#serious-discussion
1 messages · Page 462 of 1
just study some graph theory
The newest one i know if is from 2007 i think
hyperbolic curves over finite fields are determined by their fundamental groups pretty much
isomorphisms of schemes are in bijection with isomorphisms of etale pi_1
the non finite case is much uglier to state 
Bad book
Pedagogically
Read my paper instead once its done itll be better 
Jk probably dont
Lmao
Well, I am interested in the relationship between Galois Theory and fundamental groups/covering spaces of Riemann Surfaces.
moth is suffering so we dont have to
So his book seems interesting
chapter 3 is ok
chapter 4 is where things start to get
Horrid
when you have 3 contradictory definitions of curves and apply results from each interchangeably without stating any of the details

u will be able to read the paper if uve seen like Spec and the structure sheaf
Like a real paper? Or like lecture notes ?
Omg that's impressive
Lmao hi nGroupoid
No it is just expository its nbd
though i understand these things much better now in the process of writing about them
Still, it's interesting that you can publish something at such an young age.
Because now the details arent fucked
"publish"
ill probably just put it on arxiv 
but i will tell colleges that this is "published" 

Oh yeah, I am familiar with locally ringed spaces and the prime spectrum of a ring.
I would refrain from doing this imo
Well what im going to say is "paper published on arxiv"
no I mean like
your first arxiv posting shouldn't be something expository
I mean it depends on how original the exposition is
but like
you sorta don't want to devalue the quality of your arxiv postings early on
This paper was written as an elaborate call out post.
post under a pseudoname
Arxiv is just preprints
Moth Inshambles
Uh would that really matter at my age
possibly not, but it could matter later on
Jacob Scholze
In what way could it possibly matter ngroupoid
I feel like i have a lot of time to do serious things in undergrad
idk maybe im confused by what u mean by devaluing
Ppl post their undergrad thesis to arxiv all the time
I don't think your arxiv history is that important
it kinda is
by devaluing do u mean like people would be less inclined to take things i put on arxiv seriously
down the road
sorta
like the rule of thumb that kinda exists for arxiv is like
if you're posting expository stuff it's usually expository stuff that genuinely takes a very different approach to previous exposition
monkaS
Anyway moth, you can make a website and put your thesis on there if you don't wanna put it on arxiv
yea this is best practice
sure i guess it probably doesnt really matter
published on vixra
(for college apps i mean)
yea
my paper is novel and original because unlike szamuely it is correct :gigachad:
why the sully 
well i doubt there are any journals that publish expository work i could get this in and it almost definitely wouldnt be in time for college apps so

oh well
I dont know if thats true for undergrad lol

undergrad apps are funny
I mean at the same way it also doesn't matter that it's on a preprint server or not for this purpose
i think if they take any of the things i do seriously my app would be impressive but its very possibly they will not take any of it seriously
some AOs are dumb and dont know the difference between arxiv and real journals
right and I mean you don't want to sell it as a real publication either
i dont think it matters what i sell it as tbh i kind of suspect they wont take it seriously regardless
but oh well
i guess we'll see
Not having any benchmark for how solid my application is is hard
yea I mean you don't want to be dishonest about it, since that can really backfire
your application is likely totally fine lol
I would just find a way to mention the project in your application without overselling it
Im just putting it in on the list of activities which are like
100 characters each or whatever
yea that's fine
maybe i will elaborate on one of the EC essays for harvie but that would be about like
the process of doing it
yea that's important
not how good the """results""" are which 99% chance AOs would not be able to gauge anyway
imo that's more important than them possibly seeing that it's on the arxiv
I hope so 
because 1) this means nothing to most people and 2) they won't read it, so they won't know anything about the process that went into it
Yeah
I hope my rec letters are good
i have one from a columbia prof which i hope will be useful 
yea idk talking about the process of doing it is going to be more important than the finished product
and yea your letters will be fine lol
the process of doing undergrad applications sucks so bad
haha wait until you get to grad apps
Ok at least those are like. actually about the thing you want to do
Grad apps were better than undergrad apps for me
undergrad apps are stupid
Better process
its like branding type shit

I still rememebrr one of the things undergrad admissions ppl emphasized is that "we are trying to build a cohort"
yea
i have to draft another personal statement 
i am going to make one about sewing and how i am terrible at it :kek:
I'm watching Ghost in the Shell and I have no idea whats going on
If you don't understand Ghost in the Shell, then you’re dumb. This is easy stuff.
.
hhhhh
Am I still blocked?
3b1b has a podcast on Spotify, and there's BBC's A Brief History of Mathematics that I really liked.
no
those 3 episodes were p damn pog

ben, ben and blue was also p pog
sad they stopped 
but it was mostly about education ig

Complex functions are 4-dimensional: its input and output are complex numbers, and so represented in 2 dimensions each, so how do we visualize complex functions if we are living in a 3D world? There are actually 5 different ways to visualize a complex function, and this video is going to explore a bit about each of them.
Some of you commented t...
Hey, I'm soon about to take classes for the next semester, and I have a question regarding a specific class
Where can I ask you on your opinion regarding if I should take it or not
This place is fine.
So I'd possibly like to take Complex analysis this semester, and here's the list of topics that we're going to cover:
Potential vector fields, curl, curve integrals, Green's formula
Definition of holomorphicity, holomorphicity of polynomials, Moebius transforms and Riemann sphere
Holomorphicity of Laurent series, Cauchy-Riemann equations, harmonicity, harmonic conjugates, exponential function, complex logarithm
Complex logarithm, maximum principle, complex integral
winding number, Cauchy theorem, Cauchy formula, Morera's theorem, smoothness of hol. functions, hol. primitive functions
Taylor and Laurent series, isolated singular points
Residue theorem, Casorati Weierstrass theorem, Picard's theorems
Schwarz lemma, reflection principle, open mapping, Hurwitz theorem
Riemann mapping theorem, Poisson kernel and Laplacian
Riemann surfaces of mappings, cpvering spaces and analytic continuation
Little Picard's theorem, differential forms, Green's formula and d-bar equation, Runge's theorem
Functions with prescribed zeroes or poles, factorization, germs, Cousin problems and cohomology
Chain and cochain complexes, exactness, homology and cohomology gropus
Line bundles, classification of line bundles on Riemann sphere, homology and cohomology of spheres
What's bothering me is that I've taken multivariable analysis up to Fubini's theorem (for double integrals)
I haven't done stokes theorem
So I'm asking whether I can catch up on this with my current knowledge and not get blown out
You will do fine, you only need Stokes' Theorem to prove Cauchy's integral formula basically
And you basically just use the Green's formula version of it
Can I get the grasp of Stokes' theorem in 20 days 🤣?
Sure, if you are talking about the version of surfaces.
And not manifolds right?
There's a general version for manifolds which you would prolly need much more time to prepare.
Yeah
You won't need to know any manifold theory a priori.
Manifolds are usually taught on graduate courses if I'm correct/
What I would recommend tho
Is some knowledge of real analysis
Mainly topological notions such as continuity, convergence of sequences
Also some knowledge about series of real numbers
Stuff like fundamental theorem of calculus, mean value theorem and so on.
No
Do you know John Conway's book on complex analysis?
The second chapter covers the main topological notions you will need.
this seems like a pretty indepth course
but if you took multivar analysis, I think itll be fine
is this a year course(
?
thats a lot to cover inna semester
I doubt it'll be hard to pass
I guess they're just preparing us for the graduate course in complex
that seems almost like a graduate course
except it doesnt have much anal nT ig
and it is lol
I mean, we didn't cover anything about vector bundles or homology and cohomology theory at impa
tho like
we covered way more analytical number theory
feels p much like a graduate course
everything after riemann and open mapping seems non standard in undergrad
well I guess some other things are standard
but not chain complexes
but I like how it looks
it seems to have a little focus on things required for PDEs too
which is cool ig
We covered covering spaces, monodromy and riemann surfaces at the end of the complex anal course I took
it's cooler 
10 dollars is not that bad, but you could have stitched it yourself
You'll be fine
This iss the standard stuff for complex
I wouldn't be too worried about it
ok choose a copy pasta
im going to submit one copypasta for each problem set I submit for an intro to CS class
I hate taking CS classes along with math classes
They seem like out of topic burden



to be perfectly honest, my worst semesters were the ones with both CS and math
Just
Too much thinking in too many directions
Idk my cs classes were less about thinking and more about memorizing
@glacial vale did you get a scam DM? if so, the moderators will look into it. spamming every channel is neither helpful nor welcome.
(and pinging everyone 10 times is just obnoxious, even if this server has it disabled)
if you dont respond, i'm gonna assume you were acting in bad faith.
Definitely not the case for me lol
We could write reference sheets for all our CS exams lol
Didn't help one bit
Fucking brutal
If a right triangle has a base of 40m, and an angle of 30. What is the height? Whoever answers first, gets $10
30 what?
gradians
revolutions
I did CS minor in undergrad
I procrastinated on all the assignments
And spent 48 hours coding session on the day before projects were due to submit them on time
I mean I'm in my last semester, and taking Linear Algebra.
last sem of?
does anyone know what the absolute value of x-1 is?
If x>=1 then it is x-1
If x<1 then it is 1-x
Computer Science Major / Math Minor 😬
oh math minor
The work used to be a drag, but when I think of what I'm going to do with what I've learned and the people I'll meet with the skills I've acquired, I just get excited.
that's not too bad then
True, true. . . But I self study a lot , lol.
You're sure it's not 30 arcminutes?

30 archimedean furlongs
delet this, Alex.
I’m American so
30 nails
30 tumours
. . . . That is such an US thing to say. . . .
30 dicks
30 sticks
I'm not even mad, I'm just disappointed.
30 fingers
Eff it, gonna make my money and just do what Evil Morty did.
30 cosmdisfimisrfmosidmvowrfwefwefw meters
||jack shit, I'm leaving. LOL ||


||America : "GO BACK TO AFRICA GUAPPI"||
||Guappi : "Aight, bet."||
||America: "NO WAIT COME BACK.||
Wtf
Is this fan fiction
My set-up
Lemme p/m you to clear up the misunderstanding and what the actual. . . .
best part is if you need to shit you just switch chairs
Alex, get that perfectly good toilet away from that filthy computer you heathen.
I mean, I don’t have to switch chairs if I don’t want to 😎
Is it a Melty Blood set-up??
ackshually melty blood is based on tsukihime
which is just part of the same setting as fate (the "nasuverse")
thats weird since tsukihime, unlike fate, is good
sorry you just have bad taste
Considering what you think good taste is thats probably a good thing
hey i know i like a lot of things that are objectively bad
thats a different matter

apparently the remake is actually good too
which is... surprising considering it was in development hell for 13 fucking years
sadly itll probably never get translated
tsukihime is good
This is not even radially symmetric
Radially symmetric means it has a symmetry group consisting of rotations
But this board is not symmetric under 90 degree rotations...
Like, rotations do not describe the full symmetry group here. You need reflections.
Smh wikipedia
Doesn’t look symmetric about an axis to me
Tfw 180 rotation is a reflection
No
It is a reflection about the center of rotation
But not about any axis
Take playing cards for example
The cards with people
show the reflection you mean, pt
,w queen of diamonds
Point reflection 
Yeah but this doesn’t count as reflectional symmetry
🤷♂️

Reflections generate the full isometry group of the plane
Rotations, translations and glide Reflections are all compositions of Reflections
I don’t think composition work in symmetry
pt memeing




Hello 👋
Hi
Mmmm I need help I'm very much scared of maths
How happy are you
Well, it doesn’t bite
And my fear is increasing
Yeah that username is definitely a lie
Idk why buy i can't understand a single question
Only one question is troubling you?
Mmm 9 th grade
For some reason my phone likes to autocorrect question to queen
#❓how-to-get-help and ping me in the channel you chose
What about you? What math you doing?
Sounds awful
Thanks
That was really nice of you
I’m entering uni
Engineering
So the math I know atm is some mech and calc 1 and 2
Some statistics too
mech?
Mechanics
You know?
Free body diagrams
Newton’s law of motion
Work-energy principle
Those stuff
mathematical physics
I took A level math
what engineering?
It has mechanics
seems like mechanical eng?
did u take a level further math?
I did
I am 17 year old what are you talking about
mk
I didn’t take calc 3 yet
suggest you read calculus on manifolds by spivak
All I know about pde’s is that there is a triangle that does some stuff
Umm.. probably won’t thanks lol
Okay gtg
it requires knowledge on linear algebra right?

most engineering math isn't that complicated
umm algebra
algebra
and some more algebra
and some more more algebra
linalg, multivar calc, elementary real and complex analysis, and cookbook pdes
some basic counting technics and stats, too
i would say those are the basics for most engineering courses
I've never actually used derivatives in field work. It's all algebra in civil engineering.
mostly, electrical is a bit math intensive
but
So algebra, commutative algebra, algebraic geometry...
that's as good as it gets.
nah, more like the algebra we study in high school. Rearranging equations and stuff.
same but little bit sticky
I was doing multi variable calc that time.
Hi
I was doing convex integration over cohomologous perfectoid spaces at that time.
i was learning to count
my sigma grindset kicked in much later
A googologist in the making
Einstein mastered calculus by the age of 14
You better work on yourself more
Says who?
Yeah I was planning to study multi var in Summer but I got lazy lol
I think the the only reason school exists is the pressure not the teaching
Imagine mastering a subject before inventing it
It’d be super dope ngl
I mean I don’t have the motive to learn anything on my own except if they tell me there are some unimportant numbers that are calculated based on how much I know the subject
nice jojo pfp
Lol thanks
that might be the only anime I haven’t watched. The animation is a huge turnoff and I don’t understand why. I have watched other show with terrible animation.
its super good
i think the art style is awesome but i see why people feel indifferent to it
bruh?
me trying to do integrals with three hours of sleep
Hello everyone, im trying to order a math textbook from the AMS bookstore. It wants me to make an account, but when I try it wants me to type my address and the drop down menu to select which state I’m in does not work. I have tried multiple OS/browser combinations. Very strange issue. Has anyone else has this issue or heard of anyone having this issue?
Why should I care what Einstein did?
The same reason you should ping me about sth happened before they invented time
Math is complex.
well said bro
nice thing about math is that if your good at it you never be wrong
maths never wrong
No, just opposite. The better you get, you create more theories and make mistakes
hmm
u have a point
Does a point point anything in math. I am confused.
ur confusing me
were both confused

What can a non math background person do with his math knowledge?
add on his fingers
What to add?
numbers
counting on fingers better said
Which type
lots of professions need at least some mathematics, all kinds of tradesmen need to be comfortable with fractions and trig, office jobs juggle spreadsheets all day, which obviously needs math as well
generally the word mathematics in ancient greek means something like "the art of learning", so there is also the idea that teaching people mathematics helps them reason better about anything
as an example, i'm a "non math background person" who uses math to both offend everyone by being bad at it and to make nice ultrasound, x ray, radar, etc. images
So you are a hospital lab assistant?
This reminds me of a book
Digital Signal Processing: Principles, Algorithms and Applications
John G Proakis
that's code for needing a masters and phd to be bad at statistics and linalg
I saw someone with the hot take earlier that in the future, we'll be teaching Groebner Bases to undergrads like we teach them Gaussian elimination
very hot take
So hot it reached negative kelvin
don't lol
Cool thanks I won't.
toddlers can totally handle topology and algebraic structures and group theory
and babies can handle vector calculus and linear algebra and trigonometry
which implies kindergartners are doing vertex algebra and more abstract mathematics
and late on kindergarten, they would get Ph.D's
by 1st grade, they would be professors
or do research
before teaching addition, i force 2 year olds to study peano axioms, zermelo-fraenkel axioms, number fields and field extensions, etc.
after all...
too much mathematical rigor and abstraction is healthy for children
they need it to grow their tiny brains
also if it traumatizes them or smth, i'm not responsible
they need it
What novelty
Hyuck
personally I don't think we should teach kids how to add until they know enough set theory to rigorously construct ordinal addition from the ZFC axioms
personally
Nothing personnelly kid.
construct the naturals in analysis 1
what kind of analysis 1 class did you take Ultra
who constructs the naturals in analysis 1
at best you construct the real numbers
but what kind of analysis class isn't taking the naturals for granted
you don't
you're just given the naturals
ok just so we're clear
when you say analysis you mean the branch of math that covers the properties of the real numbers and functions on them and integrals and stuff
not set theory
my analysis courses never constructed R but they certainly axiomatized and then constructed N
my analysis course did neither
the von neumann ordinals were mentioned in an aside
you dont know sets exist, theyre a primitive
barely covered derivatives
er
let me rephrase
you know they exist because theyre a primitive
no it only shows their existence is consistent ultra
god
no but when I say
personally I don't think we should teach kids how to add until they know enough set theory to rigorously construct ordinal addition from the ZFC axioms
I'm talking like Principia Mathematica kinda stuff
not just Peano axioms lol done
i mean if youre using zfc its not hard either
principia is not zfc
principia is a lot more involved
well that's what I mean
zfc is easy mode
constructing them from zfc is for the remedial students
the advanced students need to start by rederiving language
i was reading Russell the other day and he used the word "set". i was like, daddy russell, how could you do this to me? your theory's supposed to be a type-theory-kinda-except-not-really! was what i read from a programmer's blog on HoTT wrong???
i figured my sarcastic tone would be fairly clear
should i have added more exclamation marks
perhaps a :smug:
oh no i forgot, discord stole my goddamn :smug:
im quitting this platform
does parler have :smug:
The existence of God only implies the existence of God.
God → Con(ZFC)
(here "god" means in godels ontological sense)
the paper, despite the ??? typesetting and cranky claim
(the stupid sense)
is legit
which is absolutely hilarious
honestly im in the wrong field
i dont get to call anything
"divine"
all my adjectives are boring
The Final Proof of the non-Existence of God was proved by a Babel Fish.
Now, it is such a bizarrely improbable coincidence that anything so mind-bogglingly useful could have evolved purely by chance that some have chosen to see it as the final proof of the NON-existence of God. The argument goes something like this:
"I refuse to prove that I exist," says God, "for proof denies faith, and without faith I am nothing."
"But," says Man, "the Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It proves that You exist, and so therefore, by Your own arguments, You don't. QED."
"Oh dear," says God, "I hadn't thought of that," and promptly vanishes in a puff of logic.
"Oh, that was easy," says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing.
Is that from hitchhiker's guide?
If yes then I definitely have to read that again

yes
I just started rereading Hitchhiker's Guide a few weeks ago and yes it is very good
What's it?
it's a book series
Math?
That 42 thingy?
yeah, that's the book.
Is it ok to ask questions here?
???
??
What
What are you asking?
i feel like this book is familiar
Im yet to disclose that
Apostol lol
So
I wanted to know how introducing another variable 'b' makes the case "particular"
Like how is it different from choosing an arbitrary point 'x'?
Is this not the right channel to do that?
My response is not getting displayed I think.
It is not
@cold needle : What's the red color coming across my response.
Am I muted?
it means your message didnt send
try resending
I think it's just like x, but b is the length of the box.
yeah must be some internet issue
discord is a piece of shit app that likes to stop messages from sending every once in a while
Network issues
spanish
Box?
spanish
It's the limit of the rectangle.
How does that makes it "in particular"
There is nothing special about 'b'
Sorry, discord making me do more mouse moves.
Ok
visible concern

actually metal, i will not worry about it. i will respect your boundaries and inquire no further
ninja metálico veintisiete
Meow

Feels like breaking the rules is way more convenient way to get your queries resolved
or banned
then you just come back with an alt
that's what Namington does
except he does it even when he doesn't get banned
fun fact: half of this server is just Namington alts
Bro that was just an honest feedback
I am not
suure
It is not.
Your best bet is to follow the rules, show your effort at solving, co-operate if someone is trying to help. At the end it has to be acknowledged that everyone helping here is a volunteer, so there can simply be times where no one helps.
NinjaMetálico27
trueeee
ciertoooo
ninja-de-metal27
toki mfkin doki
toki-de-doki
ed-d-de
Petition to gib sat_3 server owner
Guy managed to understand my bullshittery without losing their temper
I did not know that 
study a field of math you hate for 6 months
Says the Namington alt
Moment
Topology 😫
That's where you're wrong bucko
I did a semester of algebraic curves
Does that count
Algebraic curves sounds fun though
Yeah but I hate algebra

I am aware. It is still sully.
Sylow Theorems are awful
i agree
You do like three of those exercises and then move on to more interesting stuff.
Algebra is only fun when some other subject is tossed in
Like topology
I more or less think the same thing about real analysis, it's only fun with fourier/PDEs
You know that's fair half the reason I like algebra is that using algebraic methods to solve problems from elsewhere is just really cool.
But Complex makes real more bareable
Also Algebraic Geometry is so cool
I wish I understood it
Why do you Sully me Ryc
I'm reading Cox, Little, O'Shea right now and it's a super accessible intro to AG and commalg.
moonbears crank reveal
I read through Fulton's algebraic curves
real analysis bad 
and did some stuff on Riemann Surfaces
I don't think it's bad
I just think it's kinda dry
Oh okay yeah that's a bit more advanced AG than what I'm doing now.
All math is slightly dry at the intro level, at least compared to the upper levels.
Other than real analysis. The best parts of that course are when you spend the first few lectures screwing around with Dedekind cuts, the most fun and intuitive construction in all of mathematics.
How tf did I write that
yy
I think the most fund I had in real was when we got to fourier
And did some special function stuff
Then applying it to number theory (in a different course)
Was a lot of fun
I'm TA-ing for point-set topology at my university right now
The professor took topology back in 1995, and hasn't touched it since
That sounds like hell.
So she's havin' a hard time
It's kinda fun
I had to take point-set topology 3 times
well, I choose it once when I shouldn't've
what even is that, if you don't mind
In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. Another name for general topology is point-set topology.
The funda...
it be difficult?
I suppose that's up to you
well, isn't almost everything in that case
Yes
astonishing
does anyone have any stories about a time someone in humanities major surprised you?
high school algebra or abstract algebra?
abstract algebra is OP and good
I'll let you decide for that one
I like it
I enjoy HS lvl math, and working with students through it
to me, high school math is too cringe
because no interesting stuff
and also because it's basic
Id have to disagree with you on that MoonBears
Do you enjoy repetitive menial tasks?
factoring quadratics is just doing something to get the solution(s) or prove something
it's boring
and has no other purpose imo
Hrm, and have you taught factoring quadratics?
Yeah
Have you learned the historical development
why do teachers who work with high school students spend so much time on quadratics
like
yes i suck at teaching
just complete the square lol
Iv'e done a fair bit of teaching
Where did the equals sign come from
/tutoring
idk because 60% of algebra is quadratics
How does it lead into modern mathematics?
My enjoyment of math doesn't come from repetitive tasks, it comes from having to think/find a solution
I think it's interesting to think about
Highschool maths for the most part is the first part
same and also abstract math
and ideas
How many different ways can you solve the same problem, how many ways can you interpret it
and proofs
According to the VNR Concise Encyclopedia of Mathematics, the equal sign was invented by Robert Recorde, the Royal Court Physician for England's King Edward VI and Queen Mary. Recorde, who lived from 1510 to 1558, was the most influential Welsh mathematician of his day and, among other things, introduced algebra to his countrymen
and creativity
That's the only reason I can think of we teach students 400 different methods of factoring quadratics
but tbh there are more interesting problems where that principle can be applied
many
And they tie into different parts of Math
It's interesting to think about
How much is embedded in so little
i'm not an expert in mathematical history lol
or history in general
solving something that could be done with a calculator or with a formula doesn't seem particularly motivating for a student that does't already love math
That's why I try to motivate it when I lecture
I mean, I find it cool, but most don't
unless you prove or derive the formula
then it gets interesting
I try to make it more natural, where the answers/questions arise naturally from examples
It's like crafting a historical narrative
who are already at university and give more fucks
I have to lecture 8 hours a week at a university for the remedial algebra
i usually require proofs and use too much abstraction and mathematical rigor lol
I have great freedom in what I do, so I get to have fun with it
no wonder i'm bad at teaching
You have to motivate the proofs or the techniques - you have to pull them in with leading questions
is remedial an insult
And it ties back in to other parts of math they already know
i don't like math in school. i'm ok being lectured by a professor but not by school teachers
everything's an insult if you're easily offended. remedial algebra is exactly what it is
Sorry they didn't pass it the first three times
Or maybe they did but didn't learn
oh it says for learning difficulties people
where are remedial analysis classes when you need them
I have freshman that can't add 1/2 + 1/3
its not uncommon
Freshman at a university
im going to go out on a limb and say half the population cant do that
world population
and i'm wondering. why aren't schools letting Ph.D's and actual experts teach? why can't mathematicians teach school for kids?
they probably dont apply to those jobs
Because most mathematicians are bad at teaching
WTH LMAOOOOOOOO
And have no training in being a teacher
so? i don't care
i'm not sure how good terry would be at teaching high school students
troll spotted
probably pretty good
who terry
Terry Tao
terence tao
field medalist
12-13 year old IMO gold medalist
math professor at UCLA
Bill Thurston was on some math outreach journal thing
i've watched a lecture of his about primes
I wouldn't limit that to mathmaticians
Just because you're good at something doesn't mean you are a decent teacher for it
I'm not limiting it to that, I'm just addressing the issue in having mathematicians teach grade school and up
Most people trained professionals arent trained at explaining
People often mistake the two
why do schools require education credentials?
makes no sense
moonbears he is trolling

just let experts teach
pls dont take bait
I'm against teachers licenses also
||The best math professors I've had are at CSULB||
for you 
He just lectures like he's trying to get somewhere
no, he's still too slow... it needs more mathematical rigor and abstractness
{sqrt2}
This was my topology professor @deep mango
Look at these reviews
They are ridiculous
??
Aww, that's nice
This was my algebraic curves prof
This was PDEs - the first review is hilarious
Professor VB is a cold stone fox. Very attractive man with his smooth, soft face. Despite his gray/white hair, he is a total babe. (Maybe in his mid 30s?) His personality at first seems cold and isolate to student but as the time progress, he started to show his bright side by started telling his funny/ embarrassed stories. Love that professor!
These guys were like at the pinnacle of teaching
I think Terry is better at office hours
Than he is lecturing
Cuz then you can ask questions, get one on one help and see how to solve problems
yeah he was really good talking one on one
a lot less frantic
i was expecting it to be like a bulldozer
He just has too much planned for each lecture
I think he structures his classes so that office hours are almost necessary
UCLA Department Of Mathematics
Terry Tao, Ph.D. Small and Large Gaps Between the Primes
I heard his Fluids class was ridiculous
In which sense
I am planning to take up a challenge to excel in a math field in 6 month.
What do you suggest, if I can give 2 hours a day? 🙂
I am a good grasper.
Yo I heard Russell’s paradox about sets containing themselves
Maybe this is a dumb question, but how could a set contain itself?
Ok to fully understand the paradox would I need an understanding of formal logic and stuff like that
Cause I have no idea what an unrestricted comprehension is
2h a day is far from enough to “excel” in a math field
Well my intuition tells me that’s impossible because it would contain infinitely many nested copies in itself. But I feel like in this context there’s no such thing as infinity or nesting, and the only thing that matters is sets and properties
Oh that’s not so bad
Haha to understand, I mean
But yeah
Ah
So Russell’s Paradox is about showing that allowing unrestricted comprehension leads to a contradiction?
Ah that makes sense
“Comprehension” in this case refers to the rules about what P(x) can be, right?
Since I don't know which topic in math I should choose to study, what I am planning to do is first go through
Mathematical Methods for Physics and Engineering book(I am interested in physics too) and later choose the topic that interests me for further studies.
What do you think about this method?
Sick
Ok wait what do you mean when you say “restrict comprehension to subsets of already-known sets”
yeah "sets can't contain themselves is just Foundation, right?"
or like an equivalent form of it
and Foundation is really only there for convenience since any model of ZFC without foundation has a submodel where Foundation holds
Ohhh
wait a second I feel like I forgot something
what if your model of ZFC without foundation is just ZFC?
*a model of ZFC
but then doesn't your model contain a submodel of ZFC?
violating Incompleteness
right
but Incompleteness would need a proper submodel
or rather a set model
nothing I just momentarily forgot how set theory worked
WF is well-founded sets right?
that's the submodel you take?
but it's not a set model
is it ever a set model?
Wait how do you use the Mostowski collapse again?
when I say set model I mean it's a set in the model of ZFC
take some model M of ZFC
take what M "thinks" is WF
is that ever a set in M?
oh duh
I was going to say "no because WF contains ON"
but I feel like that's a bit more elegant
idk
🤞 ZFC
Wanted to know if theres enough information to solve this problem
If you replaced the R in your name with a D and remove the Pang your username would be perfect
first semester combinatorics
isnt this super lengthy?
no
1 liner
think of the negation
there are 18 people not doing swimming, 14 not skating, etc.
compute the maximum not doing at least 1
Well i actually went in that route
$\abs{a \cap b \cap c \cap d} = 60 - \abs{\overline{a} \cup \overline{b} \cup \overline{c} \cup \overline{d}}$
Namington
Why m i never confident whenever it comes to negation
It was actually the first thought that crossed my mind as soon as i saw that problem
Yeah
So
What if
Some of the people who dont swim also dont skate or tennis or bowl?
By looking at the answer, i know i shouldnt be worried about this case
But still i am
we're thinking of the maximum
that will not occur in the maximal case
in the maximal case, we can assume everyone is perfectly arranged so that the sports they dont do dont overlap, so long as there are enough people (pigeonhole)
the sum is less than 60 so thats valid here
I didnt get it
Minimum number of people who play all 4 sports = Total - Maximum number of people who dont play all 4 sports?
@leaden torrent
yes.
Why do we have to assume that theres no overlapping?
its a safe assumption since we're looking for a maximum
if theres an overlap, it wont be the maximum
since we could swap out one of the students in one of the sports to get rid of the overlap
(caveat: we need enough students to actually do this, so if there were, say, only 30 students, this wouldnt work)
(but in that case the answer is trivially 0)



