seven fucking volumes
#book-recommendations
steel viper
Fomenko also merges the cities and histories of Jerusalem, Rome and Troy into "New Rome" = Gospel Jerusalem (in the 12th and 13th centuries) = Troy = Yoros Castle.[20] To the south of Yoros Castle is Joshua's Hill which Fomenko alleges is the hill Calvary depicted in the Bible.
this one is my favorite part
quick hornet
wait does he think jerusalem being in palestine is just fake news
if so, are we sure he's not just campaigning for a bold solution to the israel-palestine conflicts
sudden kindle
wtf are you talking about
steel viper
this is in tom dieck its literally how he does classification of coverings over a space B
dont ask for more details im still reading that chapter
gray gazelle
Is tom dieck related to grothendieck?
lone sand
link for precalculus book
warm glen
https://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2019/alggeom-2019.pdf
ty very much
barren night
broken meadow
"one handed reads"
barren night
Exactly
After that book
You can fuck 20 women a day
If you are into women everything else is okay too
hasty turret
Ok,This is definitely nsfw
gray gazelle
Was ist nsfw?
karmic thorn
Not Safe For Work. Content rated 18+.
gray gazelle
This wasnt the type of book I was expecting here.
prisma snow
None of us were expecting that
There was also once a guy who told is we all had to read crime and punishment and then proceeded to describe the plot of pride and prejudice
pale linden
At my school someone in a cs class lecture asked for a link to the textbook in a class of 1000+
And someone shared a porn link
worldly basalt
I must ask
How do you have 1000+ students in a class??
pale linden
CS classes are very in demand
worldly basalt
No, I get that but how does 1 class has 1000+ students
Shouldn't the students be divided
gray gazelle
Ofcourse for research purpose
gray gazelle
No, I get that but how does 1 class has 1000+ students
Zoom
pale linden
You let the GSIs and UGSIs manage those sections
pale linden
Recorded lectures, not everyone shows up
gray gazelle
Iirc the limit is 500
Even the paid?
pale linden
It's definitely doable, my uni does it every semester lol
gray gazelle
CS has one more paper compared to others.
narrow talon
Wtf, seems like you’d lose a lot of the benefit of paying for a class with 1k students. More a mooc at that point
flat osprey
Do any of you know what that purple logic book that uses 1 0 and # as truth values is called?
gray gazelle
Iirc the limit is 500
the real limit is whatever the size of the lecture hall can support but online it doesnt matter
i dont really get it, the entry level market is a bloodbath if you dont have coops and work experience though
having a degree helps but its not going to be the important thing
and plenty graduate unable to code
pale linden
everyone wants to make the big silicon valley bucks
gray gazelle
CS goes through booms and busts
gray gazelle
Also plenty able to code exceptionally well compared to high graders list.
strange mulch
Everyone can code but not everyone knows complex analysis
Everybody codes* there, fixd
gray gazelle
My point was , just attending class doesn't make you understand 'complex analysis'.
just coding doesn't make you able to code
you gotta get beyond the cargo cult thinking that a lot of people start with for programming
cargo cult thinking?
strange mulch
My point was , just attending class doesn't make you understand 'complex analysi...
I agree, it is beyond me why anybody would pay to listen to recorded powerpoint presentations. The only times I found lectures useful are when the lectures are interactive as in the lecturer not being stressed out due to fucked up schedules. I guess what they are really paying for is for somebody to look at their code and tell them it is ok.
gray gazelle
Do this maths server have lectures? It would be cool.
I would be willing to pay as well.
it does not
Any ToS preventing this?
no
not that i'm aware of
that said
some degree of mathematics goes on in vc
occasionally
gray gazelle
everyone wants to make the big silicon valley bucks
All cs majors are eventually going to become reduntant
gray gazelle
All cs majors are eventually going to become reduntant
if you're talking about AI I have some magic beans Id like to sell you
tight crag
I think this is a correct statement, but probably not for a while
gray gazelle
if you're talking about AI I have some magic beans Id like to sell you
Not just AI, I think most cs majors cannot really do anything outside of software dev
As the field progresses it will increasingly require more domain specific knowledge
gray gazelle
hearty steppe
Damn I didn’t realize how big Riley et al math methods is
Nice you have a soft cover of it
Good find
gray gazelle
I don't think they make hard cover this thick book 😄. It's already heavy
hearty steppe
Do you have more of your collection to show? It’s very nice so far
gray gazelle
@hearty steppe I have other subjects. Physics, economics, politics. Maths this much only.
gray gazelle
It's good. I just got it 3 days back.
Concepts of Modern Mathematics is a book by mathematician and science popularizer Ian Stewart about recent developments in mathematics. It was originally published by Penguin Books in 1975, updated in 1981, and reprinted by Dover publications in 1995 and 2015.
hasty turret
<@!589919253109407766> I have other subjects. Physics, economics, politics. Math...
Are you a student?
hasty turret
How is software engineering?
gray gazelle
Good. Interesting.
why do you have these books then
i mean have you read all of em ?
oh it was you who said they have lots of books, like collecting books
heavy collection ngl
do you rent these
gray gazelle
do you rent these
No, Once I read completely I give away.
molten wave
"design patterns" 
pulsar geode
Not just AI, I think most cs majors cannot really do anything outside of softwar...
yeah their background is often quite pathetic
gray gazelle
As the field progresses it will increasingly require more domain specific knowle...
meh domain experience comes with years on the job but you have to be willing to learn as you go
some people have 10 years of experience
others have the same year 10 times
gray gazelle
Nope. Software Engineer. 10 years in it.
2009, almost 11 years at the current company
for me
Why would you have software engineers learn the domain when there already are trained professionals with years of experience in the field?
gray gazelle
Why would you have software engineers learn the domain when there already are tr...
lol
the amount of "trained professionals" with "years of experience" who can't even write fizz buzz is ridiculously high
Learning programming/algorithms is the easy part
gray gazelle
Learning programming/algorithms is the easy part
you'd think so....
but you'd be wrong
and algorithms don't mean much outside of your cs courses for the most part
might be useful for places that use stupid leetcode interview questions as a gatekeeping method
but the leetcode has nothing to do with day to day
For most interviews what they ask is advanced DS/Algo and rarely we use those in jobs.
hasty turret
What do you actually use?
karmic thorn
Stackoverflow
quick hornet
the amount of "trained professionals" with "years of experience" who can't even ...
how do you not know how to write fizzbuzz
wtf
like even the inelegant solution
do these programmers not know that divisible by 3 and divisible by 5 implies divisible by 15?
or what
but even then
you can just have 2 checks
yeah
flag = false
if div by 3, print fizz, set flag to true
if div by 5, print buzz, set flag to true
if flag is still false, print the number
print a space
well thats what i mean by the inelegant solution ultra
gray gazelle
Do tower of hanoi iteratively. That's the basic one.
quick hornet
is the concept that they're missing just
using a flag to act as an "else" for multiple "if" statements?
gray gazelle
Stack Overflow(literal)
Also a lot of algorithm in CS comes with natural recursive solution bcz it's mathematics. Anyone can solve that, iterative is the difficult one.
quick hornet
iterative tower of hanoi doesnt seem that insightful to programming abilities
hasty turret
Do tower of hanoi iteratively. That's the basic one.
You mean solve the reccurence?
quick hornet
dont you have to do random adjustments
depending on like
the parity of the total number of discs or whatnot
gray gazelle
iterative tower of hanoi doesnt seem that insightful to programming abilities
It's not about programming abilities. It's just for though process.
quick hornet
thats the kind of thing that'd be easy to see in an IDE
but seems tedious without it
¯_(ツ)_/¯
gray gazelle
Most of the DS/Algo interview isn't even for solution, how do you approach it is what they check.
gray gazelle
You mean solve the reccurence?
No, Use loops rather than recursive calling.
quick hornet
i mean i dont think i'd be able to observe right away that you need 2^n - 1 moves
if i didnt know it already
gray gazelle
Hints will be given.
quick hornet
¯_(ツ)_/¯
gray gazelle
It's pretty sure that even the interviewers just get those question from leet code or etc..
hasty turret
gray gazelle
I have forgotton most of the process. Need to start working on these again.
hasty turret
T_n is minimum number of moves required to do that,if there were 3 pegs
gray gazelle
how do you not know how to write fizzbuzz
the concept of if statements and remainder eludes them
like even at a conceptual level
let alone get it into code
hasty turret
How the heck do you not understand if statements?
gray gazelle
How the heck do you not understand if statements?
programming requires a little bit of a conceptual leap from jamming stuff in from stackoverflow to appease the compiler gods to thinking through how you want the program to work and adjusting it when it doesnt
some people never make that leap
some people with "years" of experience have never made that leap
it's weird
but it is what it is
gray gazelle
Most of the DS/Algo interview isn't even for solution, how do you approach it is...
we have problems that people need to solve but like if they get stuck we'll give them hints and guide them to it
how they adjust to feedback and figure out that and work towards a solution is more important than what they come up with
"how would you test your program to ensure it works?"
ok "how does your program handle this case?"
also do they ask for questions/clarifications is one I tend to look for me now
because the people that don't tend to also fixate and never ask for help
real world stuff is about getting stuff done, nobody cares that you figured it out all on your own
gray gazelle
@molten wave do you have recommend reading material on types and categorical logic aka abstract nonsense?
molten wave
for types, the HoTT book gives the best introduction to MLTT
gray gazelle
Holy shit!
opaque birch
any suggustions for an intro-level partition theory text book? Something at the undergrad/begining grad school level?
sudden kindle
What intro level stuff is there for partition theory?
opaque birch
My school has a partition theory seminar and I was wondering if there's any material I can look into that might help me understand what's going on a little better.
sudden kindle
look at the papers they talk about
idk much about partition theory but it seems accessible enough
unlike algebraic geometry which takes literal years to get the basics
tranquil ocean
@opaque birch I feel like it depends what type of partition theory they do idk
Some people approach partitions from a combinatorial point of view
While others (such as Ono) use things like (mock) modular forms to talk about partitions and this ends up being a pretty different point of view
And these two things need somewhat different prereqs
gray gazelle
Elements function analysis by Kolmogrov? Good?
there's actually 2 different translatations of different editions of it
i think I read the introductory real analysis version but I found it interesting
gray gazelle
i think I read the introductory real analysis version but I found it interesting
I see two volumes combined and total 281 pages. Isnt it too small?
i believe thats fine
Also self study is ok with it?
I read it but I didnt go too in depth
maybe someone else will know
gray gazelle
are there any books that look at analysis from a categorical viewpoint?
tranquil ocean
condensed mathematics
gray gazelle
condensed mathematics
so Scholze is the main person to look at for stuff in this area?
ripe granite
there are a bunch of lectures on youtube by Scholze and Clausen
crimson pagoda
there is condensed.pdf and analytic.pdf
ripe granite
look up condensed mathematics masterclass
crimson pagoda
depending if you are an infinity memer or not
tranquil ocean
are you an infinity memer
crimson pagoda
gabe
gray gazelle
depending if you are an infinity memer or not
i dont even know what that is
ripe granite
do you read stuff on the nlab
gray gazelle
only briefly if i come across it looking for other stuff
ripe granite
do you like it when you do not have well defined compositions
do you like to mumble about "higher data"
gray gazelle
i come from physics/engineering originally and work as a programmer so.... https://twitter.com/davidduchovny/status/913401280160202754
gray gazelle
no
dapper root
Math Bookworm doesn't seem cringe so they're safe
tranquil ocean
As an actual answer, infinity memer means infinity categories
gray gazelle
so categories all the way down?
opaque birch
Some people approach partitions from a combinatorial point of view
Thanks! I'm interested in the combinatorial side
sudden kindle
Categories all the way up
tranquil ocean
Okay yeah, I really only know about the latter side of things so don't know what to recommend
sudden kindle
Thanks! I'm interested in the combinatorial side
Are you interested in algebraic combinatorics?
opaque birch
Are you interested in algebraic combinatorics?
Yes, very much
sudden kindle
Ok let me see if there were some book recommendations from the polymath REU
gray gazelle
i think this sort of thing is probably more what i was looking for with the category theory +analysis https://www.maths.ed.ac.uk/~tl/cambridge_ct14/
manic cape
Anyone have any good recommendations to learn about differential forms ?
sudden kindle
Mfw i went to check my email for the book and then see a grad school offer 😂
opaque birch
Congrats!
sudden kindle
Yes, very much
A lot of these recommendations are particular to symmetric functions
But if you're interested in algebraic combo, that's something you should look into
Partitions come in when you try to index bases of symmetric polynomials, for example schur functions
gray gazelle
Is there any analysis website for Tao's Analysis? More eg., explanation etc.
karmic thorn
Math Stackexchange
gray gazelle
Nowadays they downvote everything. Can't ask such simple question.
calm crane
i mean they assume you spent like 40 hours thinking of the qn lol
which i would usually like to assume as well ngl
woa
karmic thorn
Nowadays they downvote everything. Can't ask such simple question.
Try to add more context to your problems, format it in good MathJax, show your efforts. You could be forgiven for formatting(not if you do that consistently either), but the other two are important.
narrow talon
Is there any analysis website for Tao's Analysis? More eg., explanation etc.
Just ask here
gray gazelle
Is there a solution manual as well. I am trying to do the exercises.
gray gazelle
Git gud
narrow talon
Try to add more context to your problems, format it in good MathJax, show your e...
Lol, I’ve asked questions to stackexchange and bountied them and usually it’s no response until eventually I answer my own question, then someone says my first question was wrong without seeing my own answer and I get salty because of course my question had problems, that’s why I needed help from stackexchange and I figured it out 
gray gazelle
@gray gazelle your axiomatic set theory questions fit in the #foundations category
The maths stackexchange now is not the way it used to be 5 years back 😦
karmic thorn
Lol, I’ve asked questions to stackexchange and bountied them and usually it’s no...
Your problems might be in the borderline category-too advanced for MSE, too baby for MO. 
Most questions which go unanswered usually fall in this category.
gray gazelle
Why don't we have two sites for physics like MO and MSE, why only for maths
karmic thorn
The maths stackexchange now is not the way it used to be 5 years back 😦
I'm a rather recent user, but I agree the overall quality is declining.
Too many homework problems have been repelling the advanced users.
karmic thorn
Why don't we have two sites for physics like MO and MSE, why only for maths
I read somewhere(probably on an MSE meta thread) that there used to be a Theoretical Physics Stackexchange, analogous to MO. Even though it looked good in the beta trial, it couldn't attract a lot of users.
narrow talon
Your problems might be in the borderline category-too advanced for MSE, too baby...
Yep, either this or too broad. I ask pretty open ended questions sometimes which I shouldn’t
karmic thorn
I see.
timber mesa
Why don't we have two sites for physics like MO and MSE, why only for maths
too many people asking HW questions on what used to be MO; not sure if that's a thing in the physics one
karmic thorn
PSE cracks down on homework problems even harder.
Like
I still don't know what kind of question you can really ask on PSE
I've had two-three closures there, but at the very least the core philosophy of MSE and PSE differs.
MSE is more humble and the community would receive problems positively in general, provided you show your share of effort.
gray gazelle
Is there any analysis website for Tao's Analysis? More eg., explanation etc.
i can't speak to the quality but https://taoanalysis.wordpress.com/
may help with self study
if you are stuck on particular problems
there's also this which seems mostly dead https://old.reddit.com/r/TaoOfAnalysis/
The first link is helpful. Before I was wondering whether the solution has a easier approach. Seems that it doesn't.
gray gazelle
_which i would usually like to assume as well ngl_
meh if you want to feel the sense of accomplishment of struggling through a hard problem yeah spend hours and hours on it
calm crane
tbh not hours and hours on it
for me if theres a rather challenging problem
the most effective way is jus think about it in the background
gray gazelle
oh I totally agree with background thinking
marble solar
Lol, I’ve asked questions to stackexchange and bountied them and usually it’s no...
This is my experience with stack exchange
gray gazelle
im totally in favour of them
but if you don't want to use them you dont have to
it's not like their existence harms your ability to do your workflow
and ultimately if you achieve understanding through struggle or seeing how someone else did it you end up in the same place
calm crane
re posting solutions online my sentiment is the same as well
there's no reason to post your solutions online
gray gazelle
again not everyone learns the same way as you
if you don't want them, don't look at them
narrow talon
Best thing is to have a tight feedback loop, get to a point where you think you've solved it and then see if it's the same as the solution given, if it's close but not quite try and figure out what's wrong. If you had nothing, look at the beginning of the proof and stop there and keep trying.
gray gazelle
exactly
narrow talon
Did that not too long ago when I was trying to remember the proof of monotone convergence, helped me realize that I was implicitly assuming uniform convergence instead of pointwise and that I do that somewhat regularly. (research supports this method too, not just this anecdote)
karmic thorn
That's my usual way of learning things on my own, although exercise solutions are not always accessible(more like, I choose not to refer to solution manuals for some reason).
gray gazelle
sometimes though you are just straight up lost and even seeing the solution is enough to get you going on the rest of them
karmic thorn
I rather let someone else critique my work, or give me a hint.
With Stackexchange and this Discord, it usually works.
gray gazelle
imo having the widest variety of resources is best so people can learn however they find works for them
narrow talon
Did that not too long ago when I was trying to remember the proof of monotone co...
I still have lots of bad habits like this, biggest one is changing up orders of \forall and \exists (ie. uniform continuity, and other fixing a point and varying epsilon as though there's some specific point in every epsilon ball rather than some arbitrary point in each epsilon ball type arguments) and assuming observations instead of random variables when doing statistics/data science stuff
pale linden
There are some problems that one may simply lack the requisite knowledge or familiarity with a particular domain specific strategy to make it tractable
I think you gain more by familiarizing yourself with how such a problem is solved than trying to reinvent the wheel
gray gazelle
sometimes you're also mostly there but you are missing some nonobvious leap
pale linden
Yeah, I do think making those sorts of leaps probably becomes easier the more you do it yourself, but I just don't think under time constraints is it very practical for every problem to be a research project
gray gazelle
or you see the leap once and realize you're going to need to do similar leaps in other problems which is enough to get you more in the ballpark
pale linden
Yea. On the other hand, I think the accessibility of solutions can lend itself to people not really thinking for themselves, or maybe just thinking for a little bit for themselves and then just trying to internalize the "right" solution, whereas more could be gained from a wrong attempt carried through to the end
gray gazelle
from what I've tended to notice during my degree, the better arranged textbooks were where say the odd ones had solutions but the evens didn't, the odds and the evens would have pretty close steps to go through, essentially forcing people to try to go through https://en.wikipedia.org/wiki/Transfer_of_learning but providing a guide
the shittier ones were just a random hodgepodge of problems that learning one didn't feed into any of the others
pale linden
Trying to keep you on your toes
gray gazelle
Reading Tao - Analysis I for the first time and seeing him demolish all the less than rigorous stuff you get away with in most courses in Engineering and Physics in 12 pages....
karmic thorn
wooden sparrow
my degree is electronics engineering
gray gazelle
hehe
I was actually Eng Phys until I decided I just wanted to get out of school and not go to grad school
electronics was the closest non honours so I didn't need to do the thesis rigamarole
wooden sparrow
@gray gazelle What made you start analysis? 
gray gazelle
<@456226577798135808> What made you start analysis? <:catThin4K:8113543204605788...
it's interesting
wooden sparrow
Ohh good 
gray gazelle
damn 11 years
Time flies huh
but lets make it go faster
cause 2020 and 2020.1 (2021, but it's still 2020 except the latest version) has been pretty shit
I mean duh
limpid widget
any refs or advices pls about good book for trigonometry (circles and triangles) ?
gray gazelle
SL Loney's books
Which standard are you?
fathom elk
What book is recommended for a rigorous intro to predicate calculus. I have tried to read a set theory book and realize I am on over my head.
gray gazelle
What's a predicate calculus--> Applied calc?
flint forge
I think Type Theory for Functional Programming does a good job w the theory with an eye toward type stuff
(i am not a programmer by any description)
gray gazelle
Oh, is this the same dieck as the algebraic topology dieck?
sudden kindle
Oh, is this the same dieck as the algebraic topology dieck?
Yes
sudden granite
where are its eyes
hearty steppe
Oops wrong channel
hearty steppe
Yea sorry about that
sudden granite
i havent seen chill in so long
gray gazelle
COMPACT LIE GROUPS
gray gazelle
compact lie groups <:hype:484391278704853022>
have you been exposed to the averaging trick?
sudden granite
what is the averaging trick
hollow peak
what is the averaging trick
sudden granite
lmao
gray gazelle
since a lie group is compact, you can integrate over it with no issues, yeah?
hollow peak
since a lie group is compact, you can integrate over it with no issues, yeah?
indeed
sudden granite
yeah mmm hmm
gray gazelle
you can often construct things on compact lie groups or manifolds acted upon by compact lie groups by integrating over the group
one example is a bi-invariant riemannian metric on the lie group (or possibly a group-action-invariant metric on the manifold being acted upon)
hollow peak
interesting
gray gazelle
(all lie groups are orientable too so you don't have to worry about that)
hollow peak
I can't say I'm particularly surprised that a structure with two of the nicest mathematical attributes has useful properties in smooth manifold stuff
rank the adjectives
- compact
easily
all good things are compact
gray gazelle
on a compact lie group you do this
gray gazelle
so you're basically averaging over G the things you get by "right-translating" the original metric
and if you do the computation you get a right invariant metric!
marble solar
Is that a spivak question
gray gazelle
it's from do carmo's RG
marble solar
Ah
gray gazelle
spivak doesn't really touch on riemannian metrics
everything's a submanifold of R^n so he just uses the induced metric
sudden kindle
COMPACT LIE GROUPS
COMPACT LIE GROUPS
gray gazelle
COMPCAT LIE GROUPS
sage python
DID SOMEONE SAY COMPACT LIE GROUPS
gray gazelle
YES
sudden kindle
any compact abelian lie group is a torus
sage python
Yeah that's true
Apparently the key to this is that the exp(X+Y) = exp(X)exp(Y) when [X,Y] = 0
gray gazelle
valid moth
on a compact lie group you do this
so it cannot be affected by bi people
gray gazelle
so it cannot be affected by bi people
what conservation law does this represent according to Noether's Theorem?
valid moth
the law of joe @gray gazelle
uncut zealot
If I'm self-studying a book, what's a good rule of thumb for how many questions to go through? I'm working my way through Rational Points on Elliptic Curves by Silverman and Tate, chapter 1 has 22 exercises (almost all of which are proofs) and I've so far done the first 10 over the course of about a week. I'm more than willing to go through every single question if it's necessary, but I also would rather not waste my time if it would be better spent doing other learning (like the next chapter, or the homework for the actual classes that I'm in).
pulsar aurora
That depends on person to person. Usually if you feel comfortable to move on
tranquil ocean
I don't really think there's a great answer. Silverman Tate you definitely don't need to do every single exercise to understand the material, but it's hard to say how many you really should do. I think it's mostly up to how well you feel like you understand the topics. Another option is to look up a course that used the book and do the exercises that they recommend but
hearty steppe
I prefer skipping the exercises I know I can answer with barely any effort
I’m also a masochist.
Like honestly I’m usually a semi-completionist when it comes to psets these days
uncut zealot
Honestly going for the hard questions sounds like the right thing to do; it'll certainly help more than just going over the easy ones.
hearty steppe
Some problems can be trivial enough while the ones that really test your understanding and are demanding your attention are the ones you should work thru
But you also should check to make sure if those harder problems matter at the end of the day
I skipped a whole section of linear algebra application problems one time as an example because quite frankly, they were overly trivial and quite random
uncut zealot
As an aside, does an average of an hour or two per problem sound reasonable for an advanced undergrad book, or am I working absurdly slowly?
Some questions only take me like 30 minutes, one took me two days and I wound up asking for help here, but so far if I have a reasonable grasp of how to go about tackling a relatively tough problem I tend to take an hour or two on it.
hearty steppe
So here’s the thing. Don’t worry too much about how long it takes to solve a problem. It seems many people mention that certain problems require certain levels of knowledge and might require a certain amount of work to be done to appropriate a solution.
You can always look up on average, how long it takes a seasoned math major to solve certain kinds of problems maybe?
Like get an idea for an exam how long it should take you to solve certain problems by simply looking that up in a search engine I suppose. Usually that strategy works for me.
uncut zealot
Thanks
hearty steppe
Math Exchange website should have an answer for this already I’m imagining
tranquil ocean
No that is very reasonable
I don't think this is really something you should think much about though
pulsar aurora
Depends on your goals, but if it's just understanding, take your time.
uncut zealot
Yeah, I'm not super concerned about speedrunning the book or anything like that, but I'm reading it as an introductory book on elliptic curves because I want to get a solid foundation in some of the more advanced areas of number theory before I apply to PhDs in a couple years. I have a reading list with a couple books on it already that I also want to eventually get to.
gray gazelle
you can always do a pass through of a book or books to get the lay of the land
without necessarily doing all the problems upfront
or focusing on grokking everything
in fact in a new area that may be helpful and get you exposed to some of the terminology and allow you to see what is highlighted for when you deep dive
ie pay attention to what terms are being thrown around all over, what theorems are being used regularly
uncut zealot
Yeah, I did a skim of the entire book in a few hours before I started working on the problem sets.
molten wave
wait
@gray gazelle
I was just scrolling through history on a totally unrelated server
sudden granite
valid moth
<:catKing:812386361297862747>
marble solar
I don't really think there's a great answer. Silverman Tate you definitely don't...
What I say is attempt 2/3rds of exercise, solve anywhere between 1/3rd and 2/3rds, ideally closer to 1/2
That way you aren't doing so many you feel bad, but you're doing enough to learn
zealous elbow
What are some good books on quantum physics for those with a strong linear algebra + complex background and not so much physics.
tranquil ocean
I enjoyed reading townsend as someone with that exact same background
subtle siren
I think a standard book is Griffiths but I don't know if that's good for 'not so much physics'
Either way 'physics' manifests itself as some conservation laws usually, which are just constraint equations more than anything
zealous elbow
Should I give a motivation?
I did some quantum machine learning and just learning about quantum circuits and the like inspired me to want to learn more.
subtle siren
Well you probably should be more specific than 'quantum physics'
I assume less dynamics and more statics essentially
Well I'm woefully inept to comment on quantum circuits/quantum computing so I can't say
zealous elbow
Qubits, unitary matrices, quantum circuits, hilbert spaces, different gates.
stuff I learned about for the competition i did
but I figured maybe studying some physics would give me a better foundation.
I don't understand what entanglement even is.
The field is interesting.
Maybe I should look more specifically to QML topics/courses.
subtle siren
Hmm I feel like Griffiths would be a good foundation, but you probably won't get entanglement from it - a higher level book would probably be better
If there are no books perhaps surveys from Reviews of Modern Physics would be good as well, they are rather comprehensive on the topics
subtle siren
Nice
gray gazelle
there's a version on the library that shall not be named that has those supplements spliced in
there's also a solution manual floating around if you are doing self study
mainly I liked how it tries to cover as many topic areas as can be reasonably gone through
griffiths might go more in depth into the nuts and bolts
but this will expose you to the field
and you can branch out from there
hearty steppe
I’ve never heard of Jay Cummings
gray gazelle
"In some ways, 2 is the oddest prime."
shadow tusk
karmic thorn
Ted talks are good.
gray gazelle
this guy tries to be clickbaity but he ends up being dry and informative: https://www.youtube.com/watch?v=PgrRt9PpaxI
hearty steppe
Oh I love Bri he’s dope
undone fable
in this pandemic, it's kinda hard to got to library to borrow or buy book :/
karmic thorn
in this pandemic, it's kinda hard to got to library to borrow or buy book :/
I've frequented a certain library to borrow books a lot in pandemic.
gray gazelle
I have started the Set theory of Tao-1
karmic thorn
Advice: skip it.
Learn set theory from Velleman or any introductory set theory/proof book
Tao's introduction of axiomatic set theory is too intimidating and unnecessary for learning analysis, at least. Probably revisit chapter 3 before starting chapter 8.
gray gazelle
What's actually good in Tao? Ppl say second chapter is long and over explained. 3rd chapter can be skipped. Are rest of the chapters like that? 😄
karmic thorn
No
Long and overexplained might look bad to those who already know some stuff
But being walked through wordy proofs is a boon as a self-learner imo
Plus, his explanations and presentation are extremely neat.
gray gazelle
No, may be 8 of them fully and 5 of them partially.
Have you also read TAOCP
What's CP? I don't know. I am reading TAO-1.
And I have ordered
Don't know how good is it.
lol
taocp is knuth's magnum opus
the art of computer programming
That I have PDF (and I haven't read it yet) so can't count in books. The Book set is very expensive by Indian standards. It's 200 dollar. for eg the above book is just 10 dollar.
gray gazelle
That I have PDF (and I haven't read it yet) so can't count in books. The Book se...
You randomly buy any book ?
@gray gazelle No, I buy computer related as I am a software engineer. I buy phy+maths+fictional+economics+politics+gk books bcz I like reading them.
sudden kindle
gray gazelle
Nice.
gray gazelle
Plus, his explanations and presentation are extremely neat.
I liked that there was clearly a lot of care to the examples and proofs being a nice progression
and gotchas with stuff
karmic thorn
Yes!
gray gazelle
Without some mentor help I am not able to verify whether my answers to exercise are correct or not.
Especially it is asking to use particular axioms.
karmic thorn
You can ask in the help channels here.
gray gazelle
imo you probably wont develop a feel for what makes a good proof without feedback from others
it's just like going through the code review process at work
"Programs are meant to be read by humans and only incidentally for computers to execute."
at least thats the impression I get (still early with actual proofs)
molten wave
reading mathematics made difficult, is it weird that I'm not really seeing anything new?
I wonder what that says about me
gray gazelle
it says you have achieved oneness with the abstract nonsense
molten wave
smh my head, Z is a coequalizer not an equializer
but also like, coequalizers is just one of the ways how you make higher inductive types
I guess that means I am the guy who breaks people's legs
gray gazelle
You can ask in the help channels here.
Can I use latex in MS Word to write my proof to show it here?
Or any alternate?
karmic thorn
I don't think MS Word can be configured to use LaTeX
I just suggest you start with LaTeX on Overleaf.com
If you're going to be self-learning maths in the time to come, it would be an indispensable skill anyway
gray gazelle
if you saw the amount of cringing people were doing looking at Kripke's paper earlier
you probably don't want that
gray gazelle
If you're going to be self-learning maths in the time to come, it would be an in...
Yes, But the issue is that I won't be able to give time consistently.
So paying 120$ would be waste for me I htink.
karmic thorn
Huh
gray gazelle
oh
karmic thorn
Overleaf is free to use
gray gazelle
what editor do you use for work
karmic thorn
What are you looking at?
gray gazelle
Overleaf is free to use
It's asking me to register and use free trial for 1 month.
karmic thorn
Let me get the link
broken meadow
overleaf isnt free anymore?
gray gazelle
I didn't click Student earlier, thinking will ask for college name , ID etc..
karmic thorn
Nah
gray gazelle
Registered, and any example link where some mathematical notations are used?
karmic thorn
Use one of their maths notes templates
static crest
karmic thorn
For some reason I could not make VSCode compile my TeX
gray gazelle
just use vscode
i concur with this statement
gray gazelle
getting the stuff set up at the start is a bit annoying
but then it pretty much just works
karmic thorn
Overleaf was just get-set-go for me haha. ¯\_(ツ)_/¯
gray gazelle
yeah I hate setting stuff up
always a pain
it's why I no longer use linux for stuff
all setup all the time
static crest
I use linux for nearly everything
gray gazelle
Guys I actually got some additional unexpected benefit using overleaf. Thanks 😄
static crest
it's like solar panels, one time cost at the start, but it pays off as you use it more
gray gazelle
it's like solar panels, one time cost at the start, but it pays off as you use i...
to mean it's more like you have to keep cleaning dust off the solar panels to keep it working
yup
everyone factors in the upfront cost
nobody tends to factor in maintenance
cobalt arch
Any book recommendations for combinatorics and graph theory? (Not a discrete math text but a separate treatise).
Preferably peppered with rigour
hollow peak
with rigor 
cobalt arch
obsidian valley
@cobalt arch you should literally go learn Lean and then start contributing to MathLib and formalize an entire undergraduate curriculum
then you will finally achieve peak rigour
actually don't contribute to mathlib make your own mathlib
polar tulip
the most profitable area of mathematics
cobalt arch
subtle siren
gray gazelle
Maths and Profit are extreme ends.
cobalt arch
At this point in time recommending me books is a tongue in cheek
For some reason appears like that to me:
Thank you Jesse for the recommendation!1
obsidian valley
gray gazelle
Any book recommendations for combinatorics and graph theory? (Not a discrete mat...
I haven't read it but Bona - A Walk Through Combinatorics gets recommended a bit
karmic thorn
Yes!
gray gazelle
karmic thorn
Strongly recommend.
gray gazelle
it's a maze that's constantly permutating out from underneath you
karmic thorn
Combinatorics is truly giga-brain.
Like, I'm generally clueless while writing proofs in analysis and elsewhere, but the cluelessness intensifies with combinatorics because there are literally so few tools at your disposal
cobalt arch
Is graph theory a branch of combinatorics?
karmic thorn
You have to resort to great ingenuity to set up an argument which can make use of those tools
sudden kindle
What about a drive thru combinatorics
karmic thorn
Only Gowers has a license
karmic thorn
Is graph theory a branch of combinatorics?
I think so?
gray gazelle
What about a drive thru combinatorics
i love how every combinatorics book has the subtitle "NOW WITH EVEN MORE GRAPH THEORY"
broken meadow
i should take combo at some point
gray gazelle
This book's cover page looks like those useless math books I studies during my HS.
sudden granite
What makes Calculus by Spivak an Intro Analysis book?
gray gazelle
it introduces basic topics from analysis with the assumption that you're somewhat familiar with calculus but not with abstract mathematics
sudden granite
What is analysis 😳
static crest
this cover is so ugly
quick hornet
What is analysis 😳
topology but you only care about metrics
and topology is algebra but you only care about the algebra of the union operator
static crest
everything is algebra?
gray gazelle
everything we can actually do is linear algebra
broken meadow
everything is algebra.
quick hornet
everything is algebra?
well this is oversimplifying it
static crest
everything we can actually do is linear algebra
actual engineering moment
quick hornet
algebra is the category theory of concrete categories
and category theory is just physics
like theres no "but"
its just physics
static crest
catego-
broken meadow
cat
broken meadow
h m m
gray gazelle
so in reality you should just go straight to math phys
gray gazelle
GO STRAIGHT TO MATH, DO NOT PASS GO, DO NOT COLLECT $200
molten wave
cat ego
broken meadow
ry
manic cape
intro diff geo books?
hollow peak
introduction to smooth manifolds by tu, differential geometry of curves and surfaces by do carmo
sudden granite
topology but you only care about metrics
This is similar to looking at math definitions, coming across and unfamiliar term, and entering a loophole figuring out definitions
quick hornet
well i was shitposting
sudden granite
I understand 😆
quick hornet
if you want like
a more serious answer
the motivations for introductory analysis are "let's actually understand what's going on when we do calculus"
since calculus as usually presented is a bit imprecise
arguing with vague notions about infinitesimals and whatnot
it works but analysis:
(a) lets us understand why it works
(b) lets us create a framework for what properties calculus formally "requires" so we can build off of it into exotic settings
the real motivation for introductory analysis is (b)
quick hornet
to be a bit more mathematically savvy about what analysis studies
it studies limits, convergence, smoothness, continuity
this is a bit vague since one can say e.g. topology also studies continuity
the way to clarify this is to say "well analysis studies analytic continuity" which is about as useless as it is tautological
quick hornet
<:frogN:813948272069705799> is this new?
yeah apparently i got emoji perms when mniip restructured the roles
so
corruption
your doing
dapper root
I see
quick hornet
is unironically a great emoji
for like
"I want a thinking emoji but dont want the sarcasm of a usual thinking emoji"
i might remove but i think is here to stay
dapper root
gray gazelle
We are definitely missing some emojis
For example, this one should be an emoji
There could be a better emoji for a smug fuck you, I've been using 
for this, it's okay/it works, but I've wondered about better one
quick hornet
theres 
gray gazelle
But I want a smiling one
I guess smug is not exactly what I'm looking for, but something like that
quick hornet
there are 3 types of emotes
i think i am a better person than you:
i think i am a smarter person than you: 
i am making a joke and am too cowardly to make it without making my sarcasm obvious: 🧠
every other emote fits in one of those 3 genres
gray gazelle
I guess the yellow face is sort of what I'm looking for, but it should be a anime girl and not be doing a weird eyebrow raise
sudden kindle
gray gazelle
Ah yeah sort of like but it's not quite what I'm looking for
It's not "fuck you" enough
Or maybe "get fucked" is more what I want
quick hornet
I guess the yellow face is sort of what I'm looking for, but it should be a anim...
youre welcome
sudden kindle
Woog emotes: 
Mniip emotes: 
broken meadow
hmm the rest of the body was optional namington
are you a fan of the boob sword girl 😌
🤨
broken meadow
Woog emotes: <:awoogenzoom:640699498359947284> <:angerywoog:545476186235731978> ...
flimflam
quick hornet
sudden kindle
broken meadow
i like the reading frog
it feels like
idk
the words aren't there
but
yes
it gives off Hmm vibes but better
sudden kindle
Now I read
buoyant spire
it gives off Hmm vibes but better
lmao yeah, for me it's the nearly closed eyes, like the frog is thinking "wtf am i reading rn?"
broken meadow
yeah lol
reef oar
Anyone got any good suggestions for complex analysis textbooks?
static crest
ahlfors
wooden sparrow
@reef oar Nice nickname
reef oar
<@!625155833751142433> Nice nickname
Thanks
reef oar
ahlfors
Is that the name of the author?
It's an unfortunate name
Jesus when was the last edition of that book released
karmic thorn
gray gazelle
yeah he really likes to get down on ahlfors with complex analysis
tribal kernel
Anyone got any good suggestions for complex analysis textbooks?
Schlag is good
Kind of assumes a little geometry before you start though
reef oar
Kind of assumes a little geometry before you start though
Anything particularly ugly?
Or just basic angle and trig stuff.
tribal kernel
No worries! The goal of the book is to build up to and study Riemann surfaces so maybe not what you’re looking for!
sudden kindle
Reimann surfaces are lit
sudden kindle
I really wanna learn them
tribal kernel
Ye they are cool
Churchill I think is the one my undergrad university uses. I hear people like that one
reef oar
As Springer texts go it's not bad but some of the conceptual explanations are a little lacking
reef oar
Churchill I think is the one my undergrad university uses. I hear people like th...
I'll look into. Do you know what the most recent edition is?
tribal kernel
I think it’s actually in its ninth edition now, but you can get the earlier editions for pretty cheap
And if all you want is supplemental instruction, I think that’s fine
hasty eagleBOT
The struggle ∈ ℝ
gray gazelle
RIEMANN SURFACES
sage python
@tribal kernel did someone say Schlag
gray gazelle
What is a good group theory book for an under graduate in Engineering? Most basic possible.
silver herald
What is a good group theory book for an under graduate in Engineering? Most basi...
What's your experience with proofs and Lin.Alg. before?
gray gazelle
What's your experience with proofs and Lin.Alg. before?
Linear Algebra in HS + 1 year under graduate.
Nothing specific in proofs.
silver herald
So, you haven't done any proofs using induction and similar?
gray gazelle
Yes, induction I have done. Don't remember any specific chapter for that.
I get it , contradiction , induction etc. I have done. Not advanced only undergraduate stuff in engineering.
silver herald
Ah okay -
You can take a look at Artin's Algebra as it's really good Algebra text.
If you can handle Linear Algebra stuff like subspaces and inner products - Then you can take a look at Jacobson's Algebra.
Not advanced only undergraduate stuff in engineering.
Well, you don't see anything group theory specific in Engineering unless you look at extremely specific fields in Engineering.
gray gazelle
No knowledge in subspace. So I should go with algebra.
silver herald
Yup - Artin's Algebra it is
opaque birch
I might go with something a little more gentle like Gillian or Fraleigh
thick fulcrum
Any books on quantum physics?
tribal kernel
<@!401026344156135436> did someone say Schlag
Yessir, I think we’ve talked about him before
gray gazelle
Hi
Books on differential geometry 😮
for classic, do carmo's curves and surfaces
otherwise, there are many good books. the most common recommendation is lee's introduction to smooth manifolds (for good reason)
there's also the watered down version by tu called "introduction to manifolds," still a good read but far less comprehensive and difficult
Thanks, im doing physics but i'm really into maths
topology is a requeriment?
or just basic knowledge
for at least the latter two books, it is required
for the first one, no
Okay, really thank you ^^
tribal kernel
Bumping Lee’s Smooth manifolds. The follow up on Riemannian manifolds is also great and while they do reference topology, it’s never really difficult stuff in my experience.
fluid bay
anything but "Lectures on Differential Geometry" by Chern, Chen, and Lam 
dapper root
Pls don’t use Schlag as a first book
At the minimum if you do make sure you’ve seen manifolds or sometbinf
It’s not impossible but I think it’s more pain than it’s worth
sudden kindle
Anyone have any book recomendations for learning about reductive groups
sudden kindle
Anyone have any book recomendations for learning about reductive groups
no scheme theory pls
tribal kernel
Oh and Spivak’s series on differential geometry is long and rambles a bit, but it has great exposition
sudden kindle
i dont know it yet
sage python
Yessir, I think we’ve talked about him before
Oh yeah I know it's a theme of mine to just walk in and say "Did someone say X?"
tribal kernel
Lol no worries my man. Schlag has grown on me
storm sleet
How is Reids undergraduate algebraic geometry
sudden kindle
I think it's fine
woven bane
Hey everyone, is this the right place to ask for where to find some exercises regarding boolean algebra?
If there are any online PDFs I could find perhaps or something like that
abstract helm
can we discuss books here ?
gray gazelle
See description
knotty cedar
Favorite discrete math book? Any deviations from the two recommended by the Math Sorcerer video?
He recommended starting with that over pre-algebra/etc to nail down proofs early on
gray gazelle
For discrete mathematics I recommend this book https://www.springer.com/book/9783540292975
knotty cedar
for a beginner?
gray gazelle
It was the recommended book for my intro class
So I would think it is accessible to someone having no prior experience in discrete mathematics and having maybe a bit of experience in regards to basics of proving stuff
knotty cedar
ok
gray gazelle
Oh yeah I know it's a theme of mine to just walk in and say "Did someone say X?"
what are some general topology books you have found useful/liked outside of the standard Munkres/Topology Without Tears?
rocky charm
not really topology but i like ziemer’s analysis
it has topology / measure theory / functional analysis
gray gazelle
Do you have an issue with munkres? I guess my view of point set topology is that even a basic amount of it can be good/sufficient
Eg, knowing the basic definitions, knowing that "good things happen in compact/hausdorf spaces", etc
gray gazelle
mostly looking for other things to read at that level
ripe granite
what are some general topology books you have found useful/liked outside of the ...
bourbaki /s
calm crane
lol
fluid bay
what are some general topology books you have found useful/liked outside of the ...
the pinned topology book is pretty gud
gray gazelle
what are some general topology books you have found useful/liked outside of the ...
lee's introduction to topological manifolds, although it's maybe a lot less "general-topological" than the other books
it does do a fair amount of general topology though
but a fair chunk of it is intro AT
(and intro AT > GT)
fluid bay
on the other hand, if ur goal is AT, you could read "topology: a categorical approach" and probably jump straight to dieck no problem.
steel viper
no problem
:egg_hank:
that is not how id characterize reading dieck
regardless of categorical familiarity 
fluid bay
trivial stuff
steel viper
virgin trivial problem vs chad trivialization
dieck is good but there is definitely some wack errata
like theres this one part where he applies a lemma in a way that totally doesnt work lol
quick hornet
imagine applying results in contexts where they make sense
this post made by choice gang
steel viper
quick hornet
who the fuck puts their lemmas after their proofs
thats the more egregious thing here
steel viper
that is not the problem
quick hornet
it's the real problem
quick hornet
bad opinion
steel viper
read the statement of the lemma and then read the 2nd paragraph
its not just me right
like this doesnt make any sense lmfao
the lemma applies to open coverings of B x [0, 1] except the analogous space B in 3.2.2 is actually E
dapper root
Hartshorne has a proof where he goes “by Proposition / Lemma X...”
And not only is Proposition / Lemma X below it
It’s just a reference to Matsumura
Or something like that
steel viper
based.
eventually textbooks will just be an unreadable list of references of references of references to books that u can access anymore
quick hornet
It’s just a reference to Matsumura
this is the standard of the field though
no one in AG actually proves anything
they just cite EGA in new and innovative ways
AG is really just the study of the permutations of the theorems of EGA
dapper root
And FGA and SGA
raven citrus
Is it just me or is Dieck ridiculously terse
steel viper
he is
in some ways its good
it forces u to fill in a lot of gaps in arguments urself which is good for understanding
but sometimes its cringe because you think you dont understand the argument when its actually just uhhh
wrong
raven citrus
Some people say Munkres is terse
But to me it's more like, to the point
Things are clear, but not pontificated about
Whereas Dieck just jumps a lot of stuff
raven citrus
Sure, yeah
steel viper
also if dieck was fully detailed in every proof itd be ridiculously long
raven citrus
But its also funny, cause at like the beginning of the gt recap, he's like, "oh yeah, you may not have seen quotient"
steel viper
lmfao yeah
raven citrus
And then he presents quotient in like one paragraph
steel viper
dieck as a first intro to AT seems brutal honestly
dieck if uve never seen a quotient space before sounds
death
raven citrus
also if dieck was fully detailed in every proof itd be ridiculously long
I'd prefer just not giving proofs then
Instead break things into small problems
steel viper
eh i think thatd be wayyyy harder though
raven citrus
You'd have to break proofs down quite a bit
raven citrus
I mean it's a pretty standard graduate presentation
Definition theorem proof
With mistakes to challenge the reader
steel viper
xd
raven citrus
As an undergrad, you learn from exercises, but the grad student needs to transition to learning from realizing the text has a mistake
ionic wren
ah yes
steel viper
ionic wren
F_b defined using itself
moth cant you see? it has a different pixel, its a different character
the one is F
the other is F
hearty steppe
Face_book
valid moth
As an undergrad, you learn from exercises, but the grad student needs to transit...
also when the book whips out a problem with notation that hasn't been defined
fortunately it's standard enough that you can find what it means with some digging
raven citrus
another fun situation is when the book relies on a slight technical redefinition
or uses an opposite of a convention
"larger" and "smaller" topologies are a fun one
because these are used in opposite ways
valid moth
to be fair, in my case im literally using like a 2013 beta version of a now finished book i believe
in like 2017
(because im roughly following the schedule of a 2014 course that used that book)
clear sail
is spivak calculus on manifolds the best textbook to learn multivariable well?
or should i stick with baby rudin
manic cape
I wouldnt do it with either lol
grim pivot
@clear sail would this be your first endeavor with multivarable? Because choosing a book depends on how much experience you have with a topic and how much depth/breadth you want
flint forge
all abstract math books are terse because abstract arguments are impossible until they click
but once they click you become incapable of remembering
what was hard about it
in the first place
gusty sable
Does anyone know a good book or script about measure theory for self-study?
narrow talon
Yeah what level of measure theory?
There’s about 4, but I could probably only point you to maybe 2.5
Actually 2 or 1.5ish, measure theory is pretty broad
gusty sable
Introduction to measure theory
narrow talon
People seem to like Royden (I haven’t used it). I used Rudin and thought it was good (makes a good reference text later too). On the probability side there’s the first two chapters of Billingsley which would bring you up to speed at least with Lebesgue measure
flint forge
Rudin introduces it w a heavy eye toward a specific measure which lets you dip your toes
but yeah you need a real measure theory book to go further
narrow talon
I would just say to make sure to learn at least a little about Radon measures in the context of duality
Treves has a book which covers this very nicely in like 10 pages actually, iirc, so maybe don’t worry about that and just read that section from a pdf somewhere
grave egret
Introduction to measure theory
Schilling duh. #books-old .
Its the best by far.
If you can cope with chapter 3 you'll probs be fine.
At least that was my experience.
grave egret
Maybe my opinion is biased. 👀
grave egret
Yw.
narrow talon
Link won’t work for me, but it looks like it links to Princples of Mathematical Analysis, we’re referencing Rudin’s Real and Complex Analysis
gusty sable
oh
silk quartz
Please don't directly link to copyrighted materials.
thorn gust
Is there such a thing as a begginer module theory book? Can one/ should one jump from linear algebra to that or would i be missing a lot of prerequisites regarding groups?
I would appreciate any group/module theory book recommendations
obsidian valley
shouldn't you do intro abstract algebra first?
quick hornet
well module theory is part of abstract algebra
but im not sure why youd want to start with it
ostensibly you dont need the theory of groups but you do need the theory of rings
the field theory necessary to understand vector spaces (hence linear algebra) is very minimal because fields are very well-behaved (and you probably covered most of what you need to know in middle/high school)
the same is not true of rings
(though to clarify: you can speedrun most definitions of vector spaces in a module context and you'll be able to parse them; it's just there's a lot more module-specific material covered after that which you need ring theory for)
pine igloo
introduction to tropical geometry books?
quick hornet
this stackexchange answer might be relevant https://math.stackexchange.com/questions/2848922/tropical-geometry
pine igloo
thanks
thorn gust
definitions of vector spaces in a module context
I am not sure what u mean by this
quick hornet
like
taking notions like basis, quotient space, subspaces, direct sums, and those sorts of constructions
and changing them to use modules instead of vspaces
linear maps to module homomorphisms, that kinda thing
thorn gust
Oh sure, but it does depend a lot on what type of ring it is i am guessing? Are the more general constructions made assuming the least structure of a ring?
quick hornet
in some cases the changes you need to make are minimal, in others you want hypotheses like your ring being a PID or the thing you're quotienting by being a prime ideal
but typically those definitions arent radically different
thorn gust
And yeah, i guess i'll just go with an abstract algebra book, any recommendations?
I was thinking of getting either "A book of abstract algebra by Pinter" or "Elements of abstract algebra by Clark" has anyone given a shot at one of these?
gray gazelle
check l*bgen and see what book suits you best
thorn gust
I mean, i just wanted some reviews outside of amazon's
karmic thorn
Have you done Linear Algebra before?
thorn gust
Yeah sure
grave egret
Is F.Klein's book on the quintic and icosahedrons good?
full linden
By the way.. on linear algebra.. for a first course in it. Which would you pick?
Linear Algebra:
- Introduction to Linear Algebra, Serge Lang
- Basic Linear Algebra | T.S. Blyth
- schaum outline linear algebra
Schaum
sudden kindle
Stop
karmic thorn
Yeah sure
Pinter is a rather baby book, I haven't heard about Clark before. Dummit and Foote, Jacobson, Artin are the standard recommendations.
grave egret
Dummit and Foote is like a dictionary tbh. I dislike it. Artin is good though.
quick hornet
that is... not how id describe d&f
in fact, if theres a flaw, i'd say it's that it's the other way around
it's really doting
and full of lots of exposition that doesnt really illuminate significantly more than a less wordy text
i still like the text personally but i may be biased
since its what i learned out of
i dont think its a good reference though because of its rambly-ness
sudden kindle
Yeah there a tons of examples in D&F
static crest
ya, I would never use d&f as a reference text
but it's definitely amazing for self learning
it goes into excruciating detail and has extremely easy to understand proofs
and the exercises are wonderful
narrow talon
By the way.. on linear algebra.. for a first course in it. Which would you pick?...
Wtf there’s a massive jump 
full linden
Yeah I believe you're refering to schaum?
narrow talon
Yeah, the difference between Lang and Schuam is pretty massive
tribal kernel
I know people have nasty things to say about it, but Aluffi works for me when it comes to algebra
clear sail
<@734628928420839496> would this be your first endeavor with multivarable? Becau...
nope i took a course on it but i feel like i didnt grasp the concepts well enough
gray gazelle
I have to admit, all the shit like curl, divergence blah blah blah make no sense almost
grim pivot
nope i took a course on it but i feel like i didnt grasp the concepts well enoug...
In grasping the concept, I used Multivariable Calculus second edition by Briggs, Cochran and Gillet. It’s quite intro-y but really good for teaching it with the aim of understanding
dapper root
I know people have nasty things to say about it, but Aluffi works for me when it...
Based response
cobalt arch
Rigorous text on topology?