#book-recommendations
1 messages · Page 240 of 1
You eat food
你吃饭了吗?
Have you eaten food?
了 signals past tense and 吗 makes it a question

Oui, j'ai mang3 le riz
hey does anyone have any book recommendation for topology!
Munkres is the standard topology book
Mendlesons intro to topology is a very easygoing (maybe too easy) Dover Book. I used it to get a basic intuition, then moved to Munkres
Munk munk munk
munkres is popsci for nerds
"Standard"
A lot of standard books are trash
Ahlfors is trash

Hartshorne is trash
Me neither
Munkres feels way too long for most people lol
wait i need it to be proof heavy btw
id be surprised if there was a topology book that WASNT proof heavy
i don't mind it being too long as long as it's good hehhe
what are you doing in topology if youre not proving things?
computing standard bounded metrics??
learning topology from munkres can be pretty bland I think.. lol
true true!
so mendlesons is good right ty i'll look into it!
RIP Miura
🤔
What about just modern-ish?
Like a Big Hero 6 kind of thing
That's not common?
hi ragh 
So,Pixar?
This just in: conversations have context
Hmm not really
More like Worm?
Should have thought of that; it's a better example of what I meant
What was the name of Sivik's book for calculas?
maybe topology without tears ?
you can also check out the first chapters of lee's topological manifolds, depending on what you're looking for, it may be a nice choice too 
Shika's book might be good, without contradicting that I'll toss in my 2 cents: I don't think point-set topology is something to spend too much time on
Unless you're doing specific things that rely on heavy stuff
So I'd find an efficient treatment and move on. Maybe topology without tears is efficient, idk. I learned it out of chapter 1 of Bredon's topology and geometry book. Also these notes seem good: https://pi.math.cornell.edu/~hatcher/Top/TopNotes.pdf
these notes are a bit too terse imo
(also iirc you're in prepa, if you're looking for something that covers in depth normed vector spaces and less metric/general topology, these aren't great recommendations)
prepa
Baguette confirmed
I do actually want to study actual topology :D
so thank u so much for the recs!

sadly yes 
Jokes aside good luck
tyty :D
I used this because it's what my course used
I would say it's a good choice if you like a looooot of explanations. Like iirc, it even explains like proof techniques
Did you mean to reply to ange 
I meant this

thanks everyone!! :D
Hi. What are good books on functional analysis and measure theory that have not just theoretical exercises, but also more "computational-style" exercises and also exercises showing applications to other things (like "how to use this theory elsewhere")? Thanks.
I think kreyszig is kind of an easy FA book with applications but it doesn't use or contain measure theory
I don't know a good measure theory books with a focus on applications
nontheoretical measure theory 
Let me rephrase
any good books on trigonometry?
Search this channel for it, lots of recommendations
people seem to recommend Lee a lot
Oh i'll check then
你吃了饭吗

This is high level trolling
I've been wondering if there is a book with everything about science in general
Or a site
I just want to find some organized place with a lot of information
w i k i p e d i a
Except Wikipedia
scholarpedia?
Wikipedia isn't helpful if you want to learn advanced material
It either doesn't exist or the wikipedia answer is too difficult to understand
But is there any place with a lot of deep information about mathematics and physics
nlab?
Looks nice
Depends on what you mean by deep and lot of information, but Wikipedia is more or less canonical for some stuff. Other than that you'd probably have to hunt multiple sources, usually not so tough to find.
i would not recommend any of these (nlab, wiki, planetmath) as a learning source
theyre not designed to be pedagogically sound or self-contained
as a compliment to another source, sure
but youre not gonna find a one-stop place to learn things
do any of you know good books for counting and probabiliy?
So. Do you know something that could help me?
That is the problem i don't know what the topics are. I want to have an overview about every kind of math
So then i could pick topics
It looks nice
Thanks

I am in high school
This looks like something that can be a little helpful for me as well
Even tho I’m not in high school
Highschool math is basically just algebra and geometry
Not sure if this the appropriate channel to ask, but is there a "curation" of NPTEL courses? Like a rank of the various better ones for math, physics and engineering out there.
It's usually better to use other sources compared to NPTEL, except for very specific topics
What topics do you want to learn?
I had this one in mind -> https://www.youtube.com/playlist?list=PL5E4E56893588CBA8
Opps
no no
Yea, Balakrishnan is pretty good
wrong link
as far as I have heard
Selected Topics in Mathematical Physics by Prof. V. Balakrishnan,Department of Physics,IIT Madras.For more details on NPTEL visit http://nptel.ac.in
same professor though
Anyone have any textbook recommendation to learn about transforming highly nonlinear and complex models into finite-dimensional problems? In particular psudeo-spectral methods.
Yea but the Napkin book is one of those books to help people ease into higher level math
@hasty turret btw... sorry to insist on this.. but are the nptel stuff that bad?
I think I saw some kind of programming video off nptel that was really bland
Plain trigonometry written by nathan o niles is a good book to start learning trigonometry?
@vagrant sedge no there just tends to be better alternatives for very mainstream courses
Thank you.
Hi
Usually yes
It's usually some guy reading a textbook word to word
Balakrishnan is an excellent expositor, I'm sure following these lectures with a textbook would be worth it.
But yes, most courses offered by NPTEL are...bad.
The ones being offered recently are improving on a pedagogical level, especially by the younger faculty.
did someone say tiddies?
Yeah, Pugh's Real Mathematical Analysis
Or in fact
Gimme a moment
@fast portal
There's also a playlist on Knot Theory on YouTube, the animations are very nice.
no, they are knot
To be or knot to be
Ok?
Homotopical Topology
i love pugh

the book is good if used right
let me tell you, it does not pair well with an analysis class where rigor and proving everything is the norm
It's probably more of a book actively used along with a class, not so much for studying on your own.
Lol
i am coping

a month and a half after the end of the course and i am coping 
Your brain on pugh
please
i try so hard
and it keeps coming back to haunt me
Yeah, Pugh is for moral understanding
rigor != proving everything, is it ? 
did you come out ok?
yeah i got an A-
Like I don't think it's not rigorous to not prove something you'd be able to prove (I mean, outside of any school context) 


Honestly props for not getting traumatized
I feel like if I did poorly I'd have probably just let it get in my ahead and avoid it
hey, any recommendation on a book to teach myself calculus?
Spivak calculus
my background is :
ive completed precalculus and thats it
oh okay
ill take a look at it
:)
there isnt much of a big difference between a book and another right?
like, they are going to teach me the same things
i assume in different approaches or smthn
Spivak Calculus is if you want to have a very rigorous, theoretical treatment of calculus
oh maybe thats not exactly what im looking for then
I guess Thomas might be better
Most textbooks/youtube will give you a mechanical intro
i see then
I wouldn't pass up Khan Academy as he has a curriculum
Stewart's the standard for calculus
oh yeah i think ill use khan too
just thought of a book as a complement to khan
or khan academy as a complement to a book
Eh idk if I should recommend Stewart
Thing is I feel like a lot of calculus books at that level are kinda isomorphic
what do you mean by that
Like the price difference between Stewart and other books is gonna be wayyyyyy higher than the quality difference
And there may very well be a cheaper book that's equally good/better
you shouldnt do stewart if possible
or any of the other isomorphic ones
like if you have to do it
mentioning piracy is against the rules right
at least find a pdf somewhere
what ab paul's online notes to learn calc
is apostol one of the isomorphic ones?
no
Nah Apostol is more like awkward Spivak
ive posted this before but
uhh regarding price, lets say i have uhh
Discover incredible free resources to study mathematics - textbooks, lecture notes, video and online courses.
i might do a little bit 🏴☠️
So the rule here on piracy is, we're not gonna like
Report you to the cops because we suspect something
And I don't know how many individuals here care that much
ah great
But discord TOS is that we don't promote/encourage/engage in illegal behavior
Oh yeah i get that
So yeah I'm just gonna say about Stewart that I don't think it's so special to be worth the sticker cost. The theorems are the same. If you have some method of acquisition such that the cost is similar between books, be it buying used editions or something more dubious, then I take back my anti-recommendation because I don't know the alternatives
So in that case I'd wager Stewart's probably fine
oh great
There might be better choices but I imagine if it wasn't one of the better ones it wouldn't become so standard in schools
nice
i dont think my school covers calculus
well, i hope i can go through 631 pages of math
for electrical engineering, calculus 1-3, do you folk recommend Stewart, MIT OCW or Pauls online notes?
or something else?
I’ve heard good things about OCW, Paul’s notes are a fantastic supplement in general
And the above convo recommended Stewart, so I’d opt for that and use the others as supplements as need be
sounds good, thanks
Btw... what do you guys think of Edwin Moise's Calculus book?
Hello everyone. I would like to know what's your opinion on Abbott's real analysis book. Also, I would like to take advantage and say that I'm looking for a study buddy for real analysis, if anyone is interested
Is Gamelin's book good for complex analysis?
i read from it and did problems from it while preparing for my complex analysis exam and i liked what i read
nice selection of topics, fair number of examples
the residue integration section in particular is very thorough
My impression of Gamelin is that it's the best book for people who don't have a lot of background
Thank you! I took a "Complex Variables" course that had no rigor whatsoever
And would like some proper complex analysis
Complex analysis is very cute
The only other complex texts I knew of were Alfors and adult Rudin, and I have sufficient fear of God, so I'm not touching those
What's your real analysis background?
Actually I'll just say check pinned messages
I put a review of complex analysis books
Lovely, thank you very much!
Oh, and you have an algebra one too! That's great
and I have sufficient fear of God, so I'm not touching those

don't worry ahlfors is not as hard as rudin
ahlfors is alright
I own baby Rudin
If the baby is that ugly, I don't wanna see the papa
ahlfors good
my notes r better
/s
I'm currently reading through Hubbard^2. I then plan to go to Analysis I/II (Tao), Munkres, Lee (Smooth manifolds), and then Lee (Riemann)
I'll squeeze complex and algebra in there somehow
lee riemannian manifolds 
Is that a bad choice?
no not at all
i really like that book
I want to learn diff geo (and math in general, lol).
I've been doing physics up until now, but I'd like to know what in the fresh hell I'm actually doing
Well well well
Is it good if I try to self study linear algebra from Friedberg book?
Sure
Im sure its fine, but i would also recommend Axler’s “Linear Algebra Done Right”, a very nice book i found it to be, never heard a soul not like it!
Hard disagree
Hmmm, I was afraid that if I choose those, I'll have a harder transition when I want to move to a more applicative based side
Axler thinks about char poly and determinants like a moron
You dont like it?
I don’t either
It's probably good exposition in the first part
To be fair i didnt read the last bit
I liked all of what i read, which was most of it
I just heard Friedberg has balance between pure math and application math kind idk
by last bit you mean?
So that's why I ask here to make sure o.o
Yes Friedberg is a fine book
But like he says char poly is given by, complexify, upper triangularize, product of t-diag
Which is so stupid
Ehh determinants and some of the stuff on complex vector spaces
Whats the alternative? (Im not a maths boii)
Friedberg seems good, I partially used Hoffman-Kunze which is old school but good
the alternative is just defining a determinant 
Oh oh
Yeah just define determinants conceptually
Computationally and using exterior products
Product of eigenvalues
Ehhhhhhhhhh
I don't like the idea of passing to a larger field when you can just work in the field
Real matrices have real eigenvalues

This isn't helping me figure out whether you're trolling or not lol

I'll assume you are


By the way, the friedberg book itself is self-contained right?
(means I don't need anything outside high school math, probably requiring some experience in proof writing, which I have).
Yeah would just require high school algebra
Okay 😮
The proof writing you pick up as you go
le algebraic closure of a field has arrived

Tao has a lot of foundational fluff tho
You can skip a significant portion of Tao and still be fine,I think
Duly noted. I've gone through the construction of the natural numbers already
you can skip all of tao and you will be fine
What would you recommend instead?
i just wanted to take a jab at tao 
Fair 
I thought you were going to recommend baby Rudin to me, had some heart palpitations there
Do it, i dare yah😂
i think just read around and see what u like best
I own it 
I actually like Rudin, but I'd like to use it as a supplement
go for it 😌
I do too, actually had an exam q come from it
Didnt get it for my life
If you like stuff like construction of N, you can read that. But, that's completely useless,since you usually just assume N exists and be done with it
Same for R,you just assume R exists and has the least upper bound property
Fair
i mean u can construct them definitely 
what's a good way to access research papers? (in compliance with rule 7 lol) I know that I can get them from my university but mine isn't that great so they probably won't have really niche stuff
When asking for help, do not insist on getting just the answer; we are here to help you learn, not cheat. Likewise, if you are providing help to others, try your best to explain and elaborate instead of simply giving away the answer.

hello!
i am applying to ug computing in 2022.
i'll be grateful to get some recs for sequences and series.
oh what
Are these two books good to review before I head to grad school? I never took Undergrad abstract algebra
wow stillwell is a bizarre text
in any case, that isnt sufficient if youre going to actually do any algebra in grad school
very minimal commutative algebra exposure
also very little rep theory (van der waerden only has 1 small chapter on rep theory and its in volume 2)
that said, if you managed to get into graduate school without any algebra, then you probably wont be doing any algebra in grad school
so i guess thats not a concern
in which case, probably sufficient although if youre doing analysis/topology id still recommend doing a bit more if possiblee
wait, what do you mean by review?
do you mean you learned abstract algebra but never took a formal course?
in that case my advice changes
(and you probably wont need stillwell at all)
like review some of the material taught at an undergraduate level Algebra.
I NEVER took a formal course.
but you did learn the content before?
if so then the van der waerden series should be fine
No
then what do you mean by review?
My transcript does not have abstract algebra
like review some of the material taught at an undergraduate level Algebra.
perhaps we're using different definitions
how are you defining "review"?
I assumed this definition:
view or inspect for a second time or again.
"all slides were then reviewed by one pathologist"
i see no other definition in google dictionary that seems to fit your intention
I think of review as a short introduction of the material. So that way I can have some knowledge of the terms and such.
perhaps you meant "overview"?
in that case, then sure
the VDW series can be skimmed for a solid overview
Overview sounds good
what chapters should I focus on? I was thinking of the first four
i dont know anything about stillwell
alright
besides its table of contents being screwey
what are you going to be doing in grad school?
What about van der waerden?
its a classic but is pedagogically dated
i wouldnt consider it a good source for a first learner
but if you just want a reference text to understand the definitions and common problems we care about
its fine
(its intended for grad students who already have a bit of familiarity with algebra)
I'm going for a masters in math and the program I am going to offers complex and algebra this Fall.
pure math, id take it?
in that case, my recommendation would be as much as possible
the program is mix with applied and pure
but at least the first 5 chapters
They going to teach stats
StillWall the first five chapters?
VDW
oh
you can also probably skip chapter 1
id also recommend reading chapter 7
the others arent crucial
but 2, 3, 5, 7, familiarity with vector spaces
are what id consider the core algebraic backbone of an upper undergrad/early masters student
What subject u talking of?
van der waerdens algebra
toc
(copy-pasted from amazon preview, not piracy, dont nuke me discord admins)
Is that similar to contents of algebra by lang
like the first half of lang
ish
van der waerden comes in 2 parts and they only have pt 1
is chapter 4 good if you forgot about LA?
Someone recommended me algebra by Lang when I said i wanted to refresh my algebra, but I meant hs algebra
Lol
sure, it can be a good refresher
🙂
not high priority, mostly buildup to galois theory
knowing stuff like what a root of unity is is certainly a good idea though
SO I have Chapter 1, 2,3, 4 (up to 4.5), 5 and 7
(an nth root of unity is a solution to z^n = 1; there exist precisely n in ℂ for each n)
I will learn that in complex
Why don't u read it all
again, thats what id consider the minimum working knowledge
if you can do more, do more
I don't want to stress myself and being burn out by August
Also, health is important too.
U have a deadline?
I don't have a deadline
Then just go at it slowly and take break days
Yea, I am starting like June 6
Do u have to kno it by a certain date
Not really. It would be nice to get to 4.5 by July 26 or so
Then take ur time and learn it all
Can someone recommend me a good trigonometry book?
I am in the 9th grade from Romania(( choose the hardest type of math that I could
Search this channel with "in:book-recommendations trigonometry book"
Plane Trigonometry
by SL loney
Is there a set of lectures available online for grad PDEs? Just to follow along with Evans
what is your pde's consisted of?
just basic existence, uniqueness, and regularity results of elliptic and parabolic PDEs
I like Brezis a lot and have read enough to not be somewhat comfortable with Sobolev spaces but that’s all
I you want to look at abstract and Kernel methods for Parabolic pdes Ouhabaz's book "Analysis of Heat Equation on Domains" is a very good one
Sure, sounds a bit more advanced than basic PDE theory but Ill trust your rec
You don't need other stuff than basics of semigroup theory, and basic Sobolev Spaces knowledge. Notice also the above book deals with semigroup theory almost from scratch using accretive sesquilinear forms (then later in the book it is given some sufficients conditions to extends the involved semigroup on Lp using almost full abstract Functional Analysis arguments)
👍 thanks! That’ll probably be most useful for me then
After a quick skim through Chen’s Napkin it would be hard for me to recommend it to high schoolers. Maybe gifted high schoolers that maybe did some Olympiad but if you don’t fall into that category, save yourself from using it as first exposure. Seems like a good reference read or something to reflect back on after learning a bit of modern algebra
Is this available somewhere on the 7 seas?
Weird, I searched the text name and found nothing, but searching the author worked. My bad 
almost always like this for me
if you're looking for texts that cater to wider audiences instead of proof heavy texts, i think the diff eq book by nagle, saff, and snider and the linear algebra book by lay are both good options
the explanations in both are pretty easy to follow
Hi. I have taken a first course in linear algebra (twice actually) using Hoffman & Kunze. I was looking for a material good for self-study that would serve as a course after that which was focused on preparing for a more numerical methods/analysis and optimization sort of use of linear algebra. Any recommendations? I have "Matrix Analysis" by Horn and Johnson in mind. What do you guys think?
For numerical linear algebra, I would suggest either Demmel or Trefethen and Bau
These are the two standard texts on the subject
has anyone read "geometric approach to differential forms" by bachman
it seems cool
and has very few prereqs
Any good math blogs to check out that are not geared at professional mathematicians? I know tao is quite popular but many of his posts go way over my head
good question actually 
undergraduate math blog when
math3ma,lolialgebra,mean green math
i read this, and really enjoyed it.
but honestly
i have to recommend shifrin's multivariable mathematics or spivak's calc on manifolds for a more complete intro to the subject
bachman is a really good primer though
nice that's cool
ty for the info
i been looking for stuff like bachman that i could self study without too much stress over the summer
math3ma looks good so far since I have been into category theory the last year I'm going to have to check out her book also which looks interesting.
Have anyone read the book Combinatorics and Graph Theory by Harris?
Is it any good as an undergrad combinatorics book?
Can anybody recommend a book on dynamical systems? I'm a researcher in epidemiological applications of agent-based network models and I have a degree in math, but I've never so much as opened a book on dynamical systems.
In return I offer this
I'd be interested in both theoretical and applied approaches. Bonus points if it includes graph dynamics.
Strogatz has a book on nonlinear dynamics
what is the best book to learn do Carmo content from
is it do Carmo
or shifrin
or osmething else
tteppa 
curves and surfaces, or riemannian geometry?
Any good books on numerical analysis?
What sort of numerical analysis?
If you want numerical linear algebra, either Demmel or Trefethen and Bau
For ODEs/PDEs, Iserles has a book
LeVeque has a few as well
curves and surfaces, sorry
I was told I can waive the pre-req for geometric analysis & relativity
but i need to get some diff geo knowledge
I was just looking for a general introduction, but these look nice! Thank you
(If you know of any general introductions, though, please do tell)
I don't know of any good general introductions
@obsidian valley waive the curves/surfaces prereq for those two? I mean just do the book the class uses probably
Ah
Honestly my impression is that it's the correct™️ book for that content lol
so I'm wondering if something does do Carmo better
I don't like Shifrin
hm okay I think I will use do Carmo
There might be others but it seems do Carmo is common and I dislike the one alternative I know so yeah lol
Hello people, I just started delving into Machine Learning. Any recommendations for Linear Algebra books which will be relevant ?
You should first learn linear algebra with Friedberg's book
Then you should learn numerical linear algebra with either Demmel or Trefethen and Bau
"Coding the Matrix: Linear Algebra through Applications to Computer Science" is also quite good
How is Sheldon Axler's book ?
Axler is not that good
Thanks, will check it out
The presentation of characteristic polynomials and determinants is lacking

Axler also causally assumes choice
I should add the caveat that when I read math books I'll read multiple on a subject using a hub and spoke type model- one friendly and readable book to give motivation to the subject and foundational knowledge (hub) and others for different perspectives and coverage. Once I move through a topic in the hub book it makes all the other (potentially less readable) books much easier. So in that context Axler is a good "hub" for LA imo.
True
Because unless you're doing QM, everything is finite dimensional
choice doesnt matter in applied subjects because the cases where you need choice never arise
and choice just makes theorems for those cases line up with theorems for more finitary cases
so it only really cleans up theorem statements
with no real downside
choice doesnt matter in pure subjects because everyone accepts it anyway
so who cares
its coconsistent with zf and thats enough for me
Even if you're doing QM aren't you gonna likely stick to separable Hilbert spaces?
Anyway for the most part nobody really cares about choice. I honestly don't buy the philosophical problems people have with it even in general, and regardless in any reasonable applied setting there's no real question lol
Problem with Axler is that he teaches you how to think about char polys and determinants like a moron
the philosophical objections are valid since its a weird axiom relative to the ZF ones
so its at least worth thinking about
the philosophical consensus is almost overwhelingly "yeah its fine" unless you also reject like
the axiom of infinity or LEM
Or I guess I don't mean on a logical level so much as... idk surprising things are true in life yeah?
And I'd wager that choice is sorta "obviously true" and makes a lot of things work
which seems to me like a reasonable interpretation
choice is worth thinking about
but when you think about it
The bizarre consequences then just become facts of life
Well when I say "buy the philosophical problems" I don't mean "Shut up and accept it" so much as
If you end up disagreeing with it I will give you a lot of side-eye
i maintain that the real problem with choice is actually power set
Sleeps_irl
and you should weaken power set before choice
fixes literally all the counterintuitive shit
alas
I mean life has counterintuitive shit lmao. Like I guess Banach-Tarski is the most commonly cited thing right?
To me it's just... yeah R is a big and very fucky set
So big that SO(3) contains a copy of the free group
Tbh you could prob make a case that thanks to Planck length or something, R isn't really a "physical" object, and so Banach-Tarski isn't a physical phenomenon
Back on topic though: yeah don't use Axler, not because of choice since that's not a problem, but because char poly and determinant
Friedberg is probably the correct intro to linear algebra nowadays tbh. I like Hoffman-Kunze but it's old school
axler kekw
Best calc 1 and calc 2 book?
spivak
thx
uh Spivak is good but it is mostly proof-based and requires a decent amount of maturity.
Best introduction to module theory?
Okay but is it still the best calc book overall?
define best
There is no best calc book. It is the best for SOME people but for others it would be a horrible choice. Why are you learning calc and what are you goals @gray gazelle
spivak is the best book for a potential math major for sure
This
Something with all the topics and necessary info to have a good understanding of calculus. Preferably better than the average calc student
but idk if its the best if all you want is to compute integrals quickly
yeah it depends on what you wanna understand
like if the “why” matters
Simply put I wanna kno more calc than my peers who r also taking calc 1 and calc 2
spivak
Then try stewarts book
spivak is a solid choice but thats a not great motivation hahaha
Something like transcendentals
lmao
do you want to know how to compute more integrals or
I mean i wanna know all calc 1 and 2 b4 I move on
just learn a bunch of dumb set theory and you can flex nonsense
I just mean I wanna do well in my calc class
yeah spivak is a good choice but honestly
whatever
And I wanna understand calc well
when i was practicing calculus the textbook i did practice problems from was stewarts calc book (any of them)
Spivak would be very difficult. Most ppl ik who used it already took a discrete math class
The problem sets from MIT OCW's single variable calculus course are very good.
I just realized how this sounds
I just meant I wanna know it and understand it well
i think you are too worried about book choice
Better than the average person
if you pick a book and hate it
then whatever find a new one
but youll be fine w basically any choice
im not really sure you know what you want well enough to determine if a certain book is more fitting for you than another
I heard Courant is also good
because "better understanding" is vague
like spivak will help you understand some theory better is what i hear
I mean the problem is "being good" is vague
then do spivak
right if you've already taken ap calc i see no reason to do stewart
If you wanna know the theory then Spivak is the objectively correct answer
Alr then I'll check that out
If you're more interested in computations but really getting good at them then... honestly any calc book works. Stewart at its sticker price isn't worth it. Tbh it's more at that point about practice problems than books
Is there a book u prefer
Some books would have better problems tho or even more problems
spivak for theory , lots of problems for computations
from various books
just prte them
shoot
Just use spivaks calculus on manifolds
p*rate
\s
You can find problems online. Stewart if you can get a used copy or [REDACTED FOR TOS] is probably good but no calc book is worth $200 lmao
who said piracy
i mean uh
i meant parote
parote.
porate*
How dare you
yes you should keep that as a secret
I guess for problems I can just find different books and do those problems
@lucid yew
But for theory spivak is good
i will also say that like
Exactly
Alr thx
breathe
unless ur training for an integral bee or something
calc 1/2 isnt that scary if you like math and are willing to do the work
It's becuz I don't want to have difficulty understanding math later on
Really?
Calc is dum
Linear algebra, on the other hand...
Spivak is kinda like baby analusis
Metal prove the mean value theorem right now or I'll make you do a backflip
I didn't understand trig well so I had tuff time with calc regarding those sections,, so I don't wanna have any issues with not understanding calc well
rolles theoem but u do cute subtraction
I also didn't understand some specific advanced algebra topics
?
Honestly there's a pretty easy flowchart for how to prove things
oh i was responding to daminark earlier human
The key point is intermediate and extreme value theorems
Is analysis the same thing as calc? I looked it up and it said it includes differentiation, integration, series, etc..
it is not the same
its about proving why things work in calc and putting everything on a rigorous foundation
So there aren't clearly defined boundaries here
We know what it is
Some people say calculus is just analysis without proofs
well that kinda makes sense but like even then analysis has so many things you won't see in a calc class
To me analysis is a broad subject, calculus is the part that's concerned with computations of derivatives and integrals
yeah it goes further
Depends what you mean
turns out if you dont spend months calculating convoluted integrals
you can actually learn
some math
Could someone just skip calc and do analysis?
yeah
Yea
it would be hard
Thay makes sense
but doable in theory
Just use spivak
Depends on your definitions, to me calculus is part of analysis. So at some point in an analysis class, if it's self-contained
Yes, but is better to understand some of the basic concepts then do analysis.
nah.
sure
If theyre interested in analysis spivak isnt a bad choice. They have computational problems too
You'll learn theorems like product/chain/quotient rule, u-sub, etc
I kno how to do those
That will come up in a self-contained analysis class and I'd consider that to be "calculus content"
nah
Assuming you're a high schooler @gray gazelle ?
9th?
analysis is a matter of perspective not material imo
Dam no
12
They don't teach calc at 9th here
You'd have to test out of classes or self study for that
Usually on this server, you have 6th graders do analysis
thats so false
Usually?
Fr
jesus calculus in the 9th grade
There's like
and also perpetuates an already unhealthy narrative
Theyre joking
< 5 people here who know calc in 9th grade
that causes young people here to have pointless an iety
these jokes have genuinely caused hs kids on here to be worried about only being 2 years ahead of their peers lol
Yea when I was younger and i read about terence tao I thought u had to be like him to be a mathematician lol
But in the USA. to get into college. you have to start taking rigorous courses in middle school
That's kinda bullshit lmao
this is also false
I learned calculus poorly in high school and only learned it well in college
I never took calc in high school
killerwhale you should stop talking about things you dont know anything about
its not good to misinform young ppl
im in college??? i didnt think of math at all until the last year of highschool and honestly i could have just left it at that
Like when I took the calculus placement exam in college I only placed out of one quarter of calculus
Yea i've learned calc poorly as well so I'm going to spend some time strengthening it during the summer
then I don't know why high schoolers are eager to start proofs in high school
Aka I knew differentiation well enough but not integration
???
interest?
And I went to a pretty good school, did well while there
no to draw attention
no one could possibly be interested in math, ever
Killer's just full of shit lmao
Same I don't kno definite integration well
nah
Yeah human I'm sure your progress is just fine
Thx
Yea human never mentioned proofs we mentioned spivak tbh
Again I didn't know the definition of the integral until college lol
I thought it was just antiderivative evaluated at endpoints
lol
it be liek that
oof. I guess I will be a bad TA this Fall in grad school
I don't remember the definition either but isn't it just the area under the curve
i bought nitro so htat means i can sully bomb
as someone who will also be a TA this fall in grad school: yes absolutely you sound like a horrific TA
Dam 🤣
you are free to sullybomb
rigorous courses
Speaking of TAing
I'm sorry to hear that. I mean I care more about my health than math. Health > Math.
That's good


society if
this is rich coming from someone who is feeding anxiety inducing nonsense
i care more about most things than math
Wait all mentally healthy people assume that high schoolers learning proof-based math is virtue signaling
Health is important becuz it can keep ur brain healthy and able to do math
Max this is common knowledge
Well, they take Algebra 1 in middle school.

They take Basic Algebra in middle school
im taking algebra 1 this fall i must be horribly behind 
Algebra 1 is a grad class at my school ffs

my goal is to be
i took multivariable analysis in my second year of schooling, catch up guys!!!!
oh wow
or even that good
Even if I am a bad TA. The only difference between TA and a student is has to grade. TA are still students and will have bad days. Unless you are uncomfortable with that then maybe TA isn't going to be good for you
yes bro
All of UChicago's undergrad course titles are so condescending
people under 18 doing proofs is just virtue signaling
"Basic Complex Variables"
"Probability for those who don't know how to wipe their ass"
Couldn't anyone theoretically learn calc very early if they know the prerequisites?
And even other math
Ah, must be taught out of Jacobson.
In principle
Republicans just made it illegal to do proofs under 18
I think when you learn calculus is largely random in a way
yeah but like ive found u need to have maturity otherwise to do some stuff 
Like some people look it up on Google young and are like :0 this is dank
r2t2 simps for discord
And get into it
i tried to self teach young
Other people just stumble upon it when they take a class on it
but got bored
The rush to calculus is real in high school. Why rush to calculus?
like you only begin appreciating things once you spend a little longer with the defns n stuff 
in my defense
If my school didn't spend so much time reteaching previous years and teaching stuff that didn't take long I'm sure everyone could've learned calc in 10th instead of 12th
Based. Teach hsers algebra
calc is boring
Killer depends on what you mean by "why"
Why do students rush? Why does education frontload calculus?
rush to calc is commonly frowned upon here and discussed in #math-pedagogy
i have that channel muted
By reteaching I mean they spend a month teaching content from previous year
😌
Students tend to rush to calculus because either they just like math and that's the standard accelerated math path
My school disnt offer ap calc we only had higher topos theory instead
Or they're told that to get into a good college they need to have AP everything
They rush because they think is a good approach into getting top schools. Every school thinks taking calculus 1 in high school will prepare them
Which is an unfortunate phenomenon but it happens
tfw knowing how to differentiate polynomials = good indicator of success
A lot of people in the calc classes I TA did some kind of AP in high school
Calculus is also useful in a lot of science and engineering disciplines
Now I actually thought AP was kinda pathetic because it's like, you're taking Calc 1 which is supposed to correspond to AB Calculus
And yet you're having a hard time
killer u know what you should do
yeah i mean it makes sense that they want to learn calculus cus of stuff like physics and chem maybe
but like
First semester of ap calc was pretty ez
idk maybe they should focus on teaching the regular math correclty before rushing kids to calc
halfassedly
The same is true of linear algebra, and surprisingly it doesn't see the same enthusiasm.
I rushed to do calc bc i thouught it was the end all be all
High school calculus $\neq$ college calculus
KillerWhale2498
Tbf UW's calc class is non-trivial but yeah I thought AP was just lol. Then I looked at some free response questions from the AP exam and tbh they don't seem like the worst
Then i stopped once i learned other math existed
Good morning.
cringe moderation team
Manan: I have actually said I'd rather frontload linear algebra than calculus
I agree.
ap linear algebra when
i would frontload stats
ap category theory 
Why so?
more important to have a vaguely data literate society
i also think stats is honestly more worthwhile
I would frontload machine learning and data science
than linalg

Jk thats cringe
statistical thinking is so important nowadays
stats is a pain
Id front load combinatorics tbh
at least for stuff on the news and all
be terrible
I'm currently taking stats and the subject is super interesting, but it is already assuming a theory-heavy calculus/analysis background.
like being able to understand expected value, basic probability, how to read graphs and look for manipulation in fitting
its scary how much data is presented oddly
I never took stats
MaxJ that's true, I guess I mean that I think linear algebra should be the default "I want to accelerate in math" choice
ok
right dami
While data literacy should be more "basic high school graduation requirement"
right
lol

++++heuristics about studies such as correlation, association, confounding factors can be stressed so that people think twice before accepting information.
I have no clue what precalc entails but tbh sure
precalc is just like
polynomials and trig
or something
idk
i didn't learn anything in precalc
Algebra is everything.
end me
precalc is commonly described as preparing you for the algebraic/analytic manipulations youll need in calc
but without any reason to it
That sounds boring lol
why did i even learn conic sections
it sucks
for the GRE
literally only used conic sections for obscure integrals in calc 3
Kindergarteners are combinatorists.
My high school math last two years was weird
WhAT
Fuck im not taking the gre
the GRE 😭
Only general 😎
Ooofffff
It was IB Math which had 6 topics
I never took the math GRE
metal theres a healthy chance youll never have to
never have to what
Why should I know what the eccentricity of a weird conic section is
That moment when you switch to cs theory to avoid math subject gre
take the mGRE
2.95 GPA got into a masters with TA. I mean anything can be possible
assuming youre interested in math idk
Lots of schools are getting rid of gre requirements
Just dont feel like wasting time on it tbh
integral tricks and nonsense
i don't really want to do the mgre
I still need to take the gen GRE if I want to apply to a PhD program
Michigan probably isn't bringing it back as a requirement
My friend got into cornell this cycle and he wouldve done horrible on the mgre
Some "algebra" (binomial coefficients), "functions" (graph of f(x+a) relative to graph of f(x)), trig, 3D vector geometry, stats, calculus, and an optional topic which your teacher chooses, either more stats, more calculus, discrete math, or "sets, relations, and groups"
Shows that it doesnt mean a lot
Grad admissions is random.



everyone is very different
