Lots of good food then
#book-recommendations
marble solar
quick hornet
oh definitely
only problem is that it's western canadian so the poutine sucks
i miss genuine poutine man, worst part of quarantine is moving back west and not having access to cheap quality poutine on demand
marble solar
IDK what poutine is. I'm from socal. Never been to Canadia
velvet briar
It's fries with gravy and cheese curds
hearty steppe
I never tried it cause at the time I was trying to eat healthy when I visited canada lol
still trying to eat healthy >.>
quick hornet
poutine sounds absolutely disgusting when like
described to someone who's never had it before
but it's actually great
and i say this as someone who doesnt like gravy all that much
gray gazelle
It makes u kinda feel like a fatass
marble solar
That sounds fucking delicious then
I don't like gravy at all
But that sounds good
velvet briar
I have never experienced "not knowing what poutine is" so I just tell everybody what it is expecting they'll think it sounds great
It really is great haha
quick hornet
it's pasta from an alternate reality where italy was full of lumberjacks
velvet briar
It's fries with gravy and cheese curds
broken meadow
i want it now
i don't usually have gravy
i don't even remember the last time ive had it
cus brown people cuisine
idk
where do i get this poutine
hollow peak
poutine is ambrosia
the canucks made one spectacular treat and now I am convinced of canadian superiority
frigid comet
poutine is very good
slender sphinx
I would like some poutine
fast gull
Anyone drop four book recs for me? Preferably highly self contained.
2 introductions to analysis
2 introductions to topology
If any of the books intersect topics that is fine too as long as they don’t assume too much from the reader that isn’t in the book.
🇮🇱 Will pay 35 shekels for this information
gray gazelle
analysis: pugh, rudin 
topology: munkres, lee
gray gazelle
fast gull
i’m doing pugh right now
but i’m trying to have plans over break
seeing if I can move through atleast 1 book in each topic over break
Also please give me your comparison of munkres and lee
6 weeks
I don’t mind spending 8 hours a day
I can afford to
i will try and post attempts to solutions here
Ok
i’ve heard rudin is notoriously hard
i am learning bits and pieces of analysis in my class rn
pugh is a lot of topology
for one section
i like topology but it seems hard to connect to analysis in general
yeah I haven’t
am in an analysis class
only 2 months
nope
it gives stupid hard questions
yea
yea
i mean i’ve been playing around with connectedness and compactness a lot because a good number of questions ask if two spaces are homeomorphic
I was told recently that a shortcut in telling if two spaces are homeomorphic are to count the ends of each space, but I was also told to not worry because it is highly topology related
frigid comet
rudin, pugh, tao
munkres
fast gull
munkres seems like the choice of topology book
how long is it? finish able in 4 weeks? 8 hours a day
frigid comet
some people don't like how long it is, but I think it is gentle and well explained
there is no need to go through everything
frigid comet
definitely no need to do the algebraic topology part of it
frigid comet
yeah being completionist with books is not wise/doable in higher maths
as you go further your needs will be more specialised
and you will pick bits and pieces from everywhere
fast gull
It doesn’t hurt to be completionist
doesn’t it only improve my understanding
or diminishing returns?
frigid comet
it wouldn't if time was an unlimited resource
fast gull
probably more effective to jump from topic to topic at this point
time is unlimited during my break
frigid comet
very much diminishing returns
fast gull
i won’t work at all
frigid comet
when I say unlimited I mean literally unlimited
fast gull
lol
frigid comet
not having free time during a break
fast gull
i won’t have a job or school
fast gull
might as well explore is what you are saying
frigid comet
it's not even about exploration necessarily, am not recommending you dip your toes in lots of different things
just that in the typical progression of a mathematician, you will not need more than some of the munkres material for quite some time
and even then, only if you go into certain areas
fast gull
what should I do after first two relevant chapters?
and wanting to learn more topology
frigid comet
hmm, well let me open it and see what I know/use lol
fast gull
6 weeks and two chapters is definitely doable
yea ofc
how many exercises per chapter 150?
hmm
i don’t know what is specifics of each
yea ofc
but how does differential compare to algebraic
generally speaking
how so
frigid comet
In part I, I would say I know all of it, although I have forgotten some of the metrisation theorems / they are far removed from my work. Have covered pretty much all of part II as well but almost never need any AT. I would say there is very little that I use directly from this book, as I tend to work in a less abstract setting, eg specifically on manifolds where some of the more pathological topological possibilities are not relevant. It is of course important to completely assimilate the basic topological notions like compactness, connectedness etc though.
fast gull
wikipedia gives descriptions I can always read there if need be, but want y’alls input
wat is ur work gemez
frigid comet
Yeah slim, I like munkres but have never systematically worked through that book in particular.
I am a microlocal analyst @fast gull . My work involves the study of the interaction between PDE/spectral theory and geometry/dynamics using ideas from harmonic analysis and machinery like pseudodifferential operators and fourier integral operators.
frigid comet
idk probably, spivak's calc on manifolds I more or less systematically worked through. but generally you will have encountered some of the topics in books before, and will not need to go through in such detail.
frigid comet
tools is a little more individual. I would call integration by parts a tool
machinery is a whole setup of tools that interact with each other
frigid comet
eigenvalues and eigenvectors
gray gazelle
did someone say spectral theory 👀
fast gull
i wonder when i’ll be ready to learn about pdes
frigid comet
but linear algebra mostly studies the finite dimensional case, in the infinite dimensional case you need analytic structure to say much, and that is what the subject of functional analysis is about
you need a fair amount of analysis to get to the more interesting things in PDEs, I hated the subject at first because my first undergrad encounter was computational and boring.
more about solving simple PDE than proving theorems about PDE
fast gull
ok
so i should probably refine my ode understanding and analysis understanding, then learn about computing some pdes and then learn da theory
imma give it one full year
i can’t really take classes for this stuff until 2 years from now
frigid comet
yeah, when you eventually get to it, Evans is a good first book for PDE
fast gull
so i gotta use winter and summer breaks
frigid comet
and the early chapters you can handle without tooo much theory
fast gull
ok
frigid comet
but you should be quite proficient with multivariable calc at least
and basic ideas in analysis.
fast gull
what are some proficiency tests. My metric was going to be: finish 5 questions from every preliminary exercise in pugh, to test for analysis proficiency
i’m not sure for multi variable or diffeq
it’s not like I can retake classes and I don’t want to tutor so I think i’ll need to pull exercises from books
frigid comet
idk hard to tell, just see how you go
fast gull
tru
but i got a year and a good amount of free time each day
would like to plan it out at least
What are some things I can do to test my understandings of diffeq and multivariate. I don’t want to go through the fill in the gaps as you learn method
tribal kernel
Evans is a good but pretty theoretically difficult book. A big step up from other PDE introduction books I’ve seen, but the one that gives the lost care to theoretical development
fast gull
ok ty for help men
i spent a good 30 minutes making a book list
imma try and finish the books in two years
completing the parts that are necessary atleast
narrow crest
silk quartz
Please read #❓how-to-get-help and do not post the same question in multiple channels.
marble rock
hi
i want spicy hard advanced group theory text
with hard exercises
im done with real single var analysis
and read dummit and foote abstract algebr
uptill field and glaois theory and hoffman kunze
gray gazelle
advanced group theory exercise: prove the classification of finite simple groups 
marble rock
no srs please
some group theory ( or algebra tbh) text that dives into advanced shit
and will just improve me
atm ath
pearl imp
My calc book doesn't give many proofs (or so I think at least)
I'm looking for a calc book as supplementary with many and good proofs
calc1 to calc3
I'm still beginner
Please ping me
random spear
@pearl imp I'd just try Calculus by Tom Apostol*
random spear
I wouldn't say so. Has good proofs, gives good challenge at the reader simultaneously, and it's pretty intuitive.
It is a bit strange imo (from what I was used to) that it starts off with integral calculus rather than derivatives, but in the end it's pretty intuitive regardless.
pearl imp
Apostle is something with religion?
I'm not native English speaker
someone who forebodes or sees future
thanks again
marble rock
no
what is the name
@inland coral
what else
do you recommend
ii skimmed it sounds like alot of writing
any other rrecommendation?
i meant like
idk
is there a textbook taht like
teaches group theory at an advacned lvl but like at the same time
oges to another field
so i cna learn morre?
like for example a text on group theory and representations
or like group theory and topology
hasty turret
Dummit and foote?
marble rock
other than that cuz i got bored of it
thats where i learnt all my alg from so
want something new
hasty turret
Any other algebra book?
marble rock
what doyou guys thinnk of bell groups and representations by alpeprin
let me check the char theory
hasty turret
Maybe,read galois theory?
sudden kindle
だから いっそ いっそ いなくなれ
hasty turret
crystal kraken
timber mesa
we don't speak anime here
hasty turret
nani
rigid badger
Hello! Is there an online website that covers all 7th - 9th math?
wooden sparrow
Hello! Is there an online website that covers all 7th - 9th math?
@rigid badger khan academy?
rigid badger
Is there anything else that’s free?
rigid badger
I suppose ill check it out, thank you
stray veldt
what' wrong with khanacademy for your purposes?
gray gazelle
That is the point of Khan Academy. To be non-commercial.
tribal kernel
So khan academy would likely be better than libgen for the purposes of 7th-9th grade math
gray gazelle
I suppose one might assert that.
Although I have seen some very well written books pertaining to arithmetic.
By books, I mean a single one.
tribal kernel
Which one?
gray gazelle
"Elemente der Arithmetik und Algebra" by Harald Scheid. I am however unsure if there is an English version of it.
native dome
captain underpants is rlly good
gray gazelle
yeah it does
broken meadow
thank you
tribal kernel
What happened?
broken meadow
just chicken nugget spam
tribal kernel
Oh and was deleted I guess. Cool
broken meadow
Banned.
wooden sparrow
Nice
gray gazelle
guys, I want to search for a chemistry book that is totally for beginners, (that have no knowledge about chemistry).
silk quartz
Maybe ask on the chemistry server in #old-network ? This is the math server. We do math here.
gray gazelle
true, I am going to the chemistry server, sorry about this 😅
slender sphinx
@gray gazelle yeah not the right channel; I would recommend zumdahl's chemistry though
gray gazelle
zumdahl's chemistry? Is that an other discord server?
oh wait, I found in chemistry discord server the resource channel
and found zumdahl's amazon book.
slender sphinx
Yes, zumdahl is the author of the book
gray gazelle
Ah, I recall this man, zumdahl
hearty steppe
I just started reading Zumdahl. It’s pretty good
smoky surge
chemistry KEKW
tribal kernel
Labs are bleh
Chemistry and physics are cool though
I’ll trash physics a ton but I also have a degree in physics
gray gazelle
Do you use Gauge spaces in physics?
tribal kernel
Physics can additionally motivate some really cool questions in math. I lot of the really awesome pure math research I’ve read has come from mathematical physicists who found cool math related to physics problems
storm sleet
Physics presents a great lens to look at and reframe mathematical problems
I should rephrase
Some mathematical problems
sage python
Physics does give some conjectures
Quantum chaos is an example, I just did my NSF on it
gray gazelle
String theory is also very interesting mathematically.
I'm not sure how interesting it is from a physics standpoint anymore however.
tribal kernel
My stat mech professor in undergrad used several lectures to rant about why string theory wasn’t a good theory
hearty steppe
In what way isn’t it good
silk quartz
It makes no testable predictions, so far.
tribal kernel
He said that a theory that try’s to preserve symmetry and beauty is necessarily not going to be a good theory because nature isn’t built to be beautiful/symmetric
But also that the assertions of string theory only match some of the current theory while the background behind sting theory is currently untestable or unnecessarily complicated.
marble solar
But that doesn't mean it is useless just because we can't test it now
Or a good theory. Just because something is unfalsifiable now, doesn't mean in the future it won't be
Also, earlier physics always had experiments able to weed out bad theories, like the aether theory
String theory hasn't had this axe to chop off the excess info, so it's hard to say what is excess and what isn't
Plus Ed Wittens work has been important in giving a description of the Alexander Jones polynomial
(Also RIP Alexander Jones)
tribal kernel
I don’t know enough to make a judgement on it for now but it seems quite complicated. My professor really didn’t like it though lol 🤷♂️
soft terrace
did they ever have any textbooks or popular books on the aether theory that you can still read?
tribal kernel
There was a unit on it in my modern physics textbook with a couple calculations, but it was more a thing to show why that didn’t work
Not sure how long we had the aether theory
timber mesa
I think it seemed like a feasible theory until the https://en.wikipedia.org/wiki/Michelson–Morley_experiment, 1887
iirc Berkeley Physics Course vol. 1 has a chapter that briefly explains this experiment but I think s00mb means a pre-1887 physics textbook that describes aether theory
tribal kernel
I think it was probably almost always in journals before then. I don’t think it was around for too long after the classical electrodynamics theory
timber mesa
guess https://en.wikipedia.org/wiki/Aether_theories#Historical_models is a good place to start
some works by Newton, Riemann and Kelvin are mentioned, in the case of Newton even the specific treatise where he develops the theory (the third book of Opticks, 1704)
tribal kernel
Ah shoot I lie don’t listen to me lol
hoary creek
The book "Scholars Advanced Technological System" is great, it is a novel based around math and science, makes high level math very interesting. Not quite a textbook, but covers a lot of scientific history.
tribal kernel
Ooh that sounds cool
hoary creek
the sheer amount of knowledge in this book confuses me
i think it was written by a group of people
but there had to have been at least 3 or 4 phds
in the group who wrote it
prob more
i have googled random stuff through it
hundreds of professors, theories, and methods have been mentioned
and all of them are accurate
now that i think about it
the translation group must have a massive number of phds too
clever yarrow
Which book is this, I cant find it
hasty turret
"An introduction to numerical analysis" is what I get when I google this
clever yarrow
But the page 256 is nothing like it should be
The reference should be the derivation of SImpsons rule by substitution
hasty turret
Maybe some other page?
clever yarrow
No Sympson's in the context whatsoever
clever yarrow
Thank you so much!
unborn dragon
Can i get some recommendations for introductory textbooks in representation theory? Assuming the usual undergrad knowledge background.
pearl imp
Alternative calc books with good proofs (less than apostol also OK) but not as old as Apostol?
I like new format, maybe some links inside the book etc.
Apostol didn't have that.
sage python
@unborn dragon so depends a bit on what type of stuff. Serre is the correct answer for rep theory of finite groups
People like Fulton-Harris too, more examples and afterwards gets into Lie theory
For a fairly general book check this out: http://www-math.mit.edu/~etingof/reprbook.pdf
gray gazelle
Bokuno..... Pico?
gray gazelle
Wait y'all can react in this channel? I don't have the option to
honorable role can i think
they can do the initial react
crystal kraken
What is the logic behind these restrictions ,anyways?
pine igloo
🤣
broken meadow
no clue
silk quartz
Not sure about the reaction thing.
The nickname thing is, we have several thousand users, and people abuse the ability to change their nicks.
It makes it hard to keep track of folks.
gray gazelle
Big brother wants to keep track of you 👀
crystal kraken
gray gazelle
crystal kraken
Don't sully my sully
fast portal
It makes it hard to keep track of folks.
@silk quartz you can always use the user ids iirc tatsu did that when asked to keep logs
You cant change that all
And it is less tedious than using noted
crystal kraken
gray gazelle
sleek python
wait can't non hounourable react in any channel? Even #chill ?
I thought it was just because this is a serious channel
quick hornet
i think the reaction thing is back when this channel was straight up closed
to non-honourables
like read-only
chances are, no ones bothered to change it yet
ill bring it up
prisma snow
Why could the dishonourable not talk about books?
timber mesa
us plebeians don't read book
stray veldt
it's back when this channel was being tested
prisma snow
We no read book, we watch utube
quick hornet
ok you should now be able to react here
marble solar
Solving the important issues
Anyone have experience with Apostols Dirichlet Series and Modular forms text?
soft terrace
anyone got a good recommendation for a book on solving dynamical systems?
soft terrace
nm
obsidian basalt
My university uses this book as official recommended bibliography for Algebra I
Is that a good book for introducing myself in Algebra for pure mathematics?
Should I stick to that one or there are better options?
shut grail
@obsidian basalt I used this book and I found it a pretty cool source as an introduction to abstract algebra
Contemporary Abstract Algebra https://www.amazon.com/dp/1305657969/ref=cm_sw_r_cp_api_i_LeBNFb5GG4T44
fast gull
cool
soft terrace
If I am using an older textbook to study a intro topic, how old is too old in general? For example if I am reading a chaotic dynamics book, is being published in the early 90s too old?
sleek python
90s is recent in most domains
sage python
There has been more time from 1990 until now than from the beginning of time until 1990
soft terrace
ok
dense wren
If it’s introductory chances are not much has changed
runic hatch
i feel like it'd mainly matter if you're doing active research into the topic
marble solar
The first edition is from the 50s
I once got a copy of hartshorne from the library for class
The guy was like the most recent one is from the 70s
Is that it?
I was like, yah that's the one
sage python
Euclid elements is kinda up for debate tbh
Mostly culture
But yeah for a lot of areas the foundations are pretty set in stone
runic hatch
is elements actually a good book to learn from?
like say for euclidean geometry and basic number theory
or has it been surpassed now
heavy barn
I hate synthetic Euclidean geometry
valid moth
@sage python that was like my first math book actually
because my dad is a history nerd
and not much of a math one
all i remember about me and math in single digit age was my dad reading elements with me and teaching me 'advanced operations' (as in multiplication and exponentiation)
fast portal
Damn what a based dad
obsidian basalt
Does anyone have some cool book recommendation that is about showing many fundamental theorems of mathematics, just from the axioms and logic?, that is really good at leading you through that travel?
hasty turret
Any algebra book?
obsidian basalt
Like for example a book that really focus on trying to prove the really most fundamental parts of mathematics, like addition, multiplication, etc... and so on, and at the same time is kinda friendly to read (I mean that with some background in logic, set theory, algebra, arithmetics and experience doing basic proofs) can help you to go in such travel.
Yes, probably that is what I am looking for actually, some kind of rigorous algebra book, I don't care if it is really long as long as it is a bit friendly with explaining the processes
gray gazelle
Bourbaki the elements of mathematics.
I would not recommend it usually but it seems to exactly fit your description
Or elements of set theory would be another one.
gray gazelle
It is what was asked for however.
calm crane
no
it doesnt fit it
at all
it's garbage
i lost brain cells reading it
usually analysis books have some discussion on like
peano axioms
and constructing reals
if you want that
molten wave
if you're working in ZFC, you'd first wanna prove induction from infinity
and make a very delicate construction of recursive functions
calm crane
axiomatic set theory jech is pretty decent he has basic set theory with someone else and another one jus called set theiry
molten wave
to define addition and so on, on naturals
gray gazelle
peano axioms
and constructing reals
These two don't fit together.
calm crane
?
gray gazelle
The peano axioms talk about natural numbers not real numbers.
molten wave
I'm sure they mean peano axioms internalized to ZF
calm crane
yes
gray gazelle
Okay
molten wave
proving them is tricky tho
gray gazelle
Eudoxus reals 
molten wave
prove that there exists a function + : NxN -> N that satisfies the two axioms
it's not easy
calm crane
you end up with proving some form of induction
gray gazelle
Just double induction
obsidian basalt
Thanks a lot you both for the information and recommendation
molten wave
and that is pretty tricky to get working in ZF
gray gazelle
Then define *
molten wave
Define +1 recursively on the finite ordinals
@gray gazelle what gives you the power to do that
gray gazelle
The axiom of infinity and recursion theorem
calm crane
recursion theorem?
molten wave
yea I'm talking about a form of recursion theorem
it's very nontrivial to prove and/or construct
suppose you have a set X with an element x in X, a function s : X -> X. Then there exists a unique function f : N -> X that would satisfy the recurrence relations f(0) = x, forall n, f(succ(n)) = s(f(n))
that's the theorem
furthermore an explicit construction of this function can be provided
if you're not into iota quantifiers
it's by no means an easy result
which I came to appreciate by proving it in coq 
trail tusk
Proving 1+1=2 via jargon, nice
hasty turret
*Defining
trail tusk
Nice
quartz pawn
Any of y'all got recommendations for books on the philosophy of math
gray gazelle
It's not a book but I recommend the videos JDH made for his class.
quartz pawn
JDH?
quartz pawn
Thanks 
gray gazelle
This is still ongoing but it's pretty good so far.
gray gazelle
I find wildberger very manipulative and unprofessional.
velvet briar
He often goes for something like "This thing can't be done in real life, so we can't do it in math"
Not that I have watched him throughly
gray gazelle
In a debate on his channel he just ended the video while the other side was trying to refute his argument.
velvet briar
Debates are awful lol
gray gazelle
He has been a big let down for me personally in terms of philosophy.
random spear
I saw talk of Peano Axioms and I actually just shared this in another Discord so I figured I'd just copy paste here: https://cdn.discordapp.com/attachments/206376365774077952/772579042763341834/7_Peano_Axioms.pdf
molten wave
that is an odd presentation
random spear
@molten wave it was my uni's quick little introduction to it (and some other stuff) for prefrosh.
It was just a quick little program. It was nice though.
molten wave
After all, “=” is merely a symbol until we declare it to have some important
properties.
immediately writes "x ∈ N" on the next line
and like I would be on board if "_ ∈ N" were consistently used as an atomic one-place relation
but on the next page it says "N ⊂ V"
random spear
Lmao
@molten wave sorry haha, but we do expand on that in earlier chapters.
This was the 7th day of it.
molten wave
Zermelo-Frankel (set theory)
random spear
Oh mb.
molten wave
mathematics really doesn't like being suspended in air
random spear
And in that case yea, I suppose so, I didn't realized there was an independent model of it.
molten wave
you could construct a concept in terms of other concepts
or assert the concept axiomatically saying that there's no concepts below it
doing both at the same time is kind of inappropriate
random spear
Yea I suppose I see what you're saying.
cobalt arch
Any recommendations on ODE books? I want one written with rigor and clarity of thought.
inner sentinel
Edward and Penney
gray gazelle
i looked into this a while back. sec, im eating right now tho
i think the main ones i was looking at were hale, perko, arnold, and tenenbaum
wooden sparrow
Yea what are some more good diff Eq books
@hearty steppe do Differential equation books contain both ODE and PDE?
soft terrace
usually just ODE but might have an intro section on PDEs @wooden sparrow
wooden sparrow
Okayy
obsidian valley
@quartz pawn sorry to necro but I'd also recommend Linnebo Philosophy of Mathematics if you are new to the field. It's a bit heavy on Frege, but thats for a good reason. Its a very very new book as well. You can probably find it for free in your universities library.
Gives a very good background and introduces you to a lot of the core ideas pretty well IMO.
wooden sparrow
Hot take: Lang's basic mathematics needs revision because of existing erratum and for improving illustration
hasty turret
I mean every book has mistakes
marble solar
Hotter take: You can update it with visualizations
gray gazelle
Tfw we will never get algebra 4th edition
wooden sparrow
Also,Lang isn't alive
@hasty turret Won't we get some compensation if we revise the book and give to the publishers?
karmic thorn
Unlikely. If they're interested at all, you might get your name mentioned in the preface of a revised edition.
gray gazelle
I would kill to have my name in Lang's book
fast gull
Anyone have any sources on what it’s like to write a math book? An example being a blog or short article. I wonder what the process was like now compared to before.
karmic thorn
Is Maclane's Algebra a good introduction to algebra at the undergrad level?
I skimmed through the contents and it looks pretty decent, but I'd like to know from someone who has used the text before.
wise vine
Does anyone have a copy of Kostrikin's Introduction to Algebra? Apparently, he cites it frequently in his other book (Linear Algebra and Geometry). Sadly there is no english copy on libgen available.
hollow current
i have russian one 😄
prisma snow
@hollow current is volunteering to translate the whole book for you, free of charge! How nice of you.
hollow current
@hollow current nah, i said i have russian one so you can translate it to him
and as you said, free of charge!
prisma snow
I don't speak Russian, but I'll try!
wise vine
What a shame that many wonderful russian books are untranslated. I guess I'll stick to Vinberg for now haha.
wide sail
Some German Students here?? Want to exchange some opinions about good literatur for analysis
stray veldt
@wide sail Amann, Escher is the standard, but maybe better as a reference
i also like Behrends as an easy introduction
hasty turret
Rudin is not the standard?
stray veldt
not when it comes to germany
(and it shouldn't be, Amann Escher was translated and is better)
prisma snow
@stray veldt I'm curious so looking it up on libgen. Are there 3 volumes?
stray veldt
Amann, Escher is a 3 book volume, yes
basically single variable, multi variable, measure theory
the first book has a lot more stuff, it even does group theory and linear algebra at the beginning
because that is needed later
the series is 100% self contained
wooden sparrow
@stray veldt when can these volumes be read? What're the prerequisites?
stray veldt
there are no formal prerequisites
but they are famously hard to read (kinda like rudin)
wooden sparrow
Oh, but they're the best to study analysis from you said, right?
stray veldt
best analysis books imo, but maybe not best to study from
especially not self study
but i don't know, i haven't really done it so 🤷
wooden sparrow
Ohh okayy
smoky surge
If had an interest in learning about manifolds would that just be topology ?
or could i like just focus
on that
tribal kernel
Manifolds are studied by themselves in any differential geometry course, but then you restrict yourself to studying smooth manifolds. Nothing wrong with that, but you won't discuss many topological manifolds. Most intro topology/AT courses won't focus only on manifolds
sudden kindle
Yeah diff geo
sage python
Diffgeo in principle does more than just raw manifold stuff
You're usually considering some structure beyond just smoothness, like a Riemannian metric
smoky surge
ok so if I was interested in dif geometry or just focusing on manifolds for the topology what preques? It looks like in the #books-old it doesnt mentioned any preques for topology and I dont see diff geometry in there
this will entirely self study mostly because im interested in manifolds in the context of dimensionality reductions
steel viper
oh speaking of
@sage python can we update the #books-old channel w/ some alg top recommendations
i think at least hatcher and bredon could go there
and i havent read it but tom dieck
also the algebra section should at least have artin
and D&F
marble solar
Spanier AT
steel viper
as far as i know bredon is basically updated spanier
in terms of style
though i dont think bredon does obstruction theory
sage python
Bredon and Spanier are kinda different styles I think
steel viper
i might be confusing it w/ tom dieck or hatcher but i heard that one of them at least was like
very similar to spanier in style and order
but just new
i havent read spanier tho so like
¯_(ツ)_/¯
steel viper
but yea we should for sure add some AT books to that last and some alg books there
maybe it doesnt have to be as comprehensive as the ones in the pinned list here but like
dapper root
I thought there was a Dami algebra book breakdown?
steel viper
ya but its not in the books channel
marble solar
AG book rec = Vakil
steel viper
and uh maybe number theory should have ireland rosen because everyone shills that
but yea this should be forwarded to ashura i think
hollow peak
and uh maybe number theory should have ireland rosen because everyone shills that
apostol and ireland and rosen are god tier
marble solar
I'm interested in Apostol's dirichlet series and modular forms
hearty steppe
lac?
karmic thorn
Expository papers by K.Conrad on proof-writing, group theory, elementary number theory and more.(Can be pinned): https://kconrad.math.uconn.edu/blurbs/
obsidian basalt
A good book to get started with probability and statistics?
That is a field in mathematics that still remains unexplored for me. Or to put it better, I don't know sh*t about it
night knot
I liked Probability and Statistics by Morris DeGroot
rotund sphinx
Does anyone have a recommendation for a book on linear algebra that has a lot of practice problems?
gray gazelle
friedberg's book has a ton of practice problems ranging from computational and straightforward to trickier proof questions
also has true/false questions at the start of each exercise section, which i really like (each one comes with answers)
calm scarab
Hi guys, I need to pick up machine learning for a research project I'm starting soon. I'm looking for a textbook for neural networks, something purely mathematical and formal. I've done a discrete math undergrad course. Do any of you know of any?
I'd also appreciate any general advice you may have for picking up ML. No clue where to start.
gray gazelle
I'm not sure what you mean by mathematical/formal (I'm guessing you don't mean something theory heavy), maybe have a look at the neural networks chapter of bishop's pattern recognition book? Or there are probably lecture notes or something on the internet
calm scarab
I'm guessing you don't mean something theory heavy
Oh I do
bishop's pattern recognition book
I'll look at this though ty
gray gazelle
You could perhaps try understand machine learning by shai etc. for some PAC type stuff, idk if they cover any optimization stuff (I've only read like a quarter of it)
Although this book is basically a math book/requires some mathematical maturity
marble solar
@rotund sphinx Schaum's outline to linear algebra
20 bucks, lots of solved practice problems
rotund sphinx
Thanks Ill check it
calm scarab
@gray gazelle Thank you 🙂
Notation seems pretty standard, scrolling through maybe it'll be okay
grave monolith
https://youtu.be/uo1xDbsYAcU
@N/𝔄#0985 Thanks for this, very enjoyable.
obsidian basalt
I am reading a book someone recommended me here (The Art and Craft of Problem Solving by Paul Zeitz) and I was wondering if there is a way to train logic, I mean if there are books that are about "logic exercises" mostly, without involving math at all. (Propositional logic)
warped wave
Velleman's chapter on logic???
idk if this is what ur looking for
there's math obv but u can look for non math ones
slender sphinx
@warped wave surprised to see you here, hey 👋
warped wave
sup
slender sphinx
@obsidian basalt yeah, velleman's "how to prove" it has some nice exercises
honestly though, the rest of Zeitz's book does not rely on propositional logic that much
Assuming you understand the ideas and basic rules, you should feel free to gloss over it a little
obsidian valley
Grind UCLAs Logic2010
I'm not sure if you can get a student version without it being attached to a class though
obsidian valley
I'm sure this question has been asked many times but I can't find anything in #books-old so,
Where is a good starting point for learning abstract algebra? Maybe out of (Dummit and Foote), Artin, Fraleigh, Gallian
karmic thorn
I'm using Gallian and I love it.
obsidian valley
The "groups and symmetry" course at my uni uses it
But the "groups, rings, fields" course uses Dummit I believe
karmic thorn
Dummit is certainly more advanced, I guess you can skim through the contents of both books and see which one suits you.
Gallian has coverage of applications which might justify its use in a "groups and symmetry" course.
obsidian valley
I have a moderately light semester in the winter so I imagine I could make time for Dummit.
Ah. Any opinions on Artin or Fraleigh?
karmic thorn
Haven't used either. I guess Artin is also the standard reference besides Dn'F, never looked at Fraleigh. 
obsidian valley
hm well maybe I'll grab all 4 ||(thanks libgen)|| and try to pick one as my main source.
thanks
hasty turret
Dummit and foote is excellent for group theory
Not sure about other parts
It has a ton of examples
So,It may feel "fluffy"
obsidian valley
I think that probably should be my #1 choice as well, from what I've heard.
It's annoying that the algebra course I have to take uses Gallian
¯_(ツ)_/¯
sudden kindle
DUMMIT THICK
karmic thorn
Gallian is good at what it does. 🤷♂️
prisma snow
Dummit and Foote is too fucking wordy and long.
It takes forever to work through it imo
quartz pawn
I think some of the extra exposition it gives is good though; this is on my limited bit of reading through the first few chapters.
Some people think a decent bit of it is extraneous though.
Artin is real terse.
I'm using it now.
gray gazelle
I like short books
hearty steppe
There are short books then there are deceptively terse books like Artin
gray gazelle
short books
do carmo's riemannian geometry ☺️
gray gazelle
51
i wonder how quickly one could read it
well i have a week off of class
Oh, is it the one on libgen, 31 pages?
gray gazelle
to a decent extent, i think
i mean, i took a course that roughly followed lee, and i'm halfway through a riemannian geometry course lol
Speedrun milnor DT challenge
I guess I'm not even sure what DT even is
sage python
Did someone say differential topology?
gray gazelle
Dami could you read me milnors DT for bed time story tonight
sage python
Sure, and when we finish what do you want to follow it up with? Shouldn't take more than a few minutes tbh
marble solar
I read through Milnor, took careful notes, made sure to fill in gaps
Got to grad school, prof was like "I hate diff. top."
I was like nice
wise crater
Anyone ever read Undergraduate Algebraic Geometry by Miles Reid
its a Cambridge Press book
and I found it under a pile of books
Nice!
dapper root
I read a bit
I still don't understand the drawing on the like first few pages
It's like of a conic or some shit?
Idk what he's drawing there
wise crater
they're elliptic curves
they show up a lot in alg. geometry
unless youre talkin bout the stuff where two ellipses intersect
i just started reading so im not quite there yet
wise crater
oh okay
Yeah lookin through the table of contents it seems theres nothing bout schemes (i've very lightly looked into algebraic geometry)
wise crater
are there any other undergrad texts for algebraic geometry you'd reccommend
i'm doing galois theory next term and planning on doing a reading on this subjects using these books over the summer if I cant do work with my prof
sudden kindle
I havnt read it but my prof recced Basic Algebraic Geometry by Shafarevich
wise crater
gonna pirate harshorne lmfao
sudden kindle
Hartshorne
dapper root
The pdf probably has the same quality of binding as my physical copy
wise crater
oh fuck why are these books so fucking expensive
sudden kindle
Hartshorne is not a good introduction
wise crater
i figured from your reaction
dapper root
yeah but you have to use it as your first book and skip the part on varieties too
that is the path that has been laid out for generations
wise crater
i forgot how expensive textbooks can get jesus christ
calm crane
liu exposition as replacement for hartshrone ch2 for me
dapper root
I feel like
I should have read Liu for divisors instead of
whatever hell I went through with Hartshorne
calm crane
dapper root
I feel like a person who cares about arithmetic curves and shit would be good for divisors thinking about it now
marble solar
I dislike Shafarevich
I think the best way to get into AG is Algebraic Curves a la Fulton
And then Learn Elliptic curves
Then dive in
For a brief stint, I did try to get into AG
But then I got sucked into 3-manifolds so 🤷
calm crane
oh nice which book
calm crane
ah ic
marble solar
Those are the three papers I read in depth
The first one and the last one are related
marble solar
Basically Blair et Al. were able to find another class of knots where Pardon's technique doesn't work
But they came up with a similar method that does work
Yet their method doesn't work on p,q Torus knots
Geometric Topology is a super fun subject
I wish it was taught more
calm crane
yee
marble solar
Or more popular
calm crane
4D
hasty turret
Dummit and foote ch 17?
gray gazelle
Cohomologay
gray gazelle
Thanks
Thanks
and lol
molten linden
Does anyone know a good book for probability and statistics with a lot of practice questions?
hearty steppe
molten linden
Thanks
halcyon hornet
I am in 7th grade.
I really love mathematics, and want to be great at it, and master it, especially the basics now.
I want to be able to solve difficult sums and understand them.
I really want to win the IMO.
So guys can you please recommend me some great books for it, for being able to solve and understand difficult sums and winning gold medal in the IMO(in the future).
Or something like a method or steps to do that, win the IMO and understand and solve difficult sums.
Thank you, your help is greatly appreciated.
hasty eagleBOT
ariana:
gray gazelle
maybe difficult infinite sums?
runic hatch
My guess is hard algebraic equations
karmic thorn
@halcyon hornet Consult books by AoPS. They are geared towards olympiads such as IMO.
gray gazelle
the fbi is after you.
halcyon hornet
But could not get all, if someone has some, please give.
gray gazelle
Maybe check out some day Terence Tao's book "Solving Mathematical Problems"
calm crane
libgen /shrug
pine igloo
Does anyone know a good book for probability and statistics with a lot of practice questions?
@molten linden there is one called "Probability and Statistics for Scientists and Engineers", Pearson edition I guess, highly recommend it
molten linden
Thanks
pine igloo
👍
royal viper
Hello, next year I want to go to the UK to study and I wanted to know what textbooks should I buy to learn A and AS levels (both in Maths and Further Maths) thank you 🙂
gray gazelle
@royal viper it depends what exam board you are doing but for edexcel you can get the pure mathematics book 1 and 2 then your option for further math studies. As for maths i'd reccomend edexcel as and a level statistics and mechanics and pure maths both books 1 and 2
1 is as level by the way and 2 is a-level for non further math options
royal viper
@gray gazelle I'm not doing the exam, just learning the British syllabus because it's a bit different from the French one.
brittle marsh
what book(s) would be good as a first course in real analysis?
gray gazelle
i think ross elementary analysis is a common first book in analysis
tribal kernel
Abbot, Marsden and Hoffman, and Bartle and Sherbert are good books
Marsden and Hoffman is probably my favorite out of that bunch though
marble solar
I've heard good things about Bartle
I still think the best is Spivak's Calculus
Then move onto Pugh's Real mathematical Analysis
If you've had your calculus sequence, I like Spivak's Calculus on Manifolds too
hearty steppe
ill def check out Bartle sometime myself
obsidian valley
If I've done Calc I and Calc II and multi var but not any sort of analysis courses, would I gain much out of Spivak Calculus or is it better to just go straight to calculus on manifolds
I think I have the "mathematical maturity" for calc on manifolds, I just don't know if I'm missing out by skipping Calculus
gray gazelle
spivak's calc on manifolds doesn't really require much serious analysis i feel
like nothing you wouldn't have learned in calc 1 and 2 and mvc
obsidian valley
am I missing out on some interesting stuff by skipping calculus
gray gazelle
what are the course codes? i can give a more confident answer
obsidian valley
or are there specific chapters I shoudl check out
I've done the equivalent of MAT137 + a bit of 237
gray gazelle
hmm
obsidian valley
UTSC has nothing close to 157 😢
gray gazelle
😔
i think you could brush up on some basic concepts from topology (even though spivak introduces most of what you need)
like
the heaviest analysis in that book is in the very first chapter + the integration chapter
gray gazelle
(i mean spivak introduces those in calc on manifolds)
gray gazelle
like you might wanna know some basic facts about sequences and series of functions for calc on manifolds, but nothing too in depth
i think spivak's calculus covers what you need well
idk if 137 covers that
obsidian valley
Not much of sequence and series but that was mostly cause covid
brittle marsh
how much on sequences and series would one want to know?
gray gazelle
ah you should probably be comfortable with sequence arguments for calc on manifolds
stuff like
what's that one where any bounded sequence has a convergent subsequence
obsidian valley
Right I remember doing that proof
brittle marsh
oh alright
obsidian valley
Yeah probably a good idea for me to refresh though, been a bit
gray gazelle
take a look at the book "advanced calculus" by folland, it's the mat237 book at utsg i think (also the secondary book for 257). the first chapter covers what you'd need for spivak's calc on manifolds (and in a better way too i feel)
gray gazelle
it's a good book
i think it's a great complement to spivak's calc on manifolds
257 was such a fun course ☺️
obsidian valley
I think our 237 uses... Kolmogorov?
err the analysis part of our 237 at least
so MATB43
gray gazelle
lol
dapper root
FOLLAND POG
gray gazelle
good book
valid moth
is this comparable to spivak
hearty steppe
What does POG mean
shadow nebula
when halloween is 11 months away
gray gazelle
so, it looks like we learn today that 4 times is considered spam
gray gazelle
oh, i only saw it 4 times
halcyon hornet
I can not find PDF of some books from AoPs.
Can someone help me in that.
I searched even Z Library.
And after all, the book I got was in multiple images form, so can anyone help in getting the PDF's.
The books are - Introduction to Geometry (which is main)
Intermediate Algebra
and
Calculus
All by Art Of Problem Solving.
quick hornet
ah wait i see what you mean
yeah thats not in pdf format unfortunately
:/
if its not on libgen or pdfdrive, youre probably gonna struggle to find it unfortunately
gray gazelle
you can prolly find a file converter online to convert this to pdf
quick hornet
png to pdf?
gray gazelle
I always use those for djvus don't know if there's one for 7z
quick hornet
ive never heard of such a thing
a 7z is a zip file
this zip file contains a bunch of pngs
gray gazelle
oh
quick hornet
like png to pdf is a thing but
it wont be GOOD
certainly wont be as good as djvu to pdf
better than nothing i guess though
¯_(ツ)_/¯
gray gazelle
yeah
halcyon hornet
you can prolly find a file converter online to convert this to pdf
@gray gazelle can you please name them.
halcyon hornet
Yeah
gray gazelle
I didn't find anything for "mp3 to pdf converter" online, what am I doing wrong?
shadow nebula
gray gazelle
I didn't find anything for "mp3 to pdf converter" online, what am I doing wrong?
dunno
crystal kraken
Not literally that. TTera meant like .jpeg to pdf converter
prisma snow
I didn't find anything for "mp3 to pdf converter" online, what am I doing wrong?
@gray gazelle trolling, right?
gray gazelle
it was a joke
you spelled tterra wrong
Not literally that. TTera meant like
.jpeg to pdf converter
Yeah I caught up on that very quickly
smoothbrains revealing themselves tonight
crystal kraken
gray gazelle
crystal kraken
Sorry, TTerra
gray gazelle
😤
shadow nebula
TTTera ur name is in Torterra
gray gazelle
that's the one everyone brings up
but
it's not actually in reference to that pokemon
hasty turret
It's TT era
gray gazelle
also incorrect 
calm crane
imagine using online converters cant relate
gray gazelle
so what do you use @calm crane ?
shadow nebula
do u have a djvu to pdf converter that preserves searchability? @calm crane
and also table of contents would be good as well
gray gazelle
ddjvu?
shadow nebula
is that for linux? I'm on mac
calm crane
i wrote a script with some commands that came with my arch install lol
shadow nebula
ye I have a script for toc rn
obsidian valley
what actually is djvu i only know it as the thing all my libgen docs come in
calm crane
djvu is a format better optimised for scanned documents
so file sizes smaller
which is really good for like libgen
obsidian valley
ah ok I figured it was some sort of optimized pdf
calm crane
where you have lots of books stored
gray gazelle
how do you even open a djvu file?
calm crane
use a actual reader lol
obsidian valley
get a djvu viewer maybe?
obsidian valley
if i cant open the doc in edge or chrome i dont want it
calm crane
i use zathura and okular depending on my mood
obsidian valley
is there any benefit to the user tho
calm crane
yes
obsidian valley
or is it just a memory thing
calm crane
smaller file sizes
obsidian valley
ok but its 2020 and i dont really care about pdf sizes
calm crane
lol
then not rlly maybe djvu is faster or slower idk actly
i need to run some tests
i jus like my file sizes smol
gray gazelle
the problem is that for some books on libgen, the only filetype available is djvu
obsidian valley
yeah tahts why when i type djvu into google the first thing that comes up is "djvu to pdf" in my history
calm crane
yikes
get a proper pdf reader
that also works for djvu and epub and any funny formats
hasty turret
Just use ReadEra
shadow nebula
https://awesomeopensource.com/project/zegervdv/homebrew-zathura THIS WEBSITE HAS MY FACE
calm crane
my computer is old /shrug
obsidian valley
but im sure it would be worthwhile to get a pdf reader
but also i just hate optimizing my workflow ever
calm crane
yes i have most of my files as djvu
obsidian valley
hence why i dont use linux :v
calm crane
yh optimizing workflow is like
ideally good
but high effort on the few days you're optimizing
once you get it done it feels slick af tho
radiant basalt
my computer always starts dying
@calm crane ahh I thought I'm the only one with an old damn PC lol but nonetheless I crank it up to 90% CPU most of the time.
calm crane
i use vim
calm crane
i unironically use vim occasionally as a file explorer
obsidian valley
get a better wpm loser
obsidian valley
vim has everythign but idk if its worth
calm crane
yh it’s learning curve so damn high
but so good once you know sufficient to use it efficiently
obsidian valley
Yeah idk it semes a little cumbersome for large projects too but maybe thats just me
obsidian valley
I should probably get used to vim bindings or something for rsi lol
calm crane
lol
gray gazelle
I just use overleaf for latex. I've absolutely no talent with computers and stuff
calm crane
overleaf lags my computer a lot
also it's alignment is off for me idk why
lpl
same with cocalc
obsidian valley
switching from overleaf to vscode is the most worthwhile workflow switch I've made
calm crane
wooden sparrow
overleaf lags my computer a lot
@calm crane get a t h r e a d r i p p e r
gray gazelle
Back to monke
calm crane
switching from texstudio to vim was the best workflow switch i made
obsidian valley
I unironically couldn't figure out how to get the dedicated tex programs to work
calm crane
XD
obsidian valley
I was so fucking confused I went right back to overleaf for all of first year
calm crane
idk how specialized tex program sucks more than nonspecialized tex programs
calm crane
now i jus compile with pdflatex and type like :284 to see the error
radiant basalt
Huh like Texmaker or TexStudio ? They're easy enough
gray gazelle
I dunno overleaf seemed to be the easiest to learn of the lot
broken meadow
i cant use overleaf is too confusing