sorry lol, got good offer
#book-recommendations
gusty smelt
(repost)
Atiyah-Macdonald - very annotated
marcus number fields - mostly untouched
ireland-rosen - a bit annotated
lang- mostly untouched, bad binding a bit torn
artin - very battered lmao
riehl cat theo - mostly untouched
rudin baby- also very battered
gamelin comp anal- a bit annotated
Hatcher - a bit annotated
if any of you are interested in getting a copy of either of these, hmu. Im giving away my old math books
ill just charge shipping and maybe a bit on top of that
broken meadow
oh
ill dm you about rudin baby and gamelin comp anal
idk if ill be able to follow through but i just wanna know how it's bein done
tight crag
@gusty smelt I took Ireland-Rosen
gusty smelt
oop
narrow oyster
valid moth
ultra i am sorry to inform you this is the not the right channel to say this is not the right channel for this
shadow nebula
archsys this is not the right channel to say this is not the right channel to say this is not the right channel for this
i.e. this is not the right channel for jokes
gusty smelt
(repost)
Atiyah-Macdonald - very annotated
marcus number fields - mostly untouched
ireland-rosen - a bit annotated
lang- mostly untouched, bad binding a bit torn
artin - very battered lmao
riehl cat theo - mostly untouched
rudin baby- also very battered
gamelin comp anal- a bit annotated
Hatcher - a bit annotated
if any of you are interested in getting a copy of either of these, hmu. Im giving away my old math books
ill just charge shipping and maybe a bit on top of that
night knot
@gusty smelt how much on Atiyah-MacDonald?
gusty smelt
check dms
gray gazelle
How much on gamelin?
@gusty smelt
But the shipping from wherever you are to India must be
Above 10$
stray veldt
the bait of keeping the ones not available anymore in the list
gusty smelt
shh
gray gazelle
Hello, I am new to discord. So anyway I wanted to ask what are your thoughts about The Real Number System by Olmsted (If anyone has read it)
broken parrot
You're me
gray gazelle
cool
molten wave
hollow current
gusty smelt
(repost)
Atiyah-Macdonald - very annotated
marcus number fields - mostly untouched
ireland-rosen - a bit annotated
lang- mostly untouched, bad binding a bit torn
artin - very battered lmao
riehl cat theo - mostly untouched
rudin baby- also very battered
gamelin comp anal- a bit annotated
Hatcher - a bit annotated
if any of you are interested in getting a copy of either of these, hmu. Im giving away my old math books
ill just charge shipping and maybe a bit on top of that
sage python
I feel like there have been tons of reposts, let's not overdo it. This one and that's it
gusty smelt
alright sorry
gray gazelle
My apologies for repeating this but can anyone answer the question I asked above
gray gazelle
Rigorous construction of real numbers with minimal formal prerequisites
gray gazelle
Ohk, thanks
the fifth part of spivak's calculus also covers it (but it can be treated like a first part, requires no prerequisites)
i am partial to that one mostly because i did it
that one does dedekind cuts with cauchy as an exercise
yea Spivak covers that, I just noticed this while looking at its table of contents
quartz pawn
Spivak covers at the end in the Epilogue I know for sure
like the Epilogue is dedicated to that
gray gazelle
epilogue = 5th part lol
quartz pawn
Oh lol.
I have the book like in the other room but I never really noticed it was divided in to parts
just chapters
and I remembered seeing that in the table of contents Epilogue was dedicated to that stuff
gray gazelle
https://math.stackexchange.com/questions/3731176/rigorous-and-comprehensive-textbooks-on-precalculus In the answer to this question (and the long chat in the comments and chat) the person who answered suggests that the OP read Pure Mathematics by Parsonson before starting with Spivak. So I wanted to ask should I read it or jump into spivak without reading it?
pdf of Pure Mathematics by Parsonson for those who want to have a look (both volumes)
Background: I am in High School and know mathematics at the level of Basic Mathematics by Serge Lang
long bear
Do you have a background in logic?
(I'm in the exact same boat as you and I have been recommended to go through logic before spivak)
Vellemans How to prove it
quick hornet
i feel like Lang's Basic Mathematics works to build up the mathematical thought required to go into spivak
and it certainly suffices as far as a content prerequisite
so i think youd probably be fine to dive right in
or at least give it a shot and see if it works
gray gazelle
Also do you need more background in trig than the level at which it is treated in Basic Mathematics?
because the trig material seemed quite short
you don't really need much trigonometry for spivak in my experience
like
he covers the necessary stuff when it comes up
i think
But do you need to learn more advanced trig in general and not specifically for Spivak?
what is advanced trig
i have never needed more than like, sin^2 + cos^2 = 1 and the angle addition formulas. others' experiences may vary
Ohk
What level are you currently studying math at?
dapper root
Any advanced trig I've ever needed was solved by googling "trig identities" and lookin in google images
gray gazelle
i am entering my third year of undergraduate
also that lol
😆
thanks for your help
if you just know sin^2 + cos^2 = 1 and the angle addition formulas you can derive a surprising amount of trig formulas
long bear
a/sinA = b/sinB = c/sinC
gray gazelle
haven't seen that since highschool
long bear
a^2 = b^2 + c^2 -2 * b * c * cosA
gray gazelle
i have never used these outside of a highschool math class lol
gray gazelle
So only basic trig is used in undergrad math or is it subject specific?
some subjects will have more than others
but in general you can probably pick up the more advanced stuff as you go
by more advanced i mean more than what's been mentioned here
long bear
sin 2x = 2 sinx cosx
gray gazelle
and the mind-numbing "solve these integrals" part of calc ii that you might do will make you learn them anyways lol
bruh that's just addition formula
long bear
cos 2x = cos^2 x - sin^2 x
gray gazelle
one line proof
long bear
this is what we're doing in my math methods class atm
gray gazelle
actually saw it in my second
split moon
nvm
gray gazelle
lol
split moon
its not that diff
gray gazelle
yeah
split moon
I just gotta catch up 
gray gazelle
topology is basically a second year course here so it's not that unusual for manifolds to be a third year course (for some stupid reason the manifolds course doesn't require topology though...)
split moon
I gotta cope with the fact people that are active in the advanced sections are selected to be really invested in math
so I dont really need to compare myself that much 
dapper root
yeah Fractal haha
Coming on here can sometimes hit a bit deep, but you're also self selecting the most invested people
valid moth
@gray gazelle all you really need to know is e^ix 
@dapper root you should go and get me a nick sibicky autograph
i know he's in there
compact snow
Are you 30?
compact snow
I know some math majors that got degrees at 30+
split moon
ye, but a lot of these people are v young
then again, if Im being honest, this is likely the biggest math server on discord(that is active and manageable) and Im even selecting for people who are interested enough to talk
compact snow
(I could include an Erdos joke here as he got an honorary degree in his ... 60s?)
split moon
so like
I know I dont have to compare that hard
if anything, its good having the content
compact snow
Junior and Senior Uni level math majors are not very common. This is true.
split moon
(not to mention Ive only been taking this reasonably seriously for the past year and a half)
compact snow
Eh, do you like math research or is it you see yourself as a prof / teacher?
(or something else?)
compact snow
yeah there's a discussion there already
split moon
Im not sure how to answer that question
a lot of times those are interchangeable
I feel Id like to be a professor as a side occupation
compact snow
My point is be a Fermat (he was a lawyer and did math "on the side")
There are a lot of adjuncts at my Uni. Some work for NASA during the day and teach just cause they want to at night.
split moon
well
ideally my main occupation will also involve math
compact snow
(I mean they accept the pay of course)
split moon
just maybe somethig different like modelling math somewhere
compact snow
oops JPL not NASA.
split moon
oh
hollow current
My point is be a Fermat (he was a lawyer and did math "on the side")
@compact snow that is funny
that many mathematicians were lawyers
compact snow
no that you don't have to choose between your work and a love for math.
hollow current
and Edward Witten was historician
compact snow
wow did he have a degree?
split moon
I dont have that dillema tbh
hollow current
compact snow
Thanks. Did he ever get an honorary degree?
(I'm assuming it's a HE)
Just wondering how cool a cat he is in History compared to Erdos ...
Bill Gates probably has a few honorary degrees as well ... you can't expect all honorary degrees to go to ... nvm. I'm getting a computer error ... 😛
split moon
finite robin
Has anyone read the Dummit Algebra book? If so, how can I prepare for a course that uses this book in your opinion?
finite robin
Plan to
The thing is, I got accepted to two schools for masters, both use the same book for the Modern Algebra course, but one of the schools claims that a pre-req for the course is Abstract Algebra course, while the school I chose says Real-Analysis and Proofs
flint forge
abstract algebra a prereq for abstract algebra?
finite robin
Yeah I know, it's weird
flint forge
dummit is an abstract algebra textbook
do you know what chapter they start with
also analysis/proofs is not a real prereq for abstract algebra
finite robin
The prof hasn't prepared the syllabus
finite robin
That's the funny thing, all I have is this
Course tittle: Graduate Introduction to Modern Algebra
Description: Groups, Rings, Fields
flint forge
yeah that seems standard
i bet they just want you to have seen it in undergrad
which might be a real issue depending on how fast the course plans to go
yeah wait which class is that one
i want the title for the one requiring abstract algebra
finite robin
i bet they just want you to have seen it in undergrad
If that was the case, the pre-req would of been Ungradaute Abstract Algebra.
finite robin
At the other school, the class is called "Modern Algebra"
flint forge
if you're taking grad algebra and it says it wants algebra
then it means undergrad algebra
finite robin
I have no course in Abstract Algebra Undergraduate, only Real Analysis and Proofs
flint forge
mmm not sure what my advice would be then
they are using an undergrad textbook
so like
in theory you shouldnt have to prep
but they might go really quick
finite robin
I have a undergraduate abstract algebra book just in case, I'm just worried that Im taking a class I'm not prepared to take, despite meeting the requirements
hearty steppe
That happens in university
finite robin
I had a bad experience taking a class that I didn't have the suggested requirements. I'm trying to avoid a repeat. But if they say I qualify, maybe I shouldn't worry
flint forge
Yeah my expectation is that
this class assumes everyone has taken algebra in undergrad
but you will be fine without it
if you work hard
hearty steppe
Basically the issue there is that there was an improper assessment of some potentially missing prerequisites that other advisors and the tenure professors that handle modifying the curriculum expectations may have made an error on
But also what max said
They may have some expectations based on how other students performed
So they make those assumptions based on that
finite robin
This was actually the issue that occurred with Numerical Methods. It used to been ODE as a pre-req, but they changed it to Linear Algebra and Proofs after an incident. I didn't listen at the time. Im tried contacting students that have taken the course but no response. I think I'm just worrying to much.
hearty steppe
You should be worried if your knowledge is below the other students taking the class
finite robin
That's what I'm trying to figure out
hearty steppe
So ask advisors and professors about that
flint forge
i mean again they are gonna expect most people have seen it all before
and your knowledge base will be lower
hearty steppe
Exactly
finite robin
They said I will be fine, but that's what they said for Numerical Methods and that didn't go well
hearty steppe
Professors value effort even if you are performing at the curve
flint forge
anyway
hearty steppe
Most professors anyway
flint forge
if you want just read dummit and foote as much as you can before the class starts
hearty steppe
If your below the curve then you should be concerned
flint forge
or dont because it shouldnt really matter
if you want to put in less effort during the year just start reading now
hearty steppe
Oh god everyone here told me to not read that book lol
finite robin
I was planning on it anyway due to some independent research I want to conduct.
wooden sparrow
@hearty steppe what's the curve?
hearty steppe
Grading curve
trim narwhal
Good book for Calculus 1?
pulsar aurora
Any college level textbook should do, but people have suggested Stewart's calculus for college calculus level.
gray gazelle
T. Apostol Calculus I
smoky surge
is this really suppose to be helpful... it seems extremely brief
flat osprey
Helpful for what?
flat osprey
It looks helpful to learn what a gamma distribution is
What do you think it's missing?
smoky surge
an example, pictures, how it fluctuates with lambda and alpha
what a gamma distribution is used for
it literally just is a definition
flat osprey
Ah I understand
smoky surge
slightly frustrated by that i found a good video to help
flat osprey
Some motivation could be nice
smoky surge
yea
quartz pawn
Y'all ever heard of the series of books by D.J.H. Garling and have any opinions on them?
quick hornet
everyone i've seen who's talked about garling's galois theory book has liked it
but its not the most popular text, so that might be sample size
havent heard of any of his other books
quartz pawn
I was talking about his volumes in mathematical analysis. Can't find much about them, but the content looks pretty decent for a first course in analysis.
I was thinking of using them.
soft terrace
any good books on logic/metalogic people would recommend for a self learner? looking for senior undergrad level and beyond, would prefer it include kripkean and leibnizian logic/semantics. Especially interested in pdf's as I am poor 😦
soft terrace
is that logic or just proofs?
quick hornet
thats a proofs textbook
it includes baby logic but not formal at all
and no metalogic or semantics content
https://www.logicmatters.net/wp-content/uploads/2020/07/TeachYourselfLogic2020.5.pdf is an oft-recommended self study guide for logic
i cant speak to its veracity personally
but i've heard good things
soft terrace
thats ok i'm not familiar with the word veracity 😉
i took formal logic back in 2012 and the book I had had a bunch of different "semantics" or types of logics and I was trying to find a similar book to refresh myself
i wish i knew the word for it
I am glancing through that pdf and digging it
hearty steppe
We definitely need to work on book recommendations on this server based on personal experience. Personally, I had to go out of my way to find book recommendations that worked for me. Velleman is the only book referred to in #resources that stood out for me personally. Spivak calculus is not something I need to learn calculus since I already know calculus to that level but its great for reference when you know the material Pauls Notes is good too (probably the best for reading and learning).
There will be a handful of maths people that pick up reading dense books intuitively but we need more friendly book references in the future to clean up #resources . Initially I had confidence that those books recommended out in the open in that pinned channel were relatively fine for the absolute beginners getting into those subjects but now I question this "veracity". We really need to work on doing better for people that don't have the privilege of immediately going to school or going back to school to learn.
soft terrace
hmmm speaking of book recommendations might I interest you in the Dark Arts of umbral calculus?
soft terrace
I could definitely recommend some really interesting books and papers 😄
quick hornet
its currently low-priority, they brought me on mainly to work on an overhaul of the rules
hearty steppe
not only that but most of the books are not very accessible to people not on university REU level
soft terrace
they should put Kranes discrete differential geometry stuff on it
inner sentinel
Textbook list my friend who graduated a year early to go to harvard and who is far, far smarter than myself sent to me, it’s pretty nice, a few aren’t on the book list
hearty steppe
like as someone who personally tried to read books like Artin, Rudin, and Hoffman-Kunze, we have a lot of work to do here. And I have been working around that putting together my own recommendations list soon as well as a learning ladder for diff topics. I'll hopefully come back with some list in a year to help with the overhaul of books I'm going through and may be finished with soon.
inner sentinel
Halmos if pretty good, same with Edward and Penney diff eqs, can’t attest to the others
Personally
hearty steppe
I'd love to help in the future when my level of math maturity is much better for sure
Halmos is alright. Enderton looks much cleaner honestly.
err
sorry I was thinking of Set Theory
lol
soft terrace
I love stephen abbots understanding analysis
hearty steppe
yes that one is very VERY good but not as much depth as rudin. Rn I am going to finish Velleman before progressing more into Abbott
Schroder is also great. I also like Apostol but not as much as Schroder
soft terrace
Abbot had the best proofs imo
inner sentinel
sorry I was thinking of Set Theory
@hearty steppe I was talking Halmos set theory, I love how he complains constantly ab notation
soft terrace
There's stuff in abbot that I have a hard time finding elsewhere
hearty steppe
I think Enderton's set theory book is better honestly. Halmos is a little messy and the chapters are too short
inner sentinel
I like the short chapters
A lot of information but short chapters so it’s not so intimidating
hearty steppe
meh not a fan of short chapters here mate. I like explanations lol
tight crag
Enderton's logic book is very nice
hearty steppe
yea i think it is set theory logic book im thinking of
tight crag
No you're thinking of a different book
soft terrace
Short chapters is nice to bump up your motivation after quick successes
inner sentinel
^
hearty steppe
so basically a smart way of going about instant gratification lol
inner sentinel
Plus then I can read a full chapter when I’m bored after college apps, it’s a lot more fun than essays
soft terrace
yeah it keeps you from getting dismayed
hearty steppe
oh this chapter is short and i understand it. It might not explain all the nuances of what it glosses over but hurray I get what this is saying
soft terrace
plus sometimes you just have to accept your book doesnt explain it the way thats good for you and you have to cross reference another book
inner sentinel
I don’t like to stop halfway through a chapter/section and larger chapter books I’d have to spend a lot more time working straight through it so I don’t stop near it’s middle. Which is why I like Halmos there
hearty steppe
from my experience math books so far seem to be notorious for the book juggle approach.
I don't really struggle with that learning biology
pearl imp
so, I'm precalc level
I'm looking at buying a calculus book
had a look at Ron Larson's and seems decent
I'm just a little bit confused between the different versions (not editions) that are out there.
- Calculus of a single variable
-Multivariable Calculus
hearty steppe
I had a feeling physics does this too honestly
quick hornet
the former textbook would cover calculus in 1 variable
(calc 1-2 in the US)
the latter would cover calculus in multiple variables, vector calculus, etc
(calc 3 in the US)
pearl imp
there is also one version that just says "Calculus" and has more pages
quick hornet
no clue what the difference between those would be
pearl imp
OK, thanks
marble rock
hearty steppe
is that a meme? @marble rock
hearty steppe
no don't just read rudin. Unless you already know analysis lol
Take it from someone that has started reading analysis texts to learn analysis a little over a month and a half ago
gray gazelle
that was a joke
hearty steppe
.>
gray gazelle
polynomial (old server member, got banned) used to recommend rudin to people in highschool lol
or so i remember
hearty steppe
oh my god
i feel so bad for those kids
so here is my thing with rudin. I was able to get halfway thru the first chapter before I felt like it went over my head but like... I feel like I'd love this book if I already knew analysis
gray gazelle
i love using the book as a reference, but i don't think i'd ever recommend learning out of it to someone unless they're already quite comfortable with reading mathematical texts
dapper root
I say let someone go for it and figure out for themselves if they really want to
If you don’t k ow calculus already then...
Yikes
But if u do and you’re ambitious I think you don’t lose anything by trying it, there certainly are people who could take on Rudin for their first analysis text
compact snow
Because it's math and not chemistry ... budum ts ...
long bear
wooden sparrow
Bruh
inner sentinel
One thing I’ll say about Halmos is he’s a psychopath for using the notation $\underline{\leq}$ instead of $\leq$
hasty eagleBOT
Riemann-Zeta1:
tame sluice
Recommended book for multivariable calculus? (math degree)
More specifically, I need a book which talks about:
- metrizable norms and equivalence of norms
- Multivar limits and continuity
- Connectedness and path connectdness
- Partial and directional derivatives
- Gradient and differentiability
- Implicit, open and inverse mappings theorems
- Lagrange multipliers
- Optimization
- Hessian matrix and critical points
- Fubini theorem
molten wave
$\leqq$
hasty eagleBOT
mniip:
stray veldt
\underline{\leq} is some real ghetto tex
molten wave
$\rotatebox{-90}{\textsf{VII}}$
hasty eagleBOT
mniip:
gray gazelle
@tame sluice folland's "advanced calculus" covers all of those topics i believe
except for maybe the first, and he might not go into path connectedness (he definitely does connectedness though)
"optimization" is pretty vague but he covers the basics (e.g. critical points, positive definite hessian, and lagrange multipliers for equality constraints; no inequality constraints)
tame sluice
@gray gazelle Thank you for the suggestion!
@gray gazelle Are you familiar with Multidimentional Real Analysis 1 & 2 of Duistermaat? (that's one the recommended books in 'books' channel)
gray gazelle
not particularly familiar with it, but ive seen good things said about it
tame sluice
@gray gazelle Alright, thanks 🙂
valid moth
can i read AM
and say ik AG
?>
stray veldt
lying is technically not illegal
hasty eagleBOT
Whoever:
valid moth
@crimson pagoda need answer
flat osprey
What is AM
hearty steppe
So what is a book like AM useful for?
gray gazelle
studying commutative algebra
valid moth
we live in a matrix ring
velvet briar
The matrix ring
quick hornet
normally, after going to work, i pick up ice cream from the grocery store and drive home
but one day, i went to the grocery store in the morning, and then went to work
when i got home, i was surprised to learn that my ice cream had melted and my day was ruined
valid moth
persia?
tender yoke
...praise
valid moth
lol
quick hornet
wait wtf i thought it was "praise"
but its actually "peace"
have i been gaslighted
valid moth
persia be upon him
quick hornet
for decades
yeah i cant find it on google
so ive just been
totally wrong
for like 15 years
valid moth
man
i remember when i first found out about pearl harbor
for some reason i didn't realize like
maps represented globes
and uh
i wondered why the fuck they would pick hawaii
velvet briar
Lol
valid moth
which seemed like the furthest possible place for them to target
velvet briar
"They flew over America to get there?"
valid moth
basically
valid moth
i dont have nitro
hearty steppe
Oof
valid moth
but im open to receiving it
hearty steppe
Same
quick hornet
nah its okay we live in a commutative world so every flight path is the same
hearty steppe
What does that mean tho... living in a commutative world
quick hornet
thats how commutative diagrams work
valid moth
it means that superman modulo the cape has a regular outfit
flint forge
Broke; all diagrams commute
Woke: all paths are homotopy equivalent
Bespoke: all paths are the same path
Ive been infinity pilled honestly
quick hornet
the more \inftys your work has, the more comprehendible it is
tender yoke
covariant derivatives commute so earth is flat confirmed
quick hornet
thats why people in #calculus always compute limits by substituting in infinity
in related news, e = 1
actually wait
how have i not seen any jokes about this before
with e being the identity element in groups
but also e = 1 when you evaluate the limit naively
idk man most of religion is pretty incoherent
im not sure this is compatible with church of commutativity dogma
inner sentinel
Stewart or Edward and Penney for Calc III
inner sentinel
Any1?
gray gazelle
||folland :)||
hearty steppe
I’m checking out Treil rn and it seems to read much better than Kunze. Comparing to Janich, I am not sure if it’s better for those trying to learn or review and learn more linear algebra
It is probably a good idea to take a look at both books but I’ll provide more criticism later
waxen elbow
hey, any recommandations for a short category theory textbook ? with corrections if possible
hearty steppe
Definitely don't recommend reading Treil without Janich. I think its a decent supplement for learning linear algebra while using Janich. Even for people like myself that haven't learned linear algebra super extensively through a formal linear algebra course but have an ok amount of exposure, I recommend this strategy.
I been told Ikramov is the way to go for doing problem sets, so I'll give that a shot too and provide my criticisms.
waxen elbow
do you know what are the requirements for this one ? @flint forge ty btw !
gray gazelle
What do you all think about this book?
Good for the subject matter it treats?
Worth reading?
wise vine
Lax's Linear Algebra seems pretty decent, and it has applications. Problem is, exercises aren't that quite challenging.
gray gazelle
Hey guys... I just had a quick question 😄 is this channel for regular books or math books?
stray veldt
math books
gray gazelle
civic carbon
Darn, I can't recommend Secret History then
valid moth
you just did
gray gazelle
What's that
hearty steppe
Axler’s Linear Algebra book seems to be a mixed bag on here. I may take a look at it for curiosity at some point
@wise vine
glossy bison
Do you guys have any recommended books on advanced trigonometry? I couldn't find anything in the books channel.
gray gazelle
ladr is a mixed bag here probably just because it avoids determinants (and maybe because of the arrogant-sounding title)
quick hornet
i'm announcing my new textbook
Linear Algebra Done
it just does linear algebra, no fancy strings attached or anything
valid moth
do you introduce determinants in the first chapter though
quick hornet
i expect students to know determinants going in
of course i define matrices and vector spaces and whatnot in the first chapter
quick hornet
but you better have knowledge of determinants as a prereq
hearty steppe
Oof yea I would avoid Axler then if it doesn’t cover determinants
quartz pawn
It does but it's not very large treatment
hearty steppe
Linear Algebra Done Wrong by Treil is one of the less dense analytic texts tho but I think it’s good if you read it with Janich for refinement
gray gazelle
the only right way to define the determinant of a linear map is as the unique scalar by which the pullback on top-degree alternating tensors is scalar multiplication
from that you can do the geometric intuition
don't ever give me any of that leibnitz formula crap
hearty steppe
I think I see why Janich is not recommended over Kunze here tho, because there’s is not much depth past Eigens. But there are other books I’m gona check out for continuation
Kunze definitely not recommended from my perspective tho. At least for a first course
Like we gotta do better with the book recs. I said that here in the past but as I’m learning I want to eventually help out with getting a nice book list for the server together as my knowledge matures for topics like linear algebra, abstract algebra, and probably analysis
velvet briar
I love LADR but know what determinants are before you start imo
Or find some way to learn them somewhere
sage python
Axler isn't good for determinants
Like he avoids them because their standard treatment lacks conceptual content when really the answer is to include the conceptual content
Hoffman-Kunze is my favorite book that I've read, I don't know Janich so I can't say
finite robin
Does anyone have the website of the professor blog giving a list of recommended books for each subject, for undergraduate and graduate?
Purple text, green text, blue text. I'm trying to google it but I can't find it
Nvm I found it
waxen elbow
@finite robin what is it?
hearty steppe
I'm not saying Hoffman-Kunze is bad, but I certainly don't think it is friendly to someone learning linear algebra for the first time or brushing over it without taking a whole formal course on it.
I think Hoffman-Kunze will grow on me when I progress through analysis and at least read a few linear algebra books
brittle latch
@finite robin can you share the link please
also i see a lot of people here discuss textbooks almost as though theyve read them cover to cover so my question is how do you approach textbooks? im home from college for a year and i wanna teach myself some math some physics and some computer science. i was thinking about taking a textbook approach to math and physics but reading it front to back doesnt seem like the smartest thing so idk
any ideas? or ig just how you guys approach and consume textbooks? @ me pls :)
flint forge
Read the pages u vibe with
finite robin
@finite robin can you share the link please
@brittle latch https://marktomforde.com/academic/mathmajors/textbook-suggestions.html
Sorry for the late response
@finite robin what is it?
@waxen elbow Link is above
waxen elbow
when its not coloured, it doesn’t mean anything particular ?
soft terrace
anyone got a good place to start in recommending an intro to metalogic book or pdf? I assume that's math enough
drowsy arrow
what dya guys think of openstax books?
quick hornet
open access textbooks are, of course, a good initiative
i havent really taken a proper look at openstax, but on a skim, the exercises struck me as very "repeat the same type of problem 60 times"-oriented
you could argue "thats just how computational calc/algebra courses work" but it still feels pretty iffy
stewart gets its criticisms (and deserves many of them) but it at least hints at students that there's more conceptual basis to everything, and even presents proofs and stuff where possible
openstax does have a brief section on epsilon-delta stuff, but i recall disliking its treatment
it may have gotten rewritten since then though
the stuff from openstax i read definitely "feels" more "AP calc-like" in character than university calculus
more geometric stuff, mentioning diffy eqs weirdly early without really expanding at all, the bizarre need to separate "computation" and "application" sections
i'm personally not a fan of this but that might just be me being biased against College Board rather than an actual substantial criticism
one thing is that i feel like these "AP calc-like" textbooks focus a lot on specific geometric figures rather than general geometric intuition
im not sure how exactly to express what i mean, but like
very rarely does visual argumentation actually help in the problems they give, since many of the examples are so simple
unless the problems are specifically constructed to be of the form
"we drew a triangle and a semicircle on a graph, compute the integral"
which like... sure this is developing the "definite integral = area" connection but it's not actually developing visual intuition skills for problem solving
i feel like even computational calc textbooks would benefit from more "esoteric" examples
sorry, let me explain what i mean by that
stray veldt
don't leave me hanging, i'm at the edge of my seat
quick hornet
sorry i had to find a good example
suppose $f$ is defined and differentiable on $(0, 1)$ with $\lim_{x\to 1}f(x) = \infty$
hasty eagleBOT
Namington:
quick hornet
does $\lim_{x\to 1}f'(x)$ always exist?
hasty eagleBOT
Namington:
quick hornet
this is the kind of problem where visual intuition greatly simplifies it
like there are formal ways to approach it but really
visual problem solving is gonna give you the best path here
this simply isnt the type of thinking that these "ap-style textbooks" encourage
they claim to focus on visualization and intuition but really that just means
"we'll throw a bunch of geometric figures on a plane and expect you to find areas and tanget lines"
rather than "we'll give you problems that encourage you to use visual thinking to reason an approach"
the answer to the above question is, of course, no; picture a function which shoots off to infty but in such a way that it's constantly oscillating, and at an increasingly fast rate (a la sin(1/x) or whatever). then the derivative is constantly varying at a faster and faster pace, and thus has no limit.
amazing drawing i know
i could do it better with pen + paper
still not great but you might get the gist
valid moth
one of the true artists of our time
quick hornet
anyway FWIW i dont think this problem is exclusive to openstax
and from the parts of openstax calc that i read
long bear
Picaso
quick hornet
its more well-written than most of its peers
at least as far as i recall
but i honestly think stewart does a better job at presenting the material, and let me tell you, i am not a fan of stewart
again though this is just first impressions based on a skim
and in any case openstax does teach calculus
so if you want the $0 calculus experience, and dont want to use libgen for whatever reason
it's a good option
(though i cant help but feel like theres a lot of lecture notes you could poach instead)
long bear
libgen gang
stray veldt
openstax is a good concept and should be supported
quick hornet
yeah absolutely
i opened with this
open access to textbooks is a good thing
and ideally would be the norm
stray veldt
although not sure if using the books is "support"
long bear
open access textbooks are, of course, a good initiative
@quick hornet
oop
sorry
forgot that tags
:(
quick hornet
i think its good to spread the word about openstax at least
since that plants the seed in people's mind that
this stuff IS possible
and it can be done in a professional way
rather than "hodgepodge collection of lecture notes poached from an assistant prof's personal webpage"
stray veldt
i dunno, i like lecture notes a lot
quick hornet
openstax textbooks are very professionally put-together even if i think they have issues (or at least their calc series does)
stray veldt
because they are more concise
like, books will cover a lot
but writing lecture notes forces a prof to make a selection of topics
so you won't spend eternity reading a book
quick hornet
oh i teach from lecture notes whenever possible
but i mean like
for self-studying
often inconvenient
stray veldt
maybe
quick hornet
but yeah i agree that lecture notes are better in a classroom setting
my classrooms are always
the material comes entirely from lecture notes
i assign a text with the note
"this text is not teechnically mandatory, but strongly advised"
stray veldt
yeah, this is the norm here
quick hornet
"all necessary material will be covered in class & in lecture notes, but the textbook will give an alternate presentation and more practice problems"
"both of which can be useful for reinforcing your understanding"
stray veldt
profs give a literature list
quick hornet
in-class i also give a cheeky line
quick hornet
"now, i'm not tenured, so i'm supposed to tell you to get it through legal sources"
smart students will figure out what i mean by that sentence lmao
stray veldt
lmao
stray veldt
my university library offers most books as free ebooks, so 🤷
it really shouldn't
the authors don't mind
for academic books at least
quick hornet
well stewart probably cared when he was alive
stray veldt
they only write books for the prestige and because they are too old to produce original research
quick hornet
only person ever to get rich off of textbooks
sorry, let me rephrase
off of WRITING textbooks
textbook PUBLISHERS get plenty rich
gray gazelle
sometimes we do both
hollow current
sometimes we do it simultaneously
drowsy arrow
i dont want to college
gray gazelle
are you being forced to
drowsy arrow
idk im not in college yet maybe the world will boom before i do
naive plank
Is Gilbert Strang's book for calculus better than Michael Spivak's calculus 3rd edition?
I've taken a few courses from school but never really took it seriously so it's not like I know nothing but I am still a beginner. So which book is better for people who have some grasp of calculus but want to dive deeper in the math behind it. Btw I am 16 (finished 9th grade) and I will need some calculus for a course I will be taking in physics this year.
If not what books/yt videos/resources would you guys recommend?
hearty steppe
Spivak and Paul’s online notes should be ok if your decently versed
gray gazelle
learn proofs before spivak
unless you're very motivated to learn proofs from a book like spivak (not recommended by me)
wooden sparrow
Proofs before calculus? I thought it'd come after calculus
gray gazelle
not necessarily
restive raptor
At my uni, in the first term, you do a mildly analysis style calculus (on par with spivak) alongside an intro to proofs/abstract algebra/number theory class
doing them concurrently was fine for everyone
gray gazelle
proofs class wasn't even a thing for me here, we just jumped right into spivak for "analysis/calculus" and a rigorous LA book
restive raptor
My proofs class was super cool. The first half was in coq, but there was a lot of focus on definitions - not what they were, but the motivation. We were expected to fill in our own definitions for a lot of stuff (ie we needed to write axioms beyond the ring axioms, we need to write in the definition of less than and greater than, etc.) in a way that coq understood
second half was inquiry based number theory
gray gazelle
that sounds kind of like what one of my friends did, really neat
i would have enjoyed a class like that
probably won't find anything like that where im at though 😔
naive plank
@gray gazelle what book would you recommend for someone like me
gray gazelle
er i didn't really read what you wrote. gimme a minute or two and i will
i just saw "spivak" and "9th grade"
gray gazelle
at the 9th grade level you probably aren't familiar with reading or writing mathematical proofs
inb4 "russian schools do it!"
@hollow current #❓how-to-get-help
hollow current
||polynomial style: read rudin do not do this is a joke||
gray gazelle
spivak is good for getting a better grasp on calculus, absolutely, but the book will be difficult if you aren't comfortable with proofs beforehand
i know nothing of strang's book
dapper root
Is it Strang's linear algebra?
hollow current
as i know his from LA strang is more practice based
dapper root
The MIT dude
I hate that book
but actually if ur 9th grade it might not be bad
Like
it's a softer intro and is mostlay like
matrix algebra
It's not a math major book, but you don't need that the first time
gray gazelle
spivak is a weird one, kind of an analysis/calculus mix. you'll absolutely get the necessary calculus knowledge out of spivak for e.g. physics, but will also be exposed to some very elementary analytical arguments (primarily epsilon-delta, convergence)
naive plank
I took a "calculus" course this summer and it lasted 2 weeks. It was pretty hard since we basically had to study all the calculus for 1st year of uni. Note that me saying i took a course doesn't mean i understood it perfectly and that's why I said I was looking for a book that isn't too difficult to read but is definitely challenging.
long bear
stewart?
gray gazelle
i say "very elementary" because what constitutes analysis is very broad, and i should really be using a different term that isn't from my point of view
naive plank
I guess i will stay away from spivak's book since a lot of people online aren't recommending it for complete beginners (even though I wouldn't consider mysey an absolute beginner).
But now comes the question. If not his book then which?
dapper root
kek
naive plank
:D
dapper root
I don't think spivak is a bad choice tbh
like
you seem motivated and
ahead
so you can just give it a shot
and if it's too much pivot into an easier book
that's less detail and proof based
gray gazelle
rudin is a fantastic book but it's not exactly the book you read for your first introduction to a topic imo
dapper root
but it's up to you what you want
If you want to see calculus rigorously it's a good choice
if you just "wnat to know calculus"
Then there's other books for that too
naive plank
Nah I want to understand it
gray gazelle
spivak > a lot of other books, then
dapper root
I mean I felt like I understood calculus when I learnt it the first time
from like Stewart
gray gazelle
i think the hardest part about spivak is doing the exercises, in my opinion, since he really talks a lot and motivates everything (good!!!!)
naive plank
Ok so what's the difference between
Spivak
And
Stewart
Because I read some stuff online
And ppl say it's "dry"
Or smt
dapper root
Stewart is like
the AP calc sorta
for engineers calculus
it works
it's treu
but you won't be really "proving it" rigorously
It'll be a lot more like the math you've done up till now
here's formulas, this is how it works, etc
I think maybe there's actually proofs in it??
Spivak will be your first venture away from math that is just
"here are the rules, this how it works, go do computations"
naive plank
Yeah i guess i will give Spivak a shot
I actually already did
Just read the first 2 chapters
gray gazelle
side note: spivak will actually teach you some computation, but some more advanced math textbooks leave you to learn the computations yourself and present purely theory to you
cough differential geometry cough
pulsar aurora
Apostol's calculus is another option: it's less analytical, but still rigorous for calculus. I feel he fills in the gaps where Spivak sort of just leaves some context out.
gray gazelle
https://pdf.zlibcdn.com/dtoken/584fb3579aaf1b1c02d19574359213ec/The_Real_Number_System_by_John_M.H.Olmsted)3610247(z-lib.org).pdf
What do you all think about this book?
Good for the subject matter it treats?
Sorry for reposting it. No one answered when I first asked this
brittle latch
dead link m8
gray gazelle
Missing the bracket perhaps?
sterile pelican
Out of curiosity where does Lang's Short Calculus lie? I did that book
No multivariable though
deep dirge
@gray gazelle link is dead
quick hornet
does anyone have experience with rotman's intro to the theory of groups? I'm gonna be TAing a group theory course targeted at students who already know proof-based linear algebra (and some abstract alg definitions)
and the prof said he's probably gonna use rotman
gray gazelle
Good books on discrete optimisation?
quick hornet
considering its marketed at students who are already mathematically mature, i was surprised that it didnt contain any rep theory material
but he actually justifies this decision by saying a 1-chapter treatment would be woefully inadequate and likely need to be retaught later, just making it a waste of time
he likens it to high school calculus
im not sure i buy this but the argument makes sense
flint forge
Idk i think you can teach some interesting baby rep theory after an intro to group actions
Its an easy-to-motivate specialization
valid moth
i mean yeah, i think a decently interesting baby should be able to do rep theory
quick hornet
yeah max thats why i dont totally buy it
like rotman's argument seems like its totally motivated based off time efficiency, like "you'll have to relearn it later anyway"
but i think theres merit in just giving students a crash course just so they sorta know what its about
since a) they may find it interesting and b) it helps contextualize a lot of group theory
sage python
I like Rotman's book
Steinberg is supposed to be good for representation theory if you don't know any ring/module theory
valid moth
rigid sky
a
smoky surge
Do y’all think it’s pretentious to want a book you’ve read in as a real copy?
sterile pelican
no
hearty steppe
I call those collectors items
pulsar aurora
I try to acquire physical books because it's easier on my eyes.
hearty steppe
Yea it can be easier on the eyes
sterile pelican
I get physical books to avoid distractions from the computer
also I take it around with me...except the big tomes like D&F
pulsar aurora
You should take the bigger ones. Impress the locals around you
sterile pelican
sure let me get Eisenbud's book then
shadow nebula
carry one in your hand at all times
broken meadow
lol
sterile pelican
why one when you can flex at two?
long bear
get a transparent backpack
broken meadow
pff
what are you talking about
all you need is like
a crisp stack of like
10 sheets of A4 paper
tucked into ur book
and then a pen and pencil and eraser in ur pockets somewhere
lol
broken meadow
transparent book
long bear
transparent hard cover?
you don't want a like
soft cover
otherwise it can bend
and make it harder to read to the naked eye
effectively making the flex more difficult
shadow nebula
transparent everything to see my giant
long bear
quite litterally
shadow nebula
book
long bear
broken meadow
crystal compass
Any book on Differential equations and vector calculus?
Multivariable calculus
hearty steppe
two diff subjects lol
hearty steppe
try Professor Leonard Youtube channel for Multivar
he goes over a decent amount of diff eq too i think
crystal compass
Ok
flint forge
The new book
Topology a categorical approach
Might be my favorite point set book ive ever seen
It introduces concepts important to algebraic topology
Using tools that algebraic topologists actually care about
And takes two very dry subjects (point set and category theory)
And makes both interesting to learn
I didnt check the exercises yet
@valid moth
It uses lots of universal properties and category tricks
To prove things
Without gross pointset ba
Bs
And like motivates coarse and fine topologies via the cont maps they admit and stuff
I would say pretty unrelated by i have a limited at best knowledge of htt
brittle latch
can anyone recommend any books on how to properly teach oneself things? @ me pls :)
valid moth
Wait it's not AT?
flint forge
It introduces fundamental groups
But no its not AT
But!! Its the first pointset book ive ever read that ‘feels’ like AT
valid moth
I see
flint forge
I genuinely could see intro point set and CT being paired together at the UG level
valid moth
a standalone CT course for UGs seems inefficient
limpid gazelle
What's CT
flint forge
Its p good
It doesnt waste time on stuff topologists dont care about
And spends extra time on things like topological adjunctions
Smash products
Etc
Mapping cones
Homotopy
sterile pelican
I bought a general topology book from willard, it looked cheap as it is from dover but it doesn't seem like it was meant as a first exposure to topology
sterile pelican
It would be nice I am slightly curious of the subject
slender sphinx
Yeah I just wasn't sure if you were asking lol
I think munkres is a good intro to pointset topology, but it is dry
sterile pelican
my bad but yeah it would be nice
slender sphinx
Shaun's outlne of topology was something I read on the side and thought was alright
Munkres point set topology
hearty steppe
damn poco you been really grinding on math lol
dapper root
I don’t really care if Munkres is dry
Like, topology to me was so easy to just absorb all the definitions
hearty steppe
oh nothing it was a complement I guess. Have you made up your mind between math and chemistry lol. Is mathematical chemistry a thing?
sage python
Well, not just try but drawn out, there's a lot that's prob unnecessary
There's a new one Max just found
sage python
It's probably not more advanced, but more sophisticated, if that makes sense
slender sphinx
Yeah
sage python
Like it doesn't presume you know anything, but it's more work
But more work = more payout
slender sphinx
Mathematical chemistry could be said to be a thing; mostly applied though
dapper root
So being familiar with category theory is only a plus IMO
sage python
I like Lee Topological Manifolds
slender sphinx
And computational ( involving computers)
dapper root
That’s true
Which is why I said familiar
Being able to use it
When it’s nice to use it is a plus imo
Yes but Hartshorne :/ AG really lends it well to arguments of the form like “limits commute”
Since it gets rid of a lot of tedious details
dapper root
Which isn’t all that deep category theory, it still falls under like the good to know avg working mathematicians stuff
So seeing it via topology might not be bad
Idk I also like Aluffi so lmao
I mean yeah
I haven’t read the book so I don’t know how it does it
But Aluffi does it well I think
It’s really feet to the ground for almost all of the book
Until right at the end with some heavy linear algebra / homological algebra
I think intro abstract algebra classes should be taught out of higher algebra.
@sweet lotus prerequisites: Math406- Higher Topos Theory
That’s fair
sage python
What's a point-set exercise?
sterile pelican
I got my hartshorne book waiting to be open :^)
but given the chat here it seems munkres is a better approach on the first course of topology
dapper root
Idk, like I said I haven’t looked at it at all
My general impression tho is that a way to avoid becoming undergrad category theorist is to learn category theory in the context of applying it something else, seeing how it can be used and is useful in applications
Instead of just “abstraction go brrrr”
Which is the only reason I even mentioned it
quartz pawn
I was going to do munkres but god it's defense af
probalby take me 3 months to finish it
I've seen Lee's intro to topological manifolds?
what is the difference and what would cause me to prefer one over the other
sage python
A lot of stuff in Munkres isn't useful to learn
Lee kinda zooms in on what's important
quartz pawn
I was considering going through Munkres to develop my mathematical maturity but if that's the case, then I might just go thorugh Lee instead.
I don't think I have any intentions of becoming a topologist.
slender sphinx
Me neither haha
valid moth
probably because it is one letter away from munke
quartz pawn
Did you do all the problems @dapper root
It seems like a lot of material from me just looking over it.
dapper root
¯_(ツ)_/¯
I mean tbf my analysis class did like lowkey topology
So I had a really easy time with a lot of the stuff just using intuition
hearty steppe
I barely started Fraleigh for Abstract Algebra but so far so good
gray gazelle
Does any person by chance have a PDF file of: Statistics: informed decisions using data 5th edition
Or know where I can get it? 🤭
gray gazelle
yea libgen has everything
gray gazelle
not everything
@long bear well if it fails me I use archive.org, never had to look beyond those two
gray gazelle
Thank you!!
gray gazelle
i think harvard had like a 70 page intro to topology book
golden halo
What's a better self-study book for introductory real analysis: Spivak or Tao?
my previous experience is mainly Stewart but I have a little bit of practice with proofs
golden halo
ty very much
marble solar
waxen elbow
hey, is spivak's calc is a bit tougher than apostol's ?
waxen elbow
is it enough for pure maths or is spivak better for this ? assuming that my proof writing si so-so
quartz pawn
I mean like Tao, really makes an attempt for show you how to prove things with an appendix and starting out with the constructing number systems.
Spivak doens't really do that. He doesn't bother to show you how to prove things
He will give some key ideas, though they are pretty barebones.
The rest is up to you to figure it out when you go to proceed to do the problem.s
waxen elbow
you mean apostol is like tao's ?
quartz pawn
Kind of yea.
But Apostol's still isn't an analysis text. He doesn't try to construct the real numbers or anything like that and he doesn't really make you "prove" things.
waxen elbow
in the US, analysis includes calculus right ?
waxen elbow
so it might be better to go with an analysis book since it covers calculus in a rigourous way + other topics ?
quartz pawn
If you can do it, sure.
waxen elbow
T.Tao made one, isn't it ?
quartz pawn
Yea, it's just called Analysis
sterile pelican
two parts I recall
quartz pawn
there's two volumes.
waxen elbow
all right, guess i'll go with Tao's analysis then, thank you sir !
pulsar aurora
apostol is good as a light entry of proof based calculus as he uses analysis to construct theorems. But not good for analysis itself.
He does have proof based questions though
quartz pawn
Yea, that's honestly a better description.
I have apostol but I haven't used it
I just skimmed through it.
And "a light entry to proof based calculus" is probably the best description.
pulsar aurora
It isn't bad. I think it's a good book for anybody who is... testing the waters of mathematics without getting hit in the head with a hammer. 😛
or even supplement for one's calc 1 and 2 classes since it brings an understanding and a means to derive integrals and derivative techniques.
which is how I'm using it slightly
gray gazelle
I have both volumes of apostol’s
Calculus books
I also have an onslaught of other random calculus books that I probably will never read because there’s like 20 of them
pulsar aurora
I just have Apostol's Calc 1, and college textbooks. I may get Apostol's calc II just to continue on, but who knows how I'll approach things after my associates
dapper root
If you put a lot of time to it definitely
slender sphinx
yeah, I definitely think it is possible @buoyant escarp
gray gazelle
Books to learn proofs?
other than how to prove it
I read most of the second book in this message and enjoyed it quite a bit
https://discordapp.com/channels/268882317391429632/556194300912861205/696811046731513897
broken meadow
the second book is nice
hearty steppe
@flint forge you realize you make studying topology sound very unappealing sometimes lol
Algebraic topology still involves topology
flint forge
Point set is boring set theory
long bear
what are the pre-reqs for AT?
gray gazelle
Math
long bear
what areas?
stray veldt
algebra and some general (point set) topology mostly
quick hornet
even the point set requirement isnt too immense
hatcher has a summary affectionately referred to as "hatcher's notes"
all you need to know
you dont need all of munkres or anything
as for the algebra, the exact requirement will vary from text to text
but i'd say a course in each of linear algebra, group theory, and ring theory should suffice for basically every intro book
and it might be more than enough for some
hearty steppe
Dope thanks Namington
quick hornet
though that said, knowing more algebra (unlike knowing more point-set) will help you a lot in understanding some of the concepts quickly
hearty steppe
Do you think that number theory will help a bit with learning more algebra
quick hornet
well, doing any math will always make it easier to learn more math, but i dont think NT will be of much help specifically for algebra