It's not a good treatment of what it covers
#book-recommendations
sage python
marble rock
i wanted to read uptill special functions
and then leave multivariable calc
later
or never
tribal kernel
Monroe has a good book specifically on measures and integration that’s good
sage python
There's a book which as far as I can tell is a pretty solid synthesis of Baby Rudin level stuff, Spivak Calc on Manifolds, and basic measure theory+ stuff. Also some extra topics
tribal kernel
Yeah this one is wack
sage python
I've also heard good things about that ADPM book. And I think Luigi Ambrosio is one of the hotshots in analysis
marble solar
I'm still a fan of Spivak Calc on Manifolds
tribal kernel
Covers so many topics in 500 pages
marble solar
My go to for real analysis is the stein and shakarchi volume 3
sage python
So there's probably a case to be made for learning from the hotshot researchers
marble solar
Just because the treatment is well executed and the exercises/problems are first rate
sage python
Stein seems fine but I don't like the doing things twice stuff
Folland/Bass seem much more efficient
sage python
I mean point is that choice I hard dislike
marble solar
I prefer doing lebesgue in depth and leaving details out in general
tribal kernel
It’s kind of the foundation of modern analysis
sage python
I'd rather you treat everything from the beginning and then have Lebesgue as the important example
stray veldt
why even still do riemann integration
marble rock
learning about derivs and integrals
yea i am doing that actualyl
well im still at limits but meh
sage python
And then sure go and cover the very specific stuff about Lebesgue measure but
stray veldt
my analysis class rushed through riemann integration, because "you will learn lebesgue soon anyway"
marble solar
It's ok, I understand sloth king
tribal kernel
Work with measures, interpret functions as equivalence classes, then create an infinite dimensional vector space out of them
marble rock
cool
marble solar
I prefer doing abstract topology to metric spaces
sage python
But when the proof in special cases aren't particularly different from the general case
marble solar
but I'm the other way around for measures
tribal kernel
Then derivatives and integrals get nicer generalizations
sage python
Then I think it's bad pedagogy
To present it just in the special case
Since okay this fact which holds for a general measure is just a statement about set functions on sigma algebras, there's no other content
But this theorem actually needs the input of R^n
tribal kernel
Well maybe not nicer but more applicable certainly
sage python
etc
marble solar
I mean many courses cover something
like
"1,2, 6"
Anytime I've needed to use general measures
it hasn't been an issue
sage python
So that's why I tend to say avoid books like Royden and SS
marble solar
even though I've spent maybe 2 weeks on it in a class setting
I guess I'm looking at it from the perspective of
"Is there a difference after you've learned both?"
And the answer is not really
But I think lebesgue is easier to learn
sage python
I mean once you learn everything no pedagogy matters
sage python
But I think lebesgue is easier to learn
@marble solar And this is the statement that I do not agree with
marble solar
Well, I think there is a difference after learning both for metric space topology and point set topology
hasty turret
once u finish math
@marble rock good luck mate
marble solar
If you learn metric spaces first I think it hurts you
tribal kernel
Lol I’m doing the 100% speed run of math
marble solar
Since you don't really think about axioms in metric spaces
marble rock
can i ask a shower question
marble solar
It's ok to disagree, there's books for both of us to love sloth
sage python
Sure but even then once you learn topological spaces you'll have to eventually come back to grips with those axioms. Whatever awkward intermediates you think about will eventually be supplanted
sage python
I mean yeah it's fine to disagree, that's what we're doing. It's also fine to discuss said disagreements
karmic thorn
I agree with Ultra.
sage python
Lol
hasty turret
(It's 'I agree with Ultra here.")
tribal kernel
Shower question?
sage python
Wait but :0
marble solar
Maybe it's just me being weird cuz I almost always work in R^d
karmic thorn
@marble solar Any response to that problem yet?
marble rock
@tribal kernel what happens if you do like limits and convergence and sequences on other topologies
karmic thorn
Last time I saw there was just some more views and nothing else
sage python
mo2men: depends on how general you are
marble rock
and like define conergencre to a limit say l
if the metric is less than epi
for all n >n
N
like
what happens
do i get new calculus
sage python
I'm gonna say first countable and Hausdorff are the 2 topological axioms where there's not really that that much more to work with than metric spaces
sage python
I mean it's hard to say if you can even do "analysis" on metric spaces
tribal kernel
You instead of working with distance work with open sets. The limit of a sequence is the limit point of that set, i.e for all open sets around that point, it contains an infinite amount of sequence points
marble solar
Analysis is usually done on complete spaces
marble solar
Unless you're a freaking weirdo
sage python
Or at least a reasonable topology
And then you want some kinda linear structure
This I guess is more for differential stuff, integration is different
But yeah so, you can cast stuff like sequences and limits just in terms of open sets
tribal kernel
Also uniqueness of limits is not guaranteed by this definition in a non-Hausdorff space
sage python
And then make sense of it whenever you are able to make sense of open sets
But again you want 2 things to hold lest things go badly
As Squidward said you want spaces to satisfy a condition called being Hausdorff, in order for limits to be unique
(If a sequence converges to both 3 and 7 that's bad)
tribal kernel
In finite compliment topology 1/n converges to everything in R i think
sage python
You proved it in metric spaces
marble rock
yes
sage python
Hausdorff spaces are more general
And they're basically all spaces for which uniqueness of limits still hold
marble rock
bro wtf
when i read about those
this wasnt the definition
it was lilke
that 2 open shit arent in the same
region or something
are those the same definitno
tribal kernel
General topological spaces aren’t necessarily induced by any metric so we need a new definition of limits, this definition does not guarantee uniqueness
marble rock
wow
so like topology is motivated with
what can we do analysis on?
yet there is topology that has like
tribal kernel
Topology is the minimal structure where we can talk about continuous functions
sage python
I mean when you get sufficiently general with topological spaces you're no longer doing stuff that can reasonably be called analysis
dense pewter
is there any kind of "real math" where it's actually important to use nets instead of sequences
like, the vast majority of examples I know of nets coming up
dense pewter
are just spaces which are explicitly constructed to make nets necessary
marble solar
To get bounds
For your asymptotic analysisy stuff
No they aren't
Stop bullying me
It has the same word ok
...no...
marble solar
The world will...never know
sage python
Yeah that comes as a surprise to me I'd definitely expect net in the sense of everything within epsilon to work
marble solar
(It's definitely not the epsilon-dense thing used in Terry Tao's RMT)
(100% not that)
sage python
Wait but
dense pewter
so ultra that's borderline but yeah I guess I would count it as "real math"? like, as long as nonseparable hilbert spaces actually show up places
sage python
I'm checking page 127-128 of Tao's RMT
And that's exactly what he seems to mean by net
marble solar
What? No way!
dense pewter
my idea of "show up places" is not precise, but like if the only reason people care about nonseparable banach spaces is because it gives them a place to play with nets, then that doesn't count
marble solar
I didn't learn RMT from Terry tho, I learned it from a prof who learned it from Terry so he just did it almost the exact same way as that book
dense pewter
I guess like my exposure to banach spaces and functional analysis was just like
marble solar
Even though he didn't look at the book
dense pewter
let's solve optimization problems because we can solve pdes
in random sobolev spaces
and those were always separable I believe
marble solar
yA
dense pewter
also lol you are losing me again
ultrapowers are something else which I don't believe have any real use outside of logic
not that logic isn't "real math"
i'm half expecting an example that's just going to be some kind of model theory or something :P
I was right hahahahaha
sage python
Damn lol that was a funny exchange
dense pewter
I guess it's just hard for me to see because like, on the one hand I recognize that I (like any individual person) know so little math
but on the other hand
I feel like "if people actually used ultrapowers, why have I never actually seen them outside of model theory talks"
sage python
Buncho: so Charlie seems to be of the opinion that among "mainstream" math, nets primarily come up in making sense of the Riemann integral
Since if you're defining it as lim_{||P||->0} that's really in the sense of nets
dense pewter
dami that's not a bad example, although you can define the riemann integral without that
just like, sup of lower integrals = inf of upper integrals
marble solar
Wait
Sloth say more about that remark
I heard it as like mesh goes to zero or something
sage python
Yeah here I'm being specific about saying Riemann formulation, since the upper/lower integrals is "Darboux" or something
dense pewter
a supremum is something which exists axiomatically on the real numbers lol
marble solar
No not that
dense pewter
wait did ultra delete their comment
marble solar
it appears so
dense pewter
about sups being limits of nets
sage python
Moon: I'm pretty sure what's happening is that you have the set of partitions of a given interval
And then you're thinking of that as a net by inclusion
marble solar
I've never seen Terry at a whiteboard
dense pewter
oh I see
marble solar
RIP
sage python
But yeah other than that I haven't seen that that many nets come up. Mostly being in settings where I want to say that theorem X is true and being like wait fuck no it's not unless I replace sequence with net
And by settings I mean this one problem from Brezis
That me and my friends thought was trivial
Until it wasn't
I think it was something like
If E is a Banach space which is reflexive or has separable dual
Then there's a sequence living in the unit sphere which converges weakly to 0
And we were all like
Hold tf up
Didn't we show that the weak closure of the unit sphere is the unit ball?
How is this not too trivial for words? And where are these assumptions coming from?
And then we were like
Oh wait
Dual spaces aren't even first countable so technically you only know there's a net
The assumptions kick in to actually make it a sequence
Specifically if a Banach space has separable dual, then its unit ball is weakly metrizable
If you're reflexive, then you pass to a separable subspace. That guy is reflexive + separable, and then that implies its dual is reflexive + separable
So you reduce to the previous case
random spear
I can vouch for @marble solar UC’s like UCLA are straight time consuming for mental health. I also go to a small state university in california kinda close to moonbears, and my time with the math department have been amazing compared to what I hear happens at some UC’s. One of my professor’s had a social gathering with both his grad and undergrad students at an outdoor bar. I went and it was a fun time. A lot of the professor’s at schools like these treat students like friends and we have a pretty close knit math community. Yah they might be tough during class time, but as a prof outside of class time, you sometimes get to know them on a personal level; and ofc they always lend a hand with trying to help their students succeed and put their time aside to make sure it happens as long as you put the effort in as well.
@shut grail that excites me :)
At least the last part. Do you think this applies to specifically California state unis or just California unis in general
Oh shoot sorry Moonbears, I didn't get rid of the ping.
My bad 😅
marble solar
I know it applies to Caltech, Stanford, MIT, UCLA, Cal
I've heard nothing but wonderful things about: UCSB, UCSD, UC Davis, etc.
So just play it by ear, get info from people that attend schools
random spear
Thanks. Sorry if I'm asking a lot of questions Ig I'm just really nervous about screwing up/falling behind Ig.
shut grail
You’ll be fine m, And you’ll know what feels right ultimately.
random spear
Thanks :)
gray gazelle
What book(s) would you people suggest for learning second order Differential equations non homogeneous DEs etc
Any opinions on how Courant's Differential and Integral Calculus compares to his Introduction to Calculus and Analysis with Fritz John
granite sluice
https://youtu.be/IS9fsr3yGLE
@sweet lotus This was a good talk, thanks. 🙂 The bridge between continuous and discrete things is one of the best things about math, imo. The connection to voting theory is also pretty interesting. Unfortunately I only vaguely understood the example applications he gave. 😦
Well in particular the polynomial regularity lemma seemed kind of unmotivated to me, so I skipped over the proof. 😐
maybe I should give it another shot lol
The Szmerdi <-> Furstenburg connection he sketched was really neat (though his ink started to run out and it became hard to read some of the exponents...)
no it wasn't that
that's Ax-Grothendieck
it was something about polynomial rank
expressing degree d polynomials a function of some number of degree < d polynomials
it was unclear to me why someone would care, beyond it being a question that one could ask
the Szemeredi regularity -- ok, well I'm already convinced the arithmetic progressions are interesting objects because of Dirichlet's theorem.
lol, ok
He mentions at some point that ultraproducts are boolean schemes -- I guess he means like Spec of a boolean ring?
The connection isn't really clear to me though
Principle opens?
Or maybe closed sets?
Closed would maybe make more sense, bc intersections.
No but all the points are closed
yeah
one sec
it was one of his "but dont worry about that" moments I think
Ohhhh
"avoiding schemes?"
14:06 (wrong time!)
misheard
not that I know what that means
actually I can't tell
avoiding is the subtitle
sry 16:06!
omg
lol
VOTING schemes
ok
not Boolean schemes lol
but yeah the voting scheme connection is super interesting
oh, makes sense sort of
like the "eventually constant"
or, equivalence classes of things that are eventually equal
or, well in the ultrafilter context its "equal on an alpha-large subset"
which is not quite the same thing
(alpha was his ultra filter)
but in a funny way, since 'evens' can be eventually but 'odds' not
You mean something like, if I have two sequence of things, then picking different ultra filters can produce non-isomorphic objects? I think that makes sense, along the lines of what you were saying. Tao mentioned a theorem to the effect of "any first order predicate that is true on an alpha-large subset of your indices will be true in the ultralimit", so I think one could use that to make such an argument precise.
(E.g. the predicate being 'the object is empty' and taking an alternating sequence of empty set and singleton sets)
Sorry my phone died.
@sweet lotus Sorry for your loss.
Logic is cool stuff. I'm glad I'm getting to learn more.
I finally learned a proof of Goedel's theorem (about how there are sentences in theory of natural numbers that are not provable in PA) a few days ago!
The next chapter does it -- the book gave Turing's proof, which is pretty natural for a tcs-informed kind of hindsight.
The main idea is to show that membership in theory is undecidable, by a reduction from the Halting problem. But since all the sentences that can be proven in PA are recursively enumerable, it can't be the whole theory.
And the fact that such a reduction exists makes a lot of sense -- it's a lot like the Cook-Levin theorem. (Essentially even the same idea, I think, but not paying attention to time as a resource.)
quick hornet
thats a very elegant argument yeah
honestly godel numbering always felt a bit... overengineered? thats probably not the best term
since its a useful tool and you cant go without it or anything in proofs that rely on it
but its certainly creating a loooot of structure that you then proceed to just assert one thing with and toss out
which always felt a bit strange
i definitely prefer more halting-esque arguments where possible
granite sluice
Yeah I think that was what was intimidating about it, lol.
I'll probably read it at some point. Seems like a good idea to understand, even if I'm mostly interested in relatively small complexity classes, haha.
quick hornet
its a very impressive proof strategy for the time though - hell, the idea of sort-of encoding a logical system in the integers is IMO a very early hint at a lot of the ideas that would motivate computer science in coming decades
even if i certainly wouldnt call godel a programmer
granite sluice
Yeah I agree! It's super cool.
Apparently Goedel has a letter where he suggests the P vs NP problem
earnest glacier
gray gazelle
Try searching for a pdf before buying it
hasty turret
Do you know libgen? @earnest glacier
gray gazelle
They save a lot of money
subtle shoal
restive raptor
What's a good very gentle book for someone who hasn't done math in a while to get into problem solving?
karmic thorn
Zeitz is great but I'm not entirely sure if it's good for everyone who's been out of touch with maths. It's definitely great for people who enjoyed doing maths previously, but others may be intimidated by the difficulty of problems.
slender sphinx
I loved the book so i can second the suggestion
gray gazelle
Agreed with Ted
karmic thorn
flint forge
id suggest hartshorne
hasty turret
I agree with Ultra here.
restive raptor
@flint forge what's the title of the book?
flint forge
oh i was memeing
hidden abyss
yea i read it before it was a pretty good intro to problem solving
gray gazelle
pst
gray gazelle
role for the secret club
limpid granite
good stats textbooks?
warped cedar
limpid granite
introductory
limpid granite
Nice ty
limpid granite
nahh would prob be a nightmare to ship where I am
tribal kernel
I used Mathematical Statistics by Wackerly Mendenhall and Schaeaffer when I was an undergrad
heavy barn
Does the HoTT book have any prerequisites? I.e. can I read it even if I don't know much topology, category theory, or type theory?
quick hornet
from what i've seen, you don't formally need anything besides some intro algebraic topology, but it's strongly recommended that you have experience with category and type theory, particularly typed lambda calculus
such as familiarity with the basics of kan complexes
and knowing as much logic as possible will help motivate it
but honestly i dont know why youd be particularly interested in reading the HoTT book
unless you're planning on doing proper research in formal logic
its a pretty niche subject within a pretty niche subject
heavy barn
Idk, it just looked interesting
I don't know any topology so I probably won't want to learn about it now
Thanks for the info!
unkempt grove
can i post book requests here?
unkempt grove
aight. anyone got the solutions manual or correct slader site for "Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds"?
somber mica
does anybody have any recommendations for introductory texts on mathematical logic? so far I've heard very good things about A Tour Through Mathematical Logic, by Robert Wolf
marble rock
mathematical logic by shoenfield
only prereq is basic math and like some basic concepts
in algebra
tight crag
@somber mica i think enderton is good
magic wasp
Spivak vs. Baby Rudin vs. MIT OCW 18.01
Background info: Over the summer, I went through a little more than half of AoPS Calculus but found parts of it kind of easy and it didn't feel very rigorous so then I stopped to grind olympiad math. I heard Spivak is a good calculus book, but I don't know if I need this after AoPS Calculus. I've also heard Baby Rudin is good, but will it be too hard? Also, is it recommended that I do Spivak or MIT OCW 18.01? This is probably irrelevant but I'm a high school freshman.
tight crag
Do spivak
@magic wasp do you know the proofs of the basic theorems of calculus from AOPS calculus (eg intermediate value theorem, extreme value, mean value, FTC)
magic wasp
I know the proofs of Intermediate Value theorem and extreme Value theorem sort of but not FTC
tight crag
Oh really, that's interesting
I would still recommend doing spivak before you try rudin
What proof do you know of IVT?
I'm always curious how people prove that stuff without using words like connected and compact
magic wasp
I don't remember all of the details, but I can sort of remember the structure of it but I'm not sure I understand all of the stuff in it, so I don't think I can say I fully understand it.
tight crag
Oh ok, in that case you should definitely read spivak
magic wasp
Would it be reasonable to skip to chapter 5 of Spivak since the first four aren't calculus, or should I read them anyway
magic wasp
Ok thanks so much!
karmic thorn
Need book recommendations for combinatorics at an elementary level. I'm looking for a text which doesn't assume background beyond HS maths but has a lot of proof-based examples and problems. (Is AoPS good enough?)
steel viper
@magic wasp I second spivak by a lot, I'd say it and AOPS serve fairly different functions. Also the first four chapters of Spivak are essential so I highly recommend not skipping them like liquid said
tribal kernel
My sister used Alan Tucker’s Applied Combinatorics as a freshmen in undergrad and I believe she enjoyed it
karmic thorn
Thanks, will take a look at it!
civic carbon
Brualdi is my favorite intro combinatorics text but it is stupid expensive
karmic thorn
XD
civic carbon
yeah, that's why I don't use it when I teach combinatorics
but if the cost of all books is equal, it's the one I'd pick to meet the description of "intro friendly"
and then for more advanced combinatorics I like Van Lint and Wilson
(though that book is more of a reading book than a textbook, I would say)
civic carbon
yeah, Van Lint and Wilson is just gorgeous.
sage python
Also I just came up with an idea to get out of the pickle I'm in re AG
I'm kinda behind and too busy to catch up well, also the lecture format isn't great for me. Also the psets are graded on completion
civic carbon
just cite a random result from Beauville even though none of the hypotheses apply and mischaracterize the conclusion
sage python
So I'm just like yo
civic carbon
it's what everyone else does.
steel viper
dami i might be doing a research project thing in topological combo lmao
i guess combinatorics got me after all
sage python
What if I just ask my prof to diverge from the lectures a bit and work straight through either Liu or Mumford-Oda or something
And do some problems from there in lieu of the assigned psets
civic carbon
working through Liu did a lot of good for me. I did not find Mumford-Oda quite as eye opening as others have. Though Eisenbud and Harris is a spinoff of that project and I consider it a godsend
steel viper
are we talking AG books
sage python
Project?
steel viper
yeah something like that dami
i think its probably going to be baby research but itll be fun i think
he told me to read this book on the borsuk ulam theorem and applications to combinatorics
steel viper
maybe :D
civic carbon
Yeah, Mumford's original Red Book was a project with lots of hands trying to address the difficulty of learning algebraic geometry. The Mumford-Oda book that got passed around by literally photocopies of photocopies of photocopies was sort of the "last remnants" of the project post the Red Book. It was interpersonal drama, and if you know anything about the people involved, you know who with.
sage python
Zeta: yeah I guess I don't have a particular preference I'm just hoping for something that I can work through linearly and somewhat efficiently
civic carbon
But Eisenbud and Harris, eventually published just a small piece of the other stuff as Geometry of Schemes
sage python
And that gets to the point, so starts with schemes
Hartshorne just feels like too much of a slog for me
civic carbon
I think, unfortunately, "work trhough linearly" is not ideal
"You can understand how to do every exercise in Hartshorne and not have any idea how to do any meaningful AG" is what my faculty all told me.
have you tried Vakil?
if I were doing it today, I'd try to linearly work trhough Vakil
(in fact, I start doing that every now and then)
steel viper
that is somewhat terrifying zeta
sage python
Vakil also, I guess it feels like Liu is a bit more efficient/quicker?
steel viper
i still am not sure i understand what AG even is
marble solar
It's a strange subject that has fingers all over modern math
sudden kindle
True
marble solar
Anything you're interested in, there's probably some AG trying to make a connection
Yeah we need border patrol to keep analysis clean of algebraic geometers
In all seriousness though, there's a lot of routes into AG
Hartshorne looks like has fallen out of flavor
steel viper
the end of an era
sudden kindle
They still use Hartshorne in my school
marble solar
Cal?
sudden kindle
At least the instructor did last semester
steel viper
monkaS
marble solar
I almost did a reading course on AG where the prof was a student of Hartshorne
but then I did 3 manifolds instead
So womp
sudden kindle
Lucky?
steel viper
being in state for it
sudden kindle
Yeah its pretty nice
civic carbon
I think Vakil is a lot less messy than Liu. Liu has a fixation with stating things in the maximal generality, which is great as a reference and gross for learning, because instead of saying something is true about maps of varieties, you get a list of the dozen pieces of the definition of variety that are sufficient
marble solar
On the other hand vakil doesn't touch varities for 300 pages or so
civic carbon
yeah, pedagogically I think AG should start with "Curves and surfaces"
but no one really does taht.
Liu randomly the last chapter is about curves.
marble solar
My MS institution did a semester of algebraic curves a la fulton
Then did a semester of Riemann Surfaces
Oh yeah, CSULB
civic carbon
I think that is an excellent start. It's slow, but I think faster in the long run
marble solar
Murray taught the curves, Brevik handled the Riemann Surfaces
civic carbon
and gives you way more understanding
I do think Miranda does curves and Riemann Surfaces pretty well in one volume
marble solar
That's what Brevik taught out of
civic carbon
(though note: when I say curves and surfaces, I don't mean Riemann Surfaces, which confusingly are curves not surfaces)
civic carbon
the fact that there are two really natural anwers to what dimension C is causes all manner of confusion, yeah
marble solar
I had Terry Tao for 3rd quarter complex, where we did Riemann Roch and what not in 2 weeks
I thought it was too fast for any of the ideas to really stick
It was more like "Here's this and this and this use it to solve these problems"
sage python
Man someone should just write the ultimate AG book that subsumes them all tbh
civic carbon
I'm completely biased, but I think Elliptic Surfaces are a great thing to learn to build broader intuition.
gray gazelle
stacks project
marble solar
Stacks project isn't where you go to learn
sage python
Well, the ultimate book that's good in a class
It feels like the current books are like
civic carbon
If I wrote an AG book, I would try to do the opposite, and make it as narrow as possible haha. Llike Harris' examples in AG, but for arithmetic examples
sage python
Hartshorne, Vakil, Liu, Gortz-Wedhorn
marble solar
The more math I learn, the more I appreciate narrow books
sage python
And then a few like Mumford-Oda and all
marble solar
I think AG is a super interesting subject, I just hate abstract algebra
I really like the geometry
sage python
And like none of them is really "the correct choice", not even once you input your background/goals
civic carbon
my best advice for learning AG is to try to think about commutative algebra the absolute minimum amount you can
because when you are doing AG, you are never going to do commutative algebra
marble solar
There's jut all this cat theory, field theory and stuff that I have almost no interest in
civic carbon
(here by learning, I mean, "learning with the specific intention to use what you learn for research")
sage python
Hartshorne requires you to finish a full blown commalg book before touching it, is a huge slog, and doesn't do things general enough for arithmetic folk
Liu doesn't really do enough cohomology, and apparently is a mess
Vakil feels like it'd take 2 years to get through since it's long and mostly problems
civic carbon
yeah, it is disappointing that for how disgusting Hartshorne is, it also does not actually give you any usable results 😛
civic carbon
Harder is good for cohomology
sage python
Like damn can someone just write something that you can go through in a few months to a year
civic carbon
although his order is REALLY weird
I always like to say, I was in grad school fro 5 years, and three of those years I took a year long algebraic geometry course, and I am no where near as comfortable/fluent with it as I would like to be
also, fwiw, Eisenbud is a great commutative algebra book for those rare occasions where you actually need to understand something about commutative algebra.
sage python
I mean yeah at some point you're never fully comfortable but, I feel like there's a way to just do it over a year and you're more or less capable of doing things. Like if you're AG-adjacent like me, you can just jump in and pick up some specialized topics as you need them
If you're actually doing AG straight up you can more or less start thinking about problems
etc
Like idk I feel in analysis for example
civic carbon
also, Silverman's Elliptic Curves is a great place to get some intuition for AG. Also Hindry/Silverman Diophantine Geometry.
sage python
You do Baby Rudin, then something equivalent to big Rudin, some functional analysis, and now you have a clear path for whatever research thing you're doing that's analytic
civic carbon
I think it is clear taht Silverman does not like algebraic geometry, per se, but it is useful to a lot of stuff he does like, so he uses it in the places where you really see it's power.
marble solar
Zeta why did you leave LB? You could've taught some cool courses man
T_T
It's alright
gray gazelle
what's LB?
civic carbon
I never taught there actually. When I first applied I was their second choice, and when I applied the second time they were my second choice.
marble solar
CSULB is a public university in Long Beach CA
civic carbon
with one of the friendliest math departments I've ever seen.
marble solar
With a small math department, but the community is great
Recently, LB started attracting exceptionally talented students and many of them are now getting into good PhD schools
gray gazelle
30k students 
marble solar
But the math department is small, with few active researchers
sage python
Harder actually looks pretty good @civic carbon
civic carbon
Harder is difficult, but I found it very rewarding to work trhough.
but yeah, Fulton or Miranda will tell you about curves, and for a lot of applications, curves are all you need
or at least will give you a foundation to think about higher dimensional stuff.
sage python
I guess I'm sorta in that Langlands adjacent region where it feels like I'm pulling tools from AG but not doing foundational stuff
civic carbon
never be afraid to blackbox things
sage python
So that's why I have such a weird relationship with it, the "meat" of AG seems really cool
But like fuck the whole quasi-separated morphism of finite type over blah is quasi-compact etc
civic carbon
Hot Take: The cool thing about algebraic geometry is that it exists. Just don't look too close or it gets disgusting.
sage python
Stuff like algebraic groups, elliptic curves, complex geo, Hodge theory, moduli business
That all seems fantastic, and likely relevant
civic carbon
something something modularity conjecture
sage python
Morse theory is fantastic
I think one prof here at least partially thinks about stratified Morse theory
civic carbon
yeah the parts of algebraic geometry I actually think about are pretty removed from the "These are the sixteen definitions of the dimension of a scheme" part
like probably Jacobians are the nastiest things I work with, and just knowing a theorem that says their basic properties is really enough (though proving it has a variety structure is godawful horrible)
steel viper
tbh i dont even know what the proper prereqs for AG are
hartshorne only needs atiyah macdonald right
marble solar
No one does
Eisenbud is like the "proper" one but as @civic carbon said doing Fulton and Miranda
and then going into elliptic curves
civic carbon
I think what the prereqs are depends on your meaning of the word "understand" is.
marble solar
Seems to be a good way building up your senses
civic carbon
(I mean that non-faceitiously)
marble solar
And then after that just let yourself loose
steel viper
ive tried to do number theory but i just bounce off
marble solar
You don't need any
sage python
You don't number theory to go into AG
steel viper
isnt the elliptic curve stuff NT related?
or is it just applied to NT and the foundations arent
civic carbon
Elliptic curves are everything related.
marble solar
sage python
You don't need need the NT side of the picture, elliptic curves are more applied to number theory than use number theory
civic carbon
They originally showed up because of calculating certain integrals that pop up in physics.
sage python
Especially if you work over C
So basically AG is a subject which is enough of a slog that going into it you ask why do you care?
And the answer is gonna be one of a few things
civic carbon
yeah, modular forms are a moduli space for elliptic curves, so if you grant that modular forms are important, then understanding elliptic curves is important.
marble solar
Is there a relationship between elliptic curves and elliptic PDEs?
gray gazelle
not liking nt is sad
marble solar
That's probably a stretch
steel viper
i dont know any of these things
sage python
Either you like geometry, commutative algebra, number theory
steel viper
civic carbon
I mean, the way you prove this stuff about elliptic curves over C is through differential equations.
steel viper
inb4 "no one likes logic"
sage python
Well, does AG give to homotopy theory or mostly take?
sage python
Analysis maybe but that becomes a bit of a stretch, like you need to be in some mad specialized parts of analysis for AG to matter enough to go through in any real depth
marble solar
Some of the exercises can get a little hairy
steel viper
ugh ill get into it eventually
the list of books i have to read grows so fast
its insane
marble solar
You'll be able to dwindle it down when you get to Uni and you find more about what interests you
marble solar
I think analysis is the most intuitive of them all
sage python
I feel like the "typical analyst" who does like, geometric measure theory or harmonic analysis on R^n or something
Oh I guess I had that in mind under geometry
Like complex geo
marble solar
several complex variable analysis is a book by hormander
sage python
I feel like the typical people who think about reductive groups are either algebraists coming at analysis or they're in the "mad specialized" category
marble solar
In garnett's words
"Several complex variables is a dead field and there's nothing interesting in it. I have friends that devoted their lives to it, and nothing came of it. They would kill me if they heard me say that"
steel viper
well thats unfortunate
sage python
I mean I guess I wonder how much of a distinction people tend to draw between complex geo and SCV
marble solar
Garnett is a man of strong opinions and even greater passions
steel viper
what even is an example of a dead field
marble solar
Euclidean Geometry
steel viper
lol
sage python
I feel like both are definitely a thing but for different reasons, one is very PDE and the other is more diffgeo/AGish
steel viper
btw dami what happened to your anti diff geo screeds
sage python
Diffgeo still sucks don't worry
marble solar
I think if you met Garnett it would become clearer
steel viper
lol
marble solar
Bruh he's like 85 years old
sage python
The more I talk about diffgeo the more I remember that it's now a highly non-trivial part of my scope
And the sadder it makes me
You think 85 year olds are exempt from being called plebs when they do pleb-tier things? @marble solar
marble solar
He once told us he rejected a student from coming to LA because the student liked Category Theory
sage python
Okay this is where I'd consider forcing someone to retire
steel viper
thats a dick move
sage python
Honestly everything you told me about Garnett makes me think he's just bad
Slow at teaching, stupid but strongly held opinions
Like it's fine to have strong opinions if you're right but
marble solar
Like there were office hours where you'd go in ask a question
He'd sit down and think for 40 minutes
Not saying anything, get up to the blackboard
and solve the problem
steel viper
??
marble solar
It's not something you can understand without knowing him. I admire him greatly
sage python
He almost feels like he's going senile but still thinks he's got it in him or something
slender sphinx
hello moth
sage python
Or really he's just a hyperboomer probably
steel viper
hi poco
slender sphinx
do i call you sloth, moth, or hegel
marble solar
Definitely a hyperboomer. He told us once that the way to learn math is lock yourself in your apartment with books and papers
Don't talk to anyone
slender sphinx
which do you prefer
marble solar
Don't go to lecture
marble solar
It's ok, he's already retired
sage python
Ah that's good
marble solar
But he'll always be a legend
sage python
Honestly I wonder if Princeton's old policy of saying everyone retires at 65 is a good one
If Chicago did this we wouldn't have Peter May which would be vsad but
marble solar
I mean the UK still does that no?
sage python
No clue
steel viper
tenure was a mistake
sage python
I'm fine with tenure in general modulo, they should be much harsher on the "misconduct can get you kicked out" side
steel viper
i wasnt being serious
sage python
Apparently even sexual harassment type stuff doesn't always cut it for booting people out which is just garbage
steel viper
i dont have enough exposure to academia to say anything about the quality of tenure
ivan talked abt that dami i think
its why he quit his phd program
sage python
But for the most part I think it does 2 things. One is it attracts talent, since academia can't really compete with industry in terms of pay a lot of the time
slender sphinx
mfw ignored by sloth
sage python
And it does give some kind of independence to academics, which I think is overall a good thing
sage python
My class vaguely ran out of Brezis
sage python
Also we were recommended Lax and this one online thing
Buhler and Salamon
But at the end there was one by Einsiedler and Ward which my prof said he'd use if he taught the class again
marble solar
That's a crazy first chapter
I have stein and shakarchi volume 4
But it doesn't seem like it's interested in doing functional and more interested in doing harmonic stuff
or probability
sage python
Oh yeah I remember being confused by it
sage python
Lol for the most part the books all don't seem like my style
sage python
Fourier I'd prefer just waiting to the measure theory, complex seems like it's afraid of topology, and what the fuck is with the toy contours
marble solar
The complex one is notoriously bad
For that reason sloth
But there are other good topics in there
sage python
Real I've talked about before, and functional idk but yeah contents are bizarre it seems
marble solar
A lot of the early chapters are a simplified version of stein's harmonic analysis book
like the calderon-zygmund decomposition
Yeah, but the first 3 chapters mimic the beginnings of Stein's harmonic analysis book
sage python
Woot Zygmund
stray perch
It seems to be an absolute pleasure to spend the night reading springer books
when you have time to do so
marble solar
Springer books have been going down in print quality
I got a first edition of Pugh way back
maybe 2014? 2015? And the second editions print quality is so bad
stray perch
Oh
Quick question, why do I hear Hartshorne everywhere xD
Is it such an incredible book that every math student must buy it?
marble solar
It was the first way to get into AG without reading thousands of pages of french
Very easy french mind you
But still french
stray perch
Why french xD
stray perch
Oh
civic carbon
my advisor would always say "just cite it from the EGA/SGA"
stray perch
Grothendieck had no country at some point of his life. But yeah a whole institute was built for him to stay in france
civic carbon
I was never that much of a masochist
quick hornet
EGA is easy for me to "read through" but very hard to skim/find a specific result in
and god forbid trying to ctrl + f a key phrase
i dont have the same "fluency" with french, even if I can read it
sage python
My impression of EGA is that he makes every theorem trivial
sudden kindle
in what sense
sage python
Like every line of a proof is its own lemma
So it's fine until you have to backtrack
And then may God bless your soul
quick hornet
proof by series of confident assertions that everyone kinda just takes your word for because itd be a pain to check them all
flint forge
isnt that just a proof
steel viper
lmao
sleek python
gray gazelle
imagine not being asian
grim raven
@sudden kindle https://github.com/ryankeleti/ega
velvet briar
This would be a cool application for neutral networks. I'm sure this wouldn't be hard
sudden kindle
cool
gray gazelle
imagine not being human
hasty turret
Imagine being human
karmic thorn
Imagine being
radiant basalt
Imagine Imagining
gray gazelle
Im(a)
can anyone recommend good functional analysis textbooks that contain a lot of examples? i'm reading pedersen's analysis now for a course and, while i feel like it presents the theory just fine, it doesn't really discuss a lot of examples outside of the exercises and i think it'd really help my learning of the material if i had plenty of examples to work with (and see discussed)
the lectures are more like the professor's stream of consciousness about the material so they aren't exactly helpful
LOL
yes
they are certainly something
i looked it up and all i find are programming books
ah i see
thank you
i'll check it out
dapper root
who tf is George
gray gazelle
lol
quick hornet
😉
gray gazelle
ultra definitely knows
nami too
everything george says is an exercise according to him ☺️
437?
ill see if i can fit it into my timetable
namington...
hmm
yeah the followup is mat437
k-theory and c* algebras
this is exactly something george would say lol
quick hornet
tbh i still dont know what an abelian group is
gray gazelle
i've already got a bit of a stacked timetable for next semester, so if i end up liking this one enough i'll try to fit the followup in
hasty turret
The underlying group in a vector space :)
quick hornet
absolutely try and take the course by the time you graduate
but yeah its uh
well his teaching style... values independence
we'll put it like that
oh i adore it
but its a lot of work
dapper root
Max Lieblich moment
gray gazelle
m*x 
gray gazelle
my plan for george's course right now is to just do like, a fixed amount of the book every week and try to get to spectral theory at the end
quick hornet
george is the epicenter of this server
gray gazelle
me
ultra
nami
gray gazelle
probably not
unbounded is ch5
in my pdf at least
3rd after the intro topology one
quick hornet
brb adding a #math-436-437 channel since apparently there seems to be demand for it
gray gazelle
i could be going through the book a little faster
seems like it
i'll probably end up doing measure stuff another course
the topology sections are good references imo
ivan's notes
i'm not sure
i didn't take it in the summer - he might've done it then since i think ivan took a summer off
all i know is ivan taught topology for a few summers, but he didn't last summer
his notes were great when i was taking the course
i really like the idea of the list of problems to work on
slender dragon
Is it a good combination to see Youtube Lectures and Follow a Book?
Or just a Book
gray gazelle
there's a two page long problem about vector bundles in the big list lol
that might be good for me to look at
@slender dragon i'd say it depends on the quality of the lectures. do you know if the lectures you plan to watch follow any particular book? if that's the case it might be a good idea to do so
i mean on youtube you can't really talk with an instructor about the material, and stop and ask questions when you're confused
but i have no right to comment on that since i've been watching recordings most of this semster lmao
slender dragon
@slender dragon i'd say it depends on the quality of the lectures. do you know if the lectures you plan to watch follow any particular book? if that's the case it might be a good idea to do so
@gray gazelle
I think yes
gray gazelle
i think the biggest thing you'd be missing out is the chance to talk to the instructor
other than that, why not?
slender dragon
Right know I attend a Moore Method course in Abstract Algebra
gray gazelle
I had a question, do you need to read a book on mathematical logic before starting out with spivak?
slender dragon
I think is ok to do online
slender dragon
I had a question, do you need to read a book on mathematical logic before starting out with spivak?
@gray gazelle
I didn't have to, but I suffer and enjoy the problems
gray gazelle
you should be somewhat comfortable with it. you might not need something on the level of an entire mathematical logic book, but definitely make sure you can pick up that stuff in the first few chapters or be comfortable with proving things from the start
thanks
slender dragon
i think the biggest thing you'd be missing out is the chance to talk to the instructor
@gray gazelle
You're right, that's the most important thing, I think
gray gazelle
it's not really the kind of book you just open having zero abstract mathematics experience. my first year course did that and it has a 50% drop rate lol
i guess spivak wrote it with the intention to let it be one's very first intro to abstract mathematics
slender dragon
Yes, but is a beautiful book
gray gazelle
but uh
slender dragon
It's less abstract than Apostol
At least at the beginning
I think you can read a Discrete Math Book before
gray gazelle
that might be useful, especially for some of the combinatorial stuff in spivak's book (2nd section's exercises lol)
oak bear
Hello, can someone recommend me a good book to learn partial differential equations?
Preferably one that includes many exercises and examples.
(Btw I'm a Physics major, so if you have a book in mind that caters more to physicists, that would be great!)
wooden sparrow
@oak bear there's physics server in #old-network . Sure you'll get book recommendations for maths topics here but do check it out for more physics oriented books
oak bear
Oh, I have already joined that server. I will ask there too.
wooden sparrow
fickle lance
Hello. I find that the exercises in Pugh's <Real Mathematical Analysis> are often too difficult or too abstract. What other texts can be a companion to Pugh to solve such problem?
gray gazelle
Has someone here read this
I was thinking if reading a pop maths book this looks good
Feel free to give me a recommendation
maiden stratus
derbyshire's prime obsession, g.h hardy's a mathematicians apology ofc, and fermats last theorem book by simon singh are good pop maths books
prisma snow
The way MEN is emphasized by being a different colour is weird and puts me off. Don't know why, it's probably innocent.
maiden stratus
it's an old book so, could be a product of it's time and that whole thing
hasty turret
The way MEN is emphasized by being a different colour is weird and puts me off. Don't know why, it's probably innocent.
Pls don't start about how this promotes patriachy, because there is "men" on the title
slender sphinx
@gray gazelle I actually do have it cause I got it as a present from an acquantince
slender sphinx
I didn't like it but I also don't generally like math history/popmath
so perhaps I am more biased aganist it
karmic thorn
"Mathematics and its History" by Stillwell is a much better text I guess
gray gazelle
wiki suggests its a bad book
@runic hatch which one mathematics and it's history or men of mathematics
velvet briar
I guess it's maybe trying to say "it's specifically about the men" but it comes off weird yeah
runic hatch
men of mathematics
maiden stratus
it has pretty decent reviews on goodreads
gray gazelle
Just felt like learning history of maths because wanted to know how development in mathematics come because we don't get taught that stuff in school
runic hatch
history of math is pretty cool tbh
maiden stratus
yes
gray gazelle
Plus mathematics and it's history is not available in my area cheaply
It's overpriced
karmic thorn
Libgen
maiden stratus
also smart monkey here's a whole list from goodreads https://www.goodreads.com/list/show/8231.Best_Books_About_Mathematics
gray gazelle
Don't want to read PDF because my heavy screentime
maiden stratus
I can recommend the fermat's enigma book
gray gazelle
This is one of the reviews
When I was younger, I liked this book a lot. Later, however, it is easy to notice that there are several great mathematicians who are curiously omitted simply because they were female, and that some of the biographies have a few liberties taken with them to be more dramatic. As another reviewer said, this is a product of the times in which it was written
maiden stratus
must've been a book that just focused on the men
guess that's why it was highlighted
gray gazelle
Yeah
maiden stratus
check out a mathematicians apology if you haven't already btw
maiden stratus
yea I mean the author was born in the 1800s lol
runic hatch
oh lol
maiden stratus
I think it was pretty cool
runic hatch
apology seems pretty short
valid moth
@white pebble @white pebble
maiden stratus
some of the stuff he said was really interesting
valid moth
osu multi when
maiden stratus
short book is good
runic hatch
ye
white pebble
i can in a bit
runic hatch
i disagree with hardy's points though
valid moth
I technically have work to do
runic hatch
at least based on the wiki summary
valid moth
But probably not too much
runic hatch
good idea
maiden stratus
but there are lots of gems
runic hatch
i do like his divergent series book so far
gray gazelle
hearty steppe
So I kinda don't feel ok with people constantly recommending libgen here.
Talk about that shit over DM. When good sites get shut down, there is nobody else to blame but the people OPENLY PROMOTING PIRACY on public chat servers.
Can we please moderate this?
Mind you sites like libgen are not just for piracy. There is free content on sites like this, but these sites are being promoted for illegal purposes (often) around here.
hearty steppe
or maybe when people talk about libgen, at least point to free content that can be downloaded that publishers do not expect payment for.
I guess...
flint forge
if you think that a math discord will be the nail in libgens coffin
idk what to tell you
i will say tho that losing kickass torrents was the greatest pain ive ever felt
tpb is garbage
im a cia agent actually
libgen is just an open secret at this point
stray veldt
the people who want libgen shut down already know it exists
and i dont think regular users can expect any consequences
pulsar aurora
Plus, academics textbooks can cripple a student's finances.
stray veldt
most students should have access to libraries
pulsar aurora
Not all libraries carry textbooks for their classes or their personal interests
My campus library got like some here and there, but rarely the ones used in courses
stray veldt
university libraries should
flint forge
idk about that most schools probably dont have all the math books you could want
pulsar aurora
That said, I do like ownership of physical books. Plus, fun to go to a used bookstore and play bookemon.
hearty steppe
wdym @sweet lotus
the latter
but I mean I have been trying to look into the libgen case. Apparently it is in the grey area, which is why it hasn't been shut down for good? Or that its impossible to shut it down cause of the people running it?
pulsar aurora
well, i was not entirely arguing the former, but that people may suggest it to help which contributes to talking about it
broken meadow
Good Cockroach
marble solar
EU does multi-million dollar study on how piracy changes sales
It doesn't
Everyone hides this fact
Gotta love it
hearty steppe
its the publishers that are worried, not the authors?
pulsar aurora
Capitalists just likes to crush competition
marble solar
Capitalism isn't the same thing as crony capitalism
flint forge
if anything libgen has made me buy books
its very nice to own physical copies
but i dont buy books just willy nilly
flint forge
Capitalism isn't the same thing as crony capitalism
@marble solar this is a nuanced argument but I actually disagree with this
or maybe I think the correct version of my take is that Capitalism even with the best-intentioned setup necessarily turns into crony capitalism
pulsar aurora
Some scans are crap too. That Apostol Calculus PDF that is floating around the internet is utter garbage with weird text glitches
flint forge
(integrity is commoditized, in some sense)
marble solar
Yeah, that's why government regulation is necessary
flint forge
yeah but I don't believe its possible
lost fjord
to an extent
flint forge
unless you manage to completely remove the influence of capital in government
I don't see a realistic way to do this
i dont think markets are necessarily corrupt
marble solar
I mean it's very obvious that money isn't speech, and the supreme court should overturn this
flint forge
but i think a society built around markets is inherently corrupt
I mean it's very obvious that money isn't speech, and the supreme court should overturn this
@marble solar if you remove the legitimate ways for money to influence politics this will still probably result in an outsized amount of illegal capital influence
i.e. i dont think you can regulate it away
people already break the existing rules and most get away with it
Well I agree that a labor market is inhernetly corrupt
but imagine everyone just got money to spent every year without any work and markets were just used to decided which products were best
this is an overly simplistic model
but its the type of idea i think markets can be used for productively
like i said overly simplistic. but I don't think it is trivial that a labor market is necessary to use any form of market
marble solar
I think government is inherently incapable of mass resource allocation
flint forge
back to people, potentially
if you're interested
the book 'Radical Markets' puts forth a nontrivial example
its kinda bad imo
but it makes me think there might be a place for markets
gray gazelle
How does this relate to capitalism, it's a maths server
Also it's not related to capitalism nor crony capitalism, it's actually an anti free market sentiment to protect copyright so it really is the opposite.
Just go on libgen if you need books.
And SciHub if you need papers.
gray gazelle
Please do not promote websites that engage in illegal activity.
flint forge
Illegal is a state of mind
gray gazelle
huh
quick hornet
copyright is illegal
so libgen is actually legal
(disclaimer: do not use this defense in court)
granite sluice
Illegal is a social construct!!
gray gazelle
this is true
timber mesa
mmmmmmmmmm yes https://en.wikipedia.org/wiki/Illegalism
hasty turret
Isn't that just a fancy way of saying criminal?
timber mesa
shhhh
gray gazelle
google drive is illegal, my friend told me he found a drive with the entire gtm series on it and it downloaded them all
How does that make drive illegal ?
runic hatch
Yeah