#serious-discussion
1 messages Β· Page 442 of 1
they're still holy grail type shit for me
shutup nerd

oof
π
tterru moment
torterra
Wdym all iso theorems
i only remember first
all of them in one gigantic diagram
They're all first iso thm in disguise
for the memes
also 3rd iso best iso fite me
:yamin: moment
Wait how many for rings and groups?
i don't even remember them all 
$\begin{tikzcd}
G & H \
{G/\mathrm{ker}(\varphi)}
\arrow["\pi"', from=1-1, to=2-1]
\arrow["\varphi", from=1-1, to=1-2]
\arrow["{\tilde{\varphi}}"', dashed, from=2-1, to=1-2]
\end{tikzcd}$
Namington
shutup
third is G/H / H/K = G/K
without redoing all the arrows
quotient of quotient and corrospondence of ideals
oh yeah that one was kinda nifty
isnt that just lagrange theorem?
no that has to do with order
rip

second is G/H = K/(H intersect K)
its some composite homo meme
It is sometimes better to be in a group of less talented/experienced people
r u sure about that one lol
wait wot
Isn't it about doing the KH/H thing
K is just some random set?
yes 
well yes
wtf
it's when HK = G
everything closed or smth
I mean top 1% of some community colleges publish more results than top 75% of some Ivy league colleges
\begin{tikzcd}
G && H \
& {G/\mathrm{ker}(\varphi)}
\arrow["\varphi", from=1-1, to=1-3]
\arrow["\pi"', from=1-1, to=2-2]
\arrow["{\tilde{\varphi}}"', dashed, from=2-2, to=1-3]
\end{tikzcd}
Namington
no thats worse
i forgot what notation HK is is it HK={h.k in HK| h in H and K in K} for H,K subgroups of G?
yeah
universal property of quotients 
So if two sets added equal the big group then the quotient of their sum over one of them equals something?
Why r u talking like euclid 
Its natural speech
no 
Its stream of consciousness typing
hello woog
lol mizzy there was euclids axioms in the logic book
actually obnoxious
the language is so meme
ikr i think i know what u r talking about
i didnt even read that part
like in the peano axioms thing
my eyes glazed over
shonkie
also btw peano axioms trigger me
mizzie
peano axioms fucked so hard with my head
makes me feel v uncomfy
when i was new
give some examples
But why?
im new
Search mirzathecutiepie in the analysis channel
sift through the 3 accounts and mayble you'll find the thread 
The peano axioms themselves aren't too bad, the uh specific way it was done in the book was kinda dumb tho
+(a,b)
The other few accs 
wtf is minus???? omg
shutup ryc lmfao
how 2 understand piano axioms
-(+(a,b),b)=a
wait this isn't google
It was bcs i had trouble like seperating convention and understanding that u could axiomatize them
it makes me uncomfy cause like, i feel like we are defining N in a way that already requires you to know N
idk
Well yea we need intuition for the things we make rigorous 
they're inconsistent. you can't say on one hand that a fifth is a frequency ratio of 3/2 and at the same time is a ratio of 2^{7/12}
you need an IQ of atleast 80 to learn peano axioms
You need an IQ of at least 80 to learn to play cool piano songs.
what about the peano axioms requires you to already "have N"
langugelet
1,3,2,... as a model of the peano axioms where 3 is what we usually use for 2 and vice versa
or "know N"
Yeah everyone knows me 
π
no just like 6
or is it boring logic poo
just making the natural numbers rigorous
lay it on me mirzaalqt314
like we are defining it by doing s a bunch of time, but like, isnt us saying that a certain string of succ is different from the other needing us to count the numbers of succs
isnt that like
N
So we have like basically axioms that axiomatize addition stop u from wrapping around n stuff like that
How can two strings of succesions be different?
Since there is no inherent meaning to the symbols "1,2,3,...", we only care about how they interact with each other
Only if they arent the same number right?
ok but how do you know that they are different. you have to count the succs
or you can cancel the succesions out?
and I am saying that I am not convinced the concept of counting exists before defining N
matching them
you dont need to count to match and remove
remove a succession from each until no more on one
and boom
one bigger than other
0={}, 1={{}},2={0,1},...
well you just formulated order from canceling
If there is one-one correspondence between S and n then S is of cardinality n?
i feel like i need N to even say that one thing is bigger than the other
no u dont for naturals
just cancel succesions
sure
one string runs out first then its less than other string
I see
idk for rationals though
and you just say empty string != anything else
and we dont need any more than that hmm
i hev so mani pillows
ye
ok i think thats better actualyl
that helps
like i guess im so uncomfy bc like
its like you have a building
but then you are removing the ground floor
and trying to remake the ground floor

like, if the ground floor doesnt exist then what does you know what i mean
or maybe im naive
logickk
I get what you are saying
so i feel very iffy cause i feel like, i cannot use anything
ah yeah
I can can assure you that N isnt naturally concieved of in humans
u mean u feel uneasy bcs what if this doesnt make sense to u and it cascades over
kinda ig
There is evidence that humans counted 50,000 years ago
many anthropologists have shown that counting isnt natural
i like it, its v challenging for me to think of these stuff in this framework
if wildberger can do math then so can you john 
Yes it was invented
children were born counting bro
And humans as we know it didnt exist for that long
I was counting in the womb
or wait
I was counting as a sperm
am i missing 0s
how do u think i won the egg fertilization
mon i feel sick
superior math ofc
homo homo sapiens were around 30k ya or 300k ya?
what is the point of this 
counting isnt natural for humans
why 
The point is counting is somewhat natural
if they aren't natural then why are they called natural numbers
Its intuitive but not natural

idk i just woke up like this
π
sik time
are we allowed to say brainlet?
its messing with ur chemical balance in ur brain
Though I don't like Kronecker, I kinda like this quote "God created natural numbers, everything else is work of man"
sully
Though the quote is not true
π§
yes because god isnt real
I remember i did analysis for a month
tbh man isnt real
Yes that's one reason
was depressed and sick everyday
hea natural
And another is numbers are also an invention
john is literally me
we have already established this.
I kinda like that quote because, it atleast reminds us about starting point
If I assume 50,000 years ago to be a starting point
I dont associate with humans that old
ultra boomers
they probably thought they were the shit for counting maize or whatever
It's okay but still they were our ancestors
not mine
All human beings are related
so true...
By a classification
Infact all living beings are related
what is the relation...
I dont associate with β¦.
so true
Oh that reminds me
All share a common ancestor
very true nine9s
Everyone on this planet is related to each other
That's the reason for the name Earthling
everyone participates in incest.
I disagree
Distance between people matters
False

you cannot produce fertile offspring
I am talking about incest
entomology
so mules and horses can breed
look up arachnids
Mules and horses can breed
it happens often
but their offspring cannot reproduce
speciation is classified by ability to produce offspring, not fertile or not
and something else
i forgot the something else
Anyway this is bio
hmm pretty sure mules and horses are classified as different species?
yes they are
its been a hot minute since i studied this meme kek
like i remember some speciation stuff and i guess they did stop offspring
mules are infertile
but wouldnt something that made u have infertile offspring like
be a speciation event
it makes hybrids
hybrids are different species from parents
different species can have sex and concieve but its an unknown problem if chromosome pairing happens
and when it happens
you're such a baka π
Lets leave non-human animals, but I want to understand why people are hesitant in accepting that every human is atleast distantly related to every other human being
The African wild ass or African wild donkey (Equus africanus) is a wild member of the horse family, Equidae. This species is believed to be the ancestor of the domestic donkey, which is usually placed within the same species. They live in the deserts and other arid areas of the Horn of Africa, in Eritrea, Ethiopia and Somalia. It formerly had a ...
hmm i mean, probably some discomfort bc of socail expection of being related
Im chalking it up to concergent evolution and some interbreeding
But we are all homonids imo
but yeah we are all related its not too tuff of a thing to think about 
Yea we family
until you steal from me or block me on twitter
iβve seen this vine
hello cousins.
bruh
one of my friends made a math meme from it
sounds pretty 2016 to me
2014
i thought nine9s was making some surrealist joke about my use of ....
I was
indeed...
doubly paralleled entantre
so this is what it looks like trying to decipher what i mean 
my humor is imacculate
except one is not a joke and the other is
mirza is actually saying the n word in her name, mods just cut her off

what is going on
ping miza and type the letter right adjacent to u on a qwerty keyboard then press the enter key.
nizra
bruh mirza this is not okay
its ok

blacke mail
My name is going back to mirza
lol
good
what are you going to blackmail me with

inb4 getting blackmailed with math help 
u r reading logic
image of me pinging myself with letter i 
Mirza's career is over pray for her π
its fine i wont unleash the beast
i might show mods if im having a very bad day with analysis though
then they are gonna give me math help too
its not populr anyways
maybe math will be popular in next couple of decades
veratasoyum is doing a good job
"when will they make the ultimate undergraduate category theorist in danganronpa 4"
"that's mirza already"


LMAO
lol.
veritasoyum π
is pmath worth learning for fun
i have yet to watch this video
very excited
you can safely skip it
it's called set theory
lmaoo that thumbnail is great
wait was that the video where he said incompleteness led to the smartphone
what 
was it really that bad?
its a good video :
I haven't watched it so I don't know but from what I've heard it was one of the better popmath videos on incompleteness
I'm not sure if it passes the test though
there are no good pop math videos on incompleteness, sadly
that I have for whether an explanation of incompleteness is good or not
you could say youtube is incomplete in regards to that topic
if it includes the phrase "there will always be true things we can't prove" or any variation of it then it's probably bad
yeah 3blue1brown hasn't tackled the topic yet
4, tao's is 2, I have a mutual collaborator with tao.
That's what I suspected, most ppl in our generation will be 3 or 4
well
Those in the correct fields

Wait ryc do you have an erdos number
Ryc said it's soon to be 4
How do you fet research as undergraduate though?
Just spray and pray?
I don't think I have much hope of it being lower
Mine will be 69
I'm counting the paper that we just submitted
Given my fields of interest
Numerical methods, fluid dynamics, earth sciences, bioengineering
Do you submit independently or with prof?
But that also doesn't matter
With prof
He just decided to gun for top journals during covid
Cuz the paper is actually good
What topic?
we're putting holtz on the paper, i want a 3 or 4
i forget
Lolllllll
she might be 2
Really
Analysis/PDEs/Harmonic/Discrete/Probability/Convexity
Totaro has 3 lol
If we add Holtz we should also add Demmel
yA gettin' a paper out with papa burt
Oh thats a lot, how long it take to make and were revisions a long time?
well, it took us about 5 months working on the project together
To get the first draft of the paper going
π
We submitted that twice, got rejected twice
Then we put in some newer results we obtained, added like 8 pages
So we're hoping that having a longer paper will help
how the fuck do you write a paper more than 6 pages
Do you get a reason for rejection?
For ryc and I, have lots of graphs
Or is it like dating
We have more than 12 pages of graphs
i also have a lot of simulations for my thing
Yeah we did
In a 41 page paper
but none of them are directly relevant
It was basically like
Maybe 15 pages?
"What the fuck is this technique"
they're like "oh this looks cool oooh"
but they provide no help to understanding the proofs
It's a crazy paper
Why would it be a problem if you cite them?
Because it's just out of nowhere and it nukes away some interesting problems
But it's hard to see what the deeper meaning of the technique is
Or even what types of functions we have
So so do you have to write motivation for the technique?
Well, we have some motivation for it
And we were able to solve the motivating problems in some sense
But there are things we don't know, e.g. explicitly constructing a family of functions that satisfies our inequality
which relates to a PDE
Via some Brownian motion shit
IDK it's crazy
I wish
I only understand the parts I worked on
The broad overview of it is very hard to parse
any applications your thinking?
We had a few applications
We were able to get some sharper bounds on stuff
Sorry I don't wanna get too specific cuz dox
Oh ok well I pray for you

am I the only one who initially thought quals where used in the grad school admission process
Well...
I've had some people tell me I can show up & take quals as I'm applying
The University of Arizona department said I could do that
yea but they won't help your application?
it's just like, if you get in things will be easier for you
oh
but still that's nonstandard
brb asking harvard if I can do their quals instead of the GRE
Harvard's quals are 
Ridonkulous
You know what MITs are?
you take 8 classes
You pick like 2 or 3
and you have an oral qual on those 2 or 3 topics
that sounds alright
pov: you're taking harvard's qual exam
MIT just seems to be the superior school for PhD program
this is like an AIME question
Harvard might be better for undergrad
I only know one person that attended harvard for undergrad math
as long as Peter Sarnak is not the one asking the questions 
So my CC teaches up until Calculus on Manifolds brofib
There was this kid that completed that honors math sequence while in HS
have you seen the meme princeton qual transcript moonbears
back in the 90s, he got into harvard
I know a lot of people who went to Harvard for ugrad math
There was a math 55 group chat
And one year, there were like 20 people who took it
I wasted so much time
Reading those
I feel bad for Terry
And by graduation, 19 out of 20 had gone into quant
Was it the guy that said
"Of course I did well on elliptic curves, I went to harvard after all"
I thought you were a candidate
nUh
MoonBears life fucked up
MoonBears academic track fucked up
I like working on math and pretend I'm sometimes productive
Ryan Alweiss
But I got straight rejections this past cycle
Ppl told me that this cycle was just stupid

but it's pretty soul crushing and humiliating
I would have killed myself on the spot if I was in that qual
To see all my friends that will be starting their second, third, or fourth year of PhD
When I started at around the same age and time as them
R: Uhh well you can first assume there is a harmonic conjugate using Cauchy-Riemann
S: No don't use that.
R: Uhh idk. I know that it's some details.
S: NO!!! You should know how to do this, it's a problem for undergrads. OK fine use harmonic conjugates. How do you prove that it exists?
R: Well you can use Jensen's formula! OK that's obviously not allowed. Stutters and then talks about how you can do the simplest thing you can do to solve any differential equation, integrate along a rectangle once you know the derivatives.
S: ANY differential equation?
R: Well I meant that it is the simplest among all techniques that are used to solve differential equations, not that it is applicable to all differential equations. The word "any" is ambiguous like that.
S: You make so much commentary! Anyway, how do you prove the mean value theorem if you can assume a harmonic conjugate?
Fuck that
LOL
So demeaning
"You make so much commentary!"
I believe it's less than 100 and the last digit is 7, but idk where to go from there
I dont want a meanie advisor when i grow up
R: This is bad notation
S: No it's fine
R: But g is a letter of the alphabet so it's inside that product
S: Whatever
R: OK, then you can write this is as (gaba^{-1}b^{-1}g^{-1})*... so it suffices to show it for gaba^{-1}b^{-1}g^{-1}. Now uhh... ok this can't be that hard, like there are only O(1) things to try.
S: O(1) things! I like the way this guy thinks! Also I like your commentary.
R: Do you actually like my commentary?
S: No not really, it's kind of annoying. It's better to just think and answer.
R: Oops. I think commentary makes me less stressed.
Holt shit
:kms:
Was this done in comedy?
A: What can you say about solvable groups?
R: Proceeds to describe was solvable groups are.
A: What can you say about the commutator subgroup?
R: Uhh wait what's that? OK so commutators are aba^{-1}b^{-1}
S: Is that a subgroup?
R: Uhh no.
S: But they generate a subgroup. What can you say about it?
A: Is it normal?
R: OH YEAH
Wow you're citing specific chapter numbers now!
uhh, last digit isn't 7
Do people really talk loke this?
no, it's just a transcription
dang nvm then
Wow you're citing specific chapter numbers now!
I mean with the connotation
the units digit at least
R: You know I never liked integration by parts, I always preferred to guess the answer.
S doesn't like that I express my dislike of "integration by parts" even though what I mean by this is that whenever I am asked to integrate something by parts I just guess the answer instead.
S: Actually you know what? I want to make sure that you know what you are talking about, write some things down on the board.
lmao
HAAHAHA

oh I'm dumb I see what I did. So last digit is 3
A: What do you know about the permanent?
me: The permanent is at most 1 and at least n!/n^n.
A: Who proved that?
me: Two Russian mathematicians whose names I forgot proved that in the 70s.
A: Egorychev and Falikman, in the 80s. But good enough. A: State Szemeredi regularity.
R: states it
S: Use this to prove something.
A: Yeah prove Roth with it.
R: This will never get as good bounds for Roth as the Fourier, but anyway you can prove triangle removal lemma with regularity, so then you have to just prove the Roth from the triangle regularity. So given a subset you split it into three parts and you make a graph out of the set in this way. I'm definitely going to mess up the coefficients. Wait YES I think I have the right coefficients!
S is amused by the commentary again
Is he these master students or phd students
phd
now it's around 8.8*10^24 = 10^26 * 0.088 and to guess the 13 root of 0.088 you can do some (1 - x)^n \approx (1 - nx) shenanigans
When you know what you're doing
you can determine the ans from there
can confirm, I know who this person is and that is an accurate description
i feel like ryan alweiss' generals were brought up in this server before
They are both meanies though, or are oral quals supposed to be very serious atmosphere with little time wasted?
I only took one oral test
ehh they are more forgiving than you might expect
S gives some life advice to not be so colloquial. At one point during the complex analysis section instead of saying Cauchy integral was true if the region was simply connected I said it was true if there was no crap in the region! S said not to use the word crap in an oral exam given by 3 professors! S also said not to say that proving the harmonic mean value theorem was "just details" or to make other belittling comments. I agreed that this was good advice. D and I leave A's office, and A and S talk a bit more. Later I come back to A's office and A says that the generals went well (and S later also tells me I did well), but that I should be clearer when explaining things and also be less colloquial.
lol
That's socal vibes
R: OK so say you have g(aba^{-1}b^{-1}...yzy^{-1}z^{-1})g^{-1}.
R: This is bad notation
No it's fine
R: But g is a letter of the alphabet so it's inside that product
S: Whatever
R: OK, then
lmao
telling a prof
who is hinting that you should change the name of your variable or whatever
During your qual
"Whatever"
Isn't a grand idea
the professor said whatever
yea
Oh
prof said whatever
Rip
lol
ryan was being pedantic
I read it as R
Ryan was being hilariously pedantic as he usually is
he is pedantic
yea
but proceeds to say crap
whatever
S also said not to say that proving the harmonic mean value theorem was "just details" or to make other belittling comments.
It seems the princeton quals don't go that badly
yeah its annoying to speak like that
yea they're generally fine
I had an oral final from Garnett
He asked me to do something using riemann integration
instead of lebesgue
And I was like
Uh no thanks
lmfao
He forced me to do it
lol
I hadn't thought about Riemann integrals in so long
and then got mad at me when I couldn't do it on the fly
I passed, but I was like fuck
Wait
Should've prepared more
calculation is that different?
No, it was a theorem
Fun fact, that same question he grilled me on for riemann integration
ended up on my applied functional final that fall

Do some gradschools actually require you know some popular european language besides spanish and english?
because princeton transcript website has german word list
did some searching and apparently back in the days it was required to know some
french is a common one to learn
yea it's really easy
again you just need to know it well enough to like, translate a few pages of mathematical text fairly well
not hard
I don't even think Irvine has a language exam
I did years of college french for nothing
it would probably be pretty easy for me considering im a native spanish speaker
i mean i've been able to effectively interpret enough of french math text to understand it in the past whenever it's come up
you just need to do educated guessing
I should learn french by reading french math
le 1 + le 2 = le 3
Is studying math required in order to get good?
Yea definitely
get good at what
Un ring commutatif
anyone else have the frustrating experience of doing hard classes and getting not great grades, but upon finishing those classes you've improved enough that you actually could do well in classes of similar difficulty, but you choose to take even harder classes, rinse and repeat etc etc
i mean i learn a lot in the process but im pretty sure it's not the best strategy for getting into grad school. i fucked up my gpa refusing to take easy classes because im an arrogant little shit and i am having regrets pls yell at me and tell me im a dumbass
Sometimes doing a masters is an option. But yeah calibrate your grad standards accordingly
i've taken like 14 grad courses as an undergrad and gotten mostly B's. Last year i made the mistake of taking 3 grad courses at a time and got my ass kicked. i feel like i've put much more work into my degree than most math majors and genuinely learned a lot but dont have the stats to show for it :(. As a community college transfer I only had 2 years (well, I'm taking an third year to compensate) to learn the ropes and I feel like I've just now managed to hit my stride with courseload management etc, but now I have to start applying.
I've taken like 5 undergrad classes
well the core quals classes don't have that kind of grade inflation
but you are right, i did manage an A in an alg geo class despite not understanding half of it
also i'm on the quarter system so it's not like 14 semester-length classes
same here so far
i've been told the more advanced the class the more lax the grading
also since it's mostly grad students taking them, so you don't wanna put too much pressure on them while they're busy with TA duties and research
also a lot of them have like, take home tests
here all my tests were frontal this exam season
same
all exams were over zoom last fall
I had one timed math exam
but everything else was take-home
those classes kinda suck
same
and no midterm on one
but that's cuz of no budget for the maths department
ok then I had 1
easily the one I was most worried about grades in
but I ended up doing really well on the final exam
that's a graded assignment
oh
you meant including final exam?
I thought you meant JUST a final exam
oh damn
so just based on attendance?
that sounds kind of awesome tbh
just not having to worry about grades
it's like auditing a class except you get 100 at the end
basically here's my timeline of courses since transferring:
In my first year, I took the quals algebra sequence and the honors/intro grad analysis sequence concurrently. Both had timed in-class exams. Got an A in the first part of the analysis sequence and a B in algebra, then basically straight B's for the rest of the year. I had no time management skills basically. Literally came straight from community college calculus (and one course in abstract algebra i took at a nearby university) and self-study.
Then in year two, I assessed myself to have better time-management skills and mathematical maturity than the previous year so that I would've definitely been able to get all A's on a schedule similar to the previous year's. So I decided to take 3 grad courses the first quarter. Quals analysis, diff geo, and alg geo. Oopsie doopsie. Alg geo was a nightmare class that murdered me, diff geo was my last-min choice after the dude teaching complex was being an ass about undergrads taking his course. Ended up dropping diff geo in the final week with my one-time enrollment exception, passed quals analysis with B+, and got an undeserved A in alg geo.
Stuck around for quals analysis and alg geo part B in winter quarter, then school added new commutative algebra course. So still 3 grad courses. B in all of them.
Then final quarter I decided to drop the alg geo sequence because it was a nightmare. School had a course in noncommutative ring theory as part of the same sequence containing the comm alg course. Stuck with that and the quals analysis, and added a reading course in category theory. I was so burned out that I was literally studying like 3 days a week. Thought I was gonna die. was not fun.
Anyway, that puts me in my current situation
im having algebraicheadache
I'm convinced that I've finally found the right pacing that works for me after all the stumbling around but it's kind of late.
Also I'm not sure it matters, but I have ADHD. It's really been a struggle for me to get my shit together. I've lost my diagnosis from high school and I'm a little bit discouraged about trying to get rediagnosed as an adult.
anyway thanks for listening to me vent about my academic bs
Im similar to you
In that I get straight B+ A-
and all feel undeserved
and time mangement is WIP
and alg geo prof is bad lecturer
i think id like alg geo but the prof has failed me twice
he didnt operate office hours correctly was the worst part
I feel like most people suck at time mgmt, it doesn't seem like an issue that's really solvable or whatever either. By actively working on it you two are probably doing more than many other ppl would.
I feel like time management is a skill and I needed more time to learn it than most
Of course. What I mean is that being self aware enough to even recognize it as a skill is more than a lot of people lol.
This is a good thing.
I see. Thanks for the reassurance. I'm hoping next year goes smoothly. Never doing 3 grad courses again lol
Same. My alg geo prof was the nicest person but he suffered from the problem of finding everything too obvious to explicitly explain.
Is it just me or does alg geo literature in particular seem to suffer from this problem? My biggest problem was that many of the isomorphisms were established but never again mentioned explicitly even when it seems to matter what the identifications are
Well the alg geo prof was my undergraduate analysis prof for two semesters
during corona too
so im giving him some leeway
one day i will climb the mountain of alg geo and conquer it. but for now i just want to nap
I loved comm alg. ah gotta dive back into eisenbud's beautifully thicc book
dude no
do atiyah
atiyah is actually metal
like the exercises oh
metal as fuck
by metal i mean spicy and fun as hell
and i dont think atiyah problems are boring or vague tbh
thats just my opinion
So in the beginning of the class we were discussing comm alg books including Atiyah and my prof was like "I picked Eisenbud because I prefer books that are actually readable"
wow really
i thought atiyah mcdonald is like
one of the best readable texts ever
like i actually think its one of the best ive eever read
yea maybe thats an unpopular opinion i guess haha
okay he didnt have exactly the tone i'm presenting but he did actually say that lol
but i do have Atiyah and I plan to put it to use very soon
exercises are metal as fuckk
i stopped at chapter 3 tho π¦
turns out i have to know topology
asked me to draw spec(Z) and i was like what
wydm by draw u idiot
turns out im the idiot
i thought it was specZ[t], which is uh even weirder
reasons for this?
draw? lol
spec(X) is all prime ideals as basis or something?
whats a better text?
actually vakil
title pls?
Also I think it's absolutely atrocious that the most popular paperback copy is under 150 pages with the print quality of a rushed photocopy and they're charging like $80 for it
but i bought it, so what does that say about me
whats the name of vakil book?
rising sea
your saying this book is a substitute in ways?
yea
oh no
its called rising sea the foundations of AG
you can get away with normal ring theory
and point-set topology
localization stuff is self contained
that is the chapter about sheaves and stuff?
I mean if you intend to study more alg geo you could check out Eisenbud.
Im only asking because I plan to study hard for my first grad algebra class
but idk the book we will use and neither does prof
ill post the description
cut off part says theory of localization
and modules over PIDs
You definitely don't want to use a comm alg book for that.
atiyah macdonald doesnt give intuition for things at all
I mean maybe as a supplement but most of your learning will come from a general alg text like dummit and foote
I dont know what more there is to basic properties of rings fields and modules
like i only truly appreciate the things i learnt from it after doing some aNT and a bit of AG
what else do you think the class will talk about?
modules
i hope it wont be mostly review so im just curious
tensor products
oh yeah barely did anything with modules
exact sequences of modules and stuff
Is this a 1 semester course?
oh okay that's a more advanced description
completions are nice
this is second semester
you give ur ring a topology and complete it with respect to it
nah, they will use an a-adic topology
its similar to p-adic topology in Q
you generate ur topology from an ideal
oh
i might be
Is it sinilar to the thing about taking prime ideals as basis?
homological algebra 
sounds like a fun course
iirc you take the powers of an ideal as a basis
i agree
or something like that
or they just looked at maps and said hey what about ker/im ?
i dont remember all the details kek
do topology b4 homological alg
or else it will be completely unmotivated
im trying to do algebra topology and algebra at same time
thats a good idea nine9s
algebraicheadaches was saying 3 classes is too much
but im dumb
so ill probably get by with minimal grades unless i study now
It really depends on the classes
if they build off of each other i think it can be good to take many classes at the same time
ill post the class descriptions
but if its super disjoint then it might be better to take one of em later
I think I need most review for analysis though
too many new things being covered
and most unfamiliar
rn im only using Halsey Royden for analysis and Allen Hatcher for AT
but im moving slowly through both
that looks like a tough courseload. That analysis course seems to go right into functional analysis territory which might be a bit intense. But a good head start could make things way more doable so idk
im still slowly going though halsey royden and just got past definition for lebesgue measure
next sections are on integral
I would personally probably just focus on algebra adjacent topic on sem
and analysis the other
could you reorder so that a later algebra adjacent course is done this sem
yea
cause having a common thread in everything ur learning will make life much easier
wait ill pull up options
lie groups and lie algebra/algebeaic geometry are only choices
and alg geo has my accursed analysis teacher
i personally think id like analysis if I learned it with a different teacher
Lie groups can be nice to learn alongside the stuff
lie theory is so coooooooool
it sounds cool
but im not sure how detrimental it would be for me to disregard analysis and continue with algebra/topology related classes
I really am interested in analysis also, but im objectively worse
i disregarded algebra completely beyond a first course
i got my first B- from analysis
didn't impact my grad apps
also lie theory is analysis adjacent
you want a common thread in everything ur doing at a given time
that way you will learn each topic better
cause u see the interconnections
yes i agree since last sem i took topology,analysis, algebra
all second courses besides topology
lie groups is more topological memes than analysis 
ok i have questions then
I literally only ever took undergrad algebra
And I got into grad school without issue
say I decide to take algebra,lie algebra,algebraic topology for 2 semesters
I have 2 semesters left
what do?
oh these are for 2 sems
im truly lost after i complete those sequences but I have some cool options
well its really the question of what you want to do vs grad apps
bc as ppl are saying you will probably be fine with the classes you ahve
man
idk wq
Well with my knowledge as of today I feel like I really enjoy most of the topics I am learning, and feel like topology is the most interesting topic in general. However for my career goals I think that knowing a lot of analysis would make me very flexible in case I decide to go down another path. My goal is to eventually work as a researcher or do R&D/ Consulting for a company. The reason for me wanting to be a researcher is just out of pure interest mixed with dumb childhood dreams. I want to do R&D and consulting because it seems more stable and I will end up with transferable skills.
Also to add on I performed better in my topology and algebra classes compared to my analysis classes. So I have a strong case to continue
But you are saying that my choice should ultimately depend on what topics I want to pursue in grad school
Well I am saying do what class seem enjoyable cause you will probably be good w.r.t to grad apps regardless
god willing, thats my biggest fear. I just want to get into any school at this point because top schools seem too daunting
@latent forge good luck! also apply to a lot of grad schools, grad admits are a complete crapshoot
grad admissions are stressing me tf out right now
I dont know if Grad applications give waivers
I would apply to like 40 if I could get waivers
is there any extra benefit to doing a masters?
don't stress! you got this
ive been told no if you have the grad classes
I think you can usually get a limited number of waivers thru your school based on need. by limited i think it's usually like 4
thats poop
Thanks man! I'm trying to take it easy n stuff lately
also don't make my mistake and look into the actual application on the portal ASAP
sometimes you have to write a lot of random things on the portal
ahhhhhh i'm allergic to being proactive
dooo it. I know how scary it is
okay i'll probably look into it. thanks
but if you do it i promise it will not be any more difficult than a school assignment
btw how early do you start emailing profs for letters of rec?
and honestly it was easier than my undergrad apps
Oh, a few months in advance is good
Also usually you make that request through the portal as well
at least in the US π i dont know if its exactly the same in europe
but yeah probably give them a heads up that you want a LoR, then submit the official request through the portal, thats how it works here
what is LoR and you need 3 letters?
The state of Quora questions
oops i think i might have been misremembering. i don't think it's thru your school actually. i think different schools have their own thing
LOL ! - MEME
I swear some of these people have never been on the internet before
There is a dark and gritty Snagglepuss reboot.
I don't know who asked for this or why, but I purchased it and will read it.
same but i'm still a year away
but starting to stress right now
u will get through it

wdym by waiver
ah






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