@leaden torrent how do i get this dude to talk to me
#serious-discussion
leaden torrent
right click (his name)
idk how to do it on controller
but its the interact button
astral marsh
ok the main questline they're giving me seems boring so i found the archery guild somehow and now i have to shoot some stuff
pog
astral marsh
kupo ratio
light needle
arch do math instead.
astral marsh
neat lintel
zoph pfp is the same color scheme as the mcdonald clown
blazing pawn
"ratio"
no reactions except himself
astral marsh
i see no reactions on your original message
1 > 0 which means it was a successful ratio
blazing pawn
average twitter user
mild nebula
leaden torrent
i outrank you peasant
blazing pawn
Not for long.
i should be given tenure at uoft so i can abuse my power to threaten namingtons career
it would be fun i think
reef carbon
@leaden torrent 
inner finch
cold needle
kupo
cold needle
what is a "problem solving" course supposed to be about
i just signed up for one
π€ no idea what it do
is this like
competition math or something
devout nacelle
Sounds like it
torn willow
Euclidean geometry
Uni course
devout nacelle
The contents seem to come parallel to something like Zeitz's Art and Craft of Problem Solving
surreal sapphire
looks like intro proofs tbh
devout nacelle
That too, but calculus and geometry are unusual choices then I guess
cold needle
i already took the intro proofs course i really hope we aren't proving anything
cold needle
π
neat lintel
surreal sapphire
it looks like the intro proofs here
torn willow
What if this is pre intro proofs
surreal sapphire
which does stuff that students struggle with in analysis/linear algebra
so just pick some stuff from wtv class and do it
cold needle
surreal sapphire
is one-credit a lot?
surreal sapphire
intro proofs light
cold needle
π the actual intro proofs class is 3 credits here
so basically
this should be trivial or something
devout nacelle
Why are you even taking it?
devout nacelle
Minus possibly geometry I don't even think there's anything you don't know already lol
cold needle
its 10 hard problems a week and we have to do any two of them for hw
that's it
thats the whole class
π ok
surreal sapphire
just do all of them to assert dominance
cold needle
you know what i might still do it just for the practice or something if they don't take too much time
toxic schooner
cold needle
this professor also does putnam related activities too which is why i thought this was like a competition maths class or something
neat lintel
it seemed more like a "here's an assortment of cool elementary problem solving techniques" rather than "here's how to solve basic mathematical problems"
inb4 whats the difference
cold needle
ok this class seems harmless so i guess ill just keep it unless i realize it's taking more time away from me than i really want
i don't expect it to be a problem though
π€·ββοΈ
cool
sharp mulch
Metal burnout speedrun
surreal sapphire
why not take actually useful classes
cold needle
idk i already have all the "useful" classes that i want
torn willow
just do all of them to assert dominance
Just do all of them in 5 minutes and submit to assert your omega status
devout nacelle
I'm already 70% into my burnout speedrun 
cold needle
i don't understand how this at all equates to me not taking useful classes?
it's one credit and only meets once a week
sharp mulch
Taking a class because it isn't a bad class is not a good reason to take a class
cold needle
i see
cold needle
i see
yeah idk i never did stuff like this though before so i thought that it would be a harmless idea to just get extra practice in
i didn't do "problem solving" in highschool or whatever
devout nacelle
You're doing it real time with the math classes you take so 
cold needle
i doubt im going to take the putnam so it's not really practice for anything but i guess just to be able to solve problems if i get them
idk
neat lintel
for fun
cold needle
but yeah ill be open to dropping it if it takes too much time
from fun stuff
okey
oh okay
that sounds like a good policy
i should do that
okay i guess what ill do is take the first week to try these courses and see if i really want to deal with them
chilly smelt
vagrant kestrel
congrats on joining the putnam team metal
cold needle
π
odd narwhal
Metal do you not have enough classes you actually want to take
That you consider taking a class just cause it isn't bad?
toxic schooner
gjkfdsgfd
odd narwhal
Bruh I have so many classes I wanna take
That I don't have room for them all in my schedule
cold needle
i do too but like they're not going to line up
i have to fit them into sucessive years
and this year 2 is like the dead period that idk what to do with
right now i have real analysis (abbott) algebra (d&f) fourier analysis (s&s) and a math methods for physics class
odd narwhal
physics π€’
cold needle
on top of that i have these two tiny 1 credit/once a week meeting classes which should be minimal work
odd narwhal
Sully me all you want
won't change my mind
physics as taught to undergrads is abysmal
odd narwhal
on top of that i have these two tiny 1 credit/once a week meeting classes which ...
What are those on
cold needle
one of them is just a presentation class where u get assigned a proof and u make a powerpoint on it and share to the class on ur assigned day
literally trivial work
then the other one is the one i talked about earlier
where its problem solving and the class is just u get a problemset and u just need to do a couple problems from it
this should also be light
odd narwhal
that's so odd
torn willow
It's an even sem
cold needle
14 credits so its even
torn willow
How much real anal,algebra and Fourier do you know as of now
cold needle
i already took a semester of babby algebra this past spring
odd narwhal
I have absolutely no idea how to translate us college credits into our system
cold needle
we learned minimal group theory stuff
torn willow
Did you do group actions
odd narwhal
bruh
cold needle
we used gallian π€’
torn willow
What about real anal
cold needle
i don't think i know any
for fourier i probably don't know a lot either but ive done computations of fourier series for some SL operator memery
torn willow
So like in these 2 weeks you can do one of 2 things
- learn one or two or all these topics
- Do something completely different as a "break" of sorts
torn willow
gdshjkghj
cold needle
2) Do something completely different as a "break" of sorts
probably this one
i will collect enough energy to destroy the next two semesters
it will be grand
just need to rest ig
sharp mulch
What
narrow rock
cold needle
hype
toxic schooner
True, I respect that
cold needle
how do i join empty2 math forum
narrow rock
cold needle
what
blazing pawn
cold needle
hollow jackal
you guys ever do 2^3 = 6
sharp mulch
broken scaffold
^
devout nacelle
limber perch
you guys ever do 2*3 = 6
hollow jackal
<#488120190538743810>
neat lintel
I haven't done a calculation in years
devout nacelle
Happens sometimes
latent forge
based
neat lintel
so it means, its prepared with a very successfull point.
latent forge
based is dual of cringe
limber perch
the pointed space doesnβt have a dual space
latent forge
cringe is pointed space?
errant kiln
Yes, #serious-discussion does get rather difficult to read, sometimes.
Very complicated shit going on in here.
thorn brook
there's so much bullshit notation baked in to this proof that I'll need to send like 3 pages just so someone could understand the notation
it's something very trivial probably
errant kiln
there's so much bullshit notation baked in to this proof that I'll need to send ...
Hatcher, I presume? 
errant kiln
light needle
Hatcher moment
crystal stone
it's so fricking frustrating
Just draw urself about 10 pages worth of material
errant kiln
Just abandon Hatcher.
thorn brook
I'm going insane
crystal stone
||Chapters 0 and 1||
thorn brook
I can't take this
errant kiln
I'm going insane
When Toki doesn't understand something at first glance
crystal stone
Just give up on fill rigor
And just go full intuition
The rigor will come eventually
thorn brook
When Toki doesn't understand something at first glance <:stare:82692003862334672...
nonono I've stared at this paragraph for ages and I still don't get it
errant kiln
nonono I've stared at this paragraph for ages and I still don't get it
what's for ages?
thorn brook
The rigor will come eventually
yeah I would like to do it but I can't understand this intuitively either
velvet dagger
@errant kiln for ages = for a long time
errant kiln
I've been stuck on a single one of Riehl's weird diagrams for like 12h
thorn brook
deets nuts
odd narwhal
Toki what is it
thorn brook
it's like a proof that a sequence of homology groups is exact
stuff with like relative homology
I don't really know how I should write it down because I'm too noob with latex
thorn brook
oof. Hatcher writes at the end of the proof that "this theorem represents the beginnings of the subject of homological algebra" lmao
light needle
odd narwhal
I think I'm almost at relative homology tho since I just did snake lemma
Tho idk since this chapter still has a while and after this there's the excision axiom
fathom swallowBOT
light needle
snake.
light needle
the diagram chasing stuff is v fun when doing for the first time
like snek lemma, the 5 lemma zigzag etcetc
odd narwhal
It's novel to say the least
Tho I stared at one part for like 15 minutes
Cuz he didn't really write out the details
Exactness does some funky stuff
light needle
yeah its fun working the details tho
thorn brook
% https://q.uiver.app/?q=WzAsNyxbMiwwLCJIX24oQSkiXSxbNCwwLCJIX24oWCkiXSxbNiwwLCJIX24oWCwgQSkiXSxbOCwwLCJIX3tuLTF9KEEpIl0sWzEwLDAsIkhfe24tMX0oWCkiXSxbMCwwLCJcXGNkb3RzIl0sWzEyLDAsIlxcY2RvdHMiXSxbMCwxLCJpXyoiXSxbMSwyLCJqXyoiXSxbMiwzLCJcXHBhcnRpYWwiXSxbMyw0LCJpXyoiXSxbNSwwXSxbNCw2XV0=
[\begin{tikzcd}
\cdots && {H_n(A)} && {H_n(X)} && {H_n(X, A)} && {H_{n-1}(A)} && {H_{n-1}(X)} && \cdots
\arrow["{i_}", from=1-3, to=1-5]
\arrow["{j_}", from=1-5, to=1-7]
\arrow["\partial", from=1-7, to=1-9]
\arrow["{i_*}", from=1-9, to=1-11]
\arrow[from=1-1, to=1-3]
\arrow[from=1-11, to=1-13]
\end{tikzcd}]
fathom swallowBOT
Tokidoki β
odd narwhal
I'm just afraid I'm reading too much at once and not retaining
odd narwhal
Lmao
odd narwhal
Hurewicz theorem was pretty tough
Like it all adds up but it just seems to hit you out of left field
And you just gotta stare at simplices till it makes sense
light needle
kek
odd narwhal
If j is the connecting homomorphism shouldn't it be Hn-1?
thorn brook
wait in my post?
light needle
I have forgotten all of my homology lol
odd narwhal
Ye
thorn brook
How do I fix the latex stuff
odd narwhal
Just edit your post
light needle
should relearn soon from tom dieck 
thorn brook
% https://q.uiver.app/?q=WzAsNyxbMCwwLCJcXGNkb3RzIl0sWzEsMCwiSF9uKEEpIl0sWzIsMCwiSF9uKFgpIl0sWzMsMCwiSF9uKFgsIEEpIl0sWzQsMCwiSF97bi0xfShBKSJdLFs1LDAsIkhfe24tMX0oWCkiXSxbNiwwLCJcXGNkb3RzIl0sWzAsMV0sWzEsMiwiaV8qIl0sWzMsNCwiXFxwYXJ0aWFsIl0sWzQsNSwiaV8qIl0sWzIsMywial8qIl0sWzUsNl1d
[\begin{tikzcd}
\cdots & {H_n(A)} & {H_n(X)} & {H_n(X, A)} & {H_{n-1}(A)} & {H_{n-1}(X)} & \cdots
\arrow[from=1-1, to=1-2]
\arrow["{i_}", from=1-2, to=1-3]
\arrow["\partial", from=1-4, to=1-5]
\arrow["{i_}", from=1-5, to=1-6]
\arrow["{j_*}", from=1-3, to=1-4]
\arrow[from=1-6, to=1-7]
\end{tikzcd}]
fathom swallowBOT
Tokidoki β
thorn brook
fuuuuck
errant kiln
thorn brook
errant kiln
thorn brook
so i_* is induced by the inclusion, j_* is induced by the quotient map and A is a subspace of X
thorn brook
damn those letters
holy moly that is super fancy
thorn brook
and this guy is supposed to be exact
errant kiln
holy moly that is super fancy
that may be nice to me but I can't read those
I think it's a T.
thorn brook
yeah same lmao
errant kiln
But I have no idea what the other one is supposed to be.
thorn brook
yeah I would guess that it's a T but idk
wild lantern
damn those letters
I absolutely hate these kinds of letters.
errant kiln
wild lantern
Anything more complicated than mathcal fonts is just too hard for me to write by hand 
thorn brook
it might be an f idk
errant kiln
I might actually have to post that in latex help or smth
I can't read without talking in my head, and I can't talk in my head if I don't know which letter that is
wild lantern
Is it from the mathrsfs package?
Looks a bit like i or j?
Idk if the pic in this helps: https://tex.stackexchange.com/questions/58098/what-are-all-the-font-styles-i-can-use-in-math-mode
slim meadow
wait yeah same I've gotten a few already too
sharp mulch
It's so exciting
I got one today about metallic ratios
Wait Megan Chang-Lee is at Brown
She's really cool
Zoph
slim meadow
oh right right
yeah she's cool, I talked with her a bit
she gave a presentation on ratatouille
sterile hare
How does real analysis change you as a mathematician? What's the key differences between a student who has only taken Calc 1-3 and then a student who has taken real analysis?
sharp mulch
Rigor and perpsective
sterile hare
Rigor and perpsective
What do you mean by rigor?
sharp mulch
Proof based math
sterile hare
doing analysis made me dislike anything related to the subject
is it the hardest math course in your opinion?
sterile hare
How big a step up is it from calc to real analysis
forest jackal
its just viewed as hard by a lot of students because it is a jump in they way you think about math, things need to be quite carefully justified that you might have previously taken for granted.
and a lot of a first course in analysis will involve proving things that were "intuitively obvious" to you. but you will then start to see why this is necessary when you start to come across things that are intuitively obvious but false, and things that are intuitively impossible but true.
point is that your intuition is actually quite bad until you do some groundwork that some (like jesse) can find boring, and some others find hard.
forest jackal
how is that a shot?
rancid meadow
i am joking
clever knot
is it wrong to say real analysis is just proof based calc?
sharp mulch
Well
It depends on what you mean by calculus
Analysis is generally a bit broader than just calculus
clever knot
oh
maybe im thinkng of a different topic
unless real analysis happens to involve lots of calc and then some
forest jackal
it is wrong to say that yes, analysis is a whole sprawling field of rigorous math
azure kettle
it is wrong to say that, but it's also how I would describe it briefly to a non-math person
forest jackal
it happens to be the field of math that is required to make calculus rigorous, but this does not really define it.
clever knot
well i guess what else dose it involve that would be outside the scope of calc
or is it more like it is applicable to lots of things and helps a lot with the ideas behind calc
forest jackal
functional analysis, harmonic analysis, fourier analysis etc
clever knot
so when you start one of this intro to real analysis do you start with some general axioms
to build upon
like "what is a number"
like what is a "real number"
forest jackal
yep, defining the real numbers properly is a common and natural starting point for a course in real/complex analysis, which is the usual first course one takes in this field.
because a few facts in calculus like the extreme value theorem can only be properly proved once you carefully define the reals, as they use a subtle property the real numbers enjoy that (say) the rationals do not.
clever knot
maybe a dumb question but obvious we work in base ten but other than switching back to base 10 when doing calculations does real analysis work with different bases
Say I wont to integrate x^2 but maybe x is number in a differnt base or something idk
forest jackal
yes the only role "base" plays is in the encoding of a real number as a decimal expression on our page
the underlying set of real numbers is the same and their properties are the same
clever knot
Man idk it seems really hard to think of a number without a base 10 representation. Like when we convert bases isn't most of the case we have an intermediate part were we representation the number in base 10 again
Say going from binary to hex
I assume most would do binary -> base 10 -> hex
modest rune
Why
clever knot
Maybe just me
Idk well maybe just any base to another base
Maybe I did a bad example
modest rune
Thereβs an algorithm
clever knot
Seeing 2^4 = 16
sharp mulch
Yeah
Hex<-> binary is very easy
Because you read the binary in groups of 4
And then just do the conversion in chunks
broken scaffold
Man idk it seems really hard to think of a number without a base 10 representati...
er do you mean like
1/3?
clever knot
er do you mean like
1/3?
i mean one that brings up a good question about doing something like 1/3 in a differnt base but idk i was more talking about like say you are converting from something like base 7 to base hex
But thinking about it maybe it is just because I am using the number involved in base 10 that i feel i am representing the number in base 10 before completely converting it to another base when i might not be
little berry
I need help monki brains
Which looks better?
clever knot
Fed illaoi πΏ
who fed>
brave hollow
I did :gigachad:
elfin ridge
what's the meaning of this?
sharp mulch
devout nacelle
Contemplation of the Royal Goose
toxic schooner
i read that as the constipation of the Royal Goose
brave hollow
golden egg
sharp mulch
astral marsh
@fervent flame
long epoch
I remember on youtube there was this guy called "Aleph Null" who changed his channel name to "Aleph 0" now.
He had a video called "how to teach yourself pure mathematics" and now its just disappeared off the face of youtube
Anyone know what happened?
leaden torrent
pure mathematics was cancelled
rancid meadow
yes i remember that video
it had his face in it and so its possible he didnt want to have it uploaded
since all of his new videos are just w the paper stuff
leaden torrent
the paper stuff
i think its called "paper"
rancid meadow
yes but the style of his videos is paper stuff
like minutephysics is whiteboard stuff
leaden torrent
surreal sapphire
personally i prefer computer stuff
azure kettle
i prefer rubber stuff
devout nacelle
I prefer cave paintings.
odd narwhal
Everyone knows the only way to properly communicate maths is using manim and copying 3b1b's cadence
Else why is everyone doing it if it isn't
inner finch
lolol
odd narwhal
Also using relaxing piano music is a.major key
vivid halo
videos on graduate level mathematics but using whatever animation script 3b1b uses
odd narwhal
I've seen vids like that nG
It's pretty neat but it feels extremely derivative
Wait were you agreeing with my point
vivid halo
conversely, Thurston would typically give lectures where he only drew pictures on the board, not a single number or letter
leaden torrent
read ega aloud but put random manim animations in the background
azure kettle
rancid meadow
taht is what every intro logic lecture is like slim
its just . an entire board of words
vivid halo
the fucking pi's with eyes scratching their symbolic heads looking at the sheaf gluing condition
odd narwhal
Is dry erase board fine
If you wave your hands too.much you end up.looking like a physics professor
rancid meadow
have u never followed ur prof around after class to ask them questions
thats what its like
they just talk
azure kettle
following profs after class is where the best stuff happens
vivid halo
seminar idea: you're not allowed to use any visual media, the entire talk has to be verbal
rancid meadow
that sounds fun ng
vivid halo
honestly yea
odd narwhal
Honestly I almost never look at the board when taking notes
broken scaffold
italians:
vivid halo
seminar idea: speakers are chosen on the spot, as a means of catching people unprepared
hardcore variant: you're not allowed to prepare your talks, they have to be completely improvised
rancid meadow
yeah i need to be able to gesture to talk about math tbf
odd narwhal
Profs reiterate the important points enough verbally rhat I usually just have ti listen and occasionally glance up
rancid meadow
but it would be pretty funny to try it as a joke seminar
italian moment
me too though
leaden torrent
new math party game
broken scaffold
that
odd narwhal
Seminar idea: no talking allowed, can't write more than a full sentence at a time on the board
leaden torrent
pick a person in the room and 2 random mathematical words
make them present a "talk" on those words
rancid meadow
lmao
vivid halo
I mean it can't be that random, otherwise you just get people giving shitty talks
rancid meadow
theres that website that generates things like that right
leaden torrent
"James, youre up for Harmonic Cofibrations"
rancid meadow
i dont remmeber what its called
leaden torrent
"Go"
vivid halo
odd narwhal
Ok let's randomly choose someone, say clerk. And let's just think up some random words
Uhhh
'Homotopy Type Theory'
Sounds silly enough
inner finch
lol
vivid halo
so funny story, I made a tweet about this hellish idea for a seminar and my advisor actually took the suggestion seriously and almost ran it
until too many people got intimidated by the idea
broken scaffold
odd narwhal
Your advisor follows you on twitter?
vivid halo
yes lol
odd narwhal
What was the idea
vivid halo
so I guess his interpretation of the seminar idea wasn't quite as brutal as what I was suggesting
I do actually want to try running the hardcore version and see what happens
hollow ginkgo
Was it about polytopes?
vivid halo
another hardcore variant: you're only allowed to talk about topics you haven't thought about for 6+ months
rediscover your memories as you speak
neat lintel
What if youβve never thought about it to begin with
vivid halo
even better
neat lintel
Hell yeah
vivid halo
neat lintel
2016 meme
odd narwhal
another hardcore variant: you're only allowed to talk about topics you haven't t...
I feel like these are my professors sometimes but try 6 years instead of 6 months
broken scaffold
neat lintel
I feel like that when helping in questions-0 sometimes
odd narwhal
Why specifically 0
leaden torrent
some of the weird ass conventions high school courses use man
azure kettle
sometimes I just go to #calculus and #linear-algebra and look at the latest question
to see if I can still do it
azure kettle
it's almost always intro lin alg questions
not that I think those are bad questions
odd narwhal
I do
leaden torrent
most of #linear-algebra is me being baffled by row reduction being nontrivial
odd narwhal
Intro linalg is taught badly in most places
leaden torrent
i still dont get how students struggle with it
azure kettle
I don't, lin alg is really different from all math most of those people have ever done before
odd narwhal
With too much emphasis on computation and matrix algebra without understanding the underlying structure
leaden torrent
i guess that makes me a bad LA teacher
azure kettle
I do hate computational lin alg being taught first
leaden torrent
cant sympathise with the students
azure kettle
I can sympathize with them, but can't empathize
odd narwhal
My uni has a proof based linalg course in the first semester
For maths majors
Also our calculus equivalent courses focus a lot more of theory and proofs than computations
That's how it should be honestly
azure kettle
row reduction really just is the exact same algebra people use to do simultaneous equations all of high school, but variables are swapped in favor of columns
it really don't be that much of an abstraction
odd narwhal
Fr
azure kettle
it is a bit baffling how some people just dont get it forever
leaden torrent
"whats the next step in the row reduction?"
"idk"
"well, what do you think will get you closer to upper triangular form?"
"idk"
"okay, lets take the 5 entry. how can you make that 0?"
"idk"
"theres multiple ways, you can pick any one you like"
"but what do i do"
"do you remember what the three basic row operations are?"
"yes"
"so which one will help get rid of the 5?"
"idk"
azure kettle
neat lintel
why does row reduction though?
odd narwhal
This is unironically me with smith normal form
errant kiln
if you want to solve equations, just use a computer
azure kettle
smith normal form is the devil's invention
neat lintel
I remember I saw that exchanging rows doesn't change the whole system of equation which makes sense
odd narwhal
We used it to prove the fundamental theorem of finitely generated abelian groups
broken scaffold
"whats the next step in the row reduction?"
"idk"
"well, what do you think will get you closer to upper triangular form?"
"idk"
"okay, lets take the 5 entry. how can you make that 0?"
"idk"
"theres multiple ways, you can pick any one you like"
"but what do i do"
"do you remember what the three basic row operations are?"
"yes"
"so which one will help get rid of the 5?"
"idk"
odd narwhal
The prof didn't wanna give the general algorithm cuz it's awful so we did a 'proof by example'
deep mango
idk
azure kettle
smith normal form's existence and usage in proofs is perfectly fine
smith normal form actual computations
is cancer
deep mango
what the fuck is a Smith normal form
odd narwhal
First question after that lesson was 'We're not gonna have to do this kind of bs in the exam right'
leaden torrent
"whats the next step in the row reduction?"
"idk"
"well, what do you think will ...
close that last fucking quotation bitch
odd narwhal
Thankfully we didn't have to
leaden torrent
or im banning
deep mango
What
deep mango
I thought that was Jordan or rational
Depending on the kind of decomposition you do of the modules
cold needle
(editado)
odd narwhal
I thought that was Jordan or rational
You use the structure theorem to prove the existence of RCF
neat lintel
cold needle
azure kettle
it's a diagonal matrix where each diagonal entry divides the next one down
deep mango
Oh
azure kettle
and it gives you like the minimal polynomial and factors and shit
azure kettle
which then gives you the jcf or whatever
it's really hyper cringe to actually compute the smith normal form by hand ever
the picture I posted is the only time I ever did it
azure kettle
it's just not a useful skill to have
like as long as you know that snf exists
and what it is
deep mango
Smf.
azure kettle
you should be fine
odd narwhal
Smdf.
cold needle
βbuilds characterβ
deep mango
Snf snf.
odd narwhal
Saturday night fLive
cold needle
j
odd narwhal
j
cold needle
kicked but then they came back posted one j and left
idk if they came back again tho
broken scaffold
k
cold needle
no
deep mango
like without repeating things and without editado
broken scaffold
clears throat
cold needle
nah
deep mango
C
deep mango
broken scaffold
fujjing normie formie
cold needle
oog
deep mango
I'm going to go shower
odd narwhal
Good luck
cold needle
have fun
odd narwhal
Be careful
cold needle
can i come?
odd narwhal
Yea don't accidentally slip and crack your head open and die
And make it look like an accident
bronze pelican
What's the opposite of extend?
south summit
restrict
broken scaffold
imtend
south summit
F
errant kiln
f
broken scaffold
F
bronze pelican
And you extend it by doing g βF
errant kiln
\circ F
errant kiln
foe
bronze pelican
Sush
south summit
β
errant kiln
coextend
bronze pelican
Would it be pretend?
south summit
south summit
I've seen it called pullback of F along g Not to be confused with cat pullbacks
F β g that is
odd narwhal
<:satisfiedblob:547119756768182282>
What does this mean
broken scaffold
odd narwhal
Compress
broken scaffold
unextend
devout nacelle
Contract
cold needle
squiz
sharp fog
Do you think math is misunderstood?
I mean people seem to think that mathematics is only all about algebra and calculus
hollow ginkgo
Yes
thorn brook
Trivago.
inner finch
hontel
thorn brook
bontel
leaden torrent
if theyre teaching a topology course.
pure sun
what do you mean by topology?
thorn brook
Yes. Students must praise 1 DONUT = 1 COFFIS CUP
pure sun
homotopy groups of spheres? no. but like, euler characteristic of 2D orientable manifolds? i guess you could, but why?
leaden torrent
how
just state it as a fact?
itll seem random af
and how do you assign like
homework problems
pure sun
i mean, that's how that level of math class is taught anyway lmao
but like, kids learn geometry
they learn things about like vertices, edges, and faces
leaden torrent
sure but what does a euler char exam question look like
if your kids cant prove
a euler? an euler?
an makes more sense
but looks wrong
pure sun
idk what you think middle school math exams look like anyway lol
pure sun
yes, give them some CW complex and ask for the euler characteristic
south summit
"State the definition of Euler Characteristic"
leaden torrent
pure sun
why sully, that's no less deep than what else they're being asked to do
it's all random anyway lol
sort of separately but also sort of related, i feel like middle schoolers could discuss questions like
could an ant living on a donut tell that it wasn't living on a sphere?
south summit
Isn't V-E+F=2 thing also called Euler Characteristic
Or are these the same thing
Somehow
leaden torrent
south summit
For polyhedra
rose dock
Should math teachers teach topology
math teachers should focus on teaching subjects that are an appropriate level to their students.
bronze pelican
1 donught = 1 elliptic cuve
2 donuts = 2 pentagons
rose dock
idk
icy forge
Topology of the set {{}} maybe
south summit
Excuse for field trip to trampoline park
icy forge
Excuse for field trip to trampoline park
Already covered by general relativity for high/midschoolers
south summit
rose dock
I mean even if you could teach your class topology
thorn brook
bro just give them this video like it's not even hard bro https://youtu.be/aewo8otGAAQ
icy forge
they'd be incredibly bored probably
BUT DONUT EQUALS COFFEE CUUUUUUUUUP
rose dock
neat lintel
south summit
COFFIS
icy forge
I mean that's the scam they start with
sharp fog
I don't mean teaching a full-course about topology.. I just mean speaking about it and let the children know that it exists and math is more than X and Y
thorn brook
icy forge
I don't mean teaching a full-course about topology.. I just mean speaking about ...
I think standard discrete math/proof stuff would do it
Generally a lot of students confuse applied math for pure math
thorn brook
I remember watching that video a loooong time ago and I was so incredibly confused lmao
bronze pelican
Learning topology to understand category's theory nonsense. Based motivation tbh
south summit
I hope you understand all of it now toki π
bronze pelican
Learning topology to understand category's theory nonsense. Based motivation tbh
At least you're not doing it the other way. Learning category theory to understand topology nonsense. That'd be cringe
rose dock
yes, but how would you describe topology to students in a way that is both representative and understandable
thorn brook
I do except for the motivation
leaden torrent
you dont
south summit
I do except for the motivation <:kekw:752021756650455061>
Motivation is nonsense
leaden torrent
every attempt to popularize topology has ended up summarizing hlaf a lecture of alg top at best
(with no proofs)
sharp fog
Abstract algebra topology analysis fractals non-euclidean Geometry. people don't know anything about them I just want to let people know that they are exist
leaden torrent
ONE DONUT EQUALS ONE COFFIS CUP.
devout nacelle
I think Tadashi Tokaida has an interesting Topology and Geometry playlist online, but it would still probably only be accessible to motivated HSers.
sharp fog
As a teacher
south summit
ONE DONUT EQUALS ONE COFFIS CUP.
I am motivated now
Manam
Did you watch the ring theory lectures
devout nacelle
Moldim
bronze pelican
The best motivation for topology is Poincare's original Analysis Situs paper
south summit
rose dock
noneuclidean geometry is a standard topic to go over briefly at my high school
devout nacelle
I'm working through groups rn
leaden torrent
π© β
Abstract algebra topology analysis fractals non-euclidean Geometry
wow fractals really hit me like a curveball there
south summit
I'm working through groups rn
In parallel?
rose dock
I don't think anybody is more interested in math after experiencing our short week of spherical geometry, probably the opposite.
leaden torrent
thanks for keeping me on my toes
bronze pelican
Poincare was so fuccking cool
devout nacelle
In parallel? <:catThink:526983414226747393>
The Algebra 1 course from IMSc is going in the groups->rings->modules progression so
When I get to the rings bit I'll go back and forth
south summit
devout nacelle
Also the linear algebra assignment by IISc is bruhhhh
bronze pelican
These papers provided the first systematic treatment ofΒ topologyΒ and revolutionized the subject by using algebraic structures to distinguish between non-homeomorphicΒ topological spaces, founding the field ofΒ algebraic topology.[3]Β PoincarΓ©'s papers introduced the concepts of theΒ fundamental groupΒ andΒ simplicial homology, provided an early formulation of theΒ PoincarΓ© dualityΒ theorem, introduced theΒ EulerβPoincarΓ© characteristicΒ forΒ chain complexes, and raised several important conjectures, including the celebratedΒ PoincarΓ© conjecture, which was later proven as a theorem. The 1895 paper coined the mathematical term "homeomorphism".
rose dock
I don't think the average high school student has any interest in pure mathematics, and forcing introductions upon them probably ain't gonna help
devout nacelle
I'll share
leaden torrent
if anything we should be actively disincentivizing pursuing pure math
for their own good
south summit
Let's start by cutting nami's funding
blazing pawn
Based
south summit
Change starts at home
leaden torrent
as if i get any funding
bronze pelican
if anything we should be actively disincentivizing pursuing pure math
Sounds like gatekeeping
leaden torrent
i should find some ridiculously specific techy niche and write a $20 program on a site i host with 2003-era html
and edit it into all the wikipedia pages
blazing pawn
Pog
neat lintel
Guerilla marketing
leaden torrent
this is what most hex editors are like
rose dock
discrete math might be cool to have in high school though
leaden torrent
and theres like 15 competing hex editors despite vs supporting it natively
so like
neat lintel
I never really look at my exercise solutions after I write them tbh
leaden torrent
there must be a market
for this shit
hell i could make a poweriso alternative that does literally the same thing except its "mount" button is in a more sensible place
and make a killing off that
devout nacelle
@south summit I DM'd Moldilocks
neat lintel
ill be your first customer
neat lintel
Wait no
south summit
<@853484697790447629> I DM'd Moldilocks
Then I check tomorrow when I am on pc lol
south summit
neat lintel
What is this coldilocks/moldilocks issue
south summit
People send stuff to moldi thinking that's my alt
When it's really saketh's alt pretending to be my alt
devout nacelle
inner finch
so true
south summit
So I would have to mail him and ask to forward whatever manan sent him and I only write mails from pc
neat lintel
inner finch
im being gaslit by wojak rn
blazing pawn
hm
azure kettle
sleek wing
12 squared :)
latent forge
This is yours? You building the pdf?
blazing pawn
Yes
latent forge
I thought there was some program so that you dont need to rebuild each page
neat lintel
I use arara
latent forge
nope nvm
neat lintel
But im not understanding what is so odd about this
blazing pawn
I think thats mostly at the length of the document
It is very long
and still expanding
neat lintel
Owo
rancid meadow
is that the stuff youre working on w the prof at columbia or whatever moth
hopefully not
neat lintel
anywhere but uoft
blazing pawn
No jesse its just ridiculously long atiyah macdonald notes
i have to email the prof later today and ask for topics so i can start writing lol
oh no this is just notes/solutions im doing on my own
Yea
well it will probably be something expository connected to etale pi_1 of curves
no schemes schemes scary
i am applying early to harvard
then if i dont get in i will apply ED to uchicago
blazing pawn
uchicago has like a second round of ED
yea im a rising senior
Woke
They probably are
latent forge
envied
cold needle
they are.
latent forge
do essays or regret
cold needle
state schools moment
blazing pawn
Lol i think this proof is invalid
Atiyah macdonald moment
i dunno if ill get aid
i guess ill see
Hope so
Money please
moneys pls
probability is scary
Hurb
a_i in A_n-ki
Ok but how do u knwo that the a_i x_i are n A_n
very true.
cold needle
my dear watson
blazing pawn
is it bad
Oh
I liked the DVR chapter
I mean its not really hard to understand
or written confusingly
_> he is just doing graded things
blazing pawn
why are u trying to bankrupt me
crystal stone
Lol
blazing pawn
but i am applying to berkeley yes
crystal stone
They have scholarships for talents
blazing pawn
I checked and i couldnt find any
crystal stone
UCLA has a full ride for a math scholarship
crystal stone
Rip
blazing pawn
blazing pawn
I did they said to ask again at the end of the summer
well i emailed the math dept
idk i dont remember who exactly
crystal stone
Go to department head
blazing pawn
Based
blazing pawn
Whether it is 2022 or 2026 is too far ahead for me to give you a definitive answer. I can only tell you that this is not an endowed scholarship which means the money is supporting this scholarship is not guaranteed. We go year by year and should have an answer for students by the end of summer for the Class of 2022.
this is how connie from math advising answered
crystal stone
Yeah Connie sucks
One of my former classmates came out as trans at UCLA
He runs an LGBTQ thing in math at la
Er she sorry
I am a little drunk
blazing pawn
@jovial ember 
crystal stone
One beer is enough to get me a strong buzz now
Work lunch break is almost over lol
blazing pawn
it seems like dimension theory would be important
to know
thats the last chapter so i should probably finish the book
i would be suffering less if this proof was correct
rancid meadow
yah
go to chicago
and become maryanthes student
idk if harvard has anyone
moth u can go and raid woodins office and publish all his unpublished results
blazing pawn
moth u can go and raid woodins office and publish all his unpublished results
its time
its for the greater good
rancid meadow
yeah hence why i said cringe ultra
i dont know any of those people
and clearly i know the field very well.
isnt mazur like a pop math author or smth
slim i dont know any other fields of math
or well
to the point where i would know names in the field
rancid meadow
moth do u want to do a senior thesis
does uchicago do senior theses
i wanna do a senior thesis but i actually dont know if anyone at uoft does them
rancid meadow
yeah but that list is bullshit moth so dont worry
blazing pawn
even if a place i go doesnt do them i can still find other ways to work w/ people
right
rancid meadow
set theory seems very male dominated
yeah
im sure you can just get a reading course that ends up being a senior thesis lol
blazing pawn
poggies
rancid meadow
its the same thing?
velvet dagger
Literally one woman <:monkaS:585602880434864138>
Wait what's the common denominator of these people?
Arithmetic geometers?
rancid meadow
they are in the logic group at harvard
velvet dagger
Why is Barry Mazur in that list?
velvet dagger
I though Harvard had exactly one logic person and that was Woodin
Well
Yeah
That's why this list seems very sketchy to me
rancid meadow
are there any schools in the US with a high concentration of model theorists actually
velvet dagger
Notre Dame?
velvet dagger
By high I mean like 2-3 or smth
rancid meadow
CMU sort of...
velvet dagger
But yeah I tend to think of logic as a midwestern thing
Notre Dame I remember from the visit having a good logic group
rancid meadow
its so weird that mcmaster has a bunch
rancid meadow
the only person i know at uiuc is marker
ashen pike
quick question - which channel should i discuss cellular automata, particularly rule 30?
rancid meadow
caroline terry? looks like they r at OSU now
velvet dagger
I actually came very close to going there lol
rancid meadow
looks recent
i wouldnt mind going to uiuc
there was a guy from uiuc that came to my talk lol
velvet dagger
Hegel you should ignore the top schools and just apply to UW Madison so I can be your TA
rancid meadow
idk if they'll want me at princeton tho
odd narwhal
What was the error
rancid meadow
also i dont want to go to princeton
blazing pawn
Dami ur a chill TA right
rancid meadow
he was an undergrad
blazing pawn
I dont want to go to princeton either tbh
velvet dagger
Honestly I prob won't TA you but yeah my students generically like me?
rancid meadow
i don't remember his name
blazing pawn
it doesnt sound like a great culture
nimble shuttle
i don't remember his name
serves him right
rancid meadow
What was the error
I was trying to describe a lexographic order on the first digit in Q and I said (3, 2) < (1, 2)
it was so fucking stupid
he knew what i meant
odd narwhal
Lmao what a bitch
rancid meadow
threw me off so hard lmao
odd narwhal
That's a pretty bitch move
velvet dagger
Also I may have tricked them into thinking for a second that their practice test (which was just for learning the tech) was gonna count for a real grade
And freaked them out for a moment
blazing pawn
what schools
velvet dagger
That was funny
blazing pawn
Tru
rancid meadow
harvard = chicago in my mind
blazing pawn
a lot of ppl get into uchicago from my school
rancid meadow
but hjarvard seems more cringe
blazing pawn
i might have a decent chance