without losing comprehensive knowledge at least
#book-recommendations
delicate canopy
pulsar aurora
They may be geniuses, liars, or someone already acquainted with the subject. The rate one reads is partially based on comprehension be it the subject matter or the language itself.
hearty steppe
^
marble rock
i learnt some basic vector spaces/linear algebra ( known more about vector spaces and their transformation matrices , proved some theorems that i cant remember any of them ,and learnt more about dual spaces and eigen stuff which idr at all )
how cna i move even more forward
is there more linear algebra?
if so any book recommendations for more adv linear algebra stuff
or maybe rep theory for someone who knows upto galois theory
marble solar
Well it depends on what you're interested in; infinite dimensional vector spaces/hilbert spaces is one way to go from here
You can go to representation theory
You can go to algebraic curves, instead of studying zero sets of linear polynomials, you can look at higher order polynomial zero sets
You can go to differential equations
tight crag
You can go into lots of matrix normal forms and factorizations
They are pretty important but probably a bit boring to do by yourself
sudden kindle
@tight crag how prepared r u for the Algebra qual
tight crag
I've done a lot of galois theory recently
I prepped rep theory and group action stuff/sylow stuff at the beginning of the summer
I'm pretty prepared
sudden kindle
Maybe I should start preparing. . .
quartz pawn
@marble rock There's a tone of resources. Right now I'm learning out of a book that is one of the standard books which would be considered a rigorous and probably hard book for a first course in LA. Friedberg's Liner Algebra, and I've got a few others too. "The beginning linear algebra student that a graduate student ought to know" is one that is pretty rigorous and "Advanced Linear Algebra" by Noehl. A standard text is also "Advanced Linear Algebra" by Roman and I've heard good things about it.
If you really want to more linear algebra after any of those and how it's used, then you probably want to get a book on Matrix Analysis. The Horn book seems to be is the standard on that.
marble rock
what does rep theory do
does it just solve gt problems by turning them into linear algebra?
or is there more to it
trim narwhal
Do you know any good book for Precalculus?
vague pelican
gray gazelle
you should meet @gray gazelle, I think you guys could be good friends
clearly not, he gives bad advice
@trim narwhal have you considered using baby rudin
it has baby in the title
hollow current
gray gazelle
odd topaz
Do you know any good book for Precalculus?
@trim narwhal
thisi s a good place to start
gray gazelle
@odd topaz baby rudin.
dapper root
This guy would tell a parent asking how to teach their 4 yr old addition that they should use baby rudin
Cuz it’s aimed for babies
gray gazelle
no, i would obviously recommend dummit and foote for someone so mature and advanced
odd topaz
"A Course in Arithmetic" by Serre
"Arithmetic of Elliptic Curves" by Silverman
this might be too advanced
I recommend starting with LeVeque's book "Fundamentals of Number Theory"
and Baker's "A concise intro to the theory of numbers"
wooden sparrow
Soo many books on arithmetic?
odd topaz
and Mordell's "Diophantine Equations" which unfortunately is out of print, but you can find it on library genesis
hollow current
masha just wonder whether are you russian or not
odd topaz
Ethnically @hollow current
hollow current
nice
odd topaz
and "250 Problems in Elementary Number Theory" by Sierpinski.
hollow current
Rosen's number theory is recommended, but i havent read it yet
odd topaz
I can only recommend stuff I actually read
then if you want some basic geometry start with "Geometry revisited" by Greitzer and Coxeter
and Prasolov's book
"Problems in Plane and solid Geometry"
And rigby's book
"Adventitious Quadrangles: A Geometrical Approach"
oh and Honsberger book
it's called "episodes in 19th ad 20th century euclidean geometry"
and then do lots of locus problems to build up geometric intution
avoid all the cheap tricks like converting stuff to algebra, overusing trigonometry, "complex number", "barycentric coordiantes", applying projective transformation to send a line to infinity
stuff like that
"invert the diagram to turn circles to lines"
avoid all that stuff
"it's enough to check statements hold at 3 points"
instead learn the underlying philosophy and intuition behind geometry properly
never apply symmetry to an entire diagram
the correct application of symmetry relates points to other points on the same diagram
gray gazelle
are you ok
odd topaz
probably not
i got into a frenzy about geometry
if you actually want to learn stuff about number theory read "multilicative number theory"
by davenport
and "number theory" by borevich and shafarevich
Multiplicative*
at high school level
undergrad level
if you just want to get good at basic math read the ones I previously mentioned
remote viper
If you want a good geo book that isn't too confusing, Ckanavi's "collection of math problems for people applying to tech colleges" is very good. My dad used it,so did my uncle, and now I use it.
gray gazelle
hey guys
is ETF better for a beginner in calculus?
im tryna find good textbooks for ap calc bc
which one of these should i use?
https://www.larsontexts.com/products/title/95
https://www.larsontexts.com/products/title/197
https://www.larsontexts.com/products/title/96
https://www.larsontexts.com/products/title/122
this is the course https://apstudents.collegeboard.org/ap/pdf/ap-calculus-ab-bc-course-and-exam-description.pdf
hearty steppe
Larson is basically like Stuart
dusky orbit
@odd topaz are you zeb brady lol
quick hornet
theres like 10 billion calculus textbooks out there, it's unlikely people are familiar with the specific ones you listed
especially familiar enough with all four to be able to give good advice
quick hornet
i'd guess the "for AP" one is probably most appropriate for an AP couse
but thats just a guess
radiant crown
I don't like the covers, I find them a bit off-putting
Also I find it weird to have a website for books specifically writen by this Larson person
When there are several authors, it seems the name Larson is systematically written first, and looking at his website, it looks like he (Ron Larson) has a bit of a personality cult...
Buying one of these books for me would feel like accepting someone's invitation to participate in their pyramid scheme if you see what I mean @gray gazelle
broken meadow
i got so scared
im taking a jazz history course rn
and im reading a larson book
its thomas larson
lol
s p o o k e d
valid moth
solemn mantle
“The day the first copy was to arrive, I went to the post office and intercepted our mailman. On the drive home I ripped the package open and started to bawl. I pulled over and sat there for 15 minutes, crying, paging through my dream.”
~ Ron Larson
burnt blaze
Is this just for math books?
gray gazelle
i see
how about this: which book is the "easiest to read/understand" for a person who is new to calculus and will be taking ap calc bc soon?
hollow current
following polynomial i would suggest grandpa rudin
but seriosly speaking for basic calculus i think there are a lot of nice books
pulsar aurora
Depends on what you're looking for. I found Apostol's digestible, but still challenging. However, it's rigorous compared to your standard calculus textbook in college or HS. So, you might spend half the book covering integral and limits, but cover little in terms of the mechanical process (in terms of what you'd be exposed to in a Calc 1 class) until far later. As well, Apostol is unorthodox by starting with Integrals off the bat, so you also be in a weird zone of knowing things in the 'wrong' order.
pulsar aurora
Perhaps, but I didn't feel I need to be familiar
After all, the first few pages goes into the computation of an area under a curve before even bringing up integrals
hollow current
for analysis for now i extremely like Zorich analysis
it ofc covers what is covered in calculus
but it may be too hard
weak fossil
Hey guys, this is a loooong shot, but can anyone see if they can find https://www.bokus.com/bok/9789127435049/matematik-5000-kurs-2bc-vux-larobok/ in a PDF?
limpid gazelle
Have you looked on libgen
weak fossil
Found it boss
quick hornet
good to hear
flint forge
Jan have you read space and quantity
Or anything by urs
Tbf urs also probably wrote space and quantity
His actual like pubs are just crazy
But tge point is that like
The*
Oh im referring to the nlab page
But maybe it was
Anyway physicsts refer to the dumbest stuff w vaguely physical terminology
Like a space to urs is any topos OR any object of a topos
And weirder stuff that ive intentionally forgotten
But quantity is also memed about
Lost me there
You could unironically ask urs
He is weirdly responsive
In a good way
Im just usrd to being ignores
hearty steppe
What book
wooden wigeon
physics > math
gray gazelle
Why #book-recommendations ?
tawdry flicker
@wooden wigeon nah math is beautiful (i personally want to study physics but just because i think math is too blank, its just numbers on paper and nothing you can really feel in the real world.) nontheless its gorgeous
pulsar aurora
Except not all math incorporates numbers.
wooden sparrow
@tawdry flicker nothing you can really feel?
tawdry flicker
Except not all math incorporates numbers.
@pulsar aurora or equations, doesnt matter lmao
i cant walk in street and be like "ooooooh this is a visual representation of this theorem in that branch of mathematics" but i can do so in physics
again, nothing against math
i love math
tawdry flicker
@tawdry flicker have you ever tried to comb a hairy ball?
@tight crag yes i totally have a hairy ball laying around in my house let me get it real quick <3
okok ngl math can also be aaa
seen irl but
alot of it cant, really
faint parrot
@gray gazelle What? Physics is fake ?
limpid gazelle
I'm sorry but physics is fake
sage python
Have you ever seen physics before?
valid moth
have you ever seen a six-toed sloth before
gray gazelle
No but I’ve seen a 7 toed cat
valid moth
believe it or not but i have seen a ten toed human before
broken meadow
i haven't
sage python
I've seen a 9 toed human
Where n toed means possessing 9 toes, not that |{toes}| = 9
In fact I've seen an n toed human for all n\le 10
valid moth
I think you mean <
edgy loom
Curious as to know what they teach in the US at Pre calc level, so looking for book recommendations for that
deft ingot
pulsar aurora
I'm sure any pre-calc textbook be it college or HS would work.
edgy loom
Yeah but idk any
pulsar aurora
Anything McGraw-Hill would work.
At least, I remember alot of those being the math texts we used in High School before the common core stuff
I will say these may not be good, but they were used in high school 😛
safe relic
Hi guys, does anybody know where I could find basic mathematics serge lang's answers? I am aware the book has answers at the end, but it doesn't have all answers.
faint parrot
@limpid gazelle How?
white wraith
sounds good
foggy fiber
@safe relic I don't think Lang ever publicly released a solutions manual for that text. There is a small set of solutions on Wikibooks: https://en.wikibooks.org/wiki/Solutions_To_Mathematics_Textbooks/Basic_Mathematics
safe relic
@foggy fiber Thanks! I will check it out.
safe relic
@sacred wagon I did, unfortunately, I couldn't find the answer there. Thank you anyways!
inner sentinel
Anyone know where I can find Bilodeau’s intro to analysis in a PDF form (isbn 978-0763774929)? It’s not on libgen and I can’t seem to find it anywhere.
hearty steppe
never heard of that one
inner sentinel
Yeah it’s weirdly obscure
compact snow
I'm going to write a book soon. Is this a good place to be? jk.
edgy loom
Yooooo, its JK Rowling, whats up where you been @compact snow ?
faint charm
any good books on multivariable calc?
quartz pawn
Try Susan Colley vector calculus. Pretty good and has a solutions manual floating around the internet. Another good one is multivariable calculus and analysis it’s a springer book.
But no solutions
faint charm
thank you!!
fluid hamlet
Hi guys, any good books on inferential statistics with problems and solutions ?
hearty steppe
I use Walpole
fluid hamlet
Thanks
hearty steppe
yea I mean there are so many books
focus on learning probability theory I feel like thats the trickiest stuff but if it sticks with you, you'll get as far as you want in stats
unfortunately a lot of it is just plug and chug
but the probability theory stuff is fun
and carries to other topics in math like combinatorics
fluid hamlet
That's the kind of advice I'm looking for
Thanks for helping
fluid hamlet
and how you personnaly deal with the fact that there are so many books
I mean, personnaly I can't focus on one book and always looking if there is a better alternative
So I rarely finish a book which is I think a very bad habit
gray gazelle
You're very right about that
pulsar aurora
I treat reading a math book like a course in class. So I spend three to four months on a single book. Then I ask if I should find another book, continue, or move on to another subject
Unless I really struggle then I drop out and find something easier
fluid hamlet
Thanks 🙂
warped wave
@fluid hamlet That's the kind of habit I want to get rid of too smh
Mine's more on chem/physics book but still applies
One day I'm reading Zumdahl then when I'm 1/2 done I go to Atkins then abandon Zumdahl. Same thing with other books 😦
smoky surge
I don’t think you have to finish entire books in most classes you generally don’t go over entire books
I feel like that might be an unreasonable expectation
quartz pawn
@pulsar aurora I pretty much do the same thing.
I basically do all of the problems in there and it takes me a while to get through them.
cobalt musk
ok does anyone have some spare time and want to help me out. It may be interesting for someone. I need some help in google data studio doing an analysis of gambling data. I have a lot and its some crazy high numbers
quartz pawn
I'm going back and understanding all the material now and to really comprehend the knowledge in a book and thoroughly understand it it takes a while.
This method has been pretty time-consuming but I find that my knowledge is becoming much more thorough
cobalt musk
if im right i think the data will prove some of that providers are not actually random at all
sorry wrong room
smoky surge
@quartz pawn do you read books soup to nuts
quartz pawn
?
smoky surge
Every chapter
Sorry Hahahah it’s an expression I know you are doing a lot of self studying too
I was curious
quartz pawn
Yea
This may stop at some point if there is particular information that I am not interested in or time constraints
smoky surge
Yea I’m reading AI by Patrick Winston and going through the class associates with it but he only gives like half the book but maybe that’s different cause it doesn’t build off each other
Tho for LADR I’m thinking about skipping the polynomial chapter Axler says it’s ok and just move to eigenvectors cause I’m super interested in them and maybe go back
quartz pawn
As of lately I've been reading every chapter but they may stop as I move to other books
sage pier
hi
is Introduction to probability and statistics for engineers and scientists a good book? I graduated with a BSc in biomedical science
sage python
Axler's polynomials chapter I hear isn't great anyway lol
smoky surge
That’s what I’ve heard
smoky surge
Lmao
valid moth
i assume he would put off multiplication to the last chapter
smoky surge
Is that a criticism of him staving off determinates? Is that an unpopular opinion
sage python
It's a bad choice
Like I get what he doesn't like about the standard treatment
Namely what happens sometimes is that a book writes down this
smoky surge
What do you mean by a book writes down this
sage python
$\det(A) = \sum_{\sigma\in S_n} \text{sign}(\sigma)\prod_{i=1}^n a_{i,\sigma(i)}$
hasty eagleBOT
Daminark:
sage python
If you read this you think
Okay this doesn't feel too conceptual you know?
It's like okay I just take an array and spit out a number by an algorithm
Sure
smoky surge
That’s exactly what it looks like
sage python
So books do that or something similar (e.g. defining it inductively using minors or something), and then they go and prove that linear maps C^n -> C^n have eigenvalues
Conceptually that's the most unsatisfying thing in the world
Like okay hold on linear maps having eigenvalues is a geometric notion, it means they fix a line
And I prove that by........ bashing out numbers?!?!?!?!??!!
smoky surge
Yea it doesn’t help with understanding it just makes it feel like a formula
sage python
This is a very valid criticism of the standard treatment, that it kinda obscures what's going on
smoky surge
I get that
sage python
Now it turns out that determinants actually have a pretty good conceptual interpretation in terms of multilinear algebra
And if you specialize to the real case it's even a geometric notion
Axler's solution is to completely sidestep determinants
But uh
This isn't good for certain topics, like characteristic polynomials
My theory here is that he's so dogmatic about this because his own research is kinda functional analytic
In functional analysis determinants are less prominent compared to finite dimensional linear algebra
valid moth
it's actually a master strategy
if he doesn't teach you determinants, how are you supposed to determine you shouldn't read LADR?
flint forge
i think thats the opposite of a good approach
i think its much better to think about inf dimensional stuff
as being its own beast
like i think its reasonable to even rename the intro linalg classes
"Finite Dimensional Linear Algebra"
sage python
Well, I don't think he's making a pedagogical choice to do things as if in infinite dimensions
It's more like
He doesn't think they're important in general aside from the change of variables formula
Because they don't come up in his work
I think the correct answer is to just teach students multilinear algebra
This obv assumes we're in a class of math majors, if not... tbh I'm not sure exactly how much conceptual content is important in a class tailored for users of math. Not necessarily proofs but like, is there a situation where thinking about determinant as just input output machine satisfying blah blah is a disservice compared to at least having a geometric picture? Idk
sage python
Axler doesn't not treat determinants lol
flint forge
and a lot of intuition
flint forge
idk even the intuition in R^n
sage python
Which is like
flint forge
is nice
sage python
Fam really?
flint forge
thats woke af
Yes
in fact many texts and papers intentionally start by saying all rings are commutative
so like
yes
sage python
It's not just that oh a number of theorems die, it's like the subject just changes
dapper root
Hot take: non-commutative rings sucks.
Giga brain take: non-commutative rings are scary and I’ve lost track of what holds for them so I pretend they suck so I don’t have to come to grips with this fact
sage python
Actually Lie theory is starting to become relevant to me soon
More generally my stuff is getting into rep theory stuff
sage python
So yeah noncommutative world here I come
dapper root
Also on this topic
Fuck me if I ever deal with non-unital rings
I have never ever ever thought about them so like
I mean Spec A wouldn’t even be quasi compact so
Or at least the proof I know doesn’t work
sage python
I think that'll be relevant pretty soon, right now in a couple sections it's the lie algebra gl(2,C)
dapper root
Is that non-unital?
sage python
But next chapter is where it'll get pretty serious
sage python
Yeah
flint forge
if people keep saying ultraproduct
dapper root
I think
flint forge
we will summon jan
dapper root
Lol
It’s a logic thing?
What’s a product in this sense?
Like a categorical product
I see
Cursed
sage python
Actually the next like, 5 chapters of this book are rep theory lmao
sage python
All sets are compact
dapper root
Like if it holds for all finite stuff
There’s a model for it
Or something idk
I know you can do some weird cool stuff
Like umm
Nilradical = intersection of all primes
Can be done using something equivalent to it
And it’s weaker than Zorn’s I guess
I’ll be honest I don’t know Jack shit about Logic or any of this sort of stuff. So sentence I think is a FOL statement
But theory is like all the stuff you can prove?
Okay
So for the subsets
A model is like
A theory in which all the stuff is true I guess like uh
Idk how it works I think you can like add axioms?
Something something
Forcing
Can be used to make models
Like
What does that mean in this case
Like ZFC
Is a model?
Is a model just a set then
Where all those statements are true
I see
So... what’s the universe we normally work in?
I took a set theory course but this bit was sort of
Not touched upon
So I thought all our sets were built up from like the various axioms of ZFC
But then like V = L and stuff
Yeah I don’t know any of this stuff
Oh wait
V and L are both models right
Oof okay I guess I can sorta see it then
So both are models do ZFC?
If we say they are models
Okay but
In each one still we can find differences
Like something might be true in one but not the other
I see okay
So if ZFC is a theory
And a theory is like all the sentences that are true?
That was correct right?
Oh okay
So ZFC is the set of sentences you can make via the axioms of ZFC?
Ohhhh
Okay
Gotcha
So like barring the axiom schema or whatever which is like
A lot of sentences I think?
I didn’t really get that bit lol
A subset of this theory in the sense you said might be like
Okay I want ZFC
But forget the power set axiom
And then a model of that is some universe of sets where everything in ZFC is true except I just don’t need the power set of every set to be a set within this universe
Okay
So I think I can finally start to understand the thing you originally tried to state, sorry for that
Yup
Sure thing
That meaning a model for that subset right?
valid moth
I think you should be a model 
dapper root
What’s the poset relation here?
Like, inclusion of the subsets?
Oh okay
This is a subset of P(I)?
Because I’m not sure what you mean for an index to contain i
Oh
Yeah
Right
Sure okay
Principal meaning?
Okay
gotcha
So this is the compactness theorem?
I see
Because of Los theorem?
Yup
I see
So if the sentences are like
“There is a number > 0 and less than 1/n”
Indexed over all N
Then for any finite subset
You can find the maximal n, provide a number below 1/max{n} but > 0
So you can do that sort of thing
Because it isn’t about a theory?
And providing models for it?
Ah sure
I think for now my brain has been expanded as much as it’ll go
I still have to finish some algebra stuff
so I think I’ll have to call it for now, but thanks for the overview
I don’t think I’ll ever study this stuff seriously but I had been curious over the past week or so what model theory like actually is
I don’t really care or sweat the foundational stuff, and my set theory class bored me to death but it can be sort of interesting at times
long bear
Any logic/proof books recommendations?
gray gazelle
rudin pma
hot prism
does anyone have a pdf, of just random proofs?
limpid gazelle
"Proofs from THE BOOK" probably
hot prism
I don't have said book
edgy loom
Then get it?
hollow current
no u
limpid gazelle
rip can't dm
hot prism
I can't cause of this whole corona thing
limpid gazelle
@hot prism allow me to dm you it
hot prism
k
gray gazelle
Whoever is really mean
limpid gazelle
no
shadow nebula
@Whoever
wooden sparrow
"Proofs from THE BOOK" probably
@limpid gazelle you learnt proofs from this?
long anchor
yea velleman if you wanna learn
edgy loom
whats recs
white cradle
recommendations
gray gazelle
why is everyone so mean to me
maiden slate
whos mean to u
gray gazelle
it'd be easier to list who isn't mean to me
maiden slate
how are they mean
gray gazelle
mathematical logic by kleene is my favorite logic book
dusty plume
oh
yall should read anne of green gables
seriously give your minds a break now and then
dawn river
You left college about a decade ago. You want to start a serious journey into machine learning but you want to ensure your maths is rock solid. What book(s) should you read?
Thanks in advance
faint parrot
Any Calculus textbook recommendation?
robust marlin
@faint parrot I'd recommend Strang's Calculus
You can download it free from the MIT open courseware website
I'd avoid stuff like spivak and anton
It also has a free corresponding lecture series which I would also recommend
Gilbert Strang is fantastic
limpid gazelle
@wooden sparrow he asked for a book of random proofs
mossy flume
@dawn river it depends where your knowledge base is at
if you aren't comfortable with algebra 1, 2, precalc
then I'd actually recommend Khan Academy
and then when you reach the calc sequence I'd look at books
dawn river
@mossy flume I am a little comfy with algebra but never touched linear algebra
Do you think I should revise algebra first?
mossy flume
yea when I mean algebra 1-2 Precalc I don't mean linear algebra
I mean it's up to you
do you know calculus?
dawn river
Yes, back then
mossy flume
Hm
I would maybe restudy calc 1-3 (I don't really have book recs)
and then learn linear algebra
dawn river
Mmmm. Okay
mossy flume
and then after that idk what math would be useful
dawn river
Okay
mossy flume
Graph Theory?
dawn river
My BSc was in Comp Sci so did back then.
But will have to revise all, I guess
Goal is to be rock solid in the important math topics for ML
So that I would have a good foundation to build on
smoky surge
@dawn river I was doing math review for the same reason used khan academy to briefly review some calc then did the MIT OCW calc s, did strangs linear algebra and am now going through LADR
MITs OCW 6.034 is good too for a high level overview on AI
hearty steppe
Hey Billionaire. So you want to be mathematician and not computer scientist/software engineer? Welcome to my world. We both got robbed of knowing enough math going for the CS bachelors! I started learning pure math this year myself. Got my comp sci degree a couple years ago.
smoky surge
i would guess the mit intro to data science would probably be beneath you tbh but might be worth looking at if you need a refresher
@dawn river also the AI sister discord is fantastic and has some resources for you as well
quartz pawn
@hearty steppe I know it's not necessary for a lot of jobs but It kind of bummed me out that we didn't make sure that people had solid foundation in the math required for CS at my school.
You can always learn more on your own but It would probably make everyone better programmers if they made sure people had a keen understanding of the math required i.e. discrete math, LA, graph theory, some prob and stats because that would translate over into algorithm analysis and complexity theory which can help you write better code.
smoky surge
you arent meant to know the math before starting uni
that seems like an unrealistic expectation
robust marlin
Meh. It depends on the uni. The entry standards of my university rise year-on-year, but yeah, you still get many students who get disgruntled when you try to teach them something that is not directly related to what they want to do.
gray gazelle
@gray gazelle wtf do you mean
the UK at least teaches math at a high level in high schools
A LOT of countries
do not even teach calculus
smoky surge
you expect students to come in knowing multivariate, LA, etc..?
gray gazelle
except in very specialized schools
smoky surge
or do you mean like calc 1?
gray gazelle
in fact, you could name all the countries that do teach it on one hand
(apart from some very special schools)
smoky surge
honestly we are off topic here
hearty steppe
For someone with a CS background, I know a lot of math and I’m lucky to know as much math as I do. I was able to teach myself multivar. I’m teaching myself proofs and analysis. I learned more stats earlier this year. I will be learning abstract algebra and more linear algebra starting in August on top of proofs and analysis
Yea they don’t really teach you math in CS for undergrad. They barely scratch stuff that can give you enough surface knowledge to get into data science “eventually”... keyword “eventually”.
People been saying graduate level CS is basically math if you go the PhD route.
Honestly to be honest with you, data science doesn’t seem like as much math as I’d hope it to be. People seem to confuse machine learning with data science. But perhaps it is the expected learning curve for each. If you want to do theoretical stuff then sure it’s math heavy. Otherwise you probably gona set yourself up for disappointment if what your really interested in, is a career in mathematics (like myself)
faint parrot
Is there books on probability?
hearty steppe
Depends on what your looking for. Ross seems popular around here?
faint parrot
Ah okay
faint parrot
Ah okay
hearty steppe
But yea A First Course in Probability is by Ross
dawn river
@hearty steppe , exactly! Now I'm finally able to seat down to deep dive as much as I want. These days, I'm much more keen on the applications of maths and I found ML to be well suited.
I'm going to be doing this for 2 years but don't have a roadmap yet. Thats why I cam here for help.
@smoky surge , thanks a lot. Can you point me to where the discord for AI is. Will like to check it out.
@hearty steppe , I'm trying to build a roadmap for my journey back to maths & its application. I'll share here once I'm done.
Thanks a lot everyone. I'm happy to be here.
hearty steppe
Depends on what you want to end up doing.
Personally I decided to just hop on the “math as a career change” band wagon. Perhaps it is some self reinventing that I am putting myself through but I’m happy with it so far. At my age I should know the math I’m learning but life happens.
dawn river
I see ML as an opportunity to build something from the scratch.
pulsar dome
hi, would you consider calculus by tom apostol to be a calc 1 book or analysis??
hearty steppe
Maybe you want to be an ML engineer?
hearty steppe
Oh so your a software engineer
hearty steppe
Ok well I personally don’t feel like learning the math required for that isn’t too bad. I think you can get away with learning enough probability and stats, calculus 1,2 and multivar, and then linear algebra
And some graph theory
dawn river
I want to lateralize my learning.
pulsar dome
https://ia800305.us.archive.org/19/items/CalculusTomMApostol/Calculus vol. 1 - Tom M Apostol.pdf this is the book I'm asking about
hearty steppe
Use Paul’s online notes
pulsar dome
I want to lateralize my learning.
@dawn river what do u mean by that???
dawn river
I mean, my plan is to overlap/translate various topics (theories) of maths into real applications
hearty steppe
Sounds like you want to be a computational mathematician then
hearty steppe
So that’s quite a bit of a learning curve but I don’t want to discourage anyone. If you enjoy math, the best place to start I think is with proofs and then jump right into mathematical analysis after you done a bit of calculus.
hearty steppe
I mean personally I haven’t regretted it. I spent the last few months learning proofs and analysis so far
hearty steppe
I mean if you want to be a mathematician, why would you plan on learning math for 2 years lol.
pulsar dome
use MIT's open courseware, they've got full video lectures and notes on most of those topics
hearty steppe
Again depends on what you want to learn
It could take you that long to learn enough
smoky surge
@dawn river general on-topic discussion of AI/ML. link people to https://discord.sg/ai for an invitation.
dawn river
Self-study for 2 years to find my ffet.
hearty steppe
If you want to do more, learn more haha
dawn river
True
hearty steppe
Ok yea I feel you
dawn river
@smoky surge thank you!
smoky surge
yep
hearty steppe
Like, basically if you have a goal of what you plan on learning, you basically take note of your progression. Then you come to a point to reassess that
hearty steppe
But like if anyone wants to deep dive into math, implying they’re going further than multi variable calculus and a semester of linear algebra, I think it is relevant to pick up a proofs book and go thru that. Analysis is very useful for theoretical computer science even
smoky surge
is to hang out in the topical questions and try to answer some of the questions ther
dawn river
Correct!
Someone I really admire is Stephen Wolfram.
Not only for his popular WolframAlpha but for Wolfram Mathematica
Maths heavy, applications heavy.
pulsar dome
what???
hearty steppe
However I’m building My way to that book. Gona start with some of the shorter Rudy Rucker books and see what he’s about. Quite a few people seem to admire Rudy Rucker. I’ll admit I am a Douglas Hofstadter fanboy and I’ll indeed read the rest of his books I want to read but I love Godel Escher Bach.
I thought James Gleick would be interesting but he’s just pop science history.
dawn river
I have never heard of Rudy Recker
hearty steppe
So save yourself the time from reading his book “Chaos”
dawn river
Godel is my fave.
hearty steppe
Troll
hearty steppe
They probably dislike his ongoing tangent of formal systems using his MIU system for the first two chapters. Honestly that part wasn’t so bad.
But if you get past that, you get to see why people praise the book
hearty steppe
But the reason he spends so much time talking About his MIU system is because it comes full circle rather nicely
flint forge
a lot of people take GEB and pretend they actually like
understand godel's proofs
which is false
hearty steppe
It’s a shame people can’t get past that part of the book and then say “this sucks”
dawn river
Yes it is very interesting.
flint forge
im of the opinion that all good formal ideas start as false and informal ideas
so i dont take issue w it
hearty steppe
I mean I think a good trick to get to the good part of GEB faster is probably read the first couple paragraphs of the first chapter then hit chapter 3
dapper root
What’s GEB?
hearty steppe
But then you skip a lot of nuance with his MIU system which I found interesting. Maybe it’s because I enjoy math and learning about logic and stuff like that.
I will say however
north spire
What’s GEB?
Godel, Escher and Bach
hearty steppe
My one nitpick is he spends a lot of time with the Lewis Carroll renditions
flint forge
idk if its fair to call it pseudointellectual as a book
dawn river
What’s GEB?
@dapper root
Godel Escher Bach.
hearty steppe
I just skim through those parts
flint forge
i agree most readers end up being pseudointellectual morons
but thats not the books fault really
hearty steppe
Yea the book definitely is not pseudointellectual
Like to be frank, he is much more insightful than Ray Kurzweil is imo
And that’s saying something cause I like Ray Kurzweil’s books
No he’s not
His predictions are definitely off
But he’s on the money
How so
How is he a paranoid freak
When he is absolutely right about what’s going on right now
Like he has made some pretty interesting speculations about the future which we can’t tell yet but a lot of the stuff he said about the singularity is on point
dawn river
I like Kurzweil. Truth is, predictions are very hard to make.
flint forge
who tf is ray kurzweil
dawn river
Singularity
hearty steppe
My only nitpick is his predictions are too soon. Like he makes predictions that are at best 15-20 years away realistically
flint forge
oh
hearty steppe
From now that is
flint forge
i mean are you saying the concept of a singularity in which generalized intelligence is created is false or?
dawn river
Yup
hearty steppe
But some predictions seem more realistic a century or two from now
flint forge
like i believe its possible to make human-equivalent AI
hearty steppe
Kurzweil is very spot on too about engineers being in trouble soon too
dawn river
Hahaha. Yes
hearty steppe
Like software engineering isn’t worth it if you don’t want to make your life software
There’s way too many people right now competing for jobs and it’s only going to get worse
dawn river
Yes but I find that a bit extreme, thats why they call him a freak.
hearty steppe
Well depends on the extremity we talk about here
I think ML engineers and data scientists will be ok
dawn river
Because of what he's doing to himself
Hahahahaha
What he does to himself for longevity seems a bit extreme to me.
hearty steppe
But I think ML engineers and data scientists are basically corporate mathematicians
flint forge
oh i guess
dawn river
Hahaha. Yes. Corporate do money.
hearty steppe
Make profits
Screw taking our time publishing papers
Anyway
A great book for those who are interested in math I recommend this. It’s a short read and it’s fairly inexpensive
dawn river
I have this habit of checking books on goodreads before I buy.
But not for math books.
So I'll buy this.
Seems to cover the philosophy of maths, no?
Okay. Thanks
This is Vol 1, right?
A great book for those who are interested in math I recommend this. It’s a short read and it’s fairly inexpensive
@hearty steppe
limpid gazelle
Mathematicians are people? I can’t believe it
fleet tide
they're mobile husks of people
gray gazelle
Anyone here read digital control of dynamic systems by Franklin?
It came highly recommend by my linear algebra prof since one of my favorite parts of the course was signal processing and discrete dynamics. I'm trying to decide if it's worth it to get the first edition and read the new chapters from a PDF. Since there's like a 60 dollar difference between the 1st and 3rd edition.
gray gazelle
there is a pdf of the third edition on libgen
@gray gazelle
Yup, I have that. I was wondering what other people thought about the content though.
Also, the libgen copy is booty, and it seems comprehensive enough that having the actual book would be helpful.
dusty plume
i'd like to recommend the iliad by homer if you haven't read it yet.
it's very good HAHAHHAH
quick hornet
...
valid moth
valid moth
flint forge
?
tight crag
@echo kiln your answer was incorrect
The other possibility was that you have 3 real roots, which you do
This does not belong in this channel though
echo kiln
frosty kettle
If you would like to learn the philosophy of math, read a philosopher of math. Imre Lakatos, Penelope Maddy, and James Brown are among my favourites. Max Tegmark is good for a fringe view.
@sweet lotus which book of Tegmark's would you recommend? "Our Mathematical Universe"?
turbid sorrel
Quick question
Is there a reading club or sth that works through books in this server?
molten wave
they all die undergo exponential decay
hearty steppe
I will be checking out Imre Lakatos soon.
wooden sparrow
they all
dieundergo exponential decay
@molten wave why though?
molten wave
that's how people be
wooden sparrow
gray gazelle
edgy loom
mniip is foreshadowing something
north gulch
night knot
at what level? Undergrad?
valid moth
the most frequently recommended texts seem to be ahlfors, stein shakarchi, narasimhan
marble solar
Stein and Shakarchi is good for exercises
The reading is bad
Ahlfors is great for reading but the exercises are lacking
Marshall's complex analysis looks good on both fronts
dapper root
I used Gamelin
marble solar
Ask UW nerds for more
lilac terrace
@night knot nope grad
dapper root
It builds it up interestingly
no matter what
just don't use "A concise course in"
the one from the UChicago lectures
dapper root
Stay away from anything that says "A concise course in" that was adapted from UChicago lectures
unless it's like your second pass
unbelievably difficult stuff
lilac terrace
Haha okay thanks
marble solar
Terry Tao has public lecture notes on complex
Ucla 246A,C
In fact he's teaching it in the fall and I'm pretty sure he lets anyone attend
Via zoom
marble solar
Yeah, the hours might be wonky
lilac terrace
Is anyone allowed to attend
lilac terrace
Okie
Also what's the prerequisite to study string theory
The mathematical background
I kind of got interested in it
And the physics one
really?
Won't we need quantum
sage python
@dapper root HAHAHAHAHA
Yeah Concise Course in Algebraic Topology and Complex Analysis are both tough
That's how grad classes in Chicago run
hearty steppe
I mean its higher level math, what were you expecting? lol
I like Dami's intuition... Just stare at the theorems and bang your head against them until they make sense 
Analysis is awesome though. Kicking my ass but its awesome. Love it
gray gazelle
Now that everything is online I've had more time to learn on my own from the books that I actually like, but I do miss learning with other people. So I was wondering if any of y'all would be interested in doing like a book club(or any learning method) it doesn't have to be the same book, we'd just talk about what we've been learning from our respective sources. For me the fun part of math has always been getting to talk about it with my classmates. If something like that already exists I'd love to know about it.
solemn mantle
Anyone familiar with “a concrete approach to abstract algebra”
wooden sparrow
@gray gazelle sounds good 
gray gazelle
I haven't read that particular one, but it seems to be written to be very accessible and self contained. I can say that I thought the book I used "A first course in abstract algebra" by Fraleigh(2e) was really good at keeping everything simple and informal, so if that's what you're looking for maybe check that out. @solemn mantle
solemn mantle
Yeah definitely, thanks
I’m looking for something a little informal and self-contained, as in I don’t need to use it alongside lectures
gray gazelle
Then definitely check out Farliegh, his writing is Griffiths-esque.
solemn mantle
Alright, thanks so much
dapper root
I mean its higher level math, what were you expecting? lol
@hearty steppe these are different. Not comparable
hearty steppe
wdym
dapper root
Like
Sure, higher level math expect things to be hard
The level in those books are ludicrous
gray gazelle
Why does no one recommend the Princeton Lectures for analysis anymore? I haven’t read them but outside of this discord I hear great things about them
marble solar
They're fantastic
Volume 2 is by far the worst, and it's still pretty good
I think Volume 3 is the best, I haven't read all of volume 4
I tried to get into hardy spaces and all that jazz but my research advisor at the time was like nahhh
But stein and shakarchi is the way an analyst should learn analysis
gray gazelle
just downloaded all of them and they seem cool. weirdly enough, I’ve taken real/complex analysis and there’s only about a 1/2 overlap between the TOC and my actual class. so I’ll probably test them out in the coming days
Is it normal for a functional analysis textbook to cover brownian motion?
gray gazelle
I checked ye'old Libgen to no avail. Anyone got a PDF, it's referenced in by Dynamical Systems book and it seems interesting.
Arms and Insecurity: a mathematical study on the causes and origins of war
marble solar
That's what's great about Stein and Shakarchi, it has a wide breadth of material
That you can keep coming back to
With challenging exercises/problems that help you learn the material and help you prepare for qualifying exams
hearty steppe
I don’t understand your point Mathemagician.
From my point of view, Math is going to require actually doing more than watching YouTube series and just punching in formulas to deal with problem sets. That was a definite realization I’ve had a little earlier this year. The point of transition into higher mathematics involves a lot of personal commitment so yea it’s going to be hard and it’s going to kick your ass. Some people don’t like their world rocked when they learn and that’s on them.
sage python
He's saying that it's not just, oh algebraic topology and complex analysis are harder subjects than calculus was
"A Concise Course in Algebraic Topology" is harder than most algebraic topology books
sage python
"A Course in Complex Analysis and Riemann Surfaces", previously named "A Concise Course in Complex Analysis and Riemann Surfaces" is way harder than most complex analysis books
hearty steppe
I mean like if a book is too hard then find a book that’s easier to leverage?
hearty steppe
For me, Rudin on its own to learn analysis is too hard
sage python
That he doesn't think those two books are good intros to the subject
Because they're too hard
granite sluice
and harder doesn't mean like, ooh if you read it u r smarter. it means its an ineffective pedagogical tool.
sage python
That was the point he was making earlier, and when you commented "I mean it's higher level math"
hearty steppe
Yea lol
granite sluice
i feel like math is the only topic where people fetishize having shitty learning material
sage python
He was saying no this isn't just higher level math, those books are specifically deadly
granite sluice
or shitty technology
like, imagine there was a car. and the car constantly backfired, the wheel was unresponsive, the horn only worked sometimes...
hearty steppe
Well reading a math book is not like reading a liberal arts book or a biology book, or maybe even a physics book
granite sluice
a mathematician would be like
sage python
lorenzo really? I would a priori expect in most areas there's some variant of the attitude that like
granite sluice
wow this car is so great -- I mean, don't get me wrong, its dangerous and difficult to use. but if you can drive this car you can drive ANY car.
sage python
Yeah I read something that's super difficult to learn from and pulled it off because my dick is just that big
granite sluice
@sage python yeah you're probably right
hearty steppe
Like the closest thing I can compare to reading a math book, is reading a metaphysical ontology based philosophy book which does a lot of hedging to prove its points.
sage python
Like that's sorta where this sentiment comes from, that if you have something hard to learn from and you succeed it's a show of strength
gray gazelle
Tao’s > Rudin
hearty steppe
Like for instance, Reasons and Persons by Derek Parfit
It’s not necessarily a bad book but god fucking damn
hearty steppe
So much metaphysical conjecture to basically argue points about morality
granite sluice
proof by vagueness
hearty steppe
But yea exactly Dami
sage python
Proof by obviousness was something I attempted to employ a lot in undergrad
gray gazelle
proof by trivialness
sage python
I remember seeing some people say that you shouldn't say "trivial" because it's sorta condescending, if it's that obvious just say it without comment
And I'd just be like'
hearty steppe
Philosophers are almost mathematicians but not quite. They know how to make logical arguments and construct crazy metaphysical abstractions
sage python
You do realize that I say trivial specifically because I want my TAs to feel like idiots if they take off points
sage python
Like are you really going to attempt to say this isn't obvious? Are you that smooth brained that this isn't immediate for you?
sage python
Eventually I realized that people who grade pedantically are not deterred by the possibility of being judged by an undergrad
But the habit stuck
granite sluice
lol
sage python
But as a result I do think that this grievance against the word trivial isn't effective because people who use it know what they're doing, it's very deliberate psychological warfare
granite sluice
one just has to develop a counter arsenal of being ok being perceived as an idiot
sage python
The funny thing for me is that, I tend to not want to grade pedantically
And also this kind of thing would actually work so well on me
Since the idea of being thought of as stupid just terrifies me to no end
granite sluice
i comfort myself by knowing that if someone perceives me as stupid, that person understands reality slightly better for it
and thats a net plus overall
from my point of view as an .... uh... epistemological utilitarian
a made up viewpoint wherein i want to maximize the total number of truthful propositions believed by humans
gray gazelle
wow that’s deep
wooden sparrow
a made up viewpoint wherein i want to maximize the total number of truthful propositions believed by humans
@granite sluice fucking have my love and support already!!
broken meadow
and im 14
broken meadow
huh
gray gazelle
bruh you've posted this in three channels
no, four
5...
<@&268886789983436800> this guy's pulling some shit
sage python
Gone
dapper root
What was it lol
limpid gazelle
Not here please
sage python
Stop spam
gray gazelle
ok
dapper root
Don’t say that
sage python
This is your official warning
dapper root
Dami btw Woog already said I can’t get @everyone perms
Apparently it’s not for people born in August or November so
I can’t let everyone know about my birthday
Just in case you saw the ping earlier
And were still considering it
;)
sage python
I'll keep it in mind
sudden quail
I have too many books..
fast turtle
What are your thoughts on Robert Ash's "Abstract Algebra: The Basic Graduate Year"?
for self-study
marble rock
p good
gets into ANT and AG and it's cool imo
an easy pass to category stuff and homological algebra
which sounds cool
fast turtle
I've heard some critizism of it not being formal enough, is that a problem?
marble rock
idk i dont think so
fast turtle
Okay then, thanks! ^^
fast turtle
are they easy to follow? i have trouble with algebra in general, I kinda find it hard to follow thru
marble rock
umm
if you want an easay to follow not-so-grad-but-adv-ug try dummit and fote
but warning : it's dry and boring
i never read lang or hungerford
but ig just try them out
check pinned
flint forge
If you want really easy to read
You can try Pinters book
Which is slow
But very readable
It was my first exposure to algebra
fast turtle
I see, I will check them out, thank you
quartz pawn
Hi friends. Anyone logicians here who can recommend some good books for learning math and formal logic?
granite sluice
I really liked this : https://mileti.math.grinnell.edu/MathematicalLogic.pdf
dapper root
are they easy to follow? i have trouble with algebra in general, I kinda find it hard to follow thru
@fast turtle if you have trouble with algebra don’t use Lang. It’s better as a reference or like second pas textbook. First textbook only if you’re a maverick
gray gazelle
Ik I'm late to this, but on the topic of easy textbooks and complex analysis Needham is the one true source.
gray gazelle
@limpid gazelle does proofs from the book teach you anything lol
sudden kindle
@limpid gazelle nice pfp
limpid gazelle
Thanks
brittle latch
has anyone here read "how to not be wrong"
by jordan ellenberg
i might get it but idk
interesting, i have some cash to spare so i'll check it out
is there anywhere here where i can find like a general list of recommendations tho? ive been reading a bunch of programming books but im a math and computer science double major so id be remiss if i didnt seek out math books too
yeah i have a friend who calls them somewhat crudely math porn lol, but i find it pretty accurate
awesome thank you, i'll be sure to comb through it
do you know of any more approachable yet "advanced" books tho? i know a lot of books in this field tend to be hyperfocused on a single subject so it's a bit of a vague question but im open to any suggestions tbh i just wanna build up a sort of backlog of books to read if that makes sense
quick hornet
if you want something "between" this sort of "math porn" and actual mathematics
i'd say Counterexamples in Topology
valid moth
try spivak maybe?
quick hornet
although only if you have point-set background [and didn't hate the contrived spaces people came up with]
valid moth
(spivak's calculus)
quick hornet
nah spivak is straight up a textbook
brittle latch
yeah thats another thing if i read a textbook i default to taking notes my brain wont let me just absorb cuz i know it wont retain, that's why "math porn" has felt like a good start
or have you guys just straight up read textbooks cover to cover
valid moth
you don't read textbooks like a novel
you put concepts into short term working memory
and then do problems to cement it
but yes you have to prioritize understanding not memorization if that's what you're getting at
actually something you might find suitable is
evan chen's Napkin
unfinished as of now
brittle latch
👀
quick hornet
napkin will never be finished
quick hornet
infinitely large napkin isnt exactly infinitely large but
i think it has like 1000 pages or something
valid moth
i mean
the final draft can be infinitely large as long as chen plans on never publishing it and always adding new pages
quick hornet
well, supposedly the name comes from
valid moth
this would require chen to be immortal
quick hornet
he's a competition math coach or something and was explaining his research to a student at lunch
valid moth
maybe he can pass it on to his heirs and then they can eventually become immortal
quick hornet
but then he realized that to define what he was talking about, he needed to define some concept
valid moth
no no, not a coach
quick hornet
and then he needed to define groups and axioms and etcetc
quick hornet
which obviously wouldnt fit on a back-of-the-napkin sketch
so the textbook is his realization of his "napkin explanations of higher math" if these explanations could have arbitrary (reasonable) length
i havent actually read it but i've heard it recommended a lot, and on a skim it seemed solid
valid moth
the chapters are pretty well sized
enough detail
but also brief enough
for the purposes
brittle latch
napkin looks awesome i'll def read more into it
brittle latch
you know what i meant lol
thank you for recommendations tho!
also im new here, can anyone explain the pinned message pls?
quick hornet
the zetamath one is a shitpost
valid moth
no i mean i took it as you saying you would read more about Napkin to decide whether you would read it or not
brittle latch
that much i gathered lol
quick hornet
basically uh
valid moth
whereupon i recommended you just read it
quick hornet
a holomorphic function is a certain type of complex function
valid moth
(namely because you can get it online so there's no cost)
quick hornet
i.e. a function from C to C
brittle latch
(i meant the latter @valid moth lol)
quick hornet
it turns out that holomorphic functions are REALLY nice
broken meadow
lol holomorphic functions are constant
quick hornet
by "nice" here i mean
they come with a lot of "structure"
that makes them very "intuitive" and "easy" to work with
(at least relative to real functiions)
for example, holomorphic functions are automatically complex analytic
broken meadow
