You think the problems presented came out of thin air?
#book-recommendations
cobalt arch
obsidian valley
Most working mathematicians probably don't give a shit about the philosophy lol
cobalt arch
If you want to understand something start from the start
obsidian valley
It doesn't affect the math in any meaningful way
obsidian valley
Have you read literally any philosophy of math
cobalt arch
Because every problem that math can't solve philosophy can define
hasty turret
Are you an amateur philosopher,by any chance?
obsidian valley
End of the day I'm not here to bully you, I just don't want you to waste your time banging your head against very difficult foundations books
karmic thorn
obsidian valley
or worse, think you understand the foundations when you dont
cobalt arch
No I am not I just want to understand why all of a sudden it seems implausible for me to recommend books as if I can't understand what I am reading
Okay
karmic thorn
I've already had my fair share of suffering banging my head trying to understand foundations last year lmao, I don't think I'm touching any mainstream set theory book for years from now at the very least.
obsidian valley
If you want to learn analytic geo read some pearson book on pre-calculus idk
hasty turret
I have never done set theory and I don't think I will ever need to do it formally. Your Intuition just works 99% of the time
karmic thorn
Coxeter's Geometry is good for analytic geometry afaik, btw.
gray gazelle
I have never done set theory and I don't think I will ever need to do it formall...
You need set theory for CS 
broken meadow
why do you keep asking bro just read rudin if you care so much about starting ground up or whatever rigor stuff you wanna do
obsidian valley
just read principia loool
every real mathematician can reproduce the Principia proof of 1 + 1 = 2
gray gazelle
You need to study at least a bit of the foundations, including propositional logic, predicates and quantifiers, provability, and naive set theory
obsidian valley
Those aren't the foundations being discussed here
cobalt arch
I am asking because I want to know what is best for me to read. I don't want to waste my time reading something for a year that will eventually not be of any benefit to me. I am here because I know I am not that good at maths but I want to get better. I recommend books because I like doing so since I have done my fair bit of research by looking at reviews and whatnot.. I don't understand why there is so much malice because I am not well read.. I am doing it to help other people and I am not recommending books I haven't searched about myself.. Whatever we can leave that aside.
karmic thorn
I guess you've been promptly suggested books to read every time you asked.
The onus to read those books now falls on you.
broken meadow
if you didnt like what they advised why ask again
prisma snow
I mean, you say you're bad at math and you aren't well read but you're trying to argue with everyone that mathematicians should read philosophy to understand math. That's picking a fight lmao.
obsidian valley
I was just confused by what level of math you do
lol
There is a reason people learn things in a certain order
karmic thorn
I sensed very early on the onset that you were a beginner to proof-based maths.
obsidian valley
Hence why you shouldn't be asking for an analysis text alongside an analytic geometry book
cobalt arch
Well then I can regress back to the nothingness I came from
broken meadow
ok bro
obsidian valley
karmic thorn
¯_(ツ)_/¯
obsidian valley
We tried.
broken meadow
its ok
cobalt arch
Thank you for your advice. Sometimes I want to be proven correct whilst the opposite holds true.
fossil island
So you just want to be wrong
obsidian valley
Don't we all
cobalt arch
I am
fossil island
Someone on a math discord admitting they're wrong, what kind of world are we living in
broken meadow
the cursed timeline
stray veldt
generally i never met a mathematician who had trouble admitting they were wrong
hasty turret
Have you met mochizuki?
stray veldt
no
hasty turret
Makes sense
graceful bridge
I just read the above discussion. Out of interest, @cobalt arch, are you trying to create a "custom" roadmap for your mathematical progression? And is this smt you do on top of formally studying math?
cobalt arch
Yes to both of these questions
I want to become well versed in many areas of math
By that I don't mean something extreme
cobalt arch
Cat theory 
hasty turret
Eh, Who cares about cat theory
cobalt arch
My cat
hasty turret
It's something that organizes existing theory.
graceful bridge
Okay, that's an interesting project. Obviously it's quite demanding if you're studying full-time. I also want to add something on top of my studies that interest me, but it has to be realistic.
karmic thorn
Probably some comp math book?
The kind of f(tan\theta)=something, find f'(1) seems familiar from comp math.
late token
comp ... LOL
karmic thorn
Yes, AoPS and Art and Craft of Problem Solving are my best recs.
late token
Alcumus or community thing
karmic thorn
Careful with the choice of words, mate.
late token
@fast portal be careful or I'll call mods : D
as I said, did u see it in something like Alcumus or in the community ones
karmic thorn
Regardless, you could avoid engaging completely instead of reiterating some self-deprecating statement they made.
karmic thorn
as I said, did u see it in something like Alcumus or in the community ones
I'm not sure what Alcumus is.
karmic thorn
Yeah, you should be able to find lots of similar problems on AoPS.
And their books.
late token
I can find such one in their books?
karmic thorn
Most likely, yes. I'm not entirely sure in which books in particular.
late token
: (
karmic thorn
You could probably ask for references in the mathematics olympiad server in #old-network .
karmic thorn
hollow peak
is royden considered an intro graduate text for real analysis? this is so in depth
cobalt arch
Is elementary algebra subsumed by abstract algebra?
Elementary algebra as in hall and knight's book Higher Algebra.
marble solar
is royden considered an intro graduate text for real analysis? this is so in dep...
It came out of Stanford in a time where it wasn't normal to have Rudin's analysis at the undergraduate level
If you look at a history of the undergraduate mathematics major, real analysis was a first year graduate course
They had an advanced calculus course that covered baby analysis and lots of harder calculus examples/problems
quick hornet
Elementary algebra as in hall and knight's book Higher Algebra.
i mean, most of it can be regarded as either the field theory of R or C or the group theory of permutation groups
buuut in practice youre not likely to actually like
learn elementary algebra
in an AA course
youre expected to be familiar with them going in
AA doesnt focus much on the field theory of R and C since its assumed youll already be familiar with it
also i think Hall-Knight have some stuff on finance which wouldnt be covered in algebra as well
alongside a bit of stuff on inequalities, convergence, and series, which is naturally more calculus/analysis
in any case i wouldnt consider AA a "replacement"
even if AA generalizes elementary algebra
static crest
time to write a textbook that just starts with abstract algebra
no fake elementary algebra to be seen
quick hornet
name it like a generic middle school math textbook
"MathSmarts 8" or something
and then it just opens with HoTT
sudden granite
quick hornet
sudden kindle
@median sand
gray gazelle
I would buy a math book with a raccoon on it
i would buy a raccoon with a math book on it
sudden granite
i would buy a raccoon with a math book on it
gray gazelle
i am a raccoon with a math book on it
static crest
smh I'm getting traumatic flashbacks
I remember math makes sense
had to use it from like grade 3 to 8
sudden granite
sudden kindle
So contempt
sudden granite
I never used these books because Common Core replaced em
broken meadow
i raccoon buy book with math
cobalt arch
@quick hornet So I have to learn from hall and knight
I mean if I can't learn elementary algebra through aa
I wish I could
I mean axiomatically you build algebraic structures and you impose on them operations..
Which in a way is starting from scratch
I mean do you learn about vieta laws in aa?
Or anywhere else
I mean it can't be the case that you don't encounter them later on
quick hornet
vieta's laws are a pretty specific example though, theres lots of things that'd be covered in a typical introductory algebra course that abstract algebra doesnt cover
cobalt arch
Hm like what?
quick hornet
how to manipulate equations
it'll be assumed you know that going into abstract algebra
cobalt arch
I mean I am asking because I don't want to have no gaps whatsoever
quick hornet
also stuff like exponentials and logarithms
and the behaviours of specific functiosn in general
cobalt arch
I know these things
quick hornet
abstract algebra mostly cares about polynomials
cobalt arch
I see
quick hornet
(and rational functions, which are just ratios of polynomials)
cobalt arch
And galois theory specifically about the solvability of quintic polynomials?
Or am I wrong?
quick hornet
galois theory discusses solvability of polynomials, and indeed unsolvability of the general quintic is one famous result
cobalt arch
Yeah
quick hornet
although if that was the ONLY purpose there wouldnt be much use for galois theory
since that was already a theorem before galois was born!
the proof just sucked until galois theory simplified it
cobalt arch
Hm so I will have to read hall and knight to see if I have any gaps.
quick hornet
(for context, ruffini gave a partial proof of abel-ruffini in 1799, and galois was born in 1811)
(abel "fixed" ruffini's proof in 1824, while galois was just barely a teenager)
(galois theory lets us prove it in way better/nicer ways though)
anyway uh
theres no reason not to read abstract algebra on the side/alongside elementary algebra
cobalt arch
What a tragic life galois' was..
quick hornet
if you think you're up for it
karmic thorn
@cobalt arch Dw too much about the gaps, basic algebra isn't something you should be worrying too much about; to save time, do course challenges from Khan Academy.
quick hornet
the worst case is that it doesnt "click"
but thats fine, you didnt lose much
i'd certainly focus on making sure you keep up to date with your course content
like
i wouldnt read abstract algebra as a SUBSTITUTE for elementary algebra
cobalt arch
Yeah
quick hornet
but its certainly possible to read alongside
cobalt arch
Ty @karmic thorn
cobalt arch
I guess I worry over the details
quick hornet
like
heres the reality
it might not work out, its hard to say if itll mesh easily
karmic thorn
Filling in gaps while you study is a part of the process.
quick hornet
but if it doesnt... then you can just stop studying it
and defer to the elementary algebra material
and nothing's really lost
and if you want to try abstract algebra later, you'll have a bit of experience going in
so if you're genuinely interested it's at least worth a shot
assuming you have the time, at least
cobalt arch
Yeah
quick hornet
i think if youre genuinely confident in most of elementary algebra though you should be fine
the main barriers there would be proofs, and maybe a bit of complex stuff depending on what AA book you use
cobalt arch
I don't know:/
karmic thorn
Sure, D&F might be good then.
I've seen Jacobson being recommended frequently as well.
cobalt arch
Hm does he cover a lot of material too 
?
karmic thorn
Yeah, there are 2 volumes and I think the second one ventures into graduate algebra.
karmic thorn
Not entirely sure. Also depends from uni to uni how much algebra they offer at undergrad level.
cobalt arch
Yeah
karmic thorn
For example, the group theory course at my uni doesn't cover free groups or fundamental groups.
That might be a part of the undergrad curriculum elsewhere.
cobalt arch
Yeah ig ty ted:)
And yohan:)
They use hall and knight for competition level math in india right?
cobalt arch
Yeah
Although from the contents of h&k it seems like some stuff are taken to the extreme
If you browse through it you will see
karmic thorn
I was momentarily confused, because H&K is usually used to denote Hoffman and Kunze's LA book lol.
cobalt arch
Hahaha
karmic thorn
Dw too much about it, abstract algebra doesn't assume a ton of algebra knowledge bar addition and multiplication lmao.
cobalt arch
I see I am good then but I will go for it anyways
dapper root
For example, the group theory course at my uni doesn't cover free groups or fund...
Fundamental groups are a topological object (I mean it’s algebraic too) so an algebra class wouldn’t cover them anyway
sudden granite
Nice.
calm crane
For example, the group theory course at my uni doesn't cover free groups or fund...
fundamental groups are never covered in intro group theory
and yes i suggest jacobson
cobalt arch
Why jacobson?
prisma snow
I want to find someone who loves me as much as ari loves jacobson
cobalt arch
So love equals materialism I see 
Tesla had a very intimate relationship with a pigeon so why not have the same intimate relationship with a book
median sand
<@209984108913360906>
?
cobalt arch
Materialism equals monism and monism equals oneness so in essence what you have to love is yourself
calm crane
Why jacobson?
i like cuz concise and some cool exercises
calm crane
jacobson covers more afaik
calm crane
I want rigor 😩
concise and rigor aren't disjoint
cobalt arch
Hm I see I will check it out
I know I just want to be sure that everything is laid out
calm crane
that is not a worry that one really should have for any decent intro algebra book tbh
cobalt arch
But isn't jacobson a bit outdated so his outlook on things might be drastically different.
calm crane
jacobson isnt outdated afaik?
and tbh nothing much changed for intro algebra
1989 is decently recent
or 1970s
cobalt arch
I see
hasty turret
1989 is decently recent
tfw d and f is more modern than jacobson
calm crane
tfw jacobson's feels more modern
karmic thorn
tfw just use Gallian.
sage python
Idk if a book written more recently would necessarily give a more "modern" take on the material in this case. We think about groups differently now than Galois did for sure
But since 1974? Idk if much has changed about intro material
karmic thorn
Gallian has some cool applications(crystallographic groups, Frieze groups, coding theory, etc.) as well.
hasty turret
tfw odin rhymes with rudin
sage python
I feel like I probably at some point saw people mention Gallian here, looked it over, gave my take, and forgot about it lol
hasty turret
I think Gallian is good for speed reading, not so much as a proper textbook
calm crane
Gallian has some cool applications(crystallographic groups, Frieze groups, codin...
ig a very modern take would be this
but not rlly necessary for an intro book ngl
once you get a sense of whats going on
it shouldn't be too hard to jus read introductory material on random applications
karmic thorn
Fair enough.
karmic thorn
I think Gallian is good for speed reading, not so much as a proper textbook
Not really, the book is loaded with exercises.
sage python
Okay so
8th edition of Gallian is out
And it's weirdly colorful
Which gives me Stewart vibes
karmic thorn
sage python
This book is extremely slow
hearty steppe
What is Gallian
hasty turret
The exercises seem to be super easy
karmic thorn
It's actually good for introducing a fresh undergrad to AA. ¯_(ツ)_/¯
karmic thorn
I could start with group theory without knowing any LA or proof-writing.
hearty steppe
Is that modern algebra oh
sage python
The only prereq for Artin is the English language lmao
hasty turret
Just learn proof writing via intuition
karmic thorn
hearty steppe
Artin is kinda hard to read
calm crane
if you want exercises just open herstein
hearty steppe
The way it’s worded
karmic thorn
Just learn proof writing via intuition
Tried it, only to hear "what the actual fuck do you mean by that".
sage python
I haven't used it as much as D&F but at a glance it seems very smooth
D&F is like
Very drawn out
Which I think makes it unironically okay for intro to proofs lmao
calm crane
proofs are boring to read tbh
sage python
True but Jacobson's writing is alright lol
cobalt arch
I need some book recommendations for some upcoming classes
Linear Algebra, Discrete Mathematics, Number Theory, Probability Theory and ODEs.
For linear algebra h&k seems like the standard text?
Is it comprehensive and rigorous?
For the other four I don't know anything.
gray gazelle
doing a lot of contest math problems
gray gazelle
Surely effective, but maybe not efficient
I don't know any books, besides eg AOPS problem solving books
cobalt arch
Hm I see
hollow current
if you have something to cover determinants you can also use axler for linalg
it is nice book forgetting that it avoids determinants
cobalt arch
For the other four?
hollow current
well discrete mathematics is broad
hollow current
but i used Kenneth Rosen Discrete Mathematics and Its Applications
cobalt arch
I see
hollow current
for ODE you can try Kreyszig Advanced Engineering Mathematics
cobalt arch
Is there another book that is more rigorous?
gray gazelle
beautiful
hollow current
for number theory Ireland and Rosen is considered to be classics but i did not read it
cobalt arch
Hm it seems good but I would like something with more rigor since I major in math and I want to get acquainted with more theoretical textbooks.
hollow current
i am unsure if i have rigor one for ODE
cobalt arch
Hm:/
hollow current
i mean ODE is specific subject
i personally do not expect there rigour level of real analysis e.g
hollow current
dunno any good books
cobalt arch
Hm okay
gray gazelle
What about probability theory?
S Ross or William Feller's book
cobalt arch
Are they rigorous?
gray gazelle
Yes.
cobalt arch
I mean there are some books that start with measure theory and then move on to pt
I don't know if that is rigor
gray gazelle
Not as much as the measure theory stuff, but fit for undergrad
cobalt arch
Hm it would be good to get acquainted with such a book
I know that it might lack motivation
I just want to understand the theory well so that I am steady on my feet. It seems that it will help me the most in the long run.
verbal abyss
cobalt arch
Can someone recommend a theoretical and rigorous ode book?
obsidian valley
You know what I think.
stray veldt
taking a course inside a german seems uncomfortable
silver herald
Any recommendations for a functional analysis textbook? I have already done intro real analysis and some complex analysis already.
hollow peak
I am no functional analyst but that depends on what part of functional analysis you care about
for operator theory I've heard yosida is really good
I own a copy of conway and it's okay
but if you're just looking for some advanced analysis in a vector space setting, royden seems very good
marble solar
I like stein and shakarchi volume 4
It's got a bit of harmonic flavor to it
Another good functional book is Hunter and Nochtergale
More applied/Differential Equation type stuff goin' on, but it's good
And then of course there's the legendary text by Peter Lax
hollow peak
peter lax's book is truly legendary
I know a lot of people here are partial to Analysis Now by pederson
marble solar
The hunter and nochtergale text is free
silver herald
I am mainly looking for something which covers analysis on different function spaces and some operator theory.
marble solar
Lax
hollow peak
realistically any good graduate text in analysis will cover many of the same topics
just pick what you like
silver herald
Thanks for the suggestion people! I will check 'em out.
sage python
@silver herald how is your measure theory actually?
silver herald
Kinda wack. Have worked with some sigma algebra and that's prolly about it
Should I work towards that as well?
sage python
Just that it influences the book recommendation
Since some of the more important examples of Banach spaces are L^p spaces
In principle I guess you could just say, take space of f such that |f|^p is Riemann integral, put the L^p norm, that's not a Banach space, complete it
silver herald
Ye, I heard that those use Lebesgue Integration
sage python
But yeah some books might reference it
So my analysis class did functional before measure theory and we used "Elements of the Theory of Functions and Functional Analysis" by Kolmogorov and Fomin
Which is well-written but uses somewhat weird terminology. Idk if the books recommended so far use measure theory or not tho
silver herald
Interesting. I will take a look into ahem PDFs and do a search and scan for measures.
marble solar
Yuh
cobalt arch
https://www.amazon.com/Theory-Ordinary-Differential-Equations-Coddington/dp/0898...
Can you guys check out this and tell me if it is purely theory?
sage python
@cobalt arch Kriz and Pultr which I told you about yesterday I think does some ODEs
So just read that lol
sudden granite
Should I read the Lord of the Rings or the Count of Monte Cristo
static crest
monte cristo
pulsar aurora
Monte Cristo is bomb
pulsar hemlock
Can anyone recommend a nice intro to complex analysis?
static crest
ahlfors
full linden
Hey guys, I believe I am not ready to take spivak at my maximum potential.. What would you recommend? Another book to get ready for it or another calculus books?
pulsar hemlock
Can anyone recommend a nice intro to complex analysis?
on this again, which book in specific do you recommend as the first look?
from ahlfors
static crest
the one named "Complex Analysis" would be a good guess
pulsar hemlock
yeah i just wasnt sure if thats an intro book
he has a lot of complex analysis books
static crest
only one of them that looks like an intro book
(also like the intro one is what people refer to 99.9999% of the time when they say ahlfors)
hasty eagleBOT
hollow peak
incredible
static crest
,w graph y = x
hasty eagleBOT
static crest
we learned about lines in geometry
hollow peak
woah
sudden granite
Finally, some math on my level.
sage python
we learned about lines in geometry
Lines yeah like CP^1 
This is your brain on projective geometry
sudden kindle
Nice sphere
sudden kindle
Why is there t^-1
calm crane
for the prime at infinity
calm crane
ig a nice reason why we want that
is so that principal ideals have sum of exponents (degree) 0
sudden kindle
why
calm crane
and also in like the Q case
we get all the valuations
cuz non arch appears in primes
but arch is nowhere there
so we just throw in a point at infinity
and who doesnt like projective stuff anyways 
calm crane
so like
the spec of your number ring is some line
then the point at infinity basically glues the lines tgt (Proj of it)
valid moth
but arch is nowhere there
wtf
valid moth
sudden kindle
iiiiiiiiiiiiii
gray gazelle
Math.abs()
fluid pecan
Would anyone be having the book
Calculus early transcendentals 8th edition by James Stewart pdf
please share
gray gazelle
here, @fluid pecan is the compressed pdf
fluid pecan
@gray gazelle Thank you so much
gray gazelle
np
cobalt arch
I have found a more comprehensive analogue of Lang's basic mathematics
It is called An excursion through elementary Mathematics by Antonio Neto.
sudden granite
Lang is bae
urban oar
any good book recommendations for statistics and real analysis for beginners?
karmic thorn
A book covering both of them?
urban oar
hmm seprate subjects
karmic thorn
For analysis, Tao's Analysis. I don't know about stats.
marble solar
For analysis, Tao's *Analysis*. I don't know about stats.
Nuh
Spivak's Calculus, Pugh Real Analysis
timid vector
I really enjoyed taos analysis, so what makes spivak and pugh better
warped cedar
marble solar
Terry spends too long developping up from the Naturals
The stuff on sets/axiom of choice should be skipped
The exposition is a little lack luster, very formal and rigorous, not much imparting in the way of understanding/intuition
I think Terry's books make for good lectures, but not so great reading
marble rock
can any1 recommend a topology problem book
i read my textbook but i strill dont have confidence
and i still struggle with problems
point-set here
waxen elbow
can any1 recommend a topology problem book
introduction to topology by Mendelson
cheap, easy to read, lot of reviews
i’ve heard good things about Munkres’ too, i think it covers more topics
waxen elbow
they got nice exercices :( but idk any topo problems book sorry
gray gazelle
munkres is good
lee's intro to topological manifolds is also good
i prefer lee's book but both are good
hearty steppe
I'll second Mendelson. Very good book so far. I need a little bit more maturity with relations but so far I can't complain.
static crest
gray gazelle
maturity with relations 
i can't say i've ever worked with the formal definition of a relation in my life
gray gazelle
hollow peak
relations: a subset of X x X
gray gazelle
well, what'd it say?
hollow peak
math.....
static crest
was something like does anyone know a good undergrad rigorous textbook or something
with 0 indication of any subject
karmic thorn
The stuff on sets/axiom of choice should be skipped
I skipped that too, but I think the development of notions of epsilon-closeness, etc., which is non-standard as stated by Terry himself helps a lot in epsilon-delta way of thinking. The part on set theory can obviously be skipped if someone is familiar with naive set theory.
static crest
yes
gray gazelle
static crest
computations may somehow be useful to real life
obsidian valley
no
karmic thorn
Yes.
static crest
no
gray gazelle
static crest
it's for all books
gray gazelle
its for 18th century english literature
im more interested in literature from the 1700s
karmic thorn
@obsidian valley LMAO
static crest
where does french lit go
static crest
gray gazelle
obsidian valley
actually thats an Ag thing but idk
sudden granite
obsidian valley
just like the french
tight crag
Flabby sheaves
gray gazelle
so you are saying e is actually s, and then sort of fudge the word?
marble solar
so you are saying e is actually s, and then sort of fudge the word?
yUh
it's e with an accent
accent aigu
calm crane
etale means stale
wait i tot etale meant spread
marble solar
it was a joke
ripe granite
fort 
gray gazelle
Neat! Before I know it I will be fluent in french
hasty turret
How long would it take to complete rudin?(Assuming I am not doing the last 3 chapters)
dapper root
Don't know an answer but:
1: Define what "complete" means to you, these things can vary a ton by what you consider to be completion
2: Even then there's huge variance based on like background, how much time you put in a day, if you just work fast or get it, etc.
hasty turret
1)I just want to fluent enough in analysis to do topology(atleast being able to appreciate the constructions)
hearty steppe
Completing Rudin is probably overkill just to get into topology
gray gazelle
complete rudin, up to the multivariable calculus part
when you get there
switch to spivak CoM
hearty steppe
Mendelson’s topology doesn’t seem far out of reach for me right now. It seems like I just need to spend a little more time learning relations. Yes I’m still a bit new to pure math
cobalt arch
Any rigorous text on euclidean geometry that isn't Euclids elements?
hasty turret
gray gazelle
lee has a book called axiomatic geometry
which you could look at
same dude who wrote intro to topological/smooth/riemannian manifolds
hasty turret
Honestly, Just start reading
cobalt arch
Jesse 
obsidian valley
why are you so scared of lack of rigour
Rigour is good for the soul
but you don't need it
when you're learning intro stuff
cobalt arch
I just don't want a dumbed down version of things. I prefer rigor because it avoids this pitfall. I want to understand something from a bottom up point of view because that is mathematics at the end of the day. A language with (some) very natural presuppositions that are not false or can't be proven otherwise and a precise approach that leads to statements that are themselves true. It isn't that I prefer it, it is what math is. Well the view that math is that is a belief itself and it can therefore be rejected and more power to you if you don't agree with me but within this framework I believe you approach truth faster.
hasty turret
Geez,Just do math
cobalt arch
You are right, also I upvoted your message because I agree with you it wasn't sarcasm or irony.
obsidian valley
You learn math faster and easier if you don't go for rigour first
theres a reason that we don't teach rigour immediately
rigour for the sake of rigour is horrible for learning
karmic thorn
Forsaken, your present situation feels like an analysis paralysis. To get out of it, just pick any book at this point and start working through it.
gray gazelle
analysis paralysis
cobalt arch
I can't disagree
karmic thorn
I'm undergoing analysis paralysis but in the mathematical sense.
cobalt arch
Haha I was about to make a joke saying I will undergo analysis analysis but it would be sullied into obscurity so I didn't
hasty turret
You don't escape the sully sir
hasty turret
Now go mahboi,do rudin or smt
devout mist
Is there a notable book which summarizes or introduces vector spaces over finite fields?
gray gazelle
linear transformations in chapter 6
devout mist
Gilbert Strang delays discussion pretty much just as long
lunar ledge
linear transformations in chapter 6 <:sully:651816820122189834>
what do u mean? No its just means topic 6. Like we use a reader written by our dumb professor but i hate it cuz its soo vague
gray gazelle
huh
lunar ledge
Is this good book for these topics?
devout mist
I answered b4, but just about any book will be good on these topics
because they're so fundamental
Any famous textbook
obsidian valley
It's not a famous book
lunar ledge
ok
gray gazelle
just read friedberg or axler or h&k or ladw
devout mist
I mean, it's impossible for you to miss these concepts
gray gazelle
or roman if you hate yourself
karmic thorn
Linear Algebra and Geometry by Shaferavich is excellent, but it doesn't have any exercises.
lunar ledge
r u gay?
lunar ledge
I mean, it's impossible for you to miss these concepts
ok man
Thanks for letting me know
sonic vessel
i want to learn geometry which book would be good to start
karmic thorn
What is your current level of study?
sonic vessel
high school
you can give intermidate books too, i will read, just i need a book that there are everyting about geometry
gray gazelle
lee
sonic vessel
it can be 1000 page or 2000 idc
karmic thorn
gray gazelle
there is a book by lee called "axiomatic geometry" which may cover the things you are interested in
now that i know about this book
karmic thorn
Mmmmm Coxeter's geometry might be good.
gray gazelle
i can actually say lee to highschoolers asking for geometry recs
and not come off as a dick
lunar ledge
man
karmic thorn
I need to check out this Axiomatic Geometry book lol.
lunar ledge
stop saying bs
lunar ledge
nvrm nothing
gray gazelle
devout mist
Aghsin, r u a kid? lol
gray gazelle
lunar ledge
Aghsin, r u a kid? lol
How kid can learn linear algebra?
gray gazelle
by reading
devout mist
There are many kids being mentored by people who love math
Sometimes the mentorship goes places
sonic vessel
am i blind or there are no download links
lunar ledge
u r blond
karmic thorn
Z-Library
gray gazelle
you can click on one of the mirrors
lunar ledge
blind
karmic thorn
Click on that one
lunar ledge
click on right
sonic vessel
uh i get it
gray gazelle
tread lightly with the 🏴☠️ talk
lunar ledge
or what u can also do is find doi and create its mirror through scihub
gray gazelle
@karmic thorn 🚔
karmic thorn
sonic vessel
by the way, when reading a book, should i take notes bcs it takes so much time lol
karmic thorn
Note down the essential definitions and theorems at least.
gray gazelle
there's no such thing as learning from a mathematics textbook without a pen and paper nearby
karmic thorn
I think they're the ones who resort to taking notes the most lol.
sonic vessel
o-okay i think i need t-to go lol
obsidian valley
except dumb social sciences
cringe
lunar ledge
I think they're the ones who resort to taking notes the most lol.
and still they cant study normally
lunar ledge
Who is salty?
gray gazelle
karmic thorn
@gray gazelle The Axiomatic Geo book looks good!
gray gazelle
well of course, it's written by lee
karmic thorn
Would be my standard recommendation for Euclidean geometry here on out.
gray gazelle
there are a few pages in lee's riemannian geometry book about classic euclidean geometry too
lunar ledge
my friend asks good book for topology
karmic thorn
Topology Without Tears, Sidney Morris.
Despite the weird typesetting, the book seems very accessible for an introduction.
devout mist
Mmm does anyone have any recommendations for vector spaces over finite fields?
marble solar
think very hard?
devout mist
Is my question very niche or something ~_~
ionic marten
im looking for a book, got out nov/2020.. i couldnt find in libgen or anything.. any good place to look in?
the book is "how linux works" by brian ward
sudden kindle
Mmm does anyone have any recommendations for vector spaces over finite fields?
what do you wana learn abt that
marble solar
Is my question very niche or something ~_~
It's kind of a little too niche for most books on vector spaces, but not quite advanced to get into module and representation stuff
I remember when I took my upper division linear we thought about these examples a lot
gray gazelle
I must admit, I barely know the finite fields besides F_p
gray gazelle
These are all, right?
static crest
I do not know
quick hornet
that's all of them
and this is easy to prove
in fact a stronger statement holds
eh let me rephrase what i just said
given a finite field, it either has prime or prime power order
in the former case, it is Z/pZ
in the latter case, it contains Z/pZ as a subfield
and can be viewed as the "obvious" extension of Z/pZ
basically just introducing new field elements in such a way that their behaviour is "forced" by the field axioms
sudden kindle
You say its obvious but theres a good story behind this
ripe granite
What's the story @sudden kindle ?
sudden kindle
It's in Dummit and foote
sudden kindle
General field theory stuff:
- Prove that fields have characteristic 0 or prime p. If its char 0, its infinite.
So finite fields have characteristic p for some prime p >0. - Prove a field F is a vector space over any of its subfields. In particular it's a vector space over its prime subfield, which is the smallest subfield of F. When F has characteristic p, the prime subfield is F_p, the unique field with p elements. (Its unique because there is only 1 additive group of order p. Then it has a multiplicative structure given by multiplication mod p).
Finite Fields:
- Say F is a finite field. It has to be characteristic p >0. Then it will be a finite dimensional vector space over F_p. Thus it must have p^n elements, where n is the dimension.
Existence:
- The splitting field of x^(p^n) - x over F_p is a field of order p^n (notice the polynomial is degree p^n, and so it has p^n roots) and is characteristic p.
Uniqueness:
- Say F is a field of order p^n. The multiplicative group of F has order p^n -1. Thus any nonzero element of F when raised to the order of this group is the identity. Hence every nonzero element satisfies x^(p^n -1) = 1.
- Thus any nonzero element of F also satisfies x^(p^n) - x = 0. Also zero satisfies this. So F is contained in the splitting field of this polynomial.
- Since F and the splitting field of x^(p_n) - x =0 have the same number of elements, namely p^n, they must be the same field.
So we proved any finite field is completely determined by its order. There is exactly one finite field of order p^n and it's of characteristic p, and is the splitting field of x^(p^n) - x over F_p.
ripe granite
Oh lmao I misinterpretted 'story'
sage python
I think when namington said obvious it was more like
If you have the finite field already
devout mist
Random finite field fact; any finite division ring is automatically a field.
sage python
Then it's obvious how it's an extension of Z_p
devout mist
oops!
sage python
Tru
ripe granite
so you look at the center
prove it's a field
at this point there's two ways to go
one way is a pretty clever thing d&f makes you do
the second way is the more conceptual way
sage python
Is the center obviously non-trivial?
ripe granite
where you use the theory of central division algebras over a field
ripe granite
Is the center obviously non-trivial?
0 and 1 are in it
ripe granite
you look at the center of the group of units
and prove that that union 0 is a field
oh lmao wait every nonzero thing is a unit by assumption
but yeah whatever
ripe granite
the dummit proof makes you use stuff about cyclotomic polys
pretty neat
it's in the section on cyclotomic polys
sage python
Once I get home I'll check it out!
gray gazelle
I always thought cyclotomic polynomials are cool, they are "like" cyclones
waxen elbow
hey, any calc book that goes a bit further than spivak’s ? not for calc3, but at least a complete calc2 course
gray gazelle
isn't spivak pretty complete when it comes to a typical calc 2 course?
waxen elbow
it doesn’t covers impropers integrals if i remember correctly
gray gazelle
waxen elbow
maybe i’m... wrong...
sudden kindle
I always thought cyclotomic polynomials are cool, they are "like" cyclones
Wait I didnt realize
waxen elbow
it definitely does, at least in the exercises
well do you know another book ?
sudden kindle
If you visualize the action if taking the nth power on the nth roots of unity it kinda looks like a cyclone
gray gazelle
well do you know another book ?
not well enough to comment on quality and content
sudden kindle
But really cyclomtomic means circle dividing iirc
waxen elbow
all right, thank you anyway 😋
waxen elbow
well let me check
waxen elbow
i'd be surprised if spivak didn't mention improper integrals
he does in exercices. that’s not a problem but when i just wanna check something this isn’t the best book... : (
gray gazelle
fair
lusty jacinth
What are the best Linear Algebra textbooks for someone self studying and only armed with high school maths? I have been using Strang's Intro to Linear Algebra 5e but have found it to pretty confusing at times. This is probably cause I rarely use the stuff on the MIT OCW course but whatever. Is there really anything much better than Strang for this?
lusty jacinth
I am in calc 1 and am self studying calc 2
I only know basic proofs and can only derive algebra 2, precalc, and calc 1 topics to a basic level
I ask this because I know it is possible to do linear alg with just hs maths
lusty jacinth
Linear algebra done right
doesn't this assume mathematical maturity?
static crest
doesn't this assume mathematical maturity?
also assumes you hate determinants for some reason
sudden granite
gray gazelle
I still cannot confidently say I know what a determinant is
Well, I guess this means I have not learned the proof of cramer's rule, and various other algorithms for computing a determinant
gray gazelle
Kek cramer rule proof as contest math problem?
ornate grove
book
calm crane
Kek cramer rule proof as contest math problem?
tbh it is like
if you know the idea insta solve
if you dk the rip
cobalt arch
Here I am again:). I want a book that covers FOL in great detail and rigor.
I have been looking for like hours to find such a text
hasty turret
For what?
FOL isn't particularly useful if you are not planning to work in Foundations or some part of CS
cobalt arch
I want to read up on some set theory and model theory so yeah
gray gazelle
i must say i am not sure what FOL stands for
hasty turret
First order Logic
cobalt arch
For some reason I can't seem to find anything close to what I want. I want it to start from propositional variables, connectives, quantifiers, :=, =, wffs, etc.
Goldrei is a text I found close to what I want but still it didn't do it for me
gray gazelle
Have you looked at lecture notes posted on the internet?
cobalt arch
No
tight crag
Enderton does this
lusty jacinth
basic mathematics by serge lang
isn't this textbook super hard to go through?
oh on that note
What are some good precalc textbooks
I periodically review my alg and trig but my notes have degraded so I'm wanting to get a textbook primarilly for review
Should I just get AOPS Precalc?
I like their books
lusty jacinth
Yes, but the textbook is theorem and proof heavy
hasty turret
I guess that's depends on the person
lusty jacinth
Don't get me wrong... I personally like theorems and proofs, but the vast majority of people find them to be difficult which is why Lang's basic mathematics is being labeled as difficult by me
velvet briar
Libgen is your friend imo. Check to see if the book is to your liking before buying
velvet briar
Yeah, I mean check then buy
lusty jacinth
Yeah
velvet briar
If you know the AOPS will work for you, I can't see why not
sudden granite
does anyone have a multivar pdf they can send
lusty jacinth
Yup, now that I have given more thought to it I think I'll get the AOPS book or maybe a random standard precalc book since I just want to review.
As for basic maths serge lang, I think I'll get it as well solely to get better with proofs.... or I'll buy a proofs book idk. Doesn't matter much rn.
lusty jacinth
What is so good about it?
sudden granite
the proofs are intuitive
theorems arent difficult imo
Im not the best math student and it helps me a lot
karmic thorn
does anyone have a multivar pdf they can send
A book for multivariable calculus? Or are you looking for lecture notes or sth?
karmic thorn
Spivak's Calculus on Manifolds, or Hubbard and Hubbard. If you're just looking for a light introduction, the multivariable portion in Thomas' or Stewart should suffice. And oh, Apostol's Calculus Vol.2 might be worth checking out as well.
karmic thorn
Ah, okay.
I'm still kinda struggling with the ideas in multivar tbh, but what level is your friend at? If they have some mathematical maturity, Spivak/Apostol/HnH should be good; otherwise I'll send Thomas'.
karmic thorn
Thomas' should be fine, then.
karmic thorn
14th?
hasty turret
sudden granite
send again lol
karmic thorn
Uh okay
sudden granite
🙂
hasty turret
Just libgen?
sudden granite
🤫
sudden granite
12th edition is 210 mb lol
gray gazelle
Euler send it over
sudden granite
i dont see the issue with keeping libgen link
gray gazelle
😠
sudden granite
is a bad experience
sudden granite
🤣😂🤣
sonic vessel
can someone recommend book to me about precalculus
i dont know anyting about calculus, so, please recommend basic ones
why nobody is looking here 
gray gazelle
lllllllllllllllllllllllllllllllllllllllllang?
static crest
lang
broken meadow
long
karmic thorn
lung
gray gazelle
looooooooooooooooooooooooooooooooooooooooooooooooooooong
sonic vessel
i did not get it
is book's name lang or what
@gray gazelle can u light up my brain
karmic thorn
Basic Mathematics, Serge Lang.
sonic vessel
thx
torn fern
Guys does any of you have a pdf of the Hrbacek Set Theory book that includes pag. 87 ? I've downloaded two versions already and both have page 105 instead of 87 lmao
And I really need to find that page as soon as possible
Thanks in advance for any help~
sudden granite
lol, imagine expecting all solutions
gray gazelle
sudden granite
_ _
quick hornet
you might laugh but they came to the right conclusion
This is my first time buying a Pearson book and the last time
gray gazelle
Which book should I go for
- Mathematical Methods for Physics and Engineering(by Ken F. Riley (Author), Mike P. Hobson (Author), Stephen J. Bence (Author))
- Mathematical Methods for Physicists (by Arfken (Author))
- Mathematics for Physicists (Dover Books on Physics)(by Philippe Dennery (Author), Andre Krzywicki (Author))
I want to buy one the book. Which one should contain best explanations.
hasty turret
better ask in the physics server
gray gazelle
I went with Riley.
karmic thorn
I have a physical copy of Riley.
I think it's good, although I haven't looked into much, bar a cursory reading of the first few chapters.
gray gazelle
I had a Kindle version of Arfken. Horrible format. Wanted physical. Anyway went with Riley.
karmic thorn
👍 Although, Riley isn't a book I recommend learning something from. It's more like a handy reference book.
gray gazelle
I got a PDF of it and it looked better
warm glen
does anyone here have experience working through cartan's complex analysis book
i think im getting a physical copy for my bday and im jus curious what y'all think of it
ive seen a review on youtube for it
lusty bone
Recommendations for a book on combinatorial topology? Looking at Pintryagin but wanted to hear others thoughts
sudden kindle
What is combinatorial topology?
lusty bone
(The reason I called it combinatorial topology was because I’m eventually gonna read this: https://www.amazon.com/Distributed-Computing-Through-Combinatorial-Topology/dp/0124045782)
So I guess any good algebraic topology book recs would be appreciated as well
Theoretically the book I linked guides you through enough topology to get by but i feel like learning more
obsidian valley
Maybe check the "further reading" here: https://en.wikipedia.org/wiki/Topological_combinatorics
Seems rather niche
karmic thorn
So I guess any good algebraic topology book recs would be appreciated as well
Hatcher
gray gazelle
huh, i expected "topology" here to mean in the not-as-mathematical sense, as in like "network topology", but i am surprised to see things about "Fudanemtnal Group" in the table of contents
gray gazelle
has anyone here read art of computer programming by DE Knuth?
narrow talon
@lusty bone check out Stillwell’s book “Classical Topology and Combinatorial Group Theory” and see if you like the ToC. If not, check out the references there. There is this small school of introductory literature on algebraic topology which approach things through a more graph/network framework that seems like what you’re lookin for and Stillwell references much of it
narrow talon
What would be some recs for a short path to (mathematical) statistical mechanics and ferromagnets? I’ve got like no physics background and figured starting at K&K before going through basically undergraduate physics would be best rather than jumping into like Arnold (I’m not super familiar with say, symplectic structures and want intuition). However, most of what I care about is decidedly grad/research level and I’m not sure my time would be best spent on undergraduate physics or getting really solid on say, classical mechanics.
Idk, if theres someone else who went from not knowing physics but solid on analysis to being comfortable with math physics, what books did you read/ path did you take?
winter acorn
asking about this, its currently like 11 bucks on amazon, is it worth it ?
calm crane
l i b g e n
cost no longer an issue
subtle siren
I have had someone like Shilov
It depends on whether you like that writing style
Also physical books are kinda up to personal preference
in short if you like it buy it
That's assuming the 11 covers shipping
If it doesn't and shipping costs 200, don't buy it
sonic vessel
@gray gazelle sorry for the ping, i want to find a e book, there was a website that shows all of the websites that which book you search
what was that website's name
gray gazelle
karmic thorn
He's Mitsuki from Boruto lol.
sonic vessel
is Mark Zegarelli's books good for maths?
gray gazelle
Gura
winter acorn
l i b g e n
cost no longer an issue<:smol_nozoomi:699020658587467816>
yes, but i wanted a physical copy, I already do libgen stuff
I opened libgen, where download button
polar tulip
asking about this, its currently like 11 bucks on amazon, is it worth it ?
no in my opinion. when i was first trying to learn the subject i bought this book since it was so cheap. i wasn't able to make sense of it as a beginner
winter acorn
well i kind of already know linear algebra but not really solid at it
polar tulip
well $11 won't kill you, but my opinion is that it's pretty meh
winter acorn
ah ok
polar tulip
hoffman and kunze would be really great if you're familar with lin alg
karmic thorn
I think Friedberg is a good book.
winter acorn
oh hey its the Tao weeb dude 
winter acorn
yes
karmic thorn
Tao weeb dude
fluid bay
we need a synonym for "weeb" that starts with "e" so Ted can be an acronym
karmic thorn
sudden granite
eeb
tardy prawn
eeb
sudden granite
👍
tardy prawn
bee
sudden granite
"weeb" that starts with*** "e"***
tardy prawn
eweeb
sudden granite
😳
tardy prawn
e-weeb
sudden granite
idk about that one chief
tardy prawn
choke me like u hate me
fluid bay
i approve
sudden granite
tf
gray gazelle
wrong one
gray gazelle
sudden granite
tempting eccentric ...
gray gazelle
sudden granite
help