book-recommendations

[copper radish]

as for a calc book idk what to use

rightttt

understanding analysis or smth right

[remote sparrow]

i don't see why not

we don't live in the 60s where the only available books were way too terse

could take a detour into linear algebra instead of real analysis if you want

linear algebra proofs are pretty straightforward comparatively

[copper radish]

oh i'm working on probability & stats

linear algebra

[remote sparrow]

plenty of obvious applications

[copper radish]

and i thought of adding calc to the mix

but i'm using strang's linear algebra book so not like axler or smth

not much of proof writing or something is required

[copper radish]

yep!

[remote sparrow]

https://tenor.com/view/cirno-fumo-touhou-math-fumo-studying-gif-25993184

[copper radish]

Lol

Anyway okay thanks

[ruby thistle]

Baby Rudin

Ahh I should have uploaded that book right away

[plush rain]

<@&268886789983436800>

[timber cosmos]

where did you get access to this link?

[torn blade]

google: tong vector calculus

cambridge has like a fuck ton of lecture notes publicly available

[timber cosmos]

how do i access those lecture notes like a WHOLE list of them

[torn blade]

uhhh just google cambridge [course name] notes

i only look for lecture notes when im trying to revise for an exam tbh but they are genuinely good learning material, or supplementary material to a book

[signal mountain]

david tong has done a ton of courses and his notes are notoriously good
you can find them all here https://www.damtp.cam.ac.uk/user/tong/teaching.html

[timber cosmos]

ty

[signal mountain]

gareth (also from cam) also has a ton of notes here (lots more pure stuff than tong) https://tartarus.org/gareth/maths/notes/
and dexter chua who was a student at cam is pretty famous for his notes, he took heaps of courses, find them here https://dec41.user.srcf.net

theres tons more out there but those are the most notable i would say

[torn blade]

https://at2027.user.srcf.net/notes.html <- this has like everything lol

wow loads of people type and publish their notes at cambridge lol. i dont know a single person who does or has done that at my uni

i type my notes (to my observation im the only person who does this), maybe i should be the change i wanna see in the world 🔥

[signal mountain]

yeah there were at least three who was somewhat serious abt it in my year

i see a couple of there names on that page you ssent haha

but id say thats def the outlier

[upper plover]

I read the previous comment on the book, and that is probably why others told me to read it with Bartle. I stopped reading it because I just got into an analysis class. Though I am reading a topology book for my relaxing times. I heard somewhere it is pretty much analysis... so I will be tested..

[upper plover]

I've heard Baby Rudin is a painful book for a beginner? Unless I've heard wrong, and if so, link for a PDF?

[upper plover]

:whaaa: I just like writing on a piece of paper. Typing is too boring.

Wait, so what is a good Analysis book? A book that would "knock your hair off" or .... I have no idea usually all the books I've read does that.

[ruby thistle]

wht about tituu andrescuu

[vital bane]

"Understanding Analysis" by Stephen Abbott, it's so good that it won't just knock your hair off, it'll make sure that your next 3 generations are bald

[upper plover]

LOL

Alright, I'll give it a read.

[vital bane]

yea it's pedagogically poor, it's not good for self learning

but it's great for exercises

[upper plover]

I thought that was the case with Tao's book. :dogekek:

[vital bane]

I always recommend the Abbott + Rudin duo

Rudin for extra exercises

Rudin exercises are goated

[upper plover]

Alright. What about Bartle?

[vital bane]

exposition is trash

[upper plover]

I've heard.

[vital bane]

it's good too, most intro analysis books are great like Bartle, Tao, Cummings, Pugh, Schroder, etc.

But imo Abbott is one of the best undergrad math books of all time

[upper plover]

Well, lucky for me I have a PDF copy.

And I can also check out Rudin at the uni library.

[vital bane]

check for Abbott (2nd edition) as well

[upper plover]

My uni's math program is literally at its last straw, so I am pretty much the only mf who's going to be there. Imma ask them if they're planning to remove any math books to just give it to me.

[upper plover]

Older edition? Or new? Why should I look for it?

Though I have the PDF of it; so I should be fine.

[graceful moon]

Exposition is just non existent

Trash implies it actually exists and is bad

[marsh ingot]

@vestal junco I recommend for Vector calculus a book named: Vector analysis versus vector calculus

[vital bane]

2nd edition is the latest

[vital bane]

interesting title

[marsh ingot]

It is

[torn blade]

good books for multivariable calculus? the ones i know about are Spivak/Munkres/Apostol, are any of these fine?

i want a more pure-focused book because the only mvc ive learnt is for applied mathematicians so wasnt very rigorous

[foggy quest]

"Advanced Calculus" by Folland and https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/

[modest kite]

Are AOPS book recommendations for olympiad excellent?

[surreal token]

Any book recommendations for history of mathematics?

[earnest wolf]

check out Tao and Zorich

Tao vol 2 and Zorich vol 1

I think Zorich was nicer than Tao?

in that Tao used a lot of (albeit not very advanced) terminology from baby measure theory

so for a first pass Zorich is better imo

[slow roost]

Stillwell - Mathematics and its History; Smith - History of Mathematics Vol. 1 and 2; Bell - Men of Mathematics

Hawking - God Created the Integers

[surreal token]

Thank you so much!!

[slow roost]

the Hawking book is quite cool for containing excerpts of original research papers of all the mathematicians it covers

along with Hawking's biographies and commentary

[foggy quest]

"History of Functional Analysis" by J. Dieudonne looks really good.

[slow roost]

oh, Dieudonne's History of Algebraic and Differential Topology is great too. But you need to understand the subject well for it to make sense

[halcyon sedge]

If anyone here has read a book on liner algebra and thought it was helpful, I'd appreicate a recommendation please

[remote sparrow]

#book-recommendations message

[gray gazelle]

Do you want it proof based, computational or both?

[halcyon sedge]

Both would be nice

[molten gulch]

Friedberg Insel Spence Linear Algebra

[foggy quest]

https://mtaylor.web.unc.edu/notes/linear-algebra-notes/

[vestal junco]

Prereqs?

[marsh ingot]

Calculus and multivar

[remote sparrow]

https://link.springer.com/book/10.1007/978-1-4614-2200-6

this?

seems cool

[marsh ingot]

Yeah

One of the authors was my teacher and tutor

[remote sparrow]

you're spanish?

[warm arrow]

i have spivak

[marsh ingot]

Yeah

[remote sparrow]

https://www.rxddit.com/r/math/comments/1iwi2gv/what_are_the_most_esoteric_incoherent_or_poorly/

[woeful night]

what should i read before looking into galois theory? i assume i need sth in set theory, group theory, etc., but idk what is a good book for these topics

say for example i bumped into this calling x1 x2 x3 a symmetric group, before realizing that i cant just jump to galois theory, as there are way too much background knowledge not explained in a galois theory book

oh i cant paste pictures here ok

[slow roost]

Pinter - A Book of Abstract Algebra is a good undergrad algebra book that's on the shorter side and gets to galois theory

[woeful night]

i will check it out

tysm

[old elk]

Guys I had seen a link to the harvard page of the exams that have been done over the years notes and some exercises, I have lost the page someone knows where I can find it ?

[royal berry]

I'm still in highschool , what books should I start reading if I barely have any experience

[mortal ore]

Pick up George Polya's "How to Solve it"

Should be a great read for starting with mathematical proof

What math topics are u curious about tho?

[royal berry]

algebra and triginometry I guess

though I'm still not very good at trigonometry

[mortal ore]

Go to Khan Academy for that

[light robin]

Bro eigenvectors in chapter 2 is kinda crazy

[dusk surge]

Have an independent approach instead of reading books

[drowsy nacelle]

why

you can define them as soon as you know matrix vector multiplication

[timber mesa]

getting to the important stuff quick lol

[vital bane]

you can also define a topology on a set as soon as you know basic set theory

[vestal junco]

Anybody also know a good geometrical vector book

[grim ore]

I liked linear alg by shifrin

[old elk]

yes

[old elk]

See analysis in varieties

[gray gazelle]

khan academy is ass cheeks

use exercises from textbook

[smoky plover]

use cengage for maths

[gray gazelle]

what is that

textbook publisher?

[molten gulch]

yes

[smoky plover]

textbook

@gray gazelle from india?

[molten gulch]

Cengage is not the name of a textbook

it's the name of a publisher

[smoky plover]

name of publisher

its like a brand

you can use JEE ADVANCED series of books for maths of cengage

[molten gulch]

"maths of cengage" makes no sense, JEE Advanced is the name of an exam, so are you referring to a book series?

[smoky plover]

use this book if want to

[molten gulch]

Okay so this is a book in the "JEE Advanced" Series

[smoky plover]

ya

[molten gulch]

also don't send links without removing the tracking data

[smoky plover]

that is what i was saying

[molten gulch]

https://www.cengage.co.in/book-list/print/jee-advanced-calculus-2g sending this link would have been enough

[smoky plover]

ok thanks

[smoky plover]

from india?

[molten gulch]

Also this book is not shipped outside of India, fwiw

[smoky plover]

okkk

then use another of this publisher

[gray gazelle]

дайте учебник

[molten gulch]

Most Cengage books are INCREDIBLY expensive here in the US

[smoky plover]

okk

[molten gulch]

$100-$200 for textbooks 💀

[smoky plover]

its really expensive

[molten gulch]

yes, yes it is

[smoky plover]

its around 13 $ in india

[vital bane]

isn't that the price of a normal textbook in the US

[molten gulch]

yeah

it is

[mortal ore]

For trigonometry???

Khan is perfectly fine for the level of math it seeks to teach

[rigid trail]

Why are you thinking about ass cheeks

[wide spruce]

PDF file for Linear Algebra Done Right, fourth edition (11 February 2025)
https://linear.axler.net/LADR4e.pdf

[mossy flume]

if only it were a good book

[naive lava]

only if it was written right

anyhow

I am in need of a problem book for real and complex analysis by rudin, i read the proofs, understand most stuff hopefully, and i can do most of the exercises, but i still feel like it's a bit too in the air for me, ik it'd be difficult to find a book with similar course of action, but i'd appriciete anything at this point

tldr; need a measure theo/real analysis book with hard problems

[static fog]

What's wrong with LADR?
I'm currently working through it, and it's a really good read.

[pine tundra]

Why? I haven't still read it, but was planning to do

[mossy flume]

I think it harps on too much about how determinants are bad, and I don't see the point in only working over R and C when so much of it could be abstracted to arbitrary fields (especially since this is for a second course in LA supposedly)

[naive lava]

is it a second course? my school used it for the first course, and that's why i didn't like it

[mossy flume]

the proper way to deal with the determinant is to show that it's a unique map satisfying some properties and then go that way (which also gives a view into multilinear algebra)

I recommend Friedberg, Insel, and Spence's Linear Algebra

[naive lava]

i'd rather have some motivation and cool stuff introduced first, and only then get to the details

[mossy flume]

I love that text

[static fog]

I see we share the deepest of passion for this book. It's so, so, good. It's the best book I've read, period. I just wish the project sections and the ending sections were a bit more sketched out in detail; they were really hard (eg. WAT/Blancmange Curve/Section 8.x)

[molten gulch]

I like FIS and axler tbh

one of my friends likes hoffman and kunze

[torn blade]

Abbott glazing session lets goooo

i need more books written like Abbott

[static fog]

I could glaze Abbott for hours. It's a pity he hasn't written on other topics. Yet to find books that are similar to his style.

[torn blade]

yeah its a shame that im past first year analysis anyways :(

[shadow linden]

anyone got a good book to precede Vick's Homology theory?

[candid arrow]

"Arithmetic For The Practical Man by Thompson, J. E." I'm trying to refresh my fundamentals in math, but as a non-native english speaker i find it incredibly difficult to understand his way of explaining. Does anyone know a free book in pdf, where i can quickly refresh fundamentals in math?

[static fog]

free book in pdf
every book is free and in pdf if you know where to look.

[molten gulch]

Older books like this tend to be written in a more formal or at-least more old-fashioned way so they tend to more difficult to follow along; besides books, websites like Khan Academy can be helpful for reviewing fundamentals

[molten gulch]

Do not discuss piracy in this server

[unreal stag]

in google

[rain hound]

The really big niche it serves that nothing else does is its treatment readily generalizes to functional analysis.

But it also treats things in a way where it's not difficult to generalize it to an arbitrary field. The choice of notation of F is suggestive of this I think. Ultimately the book just does a lot of things well imo, better for what it is than anything else, abstract linear algebra. But the prep for functional analysis is its standout feature.

If you have any interest in quantum mechanics or quantum computing, there is no better prep (especially which is accessible to an undergrad) than Axler's book. The fact it's open access is just another bonus.

It still does treat determinants for the record. but it's a bit different than most books do. I think it's fine. In the most recent addition it focuses on tensors and being a form even.

Advocating for piracy is a TOS violation and puts this entire server at risk. You're jeopardizing the hard work staff has done here and that everyone else has done contributing to the server.

[molten gulch]

<@&268886789983436800> user is providing links to piracy pages against TOS

[naive lava]

what? I just said they should be shut down and i did not provide links???

but if mentioning their names was an issue i'm sorry

i won't do again

[molten gulch]

it is

[molten gulch]

Also the way you phased it made it seem like you were meaning the money stealing thing in an ironic sense

[naive lava]

alr, wont do it again, should i also delete it?

[molten gulch]

fwiw yes publishers steal money but mentioning piracy sites will get you in BIG trouble

Also yes????

[naive lava]

alr

[candid arrow]

Ill try to find something, but im not sure if every book is free, there are many that only lead to their Amazon page

[candid arrow]

That’s true i quess, i really wish that math was in english internationally

[molten gulch]

Most books are written in English these days AFAIK

[rain hound]

Not a book per se. But for high school and early university math I found khan academy very helpful.

[rain hound]

It’s not free. You might choose to ignore the harm you do or the cost associated with the book. But it gets paid anyway, one way or another.

[fluid violet]

As was already explained to you, we can't allow people giving details on how to pirate books on this server. This is just a friendly notice, don't worry.

[naive lava]

okay, thanks ♥️

[merry sphinx]

isnt axler more of an analyst? i thought that was why he did R/C vector spaces

[heady ember]

If you want to support the author, buy them a cup of coffee or something

[trail hemlock]

https://www.youtube.com/playlist?list=PLmsIjFudc1l3ZOb772LlZEu_k1nPpPFuY
not a book but still useful alongside a book. lecture series that follows cohn's Measure Theory. hopefully useful to someone else down the line.

also his accent is kinda fire

[stuck fjord]

so what are yalls fave textbooks for calculus? im in precalc rn but i rlly like math so i wanna progress further to understand more

[naive lava]

there are 2 main ways to go as of today, adams and spivak

adams is the standard text used for everyone

it isn't much rigorous, but, it covers most things you need

it's what also most uni's use

spivak, on the other hand, gives proof of almost everything, it's more demanding but you'll learn more

[stuck fjord]

dudeee

i tried to use spivak

but like

idk how to write proofs

so i got stuck on chapter 1

😭

[naive lava]

if it's your first time encountering proofs and stuff, just go with adams

[stuck fjord]

adams? pls send title

[naive lava]

that mathematical maturity is something you will build up over time

also you can def. check out some books on proof methods

they are fun too

[naive lava]

adams, calculus

[stuck fjord]

ight bet thanks

thoughts on learning calculus from mit open library as well?

[stuck fjord]

bet u got any to rec?

[naive lava]

when i was in ug, i learnt multivar calc from mit ocw

def a great source

but i think they changed some stuff about calc 1 and it's not that goods

depends on your uni tho

[stuck fjord]

oh

[naive lava]

my uni choseed to cover entire calc in 2 semesters so mit ocw fell short

[stuck fjord]

im in hs

[stuck fjord]

ohh ok i see wha tuy mean

[naive lava]

well you'll go to uni someday no?

[stuck fjord]

yeahh u right

[naive lava]

if you're in hs, you should probably stick to adams

[stuck fjord]

u think i could start proofs?

[naive lava]

sure, why not

even the most basic facts need some kind of proof methods

[mortal ore]

its good to study anything in high school tbh

even if you take a class on it later

its just a free A

[naive lava]

my uni sucked ass in proof classes so i didn't learn much

[mortal ore]

and you are prob competent enough to do research fairly early

[stuck fjord]

bet

so best books?

for proofs*

oh yeah and thoughts on leithold

[naive lava]

only one ik is proofs: transitioning to advanced math or something like this

can't remember the title

one thing to keep in mind when learning proofs is that you usually don't want to try things that you aren't already familiar with

[stuck fjord]

Mmmm okay i see u

[naive lava]

i'm bringing this up again but my class in uni was giving us new stuff each week, totally unfamiliar to us, and that was the way to learn proofs

no one learnt anything from that class

[stuck fjord]

Wait

No diddy

But what uni u at

Wqit can i even ask that

Sry dont answer that

[naive lava]

because no one even knew what topology is, and we'd just randomly get a homework with the definition of topology and stuff to ptove

[naive lava]

it was an ok uni, thankfully im not there anymore

[stuck fjord]

Mm i see

Thoughts on leithold tho

[naive lava]

no idea

[stuck fjord]

Ok ty goat

Thanks for all the info btw

Im excited to begin

[naive lava]

good luck! hope you'll have fun

calc is perhaps the most important thing you'll ever learn

it'll let you solve a lot lot more problems than before

[stuck fjord]

yes goat

wait its

Calculus: A Complete Course (5th Edition)

righgt?

[naive lava]

yeah i think so

[naive lava]

^ up

[rigid trail]

Yes

Write proofs and a lot of them

[stuck fjord]

ty goat

[stuck fjord]

any book u got in particualar?

[rigid trail]

What math have you learned

[stuck fjord]

doing trig rn

but like i remember most of algebra 2

[rigid trail]

Oh

Well you could do some discrete math

[stuck fjord]

ohg

so u got books

[rigid trail]

Probably better to focus on calculus

[stuck fjord]

ah alr thanks

[rigid trail]

I thought you already did so

[old elk]

https://link.springer.com/book/10.1007/978-981-99-2935-1

[astral dove]

anyone have a roadmap to independent study of combinatorics (starting at undergrad level), my uni has no courses in it 💔 i have an introductory level understanding (combinations/permutations, basic level problems). any videos or textbooks would be appreciated! asked this in math discussions but it’s getting buried lol

[grim roost]

Any books that cover basically all topics from calc 1-2 and some hs stuff just for review and to get better at the basics? I want to have a really good foundation for other higher level topics

[normal crystal]

this could be good for the beginning
https://www.mathematicalgemstones.com/maria/OER.html

[manic sand]

Bona, Miklos. A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory.
MIT course: https://ocw.mit.edu/courses/18-314-combinatorial-analysis-fall-2014/pages/syllabus

I am at an undergrad level of mathematics and I found this textbook very approachable for self study. Each chapter has a large bank of questions with full answers.

[astral dove]

thank you!

[hidden wharf]

Hello, I am finishing Understanding Analysis, what book can I use for self learning further real analysis( I have heard that Tao’s Analysis 2 is great, or how about Lang’s Analysis 2)

[remote sparrow]

#book-recommendations message

[hidden wharf]

Thanks

[tidal pine]

Can someone suggest me books that cover basic + advance theory and illustrations for pre-college mathematics (especially for olympiads like the IMO, RMO and InMO)

[naive lava]

are you more interested in meaures? metric spaceses? calc on manifods?

[frigid pumice]

are there any better books to study calculas in detailed
irrespective of high school syllabus

[vital bane]

you can't grow if you aren't challenged and besides I think the project sections were meant to be assigned to a group of students anyway

[vital bane]

I know right!! I think "A user friendly introduction to lebesgue measure and integration" is kind of Abbott-esque but I'm not 100% sure as I haven't used it

[vital bane]

realll!!!

He should write a book on measure theory and another one on functional analysis (I think he does functional analysis research)

he has written one book on math + theather I'm not sure what it is but I will be buying it when I get the time to go through it

[torn blade]

oh fr

ill check that out when im home

[vital bane]

but the one draw back is that it doesn't cover as many topics as your average measure theory/grad analysis book would cover

[naive lava]

You can also look at axlers new book or royden, they seem to be similar to book neam suggested

[torn blade]

yeah i like Axler’s book

[vital bane]

we meet again dogu...

how's it going?

I forget, you are in the 1st/2nd year of your PhD?

[naive lava]

How's your arcs coming along

[naive lava]

Eh, not good not bad, trying to understand proofs lol

[naive lava]

1st

[vital bane]

I need to work harder

much harder

and I need to be much smarter, not just about math but also about how I spend my time

oh wait I have something to show you too, let me ping you in my thread

[hidden wharf]

My goal now is to learn algebraic topology, but I’m not sure how to build a roadmap towards it. If I already finished how to prove it, linear algebra done right, and understanding analysis, what topic should I cover next and with which book?

[vital bane]

point set topology and abstract algebra is what you need

once you finish learning those two, you can start learning algebraic topology

as for books I'd recommend Munkres and D&F

in fact in Munkres' book part I is point set topology and part II is some algebraic topology

[gray gazelle]

guys. I would like an Algebra 1 book that have great explanation and lots of problems to solve
I found AoPS ones. Is it good?

[naive lava]

A book on algebra might help, you can also study this alongside of point set topology

Then you can probs go hatcher

Or may even idk

[queen rampart]

when you say algebra 1, do you mean abstract algebra?

or are we talking pre-calc

[gray gazelle]

like middle school algebra

[queen rampart]

ohhh

[gray gazelle]

There's Algebra 1 and 2

Then pre-calculus from what I've heard

I don't mind if the book also comes with pre-calc

[queen rampart]

a brief look over the contents page of this AoPS thing looks pretty good

[gray gazelle]

Any book recommendations for Calculus of Variations geared toward mechanical or structural engineers as opposed to mathematicians?

[naive lava]

Chapter on Taylors or Goldstein's book

[vital bane]

Not a book but this is a good set of lectures

https://www.youtube.com/playlist?list=PL2ym2L69yzkamORF9DGWRhE9qUnb0_-6H

the first few videos are about calculus of variations

[vital bane]

But also check these out if you want to read an explanation from a text

[gray gazelle]

Thanks. I saw that one. There’s also another set from Dr. Fertig that I saw which I’d start with as I have no idea who that person is credential-wise.

[vital bane]

chapter 6 of Taylor is Calculus of Variations and I think chapter 2 or 3 of Goldstein is about that

[gray gazelle]

Classical Mechanics by John R. Taylor?

[vital bane]

yes

insanely based book

though I didn't find his derivation of the EL-equations very satisfying, I mean they're fine for an intro classical mech course for undergrads I suppose? I need to check out Goldstein's derivation, I heard that's much better

maybe Stewart or Thomas

[naive lava]

Goldsteins first derivation was straight up evil

He starts from F=ma

[vital bane]

you gotta find that yourself

[vital bane]

mfw generalized force = time derivative of generalized 🇵omentum

[gray gazelle]

I was reading Zienciewicz’s Finite Element Method - Its Basis and Fundamentals and encountered the topic in Ch. 4 Variational Forms & Finite Element Approximation: 1-D Problems

[naive lava]

I believe he didn't even use generalized force

As I said, pure evil

[vital bane]

yes

[upbeat shoal]

appreciated

[naive lava]

Btw the best derivation imo is in Arnold's book

[vital bane]

Arnold ODE?

[remote sparrow]

https://www.amazon.com/Calculus-Variations-Applications-Physics-Engineering/dp/0486630692

[remote sparrow]

i heard marion and thornton's derivation was unsatisfying as well

we shall see tho

[naive lava]

No no no

Classical mech

I've never read a book on odes or PDEs and I refuse to do so

[vital bane]

Ohhhh

[remote sparrow]

why

[vital bane]

Arnold has a mathphys book on classical mech using diff geo right?

[remote sparrow]

yes

[vital bane]

based based

spivak does too

I gotta read that some time

[molten gulch]

AFAIK having at-least some knowledge of differential equations is useful in most fields of maths

[naive lava]

Cos why on earth would i

If it's in physics, it is solvable

[vital bane]

[naive lava]

Afaik spivaks that book is terrible

[remote sparrow]

what about nonlinear problems

[vital bane]

simply linearize

[remote sparrow]

that aren't easily approximated by linear problems

[vital bane]

Spivak's book on classical mech is terrible?

Slander I say!

[remote sparrow]

i think strogatz's book is cool

[vital bane]

the shoe smelling goat can never write a bad book 🗿

non-linear dynamics and chaos?

[remote sparrow]

you might like hirsch, smale, and devaney as well

[remote sparrow]

yeah

[vital bane]

because it's fun

[remote sparrow]

https://web.williams.edu/Mathematics/lg5/Rota.pdf

tbf most ODE classes kinda suck

[vital bane]

giancarlo rota?

[naive lava]

P sure that'd be easier than reading a PDE book tbh

[remote sparrow]

not sure about "most"

[vital bane]

Nice

[vital bane]

but learning functional analysis and then learning about PDEs will be super exciting imagine all the inequalities you get to use

[remote sparrow]

what about numerical PDEs

[vital bane]

oh no I'm turning into an analyst

[remote sparrow]

there's plenty of work in simulating solutions to PDEs

[naive lava]

Triangle and Cauchy schwartz

[molten gulch]

Awful

[naive lava]

Take it or leave it

Buuut

İmma learn func anal cos it sounds hella fun

[remote sparrow]

https://bookstore.ams.org/amstext-54/

[naive lava]

Neam guess which book imma use

[vital bane]

Peter Lax?

[remote sparrow]

i heard this book is good for undergrad PDEs

[vital bane]

wait I know...

Grandpa Rudin

[remote sparrow]

i do not have any plans to learn functional analysis; maybe probability at most

[vital bane]

Sour Drop measure theoretic probability arc when?

also wait what do you do? are you an undergrad?

[remote sparrow]

i'm a masters student

[remote sparrow]

nothing interesting right now; just taking measure theory and complex analysis

[vital bane]

1st year?

[naive lava]

Hell yeah you're right lmao

[vital bane]

based

[naive lava]

Then i just might switch to his last book, the grand grandpa rudin

[vital bane]

This is the entire article from Dogu's POV:

[naive lava]

Lamo

[vital bane]

huh??

Grandpa Rudin is not Rudin's last book??

[remote sparrow]

i don't think i'll grow to love analysis

[remote sparrow]

think he wrote a book called Fourier Analysis on Groups

it's published by dover

[vital bane]

WHATT

NICEEE

[naive lava]

He has like 3 more

[vital bane]

Rudin harmonic anal

[remote sparrow]

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

[naive lava]

Complex functions in unit ball in C^n or something like that

[vital bane]

[vital bane]

the prize for the best lack of exposition goes to...Waltuh Rudin!

[remote sparrow]

https://tenor.com/view/waltuh-heart-locket-my-beloved-walter-white-gif-26530050

[naive lava]

İnterestingly enough, in all the books I've tried, i found the exposition on RCA to be the just the right amount

He skips some "trivial" stuff but going faster at an abstract course helps ngl

[vital bane]

didn't you post the exact same message before

[hidden wharf]

Oh, I’m sorry, I had connection troubles, and it have been sent twice

[remote sparrow]

joe biden type shit

[vital bane]

oh I see

[hidden wharf]

Thanks a lot

[naive lava]

İf you want an alternative to munkres for topology, you can check out Willard btw

Excellent book imo

[vital bane]

This is actually a fun and informative read, thanks man

damn he feels quite strongly about this

which I commend

because I too am sick of poorly presented intro ODE courses

the only good ODE notes I've found was Paul's Online Notes

[rain wren]

bro

ok, the very next paragraph runs in contradiction to the first

ig they're just talking about existence theorems for odes

which I am hopelessly unfamiliar with

[vital bane]

how?

[vital bane]

ye

[vital bane]

same but I saw Rudin had an exercise about an existence theorem iirc?

in chapter 6 or 7

Rudin PMA

[molten gulch]

[rain wren]

existence results are inferior mathematics
existence results are extraordinarily interesting

[tawny copper]

What he is saying is kind of dumb, existence theorems are not psychological theorems. They are often the starting point of various concepts. "Since a solution to this DE exists, we can consider this object...". And uniqueness is also quite useful, you don't need to write explicit formulas, often from uniqueness you can derive nontrivial relations.

I don't have much experience with differential equations in general, but I think this kind of existence theorems are used all over the place in differential geometry

[tribal crow]

but one was in the context of ODEs, and the other in the context of PDEs, so the contradiction isn’t quite there

[tame tree]

Existence theorems are pretty useful for proving other theorems though

[heavy vault]

Thoughts on munkres for algebraic topology

If I js finish part one of munkres and an abstract algebra book (hungerford)

[naive lava]

Any particular reason that you don't wanna use hatcher?

[heavy vault]

Idk I hear mixed things

Ppl complain that it's hard to find what's important since it's buried so deep in the exposition

[royal frost]

Hello friends. Can someone please suggest what to study for IMO? And what is the best book?

[naive lava]

okay, it's time for my daily textbook question, so i talked to my advisor today and he said i should probably start learning functional analysis, i was gonna use the grandpa rudin, but there is no available as of now, so i'm looking for alternatives that cover more or less the same ground, any advice?

my library also doesn't have the full simon set

adams, spivak or spivak

[heavy vault]

If ur not involved yet the art of problem solving website (AOPS) has a really big community around competitions

I don't really know specific books but I hear good things abt EGMO by Evan Chen

[remote sparrow]

https://link.springer.com/book/10.1007/978-1-4757-4383-8

[naive lava]

can you compare this to rudin, or direct me to a place that has a review/comparison

[spiral patio]

Is there a good Partial Differential Equations book for an engineering student? What would you recommend? Thanks!

[sleek python]

This makes no sense

[sleek python]

Is this person trying to fit the most shit takes in a single text or what

[naive lava]

or should i just yolo it and read the entirity of reed and simon series

[tawny copper]

there are the books of Lax and Ward. I'm no functional analyst, but I think they are standard

you can also just use pdf/djvus

[mortal ore]

Hello! I'm looking into reading about graph theory

Ive heard about Bondy and Murty as well as Diestel

which of these is better/more rigorous?

[mellow wren]

reed and simon

[naive lava]

i looked trough lax but it seemed to miss quite a lot

will def check out ward tho

[naive lava]

not the 4 volumes 😭

[mellow wren]

it's just volume 1

[naive lava]

whaaat?

[mellow wren]

yeah only volume 1 is function analysis

idk what the rest are

they're impossible to find lmao

[naive lava]

we have like 5 sets in our library lmao

2nd volume is on fourier analysis and self-adjointness

[mellow wren]

maybe volume IV is also good

But everybody just reads the first volume

[naive lava]

3 is scattering theory

[mellow wren]

it's more than enough

[naive lava]

4 is analysis of opearators

[remote sparrow]

bondy and murty has more topics relevant to computer science, but both are good

@crimson leaf @mossy flume

[mortal ore]

i see

i was recommended both in order to better research steenrod algebras

[naive lava]

does it cover everything in grandpa rudin?

[mortal ore]

but since i think its intended for pure research ill read the latter

[mellow wren]

I'm p sure the answer is complicated
I'm not sure what Rudin covers but Reed Simon is REALLY in depth

like horribly in depth

[naive lava]

https://catdir.loc.gov/catdir/toc/mh021/90005677.html this place seems to have a list

[tawny copper]

they are available on google, except the fourth

[crimson leaf]

So I mainly did combinatorics on trees instead of actual graph theory but I learned all my graph theory from Introduction to Graph Theory by Wislon which is a pretty easy to read and work through book that covers what you need to start, my advisors book and papers on chemical graph theory, and graph theory by Diestel which I've read parts of on my own and I really liked it, couldn't get into Bondy and Murty as much myself.

[mossy flume]

Diestel is classic graph theory text

but tbh I haven't studied much graph theory formally so I sadly can't say much more than that

[mortal ore]

oh nice

im in good hands then

apparently graph theory isnt combinatorics though

i really thought it was

[mossy flume]

Uhhhhhh

it is

[mortal ore]

oh

[mossy flume]

but I think typically when people say combinatorics what they really mean is enumerative combinatorics

[mortal ore]

i asked the postdoc doing steenrod algebras about studying more combinatorics since theres graph theory

[mortal ore]

oh this might be what she thought i meant

i just meant the entire subject of combinatorics

[mossy flume]

which again some people also use to just mean "combinatorics which isn't graph theory"

As far as graph theory texts go, I'm sure Douglas West's text is good

[mortal ore]

i was confused about this, since my linalg professor is a combinatorial algebraist and a lot of his arxiv work is graph theoretic

[mossy flume]

meh it's just words

[mortal ore]

fair enough

[mossy flume]

I'd say I'm interested in combinatorics and I hate graph theory lol

[mortal ore]

i just didnt know that these words could mean something else

[mortal ore]

im historically terrible at combinatorics and have no clue what graph theory is

im only bad at it because i never really formally studied it though frankly

i think its about time i do

[severe fog]

Does anyone know a good maths integrals practice books? Specifically not just any but it would be great if they had notions related to vectorial spaces, stair functions, differential equations, riemann sumations etc...

[blazing holly]

Intro to PDEs by Strauss feels alot like Abbott’s Understanding Analysis

Am i crazy for saying that?

[livid lintel]

Unrelated but elementary graph theory is really really fun

[mortal ore]

I'm starting diestel tomorrow

Learning some graph theory for a potential REU

[livid lintel]

I’m also doing Diestel 6th edition

[torn blade]

good books for getting into foundations of mathematics?

[vital bane]

Ooh Diestel

how is it so far?

[vital bane]

oh damn really?

[brisk rapids]

diestel seems like such a fun book, will get into it after midterms

[remote sparrow]

#book-recommendations message

[torn blade]

thx, whats the general order to approach topics in foundations?

[remote sparrow]

after reading one of the books i mentioned? there isn't really an order to follow; the very basics of formal axiomatic set theory, model theory, proof theory, type theory, and computability theory don't really depend on each other too heavily

of course, as you get more advanced, there will be connections made between branches

[livid lintel]

It's really good, it's a graduate book but I think it works for undergraduate students just fine.

[deft python]

Hi , can some one help me ,i need a good book for number theory from 0 ,and where can i find problems to practice

[naive lava]

analytic or algebraic?

[blazing holly]

Yeah, again maybe im crazy
But despite it being PDEs, it feels like strauss is talking to me

Even though some of it is still over my head, the way its written just makes me want to read the next page

[deft python]

Just number theory ,if there is both give both

[naive lava]

i've used silvermans book before, it's not exactly the best, but it covers most basic things in good detail imo

[deft python]

It haves both topics analytic and algebric?

[naive lava]

those are in the more advanced class of number theory, this is basics

[remote sparrow]

#book-recommendations message

[remote sparrow]

that's just the early chapters

[vital bane]

yea I love how Abbott's book is so conversational and it's like sitting through a good lecture and you're saying Strauss is similar? I shall need to try it out!

[vital bane]

what happens in later chapters

[deft python]

Ok thanks

[deft python]

Ok thanks

[remote sparrow]

it's terse or downright way too skimpy

https://old.maa.org/press/maa-reviews/partial-differential-equations-an-introduction

[vital bane]

I see I wonder why the exposition changes halfway through the book

[proud bloom]

Is there a book that gives a good treatment to precalculus? (coordinate geometry, algebra, trig)

I am not asking for something extremely rigorous that builds everything from axiom book, because that doesn't exist, just something that's good. Khan Academy or similar books are (i) too easy, way too easy (ii) too long, this is boring because if it's easy and too long, it's demotivating.

and no, the book by Serge Lang does not cut it. it doesn't cover half the topics you learn in a standard precalculus course, is way too easy in proofs, and does not go over the computational side.

i am fine with if they are separate books on separate topics. my only requirement is that an ebook should be available.

I dont think any olympiad style treatment of precalculus exists

[quick hornet]

part of the issue here is that "precalculus" is kind of a fake term that means different things in different regions - all it really means is the course taken immediately before calculus, but the actual contents of that course can vary

the reason no competition treatment exists is because they instead use actually descriptive titles, like "algebra" or "geometry"

not just "the course before calculus in this state's/province's curriculum"

as an example, we certainly didnt cover any coordinate geometry in my high school's precalculus course - the only vaguely geometric work we did was a tiny bit of trig identities

[proud bloom]

really by precalculus, i refer to the coordinate geometry (slope, lines, parabolas, all that), algebra (complex numbers, functions, vectors and matrices, special polynomial stuff and all that) and trig (graphs, functions, identities, their special properties, inverse functions) usually covered in 11th and 12th. i am fine if they are separate books.

i cant find any decent book that go over those and you know, dont cost a fortune to buy

[quick hornet]

you can try openstax precalculus but i have no clue if that would be sufficient for you

im pretty sure it doesnt cover any complex numbers or vectors/matrices, for example

(but my high school precalc class didnt cover those either)

oh actually it does introduce matrices in the context of solving systems of linear equations

i do feel like its on the easier end but tbh i have no clue how to judge the difficulty of HS curriculum

[proud bloom]

yeah no openstax is way too long and repetitive and pretty easy

i am not supposed to do all of those problems, but i just dont like opennstax personally

[quick hornet]

i think its kind of just a standard text and youre looking for a market category that doesnt really exist

if a student is comfortable enough with mathematics to find the textbook boring theyre probably not reading the textbook at all and are just learning the material in class or from competition-oriented sources

serge lang's basic mathematics existing at all is kind of an abberation since serge lang himself wrote a textbook for fucking everything

i think he just wanted a "high school math" textbook in his usual style to "complete the set" rather than because he expected it to sell lol

[proud bloom]

its more "i read a really good discrete math book and now i am fantasizing about books for precalc that are simliar"

[blazing holly]

That’s understandable
I’m primarily interested in the first half of the book, so I’ve been spared

(I do care about eigenfunctions obv., but tbh i feel that should come much earlier)

[deft python]

What is the important of discart math ,and what is the difference between math Logic and discart math?

[deft python]

Can you give me the name of this book

[proud bloom]

discart math? discrete math? its just the study of set of discrete (separate) topics; mainly graphs, logic, combinatorics, and cryptography. a jumbo set of topics.

math logic is logic, i guess? discrete math covers logic, but not really as in-depth as those dedicated "mathematical logic" books would. i used "Discrete Mathematics" by "László Lovász". i haven't read all of it, just the combinatorics part and graphs. I dont know how it compares to other dm books.

[deft python]

Ok thanks man

[vital bane]

discart math

what about discord math?

[little coral]

can anyone suggest a book to study set theory from scratch?

[vital bane]

@heady ember

[naive lava]

naive set theory is great as i've heard

and for more advanced stuff kunnen is great

[vital bane]

Halmos?

[naive lava]

yup

[little coral]

thanks
i just want to build a foundation than for advanced things let it for later

[naive lava]

folland's ch 0 goes over the basics if you want a short and concise intro

so does langs algebras appexdix

they go over the most used stuff, if you're not interested in non CH maths these can also be considered

[vital bane]

non CH math

[naive lava]

wait till you hear about non AoC math

[vital bane]

oh never mind I misread CH as AoC

[naive lava]

then lemme introduce you to constructive math

my first analysis textbook was actually a constructive analysis textbook

[molten gulch]

continuum hypothesis moment

[rain wren]

soooooo

just math?

useful math at any rate :3

[plush rain]

might as well use the ryszyck's aops book

[quaint cliff]

i'm taking an applied probability course rn, any book recommendations? the textbook that we use in class is kinda too basic for me it's called a first course in probability by sheldon ross. i'm trynna find a measure theoretic approach to applied probability

[stable flicker]

Why are you trying measure theory if your course is Ross?

[little coral]

i am intrested in every thing
idk whats that tho

[naive lava]

Continuum hypothesis is usually considered an axiom, which says if the "size" of a set is smaller than the "size" of real numbers, then the set has either finite number of elements or as many elements as natural numbers

this is independent from the actual axioms of set theory

[little coral]

hmmmmm
well let this for later
for now i want to know what is set theory about because i dont know nearly anything now about it

[vital bane]

isn't that true if the Continuum hypothesis is false?

[little coral]

i just found two books
Charles C. Pinter (2014) A Book of Set Theory
Naive Set Theory
which is better?

as a starter

[vital bane]

oh nevermind

[naive lava]

id go with naive set theory

it's standard, it's clear, it's in bite sized pieces

i didn't read all of it(too wordy for me) but i've never heard anything bad about it from anyone

[little coral]

hmm alr what about problem solving? do you know any book with problems to solve about this topic?

[naive lava]

set theory? or general?

[little coral]

set theory

[naive lava]

sorry, i don't have any

but the book itself has some

[crude atlas]

any good group theory book covering symmetric groups in detail? Thanks

[brisk rapids]

there's a book named something along the lines of problems and theorems in classical set theory and I believe komjath is one of the authors

[torn blade]

book recommendations for set theory?

oh someone just asked this lmfao

i swear this happens every time i ask smthn in this chat

[gray gazelle]

Lmao

[torn blade]

actually ill ask a new question, any recommendations for a book that treats both logic and set theory at the same time?

[naive lava]

so i was going to actually learn "real topology" after going trough analysis but rudin is driving me insane and i think i will be more productive if i read both at the same time, so i have 2 books in hand, willard and engelking, considering functional analysis is the end goal, would willard be enough? or will i need stuff from engelking? Either way unless it's a absoulutely needed, i won't touch kelley's book, so, advice?

[foggy quest]

In my experience you have to understand PDEs to understand "basic" functional analysis (compact operators, self adjoint operators, etc.). The topology section from Folland's Real Analysis book is enough general topology background. PDE books by Folland or Taylor or Evans are all good

[naive lava]

oh that's no issue, i read most of that, but i wanted to learn topology anyhow, and i need something to go back and forth

not the pde

the topology section in folland

[analog lava]

can one read brezis'

functiona analysis without any ODE/PDE theory but wanting to learn some

?

[foggy quest]

You can, but I find it dry or unmotivated if you dont have an application in mind.

[analog lava]

the application is learning about infinite-dimensional spaces really

if you are into topology/geometry, i want to acquire the analysis enough to understand floer homology

[karmic tangle]

Hello guys

[foggy quest]

I like to read functional analysis simultaneously with PDE. Like, I need to know spectral decomposition of compact self adjoint operator for laplace operator theory, so I take a detour into functional analysis to learn it, then come back to PDE.

[karmic tangle]

Hope I'm not interrupting, I just wanted to ask some questions regarding analysis/measure theory book recs

I've borrowed a book on measure theory called "Measures, Integrals and Martingales", which I've read great things of, and in the prelude it is explicitly mentioned that the author tried to avoid topology

I've also seen it mentioned online that an approach to measure on general topological spaces can be taken, I've not had "classical" measure theory yet but my question is if there are any books that take this approach from the outset and if it'd be a good idea to start with such a book?

[analog lava]

im using bass's real analsyis but it may not be the best for your first exposure

i thikn the best first exposure is cohn's measure theoy

[analog lava]

i see

but how does one start PDEs without any knowledge of ODEs or functional analysis

all my analysis is just basic

meassure theory and basic banach/hilbert spaces and the 3 main theorems

[foggy quest]

that's enough for PDEs.

[analog lava]

i know 0 ODEs

is that okay

[foggy quest]

Yeah. For example, Taylor's PDE book covers ODE briefly. It seems that ODE is more necessary for differential geometry than PDE.

[analog lava]

i see

very cool coincidence ig

well my end goal is also topology/geometry but yeah 😄 thank you

[hollow peak]

you can just read brezis lol

The first half is just straight functional analysis

[remote sparrow]

unrelated, but schilling has a full solutions manual readily available online for this book

[ruby thistle]

how about a book called

Problem Solving strategies

arthur engle

[viscid comet]

I just got an undergraduate thesis advisor!!!!

Does anyone have any good introductory texts or papers that they recommend on domination or maximum flow/circulation problems

Looking for surveys to get acquainted with the topics at a high level atm

[dawn crow]

any good books for tensor calc fr beginners

pls

[vital bane]

complex topology when

[vital bane]

I have seen Neuenschwander been recommended for Tensor Calc

(From a physics POV)

[naive lava]

Eigenchris on yt is good, Carroll's Gr book is also good

[naive lava]

You can't pay me to study that

[molten gulch]

How different is topology on C than R

[viscid comet]

The topological properties of C are pretty much identical to R^2 under the usual metrics

[vital bane]

it's a joke based on the fact that dogu said "real topology"... so yk? complex as opposed to real

[viscid comet]

Quartenion topology

[vital bane]

But let's not do octonion topology

[vital bane]

Eigenchris mentioned, the GOAT

xylyxylyx is also very based

[viscid comet]

Quick, make C a totally ordered field

[naive lava]

Oh i thought he meant Riemann surfaces and shi

[vital bane]

[molten gulch]

Thank you :)

[molten gulch]

Ahhhh

[sudden kindle]

Riemann surfaces changed my life

[vital bane]

hopefully for the better...

[sudden kindle]

Yeah

[weak shore]

Does any one know good resources for undergraduate algebra courses?

[quick hornet]

"algebra" as in abstract algebra?

[sand path]

Advanced Precalcus by Daniel Kim. You’ll be stronger than anyone in the class

[rigid trail]

I'm excited for complex analysis

[vital bane]

it is SO cool

[karmic tangle]

very cool thank you

[gray gazelle]

hey what's a good starting point for somebody who doesn't know their math level? i'm technically a dropout due to life circumstances so i haven't been to school in years and i have no idea what i forgot or still remember. i was also never really a math person as a kid but over these past few years i've developed a huge interest in it and i've finally made my mind up on committing to learning

i've heard khan academy's good but i think i'd prefer books as i enjoy reading

[clever pier]

That really depends on how far back you need to go. Do you know the multiplication table?

[near jewel]

Do exams from 1. grade, 2.grade, etc. till you find hard to do. Then, learn what the grade is teaching.

[timber radish]

Hi, I'm really interested in complex analysis, I was wondering if there are any good books that go pretty in-depth

[naive lava]

what are you looking for exactly?

and what's your background

[timber radish]

I'm pre-university, but I've alredy finished that math outside of schooling. Now I'm more just exploring different unique topics and proofs

[naive lava]

how good are you with calculus?

[timber radish]

I finished year 2 calc material with tutor, so I'm pretty familiar

[naive lava]

linear algebra? it's not necessary per se, but it's a very useful tool to have under your pocket

[timber radish]

I've done most of the course material for linear algebra

[naive lava]

okay than you can probably read churchill and brown or gamelin

they both take a slow and steady road

but gamelin covers more

c&b has more applications

[timber radish]

Thank you, I'll make sure to check those out

[hearty aspen]

hi all, I was recently accepted to a fairly competitive summer research program, and my first listed research subject was algebraic number theory
I have a decent background in group theory from last semester, and have just finished rings, but haven't done fields or galois theory

I was thinking of starting marcus' number fields to prep for the program and get some background info; is this a good idea and are there better books for this?

[gray gazelle]

i do know the multiplication table but my mental math isn't as good as i want it to be

sorry for the late response

[gray gazelle]

you mean the khan academy exams or should i look into the ones they give kids in the school curriculum?

[daring lake]

Congrats on getting in!

I think getting some background is good, but have you verified or communicated with the program (or mentor) what topic/area you will be working on? (Ofcourse, its nice to study something on its own too).

[hearty aspen]

thanks! i have verified that i will be attending, but i haven't received additional information like my mentor or my specific project yet

i believe the program is structured for a week of classes, then to go into a 5 week research project

i've been wanting to look into alg nt anyways so it would be cool just to study it on its own

but it's more motivating now that i have this

[near jewel]

Pupils, students; from elementary to junior high school, to high school, to university (bachelor), etc.

[proud bloom]

where do i buy this online tho?

like the ebook if its available

it costs like 50$ on amazon to order, which is pretty pricey

[tardy eagle]

There’s free libraries online!! the Internet archive.org is an amazing source!

[proud bloom]

that particular book is not really available anywhere. not internet archive. not any of the book stores. not even those cough sites. i checked.

i am not big a fan of physical books, prefer paying for ebooks

[tardy eagle]

I just found it with one search? Advanced pre calculus By Daniel Kim correct?

[proud bloom]

yes

where

[tardy eagle]

Quick question but did you not Google it?

[proud bloom]

i did; i checked all the sites. found only physical copies

[tardy eagle]

https://www.scribd.com/document/790061622/Advanced-Precalculus-2-1-1 Its on google books and amazon for 33 usd

[proud bloom]

what the hell

[proud bloom]

my first result of scribd was like a scam url

so i didnt check hte other results

[tardy eagle]

How so-??

[proud bloom]

thought it wasnt a legit site

[proud bloom]

i was like going through yandex, uh, i am not sure i am allowed to send the url here, but it was like those standard "scam" url. the original url, was scribd[someothernumber], so i didnt check.

well thank you

[tardy eagle]

i have a good anti virus i can check the doc for you if you want

[proud bloom]

dont need it, its just a pdf. i have js turned off, so not a concern. thank you for the offer, though.

[tardy eagle]

ya no worrys

[finite shale]

For those interested, Springer has offers a 50% discount at link.springer.com with the code HLT50

offer ends today at 23:59 EST

[grim ore]

Thank you so much

[finite shale]

what is your question?

[mortal ore]

I think they want a multivar calc textbook

[finite shale]

I like Apostol

[pale dove]

hi, does anyone know a textbook where i can read about weighted functions spaces or more specific weighted lebesgue and sobolevspaces?

[finite shale]

Sorry I was wrong, it's 23:59 tomorrow EST

[earnest wolf]

can anyone recommend some problem-oriented resources for a first course in combinatorics?

starting from stars-and-bars

[remote sparrow]

nice

[celest bear]

Is there a noticeable difference between Thomas' Calculus, Calculus by Stewart, and Calculus by Howard Anton? I currently have Thomas' calculus paperback 14th edition and was wondering if there is a better book or should I just stick with thomas?

[remote sparrow]

no

[celest bear]

Really? What was ur experience with any of these books?

[remote sparrow]

i used stewart in high school and larson for multivariable calculus in community college

[naive lava]

they present basically the same thing, just minor changes, with the same style

you won't miss out

[celest bear]

Ahh I see

I guess I’m just a little nit picky about my book

[celest bear]

Larson teaches multivariable?

[remote sparrow]

most calculus books cover multivariable calculus

provided you're buying the right edition

sometimes publishers split them into "single-variable" and "multivariable" books for some reason

[celest bear]

What topics are included in multivariable calculus?

[remote sparrow]

your copy of thomas' calculus probably has a table of contents, no?

you can look there

[celest bear]

It does

But I don’t think it mentions multivariable

[remote sparrow]

really?

nothing about multiple integrals, for example?

or volume integrals

stokes theorem?

divergence

none of those words show up?

[celest bear]

Multiple integrals I think

Greens theorem

Stokes

[slow roost]

a lot of intro calculus book are single-variable only. Like Stewart

[remote sparrow]

ok so your book does cover multivariable calculus

[remote sparrow]

you might have been unlucky because the standard editions that are sold cover three semesters of calculus

stewart is not a "single-variable" only book

[slow roost]

oh, I didn't know that

[celest bear]

Yeah

But I’m curious what topic does multi start with

And when does it end

[slow roost]

it seems my version is explitly single-variable

[celest bear]

Bc Thomas doesn’t specify when u transition to multi yet there are topics on it

[remote sparrow]

chapter 12, vectors

[celest bear]

Oh

Well I’m not even close to that so it’ll take me a while

I heard Stewart has a problems plus section whereas Thomas has an advanced exercise section

Some say Thomas problems are easier and more drill like?

[merry sphinx]

imagine stewart being 1300 pages and only single variable

[slow roost]

I've had it all wrong, gonna have to think about buying the real thing now

[remote sparrow]

i got a copy of the 6th edition for like $12

[slow roost]

my single-variable version is still over 800 pages though

I have Colley for multivariable

it's alright I guess, never excited me much

holy smokes, the price for Colley on amazon is insane

[naive lava]

does he build everything from, like, idk, addition?

[slow roost]

oh it's probably a fair bit longer than usual because it's an instructor's edition

[remote sparrow]

well, there's a 5th edition now

https://www.pearson.com/en-us/subject-catalog/p/vector-calculus/P200000007574/9780136800101

[slow roost]

oh cool. yeah I was looking at the 4th

[celest bear]

What???

So cheap

Is Pearson good for their textbooks?

[naive lava]

you should probably choose textbooks by their reviews and not the publisher

every publisher has good and bad books

[celest bear]

Yeah

But some books got similarly good reviews so it’s kinda hard to choose between

[naive lava]

the "basic" courses have many many textbooks that are good because the way to present topics is very standard and many people published books in that subject

so adams, stewart, thomas... all very similiar, therefore you get similar reviews

if you're buying, then it'd suggest getting the cheapest one

if you're not, just spin a wheel to decide

[celest bear]

I found a James Stewart calculus 8th edition at my library

[celest bear]

Yeah Thomas was the cheapest option and not even the hardcover

I kinda regret it bc this copy isn’t in color and the paper quality isn’t on par with its hardcover counterpart

But oh well, what can I do?

[naive lava]

these are also the textbooks you won't hold onto until the end of time, so those factors are kinda irrelevant

that's how i decide which textbooks i actually wanna buy

[celest bear]

True, I just like all textbooks

[naive lava]

same, but i hate all of them

[celest bear]

[celest bear]

https://a.co/d/7MjhZhx

This is the current book I have

[naive lava]

seems like it covers everything you'll possiblily need in regards to calc

[celest bear]

Great that’s all I needed to hear

[hearty steppe]

Fractional calculus recs?

[vital bane]

you'll be VERY good at single variable calculus by the end of that

[blazing holly]

Any recommendations for literature on integral transforms & integral geometry?

[vital bane]

what is integral geometry

[fresh skiff]

what could be the good references/sources for learning AA? (My main text is D&F)

[vital bane]

references other than D&F? D&F itself is like a reference

[fresh skiff]

well thats true actually
but still if something that i can use on side exists

[vital bane]

Gallian is a nice AA book it has a lot of visual stuff, I'm not sure how well that would complement D&F though

Gallian's "Contemporary Abstract Algebra" 10th edition is the latest I think

[fresh skiff]

i have read like first 2/3 chapter of Gallian
book with a LOT of problems

[vital bane]

Oh Noicee

[vital bane]

yea it's like Abbott with the amount of problems it gives out

but don't worry D&F has even more

[fresh skiff]

[remote sparrow]

#book-recommendations message

[heady ember]

How did you forget about my boi Jacobson

https://tenor.com/view/cant-believe-youve-done-this-punch-ouch-gif-9605268

[fresh skiff]

oh gosh how i forgot this

[crystal flame]

Good books to learn probability and statistics? And if there is any prerequisites let me know that too

For linear algebra ill be using gilbert and for calculus velleman
Someone confirm on this too

[vapid cargo]

hii! just wanted to know if anyone here had any good recs for astronomy, especially books that are beginner friendly? ty in advance

[remote sparrow]

learn calculus first

[median saffron]

most people dont study astrophysics here so u will prbably have better luck in the physics server

[vital bane]

water beam in book recs? what timeline are we living in

[median saffron]

ive been in book recs b4 when i first started calculus, sourdrop recommended me a book

[vapid cargo]

oh okayy, i see!

[naive lava]

you might wanna check out lang or hungerford

[spring night]

Is differential equations with applications and historical notes by george simmons a good introduction to DEs

[fresh skiff]

Lang would be harder i believe, but yeah i have heard Hungerford is of same level of difficulty as D&F

[heady ember]

Is it as long though? If so, you might need to Hunger down.

[fresh skiff]

are you talking about Lang?

[heady ember]

No I was making a pun: hunker ~ hunger ~ hungerford

[fresh skiff]

oh LoL

my english skills issue

[heady ember]

Oh no a League player. We must run, allegedly.

[minor glen]

"I have a question. I am a high school student, and I am self-studying advanced courses, but many books do not have answers. How do you solve this problem? Can you recommend some books on calculus, preferably with solutions?"

[tender river]

why is that in quotes 😭

[minor glen]

I made a mistake in typing.

[hearty steppe]

I guess fractional calculus might be a bit recent to ask about on this server or maybe it’s just the wrong place and or it’s not taken that seriously yet

[stable flicker]

Are there even books on fractional calculus?

I know there are some works on it

[hearty steppe]

There are but I don’t like to blindly sift through books

[stable flicker]

Not sure if they have any mathematically meaningful content

[hearty steppe]

Mostly fractional differential equations

[stable flicker]

They are pretty difficult to calculate too

[hearty steppe]

Maybe I should be looking at the diff Eq focused texts

I got some diff Eq stuff on my reading list. Interesting but broad area to explore

I mean you are in analytical territory so of course lol

Oh it’s looking like the fractional stuff is new. I’ll try to get my ass kicked trying to understand it, YOLO 😂

Been doing a decent job exploring the high level stuff recently. Can’t say I’m great at it but been not banging my head as much

[dense plover]

best book for basic calculus/calculus1? also best online resource/yt vids/channels? thanks in advance if ya reply 🙂

[gray jungle]

Not sure about the base theory itself, but the general theory is extremely important, altho you'll need some functional analysis at hand for that, see pseudodifferential operators.

[dense plover]

anyone??

[limber bolt]

introduction to calculus?

do you want rigor or application

[dense plover]

i want to study it as a prereq to sucjects like linear lagebra, electrodynamic,statics. and then quatum stuff too, so yea

[hearty steppe]

I’ve largely been focusing on functional analysis books. Good thing I had that same intuition moment you just prompted. Thank you

[limber bolt]

you can study linear algebra without calculus but if you have never done calculus before, i recommend stewart's book

the 9th edition

as for youtube sources, try MIT's playlist on single variable calculus

[lofty plover]

yeah linear algebra doesn't require knowing calculus but you can apply it to calculus

[dense plover]

well i wanna study quatum mechanics and subjects which originate from it, these would serve as base for that

[limber bolt]

start from stewart's calculus

[dense plover]

alright, appreciate it, ill order that then, thanks again!

also is gilbert strang's linear algebra good?

[limber bolt]

yes its fantastic

[dense plover]

alright then

thanks 🙂

waittt, the stewart book is way too expensive X-X, is there no cheap alternative?

im a minor so i ofc wont get that big an allowance

the 8th edition, transendentals is far moree affordable, is that good?

[vital bane]

fake James is imitating real James now...

Banach

[signal badge]

I don't think there's a difference in content. Calculus and Calculus: Early Transcendentals just switches the order of certain things around.

[molten gulch]

AFAIK more specifically it's whether e^x is introduced prior to integration

[vital bane]

all my homies love e^x

[blazing holly]

That works yes
There’s also pdf’s of the 9th edition if you know where to look

[blazing holly]

Completely unrelated but
I love that anime

[gray gazelle]

Does anyone have a clean pdf of Introduction to the Theory of Numbers by Hardy and Wright?

[molten gulch]

Piracy and distribution of pirated materials is prohibited here

[gray gazelle]

Isn't it public domain yet?

[molten gulch]

No

[gray gazelle]

Mother Anarchy help us

[molten gulch]

I don't think at-least

[nova dagger]

Might be a strange request but does anyone in here know of any books that basically contain a complete start to finish of most of the mainstream mathematical fields (Algebra, Calc, geometry, topology, linear algebra, stats/stochastics basically the whole gamut)

[molten gulch]

Such a text doesn't exist

[nova dagger]

Damn

I wanted like one book I could use to get up to speed on everything over a year or two of intense study

And then branch out into more obscure and advanced disciplines once my foundation was perfect

[fresh skiff]

Reading different books is cool, you don't need a single text

That doesn't exist in actual lol

[nova dagger]

Basically I’m the typical burnt out former gifted child that competed in youth math competitions and did excellent, always scored highly but underwent a deep depressive/other mental issues spiral in late elementary to high school and stopped studying or working towards my future

I’m rekindling my fascination with math now that I’ve overcome a lot of that crap

But it’s overwhelming to even start

[molten gulch]

We're in almost exactly the same boat, you just have to pick a topic and get started

Though, ig for us it was a little bit easier due to some irl friends pushing us to keep trying along the way, but the main idea still stands, pick a topic, find a text, and start reading, maybe attend some uni lectures if possible, watch youtube, etc...

[nova dagger]

Yeah you’re right, thanks. My strongest subject was always algebra so I’ll probably start with resurrecting my foundation there

[tender river]

and ask for help when you're stuck

this server is a good place for that

[nova dagger]

With that in mind, what’s your guys’ favorite books for intermediate algebra students then?

[molten gulch]

Abstract Algebra or high school algebra?

[nova dagger]

Abstract, I’ve got high school algebra down pat since early childhood

[molten gulch]

#book-recommendations message

[molten gulch]

Oh also for future reference, Dami's book reviews are all pinned here in the channel and AFAIK @remote sparrow also has some of their own they can link to

[nova dagger]

Nice

[molten gulch]

We wish you luck with your studies :)

[nova dagger]

You as well

[molten gulch]

thank you

We will say, out of the books we've looked at, our favourites so far have personally been Artin's Algebra and Rotman's Advanced Modern Algebra; one of our friends likes Gallian, another likes Herstein, and our best friend like Lang's Algebra

[nova dagger]

Yeah the post you linked mentioned Artin as the typical best starting point

Will probably begin with that and check out the others as I progress

[molten gulch]

Yep!, Dami's post is how we learned about Artin

[hearty steppe]

That being said I hope he has some nice functional analysis book recs in mind. I’m enjoying the subject and I like looking at other takes

[gray jungle]

There is three book i use depending on what im doing: Brezis, rudin and yosida

yosida is a very nice book if you have the background for it

but all three of these require some measure theory and topology going in

more lightly is kreyzig which assumes only real analysis

[vital bane]

Have you ever used Peter Lax's func anal book?

[gray jungle]

yes i use it as a reference

[full cairn]

Afaict, in the UK a book is copyright protected until 70 years after the death of its authors. EM Wright died in 2005, so Intro to the Theory of Numbers should be in the public domain in 2075

[hearty steppe]

Yea Kreyzig is nice. I started going through Kolmogorov and Fomin

[grim delta]

Any good books on Analytic geometry??

[gray gazelle]

Hello. I'm looking for recommendations of books at the HS level (chemistry) more focused on entrance exams that have a lot of exercises

[blazing holly]

I dont think there are that many chemists in here to give good reqs, try asking in the chem server (in #old-network )

[jade viper]

Hey guys, do you have any more mathematicial books on QFT? I'm an undergrad physics & math and I want to self study a bit before I take it, but I prefer more mathematicial styles (Theorem, Proof)

[gray gazelle]

I'd like for physics too @blazing holly

[normal crystal]

if you want books for a specific entrance exam
look for books on that exam

[vital bane]

@median fossil

btw there are lot more mathematical physics people in the physics server than the math server (for some reason )

[torn crypt]

What kind of analytic geometry

[floral lantern]

Not really great options in the field. Talagrand has a book, and Pavel Etingof released a preprint of his (soon to be published) book.

Peter Woit has a QM book that does a little QFT and is very approachable

[tired hound]

can I ask a question here abt reading math books, but not necessarily a book recommendation? not sure if this is the right channel

[floral lantern]

Maybe more appropriate for #math-discussion ?