And I think having undergrad algebra = the algebra everyone should know, grad algebra = the algebra all algebraists should know
#book-recommendations
dapper root
...
Our undergrad algebra doesn’t even touch Sylow
So there isn’t even Sylow to replace with rep theory in our undergrad curriculum
sage python
Your undergrad algebra should first level up and then cover rep theory 😛
dense pewter
how much group theory do you have?
sage python
7 group theory
sage python
(Also lol you should tell us about the solvable groups! I thought you were gonna say "I've got some facts" and just start listing them since that's what I do :P)
dense pewter
hahaha okay :P so as a warm-up fact, do people know about the 5/8 fact and abelian groups?
sage python
Oh that was on my rep theory final but I didn't get it 😦
dense pewter
also let's move to #math-discussion
sage python
Tru
I'll end on a book-related note
Question for you guys: do you think it's better to read books written by relative experts in an area vs just generic author?
dapper root
I think it’s not too important. I think either one can write a really good book, but I think perhaps the expert has potential to write a better book due to being able to include relatively unknown stuff or provide some really useful intuition, but on the same side of things it might be that they’re TOO used to it and that makes things unclear as little details are too obvious to them
I think it also depends on what level the book is, I wouldn’t want to read a commutative algebra book by a non-expert as I want pretty technical and specialized results, but an intro topology book I feel could be written by many more people
polar tulip
Question for you guys: do you think it's better to read books written by relativ...
the one that you understand better and get more out of. that's gonna depend on the specific book and topic and your background
like the expert in your field might also not write a good book, or one that contains any helpful and original insights
sage python
Heh
polar tulip
or it might be great
sage python
First book that comes to mind when you say that...
But yeah I was thinking more semigenerically/food for thought
Like do S tier researchers tend to do better in that regard than generic ones?
polar tulip
reading important papers or overviews by the leading people is probably worth the effort
books are case by case imo
oh btw guillemin and pollack was a good suggestion for the grassman algebra stuff, thanks for suggesting that
sage python
Sure thing fam
polar tulip
you now for like 10,000 years when i was trying to learn differential forms, i was mega-hung up on trying to understand all this algebra stuff really carefully, and like what exactly these vector spaces are made up of
thinking about tensors from the dual space of whatever
now i understand we just do this to get the algebraic properties that make it work lol
g & p say that in the beginning of that chapter and for some reason it's not anywhere else lol
i think you basically said that to me too, it's helpful lol
gray gazelle
Nice, this will be a nugget for me when I finally try to understand differential forms
thing with algebraic property that make integration go brr
sage python
I think Bott-Tu kinda talks about this a bit
Like he doesn't even define alternating multilinear stuff
He's just like
Okay the algebra generated by the symbols dx_i with the relations blah
polar tulip
like i guess the entire thing is just
"ok we want to integrate things with orientation, so signs gotta flip"
"and let's define differentiation so that the change of variables formula is built in"
sage python
Yeah that's pretty much it
I wonder if you can almost fully engineer that
Like okay we want it to satisfy XYZ so this is all we can do
Kinda like how determinant is uniquely characterized by alternating multilinear etc
I feel like the answer is yes
polar tulip
i'd believe it
ruby oar
stray veldt
diestel is nice for a mathematicians perspective
normal rain
Thank you 🙂
gray gazelle
what book covers simplifying multivariate polynomial/monomial ratios?
calm crane
i assume you mean gcd of polynomials
any reasonably decent algebra text should mention R[x] is a gcd domain iff R is
and provide a algorithm for taking gcds
tldr, any decent text on algebra (see pinned)
obsidian valley
I had a feeling he wasn't looking for a graduate algebra text.
gray gazelle
karmic thorn
The phrasing made me think twice if it was indeed about simplifying an expression and not some grad algebra stuff I've never seen.
calm crane
I had a feeling he wasn't looking for a graduate algebra text.
wait arent the pinned ones undergrad
except say lang that book is hugeeeee
gray gazelle
I have a feeling he wasn't looking for an undergrad text either
frigid wedge
guys
calm crane
well in my defence ug alg text have basically no prereq
frigid wedge
where can i get recommendation for lin alg
calm crane
isit for math or physics
marble solar
Axler, Hoffman and Kunze, Schaum's outline, strang
Are the standard go to texts depending on your level
frigid wedge
isit for math or physics
actually for cs
calm crane
ah
frigid wedge
but i want to know also for physics
frigid wedge
i am non-native english speaker, so i have problem in understanding topics, for example 3b1b videos are so simple that i understood every of them
calm crane
hm whats your language maybe others who speak the same language have better recommendations
frigid wedge
nah, there are not such good things in my lang, i know
calm crane
ooft
calm crane
Axler, Hoffman and Kunze, Schaum's outline, strang
probably jus look at these and see what suits you the most
frigid wedge
and besides this, i also want to know english terms
fast portal
Alternatively if you want to murder your will to live, hit me up I got a book written with physics undergrades in mind
fast portal
A second
gray gazelle
attractive description yohan 
fast portal
gray gazelle
applied linear algebra
calm crane
looks pretty ok what
gray gazelle
fast portal
The book stops acting friendly after chapter 1 tbh
it only gets worse from there
This is only chapter 2 btw
calm crane
pretty normal isnt it
gray gazelle
seems normal for a la book
gray gazelle
what does free mean in this context
i havent seen this word used here
but this is just like
you can reduce to a basis right?
calm crane
i assume linearly independent
gray gazelle
ic
marble solar
Not classical differential geometry
hollow current
@gray gazelle hallo
raw herald
I await the day all of mathematics is reduced to row reduction
obsidian valley
tterra is writing his algebra final i think vimes
construct your own row reduction formal system then
gray gazelle
Oh, I thought he said he is done (with his midterm)
gray gazelle
CTRL-F "now that my midterm is over"
obsidian valley
ah yes congratulations tterra
gray gazelle
hi
obsidian valley
i hope he figured out how to prove that if |G| = 5712 then G is a normal subgroup
gray gazelle
i did terribly
obsidian valley
is it not over
are you just omega genius
finished 3 hours early
I'm currently slogging my way through a bunch of shitty formalist writings
gray gazelle
there's a morning section in china that writes as well but idk if they have different questions or not
obsidian valley
this author is literally like "yeah I don't understand half of what this dude was talking about, but I'll try to explain it anyways"
oh damn that's kinda nice of your prof
our profs literally send out emails that just tell them to adapt their sleep schedule a few days before lmao
static crest
my exams are almost all 12 hour exams, and you pick a time to start
and your timer starts and you have to submit in 2 hours
obsidian valley
Only thing is you couldn't go back a question
static crest
I only had 24 hour midterms last semester
obsidian valley
that class was actually all exams so it was chill
static crest
this sem eng department seems very against 24 hour stuff
obsidian valley
lol
Nice thing is for CSM they just stop caring after Post hits lol
after post its like only the most blatant academic offense they care about I guess
static crest
lol, there's a lot of academic offenses going around in eng too
they just make it inconvinient
valid moth
,w prime factorize 5712
hasty eagleBOT
obsidian valley
now... silo...
gray gazelle
no
the homework is due next weekend
and
i did it already
so i get to ignore that damned class for a week
obsidian valley
wow youre so fucking cool tterra omg
gray gazelle
there's an RG problem i need to get done by midnight
no it was due yesterday but the prof extended it lol
obsidian valley
i am staring down the barrel of a 1500 word essay im so nervous to start 
gray gazelle
oh god
obsidian valley
I havent written since high school man
obsidian valley
Roughly.
obsidian valley
Well, I'm skipping a bit because it's dogshit
Yeah I wish
300 level philosophy course so I think theres some expectation
i dont even know how to like... cite stuff
gray gazelle
attempt to follow a poorly written guide you found on google
that's how it went for me
obsidian valley
ill just do what i did in HS and have a word doc of all my wikipedia links
and paste it at the bottom once Im done
gray gazelle
both of the elective courses i took that required essays were for non-phil people so they didnt care
gray gazelle
fucking hps100 so easy
gray gazelle
😔
gray gazelle
ok i must go for a bit
obsidian valley
i mean:
gray gazelle
yeah that's worht it
obsidian valley
Ultra will think I'm cool so it's worth.
gray gazelle
@ Ultrastition come praise jesse
obsidian valley
ok i gotta go to too gl riemanning those geometries
gray gazelle
i'll leave you with this #point-set-topology message
obsidian valley
gray gazelle
any good math book that contains proofs of all the calculus stuffs.
i really need such stuff at this moment
let me know if anyone wants to refer something to me.
hasty turret
Any analysis book?
gray gazelle
whats 'auch stuff'
its my stupid typing
if you're looking for a rigorous calc book, then go for spivak
ok i will check it
you mean micheal spivac?
yes
I have the pdf if you want
or just get it off libgen
sterile pelican
apostol is also pretty good, I finished reviewing basic set theory and proof writing
I am currently reading his book with supplement to spivak
gray gazelle
I have the pdf if you want
i will get it from libgen. Thanks
obsidian valley
@sweet lotus Do you know what the '|' in Frege means? Context:
It's all over this paper and I can't tell if it's a typography thing or something more meaningful.
More context, if needed. The one I'm looking at is p.348, line 54
Ok. I figured.
Thanks
Oh. Nevermind. It actually has enough meaning that there's like a ton of literature on it lmao. It's called the "judgement stroke". https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.154.5708&rep=rep1&type=pdf
A notable feature of Frege’s logic is the presence therein of the judgement stroke—the
vertical line ‘|’: a symbol which marks those propositions which are being asserted. For
Frege, assertion is the external act corresponding to the inner act of judgement: “we
distinguish: (1) the grasp of a thought—thinking, (2) the acknowledgement of the truth of a
thought—the act of judgement, (3) the manifestation of this judgement—assertion”
There's at least a couple hundred pages of writing on this piece of notation... 
gray gazelle
there's logic for you
fast portal
Getting a masters in logic must be easy if you can bs this much about |
obsidian valley
It was at Amsterdam too
That's "the" logic program I hear about from the EU.
Wow
Time to apply to Amsterdam, I have a lot to say about notation.
kind flare
I’m taking the cbe for pre algebra (8th grade math) in Texas so does anyone have any resources or textbooks etc that can be helpful in it?
warped cedar
is the CBE like a standardized test for prealg?
fluid bay
i think it means "credit by examination"
brittle latch
this is more of a meta question but how do you guys approach books
ive read some pop math books and those are easy enough to digest
warped cedar
read it more than once
if its hard you might spend a bit of time per page
digesting the material
make notes
on what you dont understand
brittle latch
ye i write in all my books
but i meant more how you approach textbooks
ive tried twice and have been unable to make significant headway in teaching myself from them
warped cedar
oh well yeah it can be difficult to self teach from a text book
brittle latch
part of my problem is im scared i wont retain shit before even learning it which is me being stupid
warped cedar
professors are often good at interpretting texts into a more digestible form
what material are you looking at specifically?
it might be helpful to find some free online courses
brittle latch
im (trying) to follow along an mit ocw on discrete math but ive rewatched the third lecture like four times and im still stuck 
brittle latch
that's the only course ive tried so far but im definitely gonna go for more
brittle latch
college sophomore
hearty steppe
understanding is what matters, not retention
your wasting your time thinking you just need to memorize shit
warped cedar
or are you just ignoring the lectures?
thats true
memorization is good to keep ideas with you and then you can think about them
but dont just memorize it all
hearty steppe
if you can't understand the material, don't bother retaining it, because you won't be able to understand what you retain
brittle latch
fuck memorization ive rewatched the same lecture so many times because im trying to understand it before moving on
warped cedar
one of my best professors told me that
hearty steppe
True studying is not knowledge retention but understanding what it is your studying
brittle latch
and ive only completed two semesters in which i took calc 3 and linear algebra
hearty steppe
Most college students don't study to learn, they study to memorize and pass their classes
brittle latch
^^
hearty steppe
so in essense, they are cheating themselves out of "actually" studying
brittle latch
im currently on a leave of absence tho so im trying to teach myself for learning's sake
warped cedar
if you want a deep understanding it takes work
brittle latch
it's just hard not to feel like im stagnating sometimes i guess but ik this shit is slow ¯_(ツ)_/¯
hearty steppe
its not irrelevant for people that are actually trying to learn
its irrelevant for people who honestly don't care
if you don't care then why take classes?
oh
sorry my confusion
brittle latch
there's no one right way, it's finding what works for you that's hard
hearty steppe
its not necessarily about keeping it in your head I feel, it is a catch 22. You understand based on your interest in the subject and the amount of time you spend with it and how you prioritize concepts
brittle latch
memorization should be a side effect
hearty steppe
Too many people go to college for $$$ and by doing that, they are cheating themselves of the genuine college experience
marble solar
I was the resident male prostitute at my dorm
warped cedar
lit
marble solar
Baked Beans was my name
hearty steppe
Those people will never know what its like to be a scholar, to be studious, and to work hard with compassion beyond greed
valid moth
@marble solar actually?
brittle latch
dude being studious is where it's at wdym
marble solar
lol no I've never been a stripper/prostitute
Baked Beans is from a sketch comedy show
warped cedar
I dont really care about money and i wanna be in academia for my life
but i am not a scholar lmao
thats such a pretentious thing to say
valid moth
i see bears
brittle latch
learning is fun, leave it at that
marble solar
You should watch the show
Absolutely hilarious, idk how they got it aired
Ultra is a cultured man, he probably knows the show
hearty steppe
Not everyone enjoys learning the way we do. At least some people may appreciate people for what they do. Unfortunately not everyone does.
marble solar
Yup
brittle latch
because it's fuckin hard to enjoy it
marble solar
Surprised you haven't figured my name out yet
hearty steppe
eh I see where you are coming from. Grit can be frustrating. Sometimes you need to give yourself a break.
marble solar
Moon Bears is one of their sketches
brittle latch
hi thats me i care
marble solar
I know
But ya never put it together yaself
T_T
@hearty steppe angela duckworth's research on grit is very controversial and unlikely to be accurate or reflective of anything that's not already on the big 5
or breakdowns of the big 5
brittle latch
big 5...?
when met with an open minded person, i feel compelled to at least try to impart upon them some passion for learning, but im stupid like that
gray gazelle
I thought open minded means they are already passionate to learn?
marble solar
Open minded doesn't mean passionate, it means open to considering alternative routes to traditional/established paths
Agreeable-Assertive is the dichotomy
brittle latch
this is gonna sound pretentious but i care because most of my friends, as much as i love them, always seem to care about such superficial shit
obsidian valley
That does sound pretentious.
marble solar
It's not pretentious to say that your friends might be materialistic or overly involved in a hierarchy that you're not invested in
It is pretentious to say
That makes you a better person
brittle latch
^^not what i meant, i love my friends for who they are otherwise they wouldnt be my friends
marble solar
Many people conflate the two as they often go hand in hand
Can you be a good friend without judging their choices? Like if a friend starts destroying their life to be apart of a club
Isn't it almost a moral obligation as a friend to judge?
And to give input
brittle latch
often times criticism is a kindness, when not provided toxically
marble solar
I know many people that destroyed their lives by being overly studious
I think the most important metric is are they meeting goals that they have for themselves
That produce positive relationships with their family/friends
and/or work
It's ok if academics isn't apart of that relationship
Yes
I just wanted to elaborate for the sake of greek letters
I am not a linguist, I apologize
brittle latch
all i was trying to say was learning tends to yield enjoyment, but people differ, and there's nothing wrong with that ¯_(ツ)_/¯
obsidian valley
learning tends to yield enjoyment
For you, maybe.
marble solar
One of my friends never went to college, he ended up working at a hotel
No he's a mid level manager with 7 years experience in hotel/hospitality
Makes near 100k
now*
We're the same age. I've never made more than 15k/year in my life
Despite going to some of the best schools in my area
sudden kindle
This is why you dont have friends
marble solar
LOL
hearty steppe
sounds like you need to move to the east coast Moonbears
shut grail
West coast best coast 👌🏽☺️
Lol Imma get the most downvotes cuz west coast people are outnumbered by east coast people in this server 😢.
obsidian valley
Because the west coast sucks 🤧
hearty steppe
how can you not be living a nightmare of poverty on 15k a year in the west coast lol. Must be your spouse that makes it bareable to that exent for you.
valid moth
just live in a redwood treehouse
shut grail
I’m actually struggling to pay for rent as we speak. It’s like living paycheck to paycheck. That’s not everyone tho, some of my friends are doing better than I am. But I still like living here lol;
warped cedar
idk about everyones situations but in most cases its better to live with your parents until you get a steady stream of income
that can support you
marble solar
@hearty steppe I've been fortunate to live in houses owned by family/extended family or have financial aid pay for housing
Now, my spouse is the bread winner. I'm trying to find gainful employment but it's been ruff
marble solar
Waiting to hear back
shut grail
Will you have time for grad school while working full time tho
marble solar
(I would quit to go to grad school)
My hope is I can get part-time work or internships
shut grail
Hopefully 🙏🏽.
warped cedar
get them stipends
shut grail
What we all need lol
warped cedar
fr
shut grail
It’s to compensate for our eye bags and dark eye circles.
buoyant spire
I read that someone here was having trouble learning about discrete math from mit OCW
I just want to give my two cents and say that you might find it helpful to practice the concepts by creating a program to demonstrate them, maybe 😃
(though, I don't actually know what discrete math entails, apart from a single problem that I'd read concerning it from the first few pages of a discrete math textbook that I never got around to finishing)
dense wren
Anyone know good books on Galois theory
marble solar
@dense wren I think papa Artin has a short good book
dense wren
What about Stewart
dense wren
Idgi
marble solar
I think it's better to get a short introduction that you can master the details
And move on to technicalities later
narrow oyster
so im studying abstract algebra
i never have learned anything about combinatorics or like
counting or probability
in any context
i dont necessarily need rigor but can anyone recommend any books that can help me understand what i need to be up to like
an 8th grade level or something
should i just study number theory instead and not focus on this specifically?
polar tulip
@narrow oyster i dont have specific recs but discrete math books tend to cover both of these things in a fairly bearable way
still umbra
I'm trying to compare units between my university and a university I'm planning on doing exchange at,
Their "intro to probability/statistics" unit uses the book: Mathematical statistics with applications by Dennis D. Wackerly
Whereas my university teaches with: Principles of Uncertainty by Kadane, Joseph B.
Is the content in these books drastically different?
(of course I'm assuming you may be familiar with the content of the books)
Specifically, the course details:
https://www.ucl.ac.uk/maths/sites/maths/files/math0057.pdf
https://handbooks.uwa.edu.au/unitdetails?code=stat2062
quick hornet
kadane's text is available online fyi
if it helps you compare
wackerly's probably is too, but not legally
anyway, my impression from comparing the table of contents and expositional style is that Kadane's text is more rigorous and proof-based
Wackerly doesnt seem to include proofs of most of his results
whereas Kadane does
compare their treatment of Tchebychev, for example
the early chapters are somewhat comparable (again, Kadane's treatment is more proof-based whereas Wackerly's is more application-based "throw-computations-at-you")
but the later chapters are drastically different
Kadane includes some hints at measure-theoretic probability for instance
properly working with the riemann-stieltjes integral and whatnot
whereas this material is completely omitted from Wackerly
(or at least from the table of contents)
my impression is that the Wackerly text probably isnt targeted at mathematics majors
whereas the Kadane text would probably be appropriate for a first stats course for math majors
its hard to say whether one will be an adequite substitution for the other, however
even if there are surface-level differences
that decision ultimately comes down to whether the school accepts it as transfer credit
earnest gazelle
Is there a textbook for discrete geometry
I think so. I found problems like erdos distinct distance for points on the plane. And want to learn more about similar problems
warped cedar
maybe look a bit into incidence geometry
polar tulip
@earnest gazelle if nobody here has a rec here's a MSE post about it https://math.stackexchange.com/questions/2506075/introductory-textbook-or-material-for-discrete-geometry
earnest gazelle
oh i think i might have meant geometric graph theory. There is a chapter on it in that book anway
storm sleet
What are some good books on formal languages and model theory?
gray gazelle
@ jesse
obsidian valley
@ ultra
i just read enderton
i learned formal languages from like theory of computation stuff
storm sleet
For some background I'm a CS/Math major, looking to pursue a PhD in programming language and type theory
so if there is anything more in line with what I'm looking for that'd be pretty sick
obsidian valley
go here
Peter Smith, The Dirty Dog of Cambridge, knows all.
http://www.math.cmu.edu/~rami/mt1.09.desc.html
this is the grad course in model theory at CMU that has a few textbooks listed as well.
molten linden
does anyone know a good book that recaps all of algebra 1, 2 and geometry?
gray gazelle
i don't know about geometry, but i can recap algebra 1&2 in a few sentences. y=mx+b is a straight line, the zero can be found with easy algebra. y=ax^2+bx+c has an extremum at x=-b/2a, and the graph is parabolic. if xy=0 then x=0 or y=0. the quadratic formula is x=(-b +/- sqrt(b^2-4ac))/2a
molten linden
sterile pelican
@molten linden I would recommend Gelfand's books on Algebra, his Functions & Graphs and his other one called Geometry
gray gazelle
do you mean specifically SAT math prep?
molten linden
do you mean specifically SAT math prep?
yes
molten linden
<@!451441382192578560> I would recommend Gelfand's books on Algebra, his Functio...
thank youu
gray gazelle
hm not sure, i guess SAT math is trivial. i think the hardest part is not making mistakes
maybe good practice is waking up early in the morning
so that you don't wake up on SAT test day tired
storm sleet
For me the hardest part was remembering everything
I was in calc BC when I took the SAT, so I hadn't used a lot of the math in a while
molten linden
im doing calculus
gray gazelle
you could use the official sat practice book i guess
sterile pelican
Another book is Lang's Short Calculus it has a recap on pre-calculus and calculus. The book is really short, and concise, as well. A lot of exercise to work on.
gray gazelle
i think it's widely acknowledged that the sat math section is the eastiest section
molten linden
yes but doing it in the timeframe is stressy for me haha
molten linden
Another book is Lang's Short Calculus it has a recap on pre-calculus and calculu...
ah alright
thanks
gray gazelle
anyways about the geodesics
i must say i was mistaken, SAT is not as simple as i thought
fast portal
"Passport to Advanced Math"
elfin glacier
ah SAT
absolutely terrifying memories
hopes and dreams
we were told we would be like Bill Gates and Mark Zuckerberg if we get good SAT scores
apparently that wasn't true
calm crane
they are too busy solving SAT problems
just a different SAT
damn next thing you know they would ask for syzygies
warped cedar
i got 400 on SAT guys not to brag 😎
gray gazelle
Hello! I'll be starting uni in a few days and I was wondering if anyone could recommend a couple textbooks I should buy for my course BS-Apmath. Thank you and it would mean a lot to me if anyone could answer! I only currently own Calculus by Ron Larson & Bruce H. Edwards. I also want to rereview my highschool lessons.
warped cedar
im a math major and id recommend discrete math by levin
im sure youll get textbooks for your course reqs
gray gazelle
The only book they recommended is the Ron Larson book so far
I dunno m8 my uni kinda sux
Gonna do extra work lol BC I kinda suck at math
I hear the exercises in calculus by spivak are great
maybe you can use that with larson
warped cedar
spivak is great
gray gazelle
https://www.ocf.berkeley.edu/~abhishek/chicmath.htm
Thnx for this aye I'll have this bookmarked
sterile pelican
Hello! I'll be starting uni in a few days and I was wondering if anyone could re...
Another site you should have a look is: http://www.stumblingrobot.com/best-math-books/
And if you want a nice concise book for calculus Lang's Short Calculus is a good start (non rigorous you would need a rigorous one much later), then progress towards proof writing (which is essential on math related subjects). Two great books I read are Book of Proof by Hammack and Mathematical Proofs: A transition to advanced mathematics by Chartrand, Polimeni, and Zhang
storm sleet
Whatre some good recommendations on books for more advanced set theory for someone whos primary exposure is undergrad analysis/topology and abstract algebra
haughty dove
I don't think Jech is a good introduction to set theory - but then again he asked for advanced set theory, so yeah
Jech is explicitly interested in set theory set theory topics, not set theory for any other theory
calm crane
well they mentioned they had exposure in analysis&topology so jech is pretty ok
fast portal
Nice new pfp Niko
cobalt arch
Is jech's set theory book self-contained?
calm crane
it is basically self contained
but as with most math
self-contained isnt equivalent to motivating itself
cobalt arch
What do you mean with motivating?
sterile pelican
have you read other set theory books before like Paul Halmos' Naive Set Theory?
cobalt arch
I have had some exposition yes
calm crane
That isn't a problem
ehhh id say it is better to at least like study some topology/measure theory
cobalt arch
It explicitly states that about lebesgue measure
sterile pelican
I do not think you need to but if you are going for something like Jech's book then maybe? But not to the extend of measure theory
cobalt arch
So which chapters can I go through without much exposition to other areas of math?
I mean if the book is self-contained I don't need supplementary material or isn't that the case?
sterile pelican
I can only speak from Halmos that the aforementioned book, Naive Set theory, is approachable
cobalt arch
I know but I want a book covering ZFC
calm crane
could try Hrbacek and Jech
cobalt arch
In conjunction?
sterile pelican
Don't misunderstand Halmos' book on Naive Set Theory is ZFC but at the naive view point
calm crane
In conjunction?
they wrote a book tgt
it is called like
introduction to set theory
it is basically a strict subset of jech part 1
cobalt arch
I skimmed through it
sterile pelican
That book covers far more than Halmos but I have not read all of it
cobalt arch
Yeah exactly it is like the basic set theory of jech's book
I know that halmos is a good intro but I guess forcing in chapter 12 of a set theory book is intriguing
sterile pelican
if your goal is to go far more in depth then yes Jech is the way to go
cobalt arch
Yeah that is my goal:)
sterile pelican
I aim to read it much later as my goal lies elsewhere; to read Hartshorne's book...one day
cobalt arch
I guess I will have to learn set theory the hard way:)
I just like the outline of the chapters. It is a very well written book.
Just more advanced but I guess I can do away with that.
calm crane
I aim to read it much later as my goal lies elsewhere; to read Hartshorne's book...
haha agoomer
hasty turret
sterile pelican
Oh...that is sad to hear
kind flower
helo
for real analysis, would y'all recommend rudin?? bc tao is recommended in #books-old
i have a solid grounding in single variable calc + experience with proof writing
mostly i want to get into measure theory
stray veldt
rudin is hard for self studying
karmic thorn
I really like Tao but one might find it to be too slow at times. Rudin is the standard recommendation, although I've heard good things ahout Abbott's Understanding Analysis as well as Pugh's analysis.
stray veldt
i recommend amann escher
hollow current
i recommend zorich
hasty turret
i recommend
hollow current
i
fast portal
_ _
gray gazelle
cobalt arch
Any books with many exercises on epsilon proofs for sequences and epsilon delta proofs for functions. More so a book that has a mix of calculus and analysis so the treatment is somewhat rigorous but there are many supplementary exercises.
karmic thorn
Spivak, maybe?
warped cedar
spivak is always the answer
cobalt arch
Haha I have spivak but I don't think he has as many exercises as I would like:/
I know this is a niche topic and everyone will recommend different books so let's see
karmic thorn
Demidovich's Problems in Mathematical Analysis. I think you can find a PDF pinned in #calculus .
cobalt arch
Is it good?
karmic thorn
Not sure if it has eps-delta stuff though. 
It is good at what it does, loads of problems.
cobalt arch
Hm I hope it does
karmic thorn
I don't remember the exact contents
gray gazelle
spivak has a shitton of exercises
cobalt arch
Is that so? How is the book called? And are there many exercises on such proofs?
karmic thorn
True, not to mention a lot of them are significantly tough to solve.
gray gazelle
Is that so? How is the book called? And are there many exercises on such proofs?
all are proof based
cobalt arch
Okay
gray gazelle
and there are 750+ as I mentioned
sterile pelican
I am currently reading Apostol's Calculus 1 and I think that too is a good book, or supplement, to serve as a basis for Baby Rudin
sterile pelican
it is dryer but at all means not as hard
I think what strikes me as odd is starting with integration first though but in a historical sense that does make sense
dapper root
Is there anyone who
1: originally learned rep theory and didn’t really get it too well
2: later used a book to learn it and felt like you got it pretty well
If so, what book did you use?
I guess more generally what are rep theory recommendations, I outlined the two above points simply because I’ve technically learned rep theory before (from D&F) but I feel like I don’t understand it one bit.
velvet briar
Just started reading Reprentations and Characters of Groups by Liebeck and James and am having a good time with it
It's gentle enough for me to get going. It does backwards function application which I like
dapper root
It's gentle enough for me to get going. It does backwards function application w...
It’s always the group theory texts that do that haha
sterile pelican
out of curiosity how much linear algebra must a graduate mathematician know? Is Hoffman & Kunze sufficient?
gray gazelle
probably
you could compare with the toc of roman's book
(disclaimer: i'm not a grad student)
sterile pelican
You meant to say not yet
gray gazelle
😌
sterile pelican
But thanks!
marble solar
@sterile pelican it really depends on what field you want to work in
If you want to do applied math/numerical stuff knowing numerical linear algebra is imperative
If you want to do algebraic type things, Roman probably helps a lot
If you're just doing like general topology/analysis/combo/geometric stuff
sterile pelican
I aim to do algebraic geometry so I guess it is needed
calm crane
lol yea
sterile pelican
I do not whether I am being mocked at or algebraic geometry is sort of a meme here
calm crane
but honestly the modules part of roman seems to be like
all from exercises in AM
nah literally everyone online wants to study algebraic geometry
it is like
the most common reply
valid moth
sterile pelican
really? That is quite fascinating is it everyone wants to do Hartshorne for some reason?
calm crane
nah it has become such a meme lol
sterile pelican
Why is that though?
calm crane
probably because algebraic geometry somewhat has a reputation for being abstract
steel viper
Why is AG so popular relatively?
You'd think it would be AT
or topology in general
calm crane
probably because algebraic geometry somewhat has a reputation for being abstract
also probably like cuz the prereq is so much that like most commonly ppl ask qns on these
you see everyone basically knows point set you can learn it in your sleep
steel viper
hurb
calm crane
idt AT has that reputation other than like
homotopy theory stuff?
analysis type stuff unironically harder to do ngl
valid moth
lol
steel viper
like
steel viper
mhm ive heard analysis is generally bigger irl
calm crane
idk i feel like topology has a big reputation
i feel like it is just in public
haha coffee cup
steel viper
yeah
so you'd think there would be more people being like "i want to learn it but dont know where to start"
calm crane
i feel its more like
analysis as a whole is a lot of different areas
and that everyone doesnt really have the same path
steel viper
hm
calm crane
but then
steel viper
i dunno
calm crane
why arent there so many qns on like
introy real/complex/func anal stuff
yeah idk lol
steel viper
ya
calm crane
maybe those who do analysis is big brain enuf to solve themselves
probably the true reason tbh
calm crane
ag unironically is like the string theory of math
steel viper
and abstract alg recs
calm crane
WTF I DIDNT KNOW THERE WAS A BOOKS CHANNEL
hearty steppe
Need more real analysis recs too
hearty steppe
^
steel viper
lol
we should at least add munkres to the point set section
and an AT section with prolly ig hatcher, concise, bredon, and tom dieck seem to be the most popular recs
sterile pelican
Alright gotcha at least now I know
steel viper
inb4 lurie
sterile pelican
We talking about the Rudin trifecta?
steel viper
Is that competition as strong at the grad level Ultra?
Like is AG super popular relative to the size of the field rn among grad students
mhm
calm crane
probably soon cuz scholze simps like me ok tbh he isnt that attractive
calm crane
i am attractive
** ⓘ Official sources say this claim may be false or misleading**
steel viper
pop mather
sterile pelican
She appeared in numberphile a couple of times
steel viper
I think
calm crane
lmao samee
mossy flume
Hannah Fry I think went to my college
sterile pelican
Hannah Montana is such an old show
mossy flume
She's cool I'd love to study under her
calm crane
what does she do?
sterile pelican
She does applied stuff though
sterile pelican
I think so actually
calm crane
sterile pelican
agreed
marble solar
The problem with AG is it is a fad ~ very hot topic/commodity
If you say you wanna do Analysis/PDEs/Applied Math
mossy flume
@sweet lotus who should I know about
marble solar
You'll get a lot more mileage
mossy flume
I go to there and I barely know any of the faculty
My math prof is amazing but he's a post doc so probably no one knows him
mossy flume
Yes @marble solar
sterile pelican
If he were still alive I would like to meet herstein
mossy flume
idk who he is tho
steel viper
who is the postdoc spamakin
marble solar
Haken manifolds?!
mossy flume
Ruiyuan Chen @steel viper
steel viper
spamakin is a 1st year
marble solar
HAKEN MANIFOLDS?!
mossy flume
Yes
steel viper
logic man
mossy flume
Yea Chen is teaching a mathmatical logic class next sem
I wanna take it but no space
He's such a good prof
Kids in my class hate him but I think he's awesome
It's a good school, very happy I'm here
marble solar
nathan dunfield rings a bell
mossy flume
I've never heard of any of these guys damn
marble solar
LOL we're just nerds
marble solar
who is your TA?
broken meadow
man i wish my school had cool ppl
marble solar
it's ok, my MS institution has like no big names too ~ just local people
marble solar
I didn't even think of applying to schools in florida
It doesn't seem like a place I wanna be in
broken meadow
hopefully for grad school i get to go somewhere cool
marble solar
yA like alaska
broken meadow
the math program here is very quiet
marble solar
that's as cool as it gets
(In the states)
What's the most northern uni in Canada?
mossy flume
@marble solar my TA is some random grad student idk. Never spoken to them in my life
Homie gave me 100/100 on my last two HWs so shout-out to him
marble solar
I'm asking because I know ppl that are random grad students there
mossy flume
Uhhj
marble solar
You don't have to single them out if ya don't want
gray gazelle
i want to found the University of the Arctic
marble solar
No
broken meadow
moon university when
calm crane
isn't Haken there?
:ooo
sterile pelican
abstraction choose us :^)
valid moth
the nerd life
sterile pelican
maybe I should just go for modern algebra
valid moth
the SIMP life
sterile pelican
time to buy lang's algebra book
calm crane
lang algebra book is unironically good
but like
i doubt it works as a intro
maybe want like a more normal intro
sterile pelican
Herstein is
calm crane
say jacobson
herstein has good problems
but oml notation
ok it genuinely has good problems lol
calm crane
honestly you only need to read like
until galois theory
then can start selectively choosing which chapters to read
the other chapters are rather independent of each other
sterile pelican
how about MacLane's book?
calm crane
havent read it yet 😛
sterile pelican
I hear great things with Jacobson though
calm crane
wait is maclane the categories for working mathematician book
sterile pelican
is it needed to be familiar with Roman's LA in that case?
sterile pelican
wait is maclane the categories for working mathematician book
Oh my bad I meant Birkoff I think
calm crane
h&k is more than enuf tbh
youll learn all the module stuff in AM it seems (i havent read roman in depth lol)
calm crane
Oh my bad I meant Birkoff I think
never seen that book before ngl XD
sterile pelican
alright at least I do not need to get it for now
hmm I would get jacobson since dover is pretty cheap xD
calm crane
ya jacobson is so cheap from dover
amazing
all my GTM books i get china version cuz way cheaper there xd
sterile pelican
Also I operate far better with a physical text
calm crane
same
sterile pelican
oh the GTM one's in China are these dodgy looking covers right? xD
calm crane
isnt quite dodgy lemme send pic
sterile pelican
One has a picture of a book
calm crane
sterile pelican
Oh that actually looks nice
my biggest complaint is springer's usage of paper but eh can't complain
agreed
calm crane
there is this tho
sterile pelican
if they had a hardcover version with that material it might be awesome
sterile pelican
sterile pelican
Is that Jech's set theory there?
sterile pelican
I am a grown ass man cringe
but your name "adorable cat" is that something popular or something?
calm crane
nah i jus uh
randomly typed it at 3am
you cant trust me to make good decisions that late
sterile pelican
ngl cats are the superior pets :^)
calm crane
AGREEE
sterile pelican
even cats appreciate abstraction
sterile pelican
I see more GTM books ye gods I can't even read Spivak's Calculus on Manifolds
calm crane
even my cat is a hartshrone memer
valid moth
wow, your cat is on chapter 111 already
radiant basalt
Lol
gray gazelle
it's a plushie
valid moth
it's a cat
sterile pelican
is it a topological cat?
wooden sparrow
what book has more than 100 chapters?
hasty turret
All of them
sterile pelican
The Princeton Companion to Mathematics by Timothy Gowers I guess
I remember buying that for a friend it is even thicker than D&F
And reading D&F cover to cover scares the hell out of me
molten wave
the monster book has 22 chapters and hundreds of sections
gray gazelle
The Princeton Companion to Mathematics by Timothy Gowers I guess
they are not actually chapters
since most of them are about 3 pages long on average
sterile pelican
They are more like sections yeah
Other than that I know nothing else that has chapter 100+
Unless you want to find "The Book" that Paul Erdos preaches about, and no Aigner and Ziegler is a small taste of what Paul Erdos stated.
gray gazelle
stacks project has 114 chapters
hasty turret
Wait,"The Book" is a thing
gray gazelle
not for real
sterile pelican
No not really
hasty turret
I mean, metaphorically ofc
gray gazelle
yes
sterile pelican
Then yes
marble solar
IDK big books don't scare me anymore
It's the thin ones
(Unless it's Lurie, I won't touch that with a 10 foot pole)
You ever see "Lecture notes on" and it's like 50 pages
gray gazelle
Detailed notes
stray veldt
to me "lecture notes" implies it can be done in a semester's time
that's why i like studying with actual lecture notes, there might be an original book but i don't want to spend a year reading a book
i trust in a decent professor to make a topic selection that can be presented in a reasonable amount of time
sterile pelican
Atiyah's Introduction to commutative algebra is pretty thin, does that scare you? :^)
steel viper
AM is nice
steel viper
is it rly tho
it just offloads things into the exercises
but theyre good exercises
calm crane
look im lazy
sterile pelican
the beginning is sort of at least readable compared to Matsumura
sterile pelican
that is true
calm crane
ish
sterile pelican
I guess books like Eisenbud satisfies but again that thing is thick
calm crane
honestly suck cost fallacy i literally only haven’t properly worked through like last few chapters of AM
sterile pelican
it's fine I just skim through the books yet I am merely a noob
calm crane
sterile pelican
:^)
steel viper
hurb
why would u skim
the exercises are half the fun
except hatchers exercises are kinda zzzzz a lot of the time
sterile pelican
Sorry I worded that poorly I meant to say read the early pages to get an idea not skim through the entire thing
steel viper
oh ok
i shouldnt read more hatcher tonight cuz i ahve other work
but i rly want to
hurb
sterile pelican
I am at Apostol's Calculus so I got a long way
But I do read the first few pages of those books and try to understand them at least
Though honestly I really think, upon reading Jacobson's Basic Algebra 1, I could. The way he presents set theory for instance is really nice
dapper root
Matsumura is dope
gray gazelle
lee
steel viper
no.
gray gazelle
ism
steel viper
maybe...
gray gazelle
soft terrace
Anyone got a recommendation for a statistics book at the graduate level? kind of looking for a more challenging extension from the undergraduate calc based stats class
valid moth
@steel viper hartshorne
steel viper
no
gray gazelle
yes, i know, i'm original
valid moth
steel viper
you havent even read hartshorne
valid moth
just intuit it
marble solar
@steel viper knots and links by Rolfsen
steel viper
hurb
past yew
Wait is someone asking about a book for knot theory?
There’s a free one online that is overlooked a lot
marble solar
Moth wanted a physical book
past yew
It is very much self contained
I think you can get a physical copy
Should I write a paper on my notation?
Moonbears
Like applying it to problems which have been solved before
Reformulating stuff in terms of it
gray gazelle
@soft terrace I think the usual recommendations are casella/Berger, wackerly(wackerman? Something like that), lehmann, shao, schervish
gray gazelle
ah nvm i was thinking wasserman not wackerly
i've read good chunks of casella, and i've wondered whether wasserman is better. i feel like casella is sort of calculation heavy/doesn't given enough intuition
soft terrace
larry wasserman right?
gray gazelle
yeah that one
gray gazelle
hm maybe not
soft terrace
im gonna try out casella i think i'll be ok
valid moth
morin 😳
calm crane
goldstein
sterile pelican
Shafarevich's Basic AG 1 & 2 :^)
calm crane
honestly just ega
sterile pelican
Not everyone knows French :^) (We are referring to Alexander's Grothendieck's EGA, right?)
obsidian valley
Just get principia mathematica tbh
steel viper
i dont like any of these answers
sterile pelican
What is wrong with Shafarevich? D:
valid moth
get jacobson 2: electric boogaloo
wait i forgot there was a 2nd jacobson lol
what does it even cover
wait lol
🤔 maybe this could be an alternative to lang
valid moth
valid moth
gray gazelle
What are Pearson Modern Classics? Like Munkres Topology Classic Edition for example. It has a different page number than the regular one but I can't find any info on what makes it different.
calm crane
Not everyone knows French :^) (We are referring to Alexander's Grothendieck's EG...
honestly you can like
infer most of the words