/mg/ - maths general

[Anonymous No.10795697]

Previously >>10778812 , talk maths.
Fuck off to >>>/amg/ edition.

[Anonymous No.10795718]

I found another interesting series of nested functions
[eqn]
\begin{align}
f_1(x, y) &= \exp(x - \exp(y)) \\
f_{n + 1}(x, y) &= \begin{cases}
f_n(x, x + \exp(y)) &n \text{ even} \\
f_n(x, x - \exp(y)) &n \text{ odd}
\end{cases}
\end{align}
[/eqn] and the related series
[eqn]g_n(x) = f_n(x, x)[/eqn] so that e.g. [math]g_5[/math] looks like
[eqn]e^{x-e^{x+e^{x-e^{x+e^{x-e^x}}}}}[/eqn] Here is a plot of [math]g_1[/math] through [math]g_{24}[/math] where the color goes from blue to red as [math]n[/math] increases.

Also anyone recognize [math]\lambda \exp(x - \lambda \exp(x))[/math] as the PDF of some named distribution?

[Anonymous No.10795720]

Algebraic Topology
>easy to get into
>few pre-reqs
>lots of cool applications
>mind blowing ideas
>can easily explain it to a 5 year old

Algebraic Geometry
>years to reach the front line of research
>only big application is another clusterfuck called String Theory
>have to compete with literal fields medalists
>it's not even that cool, just a pretty boring idea, desu

[Anonymous No.10795744]

>>10795718
Oops the even/odd should be switched

[Anonymous No.10795751]

>>10795720
Thanks for the post. It's always nice to get an insight into how the brainlet mind works.

[Anonymous No.10795759]

>>10795751
Not really insecure about my intelligence. Do you maybe have anything productive to add and please stick to the topic.

[Anonymous No.10795768]

>>10795759
>Not really insecure about my intelligence
Then instead of writing all of that you'd just be honest and say that you aren't smart enough for AG.

[Anonymous No.10795775]

We are all insecure about our intelligence. That's the reason for both academia and anti-academia to exist. That is even the reason for /sci/

[Anonymous No.10795777]

>>10795768
My point is that it's quite boring. Just very much like String Theory, lots of hype from the outside, namely because it's admittedly hard to get into, but when you do get into it, it's just idk, tedious and pretty boring.
Do people just like it because it's hard so they want to be good at the hardest thing?

[Anonymous No.10795780]

>>10795777
>it's admittedly hard to get into
see >>10795751

[Anonymous No.10795785]

>>10795777
>My point is that it's quite boring.
Thanks for your opinion. We value your blogs a lot.
>Do people just like it because it's hard
We know that autists have trouble with empathy, but not everyone functions like you. Not everyone does things just for social signaling or to try and justify their choices to themselves (like the cringy post you made in the beginning of this thread). I hope you learn to pick up on this with time.

[Anonymous No.10795791]

>>10795780
>>10795785
You two sound just like the kind of weirdos who love Number Theory.

PS. don't reply any longer cause I feel sorry about polluting this thread so early on.

[Anonymous No.10795795]

>>10795777
>Do people just like it because it's hard so they want to be good at the hardest thing?
There is a part of that, especially among people working on the Langlands program or, as you said mathematial physics.
But it's also a beautiful field with ties to many separate areas of math (representation theory, number theory, commutative algebra, Lie theory, complex analytic geometry, algebraic topology etc.) and many classical problems that are a century or two old.

[Anonymous No.10795796]

>>10795777
You don't have to go full sour grapes if you just find a topic boring. I get it that you're young and trying to prove yourself by putting certain things down, but that's not a very beneficial thing for your psyche. Ask >>>/sci/. Be your own man instead of trying to make stupid excuses for your disinterest in some topic.

[Anonymous No.10795816]

>>10795791
>You two sound just like the kind of weirdos who love Number Theory.
We know that autists have trouble with empathy and feel the need to attach very specific and easy to understand (for them) labels to people they (appear to) disagree with, but not everyone functions like you. Keep this in mind for when you decide to make a cringy post in this thread, or anywhere in life really. As a former autist, I suggest trying to think about the various possible "why's" behind people's social actions/choices you disagree with or don't fully understand. As in, "why did he reply the way he did?". It should help with your condition.

[Anonymous No.10795920]

>>10795720
>not even that cool
While I don't care enough about polynomials to like classical algebraic geometry, scheme theory and derived algebraic geometry are fucking kino in terms of the base concepts.

[Anonymous No.10795922]

>>10795720
>>10795795
>String Theory
>mathematial physics
Refer to >>>/x/ and >>>/toy/.

[Anonymous No.10796086]

symplectic geometry, bros

[Anonymous No.10796193]

>>10795920
>the base concepts.
The base concepts are the same. Classical algebraic geometry did not disappear and was not just about polynomials. These fields appeared to clarify, solve and formulate new problems in classical algebraic geometry (in particular enumerative geometry, moduli theory and all that).

>>10795922
GTFO seriously

[Anonymous No.10796217]

Why do I find logical proofs like pic related super easy, but struggle so much with even basic math?

I was mediocre in math through grade school. I usually figured stuff out on-the-spot by using a primitive version of induction to check if it works.

When I landed in college I took a class on logical proof and greatly enjoyed it. I had a bit of a knack for doing proofs quickly in my head.

My prof took notice and made the suggestion, "oh you like proofs? You should get into Math. It's all about proofs." However, I struggle with any proofs greater than basic arithmetic replacements.

for example, I'm working through Riley and Hobson's Foundations, and a problem is: Given distinct primes p and q, where p and q != 1, show that there is no rational number a such that p^(1/2) = a*q^(1/2).

my approach so far is kinda like "well the roots of prime numbers are irrational (wait are they? all I really know is that they're not integers, they could be rational). So the property this is going to hinge on is something like one irrational number can only be the factor of another if the other factor is also irrational. But, again, Idk whether or not that's true or how to prove that it's true.

[Anonymous No.10796228]

What is with these long, drawn out blog/humblebrag posts. They're all over /sci/. Do the posters really think anyone cares?

[Anonymous No.10796238]

>>10796217
>Why do I find logical proofs like pic related super easy
Because the statement to prove is easy and because they are designed to be checked without the use of a brain. Of course they are super easy.
Every single human step has been literally spelt out for a machine.

The proof of a statement like the one you are mentioning, if it were to be spelt out this way, would span pages.

[Anonymous No.10796246]

>>10796217
>well the roots of prime numbers are irrational (wait are they? all I really know is that they're not integers, they could be rational).
It sounds like your problem is that you're trying to read stuff that's beyond what you're capable of right now.
The fact that square roots of primes are irrational is very primitive; in every "intro to proof" math class I've ever seen it's one of the first 5 proofs ever shown to brand-new students.
If the book you are reading assumes that you already know this, it's probably assuming you've passed a basic proofs class or something similar. If you haven't, then the book is going to treat a lot of things you don't know as obvious.

[Anonymous No.10796247]

>>10796238
also
>So the property this is going to hinge on is something like one irrational number can only be the factor of another if the other factor is also irrational.
Is wrong. For example, if x is an irrational, then r*x is going to also be irrational for any nonzero rational r (why ?)

[Anonymous No.10796258]

>>10796228
The posters think that everyone will think they're stupid if they just post
>I don't understand X
so they feel the need to buffer it with a 300 words of useless text letting everyone know how smart they are.

[Anonymous No.10796344]

>>10796193
>the base concepts are the same
>it's an algebraic geometry was always about schemes episode
>>10796217
Square both sides lmao.

[Anonymous No.10796534]

>>10796217
>I had a bit of a knack for doing proofs quickly in my head.
Thanks for making the cringiest post I've read this week.

[Anonymous No.10796545]

>>10795697
Rational mathematics when?

[Anonymous No.10796554]

I think I have an interesting physical math problem.
In a physics class our tuto stated that if a mathematical pendulum (bead moving freely on a circle with gravity) is given the kinetic energy exactly equal to reaching the highest point, it takes an infinite amount of time to arrive.
I dont see an obvioud reason for why this is necessarily true. it might also hit the top point after 3 seconds but in an infinitely differentiable fashion like e^1/t.
How could you prove it takes an infinite amount of time? the pendulum cant be precisely solved analytically (or easily at least) right.
I also think I can construct a curve where the OPPOSITE is true: it is a monotonically increasing curve bending to a side where the end point is horizontal (similar to a circles arc) but when you throw up a bead with the kinetic energy to reach the top it takes a finite amount lf time.
you just need to engineer the curve in such fashion that the distance to the last point is e^1/t for t time. Then you get the necessary radiall force at each point of the curve which gives you the necessarily angle to the vertical (how much gravity will point tangentally).
Wouldnt that be awesome? on a quarter arc of a circle it takes an infinite ampunt of time to reach the top, but on some other similar looking curve it takes a finite amount lf time.

[Anonymous No.10796559]

>>10796217
> Given distinct primes p and q, where p and q != 1, show that there is no rational number a such that p^(1/2) = a*q^(1/2).
Square both sides and apply the fundamental theorem of arithmetic.

[Anonymous No.10796561]

Suppose you have an arbitrary measure space [math]\left(X, S, \mu\right)[/math] and a sequence of functions [math](f_{n})[/math] in [math]\mathcal{L}_{p}(\mu)[/math] that converges pointwise to some [math]f\in\mathcal{L}_{p}(\mu)[/math]. Also suppose that [math]lim_{n\to\infty}||f_{n}||_{p}=||f||_{p}[/math], so we know that:

[math]lim_{n\to\infty}\int |f_{n}|^p d\mu=\int |f|^p d\mu[/math]

Is it also true that :
[math]lim_{n\to\infty}\int |f_{n}+f|^p d\mu=\int |2f|^p d\mu[/math]

[Anonymous No.10796588]

>>10796561
Yes, it's trivial.

If you really need to a hint, dominated convergence. But maybe there is a more elementary proof.

[Anonymous No.10796591]

>>10796588
I'm trying dominated convergence but I don't really see an obvious bound.

[Anonymous No.10796605]

>>10796591
|| f_n + f || <= ||f_n || + ||f||
And for some N and all n>N and e
||f_n|| <= e + ||f||

So it's bounded by twice the norm of f + e.

[Anonymous No.10796611]

>>10796561
Use the triangle equality if you learned that already.
[eqn]\| f_n + f \|_p = \| f_n - f + 2f \|_p \leq \| f_n - f \|_p + \|2f\|_p
[/eqn]

[Anonymous No.10796724]

>>10796554
>physical
Refer to >>>/toy/.

[Anonymous No.10796738]

>>10796724
fuck off and read my post, it is a completely defined mathematical problem.

[Anonymous No.10796751]

>>10796738
>In a physics class
>kinetic energy
Not even him/her, but see >>10796724

[Anonymous No.10796762]

>>10796751
>>10796724
I could write this down as only a mathematical problem for you autists but only the physical interpretation makes it interesting. What you are doing is the equivalent of
>heat equation
>>>toy
a particle travels on a circular arc with gravity pointing downwards just means that we are looking for a path in some R^d which satisfies a bunch of constraints and differential equations.
You can skip writing these down if you just use the most fundamental newtonian mechanics to describe some 2nd partial derivative of the curve as a force etc.

[Anonymous No.10796763]

>>10796605
Thanks, I think I just need to modify that argument for |f_n +f|^p<=(|f_n|+|f|)^p.
>>10796611
The bound is on the absolute value of the sequence, not the p norm. But thanks.

[Anonymous No.10796764]

>>10796561
Depends. Let p=2, take f_n=-f.
Most of the time, yes.

[Anonymous No.10796786]

>>10796554
https://www.wikiwand.com/en/Brachistochrone_curve

[Anonymous No.10796788]

Post textbook authors which are consistently good.
>Peter Lax
>Charles Weibel
>Serre

[Anonymous No.10796793]

>>10796788
>Walter Rudin
>Serge Lang

[Anonymous No.10796795]

>>10796762
>only the physical interpretation makes it interesting
There are special threads for you to discuss your physical interpretations. What's so hard to understand about that?
>a particle travels
Refer to >>>/x/.

[Anonymous No.10796815]

>>10796762
>physical
>particle
>gravity
>mechanics
>force
Refer to >>>/toy/.

[Anonymous No.10796816]

>>10796788
>>10796793
what about Munkres?

[Anonymous No.10796817]

>>10796554
The mathematically can be solved, basically exactly, the function is just weird, but you don't need that. Use conservation of Energy [math]\frac{1}{2}mv^2+l(1-cos(\theta))mg=E_{0}[/math] The initial energy given by your initial conditions therefore [math]v =\sqrt{\frac{2}{m}(E_0 -l(1-cos(\theta))mg)}=l\omega=l\frac{d \theta}{dt}[/math] Now as you see you can separate variables and get time in function of the angle. There is a singularity when the root goes to 0, and just plug the intitial conditions. Then try to prove that the improper integral diverges. I think the problem should be stated with initial potential energy, i.e. releasing the bead near the top, because you obviously can push it hard enough for the bead to start going in loops. Roller coasters kinda depend on that.

[Anonymous No.10796820]

>>10796817
>Roller coasters
Use >>>/toy/.

[Anonymous No.10796823]

>>10796817
>push it hard enough for the bead to start going in loops
>Roller coasters
epic math.

[Anonymous No.10796827]

>>10796554
>>10796762
>>10796817
Why do subhuman physishits feel the need to discuss their garbage in a thread called "maths general"? Use >>>/sci/eng or >>>/sci/amg or >>>/toy/.

[Anonymous No.10796830]

>>10796817
thanks for the reply, Im not sure I understood what you mean but maybe you didnt see what Im looking for.
imagine pic related except the pendulum swings 90° more, so it does a swing from the lowest to the highest position.
does it take a finite amount of time to reach the vertical position or does it never reach it ("infinite amount of time")?
If the circular arc was replaced by a different arc (constrained path the weight has to follow) then could the outcome change?
Which functions ould be the x-component of the weights position with time for some arc?

These are all mathematical problems because these perfect physical systems can be translated to finding ewuality snd inequality constrained paths and I find them interesting for their physical interpretation.

[Anonymous No.10796833]

>>10796827
bc the physicists dont give a fuck about this problem and any answer takes more mathematics than the physically simple problem makes you believe

[Anonymous No.10796836]

Is the partial derivative of a function with respect to 2x twice or half its derivative with respect to x?
Let's say I have f(x,y)=2x+y
If I go by the partial derivative as the scalar product of the function's gradient and the vector, it comes out as 4
However, if I make a variable change, 2x=t and derive, I am deriving t+y with respect to t which should be 1.

[Anonymous No.10796839]

>>10796830
>These are all mathematical problems
We guarantee that not a single mathematician gives a shit about this "mathematical" problem.

[Anonymous No.10796844]

>>10796833
>takes more mathematics
String theory doesn't belong in this thread either. Fuck off to some other place to play around with your toy physical interpretations.

[Anonymous No.10796846]

>>10796839
speak for yourself. I think many mathematicians would find it very interesting to be able to make statements which are extremely easy to understand about simple physical systems but completely impossible to see without some rigorous analysis.

[Anonymous No.10796849]

>>10796830
>>10796846
>pendulum swings
>physical systems
Refer to >>>/toy/.
>>10796833
>physically simple problem
See the above message.
>>10796844
>String theory
Refer to >>>/x/.

[Anonymous No.10796855]

>>10796846
>I think
We don't care what a non-mathematician thinks. There are dedicated threads for discussing physical interpretations of toys. Use them instead of shitting up this thread with off-topic physical garbage and off-topic redirect spam.
>about simple physical systems
So you're dealing with physics or "applied math" then? Fuck off to a dedicated containment thread.

[Anonymous No.10796858]

>>10796844
>>10796849
If it was 18XX and someone posted the brachistochrone problem here, would you say the same?
What's the problem with a physically inspired problem? Not all mathematics are theorems, examples are very important and interesting.
Physically inspired problems can also lead to new mathematical ideas, like the theory of variations (althpugh admittedly this doesnt really happen much anymore nowadays)

[Anonymous No.10796860]

>>10796846
>able to make statements
>rigorous
Use >>>/lit/.
>physical systems
Use >>>/sci/eng/ and/or >>>/sci/amg/.

[Anonymous No.10796863]

>>10796858
>If it was 18XX
Refer to >>>/his/.
>Physically inspired problems
See >>10796849
>new mathematical ideas
Point me to the new mathematical ideas generated by your >>>/toy/ problem.

[Anonymous No.10796867]

Why are the physishits on this board so insecure about their subject that they feel the need to shit up /mg/ with roller coaster discussions and pretend it's in any way a "mathematical problem"?

[Anonymous No.10796872]

>>10796830
Yes, the diff equation I showed you can let you put the the time in terms of an integral over the angle. Play with that expression.

[Anonymous No.10796882]

>>10796554
>physical math problem
>In a physics class
if it had any relevance to the thread you wouldn't say this.

[Anonymous No.10796894]

>>10795816
>former autist
That's an oxymoron, autist.

[Anonymous No.10796901]

>>10796872
thanks, is the final diverging integral 1/(1+cos(x)) from 0 to pi?

[Anonymous No.10796913]

Will the actual autistic fuck that lives in /mg/ only to link posts he personally doesn't """feel"" belong in /mg/ please fuck off forever?
Literally no one likes you. I don't even believe you like yourself, but I could easily be wrong because you're certainly stupid enough.
Anons like you are the reason generals are generally shitty on every board, not just /sci/.
So, whatever random fucking board you choose to redirect me to, just fuck off to that one you absolute disgrace of a "human" being.

[Anonymous No.10796915]

>>10796882
Im honestly surprised how much ppl here hate that word, I think it's super interesting to try to find physical meaning in not obviously-physical mathematical statements.
I took an introductory PDE class this semester and the physical meanings behind some theorems about the heat or wave equation were definetly enlightening. That's not just my personal taste, the professors talked about it themselves.

[Anonymous No.10796921]

>>10796915
>physical meanings
>find physical meaning
Refer to >>>/toy/.

[Anonymous No.10796923]

>>10796915
Don’t post off topic shit where it doesn’t belong and people won’t bully you

[Anonymous No.10796932]

>>10796915
What's surprising about wanting to contain physical discussions to physical threads? Do you legitimately have some sort of brain damage?
>I think it's super interesting to try to find physical meaning
You might also think cooking is super interesting, but you wouldn't discuss that here.

[Anonymous No.10796946]

>>10796932
bc it's not a physical discussion it's a mathematical discussion lmao.
that's like saying just because some PDE represents a physical system it doesnt belong into mg

[Anonymous No.10796949]

>>10796946
>it's not a physical discussion
>literally starts with "in a physics class" and "a physical problem"
Sure. Now fuck off to >>>/sci/amg/ if you want to talk about your deep "physical meanings".

[Anonymous No.10796954]

>>10796932
>>10796946
>>10796949
>physical system
>physical discussions
>physical meanings
Use >>>/toy/.

[Anonymous No.10796958]

>>10796949
well I didnt want to talk about the physical meaning, I asked a maths question and stated the system which got me to that problem as motivation, general context and bc it might make it interesting to some people. I guess I was wrong about that tho.

[Anonymous No.10796961]

>>10796958
>I didnt want to talk about the physical meaning
Is that why you decided to mention the word physics 15 times during your post? Fuck off, retard.

[Anonymous No.10796965]

>>10796949
Are you actually stupid?
Physical reality has been attempted to be described mathematically for hundreds of years.
The anon wants to discuss math, not argue with what you think math is.
If a post is off-topic, let a mod delete it. Stop doing it for free when you don't even have mod powers because that's absolutely, disgustingly autistic of you.
Don't worry your pathetically small brain with trying to link everything you think is off-topic to wherever you think is appropriate.

[Anonymous No.10796968]

>>10795720
this is a VERY good post. alggeo cucks BTFO.

[Anonymous No.10796971]

>>10796965
>Physical reality
>attempted to be described mathematically
Refer to >>>/lit/ and/or >>>/toy/.

[Anonymous No.10796972]

>>10796961
>thinks twice is the same as fifteen times.
>has the audacity to call others retarded.

[Anonymous No.10796977]

>>10796965
>Physical reality has been attempted to be described mathematically for hundreds of years.
How is that relevant to this thread? Fuck off to >>>/sci/amg/ for applications of math to other fields, you retard.

[Anonymous No.10796979]

>>10796965
see some otherr post above redirecting to lit.
>>10796554
>In a physics class
see >>>/sci/amg/

[Anonymous No.10796982]

>>10796977
Because the original anon was trying to ask a math-related question in the context of physics, but then you sperged out for an hour or so because he said physics twice in his original post.
Again, you are the retard that needs to fuck off.

[Anonymous No.10796984]

>>10796965
>the braindead retard who spaces his posts like that is also a physishit/philosopher
"surprising".

[Anonymous No.10796988]

>>10796984
>complaining about post formatting.
Not math, kindly fuck off.

[Anonymous No.10796989]

>>10796982
>of physics
How is that relevant to this thread? Fuck off to >>>/sci/amg/ for applications of math to other fields, you retard.

[Anonymous No.10796991]

>>10796982
>context of physics
See >>10796988 and kindly fuck off to >>>/sci/amg/.

[Anonymous No.10796993]

people are just fucking around i know, but the lack of respect for PDE in this thread is very well understood when one recalls the large number of seething replies to that guy who called out algebraic geometry on its bullshit. alggeo cucks are so fucking buttblasted that other people do more interesting math than they do that they can't help but link people to other threads and boards, praying that they'll get back their little fucking hugbox.
we're here to stay YOU FUCKING ANIMALS!!! I FUCKING HATE EVERYONE WHO DOES ALGEBRAIC GEOMETRY!!!!

[Anonymous No.10796995]

>>10796989
>everything in this post that isn't the word math
How is that math? Fuck off to somewhere where you can be an autist without bothering the adults.

[Anonymous No.10796996]

>>10796993
>I FUCKING HATE
Use >>>/blog/spot/.

[Anonymous No.10796997]

>>10796984
>>10796988
>>10796989
>>10796991
these posts do not pertain to mathematics.

[Anonymous No.10797000]

>>10796993
>the lack of respect for PDE
The mental equivalent of literally consuming shit deserves zero respect.

[Anonymous No.10797002]

>>10796997
I'm beginning to think this general doesn't pertain to mathematics most of the time.

[Anonymous No.10797004]

>>10796993
>do more interesting math
Are you unironically suggesting that "PDEs" are "math"? LOL

[Anonymous No.10797006]

000101001001010010010101010010

[Anonymous No.10797008]

>>10797002
That's to be expected when there's 2-3 actual mathematicians in this thread.

[Anonymous No.10797009]

>>10797000
you are a fucking braindead caveman. get the FUCK out of my thread and go to a board more fit for your mindless garbage masturbating over fake structures for little children. i'll be over here dining on my fine sobolev inequalities and sipping on well-aged estimates while you gobble on mcdonalds and call my haute cuisine "feces" as you sit in your drive-thru.

[Anonymous No.10797011]

>>10797004
you took an undergrad pde's class for engineers and never interacted with the field again, didn't you? pdes is just functional analysis in a dynamical setting

[Anonymous No.10797013]

Did any of you do TI? I'm in need of the devil's coin so I'll have to "w*rk for a bit.Been considering tutoring since there are open positions rn at my uni.

[Anonymous No.10797014]

>>10797009
Is that a PDE expert you posted? Seems like you need to be of foul blood to be even remotely interested in consuming human waste.

[Anonymous No.10797015]

>>10797008
I don't expect many actual mathematicians to be browsing 4chan all day.
I do expect autists to do so, though, and- judging from the majority of posts in this thread- /mg/ has mostly become autists LARPing as mathematicians.

[Anonymous No.10797023]

>>10797011
I consider "PDEs" to be beneath me. I don't judge you for your low intelligence though, it's fine.

[Anonymous No.10797027]

>>10797011
>pde's class for engineers
That's the only kind of PDEs class. Why would engineering-exclusive material be discussed elsewhere? It's cool that you mastered the undergrad PDEs curriculum, that's certainly something to be proud about.

[Anonymous No.10797028]

>>10797015
>has mostly become
You're delusion if you believe it wasn't always mostly just a bunch of cancerous discord LARPers.

[Anonymous No.10797029]

>>10796793
>>Serge Lang
Lang is a meme.

[Anonymous No.10797030]

>>10797014
no that's merron haile from the televion series Big Brother Canada Season 6 (easily one of the most intellectual seasons of television ever to air)
i have a lot of gifs of him saved
would you like some more?
in any case the content of your post leads me to believe that you hold explicit racial biases, which means i don't really see any reason to take anything you say seriously.

[Anonymous No.10797032]

>>10797030
>no that's merron haile
Cool, didn't even read the rest. Wouldn't want high society to think less of me for even briefly associating with such trash.

[Anonymous No.10797033]

>>10797027
>>10797023
read evans and educate yourselves, you math-racists

[Anonymous No.10797038]

number theory? yeah, I can dabble with it a little

[Anonymous No.10797039]

>>10797033
But I'm not interested in engineering. It's neat that even someone like you could find a subject you love, even if it's for the less gifted of us.

[Anonymous No.10797045]

>>10797032
sounds like you want another gif of him, he's cute isn't he?
i don't think they've really had math people on big brother. there was one person but she was just getting a bachelors in math. probably never would have made it.
they have had some sciencey people though
i like that show because it is like social chess. it is refreshing to see people who can interact in a way which is simultaneously strategic and emotional after spending all day around alg geo autists and number theory mouth breathers.

[Anonymous No.10797047]

>>10797039
let's start from the beginning. do you think that pure functional analysis (i.e. analysis on "nice" topological vector spaces) is engineering or mathematics?

[Anonymous No.10797049]

>>10797045
>pending all day around alg geo autists and number theory mouth breathers
Are there many alg geo autists and number theory mouth breathers at engineering departments?

[Anonymous No.10797054]

>>10797047
>"nice" topological vector spaces
This is not well defined.

[Anonymous No.10797055]

>>10797049
i wouldn't know, i am a graduate student in a mathematics department at a respected top 10 university
i haven't interacted with any engineers very much
you've almost used up all my merron gifs

[Anonymous No.10797060]

>>10797054
i obviously meant banach spaces, hilbert spaces, locally convex topological vector spaces, lattice ordered topological vector spaces, etc...

[Anonymous No.10797062]

>>10797060
>locally comfy vector spaces

[Anonymous No.10797063]

>>10797055
>i am a graduate student in a mathematics department at a respected top 10 university
Yeah, I've heard about those special programs they have these days. It's really nice that we can help people such as yourself.
>i haven't interacted with any engineers very much
That's interesting. You'd assume that having good engineering mentors would be of great value for anyone interested in engineering.

[Anonymous No.10797076]

>>10797063
yes, i find it interesting as well. thank you for showing concern. and thank you so much for the congratulations on my position! i don't know how special the program is but i like to think i'm something of a shining star. :)
here's my last merron gif just for you! it's not as happy.

[Anonymous No.10797083]

>>10796913
I like him. Get over yourself.

[Anonymous No.10797084]

>>10797062
they are very comfy, i agree.
>tfw your topology is determined by a collection of seminorms
just general enough but just enough structure to be fun. gotta love convexity.
>>10797063
whoops i have this one too

[Anonymous No.10797086]

>>10797060
>etc...
Mathematically speaking, what does this refer to?

[Anonymous No.10797090]

>>10797083
>I like him. Get over yourself.
We're not a "him".

[Anonymous No.10797098]

[eqn]\lim_{t \rightarrow 0} \frac{t - 1}{t^{3/2} - 1}[/eqn]
Not asking for the answer, but I've tried multiple substitutions and rationalizations of both the numerator and the denominator and I can't find any way to further simplify this. The denominator looks very much like it'd have a (t -1) factor hiding somewhere, but the fractional exponent seems to fuck it all up.

[Anonymous No.10797099]

>>10797086
i was making an abuse of notation
if you'd like, we can define a partial ordering on the set of categories of topological vector spaces, ordered by "niceness". the notation "etc..." is equivalent to the statement: there exist categories of topological vector spaces in the poset of categories of topological vector spaces within the filter of "nice" topological vector spaces setminus the set of those listed in my post.

[Anonymous No.10797102]

>>10797098
dude just fucking plug in 0 lmao

[Anonymous No.10797107]

>>10797102
Oh fuck, I meant as t approaches 1

[Anonymous No.10797119]

>>10797098
Did you try setting h=t^2?

[Anonymous No.10797125]

>>10797098

t^3/2 = t^(1/2*3) = (t^1/2)^3

so it's (t^1/2 + 1)(t^1/2 - 1)/(t^1/2)^3 - 1

also notice the difference of cubes


(t^1/2)^3 - 1 = (t^1/2 - 1)(t + (t^1/2)*1 + 1)

so it's

(t^1/2 + 1)/(t + t^1/2 + 1)

plug 0

1

[Anonymous No.10797126]

>>10797098
>thinking this is real maths
Pathetic.

[Anonymous No.10797130]

>>10797107
Oh, can you not use LHospital? Not that that's the way to ever do a limit.

[Anonymous No.10797132]

>>10797126
/sqt/ is full.
Also fuck off

[Anonymous No.10797135]

>>10797130
>that that’s

[Anonymous No.10797136]

>>10797125
you showed him how to do it >>10797107
but the fact that you did this bullshit to plug in 0 when you could have from the start indicates a severe lack of critical thinking. are you one of the people who replied angrily to this truthful post >>10795720 ?

[Anonymous No.10797137]

>>10797135
is there a problem?

[Anonymous No.10797138]

>>10797136

I had already seen the post where he redacted the limit

[Anonymous No.10797140]

>>10797136
>critical thinking
>getting upset over a brainlet asking for help instead of posting more retarded iq threads
>linking two separate posts to make a point
ebin

[Anonymous No.10797143]

>>10797137
If you think poor style is acceptable by all means indulge your base instincts fren

[Anonymous No.10797148]

>>10797138

disregard this post, I was wrong

[Anonymous No.10797152]

>>10797143
>implying that's good composition
>explicitly baiting being redirected to /lit/
Refer to >>>/b/

[Anonymous No.10797160]

But mistakes aside limit anon, that problem is just knowing your notable products and exponential rules.It seems like you need to rebrush your pre-calculus.

[Anonymous No.10797167]

>>10797160
Thanks. Yeah it's been forever since I've had to factor with fractional exponents.

[Anonymous No.10797169]

>>10797152
did you really think that that’s what my intention was?

[Anonymous No.10797171]

>>10797169
Yes.

[Anonymous No.10797177]

>>10797160
>thinking anything in a course named "pre-calculus" is real maths.
Pathetic.

[Anonymous No.10797178]

>>10797143
>fren
please adjust your style to the standards of /mg/
>>10797152
stop responding to posts directed at me
>>10797160
>rebrush
please adjust your style, it isn't fit for an /mg/ post.
>>10797167
>factor with fractional exponents
did you mean to say "factor expressions with fractional exponents"? if so, please adjust your style to the standards of /mg/.

[Anonymous No.10797179]

>>10797171
I don’t feel sorry for you but maybe take a few days for yourself away from 4channel

[Anonymous No.10797184]

>>10797177
What are you studying right now, Anon?

[Anonymous No.10797185]

>>10797184
i'm studying pde but apparently that's not real math either
so much fucking larp from people in this thread

[Anonymous No.10797189]

>>10797185
Bout to take Analysis this fall, ergo reviewing the hell out of limits / linear algebra / proofs.

Good luck.

[Anonymous No.10797197]

>>10797189
analysis is based
you could review with the first volume of tao, it's supposed to be a very gentle gradual introduction to analysis

[Anonymous No.10797198]

>>10797185
>that's not real math either
>real
It's not fake either. It's just not math.

[Anonymous No.10797203]

>>10797197
>based
On what?

[Anonymous No.10797204]

>>10797203
based

[Anonymous No.10797205]

>>10797204
Based on what?

[Anonymous No.10797213]

>>10797189
>ergo
Was the Latin really necessary here?

[Anonymous No.10797219]

>>10797098
>>10797107
Fucking epic... (pardon my French)

[Anonymous No.10797257]

>>10797098
>hiding somewhere
Mathematically speaking, what does this refer to?

[Anonymous No.10797268]

>>10797099
>setminus
Did you mean to say bigsetminus or classminus?

[Anonymous No.10797271]

>>10797198
When does math start being math?

[Anonymous No.10797274]

>>10797271
>start being
Refer to >>>/lit/.

[Anonymous No.10797286]

>>10797274
>Refer

[Anonymous No.10797300]

>>10795720
>only big application
AG applies more broadly to CFTs where the partition function can be expressed as a sort of "state sum" over modular forms (https://arxiv.org/abs/math-ph/0412039).). TMFs in particular can be used to topologically classify conformal nets (https://arxiv.org/abs/1103.4187).). In addition, RG in general likely has AG as foundation
(https://arxiv.org/abs/1512.06409).).
Besides, holography and AdS/CFT plays a huge role in understanding quantum phases of matter (https://arxiv.org/abs/1003.4965)), so string theory by itself might be a huge cluster fuck but it certainly isn't on the grander scale of things. Classification may be done with just AT but to understand dualities and brane-bulk interactions you'd need at least AG or AnalG.
>>10796086
Anything cool happening in that field right now, specifically geometric/deformation quantization related? I haven't been caught up since reading Kontsevich and Witten's papers.
>>10796554
>the pendulum cant be precisely solved analytically (or easily at least) right
A single pendulum can, just not in terms of elementary functions.
https://en.wikipedia.org/wiki/Mathieu_function
"Arrive in an infinite amount of time" requires your trajectory to be not compact, which means e.g. the time evolution operator is not compact, like the square root-ed Klein-Gordon which leads to things like Eckstein's no-go theorem. However for Sturm-Liouville problems like these if sufficient regularity is achieved in the Lagrangian then you're fine.
In other words your tutor is confused about his word choice.

[Anonymous No.10797332]

>>10797268
I did mean to say classminus. Thank you for the correction.

[Anonymous No.10797337]

>>10797300
Please adjust your style to fit commonly accepted /mg/ standards. Currently, your posts have suboptimal width to height ratio. Making use of the "return" or "enter" key and focusing on clearer sentence structure will remedy this. You can also make use of whitespace to format your post in an /mg/-friendly manner.
Furthermore, the content needs attention. Your post contains 3 separate topics for 3 separate posters. This is a common scenario in which typical /mg/ style would recommend creating 3 individual posts for each reply. In this way, we can all see that which we want to see (and quite frankly, we can not see that which we do not).

[Anonymous No.10797340]

>>10797337
last sentence is atrocious

[Anonymous No.10797341]

>>10797340
We say "The last sentence was atrocious from our limited point of view.".

[Anonymous No.10797343]

What the fuck is happening in this thread? I leave for a couple of hours and you autists throw a shitfest. I swear, if this happens again, then I'm not getting you anymore pizza rolls for a month.

[Anonymous No.10797344]

lads should i take mathematical logic or algebraic structures (groups, rings, fields) as the final course in my undergrad

[Anonymous No.10797346]

>>10797344
Depends, have you taken topology yet?

[Anonymous No.10797347]

>>10797344
>mathematical logic
You know that a subject is highly mathematical when you have to explicitly prefix it with "mathematical".

[Anonymous No.10797353]

>>10797346
yeah, but I found it too unrigourous for my liking. i'm looking for a more axiomatic and logical approach to maths, so i'm thinking of taking logic to fully understand how it operates on a more fundamental level.

[Anonymous No.10797361]

>>10797353
whats wrong with you

[Anonymous No.10797365]

>>10797347
>>
You know a post is shit posting on 4chan(nel) when it begins with meme arrows.

[Anonymous No.10797369]

>>10797343
WE'RE BREAKING THE CONDITIONING.

[Anonymous No.10797373]

>>10797353
sad!

[Anonymous No.10797375]

>>10797365
>>>
Nice Meta self-referential post, my friend. We learned this technique last week in the Creative Writing 101 class.

[Anonymous No.10797377]

>>10797343
I'm trying to keep things under control but I absolutely despise posting too much.
>>10797337
>3 individual posts
Come on.
>>10797344
>final course in my undergrad
>groups, rings, fields
L M A O

[Anonymous No.10797378]

>>10797340
This post exhibits such poor style. Oh, the irony. But yes, I agree with your post. My last sentence was deplorable.

[Anonymous No.10797384]

>>10797361
i'm just interested in getting a solid base first so i can build a more thorough understanding of maths as a whole. topology didn't seem to provide that to me. in fact i immediately tuned out when the prof started drawing a bunch of toruses.


>>10797373
cope.

[Anonymous No.10797385]

>>10797344
imagine not having taken groups rings and fields lmao
take that, you literally need to know it
>>10797353
this is a huge red flag. are you getting a fucking associates degree? lmao. it is impossible for a course in point set topology to be "unrigorous."

[Anonymous No.10797386]

>>10797344
My vote is for algebraic structures.

[Anonymous No.10797387]

>>10797377
>>final course in my undergrad
>>groups, rings, fields
>L M A O
ignored that post, but now I laughed out loud too. literally "LOL"

[Anonymous No.10797389]

>>10797384
logic and rigor are not related to mathematics. if you want to go to grad school, you had better fucking know something about groups and rings and fields. if you don't care to use pure math after college then just take logic if you want. you cant just take both? come on.
also if you are tuning out during math classes that's not the class's fault, that's yours. you clearly aren't cut out for this.

[Anonymous No.10797390]

>>10797353
Well then, take mathematical logic, then read this
https://pdfs.semanticscholar.org/6da4/9fba6462a5c3e6b528a8b3e8be3a1c1e743d.pdf
Builds topology from logic. I say this because you could just read Dummit and Foote for algebra, a fairly laid back book.
>>10797377
Last thread wasn't nearly this spastic.

[Anonymous No.10797394]

>>10797375
>openly pointing out meta- commentary
Nice post-meta post, my non-friend.
I'm glad your still learning something at least.
Too bad it doesn't seem to be math related.

[Anonymous No.10797395]

>>10797344
>final course in my undergrad
>groups, rings, fields

[Anonymous No.10797396]

>>10797390
>builds topology from logic
>most based math from most cringe math

[Anonymous No.10797401]

>>10797389
Who died and made you math king?

[Anonymous No.10797403]

>>10797394
>>openly pointing out meta- commentary
>openly pointing out meta-meta commentary
Nice non-meta post, my friend. I suggest you reconsider your intellectual writing style to match something more suitable for this gathering of intellectuals.

[Anonymous No.10797404]

>>10797396
>>10797395
>>10797394
based

[Anonymous No.10797405]

>>10797377
What horrific style. Imagine being such a troglodyte you think that it is appropriate to press the "Post" button with that text in the Reply box. Please reconsider your post formatting in your future interactions with /mg/.

[Anonymous No.10797407]

>>10797401
no one died, but no one was math king to begin with, so now it's me! aaaahhaahahahahah!

[Anonymous No.10797409]

>>10797403
Ah, my acquaintance, I would suggest you reconsider yourself as well.
Anyway, would you like to discuss math instead of non-sense?

[Anonymous No.10797412]

>>10797409
>Anyway
Anyways.
>non-sense
Nonsense is one word.
Please reconsider your style, this is a thread for mathematicians and mathematics-related discussion.

[Anonymous No.10797414]

>>10797396
>most based math from most cringe math
But the fact that you can do that means logic isn't the most cringe math, higher category theory is though.

[Anonymous No.10797415]

>>10797412
I'm a free-style kind of guy.
Read any good academic papers lately?

[Anonymous No.10797419]

>>10797407
That's fair enough. All hail the math king!

[Anonymous No.10797422]

>>10797414
okay yeah that's something i can definitely agree with
>>10797419
thanks, you're going to be my first knight
would you like to be dubbed anything specific?

[Anonymous No.10797423]

>>10797415
No. I don't read "academic" papers. I read the mathematical literature.

[Anonymous No.10797424]

>>10797422
Knight of Pure Maths, if you would, my liege.

[Anonymous No.10797428]

>>10797423
I obviously meant recently published works in mathematics.
This is /mg/, after all.
Try to keep up, old sport.

[Anonymous No.10797430]

>>10797424
i dub thee "knight of pure maths"
if any of the other kind Lords and Ladies in /mg/ would like to be dubbed, i would be happy to reward you with knighthood!

[Anonymous No.10797438]

>>10797430
>i
You are no king... [math]*\text{spits}*[/math] Prepare to die, lowborn scum! [math]*\text{unsheats a damascus steel blade}*[/math]

To all the fine men and women gathered here:
By our right of birth and divine right to rule, we hereby declare ourselves to be rightful king of maths. You can either bend the knee, or die...
Signed, Anonymous of /mg/, King of maths.

[Anonymous No.10797448]

What's the big deal with representation theory? Isn't it just homormophisms?

[Anonymous No.10797449]

>/mg/ - LARP and Literature general

[Anonymous No.10797451]

>>10797448
Making abstract algebra even easier by reducing it to linear algebra.
>>10797449
Posters have been larping as girls for years now, nothing new.

[KING of Math and /mg/ No.10797452]

>>10797438
WHO ARE YOU TO SPEAK UP TO MY THRONE, FILTHY PEASANT!?

[Anonymous No.10797453]

>>10797449
>renaming generals.
I'm sorry, this post is very 4chanesque, yet I'm not seeing exactly how it relates to maths. Care to explain yourself?

[Anonymous No.10797454]

>>10797448
matrices are easier than groups

[Anonymous No.10797466]

Oh hey, apparently Hao Huang proved the Sensitivity Conjecture in six pages of maths.
Pretty cool maths. It's a fairly simple read so if you've got nothing better to do it isn't hard to find.

[Anonymous No.10797468]

>>10797466
>Hao Huang proved
Cool. I've always believed in the Taoist way of doing things. I am feeling so tranquil right now.

[Anonymous No.10797480]

So when you're writing proofs for exercises how do you know your proof is correct?

[Anonymous No.10797483]

>>10797480
Someone smarter than you, usually an instructor of some sort, tells you whether it's correct or not.
Until then, just assume it's as correct as can be and move on with your life.

[Anonymous No.10797485]

>>10797480
You don't know, you feel.

[Anonymous No.10797487]

>>10797480
Have iq

[Anonymous No.10797492]

>>10797480
you can't write a wrong proof unless you don't know what you're doing
if it isn't so clear that you know it's correct, then either you don't know what you're trying to say or you need to word it better

[Anonymous No.10797527]

>>10797492
That looks like... ice cream?

[Anonymous No.10797528]

>>10797527
It's a root beer float.

[Anonymous No.10797608]

Guys, is there a /sci/ discord or something like that?

[Anonymous No.10797617]

>>10797608
>discord
fuck off right back to wherever you came from, trash.

[Anonymous No.10797638]

>>10796534
I'm not claiming to be a genius or anything, it was just 'oh hey I'm kinda good at this and I'm having fun'. You're awfully discouraging.

>>10796559
>fundamental theorem of arithmetic
lol how the hell have I never heard of this?

>>10796246
Idk where to start that has rigor but doesn't assume I've got any background. Everything that is supposed to be a good starting point seems to have an assumption like "of course they're well versed in trig/types of numbers/etc"

[Anonymous No.10797651]

>>10797638
not helping yourself

[Anonymous No.10797736]

>>10796858
They cannot answer these questions because they are autistic larpers that know nothing about analysis, math history, current developments of math or math in general.

[Anonymous No.10797752]

>>10797344
In terms of pure need you will never need logic unless you do logic whereas algebraic structures are everywhere and you don't need to do algebra to find them in your face.

[Anonymous No.10797755]

Does anyone know anything about the Univ of Vienna? Does it have a good grad school?

I applied there on a whim. Probably not going to be my first choice cause I have other offers already but I'm wondering what's it like.

[Anonymous No.10797778]

>>10796858
Stop fucking feeding the Troll you idiot.
This shouldn't be hard to figure out...

[Anonymous No.10797793]

>>10796788
tu

[Anonymous No.10798011]

>>10797778
I don't know who's trolling who anymore.
Frankly, as far as I'm concerned, you're all trolls and imaginary mathematicians.

[Anonymous No.10798024]

You'd have to be ridiculously autistic to assume any random anon has the exact same set of mathematical knowledge as yourself.
I seriously hope you guys don't do this.

[Anonymous No.10798052]

>>10796788
Fulton, Milnor, Milne, Jacobson, Neukirch, Borel

[Anonymous No.10798184]

What's the current non-meme recc for Real Analysis? I want to get into probability theory but figure I should be better read on real analysis and measure theory

[Anonymous No.10798196]

Math major here. When will I be able to understand this stuff?

[Anonymous No.10798203]

>>10798196
After you took Calculus.

[Anonymous No.10798208]

>>10798184
Royden.
>>10798196
IIRC that's essentially diophantine approximation, but I don't know about requirements.

[Anonymous No.10798290]

>>10797300
>deformation quantization
Have you looked at rep theory connections like quantizations of integrable systems like Calogero-Moser space in connection with rational Cherednik algebras? Also Braden-Licata-Proudfoot-Webster's recent progress on quantization of symplectic resolutions.

There's also interesting progress on the P=W conjecture, the algebro-geometric study of Lagrangian fibrations with hyperkahler fourfolds, etc.

[Anonymous No.10798311]

"When I landed in college I took a class on logical proof and greatly enjoyed it. I had a bit of a knack for doing proofs quickly in my head."

[Anonymous No.10798472]

>>10797638
if you dont know what trig and types of numbers are you could learn
or you could just look at purely logical texts like principia mathematica or shit like that which will build up everything from foundations
alternatively you could try euclid's elements, that's purely self contained and very fun.

[Anonymous No.10798477]

>>10798184
non meme recs are pugh, tao, or abbott. rudin is not a meme but it's not very readable.

[Anonymous No.10798481]

Hi i have done my first year of engineering and am now reading linear algebra done right by axler, somewhere on the start it explains whats a list and how its different from a set, and says a set with x and a set with x, x are different, can somebody explain me why? Im guessing its related to combinatorics but cant think of anything because having a backpack with one apple isnt the same as having one with 2 apples for example

[Anonymous No.10798500]

>>10798481
>says a set with x and a set with x, x are different, can somebody explain me why?

[Anonymous No.10798508]

>>10798500
Sorry i meant the first 2 lines in pic related

[Anonymous No.10798510]

>>10798508
>>10798508
That's because a set is entirely defined by what elements it contains. IIRC that was the first axiom in ZF.

[Anonymous No.10798524]

>>10798508
It's just a property of set theory that sets don't care about repetitions.

[Anonymous No.10798553]

>>10798510
>>10798524
Ok thanks friends i got it

[Anonymous No.10799114]

Is algebraic geometry more algebra or more geometry?
Is category theory more logic/foundations or more algebra?

[Anonymous No.10799117]

>>10799114
Such ontological matters are best discussed at >>>/lit/.

[Anonymous No.10799121]

Does anyone have this with the red glowing eyes?

[Anonymous No.10799184]

>>10799114
Algebraic geometry is not geometry. Varieties are purely algebraic even though you can look at them in low dimensions. Think about it, is linear algebra geometry just because planes in R^3 can be understood geometrically? Perhaps classical AlgGeo made use of geometric arguments but modern AlgGeo is purely algebraic. That's why it's such irredeemable drivel.
Category theory has always been more algebra than logic in "flavor," though of course it encapsulates much of logic (as it does much of anything really). But any argument in category theory will look like an algebra proof and not a logic proof.

[Anonymous No.10799209]

>>10799184
>Algebraic geometry is not geometry.
Never go full retard

[Anonymous No.10799233]

>>10799114
Algebraic geometry deals with a space that's locally the zeroes of a ring of functions.
Since it deals with a space, it's geometry.

[Anonymous No.10799241]

I'm going to take algebraic geometry next year
Am I going to fail?

[Anonymous No.10799333]

>>10799241
That depends a lot on the type of algebraic geometry, your mathematical background and fortitude, your experience with layers of abstraction, and so on.
Do you know which text? Is it a graduate or undergraduate level course? Have you taken courses in topology, groups/rings/fields, and linear algebra?

[Anonymous No.10799349]

>>10799241
Do you live and breathe categorical algebraic topology and commutative algebra?

[Anonymous No.10799370]

>>10799241
start reading this brainlet beginner book

[Anonymous No.10799449]

>>10799241
start reading this brainlet beginner book

[Anonymous No.10799469]

>>10798311

I'll do my phD in quick logic proofs

[Anonymous No.10799471]

>>10799241
start reading this brainlet beginner book

[Anonymous No.10799506]

>>10799471
EGA1 is "unironically" better for beginners of modern AG than most of the other suggested crap.

[Anonymous No.10799555]

How would i go about visualising this? Currently learning/reviewing subspaces.
{p (belongs to symbol) P(f) : p(3) = 0 }
Does this mean that this subspace is only one point, like when f =3, the result is 0?

[Anonymous No.10799563]

>>10799471
Anyone has this in English? because I sure won't read this in French.

[Anonymous No.10799576]

>>10799563
coward

[Anonymous No.10799581]

>>10799563
You only need a very basic knowledge of French to read it (a level where you wouldn't even necessarily be able to understand low-level 4channel posts in French). Just learn some basic grammar and read http://people.brandeis.edu/~jbellaic/French.pdf

[Anonymous No.10799584]

>>10799555
Also does this mean that only 3 belongs to the set? Because p(3) is 0 and respects all the subspaces rules?

[Anonymous No.10799601]

>>10799555
What sort of insane notation is this?

[Anonymous No.10799652]

>>10795720
t. Doesn't realize the Nullstellensatz was the beginning of a new chapter in a mathematical and philosophical strain of thought stretching back through Descartes, and ultimately Plato and Pythagoras

[Anonymous No.10799672]

>>10797006
Nigga, get this:

0, 1, 10, 1001, 10010110, 1001011010010110, . . .
Or better yet:
011010011001011010010110

(Fibonacci word)

[Anonymous No.10799692]

>>10799184
Historically a variety was defined as a sort of generalization (in the proper sense of that term) of 2-curves. So people were working with n-dimensional analogs of conic sections and such things. At the same time, we define polynomials on the basis of purely syntactic properties of a particular algebraic structure. It turns out those two notions coincide. You're right that there's not much geometric "flavor" or intuition to be had working with varieties in many cases (at least from my perspective as a novice), but the reason they're viewed as geometric objects is because "variety" was a sort of proper name refering to the class of curves over a field. It's actually kind of an interesting point though. A sort of formal or mathematical correlate of Kripke and Putnam-esque analysis of reference and intension.

[Anonymous No.10799699]

>>10799692
>Kripke and Putnam-esque analysis of reference and intension
Refer to >>>/lit/.

[Anonymous No.10799739]

>>10798290
No I haven't, those sound very interesting! I am familiar with a bit of integrable systems from the quantum cohomology/Gromov-Witten perspective and have looked around rep theory of quantum/cluster algebras, ultimately to see how these AG/SymG concepts can be applied to refine different types of TQFTs.
>>10797448
Representations of an affine Lie group form Hilbert spaces for the quasiparticles of a CFT. More generally, particles transform (are "charged") under certain representations of the gauge group. An understanding of the representations of e.g. [math]SU(2)[/math] allowed one to generalize the study fermions to spin manifolds which is able to produce novel topological invariants of 3-folds, like the Seiberg-Witten invariant.

[Anonymous No.10799774]

What's the significance to physics of $U_q(\mathfrak{g}$, the quantized enveloping algebra of a Lie algebra? Like, my research is very focused on the algebra of these things, but all the algebraists / rep-theorists just present it in terms of generators and relations with no motivation for the relations. So why do we care about this thing? How can I talk to physics-people about muh math?

[Anonymous No.10799782]

Let $X,Y$ be two random variables and let $f$ be continuous and differentiable

then does there always exist a random variable $C$ such that
$$f(X) - f(Y) = f'(C) (X-Y)$$
(a mean value theorem for random variables)

[Anonymous No.10799789]

>>10799774
[math]U_q[/math] deforms relations of [math]\mathfrak{g}[/math] like how first quantization deforms the Poisson algebra of [math]C^\infty[/math] functions on a symplectic manifold; it eseentially gives you the operator algebra on quantum states. One place I have seen [math]U_q[/math] show up explicitly is when its generators are being used as a state sum for the correlation functions of a CFT in the case [math]\mathfrak{g} = \mathfrak{sl}_2[/math]. Personally I have noticed that the relations in certain quantum aglebras look like Skein relations of knots, and there's a very concrete way of understanding correlations in CFT as knot invariants (see e.g. https://scinapse.io/papers/201303897).).

[Anonymous No.10799843]

>>10799774
Look at the Knizhnik-Zamolodchikov equation, quantization of integrable systems, quantum Yang-Baxter equations.

Another more algebraic motivation is that when you let q approach 0, you get the theory of crystals which give a new perspective on even the rep theory of classical groups that actually improves computation.

[Anonymous No.10799932]

My specialty? repeating digit analysis.

[Anonymous No.10800019]

>>10799932
cringe

[Anonymous No.10800153]

ayo bby girl can I get sum mathfucc

[Anonymous No.10800508]

>>10799601
{p ∈ P(f) : p(3) = 0 }
Doesn't this make sense? Im not sure if the name of the symbol in english is 'belongs to' tho

[Anonymous No.10800513]

>>10799555
>>10799584
explain ur notation my dude

[Anonymous No.10800514]

>>10800508
the fuck is P(f)

[Anonymous No.10800518]

>>10800508
What is P(f) ?

[Anonymous No.10800540]

>>10800514
>>10800518
Ok sorry it just says P(f) is a subspace, and from some pages ago (which are probably related) we have p(f) is a polynomial function.
Check last 6 lines of pic related

[Anonymous No.10800556]

>>10800540
Ah okay, it's the space of polynomials with coeffs in f. So, no, it is not going to be a one-element set. It has many elements. For example, all the [math](X-3)^n[/math] for any natural n.

[Anonymous No.10800651]

>tfw measure theory and functional analysis in the fall
>tfw just got by with a B in baby Rudin because I got some lucky questions on the oral exam
I'll probably fail but I will give it my all, just taking these courses to see where my ceiling is since I study mainly statistics

[Anonymous No.10800656]

>>10800651
>measure theory and fun anal simultaneously
What the fuck.

[Anonymous No.10800670]

>>10800656
Each semester is divided into quarters, so gonna have the q1 and q2 measure theory, q3 q4 functional analysis. This course is just setting up for the following course given next year

Course contents:
Integration and measure theory: Basic measure theory, integration of measurable functions (Lebesgue integrals), convergence theorems, product measure, and Fubini's theorem.

Functional Analysis: Introduction to functional analysis, metric spaces, Banach space including Lp space, basic theorems about linear operators and functionals.

Applications can be chosen among: Fourier analysis, ergodic theory, probability theory, Sobolev space, differential equations.

[Anonymous No.10800700]

Does anyone have any general tips on solving intro analysis problems? I can solve algebra problems really easily, like everything usually fits together by just writing the definitions or some theorem, but analysis problems idk how to tackle them. It sometimes feels like I have to get lucky with the inequalities. And by intro analysis I mean anything in baby rudin.

[Anonymous No.10800718]

>>10800700
Add 0, multiply by one, add epsilon, if you still fail try to make a stronger statement i.e. if you want to prove something for a continuous function try to do it for a differentiable function. Oh and I found it more useful to think in open balls definitions of continuity, openess and so on. This was how I got my B in it at least

[Anonymous No.10800721]

>>10800670
Where you from?

[Anonymous No.10800729]

>>10800556
Ok i thought of something similar yesterday but can't figure out how you got there / why it is like that

[Anonymous No.10800737]

>>10800721
Sweden, dunno how that's relevant

[Anonymous No.10800743]

>>10800737
Your post just sounded really similar to what it's like in Denmark.

[Anonymous No.10800756]

>>10800743
Do you guys also have mathematical statistics / math with focus on statistics as bachelor and masters programmes? I heard that it was just Sweden and Denmark that has it set up that way

[Anonymous No.10800766]

>>10800756
Not sure if you can do a statistics bachelor's that's different from a normal math one besides some elective classes but for your master's you can do pretty much whatever you want. Although I'm pretty sure there are differences between the different universities.

[Anonymous No.10800770]

>>10800700
. Draw stuff, seriously. This is always my number one tip
. Test the statement to prove on a couple of examples first (goes with the previous tip)
. Triangle inequality
. Cauchy-Schwarz inequality
. If you want to prove some inequality [math]A \le B[/math], see if you can instead prove that [math]A \le B + \epsilon[/math] for all positive [math]\epsilon[/math]
. If you want to prove some equality [math]A = B[/math], try proving both inequalities [math]A \le B[/math] and [math]B \le A[/math]
. Any non trivial statement about R is going to use completeness in some form or another. Equivalent forms of completeness include: Least upper bound property, Bolzano-Weierstrass, any monotone bounded sequence converges, any decreasing sequence of closed and bounded intervals has nonempty intersection
. Continuous functions on a closed and bounded interval achieve their bounds
. If you want to prove something about differentiable (or smoother) functions, recall that the Taylor formulas give you local control over the variations of a function in terms of its derivatives. Even order 1 Taylor can go a long way.
. To study a recurrent sequence with relation [math]u_{n+1} = f(u_n)[/math] with f smooth, draw the function f, study fixed points, study the variations of f, and try to find some typical range behaviour (not always possible).

These are my reflexes for anything undergrad analysis-related

[Anonymous No.10800779]

>>10800766
Cool, here we have complete separation between statistics and (what we call) mathematical statistics. Statistics is less math prerequisites and they learn relevant math within their statistics courses while for mathematical statistics you chose to specialise in that in your third year of a bachelor in math. This continues in masters and phd as well. The big differences is that those that study pure statistics learn much more about how you do surveys etc while mathematical statistics don't care about that and do more stochastic processes. probability theory and (what everyone else calls) mathematical statistics.

[Anonymous No.10800982]

>>10795697
Is there a name for spaces like the figure-8 or the line with a double point that would be manifolds if not for a few problem points. Almost everywhere locally euclidean spaces?

[Anonymous No.10801018]

>>10800982
Depends on what kind of singularities you're talking about. Conifolds are the appropriate generalizations for conical singularities. If your space if formed from a manifold with an associated group action, you can also get singularities corresponding to fixed points. Another way you can get singularities is by considering things like the cube, which are pretty easy to manage geometrically, but still singular, so manifolds with corners. This leads to stratified spaces, which are spaces that can be decomposed into manifolds, but are not necessarily manifolds themselves. So the figure eight is a stratified space.
>>10800770
Honestly, a lot of this is on point, you'd be shocked how much analysis can be boiled down to things like "apply this common inequality here" "add and subtract 1" and "just use an equivalent definition"

[Anonymous No.10801300]

>>10799782
I was trying to prove this, wouldn't you need to ask the derivative to be continuous or at least non-decreasing?

[Anonymous No.10801755]

Does anyone have a good free source for a comprehensive derivative/integration review? Havent done any math in 3+ years and even then it was with a calculator that did it for me. Im literally watching fucking khan academy to teach myself how to do this again. Khan academy helps, but I would rather have a textbook that i can blow through this weekend instead of watching all those videos. Taking exam P in either Sept or Nov and I understand how to set up everything to solve the problems, but I am shit at integration because I always used a ti89.

[Anonymous No.10801790]

How do I get into several complex variables? I heard this is an underdeveloped field?

[Anonymous No.10801800]

>>10800700
>can solve algebra easily
>struggles with intro analysis
really makes you think!

[Anonymous No.10801801]

>>10801755
Try Apostol’s single-variable calculus the problem sets will train your instincts for integration and differentiation as far non-advanced calc exams will ask.

[Anonymous No.10801839]

>>10801801
Looks good thanks

[Anonymous No.10801854]

>>10801755

this is what mathematics is for engineers ... just a whore they can use to pass the exams ...

[Anonymous No.10801946]

>>10801755
>depending on the tutelage of a calculator instead of pen, paper, and the application of one's own reason.
Sorry, you aren't cut out for the rough and tumble world of /mg/.

[Anonymous No.10801958]

>>10798184
folland

[Anonymous No.10802189]

>>10798184
>What's the current non-meme recc for Real Analysis? I want to get into probability theory but figure I should be better read on real analysis and measure theory
Simon is modern canon

[Anonymous No.10802226]

>test will be 2 and a half hours long
>it will only feature two proofs

yep, this is going to filter the brainlets

[Anonymous No.10802301]

>>10802226
Wow! Seems like pretty heavy-weight stuff you're getting into. Good luck!

[Anonymous No.10802310]

>>10802301

yeah i'm majoring in triple integrals

[Anonymous No.10802471]

>>10802189
Based

[Anonymous No.10802634]

>>10801800
kek, and all the alggeo cucks in these threads seethe when you tell them PDE is REAL math unlike their childish nonsense. they must have not understood baby rudin in undergrad.

[Anonymous No.10802910]

Terrence Tao just responded to my friend's post on Mathoverflow. God I feel like a BRAINLET.

[Anonymous No.10803152]

>>10802910
OMG so cool! If only I could switch places with your friend!

[Anonymous No.10803191]

>>10802910
Link or it didn't happen

[Anonymous No.10803329]

Convince me to study maths over physics.

[Anonymous No.10803347]

>>10803329
>math is actually rigorous and a search for beauty and truth! physicists just abuse logic and do massive amounts of hand waving to get the equation in the form they want, ignoring if such an operation is even defined.

- sad mathlets jealous of the chad physicists at their uni

[Anonymous No.10803368]

>>10799121

[Anonymous No.10803379]

>>10803329
>Convince me to study maths over physics.
If you need convincing, you're better off sticking with physics.

[Anonymous No.10803389]

>>10803329
Study econ.
>money
>simple and intuitive, but often hits you with curveballs
>you'll never touch algebraic geometry or arithmetic geometry
>dynamical systems
>convex analysis
>the original application of game theory
>you are constantly completely aware that the entire model is incorrect, but that's not the point
>tons of physicists dropped phisics to do "econophysics"

[Anonymous No.10803878]

>>10803329
>>10803347
>>10803379
>physics
Refer to >>>/toy/.
>>10803389
>econ
Refer to >>>/biz/.