yes
#book-recommendations
steel viper
sage python
Where are you taking this topology class?
tribal kernel
Hmm I could get that
sage python
Why do you take algebraic anything at NYU
tribal kernel
Using Hatcher as a book?
steel viper
its just been 5 weeks of point set
steel viper
or 2 weeks of motivation and 3 of point set
tribal kernel
Oh dang
sage python
NYU people barely know what groups are
steel viper
yea idk cuz he reached out to me
i think columbia would fucking ream me
but this is too slow
tribal kernel
hatcher is not a book
it's an experience
@flint forge lol nice
sage python
Honestly NYU is good at like
steel viper
hatcher is a great experience
sage python
Analysis and applied math
tribal kernel
I didn't like Hatcher the first tow times I read it
sage python
And that's it, for anything else you might as well go to like
flint forge
Here's the ideal schedule for grad top. 1) Point set review, weeks 1-4. 2) Concise weaks 4-8 3) More Concise weeks 8-10
steel viper
also the prof is really nice i want to get him to write me a letter of rec
sage python
University of Alabama
steel viper
weeks 1-4
tribal kernel
Now I get what he's going for and it's pretty neat
steel viper
hn
sage python
Apparently Venkatesh was there for a bit so this wasn't always true
I don't know who that is
flint forge
dami should i sneak hegel into peters proseminar
sage python
Why is he teaching this class at a pleb tier level?
steel viper
i dont know!!!!
tribal kernel
Honestly I needed more algebra experience before alg top
Not that the algebra in that class is hard
flint forge
dami tell me i need to work on my paper
sage python
Throwback to knowing what Eilenberg-Maclane spaces are before having a good handle on the dihedral group
tribal kernel
I just sucked at algebra
flint forge
i feel so unmotivated
steel viper
algebra is good
sage python
Max do it or you're a nerd
steel viper
i draw the arrow i take the quotient everything works out
tribal kernel
I don't know if it will hit the same...
@flint forge Do you're paper lol
I believe in you
flint forge
its not due for like
steel viper
i just want to go to university already
flint forge
20 days
steel viper
hn
flint forge
and im so tired
flint forge
grind hasnt quite started
steel viper
oh no
flint forge
fuck lens spaces
marble solar
Lens spaces are cool
sage python
Honestly I'm already getting overwhelmed since this semester is hitting me full force
flint forge
all my homies hate lens spaces
tribal kernel
My grind has def started
steel viper
also i officially went pass john in hatcher
marble solar
MoonBears likes them
steel viper
flint forge
were not homies then
sage python
Like thing is I'm basically now doing 4 classes, 2 reading groups, and NSF apps
tribal kernel
My algebra professor assigns me 20+ hours of algebra hw a week
sage python
Functionally
flint forge
smartest*
steel viper
lmao
slender sphinx
Who's your competition 
sage python
Well eh just 3 classes seriously
flint forge
topologyest \simeq smartest
steel viper
you, arch, john, whoever
slender sphinx
wut
sage python
Since Ginzo rep theory is something for which I can adjust commitment
flint forge
i rate my approval of the highschoolers here
based on
- politics
- how much AT they talk about
thats it
steel viper
ok well then im winning on both fronts clearly
marble solar
Don't you rate everyone based on politics max?
flint forge
yes but not on how much AT they talk about
for example I respect namington even though he never tells me about k theory
sage python
Well does algebraic K-theory count?
flint forge
algebraic k theory def counts
sage python
I've seen him talk about K-theory exactly once
slender sphinx
well I talk about neither, so I'm in last place for high schoolers
sage python
poco: well when he says politics that can be positive, negative, or 0
sage python
If you don't talk politics you're 0
steel viper
his math takes are so low
sage python
If someone has politics he doesn't respect it goes negative
steel viper
omg what happened to darkrifts
flint forge
who knows
slender sphinx
dark is gone
steel viper
i think he left the server
flint forge
we were just too gay
steel viper
maybe hes just on hopf
sage python
Idk if I've ever seen Darkrifts talk politics
slender sphinx
he left a lot of servers
steel viper
or neo hopf
slender sphinx
same dami
sage python
I've only seen him talk music theory
steel viper
its yikes
flint forge
DR's take was deadass "I don't respect gay people, I know this is bad, but Im just too damaged to change"
it sounds like a fratboy breaking up w someone
sage python
That's... interesting
tight crag
That's pretty bad
sage python
I don't see how that works by any means
sage python
Like you can't muster up respect?
marble solar
I'm much more conservative than most ppl my age or the internet, but the government has no right in telling people who they can or can't be with
Or how you want to identify
steel viper
its not necessarily a matter of government tho
sage python
Well in that case he'd presumably be neutral then no? Whatever anyway this is a channel for books not Darkrifts lmao
flint forge
dami were you here for whiteboard girl
marble solar
The thing is, they want to make things like gay marriage illegal
steel viper
like if you are homophobic but dont think that the gov should ban gay marriage you're still in the wrong
flint forge
lets go raid chill then
sage python
I've heard of whiteboard girl
steel viper
i have not max
sage python
Anyway book time
steel viper
tell me the tale
calm crane
darkriths still active in dms and i think music servers
marble solar
Which if you're conservative I don't understand, since conservatives want smaller gov't
steel viper
its almost as if american conservatism is an inconsistent ideology
marble solar
I mean american politics is pretty inconsistent in general
steel viper
maybe
steel viper
whats the big contradiction on the left though
flint forge
go raid chill sloth
steel viper
i am multitasking >_<
marble solar
I like Folland more than papa rudin
But I still prefer Stein and Shakarchi over everything
sage python
Alright someone who likes Rudin more get in here
marble solar
Rudin is great if you have an instructor who like fills in details
But a lot of ppl expect it to be you just sit there and stare at it until it makes sense
Which can be a useful thing to learn, but I think Rudin does a poor job of it
sage python
I don't actually know either book I used Bass lol
Or like lecture notes mostly and then a bit of Bass later
I guess the best part is that thanks to the prof in question
Even though I was in that class for just a couple weeks
I have already solved more problems in that book than in like
Any complex analysis book
And tbh in most books
sage python
Likely same
I have a weird and mostly not good interaction with complex analysis
I know the theorem statements but haven't done enough good problems
Or bad problems (read: contour integrals)
marble solar
It's treated as an intro to harmonic analysis
tribal kernel
Yo Folland vs Rudin
marble solar
Since holomorphic functions are harmonic
tribal kernel
I like Folland
marble solar
But I think that just jumping into PDEs or Real Variables is much more useful
sage python
Complex analysis is harmonic functions + difftop tbh
tribal kernel
Mostly cause he was in those life alert commercials
marble solar
and some alg. top.
sage python
You should have a year long course on complex analysis
marble solar
Like if you're going to do riemann surfaces
tribal kernel
“Help I’ve Folland can’t get up”
marble solar
Complex analysis still feels like magic to me
marble solar
I'm learning Elliptic PDEs right now out of Evan's chapter 6
flint forge
someone needs to write a really good second course in AT book
sage python
And then only in third quarter do you define a holomorphic function
flint forge
there really isnt anything great
sage python
I've seen a supposedly decent "first and a half" book
marble solar
Doesn't hatcher have like
tribal kernel
Nah for real I actually really like Folland. More clear and technical in the real part than Rudin is imo. Although I like Rudin.
marble solar
Lots of material you can dive into
flint forge
something that like
flint forge
introduces model categories and spectra
marble solar
e.g. if you're interested in wirtinger presentations
flint forge
and localization and completion at primes
marble solar
And how they're used, you can go further
flint forge
and spectral sequences
sage python
Spanier is Hatcher but more formal and out of date
And covers somewhat different material
marble solar
Ahh, my CC professors advisor was spanier
sage python
Not like harder or easier but orthogonal
marble solar
So he liked it a lot
steel viper
yea tbh i have no idea what topology stuff im gonna do after i finish hatcher
marble solar
You can jump into Low Dimensional
steel viper
or what the options even are
sage python
Characteristic classes is probably a good next step
sage python
K-Theory, Morse stuff you need some difftop for but it's good
steel viper
ugh too much stuff to dooooo
sage python
Bott-Tu also
marble solar
I'm a huge fan of Low Dimensional though
sage python
You should probably springboard into manifolds
steel viper
i should write up a list
sage python
Once you have AT down
marble solar
Knots Knotes and Schulten's 3 manifold Topology
There's lots of entry level research problems
sage python
For manifolds try Warner, Lee, or Helgason
sage python
Spivak too, I guess volume 1 is pretty much an older version of Lee right?
marble solar
Spivak has more intuition developed in the pages
sage python
Like they're both kinda long chatty straightforward books on the mechanics of manifold theory
marble solar
And spends more time going from the old notation to the new notation
In case you want to read Riemann's papers or Gauss' papers
sage python
So in case you're a nerd
marble solar
Yeah. The last 3 volumes are highly specialized
But if you're working with diff. geometry the first 2 are standard
sage python
But yeah Helgason is what I'm gonna be using probably for getting into the deets of diffgeo
Since it's got an eye toward stuff like symmetric spaces which is what I mainly need
marble solar
You can also backtrack and go down the analysis route Sloth
marble solar
There's a lot of stuff in Riemannian that's cool that requires PDEs + manifolds
flint forge
you cant manifold pill without me to disagree
altho smoothdyn might actually be what manifold pills me
sage python
Lol I'm gonna have to learn that too
flint forge
lmao want the lecture notes
sage python
Honestly I feel like I'm in this state where legit every single area of math except for logic is relevant to me
And like that's not an exaggeration
marble solar
IDK, I think it's ok to specialize and just learn what's important for you
like my top professor can't even define measure
marble solar
I guess you're all over the place
flint forge
dami does not have horseblinders on
marble solar
But you can't learn it all
flint forge
like a loser
sage python
Nah but yeah I do have a vague priority ordering
marble solar
and then after your postodc
It'd take a real long time to put it all together
But then you're like a jack of all trades
Master of none
sage python
For now automorphic forms is the guiding principle
marble solar
Which can be fun
sage python
So the most important things are algebraic number theory and vaguely representation theory/harmonic analysis
Tier 2 importance is what has a lot of stuff
marble solar
Ahh, they taught Rep Theory in my MS but it conflicted with my work scheduled
schedule
steel viper
i should make a list of things i want to learn
flint forge
by automorphic forms to u mean
marble solar
I was so sad
slender sphinx
I made one in pastebin sloth
marble solar
Does your TA slots ever conflict with classes Sloth King?
slender sphinx
I keep it on my phone
sage python
It's happened before yeah
marble solar
That shucks
sage python
But for the most part I've been able to work around
slender sphinx
also, my list of stuff to learn is pretty much just standard ug stuff; I wanna get a good handle and taste of everything
marble solar
See ya guys
slender sphinx
search it up on yt
sage python
Lol this is prob better than how we did it
slender sphinx
it starts at 9 est I believe, max
sage python
Second quarter of analysis for me Schlag spent just under 2 weeks during ODE
And at the end he talked a bit about Lyapunov functions characterizing stability
I don't know any more details than that, tbh I barely remember what a Lyapunov function is
flint forge
orbit decreasing
steel viper
No.
flint forge
anyone want to livecommentary the debate
slender sphinx
post sloth?
steel viper
144
steel viper
ty
flint forge
now join voice
steel viper
i think ill just come back to this when i want to review my stuff anyway
omg soon
i have like 2 pages left
of this hatcher section
subsection whatever
solemn mantle
anyone familiar with "the nature of computation"
granite sluice
anyone familiar with "the nature of computation"
@solemn mantle yes, because I'm always recommending that book
its amazing. read it.
*read it non-linearly.
wooden sparrow
gray gazelle
wut
tight crag
@sudden kindle hey
sudden kindle
Hi
solemn mantle
@granite sluice lol all the reviews say it's amazing
I'd like to read it but one person said the exercises required knowledge of graph theory and stuff
granite sluice
You can try it out and fill in background as you go. If you don't have math background it'll be a years long project -- it basically is a years long project for me, and I'm a math phd student...
granite sluice
But there's a lot at different levels. It's a huggeee book.
lost fjord
What book are y’all talking abt
solemn mantle
the nature of computation
gray gazelle
no
granite sluice
its a big mix of stuff, there are some algorithms focused chapters, and some more theory focused chapters
its just like, a cs theory degree compressed into one book, I guess
none of it is super in depth, but its all pretty rigorous and gives a lot of good intuition
hearty steppe
Just want to clarify, that I'd have to dive more into real analysis to learn about series expansions
cuz the one intro to classical mech book I'm using is referring to techniques in series expansions and I have yet to learn that yet. Outside of basic taylor/power series problems in elementary calc
earnest glacier
hey. can someone recommend that book ? https://www.amazon.com/Everything-You-Need-Math-Notebook/dp/0761160965/ref=sr_1_4?dchild=1&keywords=math+workbook+for+adults&qid=1601453713&s=books&sr=1-4
unique tree
earnest glacier
thank you . . .
karmic thorn
The reviews on Amazon itself seem okay, although what exactly do you need it for?
Practice problems?
karmic thorn
Hmm, what is your current background? How much math do you know?
earnest glacier
read comments from Benj and Steve, you'll get my POV of my math struggle as someone with ADHD
i know very little math
how should i categorize my math skill?
karmic thorn
Oh, I see. This doesn't seem like a good resource then.
karmic thorn
This is basically a companion book for middle-schoolers, doesn't seem very useful all by itself.
Being curious is good
earnest glacier
yup
Did I mention I hate math? It has always been (and continues to be) the thing with which I struggle most, academically speaking. I find that there aren't really decent resources for people like me, with minds like mine. It's written about by people who "get it", and to them it's so simple that they in turn expect you to just "get it". This book is really no exception. It's more colorful, but it's written with that same hard-and-fast "simple rules to remember" format as math textbooks 20 years ago. Nothing is in plain (enough) language, and very little time is taken to help those of us who can never seem to just "go through the motions" understand the WHY of math. For me, this is the hardest thing. Okay, you flip the fraction. But why? How does it work? Because this goes unsatisfied, I feel like I don't get it, and out of my mind it goes. Lots of folks are this way. I need to see how it works, and then I get that "ah ha!" feeling and it just sticks.
i need book that have all above lol
karmic thorn
Hmmm, maybe you could start with some non-technical books? They can lure you into studying maths for starters, then you can gradually learn it via other options.
earnest glacier
what about pre algebra?
karmic thorn
Yeah, this isn't the right book at all in that event.
Have you tried studying from Khan Academy before?
earnest glacier
i did, but i need work book with it, something abit more flaw,
more interactive,
so i really want to enjoy math , but watching videos for 30 minutes? i will forget the first 5 after 1 minutes
karmic thorn
Yeah, videos can be tiring sometimes. Let me look up for something that caters to your requirements.
earnest glacier
thank you so much 🙂
karmic thorn
Have you taken a look at AoPS books? Specifically Prealgebra?
earnest glacier
nope
karmic thorn
I think it answers the "why" and "how" part really well.
And has a lot of problems too
If you can sit down for a bit with a book, it would be a fun book to work through. Some of the problems are challenging and would need more thinking, but that's how you move forward in maths.
earnest glacier
i really want to enjoy math . i really do, as many of my field of interest involve ALOT of ,math, :). and well it attracts me, but my ADHD and i guess bad experience with math really turned it into trauma if you get me , so every time i face math issue(just look at it like equation ) (e=mc2) yup that complicated one, but you get the point.,(i dont know how to solve equations so yea)
that one https://artofproblemsolving.com/store ?
karmic thorn
Maths becomes fairly intuitive when you understand the bigger picture behind these equations or aid it with some intuition.
Yes, you can find the Prealgebra text there.
Although you may want to get some other recommendations as well, this is a book that I like personally.
(You can download a copy from Libgen and see if it suits you)
earnest glacier
thank you so much:)
karmic thorn
No worries. In case you hit a roadblock anywhere during your learning process, you can reach out here to get help.
earnest glacier
most likely will 🙂
karmic thorn
Goodluck!
earnest glacier
sure go ahead
lost fjord
Nt book recommendations?
sage python
Which kind?
lost fjord
Elementary
marble solar
Apostol
sage python
Is that for elementary or more analytic stuff?
I like Weil's "Number Theory for Beginners"
Not to be confused with "Basic Number Theory"
quick hornet
the GTM heirarchy:
for beginners < introduction to < advanced < basic < foundations of < [no adjectives]
lost fjord
Thanks for the rec, what can I expect to learn from Weil’s nt for beginners?
quick hornet
doesnt weil require comfort with cosets and stuff?
marble solar
Apostol has the first 4 chapters as elementary
quick hornet
or does it teach that on-the-fly
marble solar
and doesn't get to the analytic stuff till later
sage python
No I'm talking about mega baby Weil
Like he defines N axiomatically
So everything that is used is proven
quick hornet
hm
i remember looking at that text for a result and seeing that his proof was based around some coset stuff
so i guess he teaches that at some point in the middle
sage python
lost fjord
Is it possible to prove a something like Euler’s theorem after reading this book, or would that require more study and experience
Sorry if I sound silly
quick hornet
i'd be surprised if it can't
alternatively you can prove euler's theorem from lagrange's theorem with a bit of group theory
lost fjord
Ok thanks for your help guys!
sage python
This book introduces group theory
valid moth
@lost fjord There's a very simple proof which I can give you the sketch or initial idea of
lost fjord
What is it?
valid moth
let's go to #math-discussion
soft terrace
So after graduate level abstract algebra, whats the next logical algebra topic to study?
oh and can i get a book recommendation with that *
sage python
What did you enjoy within algebra?
soft terrace
hmmm
i like geometry, im looking at some algebraIc geometry stuff right now so stuff that goes along well with that would be good
sage python
Commutative algebra is prob a good next thing to learn
Perhaps alongside some classical/varieties-y AG
sage python
Jacobson is good I gotta read more of that
soft terrace
he had wayyyy more than i needed in it
sage python
Tbh I mostly know my algebra from lectures that went out of Dummit and Foote 1-14
soft terrace
i looked at the chapters that were covered in a normal grad course on it
i need to look at the universal stuff again because i forgot it 😦
sage python
I didn't take grad algebra here which would've covered also some rep theory (which I've seen), and some commutative algebra
Maybe basic homological stuff
soft terrace
ah
well what was suggested as normal in the book 😉
i remember something on representations and the homological stuff
yes lots of modules
LOTS of modules
ok
is commutative algebra just more stuff on commutive rings fields etc?
and modules -_-
actually whole reason i looked into algebraic geometry was cuz i was trying to learn some stuff about identifying manifolds
i glanced through a book a few years ago and was like meh but then i was told a few things and now im going back
thats homotopy stuff right?
yeah i did that a while ago basic stuff on it
dont remember without the book but i liked the homotopy stuff very interesting
glanced through it i can do bits and pieces
didnt seem very hard to be honest
i like analysis and differential geometry
in particular i like manifold theory and discrete differential geometry
marble solar
oh yis
soft terrace
butttt apparently theres some nice theories in algebraic geometry for manifolds so i am learning that
soft terrace
jacobian criterion for varieties?'
i did read some differential topology books too because they had a lot on manifolds
sage python
Did someone say differential topology?
soft terrace
i certainly did
sage python
Nah but yeah manifolds are nice. You might like real algebraic geometry
soft terrace
whats that?
sage python
Apparently there's some cool shit involved. I know exactly 2 results in that area
soft terrace
like real analysis meats algebraic geometry?
sage python
Studying varieties over real numbers
sage python
Apparently it turns out by Stone-Weierstrass that every smooth manifold is diffeomorphic to some real algebraic variety
soft terrace
oh thats cool
sage python
(Though this proof is not trivial)
soft terrace
is that both ways?
sage python
Well, you need a Jacobian type condition to guarantee smoothness
Given a real variety it's just vanishing locus of finitely many polynomials f_1,...,f_n
soft terrace
maximal rank and fiber manifolds?
sage python
But that's just the vanishing locus of f_1^2 + ... + f_n^2
So you really just need that 0 is a regular value of that guy
sage python
I don't know this is just things I've been told
soft terrace
oh ok
sage python
In general with difftop I like Milnor and Guillemin-Pollack, or Bott-Tu if you're more ballllsy and have more experience
soft terrace
ok
marble solar
Which is what makes it great
soft terrace
i'll check that out and look into the commutative algebra stuff
sage python
Yeah, for what it's worth though I suggested commalg in part because I thought your interest in AG was... I don't wanna say less geometric but that you were coming at it through algebra
soft terrace
no no manifods
sage python
If you are going into it at least in part for the geometry then I won't hard recommend that direction
soft terrace
i was talking to cruster about it and he suggested it
well didnt suggest but he told me about it
sage python
Maybe algebraic topology is worth learning
Bott-Tu if you wanna go at it hard from the differential forms
soft terrace
i was mostly looking into the algebra stuff because i need the practice in algebra
sage python
For some more algebraic stuff that's related to geometry, AG counts but you have to make it geometric, it's very easy to become commalg
Rep theory and Lie groups might also be up your alley
soft terrace
its been a while since i looked at it and i keep forgetting the definitions in the book
ive seen lie groups in my differential geometry book
lie derivatives groups lie everrrytthingggg
marble solar
Which book
and sufficient for what
Yeah it's good
Is it sufficient to get you a PhD in diff. top?
No
Yeah, tell me when you're done reading those
I like short books when learning a field for the first time
So it conveys the basics
For a lot of ppl in Topology, Milnor is very much sufficient
You don't need to be a research expert in Diff. Top. to be interested in Topology
marble solar
Topology is a big field, there's lots of stuff going on
If you're interested after Milnor, you can read more
but if you're not interested and you try Lee
I read Milnor before taking grad topology, and I found it sufficient
For the 3 courses I did
mystic quarry
Do you guys have any book recommendations for learning more about quantifiers and epsilon-N limits? My Calc 2 class is revisiting limits and our book doesn’t have this topic but I want an extra supplement
quick hornet
rudin
seriously speaking, this is the main topic of introductory real analysis
well, the first month or so of real analysis
so any real analysis book should theoretically do the job, but many (e.g. rudin) are gonna be a lot more intense than you probably signed up for lmao
for something more approachable, you could look into, for example, Spivak's Calculus
which is a text that tries to bridge the gap between the conventional calculus curriculum and this more definition-oriented thinking
gray gazelle
prove all the limits in the first section on limits or smth in ur calc book
quick hornet
heh, thats probably not a bad exercise
sleek python
Find a logics book, then come back to maths and cry because they use different notations
gray gazelle
Does anyone have experience with Paul Sally's Fundamentals of Mathematical Analysis
specifically for self-study
I know that it's not adequate on its own due to lack of solutions, but some people have suggested using Pugh and Rudin (for the exercises) alongside eachother
So I'm wondering if I could switch Pugh's with Sally's
gray gazelle
someone knows any book about techniques of euclidean geometry?
quick hornet
euclid's elements
gray gazelle
gray gazelle
hearty ferry
I need a book recommendation about epsilon delta formulation of limits, such as those in continuity, differentiability and Riemann integrability.
So the concept of limits in terms of epsilon delta
dapper root
Literally any analysis book
If you want the classical recc look at Rudin
If you want something less hard, try Spivak
sleek python
Alright I got Rick Durett's Probability: theory and examples from the library, hope it's good
hearty ferry
@dapper root something else than those ?
sleek python
baby Rudin is often recommended
I don't know if it's good tho
But any book about real analysis should do tbh
sleek python
What makes it better than other books
hollow peak
I think pugh writes in a very engaging and intuitive way, and he proves most of the basic theorems using solely completeness of reals after constructing them with cuts
dapper root
Dedekind cuts 🤢
hollow peak
his section on metric spaces and topology is also very good, and the chapter that proves all the basic calculus theorems (pre integral calculus) is very slick
hearty ferry
non good pdf of pugh are avaiable 😦
hearty ferry
can you get it :D? @sleek python
hearty ferry
Thanks!
valid moth
@hollow peak i like pugh because the only thing i ever do is visualize
that's right 
and pugh has all the pretty pictures suited for my way of thinking
marble solar
Ahh that must be the second edition
gray gazelle
marble solar
Oh dude I got that down
One sec
Smooth spheres stand so tall
as to bound a 3-ball.
Techniques by which I know not,
stretch and play
with manifolds, like clay
With no saddles, nor horse
we choose a path, not so coarse
paven by Morse.
Plane and Simple, each curves level;
from Jordan I force, a smooth radius isotopic two, of course!
With one saddle and one horse, nested or nay
make what we may -
The planes of day: figure 8's skate and slice
spheres to disks, 3: A, B, C
Containing their highs and lows,
max's and min's.
Yet a plane so great,
two disks in the
figure eight -
one is bounded and one not
shares borders with, say, A.
By paste and glue, a sphere
shall appear. A sphere,
made of clay - again push
and play, come what
may. It's critical, I say!
On this path, on our way;
we've lost our saddles, today!
Now this lovely sphere,
stands so tall
as to bound
a 3-ball.
(A proof by poem for the base case to prove Schoenflies theorem)
marble solar
Is it as good @gray gazelle?
pearl imp
hello frens
I am self learning Calculus at the moment using Larson's which is very good illustrated and also seeking help from this server.
I was wondering if there are similar books for linear algebra and probability which are academic enough to pass as an uni book but also light and illustrated enough like Larson's Calculus to be used for self learning.
Thanks
granite sluice
@pearl imp A lot of people like the book "linear algebra done right" (Axler). Maybe try it out.
pearl imp
I'm still early calculus, like just learned definite integrals
marble solar
Integrals are hard
pearl imp
like the concepts or the calculations and nitty gritty?
marble solar
Sometimes the concepts are hard with integrals, sometimes the calculations are very difficult
There's several books on Tricky Integrals
pearl imp
the mathematical definitions and formalities really get to me, but I feel I can relate with the concepts
lost fjord
Hmm ok
pearl imp
what's MSE?
marble solar
Math stack exchange
karmic thorn
pearl imp
O
marble solar
It's an online forum for math students to ask and answer questions
They range from very simple to very difficult
In all kinds of fields
pearl imp
I think I once asked a question there and was frowned upon bc I was too dum dum
karmic thorn
Happens to almost anyone with their first question lol
pearl imp
karmic thorn
But it's a good community if you can state your problem precisely and show your efforts at approaching the problem
pearl imp
👍
quick hornet
ive considered contributing to stackexchange/mathoverflow
marble solar
I have some unanswered questions on stack exchange
quick hornet
id probably want to do it under a real name though
marble solar
If anyone's trying to answer
valid moth
I wonder how hard it would be to get top 0.1%
karmic thorn
Send me the link, I'll bounty em
valid moth
Qiaochu style
karmic thorn
Uh have you tried posting these on MO?
marble solar
No
karmic thorn
Could be the case that you need some experts looking over them
I'd say there's no harm in cross-posting on MO
karmic thorn
I'll bounty this, let's see what turns up.
marble solar
oh hell ya. I bountied this once
karmic thorn
Reason for starting bounty: Draw attention?
Or should I do "Authoritative reference needed"/"Canonical answer required"?
karmic thorn
👍
Any custom message you'd like to add?
Explaining what you'd like to see in the answer?
marble solar
An explanation of how Mikhail Gromov's argument on page 11-12 of Gromov's "Metric Structures for Riemannian and Non-Riemannian Spaces"
Proves this result
I asked Gromov himself, but I didn't understand his reply
karmic thorn
Since that's included within the body of your question Ig I don't have to add a message at all, your question is fairly self contained imo
I asked Gromov himself, but I didn't understand his reply
Hahaha, really??
marble solar
Yeah
marble solar
Ty bbcakes
karmic thorn
Np; if nothing shows up I suggest cross-posting on MO lol
marble solar
It was for a research project I had to do in Knot Theory
like kinda mathematical exposition on knot distortion. I wrote like 7 pages
Just summarizing current research on it
karmic thorn
Anything that follows the word "research" naturally goes to MO lol, MSE is, imo, better for math up to the graduate level.
granite sluice
@sweet lotus lmao that gromov screenshot. I want to believe.
flint forge
Its real
gray gazelle
@marble solar yes, although i have absolutely no idea what that theorem is lol (was in lecture so i couldn't get back to it)
everyone talking about how they speed up lectures and here i am pausing every 2 minutes to think
marble solar
It says that every smooth S^2 sphere in R^3 or S^3 bounds a 3 ball
junior orchid
anyone doing phd or msc here
sage python
Me, Moonbears, Ultraproduct, Liquid, Namington, and Crustle are graduate students for sure
Or well Moonbears is in a transitionary period I guess but has a masters
Some others too but I forget offhand
dense pewter
i'm starting high school next year
dapper root
No Dami ur a first grader
dense pewter
but i'm gonna get my phd one day
sage python
Chmonkey shh
tribal kernel
I’m going for PhD now
marble solar
I currently plan on it but life has it out for me man
gray gazelle
how are u gonna coordinate with ur wife? (im assuming she has a job where u currently live together, or maybe not, i guess u guys could be LDR)
marble solar
We live together
I'm from socal, so there's a lot of schools with tech jobs for her
Currently in Seattle
gray gazelle
as in, you would be looking at doing a phd at a school in socal?
marble solar
It seems to be the most likely scenario
gray gazelle
what if you don't get into any schools in socal?
or, any schools that do any of the math fields ur interested in
(i'm just trying to get an understanding of the thought process for this kinda thing, like i'm not married but i might be interested in doing a phd at some point, and i could be married at that point)
marble solar
The likelihood of my not getting into a socal school is so low
There's Irvine, Riverside, SB, USC, ucla, and Caltech
The first 4 I can get in
The last two no way in hell
gray gazelle
i guess that makes sense
marble solar
I have 3 very strong letters + research. My GPA is lower than your usual admit
But I'm not applying to top tier schools
gray gazelle
is it because you suspect you won't get in, or because even if you got in you wouldn't go?
actually, if you got into a school where ur wife might have a hard time getting a job, what would u do?
marble solar
I'm only applying to places for which there are job opportunities
for her
My wife works for amazon as a techie right now
I'm not applying to top tier schools for several reasons. 1. is I won't get in. 2. is I don't like the students there 3. is I don't like the professors there 4. is I enjoy my free time
gray gazelle
what do you mean by 2 and 3 if you don't mind taking the time to answer?
marble solar
Ok, so I don't exactly have your typical background ~ I come from a lower middle class family. Almost went homeless due to the 2008 crisis
I didn't start doing mathematics till I was 18 years old
I went to community college. I'm not some super smart quick problem solver
I take my time, I mull it over I think about it. I talk to my friends, and then I get to it
The way top schools operate is you have to be on high performance all the time
I don't like that. I like my free time to explore my interests and take things at my pace
I'm also terrible at doing mathematics rigorously by myself
I'm a very much into following your gut and intuition, and discuss with friends to fill in details
There was one point in grad school where I was working 55 hours a week
On top of the full-time load
A lot of the people at bigger and better schools just have no understanding of what I've gone through or what it means
gray gazelle
ah yeah that sounds like hell
marble solar
I went to LA for my undergrad, and LA isn't exactly full of friendly people
A lot of them are pretty toxic, chasing status rather than developing themselves. The professors feed off of this competition
And if you're not their super star student, they brush you away
Not really a mindset I enjoy. So I'd much rather go to a school like USC where they pay you over 10k more than UCLA does
for their stipend
Even if I went to Riverside, I would just be one of the best students there and get lots of personal attention
hasty turret
And if you're not their super star student, they brush you away
@marble solar even tao?
marble solar
The ranking of the school doesn't matter as much as the work you produce
Yes
My friend had a letter of rec from Terry. He told Terry he got into UT Austin for analysis
Terry said "Good." and walked away
At most he allocates 10 minutes to people he likes
He really liked one of my friends and gave him 30 minutes on advice
In fact, the friend he really liked got into UCLA for PhD and terry told him "You can come here, but go somewhere else. It'll be better"
And they offered him 22k/year
Which is the lowest offer he got and Westwood is very expensive to live in
Like 3k/mo for a 1 bedroom apt
There's not a whole lot of mentorship at LA, no professor will "take you under their wing" and support you
Although you can get a second to none education there, especially in analysis
You ever had a final due over spring break?
You ever had 6 hour finals in a classroom?
You ever had a professor grade 1 problem out of 20 and fail half the class on that assignment? Ever had a professor say only 2 questions on a midterm, not covering a section and then put that section as one of the two questions?
Yeah shit like that made me get over LA fast
I never had night terrors before I went to LA, the stress was almost unbearable at times. I saw 5 people completely break down
Schizophrenia, Depression, Physical sickness, etc.
And these were people that studied hard. People that were taking grad courses their sophomore year
The pressure to keep performing well there is insane
And the professors don't ever let up
I will never go back to such an environment again
I'd much rather go to Riverside and raise a family
Go to USC, and make more money, have more free time
/rant.
Although, when I left UCLA I found I was significantly better at Analysis than nearly all of my classmates
In Grad School
And that the education I got truly was world class, it was just pure torture going through it at times
I'm sure sloth king or m*x have similar stories at UChicago
But I ain't standin' for it. Mental health is important
Mental & Physical health is the most important things you have
The MS program I went to was almost the complete opposite of my experience at LA, only retaining the great education part
You can ask zetamath for more on that
gray gazelle
where did(do) you go for MS?
marble solar
CSULB
Small state school right outside Los Angeles
(Not really small, but small math department. Few active researchers, but amazing professors and community)
I made 2 friends in my time at LA, and I made many more at LB
and I am an extremely social person
gray gazelle
can you talk more about what you mean about great education? (i guess to me great education sounds like stuff along the lines of, professors give really interesting lectures, or something like that)
marble solar
The two best math professors I've ever had are both at CSULB, they gave interesting lectures, good homework problems
Stopped at nothing to help you, had great sense of humors
I mean, we'd go over to dinner parties at a professors house
gray gazelle
i see yeah, i had a prof that gave good homework problems too in college and i liked that (never had a dinner party though lol)
marble solar
The grad students started playing ping pong in the TA room, and the math department chair walked by, looked mad, walked away, walked back with his paddle
and proceeded to whoop our asses at ping pong
He had a freaking ping pong paddle in his bag
Like his own
gray gazelle
nice lol
marble solar
After grad classes, we'd go to the volleyball court
and just play beach volleyball
Till we were too tired to continue
it was very much a work hard/play hard time of mentality
instead of just working hard all the time
Almost everyone in my cohort is now in a PhD program
Or full-time employed. I'm one of the stragglers
sage python
Chicago's stressful for sure but... not unbearably so? Idk
Like idk I feel there's a point where it's too far
Chicago comes as close as possible without crossing it for the most part
So like you'll be hyperventilating in exam time, sleep deprived, stressed, etc
But not as likely to completely break you know?
random spear
@marble solar are you describing UCLA or Caltech?
Oh Ig UCLA.
Ngl you kinda worry me with your descriptions haha.
I'm from the midwest, on a gap year rn as an incoming freshman and I'm going to LA for UG.
Ig LA might refer to UCLA instead of the town on the second read, which is a relief
I feel like Imma get my butt kicked by the sudden change of both education and scenery and it low key worries me.
Which Ig also is why I came here. I wanted to know if you guys had some suggestions on an order of mathematics books.
I figured I'd brush up on reading Tom Apostol's Calculus series, move onto stuff like diff eq and abstract algebra, but Idk about where everything else might be well placed.
I have books on analysis and topology as well a lot of others, but Ig I just want a general feel of what a good path might be. I'd expect there'll be some overlap, deviations, and just sheer preference, but just wanna make sure.
shut grail
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.
I also had a professor who threw a bbq once btw and that was pretty cool. I’m not suited for super big schools either for similar reasons to moonbears. Also coming from lower middle class, there’s that financial barrier of extreme debt, and the character of people at big schools. Not all big schools tho. There are a still a select number of big schools in california that have just as an amazing demographic of students in the math department like small state universities here. I would just prefer this small state uni kinda environment as it’s a lot more fun; plus, math, although tough at times, shouldn’t make us feel like prisoners to the time we spend on it. Everyone has their preferences tho. There’s always room for growth, and being in a healthy environment for that growth is what makes learning it worthwhile and enjoyable.
hearty steppe
@marble solar I’m eventually going to have to figure out how to get some letters of recommendation outside of academia and try to get some write ups published when my blog matures
But I’m essentially just starting out taking mathematics as a serious endeavor
It is a bit of a shame that I blew my chance to go to grad school for math in the near future at the moment
For me it’s not important, going back to school. All that matters is I enjoy math. A number of people, until I have my blog maturing the way I want it to, are going to probably tell me I’m wasting my time.
shut grail
@hearty steppe idt you’re wasting your time dude. Part of life is finding meaning in what makes you happy. And the struggles that come along the way. There’ll be haters, but most would just be jealous and would prefer to spend their free time putting others down. Do your thing man, everyone works at their own pace 👌🏽
hearty steppe
Yea I mean this is probably the wrong place to discuss this. I just figured I’d chime in. Most of my colleagues support my endeavor but there will always be a few engineering colleagues of mine that will not understand. I have a software engineering/comp sci background. Engineering was not for me. I knew it wasn’t right before I finished my comp sci degree. I just happen to be good at coding sure, but it just bores me these days. Coding has no meaning for me outside of mathematics.
The computational realm of math is still of interest to me but I am getting more into theoretical math
runic hatch
out of curiosity, do people study coding in and of itself?
im not sure what that would encompass
hearty steppe
I mean there is algorithms
hasty turret
Coding is a tool
hearty steppe
And you can study systems/circuits
runic hatch
ah true
hearty steppe
And languages
runic hatch
also sudden change of topic, but what books are good as companions for Hardy's divergent series?
marble rock
dang math is hard
hasty turret
Should have figured that a lot earlier
marble rock
yea
i thought like math is hard but like bearable
didnt know ppl can actually get sick
from this shit
why do people do this
passion
?
stray veldt
mental illness in academia is pretty widespread actually
marble rock
yea like wow
stray veldt
it's not a math thing
marble rock
this is something hard to believe for me
yea yea i get it
but id guess math is at the top\
i never met irl a grad stud ora nything
but yea everytime i be on /reddit math
i must see a post talking about how hard grad life is
and like 100 comments agreeing
stray veldt
well, most of them you wouldn't guess it if you saw them irl
marble rock
and by hard i mean like
stray veldt
also notice that reddit is mostly people that want to complain
marble rock
mentally exhausting no life no fun depression anxiety hard
stray veldt
like, nobody who is fine will go to reddit and write about how not mentally ill he is
marble rock
yea i get it
but i just wanna ask
why do people do it
do they get off from the difficulty
stray veldt
"just x more years, then it gets better"
marble rock
does it?
stray veldt
i don't know
hasty turret
i never met irl a grad stud ora nything
Nice jojo ref
stray veldt
but it's easy to tell that to yourself
stray veldt
speaking as a non-grad mentally ill person
marble rock
why do you have to go to uni to stud ymath?
cant you study math from textbooks?
legit asking
stray veldt
i dont think so
stray veldt
if you are super big brain maybe
stray veldt
yeah, but
they still have people to talk to
and at some point you just need guidance
because you run out of books
stray veldt
like, i think guidance in the beginning is very important
so you learn to read and do mathematics
marble rock
and like the probablity of living a financially easy and good life
stray veldt
and then later it is important
marble rock
yea yea i get it
stray veldt
because another person has to tell you what to study
marble rock
you need people to teach you and tel you what to do
and tell you which paths are bad which paths are good
stray veldt
also you need to go to uni to get a degree
marble rock
yea i meant like
why ddidnt math majors just read textbooks and get their degree in like
business
and have a way easier life
stray veldt
because math is very time consuming
and like, i don't think getting a math degree is harder on your mental health than other degress
it might change when doing a phd
stray veldt
you can just get a math degree and then start working
marble rock
yes
but like i meant like
the math 'lover' path waay
the grad school math pathway
i think imo math bsc is easy to get even if udont understand shit
u will work your way through
stray veldt
ok, you can't devote the amount of time required to mathematics, if you are doing a business degree on the side
or working a 40hr week
marble rock
mathematics is so toxic
wooden sparrow
Can I weigh in?
stray veldt
why toxic?
wooden sparrow
Ok it took a turn
marble rock
and like i just feel frustrated why the fk are u doing that
u can just do a cs bsc and be a programmer and live your life
stray veldt
just x more years until my phd
marble rock
forget all this stupid shit
wooden sparrow
@marble rock why does anyone do anything?
marble rock
but at the same time
its fun
math is super cool
so its toxic
maybe its bec i read alot of reddit posts on grad life i have this opinion
i am p sure others are enjoying their time in grad
right?
stray veldt
try talking with actual grad students
but like
they wont tell a random person about their mental health problems
wooden sparrow
I want to talk to grad student
marble rock
idk this just came from reading @marble solar
stray veldt
the grad students in my department seem happy 🤷
marble rock
yea
wooden sparrow
@stray veldt what department are you in?
hasty turret
mathematics is so toxic
@marble rock ask moonbears
marble solar
I started a shit storm in book discussion; if anyone has further questions please pm me
marble rock
yea book discussion question:
what do you guys think of reading papa rudin after baby rudin
hasty turret
Do you mean boolean algebra?
marble solar
I dislike papa rudin
hasty turret
Or is computer algebra a superset?
tribal kernel
Real and Complex is papa while Principles is baby Rubin
stray veldt
no, we study algebraic geometry and number theory using computer algebra systems
marble solar
There's a lot of detail that is left out of papa rudin
stray veldt
i.e. mostly computational questions
sage python
Big Rudin doesn't seem to do Caratheodory extension, rather he just jumps to Riesz rep
So you only know how to construct Borel measures
marble rock
yes loch
stray veldt
i only used it as a reference
tribal kernel
If you wanna study modern real analysis I think you’ll get more mileage out of something like Folland or Royden
stray veldt
for measure theory there are plenty of good books
sage python
I don't like this choice tbh, I feel like if nothing else it's bad for probability
marble rock
like i think this shit doesnt end RA
sage python
I don't know how the exposition is like
sage python
Folland looks good at a glance, I also like "Real Analysis for Graduate Students" by Bass
marble rock
i stil didnt get to measure theory
@sage python is reading more RA after baby rudin
important for non RA things
sage python
Measure theory can kick in a bit elsewhere
marble solar
Even things like proving rectangles in R^d are countable unions of open sets
sage python
Especially Fourier business
marble rock
baby rud has measure theory
marble solar
Rudin leaves it out
sage python
Do not read the last chapter of Baby Rudin
marble solar
Who does measure from baby rudin?
marble solar
It's awful
sage python
Honestly don't read the last 3 chapters
marble rock
okay