that.

[Anonymous No.12208059]

>>12208050
It's the best way to do it.

[Anonymous No.12208060]

>>12207715
>it is consistent with ZFC that
Means we need more axioms.

[Anonymous No.12208072]

>>12208043
[math]\frac{(n+1)(n+2)}{2}=\frac{n^2 + 3n + 2}{2}=\frac{n^2+n+2n+2}{2}=\frac{n(n+1)}{2}+(n+1)[/math]
is this what i was supposed to do?

[Anonymous No.12208071]

>>12208059
2(1+2+3+...+n)=
1 + 2 + 3 + ... + n +
n + (n-1) + (n-2) + ... + 1 =
(n+1) + (n+1) + .. + (n+1) =
n*(n+1)

[Anonymous No.12208107]

>>12208050
It's also the usual first induction problem in your HS book/uni intro course, at least judging by what I have seen.

>>12208072
If you would actually follow the steps you claimed to know, you would first say it is true for 0 because the sum of the first 0 naturals is 0, and on the other side of the sign you would have 0/2 = 0. Then you would assume it holds for some k and do [math]\sum\limits_{i=0}^{k+1} i = \sum\limits_{i=0}^k i + (k+1) = \frac{k(k+1)}{2} + k+1 = \cdots = \frac{(k+1)(k+2)}{2}[/math], where the skipped part is what you did but backwards. Your thing doesn't prove the claim because it is not related to anything. You are not connecting [math]\frac{n(n+1)}{2}[/math] to the sum in any way, only showing that you can write the leftmost term like you have on the far right. Write more!

[Anonymous No.12208112]

>>12207735
Power set axiom only holds for small sets.

[Anonymous No.12208122]

>>12208107
I want to fuck you in the ass.

[Anonymous No.12208128]

>>12208107
yeah I omitted the first step because it seemed obvious and not needed
I have a problem which I have no idea how to approach though, it follows:
Prove by induction that all numbers greater or equal to 8 can be expressed as a sum of 3s and/or 5s. E.g. 8 = 3 + 5, 9 = 3+3+3

[Anonymous No.12208141]

>>12208128
>yeah I omitted the first step because it seemed obvious and not needed
Get in the habit of writing out your proofs in full.
Doesn't matter that you find certain steps obvious. Writing them out in full will make your learning process much faster and let you think more clearly.

[Anonymous No.12208172]

>>12208141
I will do that. Do you have any clues for that problem?

[Anonymous No.12208182]

>>12208112
That's not a healthy way to live.

[Anonymous No.12208200]

>>12205744
>The sum terms eventually zero, so the series converges
not how convergence works
also not what they're looking for, it needs to terminate after finite [math]k[/math] and never does it say you get to sum the [math](I-A)^k[/math]. there needs to be a [math]k[/math] such that [math](I-A)^k=0[/math], that's it

[Anonymous No.12208460]

>>12208128
Idk if this is a correct type of approach, but what do you think of this observation?

Consider a particular sum of 3s and/or 5s.
If the sum has at least two 3s in it, then you can replace the two 3s with a 5 and effectively subtract 1.
If it has at least two 5s, you can replace the two 5s with three 3s and subtract 1.
After either operation, the result will still be a sum of 3s and 5s.
Any (integer) sum of 3s and 5s greater than 8 will also itself have at least two 3s or two 5s.
So you can get to any particular number >=8 by just picking some greater number that is a sum of 3s and 5s, and counting downward in this manner until you reach the desired number.
So for any integer of the form 5a+3b, you can prove by induction that all smaller integers >=8 must also be representable in that form.
You can also count upward if you prefer, maybe most simply by just adding one three and then decrementing twice.

[Anonymous No.12208510]

>>12208172
Yes. 1 = 2(3)-5. So if n can be expressed as a sum with at least one 5, you can express n+1 with 2 more 3s and 1 less 5.
If there are no 5s in n, then assuming n>=10 you can replace 5*2 with 2*5. Voila.

[Anonymous No.12208542]

>>12205796
Geometry and imagination by Hilbert. Great book.

[Anonymous No.12208548]

Sometimes I think of instead of pursuing a PhD at a university, I NEET with my parents at home and try to study and achieve results on my own.

[Anonymous No.12208589]

>>12208060
The whole program of relative consistency proofs are predicated on the assumption that the base theory is consistent. All we are do to prove Easton's theorem is show that if ZFC has a model, then ZFC+ Easton's theorem has a model. This is one of the finer points of forcing. Kunen gives a great explanation on this.

[Anonymous No.12208614]

>>12208122
Maybe some day but not now, sorry. Unless you kill my bf to claim me first, but he is a big engineering chad with military training.

>>12208128
When you begin with proofs, you should basically write a novel every time you prove something. When you get the so called maturity, you can drop the more obvious parts and make more fancy proofs.

[Anonymous No.12208750]

>>12205796
This book is fantastic
https://books.google.at/books/about/Modern_Algebra_and_the_Rise_of_Mathemati.html?id=WdGbeyehoCoC&redir_esc=y

>Leo Corry - Modern Algebra and the Rise of Mathematical Structures


>>12206988

[math]f(x)-c\cdot f'(x) = g(x)[/math]

So clearly
[math] \implies f(x) = \dfrac{1}{1-c\cdot \frac{d}{dx}}g(x) = g(x) + \sum_{n=1}^\infty c^n \left(\frac{d}{dx}\right)^n g(x)[/math]

You can make some of it also work with [math] \dfrac{1}{1-c\cdot \int^x dt}[/math]

[Anonymous No.12208778]

Could someone explain to me what rule is used when the excluded third party law is set?
The related pic is the formal proof of the absorption law, but I don't understand why Q can be removed from the material implication.

[Anonymous No.12208832]

>>12208778
You can introduce assumptions, but you can introduce tautologies, and LEM is a tautology (classically).

[Anonymous No.12208878]

>>12207619
An integral of an analytic function over a closed contour in C is zero. If the function is analytic except for at finitely many points then the residues at those points are the only contribution to the integral. Combine this with analytic continuation on exp(x) to exp(z) and you're 90% there.

[Anonymous No.12208892]

>>12208778
p a r t y

As that other anon said, step 3 doesn't follow from 2 but is introduced here in axiomatic fashion

[Anonymous No.12208903]

>>12208892
>>12208832
Thanks for your answers, I did not remember that the excluded third was an axiom and confused it with a rule of inference.

[Anonymous No.12208930]

>>12208903
You are welcome. I remember trying to do deductions like that back in the days and forgetting all the introduction and elimination rules. It was painful.

[Anonymous No.12208989]

>>12208614
how do you get a chad engineering bf?

[Anonymous No.12209072]

>>12208878
Is there a better theorem in CA?
https://proofwiki.org/wiki/Cauchy-Goursat_Theorem

[Anonymous No.12209146]

>>12208750
Not him but sounds neat

[Anonymous No.12209230]

>>12208989
Talk to nice guys online and maybe you will find one.

[Anonymous No.12209279]

If A is a subset of B and C is a subset of B then are A and B subsets of each other?

[Anonymous No.12209312]

>>12209279
Based average /mg/ poster

[Anonymous No.12209327]

>>12209279
no C is a normal subgroup of A X B

[Anonymous No.12209417]

>>12203717
Very nice, went the idempotent route

[Anonymous No.12209421]

>>12208043
Hello fellow based Gabu poster

[Anonymous No.12209489]

If [math]a[math] divides [math]b[math] and [math]c[math] divides [math]b[math], do [math]a[math] and [math]c[math] divide eachother?

[Anonymous No.12209490]

>>12209421
Cheers, lad.

[Anonymous No.12209494]

If [math]a[/math] divides [math]b[/math] and [math]c[/math] divides [math]b[/math], do [math]a[/math] and [math]c[/math] divide eachother?

[Anonymous No.12209563]

>>12209421
Hi.

[Anonymous No.12209566]

>>12209494
no
>>/sqt/

[Anonymous No.12209576]

>>12209494
>i-is this bait

Counterexample: any prime factorization

[Anonymous No.12209601]

>>12209494
sometimes

[Anonymous No.12209689]

>>12208589
Then why does Woodin think CH has a definite value? Is he not aware of Easton's theorem?

[Anonymous No.12209696]

>>12209494
>>12209279
FUCKING STOP

[Anonymous No.12209744]

>>12209689
Easton's theorem just classifies what cardinals the continuum can be over ZFC. You can use it to make CH true for instance. I don't understand V=Ultimate L (his current conjecture) very well, if at all, that is not my field of set theory. One thing though, basic Cohen forcing over L will violate CH. My very basic understanding is that CH holds in Ultimate L and Ultimate L only has trivial forcing extensions. So you can't break CH with forcing. Of course the existence of Ultimate L is a only conjecture and could be very wrong. But there is evidence, we'll have to wait and see. I think Woodin has lecture about it youtube if you're interested.

[Anonymous No.12209838]

>>12209744
>I don't understand V=Ultimate L (his current conjecture)
I don't know why those guys call those things conjecture.

Sounds like
>strawberries is the best ice cream
kind of conjectures to me

>hat is not my field of set theory
what is

[Anonymous No.12209878]

If [math]a \leq b [/math] and [math] c \leq b[/math] does [math]a = c[/math]?

[Anonymous No.12209924]

>>12209838
I guess the language is a little imprecise. The conjecture is that Ultimate L exists. The proposal for the new axiom to add to ZFC would be V=Ultimate L. My field is descriptive set theory, this stuff falls under inner model theory.

[Anonymous No.12210015]

>>12209878
Not necessarily.

[Anonymous No.12210081]

If [math]A \implies B[/math] and [math] C \implies B [/math] is it true that [math]A \iff B[/math]?

[Anonymous No.12210199]

If [math]n=2k>2[/math] with [math]k/in/mathbb{N}[/math] then [math]n=p+q[/math] with [math]p,q[/math] primes?

[Anonymous No.12210224]

>>12210081
Not necessarily.

[Anonymous No.12210237]

>>12209878
Just compute a counter-example

[Anonymous No.12210248]

Suppose [math] G[/math] is a directed graph and [math]v_1,v_2,v_3[/math] are vertices of [math]G[/math]. If there is a path from [math] v_1 [/math] to [math] v_2 [/math] and a path from [math] v_3 [/math] to [math] v_2 [/math] are there paths from [math] v_1 [/math] to [math] v_3[/math] and vice versa?

[Anonymous No.12210294]

>>12210248
Let [math] \mathcal{C} [/math] be any category. Suppose [math] \mathscr{F}, \mathscr{G}, \mathscr{H} [/math] are representable functors [math]\mathcal{C} \to \text{Set}[/math]. Suppose there exist natural transformations [math]\mathscr{F} \Longrightarrow \mathscr{G} [/math] and [math]\mathscr{H} \Longrightarrow \mathscr{G} [/math]. Does there exist a natural isomorphism [math]\mathscr{F} \cong \mathscr{H} [/math]?

[Anonymous No.12210303]

>>12210248
Not necessarily. There is an extremely simple example with only 3 vertices, see if you can come up with it.

[Anonymous No.12210375]

>>12210303
?

[Anonymous No.12210755]

>>12209878
>>12209494
>>12209279

Based

[Anonymous No.12210789]

>>12210755
What about
>>12210248
and
>>12210294
?

[Anonymous No.12210800]

>>12203008
I have done it. I derived the feigenbaum constant from the monster group. I also derived the monster group from the feigenbaum constant. Mathematics is over. Where do I publish this? Should I make a youtube video?

[Anonymous No.12210805]

>>12210800
When you say derived what exactly do you mean? What is the relationship?

[Anonymous No.12210823]

>>12210800
How many pitchforks did you have to look at?

[Anonymous No.12210843]

I am supposed to do a Gauss-Newton on a set of datapoints but one of the datapoints is approaching inf. Do I just drop it?

[Anonymous No.12210934]

>>12210081
what is C?

[Anonymous No.12210944]

If I have a weak homotopy equivalence [math]X \to Y[/math] and a weak homotopy equivalence [math]X \to Z[/math], then does there exist a weak homotopy equivalence [math]Y \to Z [/math]??

[Anonymous No.12210971]

>>12210934
A type in the first universe.

[Anonymous No.12210980]

What are some nice 2D manifolds that I can easily calculate geodesics for? I'm messing around trying to render 2D manifolds from geodesics. Pic related is the 2-sphere.

[Anonymous No.12211046]

How do I solve this? I dont know what the A, B and C is.

Please help me.

[Anonymous No.12211057]

>>12210980
cylinder

[Anonymous No.12211070]

>>12211046
Sorry bro, no applied maths here

[Anonymous No.12211072]

>>12211046
I haven't read your question or picture, but the answer is always
A=C

[Anonymous No.12211129]

>>12211057
It turns out easy to understand 2D manifolds are pretty boring.
I'm not sure geodesic rendering would work in real time. It's a shame because most games on manifolds just use charts and try to hide the transitions which is really boring imo.

[Anonymous No.12211144]

>>12211129
Actually this paper seems to do exactly what I want: https://arxiv.org/abs/2002.09533
>We present novel methods of computing real-time native geodesic rendering of non-isotropic geometries

[Anonymous No.12211308]

>>12209689
>>12209744

Which of those should I read (first)?

>In Search of Ultimate-L the 19th Midrasha
Mathematicae Lectures.
http://logic.harvard.edu/EFI_Woodin_StrongAxiomsOfInfinity.pdf

>Strong Axioms of Infinity and the search for V
https://dash.harvard.edu/bitstream/handle/1/34649600/59799476.pdf

[Anonymous No.12211329]

What are some ways in which rings can be extended to a field?
Are there canonical techniques?

[Anonymous No.12211346]

>>12211329
The obvious one is the field of fractions for an integral domain.

[Anonymous No.12211357]

>>12211346
thx

[Anonymous No.12211358]

>>12211329
If your ring is an integral domain, then you can extend it to the so-called field of fractions which is the "smallest" field that contains your ring (up to isomorphism). If it is not an integral domain you cannot extend it to a field because every subring of a field is an integral domain

[Anonymous No.12211361]

>>12211358
thx thx

[Anonymous No.12211372]

>>12211358
If [math]C[/math] is a field and [math]A\subset C[/math] an integral domain, is the field of fractions [math]B[/math] of [math]A[/math] a subfield of [math]C[/math]?

[Anonymous No.12211385]

Assuming Choice, is the cardinality of the field of fractions of an infinite ring always the same as that of the ring?

[Anonymous No.12211404]

>>12211385
Let [math]Q[/math] be the field of fractions of an integral domain [math]R[/math]. Then [math]|R| \le |Q| \le |R| \times |R|[/math], so it will be the same in the case [math]R[/math] is infinite. If [math]R[/math] is finite, then it is a field already, and so it is its own field of fractions. The answer is yes.

[Anonymous No.12211420]

>>12211404
Okay, looks good.

I didn't ask for the finite part but I also don't get it. Why is a finite integral domain already a field?

[Anonymous No.12211436]

>>12211420
Oops I somehow skipped the "infinite" in your post. A quick proof can be found for example here http://www-groups.mcs.st-andrews.ac.uk/~john/MT4517/Lectures/L4.html (scroll down a bit but not too much).

[Anonymous No.12211496]

>>12211372
Yes, that is what is meant with "smallest". The field of fractions [math] F[/math] of an integral domain [math]A [/math]satisfies the following universal property. If [math]K [/math] is a field and [math]f: A \to K [/math] an injective ring homomorphism, then there is a unique homomorphism [math]F \to K[/math] (which is also injective) extending [math]f [/math]. This property characterizes F up to canonical isomorphism

[Anonymous No.12211534]

If A, B, C are G-modules with finite cohomology groups, A is a submodule of C and B is a submodule of C, does that imply A is a submodule of B?

[Anonymous No.12211577]

>>12211534
We should write a Bourbaki style tome that restates all theorems of mathematics in this form.

[Anonymous No.12211636]

>>12211308
What's your background?

[Anonymous No.12211658]

>>12211636
I donno, I should be able to read those more or less, I hope

[Anonymous No.12211677]

Any russian anons here? What do you think of Independent Moscow University?

[Anonymous No.12211692]

>>12203730
Paul's Online Notes has a lot of practice problems and is an excellent reference guide/textbook for the standard Calculus I, II, III series plus diffeqs.

[Anonymous No.12211695]

>>12208614
Are you a tranny or an actual woman?

[Anonymous No.12211702]

>>12211658
The first one is a brief survey paper. If you know about L and large cardinals you should be fine. The second one I wouldn't even touch if you don't know how extender models work.

[Anonymous No.12211705]

>>12211702
okay, good to know

[Anonymous No.12211707]

Any Cambridge chads here? I'm a third year mathmo.

[Anonymous No.12211737]

How do you guys read through textbooks for fun? Do you read them as you do literature or do you have a notebook and take notes as if for a course?

[Anonymous No.12211740]

https://en.wikipedia.org/wiki/%CE%98_(set_theory)

[Anonymous No.12211801]

>>12211695
Yes.

>>12211737
If there are exercises, then I try to do those at least in my head.

[Anonymous No.12211807]

>>12211801
>tranny
>Madoka poster
How does it feel being a living meme?

[Anonymous No.12211823]

>>12211737
I never take notes. But I really can't read math books as literature. I keep pen and paper next to me to work through proofs, examples, some exercises, etc..

[Anonymous No.12211829]

>>12211737
unless you're an absolute god of mathematics you should definitely take notes otherwise you just won't retain anything imo

[Anonymous No.12211832]

>>12211829
>he doesn't just commit everything to memory after reading it one time
do brainlets really...?

[Anonymous No.12211842]

>>12210789
also based. I only skimmed over the thread. The real question is: [math]f\in L^{a}, g\in L^{b}, c=a+b, \text{ is } g+f\in L^c[/math]?

[Anonymous No.12211893]

Does anyone feel like the math and humanities part of their brain excludes one another? I find that when I’m studying math intensely, I have very little patience for consuming literature / films and am less interested by the arts in general. I only really think about math. And if I take a break from study, the exact opposite occurs. I’ve also noted that most of my math professors are culturally quite dumb (i.e. watch anime, have basic political opinions, etc.). Is there something about focusing your brain on high level analytical concepts that distances you from other kinds of thinking? Obviously this wasn’t always the case (e.g. all the polymaths in history of mathematics) but wonder if this is a side effect of hyperspecialization.

[Anonymous No.12211947]

Some papers for you today
>Measure equivalence classification of transvection-free right-angled Artin groups
https://arxiv.org/pdf/2010.03613.pdf
>New approaches for solving linear confluent Vandermonde systems and inverse of their corresponding matrices via Taylor's expansion
https://arxiv.org/pdf/2010.03862.pdf
>The derived-discrete algebras over the real numbers
https://arxiv.org/pdf/2010.03787.pdf
>Simplicial Neural Networks
https://arxiv.org/pdf/2010.03633.pdf

>>12211807
Pain is temporary but glory is... who am I kidding? Pain is eternal.

[Anonymous No.12212107]

>>12211947
Thansk

The abstract of the NN paper for ML fags is funny

[Anonymous No.12212371]

what the fuck is this algebraic topology holy shit

[Anonymous No.12212386]

>>12212371
a meme

[Anonymous No.12212390]

>>12212371
a subject that has been completely rewritten at least 2 times

[Anonymous No.12212524]

Are there any books for algebra like 'Counterexamples in Analysis' by Gelbaum & Olmsted and 'A Problem Book in Real Analysis' by Aksoy & Khamsi?

[Anonymous No.12212790]

Help boys, highlighted line is problematic.
If you have different proof that there is no retraction from closed disk to circle without fundamental groups, I would appreciate it.

[Anonymous No.12212810]

>>12208548
Tutorial on how not to prove anything in your life.

[Anonymous No.12212821]

>>12212371
Glorified hole counting.

[Anonymous No.12212825]

>>12212821
Gloryhole counting?

[Anonymous No.12212840]

>>12212825
You could use persistent homology to count the number of cocks visiting a gloryhole, sure.

[Anonymous No.12212843]

>>12212790
I have a proof with homology, but you're probably not interested.
Why would you try do this without algebraic topology?

[Anonymous No.12212857]

>>12212843
I'm not into gloryholes. I know proof that uses fundamental group the fact that Z is fundamental group of circle.

[Anonymous No.12212869]

>>12212857
The homology proof is basically the same proof. It works for disks of any dimension though.

[Anonymous No.12212899]

>>12212869
I'm not interested in it right now, but do you have any book recommendations for algebraic topology?

[Anonymous No.12212918]

>>12212107
Nice that someone liked it.

>>12212899
Rotman.

[Anonymous No.12212921]

>>12212899
I learnt through Hatcher, some people here hate that book though.
Ghrist's Applied Topology cover's it from a more computational perspective, I'm not sure how useful it is as a first introduction though.

[Anonymous No.12212935]

Anyone got cool less known elementary problems whose solution does not require high machinery just ingenuity?

[Anonymous No.12212949]

>OMFG
>crackpot ideas are back on the meny boys!

Time is a flat circle motherfuckers.

[Anonymous No.12212951]

>>12212949
Fuck off faggot. Penrose is not a crank, he's a respectable mathematical physicist.

[Anonymous No.12212953]

>>12212935
https://arxiv.org/pdf/1110.1556.pdf
Has some cool problems that were made to have elementary solutions.

[Anonymous No.12212957]

>>12212951
I know but he's becoming more based with every year that passes. None of that boring ebony hole bs.

[Anonymous No.12213000]

>>12212957
Oh, I thought you were mocking him. Yeah, he's pretty based.

[Anonymous No.12213025]

https://en.wikipedia.org/wiki/Replication_crisis
Have you ever read a bullshit paper in math? Besides clowns like terrence howard.

[Anonymous No.12213032]

>>12213025
>Have you ever read a bullshit paper in math?
I know Tooker has.

[Anonymous No.12213068]

>>12213025
You ever get crazy emails from that guy?

[Anonymous No.12213078]

>>12212953
Is problem 5 as easy as I think it is?

[Anonymous No.12213101]

>>12213078
No, it's definitely harder thank you think it is.

[Anonymous No.12213128]

>>12213101
all done.

[Anonymous No.12213138]

>>12213101
Yeah, I looked up the answer and it's very complicated.
But I still found the correct values of x without bothering to "think" or do "math."

[Anonymous No.12213142]

>>12213078
It's pretty easy to find solutions. Have you shown that there are no other solutions than obvious ones?

[Anonymous No.12213143]

>>12213101
This is also a good rule of thumb when doing maths

[Anonymous No.12213153]

Will I be able to manage a math postgrad as a CS grad?

[Anonymous No.12213158]

>>12213153
probably, depending on how much theoretical stuff you did.

[Anonymous No.12213160]

>>12213153
What are you mathing in? What mathing did you do before?

[Anonymous No.12213172]

>>12213160
Was thinking of doing a masters in pure and applied math, had 1 discrete math, 1 analysis, 4 calculus and 3 linear algebra courses

[Anonymous No.12213194]

>>12213172
uhhhhh, good luck. If this is a canadian masters, you're gonna be a little (a lot) fucked

[Anonymous No.12213415]

>>12213194
>Canadian

[Anonymous No.12213421]

I like combinatorics and functional analysis. What should I study?

[Anonymous No.12213441]

>>12213421
Graph theory

[Anonymous No.12213467]

>be in proofs class
>girl (female) is presenting a proof
>her proof is incomplete
>some guy asks what if (case she didn't consider)?
>"I don't think that's possible"
I almost punched my screen, like nigga you have to prove that it's not possible that's the whole point of the course. Everybody chimes in to convince her that you don't necessarily know that that's not the case unless you prove it. Eventually she finally said "oops brain did a thing" or some shit like that and we moved on

[Anonymous No.12213477]

>>12213441
idk the graph theory that I've done so far has had absolutely no analysis. Anything else?

[Anonymous No.12213683]

>>12213467
Shit story.
Everyone has brain farts like this where they discount something nontrivial. If you don't ever accidentally do this then you're probably spending too long not discounting trivialities.

[Anonymous No.12213912]

>>12213683
Guess where you need to return to? It's not monke or atlantis. You arent invited there.

[Anonymous No.12214125]

New >>12214123

[Anonymous No.12214318]

>>12213912
A bloo bloo bloo

[Anonymous No.12214600]

>>12212524
yes

[Anonymous No.12215183]

>>12211046
make a free body diagram

[Anonymous No.12215188]

Should I learn multilinear algebra and differential forms?

[Anonymous No.12215313]

>>12215188
Yes.