>intuition
Holy fucking shit. Is this the worst buzzword in all of mathematics instruction? Whenever I hear a professor say it, I know that I don't have to come to class everyday anymore because they are meme-spouting faggots.
>>7872754
Anon you seriously LACK intuition.
If you had any, you'd knew when to skip class.
>>7872754
mathematical maturity is worse
>math professors who do proofs in class
Whenever they do this, I immediately know they are plebs. Proofs are trivial. Show me the theorems, you brainlet. I can work out the proofs on my own.
>>7872754
It's just another way of telling people they have no talent or fluid intelligent.
>>7872774
>tfw i've used this unironically to try to make undergrad 1st/2nd years shut the FUCK up
desperate times call for desperate measures
too bad they have no idea what a measure is
>>7872789
Agreed. My retard analysis professor spent 2 lectures (1 hour each) going over the proof of Stone-Weierstrass when anyone moron with half a brain can whip that up in 10 minutes or so
>>7872789
Theorem: For all [math]n\in\mathbf N \setminus [\![0,\,2]\!][/math], the equation [math]x^n \,+\, y^n \,=\, z^n[/math] has no non-trivial integer solution.
Proof: The proof is trivial! Just view the problem as an orientable language whose elements are open residue classes
>>7872789
Thm: Let [math]X[/math] and [math]Y[/math] be nonsingular quasi-projective varieties, [math]\pi :X \to Y[/math] a proper algebraic map, then the following diagram commutes...
[math] \begin{array}{*{20}{c}}
{K\left( X \right)}&{\mathop \to \limits^{ch( - ) \cdot td\left( X \right)} }&{CH\left( X \right) \otimes \mathbb{Q}} \\
{{ \downarrow _{{\pi _!}}}}&{}&{{ \downarrow _{{\pi _*}}}} \\
{K(Y)}&{\mathop \to \limits^{ch( - ) \cdot td\left( Y \right)} }&{CH\left( Y \right) \otimes \mathbb{Q}}
\end{array}[/math]
Prove pls
>>7872813
shut the fuck up
>>7872814
>Claims proofs are trivial
>Can't even prove the Grothendieck-Riemann-Roch Theorem
lol
>>7872813
Not doing your babby's first AG homework, kiddo.
>>7872774
Aha. This. Fuck this.
OP if you don't like intuition...study topology.
>>7872888
I don't like the misuse and abuse of the word and the idiots who perpetuate it. Why do you mention topology? (i haven't taken a class on it)
>>7872813
what the fuck am I looking at.
only calc III here.
>>7872978
Its a triple integral.
>>7872978
The Chern character maps the K-group into the Chow ring. No big deal, once you learned some basics of algebraic geometry.
>>7872789
Wew lad, here you go:
[math]
If a $(v, k,\lambda)$-design exists with $v=b$ then
if $v$ is even, $k-\lambda$ is squarefree;
if $v$ is odd, the diophantine equation $x^2 − (k − \lambda)y^2 − (−1)^{(v−1)/2} \lambda z^2 = 0$ has a nontrivial solution.[/math]
>>7872994
do people actually focus on this shit? i learned bruck-ryser-chowla in my combo class but design theory seemed boring
>>7872789
>He has to be shown the theorems to do mathematics
>He can't rederive each field from scratch
Time to drop out brainlet.
>>7873527
>What's wrong with "mathematical maturity"?
it's the mathematical equivalent of telling a little kid "you'll understand when you're older"
you're shifting the blame off bad/lazy explanation and onto an unripe student, and it pisses the student off to no end because he can't fix it except by fucking off and waiting
sure, you wouldn't give baby Rudin to a tenth grader (I wouldn't give Rudin to anyone, but..) but you know full well that's not the context the term is ever used in
>>7873567
mathematical maturity is very important. no one uses it as "oh you'll know when you have more mathematical maturity", it's more like "this is hard, while it has no formal prerequisites you don't already know, the material needs you to be more mature. take something else"
>>7872754
undergraduate education is not for learning content (that can be learned easily and fast later one) but for you to develop the needed intuition and mathematical maturity. THAT's your goal
anyone who says intuition is not a large part of mathematics has clearly never done any actual mathematical research, and probably not very many proofs either
the proofs themselves shouldn't employ intuition, but how you figure them out sure as hell does
>>7872754
Intuition is understanding stuff better and in a natural way. What's wrong about teachers trying to help you understand things better?
>>7873567
Kek that's not what it is at all. Mathematical maturity is essentially the experiences and thought processes you hone through practice. It has nothing to do with age.
Intuition is one of the fundamentals of psychology nigger.
![[caffeine] Koufuku Graffiti - 06 [720p][61491EFD].mkv_snapshot_23.52_[2015.12.27_22.23.30].png](https://i.imgur.com/ll6D6gw.png "[caffeine] Koufuku Graffiti - 06 [720p][61491EFD].mkv_snapshot_23.52_[2015.12.27_22.23.30].png")
>>7872789
Theorem: Given the algebra [math]\mathcal{A}[/math] of bounded operators on a Hilbert space [math]\mathcal{H}[/math] with an involutive adjoint [math]*: \mathcal{A} \rightarrow \mathcal{A}[/math] such that [math] I \in \mathcal{A}[/math], then the following are equivalent:
1. [math] \overline{\mathcal{A}}^{S} = \overline{\mathcal{A}}^{W} [/math],
2. [math] \mathcal{A} = \mathcal{A}''[/math], where [math]\mathcal{M}' = \left\{x \in \mathcal{M} \mid \left[x,y\right] = 0 \forall y \in \mathcal{M}\right\}[/math] is the commutant of an algebra [math]\mathcal{M}[/math].
>>7873691
If T is self-adjoint doesn't that just mean that T is a self-inverse endofunctor?
Why would you go through the extra trouble of pointing out that it's an adjoint (since showing an adjunction between two categories is crappier than showing an equivalence between two categories)?
>>7872754
But it's true. The more problems you solve the more experience you get, therefore more mathematical maturity. I think you just don't want to put the time in, and instead be here and insult people. Am I correct?
>>7873982
Maturity and intuition are different things, pleb. Intuition refers to processing fluency while maturity refers to general background knowledge and comfort.
>>7872813
The latest craze: The diagram ... commutes!
To given an approximate explanation of [math] \pi : X \to Y[/math], I’d have to abuse the patience of the audience for 2 hours. Black on White, in Springers lecture notes, it’s about 400 or 500 pages. A striking example for how our thirst for knowledge and discovery ever more turns into a suffocating ideological delirium, while life itself goes to hell in thousand different ways - and is threatened by its complete destruction. It’s about time to change the course.
t. Grothi, 1971
>>7874020
>pi
that's an f
>>7872789
either a troll or a very sad person
>>7873729
It's not a functor, can't you read ?
I swear, the categoryfags on this board...
>>7874073
pi is for projection functions in categories with products.
>>7874051
>>7873705
Do you seriously think you can impress anyone here with babby's first von Neumann algebras? This is like 2nd year undergrad.
>>7874161
This.
Is it just me or are all algebra undergrad students this pretentious? The worst ones are the ones who incorrectly use category theory terminology in their incorrect arguments in an effort to impress the people around them who haven't learned category theory yet.
Who even learns this gay shit lol? I'm in CS, and I can;t wait to graduate and make video games.
>>7872754
'Intuition' is math for 'i'm not explaining this'
>>7873567
that isn't how the phrase mathematical maturity is used though.
Here's an example:
Graduate Algebra MA5G4
Pre-requisites: none, except mathematical maturity
I.e. this course is hard. there will be next to no hand-holding. you'll need to look up any things you are unfamiliar with and learn them yourself the same way a researcher would have to. You have to be able to pick up and understand and manipulate a large number of new concepts quickly.
>>7872789
Given any normal space X and two disjoint closed subsets A, B in X, there exists a continuous function f: X -> [a,b] in R such that f(A) = a and f(B) = b.
>>7874280
Good luck getting a job in the sea of millions of autistic faggots who have the exact same idea as you.
>>7874343
lol bich im going to activision XD
>>7874338
>first year undergrad topology
We are going lower and lower. Next poster will tell me to solve for x.
>>7873747
no, it's obviously not based on age. and no, it's not "regular maturity", it doesn't come with experiences in life but experiences in math. hence math maturity. this isn't hard
>>7874020
>mfw Grothendieck misspelled kommutativ
>>7874020
>suffocating ideological delirium
it's enraptured logical delirium
>>7874373
huh, and here I was thinking he was one of those frankreich uber alles types who refused to use any language other than french.
>>7874353
x-1=3
solve for x
>>7874020
>A striking example for how our thirst for knowledge and discovery ever more turns into a suffocating ideological delirium, while life itself goes to hell in thousand different ways - and is threatened by its complete destruction.
100% grogro
>>7874415
he once said that French language was the natural language for categories, which was itself the natural language for mathematics
>>7874447
did he support this claim in any way?
>>7873581
>>7873674
I don't like how it has become a buzzword used by lazy faggots who don't want to do any thinking on their own and demand that the professor make some youtube crash-course tier analogy for every theorem or example.
>what is the intuition behind...
Shut up, faggot. Why don't you think about the fucking theorem/proof for more than 5 minutes. There is no easy way out
This thread is every thing that is wrong with /sci/ in one tightly-distributed bundle of cancer. Holy shit.
>>7872754
really?
https://en.wikiquote.org/wiki/Physics#/media/File:Optical-dispersion.png
>>7875170
Proofs often are workarounds where the "intuitive" argument fails to formalize. That said, you are both pretentious and a pleb for claiming intuition is not real.
