#book-recommendations
1 messages · Page 239 of 1
ye
"Last time i lied" - I promise u'll like it
I know I am a little late in the conversation but I definitely feel that starting with Linear Algebra is a good way to go. Personally, when I took it, I found it to be a good intermediate between things like high school math and that which you see in university. Idk where you are Math wise but I feel that it has utility and can be fun as well while still giving you enough time to explore some other topics that you may be interested. Those are just my two cents tho.
Hello, a little late in the conversation but I definitely feel that starting with Linear Algebra is a good way to go. Personally, when I took it, I found it to be a good intermediate between things like high school math and that which you see in university. Idk where you are Math wise but I feel that it has utility and can be fun as well while still giving you enough time to explore some other topics that you may be interested. Those are just my two cents tho.
I'm mirza
How do you do
Any recommendations for algorithms analysis. I've had past experiences in doing it in highschool, and I want to understand more. At this point I just want to clarify a few things or see any books with some perspective on how you would go at analyzing algorithms with correct use of notation to help justify your point. An example would be even how I'd approach or set myself up to answer this question with reasonable english. I already can see from looking at the algorithm it will run n times but if there could be some recommendations for someone somewhat new (since this content is being covered in my uni course); i want to get a better grasp on it
Algorithm Design by Kleinberg and Tardos
Thank you
No worries
Also I'm guessing chapters 1-2 should give me a good intro - which will then help out for the later content like np, p complete problems etc
what do people think about using algebra:chapter 0 as a first book in abstract algebra
i have many rants posted here about how much i dislike the text
but some people really like it
if youre gonna use it, at least supplement its problems with another source
like Dummit and Foote or something
since Aluffi's problems are a bit shallow
Any good books that give a decent overview of nodern geometry? ( non euclidean, affine, projective etc) Or just any good modern geometry books in general
how much abstract algebra do you have
Basic undergrad level through some galois theory but willing to learn more
ah yeah I have heard that, thanks
sounds like you have the prerequisites for fulton's Algebraic Curves
which covers introductory classical algebraic geometry quite well, and sets up for a more modern viewpoint
Nice ill check it out thanks
for the differential/riemannian side (Which deals with stuff like curvature spaces and whatnot, so probably more familiar to what you mean by "non euclidean")
consider Tu's Differential Geometry or Lee's Riemannian Manifolds
i think the latter expects you to know a bit of topology though
and both require comfort with analysis of R^n
(not like, the random integral theorems from calc 3 or whatever, just familiarity with the "feel")
Theres also eigenchris's videos on YouTube

Huh Tu has a full on diffgeo book
I know about the smooth manifolds one and obv Bott-Tu
There's Coxeter's Introduction to Geometry as well.
tu's geometry is nice
it seems like it has a lot of abstract nonsense though

it has a lot of stuff
and it's very clearly written
coxeter sounds like the name of a mathematical object
something like co and ext and something
@gray gazelle wait wait wait
He was able to turn diffgeo into abstract nonsense?
Maybe this is my calling
what do u guys think about the Epp discrete mathematics book? ive heard good things about it
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I am not a mathematician but I am interested in the topics that are talked in the video. What book you might recommend for self-study (I am about to graduate physics so I am comfortable with linear algebra, calculus, vector calculus, etc.)?
I honestly have not seen it, but it’s about incompleteness right?
Yes
I guess a course in mathematical logic should suffice to get you started.
i liked Ebbinghaus
Hmm, but they've probably not seen a lot of proofy math before.
Definitely need to get into logic, if there’s a logician here I’m sure they could help but my logic friend recommended to me “Godel without too many tears”
It’s freely available and I believe the author has another book on more basic logic
Thanks for the suggestions. I'll check it.
Does the recommendations here have to be math books only or can they be a book in a different field
Math books primarily
Could anyone suggests books on topics like calculus, geometry,algebra ?
High school level ?
Can anyone recommend me some good number theory textbooks for beginners?
What background do you have
@gray gazelle
I have Burton 
Is it any good?
I didn't read much really
I have heard lots of negative reviews
I have some vague ideas about number theory
Just learn elementary number theory via algebra
It sure is very intriguing
ez
Via algebra?
The way I learnt ENT is via random bits of info in discrete math and algebra textbooks
I am doing Discrete Math by Epp rn
The text is written very clearly
Very beginner friendly
If you are a tryhard and can cope with algebra lmk i can share something 
Sure@gray gazelle
@gray gazelle i like this one
Thanks bud
Oops wrong one
Sorry
Lemme find it
@gray gazelle
Sorry again
Xd
Odd mix which is uhh something. Gl
Also,Is that an IP address?
No
Does anyone have any recommendations for some precal/calculus word problem textbooks/workbooks?
For calculus, any general textbook will usually have lots of problems. Thomas' Calculus is one such book.
For precalculus, you could probably look at the book by OpenStax.
Thanks, I’ll give them a look
Do such problems require you to graph and use tangents and secants?
Really depends on the problem, but graphs of trigonometric functions would be reasonably covered in precalculus I guess. 
Ok 👌
How much can I get into Brin and Stuck without knowing measure theory?
@gray gazelle
ok thanks
it might be too abstract for me tbh
yeah i tried the first chapter and they talk about measures and shit
ok thanks
it feels like 1.2 and 1.3 are very technical
while im interested in the technical aspects id also like application
well they use it to set up examples
i didnt think there was any measure theory in it
but maybe i just missed that example

i think ill just look at the examples that make sense to me
in the first section
and then just go to chapter 2
tehres measure theory in the end ofthe book i guess, i didnt get that far
I did chapters 1,2,3,5,7 and dont know measure theory
ok, i guess they just mention it for people who know it
The book is hard in that the book will casually brush over some details that may be trivial, and some details that are insane
What ultra
I wanna know too
makes sense
im mostly interested in continuous time dynamics
but ill definitely try parsing the other ones
and then i just skip everything that has the word ergodic
this is where most application is, right?
this book seems terse in general
any other book you'd recommend to read alongside?
i was looking at wiggin's book
"If you're interested in ODE you should read an ODE book"
i mean what other dynamical systems have application
im interested in mathematical biology
more molecular
What mechanisms
Galliumically applied math is slightly less infectious
developing and analyzing models for drug, protein, dna, etc. interaction
well i know stochastic dynamics is one route
Yeah stochastic processes matter
But you don't really study them from an ergodic perspective
What does ergodic theory have to say about brownian motion
Ergodic theory is about deterministic dynamical systems, right?
Any system with quantum effects won't be deterministic
Chemical reactions are not memoryless
dont equilibriums merely depend on the current concentration of products and reactants?
What if you're a chemist and you need to know how many times to swirl your beaker with 2 chemicals in it?
but a molecule doesnt remember which pathway it took to be transformed into another?
If you're a chemist and you want to know how many times to swirl your beaker, you swirl it and do spectroscopy to measure concentration differences
To be clear, I'm not saying that ergodic theory is useless for biochem and stuff
Dynamics as a whole definitely isn't useless
But
I'm not sure it answers questions that biochem people care about
Markov chains are for memoryless systems which I only brought up because of the Hairer notes you linked
A lot of modern work in this area is incorporating quantum effects
But also
These fields are experimental
And until these methods start giving predictions that can be experimentally validated/rejected, I don't see them being super impactful
Sure
And most biologists don't care at all about math bio stuff
what's the actual difference between math bio and computational bio?
is comp bio more bioinformatics stuff?
There are substantial cultural differences between math and bio
Comp bio and math bio are pretty close
I don't think there's a clear divide
ok dope
This is an interesting blog post
Touching on some of the cultural differences I mentioned
Sounds like mixing
Yes we were talking about mixing
Which is hard
Well it isn't hard for chemists
Haha I guess
For mathematicians though
Nontrivial
Not hard to find books on though, there’s a few people at NYU and I think UTAustin that specialize in mixing times (don’t quote me on Austin though)
Mathematicians: I'm going to write a book about mixing
Biologists: I'm going to use a magnetic stirrer to mix my solution

Anyways
An area that is of interest to math and non-math people is numerical techniques for quantum systems
This comes up in areas like quantum/computational chemistry
so a course in physical chem would probably be good?
for this
You may look at work being done by Lin Lin at Berkeley
Certainly physical chem is necessary
You also need to be familiar with QM
Or
Should I guess
see i cant tell whether i should just focus on the math part and do related science classes on the side
or vice versa
Both are important
Anyone seen a reproducing kernel hilbert space before? Papers, books, blogs on applications, importance, basically anything would be helpful.
I’m assuming you’re well familiar with kernel support vector machines?
@narrow talon Yes
Tell me about it mate. Haha
do u guys have some some book recommendations about the topics I need to learn to get into AI?
AI is fairly self contained
Linear algebra
He?

ok me/tal
Artificial intelligence
what's a good starting point for axiomatic set theory (if that's the correct term)
yeah pretty much
no
ZFC
and other forms which I'm not actually aware of but would like to read up on
right, I have no idea how I missed that channel haha
I think I found a suitable text: A Course on Set Theory by Ernest Schimmerling
For one of the most beginner friendly analysis books, Abbott definitely does have some relatively challenging exercises from the get go
the triangle inequality stuff is still kinda kicking my ass, but I suppose the structure of this book is to guide you by introducing concepts in the exercises. Not really my flavor of learning since I prefer being tested on stuff covered thoroughly in the chapter
but Abbott does a way better job really easing you into analysis compared to any other book I've looked at that has been recommended here which I would consider a more unforgiving exposure to analysis and I just can't recommend anyone touch those books without looking at Abbott if your new to math.
not even linear algebra exposure will save you from the intimidating nature of the psets you will encounter in a first exposure analysis course, just a heads up.
triangle inequality 
Just dive into it, and forgive yourself for sucking so much at solving the problems initially, I guess thats my way of saying "this is how you learn analysis". You will suck, really bad at trying to solve these problems in the beginning but things will turn out better with more exposure.
At least I'm telling myself this as I'm learning because, nothing will really prepare you to not suck at your first analysis psets
:\
Basically imagine learning a math course but playing dark souls at the same time. At least its not a video game this time and you have more motivation to get through it.
I guess... Maybe I wasted a lot of time spending too much time on Velleman psets but I wasn't sure.
where does the ass-kicking begin in Abbott?
so many people made analysis seem intimidating but your going to get your ass kicked in analysis regardless how much you try to prepare
meh sort of in the preliminary psets depending on how good your proof knowledge is. If you just got done with a proofs book, it won't save you.
analysis bad 

except for the kind of analysis ange and ryc do, of course
yo this doesn't look that bad at first glance
TTerra my math is closer to what you're interested in than that of ange and ryc smh
but i've already been through analysis so yeah i can imagine the panic had this been my very first exposure
Also damn there is an actual analysis group in this server now huh
tterra was trying to be nice to ange, all analysis sux
I didn't know about young smasher, tuong, and derivada
Brofibration what about the Langlands program
young smasher does func anal I think
Yeah young smasher is an analysis grad student
Oh huh, wasn't on my radar. Or I forgot one of the two
Also Ultraproduct I guess does analysis\cap logic
Nice nice
Hmm?
I don't really get dynamics
Like either you have continuous dynamics
Where you just have odes/pdes
Or you have discrete dynamics
Which are discretized odes/pdes
I mean... topological dynamics, ergodic theory
Ergodic theory is fancy markov chains
Also even on continuous things sometimes you emphasize more the geometric properties than the analytical ones
shapes
Geometry and topology are shapes
So there's an ODE/PDE lurking in the background but it's not at the forefront of what you're doing
yes
Is the ode/pde not useful
shapes of commutative diagrams

Not that it's not useful but saying "you just have odes/pdes" suggests it's like
THe point of what you're doing is the pde. But that's not necessarily what's up
implying im interested in math

tterra do physics
Oh okay so your opinions don't matter anymore got it
go tit
go tit
go tit
go titi
go titi
go titi
my opinions never mattered dami
God I'm looking back through that dynamics book from undergrad
"Introduction to Dynamical Systems" by Brin and Stuck
I wanna do it for real at some point tbh. But then I remember chapter 5
We didn't even get that deep into it but it's quite something
I remember I christened one theorem in there "The Juggernaut Theorem"
"for any homeomorphism of a topological space" like fucking damn

idk
It gets worse for sure
Oh no
it isnt a serious diff eq class
Brin and Stuck pulling a Federer
no analysis pre req
Why are you taking that?

Why not petition to do a real class?
Imagine having a diff eq requirement
real diff eq class needs grad analysis
An applied math major at Berkeley can graduate without knowing an ounce of differential equations
Also yeah the only diffeq I had to deal with in undergrad was
A tiny bit in calculus because Spivak's book talks about differential equations in the chapters on trig functions and exp/log
that's the req im trying to meet
Actually nah in second quarter analysis our prof spent 2 weeks on ODEs
The psets were v painful
the requirement is some class that does shit like y' = y
Well I think we spent like, an hour total on it lol
The solution is y=y^2/2
Wait so is it just a part of the quarter or what?
And wait hold on you're backtracking to take calc now?
I took multivar, I just need to do diff eq
Lemme just pull up [REDACTED]'s math major requirements
Oh so it is a full quarter of that then. Maybe take grad microlocal analysis and petition to count that instead

all the grad diffeq/other analysis classes require the grad analysis sequence
so I would need to do an entire year of analysis
I guess if you're not too into the stuff then just having a roflclass isn't a bad idea
before I do any of those
Me with algebra
You'll need analysis for the Langlands program anyway
This is true
Now you might say
Harmonic analysis is important for langlands

🤨
Dynamical systems analysis of nonlinear systems of differential equations. One- and two- dimensional flows. Fixed points, limit cycles, and stability analysis. Bifurcations and normal forms. Elementary geometrical and topological results. Applications to problems in biology, chemistry, physics, and other fields.
that's the class im doing right now
to meet this req
First-order, linear differential equations; second-order, linear differential equations with constant coefficients; power series solutions; linear systems.
Former looks much better than the latter lol
Meme on the grader with riemann-hilbert correspondence
Tbf in my analysis class the 2 weeks of ODEs were quite painful. Made me dislike the topic a lot lol
yeah I'm going to do the last homework set entirely in the language of D-modules
I would have taken the grad analysis path if I didnt have to declare major this quarter

Ah
I need to be a math major to apply for this combined masters thing
if you get into the program, and do enough grad classes you get a masters
Okay I found that really disgusting ODEs problem
Let me see if I can find the whole pset tho

cros
Oh I just realized cros = gross
Ah
Also wait you have to do diffgeo?
I just found the ODE requirement but also noticed they require diffgeo
you have to meet all the requirements
but theyre normally pretty flexible on what classes you use to meet them
I used commalg to meet the lower div linear algebra req
and a class on p-adics to meet the discrete math req
I tried to get them to use the complex geo class to meet the diff eq req
but they didnt agree
Bully them harder
Do not stutter when you're bullying smh
"Let me meet the diff eq requirement with complex geo or I'll meet the your face requirement with this knuckle sandwich"
Anyway ima play some DRG for a bit then do spectral theory
Because spectral theory ❤️
I will go write a 9 page essay 

Can someone pin this?
@formal brook the joke's gotten pretty tired and annoying by now
please knock it off
What do people think about Halmos’ Linear Algebra Problem Book? I don’t know if I actually want to use it, but the premise seems very interesting
hey guys! so i am taking the ocw course on linear algebra by strang but i cant find the accompanying book (intro to linear algebra) in my country's amazon page (well 1 is there but its really pricey) could someone please share if a pdf or an ebook of this book exists?thanks a ton
check ||libgen||
Hello 👋, I want to ask if anyone knows some good books that are similar to A mathematicians apology by Hardy or a mathematicians lament by Lockhart, I’m looking more so a few books that really express the value and creativity of mathematics, any suggestions?
Is “letters to a young mathematician” a good book in that area?
not a book, but here is a short essay, by me:
fuck math education, it is a piece of shit!
Excuse me but except the mail order I didn't receive any mail. Could you tell me, please how many mail did you receive during your order ?
A rigorous calculus book?
Spivak
Hmm, thanks
I would just go with this book mate
It’s a short read and personally it helped me be more motivated to dive straight into maths
books for complete beginners in maths please
What's your background, and do you have any particular reason for learning math?
I dont have much background and I want to learn maths bc it's fun
Are you familiar with math at typical school level?
till 8th grade
btw, that wasn't a serious suggestion
@feral pier Okay, after some thinking I would suggest Khan Academy for a review of the math that you already know, and then see what else you like.
thanks
Once you have some basics under the belt you could possibly find something more interesting to learn
I want to be a mathematician by Halmos was a good one
I was a complete beginner 6 moths ago (well... to be honest I'm still a complete beginner) when I started working through the book 'Algebra for college students' by Kaufmann & Schwitters. There is not such a thing like a perfect book, but (in my limited knowledge) this is a pretty good choice. It starts with basic concepts, properties and operations in the real numbers, and it ends with sequences and mathematical induction. So it covers quite a wide range of topics, and it has a lot problems at the end of every section and every chapter (and there are solutions to the odd number problems in the back of the book). Other option, if you are looking for free resources, could be a openstax book. I personally have not check them, but a lot of people say good thing about them... and they are free, so you don't lose anything if you want to give them a try.
thanks
Cringe
Oh can you Link it?
Thanks btw for those recommendations! @hearty steppe @gray gazelle
Ah, that was the full text, very short essay
مسوووووووووووووووووووووووت
I can’t seem to find it online, do you mind if you link it 😅
why doesnt serres books even have hints
is it cause he assumes ur not stupid_
but im stupid
author is cronge
i meannn
The more you think about harry potter the more bad it is
look i agree everyone has their own opinion but i think its really good
^
wtf ange said something correct

The plot's fine I guess
The characters are interesting I guess
The worldbuilding going on is a disaster
Is Rotman AT any good? Or whats the best first course in AT? I've got a terms worth of topology under my belt, and a year worth of undergrad/1 term of grad real analysis to boot if that helps
I also have some experience with differential forms
harry potter is pretty bad though
but then again, probably like 0.000000001% of YA fantasy is good
you can assume by default that if something is a YA fantasy, it is automatically trash
this is the way
The silmarrilion
I think its really funny that things just appear and then become important
Probably the best "easy" AT book
I first learned AT from Masseys book which is funny because it does cubical (co) homology and not simplicial (use cubes not simplices - same thing in the end though) ; the grad student teaching me at the time said "this is maybe an easier introduction because cubes are easier to think about!"
Cubes are easier to think about... Shikashi...
@manic fox So is Lang
Lang is bad

QAQ
RECOMEND The alloy of the law
Can someone tell me a very good book that will uncover lots of things about maths or science
like, a book written for a casual/layman audience?
I've heard good things about Concepts of Modern Mathematics by Ian Stewart.
what math books is a must on bookshelves, at least for undergrad (or more) analysis and algebra ? like if you were to live without internet mostly (and hence no more libgen)
probably like rudin and dummit&foote
btw i just learned of this book, coming out soon
it's aluffi's new algebra book
designed for undergrad classes
is it called chapter 1?
no i guess it's chapter -1
anyway it's super weird
it does rings, modules, and then groups, and then fields
Aluffi is weird
I feel like algebra books are oversaturated
Like why are you writing another intro to algebra book write about some other topic which doesn't yet have a good book
I heard lot of books are formerly class notes? maybe might as well make them proper textbook?
also like
But yeah for intro stuff... So the book on algebra that I decided to buy a physical copy of is Jacobson
aluffi's book is already
Rotman already exists. Algebra textbook writers can retire.
Knapp 
so i don't really get it
anyway just in general most algebra books feel quite dry to me and aluffi is one of the few i've read which doesn't feel like it was written by a robot
so i appreciate it
even though i don't think the dryness is inherently bad when it exists
ryc has not read Rotman
Tbh I'm still of the opinion that if Artin/D&F are tough then you're just not ready for algebra yet
i have never heard of rotman

and it's fucking boring and easy
So I don't really see the point in writing easier algebra books. Unless it's almost explicitly targeted at non-math people
Why
Do Knapp
maybe some people write more for themselves than for other people
there has been like 1 exercise out of the 80 or so that i've bothered to do that took me more than 2 minutes
like writing to learn a particular topic
Read my review from forever ago lol
or just for self satisfaction
It's in pinned messages
honestly am just stunned that poros did all those fucking exercises
Dami approves of Knapp 
dami wrote some reviews
But you didn't review Rotman, so it is unbased.
Rotman is too cringe to be listed
I don't have Rotman in there because I don't know it but I'm fine with that omission lol
Please stop the heresy.
Rotman overall is a good writer so I might glance at it but yeah basically my flowchart is
dami being like Stein and Shakarchi "rubs me the wrong way" somehow is all you need to know about the credibility of Dami's book reviews
I'm going to write my own intro analysis textbook because they're all bad
Algebra is fine because Rotman
I'm not the only one who's eh about S&S2 lol
I am eh about S&S2, very eh
who cares about complex analysis
His toy contour stuff is like, okay I get it but it's annoying
MoonBears said 2 is the weak link in the series
it's the other books that matter
so what's the recommendation for analysis? rudin?
Tao
That was a complex analysis review thread lmao
Tao is good!
It was specifically S&S2

Anything except Tao or Pugh. I only give antirecommendations.
I antirecommend your reviews
i was going to do jacobson but the topics are weird
like i'm trying to close up the gaps in my algebra knowledge
Knapp Knapp Knapp
not learn some dumbass stuff
Aluffi simp has arrived
i'm looking at knapp now
:(
one moment
check Knapp and Rotman maybe Ryc ? both are great imo

I need to be asleep rn
ah you already said you were checking knapp, sry too late
Wtf is wrong with me
S&S1 is like, Fourier but you don't know anything yet. Which I guess is the same logic behind Guillemin-Pollack, like wow cool you can do these things without much background
am i supposed to be looking at knapp basic algebra or knapp advanced algebra
Is that Stein and Shakarchi
But I'd probably prefer to just learn the measure theory and functional analysis then do Fourier full on
Unblocked for Rotman rec.
Basic probably
basic first, I think, Advanced is, well.., advanced
Probably both depending on which gaps you're looking to fill

@dapper root yup
the basic one is 700 pages
Advanced is like
this is not a good start
Algebraic geometry and number theory
Also ryc
Oh yeah advanced is like
and already starts further I think lol
Lowkey just ANT
Basic Algebra doesn't even assume LA
And some AG
I haven't really read Knapp myself so I'm not gonna endorse it completely but
Starts with row reduction in chapter 1
The two together seem to be an efficient way to go from "I am a kindergartner" to "I can do shit"
isn't that great Dami ? 🤔
? 
Yeah that makes it look quite good to me. Just that maybe it's typo hell or the exercises are trash
I don't know because I haven't looked at it deeply
That's why I hesitate lol
the exercises are great imo, and I didn't spot any typo yet
ok at very least i don't care about anything in the advanced book
I will soon read another book by Knapp actually
so that's good
which one ?
"Representations of Semisimple Groups"
maybe the homological algebra chapter

Knapp is a bit of a thing in representation/Lie theory I think
Also since you know analysis better I think ryc, maybe take a look at Knapp's analysis textbooks to judge if you like the way he writes and all that 
Yes ryc
Oh yeah he has analysis too doesn't he
Let me check it out
Dami have you ever seen Wilma’s algebra text?
Ligma balls
tfw when an admin of a math server of thousands of people be like "l i g m a b a l l s"
It’s cuz I was gonna say “Wilma nuts fit in yo mouth”
Or something along those lines and he knew

I'm too sharp
Sharp on my nuts
Okay Knapp's analysis looks good it does a lot
😂😂😂😂
I don't really get the point of doing Riemann integration on R^n if you're just gonna do measure theory later (which you should, corollary I just don't see the point in doing Riemann on R^n at all)
Eh no differential forms
I don't like that
i do

differential forms are for the geometers
Yeah idk this book is probably fine but a bit off to me
He doesn't seem to do weak convergence
both look better than d&f for my purposes
he has a mini sequel to basic analysis that does diff forms and stokes
Or weak topology in general. So that random topology chapter at the end is like, alright fam
Yeah idk I feel like an analysis book should basically be like
the thing i like about knapp is the section at the end on modules over noncommutative rings
Could this possibly be covered in volume 2(chapter 9, analysis on manifolds)?
What an analysis book should do:
"Intro stuff here" (chit chat about sets, R, whatever)
Linear algebra
Metric/normed spaces (including function spaces)
Differentiation
Measure Theory and integration (maybe you can have a bit on Riemann-Stieltjes and use Riesz-rep but don't spend too much time there)
Manifolds and differential forms
Whatever else you want to cover
Yeah ryc that's honestly the part that intrigues me the most about it too lol, the rest I basically am comfortable with
Also to tie up a loose ends from earlier, the S&S verdict:
Fourier is probably the same logic as G&P in differential topology, like wow without knowing fancy tech you can do cool stuff! I can appreciate it but I probably at this point prefer just having the tech and using it
Complex is mediocre
Real does measure theory and Lebesgue integration first on R^n then in general. I don't really get the point but whatever. Seems good for what it does.
Functional has a set of topics which isn't what I think of when I think of functional lol. But it seems cool
What do you recommend for complex?
Linear algebra to be covered in real anal book 
y e s 
Excuse me what is the name of the book you are talking about
Knapp, Basic Real Analysis
The flowchart is probably:
Gamelin if you don't know anything
Freitag if you like number theory
Stein if you want some awkward choices and like number theory as well as Fourier Analysis
Narasimhan for more sophisticated
Schlag if you're nuts
I'm saying in my mind that's what an analysis book should do lol
Thank you so much
"if you're nuts" why ?
Schlag is hard lol
except linalg and manifolds and differential forms, it does align with what's covered, no @karmic thorn ?
Like I know why it is that way but it's basically written for people who don't know any complex but know literally everything else
(and I don't see why diff geo should be treated in an analysis book
)
Yeah I mean Knapp's order is weird
Depending on how bad typos are, I think the book by Igor Kriz is good for analysis
I don't think this is diffgeo lol
Basically Spivak Calc on Manifolds
most analysis textbooks that attempt to cover differential forms fucking suck
I've yet to see a single analysis text do it well
that is to say, it's just too much material to rush through in like 15 pages
Not a book but maybe one day, since I have to work with differential forms, if I go deeper I will try to write something on Differential forms from analysis point of view, not sure if it will be suitable for general Analysis purpose
hi guys, what book about game theory would you recommend?
I feel the amount of work to set up integration in R^n isn't that much work
Whereas setting up lebesgue is more work
Granted you can probably just YOLO the integration properties
This part is why I say nah don't do that
I feel like you have to learn measure theory eventually so might as well just suck it up and do it there
all the integration properties are trivial if you dont think about why your simple argument fails
And if you do that, you even get more properties !
i think this is called "physics"
I was told the first was an ok intro
we actually use the second for our grad complex analysis course
for better or worse
god speaking of integrals in R^n, our "advanced multivariable calculus" course used the book Multivariable Calculus with Applications and lemme just say
terrible book
hated it
Probably for worse
S&S complex doesn't seem to be up to a grad level
In my opinion
Volume 3 & 4 definitely are
wb S&S1?
Honestly, I think having a not-quite-grad actual analytic intro would be good. My first course was engineering focused, didn't touch sequences, series, and barely touched residues
S&S1 is a great text
But definitely isn't quite at the grad level
Probably junior-senior at most schools
Volume 3 is kinda undergrad kinda grad
The first two or three can be done at the undergrad but chapter 5 & 7
Put it squarely in the grad camp for me
I think 5 and 7 are atypical topics for an undergrad class but I wouldn't say they make it not a good undergrad book
Anyone know a good functional equation text? The one I’m looking at now is Iterative Functional Equations by Kuczma but I have no idea if there are better ones out there
It is a really good text written by a really good mathematician.
imagine having kuc inbuilt into ur name
Respect please.


@still jay Read that book.
Excuse me, could anyone recommend me some novels other than following ones:
- The Pride and Prejudice
- The Picture of Dorian Gray
- Anna Karenina
- The Great Gatsby
- Don Quixote
- Emma
- Sapiens: A Brief History of Humankind
- The Haunting Hill House
- Kane and Abel
- Murder of the Orient Express
- The Mysterious Affair
- The Murder of Roger Ackroyd
- The Mystery of the Blue Train
- Harry Potter
- War and Peace
- The Lord of Rings
Witcher
Hobbit
ok, thank you so much for the recommendation 😊
The Bartimaeus Trilogy.
Read the savage detectives 
Obviously since you have read Pride and Prejudice and Emma, you should read Austen's other novels. You can also read the Bronte sisters (Jane Eyre and Wuthering Heights to start).
Then some translated fiction:
- Blindness by Saramago
- The Makioka Sisters by Tanizaki
- The Count of Monte Cristo by Dumas
If you do want to read more fantasy/science fiction stuff, I recommend:
- Annihilation Trilogy by Jeff Vandermeer
- Anything by Octavia Butler
- Anything by Gene Wolfe (probably best to start with The Fifth Head of Cerberus)
- The Left Hand of Darkness by Le Guin.
- Gormenghast by Peake
@gray gazelle for some reason I put way too much effort into this
Omniscient Readers Viewpoint by Sing Shong
Hexadecasully moment
Naruto
Oh wait
R.S. Aggarwal good math book 👌
a) House of Leaves
b) EarthSea Cycle Series
c) Bird Box
d) Kill Creek
e) 14 by Peter Clines
I'm just kidding you.
Seriously you should try to read Sherlock Holmes it's great
spivak's calculus
it's not just suitable for undergrad it's also good for everybody as long as they want to learn
Any great compilation of analysis problems to recommend ? Or maybe just a textbook with great problems, and I'll pick the problems
@whole rain Polya/Szego 
too advanced 
What kind of analysis?
The elementary kind, like just stuff that is covered in a first RA course ig 
Rudin has a lot of exercises
dami recommended me that in #math-discussion too, i'll check it out thanks
I also might have some psets from analysis the year before I took it lol
Because the guy who taught that had good psets
I will say the emphasis was probably more "multivariable calculus" than metric spaces and whatnot
The portrait of the artist as a young man
Kafka's short stories are good
If you've read War and Peace/Anna Karenina you can try read Nikolai Goggol or Dostoevsky. Crime and punishment was ok, Brothers Karamazov is a trip
I haven't personally read Goggol, but I should
Crime and punishment is only good if you try to uncover it's layers
Too deep of a novel for light reading
i liked that
...
if you are going to recommend shitty web serials at least recommend better shitty web serials
Lmao 3deep5me
Lol I get why you'd think that
I like Overgeared though
that doesn't not make it a shitty webtoon
overgeared is shitty even for webtoon standards
It has cHaRcTeR dEVloPmEnt
The best web serials are on royal road, though most are still dogshit
Hi. What are good books on functional analysis and measure theory that have not just theoretical exercises, but also more "computational-style" exercises and also exercises showing applications to other things. I mean, sort of showing how the theory is used in other places...
Not so sure if this is even a good question, but maybe someone here has something in mind...
FBI OPEN UP
smh only one character there is fbi worthy
I don't think Crime & Punishment is that deep. I wasn't a huge fan of it
Guy rolls around on a couch with a fever
But it's the go to recommendation for Dostoevsky cuz muh murder
Brothers Karamazov is great though
I think C&P is proabably one of Dostoevsky's worse works. Maybe I'm in a minority opinion here
I think it's an important piece of literature but I'm not really a big fan of it. I only commented on the "Deep" aspect of novel because my sister wrote a big paper on it for her college that explained everything from a psychological and philosophical point of view.
Maybe I should re-read C&P, it's been ten years
I re-read Brothers Karamazov over winter
Any good recommendations for English grammar?
I cannot wrap my head around rules like don't end a sentence with a preposition etc
I like steven pinkers sense of style
Ok, you need to watch pinker
Does writing well matter in an age of instant communication? Drawing on the latest research in linguistics and cognitive science, Steven Pinker replaces the recycled dogma of style guides with reason and evidence.
Subscribe for regular science videos: http://bit.ly/RiSubscRibe
Watch the Q&A here: https://www.youtube.com/watch?v=7rYAnYXIhL0
Bu...
Word power made easy?
Steven Pinker "The sense of style"
@timid drift much of English grammar rules are in flux now
Nobody knows when, I just insert it when I feel like it should be there
Like difference between a hpyhen versus a semicolon?
Oh my god what is wrong with English
Nothings wrong with it
Works perfectly fine for almost everyone
It just doesn't follow neat logical rules
why does debt have a b?
Why does receipt have a p?
queue?
Debt has a b because it's supposed to remind the reader that debt comes from the latin debitum
Receipt has a p because at the time it was common to shorten latin words, so they wanted readers to think that it came from a latin word
pt\
Anyone have a good recommendation for an abstract algebra book
I put a review of algebra books in the pinned messages
Oh thank you so much
Along with the ones listed I've heard praise of Rotman
dummit foote homie
Yes, all hail Rotman.
hi, anyone can recommend some precalculus trigonometry book?
Anyone?
ALL webserials are dogshit

no they totally all are
Web serials have literary value
some of them are more tolarable than others

which ones do you consider very good?
Omniscient Reader's Viewpoint
I dunno about literary value in that
I do
this is better than most of what im following rn so far

Any recommendation on a pre-calculus book?
Or well
A book that can teach me calculus and complement khan academy? As im abooooout to finish the last lessons and tópics of pre calculus 
I don’t know about this, but maybe as much as one can find in a typical fantasy/sci fi novel. I don’t really read them for literary merit (does anyone), more for entertainment. Also like 99.9% are shit and barely tolerable. Only a few are actually well written
I didn't say that all web serials have literary value
There exists a web serial with literary value
the existence of web serials does have literary value, yes
but also the vast majority are shit yet I keep reading them
The Count of Monte Cristo was originally a newspaper serial
good authors can be anywhere
Definitely, I don’t think the format affects literary merit
But barrier to entry is nonexistent for web serials so there’s shit everywhere
I just wish there was more creativity there
the same 10 (maybe I'm being generous with 10) general plot lines are rehashed like 100000x over

Oh no the apocalypse is happening and gates are appearing everywhere and people are gaining superpowers
if I see stupid blue game windows explaining literally everything
once more
I will lose my mind

also these people only know two fantasy settings in total
- medieval europe
- some "murim" eastern fantasy "martial arts" bs setting
please learn at least a third fantasy setting
- combine them
what is murim
Martial arts universe or something
o i cee
urban fantasy ? like shadowrun
Yes the noun is not a count noun
We were discussing in the context of web serials and stuff
Is shadowrun a web serial
tfw web cereal
No it isn't
The point is that other settings exist
But web serial authors generally stick to the same 2
murim is basically the analog of the harry potter wizard world, but with "martial artists" rather than wizards
all the shitty wuxia/xianxia inspired stories you see
they're all murim
Murim is Korean though
hwat is wuxia
Wuxia/xianxia are Chinese martial arts genres
it's not actually wuxia/xianxia, but it's inspired by it
You cultivate and become immortal
bro I've come to hate the word cultivate

What about opening acupoints

And inner qi
Cultivation manuals
what about [random adjectives and nouns] sect
lmao

pink blossom and heavenly mountain sect
Glacier rain sect
lmao
To be fair, this is how a lot of names in China come to be
Random nature words
It just translates poorly
true, it just feels a bit ridiculous in english
lol

most of these words are like 1 syllable in chinese
so it doesnt sound as exaggerated and clunky
(tonality is a bitch but it also lets you do cool things)
n

i just took a few linguistics courses in UG
mandarin was a frequent source of examples
partially because it differed from western languages in some fundamental and surprising ways, partially because half the class spoke it
No tenses
There is no conjugation
There is no noun declension
Everything is done with modifier words + word order
I remember learning something about how questions are constructed in mandarin
it was very interesting
I forgot it all now
Question words




