book-recommendations

[native cradle]

or are there better books out there

for problems Irodov in my opinion

[dim sierra]

could you? or would u be doxxing urself

[naive oyster]

Are there any legit free math books resources?

[sturdy shore]

how much do you know?

you need like, the first 4 chapters of his topological manifolds book

[gray gazelle]

what do you think about Introduction to partial differential equations by Peter J Olver?

[graceful moon]

I don’t think I should, not for doxxing issues but it just doesn’t feel right for me to share my professors work without his permission

[dim sierra]

Oh

[abstract copper]

I didn't even know he has a topological manifolds, but yeah I'll look over this book first.

[tribal crow]

it's more like a topology book with emphasis on manifolds

it does point set and then some basic alg top

[abstract copper]

Yeah it seems that way. But I'll probably go with Munkres instead if I have the time.

Probably just do the sections needed to Lee's smooth manifolds

[tribal crow]

I was thinking of doing the same with ITM

[trail hemlock]

lee my hero

[viscid oasis]

thank you very much!

[crimson leaf]

@remote sparrow do you know anything about the sale Springer is running it seems like some of the books have softcover 16.99 but other ones don't?

[remote sparrow]

there are books that have softcovers going for $16.99 regardless of their original price?

[crimson leaf]

https://link.springer.com/book/10.1007/978-1-4471-4435-9

It looks like his harmonic analysis books are also on sale

It looks like some universitext are on sale

[remote sparrow]

https://link.springer.com/book/10.1007/978-1-4939-2712-8

yeah abbott doesn't have that discount

it's only part of the yellow sale

or is it highlights

[crimson leaf]

Springer is so weird

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-662-48792-1

zorich's ebook is $16.99, but there's no sale on softcovers or hardcovers, and it's a utx

[crimson leaf]

https://link.springer.com/book/10.1007/978-3-030-43781-7

Yeah this one is

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-030-56402-5

klenke bucks this trend with a $29.99 ebook and a $39.99 softcover

https://link.springer.com/book/10.1007/978-1-4419-1221-3

another UTX with a $16.99 ebook but regular-priced softcover

https://link.springer.com/book/10.1007/978-1-4471-4558-5

at least this is on sale

[sturdy shore]

the first edition seems to be on sale but not the second

man that is sad

I really want that one

I guess it's not actually offered in softcover and that's why it's not on sale?

only the mycopy thing

man I really would have wanted rautenberg too

I'll consider klenke, and look for other good utx

[dim sierra]

huybrechets complex geometry is also on sale

[sturdy shore]

I'm looking at one of the utx books on sale, and this feels like a huge translation error right from the first sentence

I think this should be Hausdorff...

trying to prove a space is separable by finding disjoint neighborhoods for distinct points, makes sense

[sage python]

Deitmar?

[sturdy shore]

no

https://link.springer.com/book/10.1007/978-3-319-54375-8

[dapper root]

I think this is the term in some other countries used

Idk, like I would say that

Because I have been poisoned by the French

[sturdy shore]

it wouldn't be so bad (or maybe it would, this is springer we are talking about) if separable didn't stand for a concept in topology that meant something entirely different

nah, I can't excuse this

[dapper root]

I just looked it up lmfao

[sturdy shore]

who is proofreading this

[dapper root]

I forget that’s a term cuz my ass don’t be using that

[sturdy shore]

yeah, never use separable in exchange for Hausdorff lol

maybe do it in French

[dapper root]

Why the hell is separable called separable anyway

Countable dense set

Never made sense to me

Like I think a “separated space” means a Hausdorff space

[sturdy shore]

it's a terrible name but it probably made sense at the time

or I guess not

https://mathoverflow.net/questions/51494/why-the-name-separable-space

I don't think this makes sense

and it was actually coined by the French

[dapper root]

Sometimes we just cant let ppl cook

We gotta tel them that shit is jank

[sturdy shore]

Frechet's reputation just took a huge hit

at least in my head

what a blunder

[dapper root]

I’m sure he’s completely disheartened

I await the moment you teach pointset and go on a rant about what a huge L Frechet made to a room of 20 year olds like “okay grandpa calm down”

[sturdy shore]

tickled him in his grave

[dapper root]

https://tenor.com/view/tickle-tickling-tickle-armpits-gif-18925761

[violet shuttle]

My understanding is it comes from the special case of R, where it means that any two real numbers can be separated by, say, a rational number

Neat!

[naive trellis]

josh, bennett or peterson

[tribal crow]

eenie meenie miney mo

sorry, that wasn't said seriously

[naive trellis]

I need actual advise before I get send into ward

[tribal crow]

my apologies 🙇‍♂️

[naive trellis]

so I have a book other than cotton to entertain me

[tribal crow]

is it possible to get all three?

[novel hound]

I'm seeing this book (Automorphic Forms/softcover) for 15.88 Euros, but the discount gets revoked in the last stage of checkout (before payment). Wondering if it has something to do with region. Some other books I see the discount (flat 15.88 EUR) for are: Functions of one complex variable I and II (Conway), Number Fields (Marcus), Algebraic Number Theory (Lang), Classical Topology (Stillwell). I'd like to know if anyone is able to claim the discount.

[crimson leaf]

I didn't purchase but my checkout was weird basically I put the book in there the price it was asking me to pay was the discounted price but it showed the normal price

I had a similar problem with another sale by Springer so I think it might just be a bug with the site

[graceful moon]

Yeah I had the same during their last sale, I think all my receipts showed different prices but I was only actually charged the discounted prices

[sacred venture]

There is openstax
Open textbook library
Open access springer

If you want a free textbook you can search the subject you want and add free textbook or lecture notes

[graceful moon]

And if you’re affiliated with a uni you probably get a lot of free textbooks through springer and maybe other publishers

I also get loads of the Cambridge press ones

[drowsy thicket]

Also you have access to basically every research article through institutional access, right?

[graceful moon]

I think that also depends on the journal but yeah typically just being connected to university WiFi gets you most things

Eduroam is cool like that

[sacred venture]

Comprehensive analysis by Barry simon

Treatise on analysis by dieudonne

( I think neither of them are good for studying analysis, the first is great as reference)

[drowsy thicket]

You have to be connected to the university wifi?

But don't you just need to enter your user and password for institutional access?

[graceful moon]

I mean you can also just log in via your institution but if you’re on uni WiFi most websites seem to detect that

[drowsy thicket]

Ah

[graceful moon]

Either that or I signed into them all a long time ago and have gaslighted myself into thinking that’s how it works

[fresh skiff]

The later one has 10 volumes
And first one seems for graduate level.
Btw I found some good notes recently.

Using ross's book¹ as a reference along with Cummings for abbott is a good idea?

¹ Elementary analysis: theory of calculus.

[graceful moon]

Ross was the book my first analysis course used as a reference

Was pretty fine. I also imagine with a main text and another reference you’re already set and shouldn’t worry too much about how yet another book is lol

[sacred venture]

If you want to study analysis just a book and study it.

If you want some recommendations I like analysis by apostol.

And there a book called the story of analysis by robert rogers, this one only do convergence and does the ordering of subjects from historical perspective, it's very motivation orientated, also it's free (It's also has some Fourier analysis)

[maiden halo]

I liked Ross. it's a gentle introduction

[fresh skiff]

I understood it. Also when I took an overview it seems like abbott.

[graceful moon]

Yeah it’s a pretty gentle introduction similar to abbot

[fresh skiff]

I mean the sequence of topics and friendly

[fresh skiff]

Yes I am studying analysis.
I have 2 months of vacation. So my plan is to study Analysis and some other subject (maybe probability or linear algebra)

For analysis i was using abbott. I already studied 1 and half chapters but bcz if university exams I was stopped. So today (first day of vacation) I am doing revision of all old stuff.

[sacred venture]

Continue using abbott

[fresh skiff]

I did 1 exercise set completely. Now maybe I will look at Cummings book and ross.
Also will write notes.

[fresh skiff]

Okay. Thank you!

[ripe garnet]

any topology book recs

not sure i saw an undergrad one in the pins

just munkres?

[reef escarp]

what topics do i need to know before starting spivak's calculus?

[graceful moon]

My professor has reccomended the book “Introduction to topology and modern analysis” by Simmons before but I’ve not personally used it

[tribal crow]

knowing how to write a proof would be beneficial, but not strictly necessary

[reef escarp]

i think i am fine in that regard, was talking about the other prereqs

[tribal crow]

other than that, I can't actually think of many prereqs other than just generally being comfortable with proofs lol

[reef escarp]

no high school algebra?

[ripe garnet]

will check it

[tribal crow]

Spivak defines the trigonometric functions, exponential/log in the book

[tribal crow]

oh yes, that would be a prereq for sure

[reef escarp]

well, which topics to be exact

i am sure it doesn't need geometry, or prob stuff. not sure how much in-depth i need to be familiar with functions and all

[tribal crow]

it definitely doesn't use Euclidean geometry or probablility (though there's a tiny, insignificant section on conics)

Spivak talks about functions in chapter 3

[reef escarp]

so, what exactly do i need?

[tribal crow]

knowing about them beforehand would be beneficial

[slender cargo]

You should know some basic trigonometry

[tribal crow]

but idk if it's strictly necessary

[slender cargo]

It's rigorously defined... later

[tribal crow]

yes

[reef escarp]

how basic? sin-cos-tan basic, or inverse trig and all that shit?

[tribal crow]

but I don't recall having to use much trig knowledge before then anyways

[slender cargo]

sin-cos-tan basic is enough. Just know how they correspond to the unit circle

And even then, just have a basic idea

You should be good to go

[reef escarp]

is going through serge lang's book's chapters on trig, functions, quadratic equations, linear equations, inequalities sufficient?

[slender cargo]

Yes way more than sufficient

[tribal crow]

that's overkill lol

[reef escarp]

thanks, i guess, i only really haven't done functions, i guess i will complete it,

[slender cargo]

imo you just need to a basic idea of the stuff in Lang's book. The first 4 chapters of Spivak's Calculus will fill any gaps

[graceful moon]

I would also say do less worrying about what you might need and more just reading

You’ll quickly work out if you have the prerequisite knowledge and you’ll be able to fill in any small gaps

[reef escarp]

that tends to be the hard part, i procrastinate a lot.

[slender cargo]

If this is simply for self-study then I would just start on Spivak's Calculus

[reef escarp]

took me two months to go over serge lang's book, lmao.

[slender cargo]

No need to wait. Just take your time with the book

[graceful moon]

Well just launch the PDF, there isn’t much more to do about it

[slender cargo]

Oh you're way more than ready

Flip through the first 4 chapters and see what gaps you have

The actual material starts on chapter 5

[reef escarp]

thanks

will do

[remote sparrow]

by reference i assume you mean books you'll only dip into selectively. as far as references go, bartle and sherbert and schroeder are better organized.

[glossy zealot]

There’s a stark difference between Ross and Cummings book. Ross book has this Rudin flavor where he goes straight into the content, and the proofs are straightforward proofs.
For Cummings, he does motivations in many chapters, and his proofs also include details like what he is trying to proof (sometimes it is a bit annoying).
They are different so it is beneficial to refer to both of them.

[fresh skiff]

I was thinking to use it in systematic way not only in selective manners.
But i have a copy of bartle I will use it for a particular topic. Thank you

[fresh skiff]

Ah i see it. I haven't read Ross in a proper manner yet. But will start it from tomorrow (rn going to sleep maybe).
This is so informative. Thank you for this Dalliance.

I will use this strategy too. Then will figure which one is working for me.

Thank you guys

[remote sparrow]

https://en.wikipedia.org/wiki/Reference_work

A reference work is a non-fiction work, such as a paper, book or periodical (or their electronic equivalents), to which one can refer for information.[1] The information is intended to be found quickly when needed. Such works are usually referred to for particular pieces of information, rather than read beginning to end. The writing style used in these works is informative; the authors avoid opinions and the use of the first person, and emphasize facts.

[fresh skiff]

So overall, using a book as reference means using it for extra problems or further information about the topic?

[remote sparrow]

sure

basically you aren't working through it thoroughly

you dip into it to look something up

[fresh thicket]

is Abbott's Understanding Analysis a good book for someone who has never done analysis?

[fresh skiff]

I got it.

[fresh skiff]

Yes it is.

[tribal crow]

yes, it's designed for that audience, actually

[fresh skiff]

I am using Abbott for analysis. Like i started it recently

[silver stirrup]

It’s nice cuz it explicitly outlined proof methods

[covert mauve]

if anyone here has prepared for cmi/isi entrance exams, what are they like? what books do you recommend?

[slender cargo]

I think Cummings is a good book to look at if you're confused on a certain point. It has a lot of exposition.

When people talk of "references" I think they're more so talking about books they would use after knowing the material well.

I'm nearly finished with my school's Real Analysis sequence, and Rudin's book is pretty nice to look at now if I want a concise view of a proof.

It would not a be friendly "reference" for learning though.

We used Cummings as the class text for my class, and I had Bartle on hand also. Bartle was actually nice for filling in some details that Cummings missed, but Cummings had more exposition.

[gray gazelle]

ODE books recommendations?

My prof asked me to go through a PDE book but It had ODE as perquisite ( pretty intuitive )

[stone axle]

Check out the one by Morris Tenenbaum, kinda old but very good imo

[gray gazelle]

did u use it?

I saw ur message when u asked for recommendation on that as well

[stone axle]

im actually reading it rn

[gray gazelle]

so how is it so far

btw , I am only required to finish calc 2 for that

no multi required , right?

cuz I only finished a very few things in multi

[stone axle]

it's especially so good if youre in applied math, physics or engineering

[gray gazelle]

Idk if I am in applied or pure yet

I want to do pure

but my math maturity is still lagging

I only did mostly computational linear algebra course

and I am not into physics but kinda into engineering

don't ask how

I have done general phy 1 and 2 and I am done

I don't want to do any more of it

[stone axle]

the book already explains any concepts you'll need, you can skip it if you already know it

[gray gazelle]

these are the concepts I did in multi

[stone axle]

not much multi no

[gray gazelle]

tangent plane
gradient
multivariable chain rule
Constrained and unconstrained optimization
Double integrals including polar coordinates

thanks very much

[fluid aurora]

What is the name of the book?

[gray gazelle]

the ode book?

Ordinary differential equations by Morris Tenenbaum

[tawny copper]

uh so there is a sale on springer now?

[remote sparrow]

besides the yellow sale, some books in the universitext series appear to have ebooks and hard copies on sale, but i haven't seen any official announcements from springer's twitter or their websites. some books aren't on sale, and some only have discounts on ebooks, and some have different discounts.

[tawny copper]

well, Weil's basic NT is on sale

I think I will buy it this time

[sturdy shore]

I tried buying a book on sale and this happened

[tawny copper]

imagine if this costed 16 euros https://link.springer.com/book/10.1007/978-3-662-12893-0

[tawny copper]

I have it from my library, and besides the content, it is the best springer book edition I have experienced. It stays flat open from the first page, and it's actually light for its size. Also the cover is really cool

[sturdy shore]

...like

I'm not gonna try ordering to see if it charges me 90 or 20

[tawny copper]

By the way, is this the most expensive single book from springer? https://link.springer.com/book/10.1007/978-3-319-03940-4

[sturdy shore]

holy shit

1734 pages

[remote sparrow]

i had an issue with springer when i ordered from them during last year's holiday sale. three months after i ordered and received their products, they emailed me saying my credit card didn't go through. yes, i checked that it wasn't a phishing scam. like wtf

[tawny copper]

about 2.8 € per page

wait

I did the math wrong

its late, I won't bother xD

[sturdy shore]

it's just 700/1734, not the other way around

[tawny copper]

I sps I meant to say 1 € per 2.8 pages

about that

[sturdy shore]

0.4 usd per page, idk what the price is in euros

600?

[crimson leaf]

Is there a list of the yellow sale?

[tawny copper]

I don't have this issue

[remote sparrow]

https://docs.google.com/spreadsheets/d/19No2ABS5O2ZW8U0XUfhBQrOiLP4bjF0R/edit#gid=1063951618

https://drive.google.com/file/d/1dTZMe-ZvqGrAUTdcBrZxiWZdYWE5WPoy/view

same thing but in pdf format

https://www.springernature.com/gp/booksellers/sales-campaigns

[crimson leaf]

Oh nice thank you

[remote sparrow]

you can always see which books are on sale (at least officially announced sales) from the last link

[gray gazelle]

What are the most expensive english springer books?

[novel hound]

You can try the next step. At this step if I select credit card and then checkout, the page refreshes with the discount removed and asks for my credit card number (which I obviously then don't give) and I safely give up at that point.

I've sent them an email about this but they usually don't reply over the weekend...

[dry remnant]

please recommend books for isi entrance

[earnest wolf]

for me it's 695€ lol

[humble rain]

Is there some book to learn the essence of everything

Perhaps even advanced topics

I just want to know how it feels and how its gonna be

[lime vessel]

Evan Chen's napkin

Though mostly very surface level

[humble rain]

Great

That's kind of what I want right now

[still panther]

princeton companion to mathematics i guess

[humble rain]

I don't really have the time to go deep

So that works out

[humble rain]

Alright I'll check it out thanks

[lusty escarp]

John Lee is dropping a new book on complex manifolds.

[tribal crow]

Exciting!

is there an an official announcement?

[lusty escarp]

https://bookstore.ams.org/view?ProductCode=GSM/244

[heady ember]

[naive oyster]

thank you! 🙂

[vast jackal]

hi give me a good book algebra 1 and 2 up to precalculus and not too focused on rigor or anything

just a strong foundation

[terse garnet]

YOOOOOOOOOOOOOOOOOOOOOOO

What book to learn calculus fast

[native cradle]

for problems or concepts ?

[vast jackal]

is it more better than khan?

[terse garnet]

concepts

[native cradle]

no idea then, sorry

[drowsy night]

guys im in algebra 2 and am taking a placement test soon so i need some books to cover like the whole thing
my teacher is terrible

any recommendations

[thin kernel]

Any recommendations on learning geometric measure theory or measure theory on any manifolds?

[jolly coral]

Hello, I recently started reading about laplace transform but im getting confused with the frequency could anyone suggest me any book to read ?

[violet shuttle]

GMT - Evans has a book

[grand thistle]

krantz/parks is one that i used

leon simon is like krantz/parks but more detailed

federer ofc for reference

others recommend matilla, evans, or maggi, but i havent used them before

[karmic tangle]

Hello, could anyone recommend me a Set theory book?

I have a set theory course this semester where we went through the standard zf axioms, stuff related to ordinals/cardinals and choice and some statements equivalent to it and I was wondering where to go from here

[small violet]

where are you from?

[karmic tangle]

czechia

[small violet]

ok ill dig

[karmic tangle]

Supposedly the prof also went over some stuff related to finding models of the theory but I missed those lectures, I thought maybe I should now read a book on logic or something before proceeding further?

I wouldn't mind a book that presupposes some of the knowledge (but doesn't have to) that I'd mentioned but has lots of exercises so that I can get properly comfortable proving the kind of statements that come up

I tried Sets, Logic and Categories but felt like it went too fast? Like more of an overview/review kinda thing. And regarding Logic I'd wanted to go with "A Friendly Introduction to Mathematical Logic" plus some lectures we have on the topic I guess, so idk if to read that first or a set theory book

[small violet]

im currently in india

i have a book given to me by my yk training institute

it has the set theory chapter

not so in dept

but good for revision

lmk if you want the chapter, ill send pics

[still panther]

if you want to study actual set theory (i. e. stuff other mathematicians dont actually care about), the popular choices are Kunen and Jech. my personal advice is Levy's book though

[small violet]

also have you read naive set theory by halmos?

its also a good book

[drowsy thicket]

stuff other mathematicians dont actually care about

Are there really so few mathematicians specializing in set theory?

[karmic tangle]

I've read like 1/3rd to a half-ish of it? I had problems with how he didn't use mathematical notation for condensing his statements, which at one point were like 5 lines tall iirc of "such that... for which... so thath any... is such that..." and so on and I reread it like 30 times and still couldn't parse it and at that point I stopped

[small violet]

No shit i understand many people have that kind of troubles with that book

[rigid forge]

are there any books that go beyond the high school perspective of polynomials? i am not sure what I am exactly looking for, but I'd like to learn more about them.

[still panther]

set theory and logic is to math what math is to the rest of the world

they reap our results and then tell us our shit is esoteric and boring

[karmic tangle]

yeah I'd like to get into actual set theory, I'd like to overview and get comfortable in the foundations required for this course first and then learn about the other topics

[daring lake]

I guess you want to read into abstract algebra
Dummit and foote or m. artin books are good

[still panther]

then i would take either Kunen or Levy

[small violet]

good books true that^

[rigid forge]

thanks

[karmic tangle]

The author claims to cover "basic" material at the beginning of this book. Actually you need to read at least two or three really basic books before you start trying to read this one.
this is from a review of Levy, do you think my "background" is enough?

correction Levy not Kunen

[karmic tangle]

imo try taking a look at Algebra: Notes from the Underground

by Aluffi, I haven't read this one but his other book is great (from what I've read so far and from others' reviews as well) and this one too I have heard is very very good

[still panther]

i mean idk there are technical considerations in the beginning of the book that require you to be pretty comfortable with first order logic but beyond that the book builds from first principles, i didnt have any trouble personally

if you already had a set theory course id say you are more than ready

[karmic tangle]

alright thank you, I will go with that then

and it's a Dover book

[heady ember]

No need to do dove into your pockets

[karmic tangle]

fourhead

why is there no fourhead emote

[native cradle]

TOMATO, by ISI

[lusty escarp]

Bachelor or Masters or PhD?

[deep nebula]

since people are answering questions about isi, how hard is the entrance exam? and what topics would you say you need to know in depth?

[native cradle]

Wrote it today, NCERT based , but olympiad level

revise calculus and number theory for sure

NCERT based as in nothing outside of NCERT except modular arithmatic is required IMO

revise 10th grade geo too

[deep nebula]

do the questions test your problem solving skills, or logic skills? how different is it compared to other entrance exams?

[native cradle]

I didn't do great, so I can't vouch for this

[native cradle]

very conceptual

and solve tomato

[deep nebula]

well, i am starting 11th this year, and wanted to give it a try.

[native cradle]

well, prepare for IOQM first then IMO

and solve class 10 olympiad problems

[deep nebula]

isnt preparing for the computing olympiad a better idea?

[native cradle]

for instance this olympiad problem came today

[native cradle]

not sure tbh

[deep nebula]

https://www.iarcs.org.in/inoi/ nvm, seems like its only for cmi

my only problem with inoi is the cpp requirement, i am too lazy to learn a new language, specially a one with as many quirks.

[native cradle]

I'll link to ISI's website

https://www.isical.ac.in/~admission/IsiAdmission/PreviousQuestion/Questions-BMath.html

see this

[deep nebula]

slow af

[native cradle]

true

https://www.isical.ac.in/~admission/IsiAdmission/PreviousQuestion/UGA-2024.pdf

is this faster?

[deep nebula]

are you planning on giving the cmi exam aswell?

[deep nebula]

yep

[native cradle]

most probably no, way too hard and IISER is my primary target

want to minor in a natural science

and major in maths

I've applied for cmi but let's see

[deep nebula]

i would like a good more research-inclined college for cs, but i am not sure what choices i have

[native cradle]

IISc?

They have maths and computing

[signal kettle]

which book is this?

[native cradle]

A question paper

from an exam I wrote today

ISI UGB

[deep nebula]

i have seen similiar problems in a few pure math books i have been checking out, looks fun, but hard.

[signal kettle]

yea I am going to start preparing for ISI too

[native cradle]

buy TOMATO

[deep nebula]

too hard

[native cradle]

Test of Mathematics at the 10+2 level

it's by ISI

[native cradle]

good luck

[deep nebula]

yes i have heard, i will try them after i am done with spivak

[signal kettle]

how different are the questions from standard JEE questions?

[signal kettle]

thanks

[native cradle]

more concptual

so no tangents nonsense

[deep nebula]

though, iisc have way more students than cmi and isi, so getting accepted might be easier.

[signal kettle]

I can approach them after doing theory directly or do I need to do something more?

[deep nebula]

not that i am confident enough for either of them

[signal kettle]

the JEE A is required for btech

the cutoff was around 700 I think

[deep nebula]

aw

[deep nebula]

cough

[native cradle]

mostly , you need number theory though

modular arithmatic

[signal kettle]

same I am targeting IISc tho so don't know how to manage preparation for both

[swift mountain]

is schaums outlines good for prepping for classes like discrete math and linear algebra?

[signal kettle]

any standard textbooks for it?

[deep nebula]

are there no colleges besides iisc and cmi which offer cs related courses and are research-inclined?

[native cradle]

no idea, sorry

[native cradle]

post that as a question here

this is getting off topic for this channel

are the mods fine with this?

[deep nebula]

i hear Elementary Number Theory is recommended a lot

[signal kettle]

well asking for standard textbook does not seem like out of topic for book rec

[signal kettle]

it has theory and problems or only problems?

[deep nebula]

the former

[signal kettle]

oh alright thanks

[deep nebula]

i think the recommendations for number theory are pinned, maybe check them out

[dry remnant]

bachelor

[dry remnant]

yes but isnt that the last book to prepare for? like which books explain the concepts?

[native cradle]

NCERT for calculus

[dry remnant]

ok thanks. anything else?

or is it all encompassing?

[native cradle]

Not sure for number theory

[lusty escarp]

There is also this book Educative JEE Mathematics by KD Joshi and his commentry on previous year exams.

Also, you don't need to solve all problems to qualify for isi bachelors.

[dry remnant]

then?

[lusty escarp]

Point is rather than trying to spend time to learn some fancy topic, focus more on topics that know from class 11-12 and jee prep.

[remote sparrow]

#book-recommendations message

[remote sparrow]

wait so you did this stuff already, like an axiomatic treatment or a naive one?

you might get some benefit from dipping into the later chapters of hrbacek and jech

but you should probably study some logic, then get into kunen or jech for further reading

#book-recommendations message

here are some logic books you should consider reading

[remote sparrow]

kunen has an older book, Set Theory: An Introduction to Independence Proofs, which is a little easier than his newer Set Theory as it does not assume you have previously had a course in logic

as for levy, he's rather terse

https://maa.org/press/maa-reviews/basic-set-theory

[remote sparrow]

yeah

[heady ember]

He also has a prequel book called The Foundations of Mathematics

[remote sparrow]

yeah, kunen's Set Theory assumes you've read that book already or some equivalent

[heady ember]

Yes

[remote sparrow]

https://maa.org/press/maa-reviews/topology-of-numbers

[swift mountain]

ànyone have practice books for multivariable calculus

[cunning elk]

it’s rather boring but Stewart has a ton of exercises

(not particularly good quality though)

[swift mountain]

alright

is schaums outlines good

im planning on prepping for calc 3 over the summer im taking it during fall

im 90% sure that my university will use stewert if not thomas

[drowsy night]

anyone have good books to review all of algebra 2
and then one for more nuanced things in algebra 2

[cunning elk]

i learned calc3 out of Stewart, it’s ok ig if you take good notes and read thoroughly

[cunning elk]

use KA to find which topics you most need to review?

[drowsy night]

oof i dont have enough time i think

maybe just the most important things then?

[cunning elk]

they have a diagnostic test you can take

[drowsy night]

ok

th

thx

[balmy crown]

Someone reccomend me a good Real Analysis book for the summer to self teach. I'll be taking it this fall.

I'd prefer one that just spoon feeds me the ideas

[abstract copper]

Abbotts understanding analysis

[fierce hedge]

Only if IISER didn't force you to study all the subjects for 2 damn years.

[uncut venture]

any one know any good books for counting problems? need a book that holds the readers hand

[fierce hedge]

BITS does that a bit but it's not primarily research based, they'll allow you to do research and from what I've heard there's no attendance so you're free to do as you like.

[heady ember]

Schroder

Pros and cons of Schroder: #book-recommendations message

[formal bronze]

The old IITs have CS programs, and a nontrivial amount of undergraduate research goes on in their CS departments

[glossy zealot]

Grass gave a solid recommendation, however if you are interested in some topology on the real line, either Abott or Jay Cummings will cover them.
I think Abott has more content regarding topology

[balmy crown]

I'm assuming while the base idea is the same for all these books there are some differences in styles and some things covered that aren't in others?

[glossy zealot]

There are different ideas here and there, or different notation

For example, books can have different approach to the first chapter, which is the property of real numbers

They can introduce different constructions of real numbers, or skip it

Then when we move on to integration, a lot of books will introduce Riemann integral, while Jay Cummings, the book that I studied, introduced Darboux integral

Another thing is a book with some topology will approach some concepts in the context of sets and limit points

Oh I am talking about the basic chapters btw, Schroder has way more stuffs than the other books

[balmy crown]

My math will stop at real and numerical analysis so I won't need to much topology

There's just so many choices to choose from...

[slender cargo]

If you're self learning to prepare for Fall then imo take Jay Cummings Real Analysis

That book has a ton of exposition

[glossy zealot]

The topo I mentioned is topo on real line

At least in Jay Cummings, the author approaches some concepts using topo, and it is very intuitive

[balmy crown]

What's yalls opinion of Taos Analysis 1?

[glossy zealot]

It is very thorough on the foundation. The analysis part will after few chapters

There is one person in this discord server using that book

@quiet wave you can ask him, he actively and diligently works on it

[quiet wave]

@glossy zealot thanks for the shout 🙂

@balmy crown I'm on Tao 2 now, I enjoyed the first book, Tao has good exposition but is still rigorous. Book 2 has more analysis meat.

[balmy crown]

Thanks for letting me know. I was on the fence about it since the author mentioned he'd leave some ideas for the reader to solve on his own.

I'm not lazy, I'm just trying to find something to finish in 8 weeks to prepare for my real analysis class in the fall

[glossy zealot]

Do you know the content of your class in Fall?

Might want to choose something with similar content

[balmy crown]

https://mathematics.jhu.edu/online/upcoming-courses/

I can't upload the syllabus here but if you got to Real Analysis I it will have the syllabus

[vast jackal]

precalculus by james stewart or basic mathematics by serge lang what's your preference and opinion?

[rigid forge]

does anyone have a idea/book on how I can improve my problem solving skills? i can solve a problem and use that "experience" to solve similar ones, but solving new problems with new concepts without any hints is almost impossible for me.(and I am not very patient)

this problem is specially prevalent when I am doing olympiad problems or trying to prove new theorems, I have no idea how to approach things and my patience gets the best of me

[quartz agate]

guys can anyone suggest a good book on linear algebra (im a begginer)

[gray gazelle]

Stephen Abbott is better for baby RA

[gray gazelle]

Sheldon Axler

linear algebra done right

[quartz agate]

thanks

also does anyone have it on pdf

[fresh skiff]

I guess his book is free. You can very easily find it on Google

[stone axle]

I need a vector calc book that I can speedrun

Im using the knowledge to fill a math gap in another fluid mechanics book, not really for a math course if that helps

[pseudo heart]

does anyone have a differential equations book recommendation? i want to try and learn them this summer through self studying

[marsh ingot]

Evans

[karmic tangle]

Well idk, what even are the differences?

We were told we'd do naive but we went through the axioms one by one (and then ordinals, apparently they also did something regarding models of the axioms but I wasn't present for those leftures), is that naive still?

I baughted Lévy yesterday, should I cancel it still or something? XD

[remote sparrow]

imo it might be a good reference/follow-up to enderton, goldrei, or hrbacek and jech, but a bit too terse to learn from for beginners

you should also be familiar with the language of first-order logic, but you don't need to know anything from model theory

jyou'll need to know what a term and free variable are in logic

[karmic tangle]

So many choices

[still panther]

i appreciate levy because its not as terse as first chapters of jech (which are borderline incomprehensible if you dont know the stuff beforehand)

if first chapters of jech werent what they are one might as well do jech

levys maybe less than ideal for an absolute beginner, but more than adequate for a person who had a course in naive set theory

[fresh skiff]

You mean for PDEs right

[dry remnant]

but those will be useful anyway and i am not doing jee prep, so i need to learn the topics i think

[prime dune]

I am probably going to be finishing Abbott Analysis in the coming month, and I intend to do either a real/complex analysis textbook (papa rudin), a measure theory book, or a topology book. I prefer “challenging” textbooks with difficult exercises that still explain the content well, like for example baby Rudin

Is there a recommended route and textbook? I’d definitely prefer measure theory

[native cradle]

eh, I like physics maths and biology, so it's fine

though I hate chemistry

[fierce hedge]

Liking physics and biology but hating chemistry is one hell of a combination lmao

[stuck zephyr]

Can anyone recommend a me book about vectors in calculus I?

Looking for best book that explains them better vectors R² and R³

I'm currently have a Nelson textbook but it's suck

[brazen rivet]

Could anyone recommend a textbook on teaching lagrangian and hamiltonian mechanics, but written for a mathematician-inclined audience rather than physics-inclined?

[tribal crow]

Arnol'd's Mathematical Methods of Classical Mechanics covers Lagrangians in part 2 and Hamiltonians in part 3

Spivak also has a book called Physics for Mathematicians: Mechanics I which does Lagrangians in part 3 and Hamiltonians in part 4

there's likely more sources, but those are the first two which come to my mind @brazen rivet

[brazen rivet]

im looking at Arnold's book now, and quite like it actually

[tribal crow]

[brazen rivet]

but thank you, ill check Spivaks out too

[remote sparrow]

https://bookstore.ams.org/view?ProductCode=CHEL/364.H

maybe this?

arnold is standard tho

[tribal crow]

how about chapter 2 of this book by OpenStax?
https://openstax.org/books/calculus-volume-3/pages/2-1-vectors-in-the-plane

2.1 through 2.5 looks like mostly the same material covered in the Nelson book

[stuck zephyr]

I think this one is better than nelson

teacher doesn't use the book anymore

[balmy crown]

two chapters in and im already infuriated with Taos Analysis I book. It covered notations like := which didnt take the time to explain. Yes, its a simple notation but if it doesnt cover things that isnt common outside of its prerequisites than its not worth reading.

Lets hope Abbott is better

[native cradle]

I like evolutionary biology, lol

[fierce hedge]

Huh I thought I got a ping from you

[karmic tangle]

hmm so I think I can't cancel it though

Jech costs about 10 times as much as Levy here also

I don't actually know, how much overlap is there between these kinds of "usable-as-semi-kind-of-introduction" set theory books?

[remote sparrow]

jech obviously has more advanced material than levy, and it uses model-theoretic methods in parts II and III

[karmic tangle]

we have enderton in my uni library or I could get kunen's (set theory or foundations of mathematics), goldrei was kinda too expensive iirc

[remote sparrow]

you can borrow enderton from the library

[native cradle]

asked if you study at IISER

but felt that may doxx you

[fierce hedge]

I studied at NISER, it's close relative

[remote sparrow]

if you're okay with a terser introduction to logic, you can get both kunen books; they're meant to go together

[native cradle]

woah

that's way harder to get into

IMO

[remote sparrow]

maybe do friendly introduction to logic + kunen foundations of mathematics then do kunen set theory

[fierce hedge]

Let's talk in discussy instead

[native cradle]

sorry

yeah

[remote sparrow]

kunen's Foundations of Mathematics has a very terse introduction to basic axiomatic set theory; levy is terse too but more detailed. you can borrow enderton's Elements of Set Theory from the library @karmic tangle

[karmic tangle]

hmmm

what about friendly logic into levy?

[remote sparrow]

that can work

[karmic tangle]

or maybe I do Enderton since I also need to brush up for the exam and then I can do friendly logic and levy

[remote sparrow]

levy has no material on forcing or model-theoretic methods, so you need to pick up kunen or jech some time

[karmic tangle]

ah but it has some other stuff that kunen/jech don't?

[remote sparrow]

levy has applications to other parts of math. not 100% sure if there's overlap between kunen and jech regarding those applications

but you won't learn forcing from levy

that's kind of the foundation for advanced set theory

it's not like levy is going to be a waste of your time though

[remote sparrow]

maybe prepare for your exam first

[karmic tangle]

well I kinda wanted to go through some book for that

we have lecture notes but they're just 34 pages of mostly definitions and proofs

I went to about 2/3rds of the lectures but I feel like if there's motivation/explanation to go along with the stuff I'm learning if anything it'll help me refresh stuff and the whole ordeal is going to take me a shorter amount of time than studying just from those notes

[deep nebula]

What's a good introduction to set theory? beyond the very basic stuff(sets, subsets, different operations, all that bs).

[remote sparrow]

#book-recommendations message

[deep nebula]

how many books have you read in your life? you might be the most active person in this channel. thanks!

[vast jackal]

surely @remote sparrow is the google of this channel

[dense plover]

does anyone know if a series of lectures based on aluffi exists online somewhere

[gray gazelle]

Guys what some good books to learn maths. I am naturally good at it but don’t know any books apart from school books

I want to learn trig, calc, intermediate+ algebra

[crisp spire]

everything you neede to know about mathamatics in one big fat notebook

[fickle granite]

Has anyone gone through Steinberg's Advanced Calculus? Would it be recommended for someone who has taken undergrad calc 1-3 as a more rigorous basis that can then be used to eventually start learning diffgeo?

Loomis and Sternberg*

[sturdy shore]

wouldn't recommend that book if you haven't studied real analysis in one variable

[strange owl]

For studying infinite series, summation notations, all that good stuff, do you guys have any book or learning website that really goes in depth and is great for first timers?

[gray gazelle]

what is a good book on history of math that also covers Asia? And that is actually a history book, not a math textbook

[remote sparrow]

#book-recommendations message

#book-recommendations message

https://www.amazon.com/Mathematics-Egypt-Mesopotamia-China-India/dp/0691114854

[inner iris]

Any books for machine learning for beginners?

Also books like math for machine learning

[vast jackal]

@remote sparrow is basic mathematics by serge lang good enough for prerequisite to Calculus by MIT OCW?

[tribal crow]

Lang is good yes

it might even be overkill for calculus actually

[vast jackal]

damn

i just want to be pro in math soon

[remote sparrow]

more than enough

[vast jackal]

so i can be in the pro max level

it's in pre-order now

[tribal crow]

good luck

taking another look at Lang's contents... yeah it's an overkill LOL

half of the contents wouldn't even be necessary to do calc

[vast jackal]

i get overwhelmed by other books because they have lots of pages

and i like serge lang because of the simplicity and fewer pages (not really few but others have 1000 pages)

[tribal crow]

in general, math books get shorter as you go further

[vast jackal]

what?

[tribal crow]

300 - 600 pages is pretty common

[tribal crow]

huh?

[vast jackal]

half of the contents?

[tribal crow]

it was a hyperbole

but a lot of the content isn't strictly needed for calc

[remote sparrow]

yeah, authors like to respect your time. that's why the best books are the shortest ones, so you can learn things with less reading

[vast jackal]

what's the other contents for?

[tribal crow]

I choose Spivak because it's 130 pages

lmao

A&M is similar in size too

[vast jackal]

i dont like the modern books style

[tribal crow]

maybe I'll read it eventually

[vast jackal]

when i read at my phone it's too small

[tribal crow]

it's foundational in other ways, or for other areas of math

besides calc, that is

[vast jackal]

well I'm planning to do calculus based physics

[tribal crow]

I see

Lang has a chapter on determinants

that would be part of linear algebra, which is extremely useful in physics

quantum mechanics is mostly linear algebra

[vast jackal]

what's better about the book is it have some guide on YouTube lol

[tribal crow]

complex numbers are used all over QM too

[vast jackal]

aight I'm just gonna wait

[tribal crow]

you should become geometry pilled so you end up learning diff geo, then onto GR

[vast jackal]

~~ I think i will become a polymath ~~

[tribal crow]

I will say one thing about physics books

most of the intro physics books kinda suck

[quick bridge]

RD SHARMA

[tribal crow]

not as in they're written terribly or w/e

[quick bridge]

HC VERMA

[vast jackal]

HRK fundamentals of physics is good

[tribal crow]

but because I feel like intro physics is a bit of a waste of time lmfao

[vast jackal]

nah i will be doing Ipho

[tribal crow]

I see

good luck with that!

for intro physics stuff, I'd always recommend David Morin's Introduction to Classical Mechanics

take it with a grain of salt though, since it's just my opinion

[vast jackal]

lagrangian methods

[vast jackal]

most people in Phods recommend it for mechanics especially their method

[tribal crow]

or, you could always read L&L or Goldstein or Arnol'd

[tribal crow]

glad to hear that I'm not insane

[quartz agate]

what type of math do i need to start learning linear algebra

[remote sparrow]

while calculus is technically not required to learn most topics in introductory linear algebra, many books assume you have learned calculus and have the maturity that comes with completing a course in calculus. many draw on examples from calculus. and you must know calculus to understand inner product spaces.

[tribal crow]

totally not me brute forcing LA with little calculus knowledge

I think doing LA and calc simultaneously is a not a bad idea either

though yes, LA books like to use examples from calc, so it's a good idea to have some calculus knowledge going in

[hallow oriole]

i think calc 3 and linalg should be done simultaneously

[tribal crow]

agreed, LA should not be done after calc 3 at the very least

I think doing it simultaneously with calc 1 is doable, but it might be a better idea to do it with calc 2 instead

[violet shuttle]

I'll recommend Shankar's Quantum Mechanics

[violet shuttle]

But for Classical Mechanics, Goldstein is fucking amazing

[violet shuttle]

nothing but a basic facility with algebraic manipulations

[heady ember]

FIS hasn't used any calc examples 5 chapters in. I think the only time I recall seeing it, when randomly flipping through the latter chapters, was the part that used some multivar

Ok well there were derivatives and integrals as examples for linear transformations

Things along those lines; but not very heavy calc. I never needed to do any funnei integration

[halcyon grove]

do you guys know any good books to get into programming for robotics? I did calc 1 linear 1 intro java and took physics in highschool

[late mica]

is there actually anyone helping for maths

this severs changed alot

[heady ember]

!help

[hybrid sparrow]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[heady ember]

You have the studying role 🗿

That's probably why you can't see the channels

[brazen tapir]

hi, i need recommendations for combinatoric and algebra book
i feel like i need to build intuitions but still not having the best idea of how to do it, anyone got tips?
i like books like modern olympiad number theory or EGMO by evan chen

[glossy zealot]

Guys Axler vs Friedberg for LinAlg, which one should I choose if I want to study it as a second course in LA?

[tribal crow]

indeed, FIS doesn't use too much calculus up to that point

their chapter 6 uses lots and lots of it though (as examples/exercises)

it's hard to talk about general inner products without any calculus

[heady ember]

Oh really? I see

Oops sorry for the ping; forgot to turn it off this time.

[tribal crow]

dw about the ping

I don't mind

[young grove]

Suggestions for good books on set theory

Prefer if it had more problems to work out

But yeah, the main priority is to understand set theory.

[remote sparrow]

they both serve that purpose. personally, i prefer axler

[glossy zealot]

Thank you!!!

[tribal crow]

damn, missed an opportunity to shill FIS

[sage python]

Never too late to shill your favorite stuff

[tribal crow]

maybe @heady ember can do it on my behalf

[formal bronze]

Kunen

[fresh skiff]

Friedberg if first in linear algebra. Bcz his book contains both computations and proofs. On the other hand, axler is master piece. But his flow seems fast to me.
||I studied 1st chapter of both. But bcz of some issues i stopped LA and started analysis||

[twilit zealot]

can someone suggest me a book to learn mathematical analysis as a beginner

[remote sparrow]

#book-recommendations message

[lusty escarp]

Learn robotics first. You can also robotics discord server. https://discord.com/invite/zkd5z9dV

[halcyon grove]

thanks Ill check it out

[wispy phoenix]

does anyone have a concise yet rigorous book for introductions to proofs and logic? (i dont want it to cover too many unnecessary things, but not skim on too many less important things aswell)

[graceful moon]

#proofs-and-logic message

[wispy phoenix]

that is quite short, it feels more like someone's notes.

[brittle portal]

Hi guys i'm looking for the best book about differential equations to partial derivatives

[graceful moon]

You asked for concise. You also don’t need anything else for an introduction to proofs

Once you have read that you have all of the knowledge needed to just jump into a textbook on linear algebra or analysis

(Or whatever other introductory topic you’re interested in)

[wispy phoenix]

well, I did. but I was also looking for something with exercises and stuff, but if you say its sufficient, .

do you have any recommendations on books for introduction to real analysis? (assuming no prior calculus knowledge, only high school algbera)

[slender cargo]

No calculus knowledge at all? Check out Spivak's Calculus

Which is an introductory Real Analysis text. Just named Calculus

[gray jungle]

id recommend taos analysis I

[graceful moon]

Abbots analysis book is good, as is Taos. Ross’s is decent too

(If you just look up their name followed by analysis you’ll find the book, I forget the specific titles)

[slender cargo]

The thing about Real Analysis texts is they generally won't give much motivation for why the derivative and integral exist. They assume you already understand why they were developed. Spivak will give that motivation.

[graceful moon]

Oh I missed the thing about not knowing calculus, yeah I’m less sure about that then

[slender cargo]

Then imo you should check out the book I recommended. You can theoretically learn Real Analysis without any motivation for why it was developed, but why would you want to?

[gray gazelle]

Hi I was doing apostol calculus and I was really struggling with proofs what do you recommend to be able to do this book and be able to do the proofs correctly.

[graceful moon]

I would also just recommend learning calculus, it’s useful to know how to compute derivatives and integrals and gives the motivation for analysis

[slender cargo]

Spivak's Calculus was made as an introduction to proofs, so just jump right in. Keep the reference for proofs that @graceful moon mentioned on hand while reading the book.

To be clear, Spivak's Calculus doesn't actually go through truth tables, any formal logic, etc. He appears to think that learning proofs by doing them is the way to go.

[graceful moon]

I would probably tend to agree with him, I think anything more than the document loch wrote is pointless

You don’t need to suffer through how to prove it or anything to learn to write proofs. I think you learn to do that far better by reading and writing lots of proofs as you work through a textbook

[slender cargo]

Spivak's Calculus will provide all that, but I don't know of any lectures to accompany the book.

It's literally (introductory) Real Analysis plus Calculus stuffed into one book.

[gray gazelle]

How would you learn proofs running through a textbook if you have nothing to base it off of

To know if your correct or not

[slender cargo]

You read the author's proofs and try to emulate. Spivak also provides a complete answer book for students to check your answers.

[graceful moon]

Because there’s proofs in the textbook and the ones you write at uni aren’t all that different to what you’ve been doing in high school anyway

[gray gazelle]

Ah I see

[graceful moon]

I think you’re probably building up proofs to be something bigger than they really are. It’s just a logical argument

[gray gazelle]

So it's the same thing I've been doing with normal math

[graceful moon]

The difficulty tends to come from whatever you’re specifically trying to show, not from the actual techniques of the proof itself

And you won’t learn the tricks for each subject without just doing that subject

[gray gazelle]

So what if I have a different approach to the author how do I know my approach isn't dookie

[slender cargo]

Well, not quite. In proofs you're now writing paragraphs to explain your reasoning for how to get from A to B. It takes some learning to get used to. But I agree that the mechanical process of writing proofs is a bit overblown. The actual issue is that higher level math classes/books tend to take a higher time investment and be more difficult in general, and that surprises students.

Calculus is just easy compared to Real Analysis. It's not because there's proofs involved. There's just more work and thought required.

Spivak has an answer book to see if you're doing things correctly. In a class you would have an instructor to guide you. Just keep trying and you'll eventually get the hang of it.

Oh. I think I see your question more clearly. Uh... building "the sense for what you need to consider and what not" is like a lifelong journey.

There's no recipe for that. Just believe in yourself and keep getting better.

If you're enthusiastic about the material then you'll recall relevant facts more easily.

[gray gazelle]

Thank you it feels clearer now

Is there people in here willing to read my proofs

[quartz agate]

is linear algebra hard

[gray gazelle]

I don't think it would be considered harder than any math before it. If your prepared for it I think it would be the same as anything else

[merry pecan]

hello there how are you all doing

I'm new here

[gray gazelle]

Same

[graceful moon]

This isn’t something anyone can objectively answer. With the right support and background it shouldn’t be.

At least not insurmountably hard, struggling is expected and good when you’re learning

[dense plover]

whats a good book for a first course in complex analysis? so far i've taken multivar calc, linalg, an introductory real analysis class and some abstract algebra

[remote sparrow]

#book-recommendations message

[dense plover]

thanks!

do you recommend one over the other?

[remote sparrow]

try gamelin first

[gray gazelle]

Thoughts on apostol calculus as a first calc book

[flint crescent]

Hey guys, could someone recommend me a book to like get started to math and learn from basics to advanced math in a understandable and easy way?

[remote sparrow]

doable

[graceful moon]

If you need to start with the absolute basics try Khan academy, its great for pre uni stuff

[heady ember]

FIS is the best because I used it. \eeveeqed

[crimson leaf]

Agreed

[stark turret]

i picked up two books from the library because i was bored

quantitative finance for physicists - schmidt

introduction to quantitative finance a math tool kit - reitano

[dapper inlet]

Theory heavy Calculus book?

[thin kernel]

Principles of analysis by rudin

[trail hemlock]

baby rudin

spivak's calculus

apostol's calc

any intro RA text tbh

maccluer's honors calculus

[maiden halo]

that one is super short. is it just concise?

[heady ember]

Without some basic mathematical maturity, Rudin might not be good idea.

[trail hemlock]

it assumes the reader knows calculus

so yes

[heady ember]

Abbott or Schroder is a better pick for beginners

[trail hemlock]

what about tao's analysis/

[heady ember]

Wb?

Schroder covers a ridiculous amount of content for its length and how gentle it starts out.

[heady ember]

Idk

[trail hemlock]

personally i think its great

[heady ember]

Never tried it; hears mixed opinions from others

[trail hemlock]

its like rudin with explainations 🤯

[unique grail]

What is the difference between Apostol and Spivak calculus? im trying to learn calculus for first time

[tribal crow]

what's your background with proof writing?

[unique grail]

Absolutely none

I did highschool algebra some years ago

That's about it

[tribal crow]

Spivak/Apostol might be a bit too hard of an intro to calc in that case...

if you want to learn calculus without worrying about rigour, Stewart's book is a good choice. if you insist on rigour, you can learn from those two, but be prepared to struggle a bit

as for the difference between the two, I have never read Apostol

so I cannot comment on that unfortunately

[unique grail]

Too hard in what sense?

[tribal crow]

can't speak for Apostol, but Spivak's exercises are hard, and not always "calculus"

[unique grail]

I looked at Stewart's book it has a lot of exercises but little explanation, it looks more like a book for class rather than self study while apostol and spivak have a lot of text. But am I wrong about this?

[tribal crow]

they're often intro real analysis problems, as opposed to calculus

[unique grail]

Oh okay how can I prepare myself to use spivak/apostol? I see them often recommended with each other

[tribal crow]

I'll admit I've never read Stewart, but I don't recall it being a problem book

[tribal crow]

on paper, they don't require anything more than a basic high school math education

but in practice, it really helps to have done some proof writing before them

you don't need a lot, just some

Velleman's How to Prove It or Hammack's Book of Proof are good places to pick some of that up

[unique grail]

OH wow

there exists proof books?!

[tribal crow]

yes!

[unique grail]

woah

[tribal crow]

I stress however

that you do not need to read those books in their entirety

Spivak (probably Apostol too?) don't strictly assume the reader has proofs knowledge beforehand

but it's good to know some going in, imho

[unique grail]

so I should just take a few chapters on proofs from hammock for example

if im struggling

[tribal crow]

yeah, that sounds like a good idea

as for which book you should decide to read, idk

I'm pretty sure they're about the same

[unique grail]

I found this text online If your primary goal is to develop a strong theoretical understanding and you enjoy engaging with challenging problems, Spivak may be the better choice. However, if you prefer a more balanced approach that includes computational techniques and an introduction to linear algebra, Apostol may be more suitable and accessible, especially given your background in high school algebra.
But I'm not sure how helpful it is for someone with as little knowledge as me

I will try out first chapter of both books and then decide which one to pick up

Thank you for the proof book recomendation tho

Do you recommend any linear algebra book by the way?

[tribal crow]

Friedberg, Insel, Spence (Linear Algebra)

some users here recommend Axler (Linear Algebra Done Right)

others like Halmos (Finite Dimensional Vector Spaces), or Hoffman-Kunze (Linear Algebra), or Treil (Linear Algebra Done Wrong)

any of them will work imo

my favourite is just FIS

[unique grail]

Halmos looks scary it's only 180 pages long

[tribal crow]

[unique grail]

But has same amount of content as t he others

[tribal crow]

short neq scary (though there is a correlation, imo)

[unique grail]

[tribal crow]

I'm reading Spivak's "sequel" to Calculus atm

it's 130 pages

[unique grail]

Are these LA books using stuff like set theory or just algebra?

[unique grail]

WOAH

how is that going....

[tribal crow]

I cannot be 100% sure of the others, but FIS doesn't assume much more then a basic understanding of set theory and the ability to do high school algebra

calculus stuff will show up a bit, but mostly as examples, and nothing too serious (until chapter 6 I suppose)

[tribal crow]

it's going okay!

definitely a terse book though

[unique grail]

You are a godsend this is so useful for me I went from dilemma to having a library now

Time to try out first chapters of hammack spivak and apostol

[tribal crow]

[unique grail]

God bless you have a good day

[dawn geyser]

What would be good textbooks for the study (or lead to the eventual study) of physics rigorously? I'm a physics student, so the only maths modules I've taken or will take are relativity and quantum field theory (next year). I've been recommended Foundations of Mechanics by Abraham and Marsden, and Differential Topology by Pollack and Guilleman, and I was also wondering if anyone had any thoughts on these if they're familiar with them.

[fleet solstice]

What're books that're good for learning Calculus for the first time, I bought the book "Calculus by James Stewart" bcz I heard he was a good author and talks abt a lot of the topics taught in most Calculus classes in the textbook, but if their's one that might also be good for beginners, lmk.

[fresh skiff]

Sorry, what is FIS?
Tbh i have seen this name bunch of time but don't know the abbreviation.

[tribal crow]

Friedberg, Insel, Spence

[glossy zealot]

You bought the most famous one

Another famous one is calculus by Thomas

[fleet solstice]

Lmao that's what I heard

Whats great abt it anyway?

[fresh skiff]

I guess it has good explanation, a big amount of problems, book is friendly and very basic, a wide range of topics and exercises.

[fleet solstice]

I see, what kind of prerequisites should I learn before delving into the book, I've learned majority of Algebra topics, and atm teaching myself trig, is their anything specifically I should have prior knowledge to?

[fresh skiff]

I guess it's enough.

Open the book and study it. If you find some gap in your knowledge then fill it, but you will find gap rarely.

[glossy zealot]

Afzal is right, just go with it

If you think it is too much, there seems to be a category of books called pre calculus

[cunning elk]

Stewart has a great deal of issues that hold me back from recommending it to anyone who wants an understanding beyond surface level

too much focus on mechanical computation, not enough actually challenging exercises

proofs can be quite handwavy

the book seems to be written more for engineering students who just want to get calc over with

[gray gazelle]

Well the book is called calculus

All 3 are expected

[cunning elk]

ig

[severe valley]

Yo guys, What book shall I read to learn more about probability?

[gray gazelle]

With or without measure theory?

[severe valley]

What would you recommend to a beginner?

[grand thistle]

probably without measure theory then

[gray gazelle]

Yeah

Do you know calculus?

[severe valley]

Well very basic calculus

And what is exactly measure theory?

[gray gazelle]

Well if you know basic calculus then a good intro is maybe A First Course in Probability, by Sheldon Ross

[cunning elk]

Ross’s book is very verbose and dry but does cover quite a bit of ground

[gray gazelle]

Hm I didnt find it dry at all, verbose maybe

It has a ton of examples which to me is useful for beginners

[severe valley]

I see

Good to know, thank you

[quartz agate]

i wanna learn calculus from scratches what book would you recommend

[gusty quest]

i'm looking to learn number theory, i'm currently in high school. What book would you recommend

[tender river]

burton

[gusty quest]

which edition?

the 7th one?

[misty seal]

hi for ioqm what books will be helpful

[molten mason]

It doesn't really matter, the basics are pretty much the same in the editions, the newest one (7th) just has some extra stuff on more modern things and a new section on Farey sequence. If you can get 7th, great, if not, no big deal.

[tribal crow]

Salagos is back...

[molten mason]

Not until Saturday

[tribal crow]

I await your return

[vocal owl]

good resources and/or books to learn math sequences

[vocal owl]

mainly the ones that come up on optiver interviews

[fleet solstice]

I see, the one thing that's holding me from reading it, is my knowledge of trig, ik mainly jus evaluating trig functions, and im starting to graph them aswell

[fresh skiff]

I believe you know enough things to start calculus.

[fleet solstice]

I see I see, I'm also taking a trig class in the summer, so ig I can jus continue learning abt trig, when that time comes

[gaunt path]

Anyone got a book recommendation for algebriac geometry for an undergraduate. I know ring thoery, but not comunitive algabra. I've seen and understood the definitions of point set topology, and not much more than that.

[graceful moon]

Miles Reid has books on undergraduate Algebraic geometry and commutative algebra. There’s also IVA by Cox Little and O Shae

[crimson leaf]

Fulton Algebraic Curves is nice

[gray gazelle]

PDEs?

[dapper inlet]

what subjects do i need to master/be proficient in to comfortably get through by greedy approximation vladimir temlyakov? Sorry for 2x posting

[marsh ingot]

Yes

[grand thistle]

cox little 😭😭

[earnest wolf]

those are two guys

[remote sparrow]

@grand thistle @earnest wolf fun fact, david cox is the one who came up with the cox-zucker machine

[dim sierra]

Didn’t they collaborate just to have that name? Someone told me this lol

[crimson leaf]

How come Milne's course notes cover only group theory, fields, and Galois Theory? Wouldn't you need ring and module theory?

[remote sparrow]

yes

[lilac raven]

any recommendations on a complex variables/analysis book that covers “Introduction to analytic functions, contour integration, power series, residues and conformal mapping” and is rigorous enough to prepare me to go into

“Complex Analysis
Introduction (pdf)
Integrals on curves - definitions (pdf), winding number (pdf)
Analytic functions as integrals I - disk case(pdf)
Analytic functions as integrals II - disk case(pdf)
Local properties of analytic functions (pdf)
Global properties (pdf)
Power series (pdf)
Cauchy’s theorem and representation formula for regions (pdf)
Taylor series, Laurent series (pdf).
Isolated singularities, residue theorem (pdf).
The analytic function z^p, computations of some integrals (pdf). (optional)”

[dim sierra]

stein and sakarchi

^ does all of those lmao

[lilac raven]

thank you

[dim sierra]

you could also do gamelin which is prolly easier

And if you want just intuition there is a book I’ve seen recommended called “visual complex functions: an intro with phase portraits”, tho idk how good it is

[lilac raven]

the second course i listed i’ve heard assumes a lot of background so i think i’ll stick with stein and shakarchi if that’s the most rigorous

[golden salmon]

Brown and Churchill is decent and is cheap

[dim sierra]

Oh yeah ansh don’t you dare go on libgen hehe

And don’t you dare look up a pdf of the book

😉

[lilac raven]

was literally in the middle of doing it i’ll make sure i won’t

i think all of princeton lectures are free online anywyas

[dim sierra]

yeah i think there are pdfs somewhere

[lilac raven]

also is munkres topology a hard solo read?

my school doesn't have a topology course and i want to learn it eventually

[dim sierra]

It’s alright I’d say

I have another recommendation tho

Look up tom leinsters notes (on topology)

they are so clear

[lilac raven]

https://www.maths.ed.ac.uk/~tl/topology/topology_notes.pdf

this?

[dim sierra]

yeah

i think he has exercises somewhere on his website too

[lilac raven]

i like the images he uses

cool find thanks

[dim sierra]

np, enjoy

[trail hemlock]

wowzers

[frozen crown]

Any contemporary book that provides mathematical and philosophical problems of mathematical logic and set theory on which one can write a paper?

I’ve read Naive Set Theory by Halmos and I can solve set theory problems. I’ve also presented a paper at a conference on certain set theory theorems.

What I’m looking for now is a book that presents certain mathematical/philosophical problems in the contemporary debates on set theory and also provides the positions on them so that I could write on that.

The issue I’ve encountered is that most set theory text books I’ve looked through explain set theory but don’t provide any major insight on what are the contemporary debates around it.

Would be immensely grateful if someone could recommend me something on this topic🙏

[molten mason]

@torn crypt

[quartz agate]

does anyone have a book on calculus for begginers

[dense seal]

Idk if there's any centeralized textbook containing all this stuff, you might be able to find some conference proceedings or something. I would maybe skim Penelope Maddy's bilbliography, I know she has some more expository stuff talking about other set theorists perspective of things. The impression I get though, is a lot of thought in philosophy of set theory is buried within set theory writings, and unless the set theorist is primarily philosophically motivated (for example like Joel Hamkins), the philosophy is going to be pretty obfuscated. Similar deal is true of type theory, unless you're willing to read much older things.

If you want something a little less purely mathematical and step outside set theory, I do enjoy Button and Walsh's Philosophy and Model Theory.

Alternatively you can read Zach Webber's Paradoxes and Inconsistent Mathematics

[quartz agate]

what book do you propose me to understand matrices

[graceful moon]

If you want a basic introduction people like Gilbert Strangs Linear Algebra. I think Nicholsons Linear Algebra and Applications is good.

For a more advanced look I like Hoffman Kunze. People seem to enjoy Axlers linear algebra book (not for me though) but I’m guessing you probably want the more basic approach first

[viscid brook]

Discrete math books are good for matrices aswell

[frozen crown]

Thank you so so much!🙏

Can’t express in words how grateful i am for your god tier reply

One question tho - is Joel Hamkins’s work considered seriously within the mathematical community so much so that I can rely on his work to be considered for grad programs? What I mean is, if I publish on his work will i be taken seriously by mathematical logicians when considered for grad programs?

I really love his lectures on YouTube, yet I want to be both mathematical and philosophical as a scholar, at the same time. Hence I ask these kinds of questions. All of my recent publications have been in logic

Thank you greatly again!!!🙏

[earnest wolf]

depends what you want to do with them

if you just need a table of numbers, then the definition will suffice

if representing linear transformations (and all that fluff with basis change and coordinates) – then linear algebra

if anything more niche, then give more info

[glossy zealot]

The Maths Sorcerer youtuber recommends Linear Algebra bu Anton for beginner

Could be a good option

[fresh skiff]

I used this book for selfstudy. First few chapters. It's kinda good book for beginners, the author isn't assuming strong background in proof writing.
But personally, at some moment I become bore since 70%+ problems were computation.
[I read first 3 chapters, anyone who studied this book for long time can give better feedback]

[earnest wolf]

i mean, the helpee didn't give much context, but for LA there is nothing better than that Axler's book

*for EU students lol
idk much abt computation-based books for LA tho

honestly don't get why so many hate it. Axler really can write well (he is a part of Springer's Undergraduate Texts edit board lol)

[tribal crow]

[gray gazelle]

Or Halmos!

[gray gazelle]

has anyone looked through the arihant math book series (for jee mains and advanced). if so, is it any good?

[oblique hatch]

Good intro book to functional analysis?
(Slightly leaning to PDEs)

[gray jungle]

peter lax and brezis are both good options

[glossy zealot]

Axler is more like a second course book

People usually learn computational LA first

That is not the case for students in Europe though, given how you described it

[tribal crow]

Axler doesn’t cover stuff like row reduction, which I find a bit odd

the other LA books of similar rigour all cover it, so I’m not sure why he chose to exclude

[sage python]

He thinks you should've done the crunchy LA class first and learned it there

[gray jungle]

(he doesn't, he just forgot)

[tribal crow]

I mean like, there’s a good chance students never did row reduction in a rigorous way

I would like Axler more if he didn’t brush stuff like that off

[graceful moon]

I also don’t know how I feel about him just working over R and C, if it’s a second course you might as well work over arbitrary fields and rings

There’s also just something I can’t quite put my finger on that I don’t like about his presentation and writing, not sure why but I just don’t like it

[dense seal]

Ehhhhh somewhat, it's hard to say? His work is definitely taken seriously, but at the same time he's on the fringe. The main thing I will warn, is that if you're pursuing a career in academia, JDH can do what he does because he has tenure, and has the freedom to do research and take philosophical positions some consider to be odd. So if you are entering academia as a grad student/postdoc/early career professor it may be hard to get people to take you seriously if you do similar research. (This is more an issue for mathematics than philosophy however.)

[quartz agate]

@earnest wolf i want it for linear algebra

[frozen crown]

Thank you so so much🙏

So it’s generally - “prove that you know the formalism like it’s your second name by your publications, then only and only then show us your philosophical analysis?” Sort of?

[oak stag]

Is baby rudin a good textbook to get stuck in with Real analysis or should I look at another analysis textbook beforehand, for context i've finished my first year of university where i have completed modules on linear algebra, calc and sequences and series so not all the aspects should be completely foreign

also i'd appreciate any other textbooks which can help give me an introduction to applied differential equations, classical dynamics and/or complex/real analysis

[graceful moon]

Rudins book is definitely a bad way to learn analysis. Abbot or Tao are much better for learning in my (and many others here) opinion

People also like Ross, there’s also a million other analysis book recommendations but the main takeaway is that Rudin is awful to self study from

[formal bronze]

I suggest Perko for differential equations

It is a good introductory text

[oak stag]

okl

i only mentioned baby rudin as i've been told its one of the best textbooks in analysis

but i guess self studying from it isnt the best idea

[graceful moon]

Yeah people say that. It’s good once you already know the material in it. It’s basically a really handy lookup table for basic RA with great problems

[fresh skiff]

Introductory? What are the prerequisites?

[graceful moon]

But to learn from it, on your own, is less than ideal

[formal bronze]

Linear algebra

[oak stag]

alright i appreciate the explanation

cheers

[fresh skiff]

Ooh I saw the content and seem horrible lol.

[formal bronze]

Horrible in what way?

[fresh skiff]

I have take first course in ODEs, but the stuff was totally changed in contents. Like local and global theory of nonlinear systems, I saw manifolds somewhere in table of contents too

[formal bronze]

Yeah so it's a good book that covers ODEs from the start

And dynamical systems

[fresh skiff]

I see. It seems like DE book for pure maths

I will try it, when I will study LA

[gray gazelle]

Perko also expects some background in RA

[formal bronze]

Ok yes, I forgot to mention that lol

[fresh skiff]

Oh I am currently working on Abbott. I hope it will be enough

[gray gazelle]

It should be

[sudden kindle]

<@&268886789983436800>

[oak stag]

does abbott also cover complex analysis

or only real analysis

as thats another module ill be doing next year

i want to get a headstart on the content if possible

[glossy zealot]

Only real

[oak stag]

okl

do you have any recs for complex?

[formal bronze]

Stein and Shakarchi

[oak stag]

cheers

[remote sparrow]

https://www.amazon.com/Set-Theory-Its-Philosophy-Introduction/dp/0199270414

[naive trellis]

Chern Weil Theory Books?

[remote sparrow]

#book-recommendations message

[violet shuttle]

my prof recommends Milnor Stassheff

[naive trellis]

Right

Ty

[naive trellis]

Seems nice tysm

[covert mauve]

what fictional books with monarchies and politics have good worldbuilding and plot?

[glad rampart]

Hmm, a webnovel instead of physical book but Worth the Candle seems to fit that description

[hallow oriole]

you HAVE to read practical guide to evil

worth the candle is really good too

[verbal vessel]

Need something to self teach complex analysis with and preferably something that is used in a video course

MIT Opencourseware doesn’t have vids unfortunately

[gray gazelle]

try nptelhrd lectures

[remote sparrow]

http://www.supermath.info/Complex.html

use the material from fall 2015

the book followed is gamelin