book-recommendations

[slate quarry]

Algebra for college students, by Kaufmann & Schwitters

[bronze raven]

trilogy of books for becoming linear algebra goddess

[gray gazelle]

probably worth taking a look at the 4 pamphlets written by gelfand

[strange bluff]

are you looking for hardcover only or are the high seas something that does not float with you?

[quick hornet]

we would certainly never advocate for piracy on this server, oh no, even if it goes basically completely unpunished and is as simple as downloading a pdf or djvu

after all, that violates discord ToS.

[gray gazelle]

@gray gazelle this is a list of recommended books from topology by Hatcher

[karmic thorn]

Dover has generally reasonably priced books, you can go through their catalogues.

[gray gazelle]

There's Dugundji for example, and it's out of print so there's a copy online

[karmic thorn]

I don't have any specific recommendations, but this might help:
https://math.stackexchange.com/questions/359784/the-best-of-dover-books-a-k-a-the-best-cheap-mathematical-texts

[bronze raven]

where is munkres

and his book is trash

so remove it from the list

where is lee

[gray gazelle]

Munkres is too expensive

[bronze raven]

???

I got mine for free

[karmic thorn]

[gray gazelle]

According to Hatcher. Besides a little diversity in from who learnt from what won't hurt anybody I think

[bronze raven]

not harmful words but hatcher should remove his algebraic topology book

maybe for exercises only

it actively hurts clear understanding at beginning

[gray gazelle]

I don't like his book but I'm sure there are people that enjoy it

[bronze raven]

no one enjoys it

there are two types of people

those who only read hatcher

and those who have access to other books

[gray gazelle]

Sure

Don't get me wrong, normally I'd say the same thing

But I'm trying to not be too judgemental

@icy frost thoughts on hatcher?

[icy frost]

In my opinion it's a nice book I guess. I haven't read any other AT book tho so I can't say how it compares to other books but Hatcher definitely takes the more intuitive/geometric approach to the subject than other books according to like the most people I've talked to. I feel like Hatcher leaves a lot of stuff to check. So for example there's a lot of places where Hatcher just says "then blabla holds" or like "yadayada is true" but he doesn't really explain why. But idk, it might just be me

are you looking for an AT book?

oh lmao there's a whole Hatcher discussion above that I didn't notice

[forest pagoda]

yup yup

[lofty thicket]

Do you guys have book recommendation for functional analysis and complex analysis?

I'm undergrad, and I need some good theory books, and solved problem books 😄

[gray gazelle]

There's Conway for complex anal

There's also this book by Shakarchi

for functional, "analysis now"

it has many good problems

Ah yes, for fun anal there's that

[lofty thicket]

Okay guys I'll check those, really want to try better on this subjects so I'm going to try harder

any advice?

I basically paused this year and I have feeling that I've forgot how to study...

hahahah

[gray gazelle]

do exercises, discuss the material with people, and take breaks

the last one is very important :^)

[lofty thicket]

I don't know, I somehow got discouraged that nobody in my uni get A in any analysis

[gray gazelle]

sounds like a uni problem and not a you problem

[lofty thicket]

hahah yeah but it stays in my CV

[gray gazelle]

this is true

[lofty thicket]

kinda started hating math bcs of those people there

[gray gazelle]

unfortunately grades matter

[lofty thicket]

true

[gray gazelle]

I got A+ in all 3 of my analysis courses

[lofty thicket]

I'm glad to read that! Any special advice? How did you study for those?

[gray gazelle]

Umm... I'm not sure

[lofty thicket]

Like are uni professors rarely recommend even one problem book, they don't even give advice on how to study.. so any help would be appreciated 😄

[gray gazelle]

I didn't study that much tbh

[lofty thicket]

Oh so I guess you're really smart then 😄

[gray gazelle]

not really

[lofty thicket]

hahah then where did you study?

[gray gazelle]

I read about series from Sierpiński book around end of high school or something

and how to integrate etc. idk, just picked everything up along the way

[atomic hound]

Yep!

[tawny crater]

if you wanna get A study the proffessors, not the material
getting 100 means that you can pass any question the prof throws you at you, which is close to but not exactly is the same as knowing the material

[gray gazelle]

pain

[marble solar]

Yeah this is an unfortunate thing in math

[gray gazelle]

i had a class where the prof kept saying "grades don't matter"

there wasn't a single student who agreed with him

[marble solar]

It's true in like an existential sense, and eventually you graduate and what you do is more important than what grade you got

But if you have bad grades like me, it will anchor you down

Like it has for me

[sharp latch]

Hey, I’m looking for a book to help me self study elementary number theory. I have been using burton for a while but i really don’t like the exercises because there is 1 good one for every like 30 computational/trivial ones. What are your favorite elementary number theory books that you think are good for the self studier?

[brisk cargo]

Good calc 1 book? I can't find a good one

[sharp latch]

People like to recommend spivak’s calculus. However, most books will be fine since Calculus is a very common subject so there are tons of great online resources to pair your learning with (khan academy, Paul’s online math notes, etc)

[brisk cargo]

alright

thank you very much

nice i looked for spivak on google and the first result is a 900 page pdf

[tranquil ocean]

Do you know any abstract algebra?

[sharp latch]

Not really, I know the definition of a group and some examples

[tranquil ocean]

Maybe Silverman's A friendly introduction to number theory could be a good choice then

[gray gazelle]

Orbital Mechanics Bruce A. Conway

if anybody have this book pls send

thank you ! /(^)O(^)\

nevermind

[gray gazelle]

Out of curiosity, what are number theory texts which assume a knowledge of algebra?

[tranquil ocean]

Ireland and Rosen

[faint dune]

Does anyone know some nice physics book written for mathematicians? I'm particularly interested in something about quantum field theory

[tranquil ocean]

I enjoyed reading http://www.damtp.cam.ac.uk/user/tong/qft.html

[misty wyvern]

How much math or physics do you know radiateur

Tong is good

[faint dune]

For physics I know basic QM and special relativity

[gray gazelle]

Tong is rather nice for QFT

[misty wyvern]

Check out Folland's QFT book

That's the math perspective

for physics look at Zee

[gray gazelle]

Rigor QFT is probably a bit much, but the classic is PCT, Spin, Statistics, and All That

I don’t like Zee; it’s good as a supplement, at best

[misty wyvern]

I don’t like Zee; it’s good as a supplement, at best

Friendship ended with Tesseract

Yeah if you want rigor use Folland

[gray gazelle]

I've tried very hard to like Zee, but always end up despising it a couple chapters in

[faint dune]

I don't necessarily want full rigor, I mostly want something that doesn't assume much physics intuition but is not afraid to go into mathematical abstraction

[gray gazelle]

hmm, I don't know much for QFT like that (especially because QFT is still rather shaky mathematically)

[misty wyvern]

Maybe Coleman's QFT?

Coleman is a legend.

If you really want to be a meme there's Deligne and Witten's book

[gray gazelle]

Oh! Oh! Weinberg's three-part series The Quantum Theory of Fields probably fits the bill

[faint dune]

Why is it a meme?

[gray gazelle]

It is not recommended for a first pass, but hey

[misty wyvern]

Just read it and find out for yourself.

[gray gazelle]

Weinberg QM is very good for a second pass at the subject and is rigorous on the standards of physics. it's also a tad idiosyncratic

[faint dune]

Weingberg QM = The quantum theory of fields?

[misty wyvern]

Tesseract do you like or hate Sakurai's QM

[ripe granite]

it is not a meme

I bought the book

it looks pretty good

[misty wyvern]

Did you actually manage to work through it

[ripe granite]

no

[misty wyvern]

I gave up only a few sections in

[ripe granite]

rip

why

[gray gazelle]

I like it a lot actually

It does have its issues, but it's a good book

[misty wyvern]

why

I get the vague feeling I was supposed to have mastered Hatcher or some other alg top text before attempting it.

It does have its issues, but it's a good book

I like it too, I guess we can be friends again.

Usually Sakurai cuts theoretical physicists into two.

Half like it, the other half thinks it's garbage.

[ripe granite]

werent you talking about learning DAG in the physics server tho

if you know enough to learn DAG

you should be able to read the book

[misty wyvern]

I didn't learn DAG, if I mentioned it I was memeing

[ripe granite]

[misty wyvern]

The most algebra i know is C*

[faint dune]

Well thanks for the many suggestions everyone, I'll give them a look

[gray gazelle]

[sharp latch]

I’ll check it out! Thanks

[crystal lion]

Directed Acyclic Graphs are easy

because that is what you are talking about

[misty wyvern]

Close enough

[halcyon hornet]

Any Number Theory books for under grade 12? For Competition Math and Introduction to Number Theory.

[near onyx]

looking for a grade9-10 book on geometry, filled with practice problems along with some lectures. I also need to learn all the formulas needed

[coral narwhal]

what is the standard combinatorics book for first undergrad course?

[karmic thorn]

I'm not aware of a standard, but A Walk Through Combinatorics by Bona is really clean.

[coral narwhal]

yeah this looks nice thanks

[karmic thorn]

[faint dune]

Stanley is great too

[atomic hound]

@HeRoBrinE#2582 i am studying trig with this book, it has some algebra in the beggining ,but this book dont dive to deep on trigonometry.

[crystal lion]

Bona covers group theoretic combinatorics too

like burnsides lemma

which is cool

[gray gazelle]

ok thanks

It might if the exercises are relatively easy

[sharp latch]

Maybe a low level elementary number theory book

I don’t have a recomendaron for that though

[karmic thorn]

Yeah, that works. For elementary analysis books, Understanding Analysis by Abbott or Elementary Analysis by Ross are apparently good.

[fluid bay]

I learned proof writing by doing linear algebra personally

Some people are more analysis-minded though

[mellow depot]

anyone know of a good tensor analysis book? i have done linear algebra, real analysis, diff eqs

[crystal lion]

bishop and goldberg’s tensor analysis on manifolds is a classic

although you should probably know some point set topology going in, because it reviews it in 15 pages

[keen aspen]

Discrete mathematics by sussan

[analog pollen]

this is a book recommendation channel for MATH related books.

[keen aspen]

Well um

Now its gud

[cursive orbit]

Is discrete mathematics not math related?

[analog pollen]

Idk his original message was some religious book

He edited it to make me look stupid or something

Kinda weird dude

[edgy helm]

thinking of diving into Sutton and Barto's second edition of their Reinforcement Learning book - does anyone know how it is?

[serene falcon]

https://www.amazon.com/Introduction-Mathematical-Fluid-Dynamics-Physics/dp/0486615545 what math knowledge would i need to understand this book?

[hearty steppe]

oh boy im at fluid mechanics chapter of Young and Freedman and man is that one hell of a ride to get through

it seems to me that you can't really prepare yourself that well for fluid mechanics cuz its not a really solid area of physics

like very loosely defined

its trippy tho

[misty wyvern]

it's as solid an area of mathematical physics as any IMO. it just has very few good books. batchelor is still recommended to this day and that's kind of a meme by now

i also recommend bertozzi and majda, lemarie-riusette, and vi arnold

[gray gazelle]

hey

i need to pick up maths again

i have the knowledge of 10th or 11th grade, but i need to pick it up again for university

does anyone have an easy math book to get introduced to?

or is the steward book what i need?

i'll look them up

[cursive orbit]

I'd just recommend Khanacademy

[lavish parrot]

I’m a calc iii student attempting to understand this

[misty wyvern]

nice

[sage python]

@slim nacelle

[slim nacelle]

Goldfield and Hungry (hungry for a better book)

[sage python]

Lol what do you prefer instead? :P

Actually I found one recently which might be good for learning about groups other than GL(2)

By Paul Garrett

[lavish parrot]

I am trying to expand my knowledge beyond calc iii any books youd recommend?

[sage python]

"Modern Analysis of Automorphic Forms by Example"

[lavish parrot]

thanks 😄

[sage python]

Lol not quite for you

[lavish parrot]

oh lol

[sage python]

I guess Bump but it feels less explicit if that makes sense

[sudden kindle]

Bump has a lot of exercises

[sage python]

Ah yeah that's fair. I guess my thing with GH is that there are a good number of examples of like

Computing integrals of stuff over GL1 and GL2

But yeah GH has questionable organization and doesn't talk enough about newforms, Eisenstein series, Hecke operators, holomorphic theory

[misty wyvern]

Modern Analysis of Automorphic Forms by Example

Ah yes, the mysterious Calculus IV

I remember a professor in my undergrad uni, due to a clerical error, teaching a Morse theory class categorized under "applied math"

[fossil badge]

I've seen Morse theory applied before

[brisk ice]

How would you rate the openstax books? Like not just math but all the subjects they offer. https://openstax.org/subjects

They seem more geared towards highschool or maybe early classes in college

are the answers available in the books

I remember looking at in on mobile and they had some lectures or something but they were behind some monthly pay wall

Oh it appears the app has something called "study edge" paired with it

[coral narwhal]

nvm bruh I was thinking of something else I have seen these but never used these

[brisk ice]

are you aware of any other similar sites that offer free books? I know certain schools post lectures and notes etc and i guess those might even be better. Looking for "self study" stuff . I guess khan academy would be an example

[coral narwhal]

I was thinking of libretexts btw which is kinda similar

[brisk ice]

Are most books made to be self study or do they expect you to use them with an instructor?

[coral narwhal]

I think its intended for self study from just reading it but I only used it as reference when I was too lazy to go get my actual book so I don't really know also I only looked at orgchem so no clue about math or other subjects

[brisk ice]

yeah i dont have really any experience with going through an entire book

normally they are just used as reference

[brisk ice]

I was more referring to books as a whole , not just from open stax. Like if you buy some math book do they expect you to be able to go through it yourself

Guess depends on the person and the book

i mean even with lectures/classes and stuff I look up crap anyways so I guess the point is a bit moot in saying it is self contained.

[coral narwhal]

depends on the book tbh, I have not used many actual books for self study but I have seen/gone through intial 3 or 4 chapters of 3 intro analysis books and I don't think any of them was intended for self study except for Tao maybe

[brisk ice]

But I do assume some books are more purely made for reference and others more to teach you. Just have to find the right one

[coral narwhal]

I don't know if this is a good strategy but the strategy I have used is just going through some chapters myself and then deciding based on the contents of those chapters

[brisk ice]

Yeah that makes sense? So like if you struggle to understand those chapters what do you do?

find a new book or just accept that you have to find outside resources to go along with it?

[coral narwhal]

I have not struggled enough yet 😎

it depends on the kind of struggle I guess, like I haven't found a book where I had to change or stop reading because of the exercises it was usually the contents and my lack of pre-reqs that stopped me from moving further so I just went back to pre-reqs (I am talking chem books here tho)

[brisk ice]

Yeah I guess that makes sense. Sometimes it is hard to say what exact pre-reqs are needed for this or that book

and then you don't exactly know until you get into it and realize you have to jump backwards and learn x,y,z to get back to understanding the book

[slim nacelle]

I'm mostly memeing, GH volume 1 is quite good especially for computing the L-function integrals

GH volume 2 is awful

Bump I still feel is better than GH volume 1 but it takes more active work

[proven dove]

Read One Piece

[sage python]

Makes sense yea. But actually just tell me what you think of Garrett's book

[slim nacelle]

I really like Garrett's book

[sage python]

Oh lol was gonna link

But yeah this might be nice for understanding small groups that aren't SL2 lmfao

[slim nacelle]

yea I think generally speaking Garrett's book is better

for GL_2 specifically GH volume 1 is better

[sage python]

Someone should write a GH-sized volume for each small group 🙃

[slim nacelle]

yea seriously

I would really like to see this sort of book written for Sp_4/GSp_4/PGSp_4

Flicker's book does PGSp_4 in this level of detail but it has so many mistakes the book is an ordeal to go through properly

[gray gazelle]

Anyone have a good book that goes over diff equations? i need a book that has solutions and work with the problems.

[misty wyvern]

@slim peak you had a book you liked right 😌

[slim peak]

Viorel Barbu's book

Thank you for summoning me human

Here is your reward : some part of my wisdom you can contemplate.

[gray gazelle]

Thank you anatole

i downlaoded it

[frosty girder]

can i have some as well?

[gray gazelle]

Elementary Number Theory by Burton, David.
Comments?

[grand osprey]

Does understanding analysis by Abbott have a good bunch of problems?

[livid ermine]

I really liked this book

It has some nice historical interludes at the beginning at each chapter, and the main material is very readable

[livid ermine]

tbf I only read the first 12 chapters I think

[deft talon]

could someone recommend me some online resources that will help me learn more about Big-O notation for discrete maths? (please ping me if you do)
I'm struggling with my math classes on that topic

[cursive orbit]

CLRS has a pretty in-depth chapter about it

[plain barn]

do someone knows some book (or textbook idk) about logic so I can have a huge brain?

[stray veldt]

mathematical logic by ebbinghaus

[plain barn]

ok thanks

[near onyx]

Looking for good grade 9-10 geo books?

[sage kelp]

Thoughts on Garling's Mathematical Analysis books?

[pseudo timber]

Here's a little list from me

• The Collector
• Fear and Loathing in Las Vegas
• Fight Club
• Choke
• Any Palahniuk book besides diary
• Leviathan (Hobbes)
• Lolita
• Look who's back
• Paradise Lost (my favourite of all time)
• Jane Eyre
• Written on the body
• Any of Lovecraft's works.

[lapis sundial]

thanks for the recommendations

Brontës are cool

[willow pecan]

Time to recommend Omniscient Reader's Viewpoint again

[gray gazelle]

It starts with basic and upto advanced level.

[graceful dawn]

Why do we have some Contemporary Abstract Algebra books instead of Abstract Algebra?

[karmic thorn]

Are you referring to Gallian's book?

It's a bit of fancy-naming, apart from the fact that Gallian shows you some very specific developments that are more recent than what you'd see in a typical first algebra course.

[marble karma]

Man is gallian a good book? We will have a group theory course next semester was wondering if I should read dumit foote or gallian

[karmic thorn]

I'm using Gallian but DnF seems more standard. Pick your favourite, I guess. Also, Gallian doesn't cover group actions and more advanced stuff.

[marble karma]

I think I should study from DnF and use gallian as reference

[karmic thorn]

Try a bunch of books, see whatever floats your boat

[marble karma]

Yeah you are right

I should find a book that I am comfortable with

[karmic thorn]

Ideally go for one where you don't feel out of your depth at all times (like GTM Algebra by Lang for the thrill)

It's perhaps good to start with a book that has a lot of concrete examples and problems

To give a feel for the subject

[stray veldt]

no group actions is kinda bad tbh

[karmic thorn]

Knapp is the text I'll use for a second look into groups, it certainly covers them and more

Also a brief intro to categories

[marble karma]

Manan have you read that book on calculus by Spivak? I am planning to read that, is it a worth read ?

I do know basic calculus ( learnt from ncert class 12th 😑)

[karmic thorn]

Sure

[marble karma]

I am finishing the book foundation of mathematics by s kumarsen and ajit kumar and sarma then I will read it

[karmic thorn]

Goodluck!

[marble karma]

Thanks !

[misty wyvern]

So Friedberg Insel Spence's Linear Algebra book is actually pretty good, you guys weren't wrong. I think I might use it to teach.

Actually I changed my mind, students might find it hard to sail the high seas and find a current edition copy online, I try not to use books that are challenging to "obtain"

[dense wren]

What about Sheldon axlers linear algebra book? That one seems good

[marble solar]

It's good

Did you take 115B berg?

[misty wyvern]

I'm afraid people will misunderstand the determinant after reading Axler

[sleek python]

What does it say about determinant

[sage python]

Teaches it as product of eigenvalues

[misty wyvern]

I thought Axler defined it as the constant term in the characteristic polynomial

i guess i dont remember axler that well

[sage python]

And stuff like char poly is done by triangularizing the matrix

[sage python]

Pretty easily proven equivalent

[misty wyvern]

Yeah, but we're talking about reteaching engineers linear algebra here

the class is a numerical PDEs for undergrads

we're discussing how sections should be run and what they should cover

everyone's a senior and it's a fancy school so people should be smart but we try to avoid indirect presentations

[sage python]

I don't endorse Axler for really any setting

Because that way of processing determinants is incredibly bad

[misty wyvern]

can we formulate the worst definition of determinants

[sage python]

This message meant like

What I said Axler does and what you said Axler does are obv equivalent

Hmm

[misty wyvern]

the wedge product / vol form one is funny

but im sure theres worse

[sage python]

I think for serious math folk it's objectively the correct one

[misty wyvern]

i agree, but for serious math folk a group is a groupoiud with one object

still the wrong way to introduce groups

[sage python]

Yes

When I say serious math folk I mean like

I'm happy doing multilinear stuff for people learning linear algebra the first time

I don't think it's suitable for engineering people simply because it takes much longer to introduce, time you could spend doing content that's more relevant to them

[misty wyvern]

it's actually suitable for mech engineering folk IME, esp those planning on going to grad school. tensor calculus they do actually do in a way thats essential for their work

[sage python]

Yeah I guess I'm generalizing a bit here

[solemn rover]

ehh i wouldn't say that wedge product / vol form is the worst. certainly not volume form. you don't have to be super rigorous about what a volume form means but like, when i've taught linear algebra in the past, i definitely have explained the determinant as being the unique alternating n-linear map from the col space into the reals, and stressed the volume interpretation. i am not saying we should introduce the exterior algebra, but like, as soon as you understand that the determinant is unique up to scalar multiplication, it's easy enough to think of it as depending on 'one parameter', somehow it's a function of an elt of a one dimensional vector space.

not to be too explicit about what that space is or how to construct it.

[sage python]

I just mean like, people who mostly engage with a certain level of linear algebra

[solemn rover]

at the risk of being edgy you could argue that the worst definition is just a formula

that tells you how to compute it recursively

[sage python]

For those folk, having a somewhat more theoretical understanding of the determinant is less important than, say, getting to topics such as SVD

[misty wyvern]

today i watched phd physicists struggle with a generating function

gen funcs might be the worst definitions

[sage python]

So the cost benefit analysis isn't in favor of doing multilinear business

But if someone's engaging with linear algebra for linear algebra's sake

I'm absolutely willing to do it right the first time

[crystal lion]

while we're on the subject

https://www2.math.upenn.edu/~wilf/gfology2.pdf

[gray gazelle]

Use Jacobson

[misty wyvern]

use aluffi

[bronze raven]

generating functions?

like the ones that are symmetric

oh that was a while ago nvm

im using aluffi rn teafortwo

[spring saffron]

Any book that can simplify distribution theory for a beginner? I have Rudin’s Functional Analysis but it is a bit dense

[misty wyvern]

brezis

lax

[magic ferry]

I find that lecture notes are generally better for a beginner, and there are tons freely available online. Look for one that works towards something you are interested in. functional analysis can be skewed towards all sorts of directions depending on how you want to apply it

[bitter raptor]

I hear rudin’s functional analysis is pretty shite

[alpine rover]

is there a pin or link for all the recommended books on each topic or reading order for self study?

[stray veldt]

you can check the pins here, there are a few topic specific things

you can also check #books-old but its kinda not great

the "order" depends on your end goals

[marble karma]

Number theory by Burton or Niven? Which is better?

[slim peak]

In my opinion, Rudin's distribution theory introduction is maybe the most "easy to read" one , and it is the only topic where Rudin "is easier" I think.

Some people recommend Strichartz's book. If you can understand French, F. Golse's pdf about Distribution Theory and Fourier Analysis is in french but really complete, a light version of it is C. Zuily's Book, in French again.

[lilac crown]

Hello

Any book recommendations for calculus undergraduate that is for engineering

[frigid comet]

friedlander and joshi's introduction to the theory of distributions is concise and well written, with well chosen exercises.

[wintry lotus]

I just want to mention that

Functions Of Several Real Variables
by Fotios Paliogiannis and Martin A. Moskowitz

is an extremely amazing but less known book

I have not been able to find a better exposition to multivariable calculus so far

[gray gazelle]

anybody have good book on fluid mechanics

[digital lion]

Is there a standard topology book in German? I'm an English student but I'm trying to do masters in Germany

[stray veldt]

there is one by klaus jänich who is an ok author iirc

funnily i know a good topology book written by a german in English

[digital lion]

Would it have an German translation you think?

@stray veldt ill check out jänich

[stray veldt]

jänich is the only German topology book i know

(tbh just read one in english)

[magic ferry]

https://www.google.com/search?q=topologie+pdf&rlz=1C1CHZN_enSG931SG931&ei=wKBMYbWUDNb_7_UP6Ky2qAs&oq=topologie+pdf&gs_lcp=Cgdnd3Mtd2l6EAMyBQgAEIAEMgYIABAWEB4yBggAEBYQHjIICAAQFhAKEB4yBggAEBYQHjIGCAAQFhAeMgYIABAWEB4yBggAEBYQHjIGCAAQFhAeMgYIABAWEB46BwgAEEcQsAM6BwgAELADEEM6CggAEIAEEEYQ-QE6BwgAEIAEEApKBAhBGABQhBFYlhpg0RxoAXACeACAAYgBiAGeA5IBAzMuMZgBAKABAcgBCsABAQ&sclient=gws-wiz&ved=0ahUKEwi19PL-t5XzAhXW_7sIHWiWDbUQ4dUDCA4&uact=5

[crystal lion]

jänich goes way too quick for a first pass

chapter 2: topological vector spaces

❓

[flint forge]

Woke

[magic ferry]

did you become compact

cos yesterday you were just supremum

[spring saffron]

Thanks everyone

[flint forge]

my name is max supremum was a joke

[neon sky]

Hi everyone, I've recently decided that I want to go over maths from the basics aka addition subtraction and so on up to a at least post grad mathematics to make sure that I fully understanding everything since I didnt really learn a lot of things properly in the past does anyone know any good resource or suggestion for how I should do this?

I would also like if it was approached with an inventing maths kind of mindset and was easy to work through very quickly

[magic ferry]

from basics to postgrad? bourbaki

[neon sky]

?

[magic ferry]

there is this group of people all called nicolas bourbaki

and they wrote a book

that deals with math from the start to a postgrad level

[neon sky]

ohh nice, does it take the approach of inventing maths?

or does it just throw a bunch of formulas at you and tell you to memorise?

[magic ferry]

well it reinvents mathematics basically

[magic ferry]

no good text does this

actually im kidding, dont actually read bourbaki

[neon sky]

a lot of my schooling was like this which is why I ended up with a lot of gaps in my knowledge lol

[neon sky]

how come?

[magic ferry]

its not really good for beginners

[neon sky]

im not really a beginner just want to fill out the gaps in knowledge

[magic ferry]

how much math do you know. bachelors?

[neon sky]

I've graduated from electrical engineering this year

[magic ferry]

ah ok

[neon sky]

issue is I found a lot of the stuff in the last 2 years to be confusing and ended up just memorising it for exams and forgetting it

couldnt really understand a lot of stuff simply because I didnt like how they taught it and some of fundamentals are a bit shaky

[magic ferry]

linear algebra done right

start with that and see how it goes

and analysis by tao

[neon sky]

hmm I'm looking for something to start from scratch

like literally addition and subtraction and move up

[magic ferry]

tao starts from scratch. like set theory and the going up from there

[neon sky]

set theory isnt really from scratch tho no?

[magic ferry]

well its the most basic part of math

[neon sky]

hmm its not quite what I'm looking through but will try reading through it and bourbaki see if they help out

[magic ferry]

no dont actually read bourbaki lol

[neon sky]

its too complicated?

[magic ferry]

its very formalistic

[neon sky]

hmm yeah thats fair then I find the formal approach makes things seem a lot more complicated than they really are

[karmic thorn]

Why do you intend to do so? And do you have the time/resources to dedicate yourself to learning math?

[karmic thorn]

It will take some time to familiarise yourself with some indispensable basics. Depending on your background and preferences, you may focus on a particular aspect and build up the prerequisites to get there, but I think large chunks of maths one learns at school would still be indispensable.

[neon sky]

I want to really understand maths I really like maths when I understand it but hate it when i dont (memorising formulas and stuff)

as I said before the way I was taught was honestly really bad combined with me being quite lazy in my younger years I dont feel like I understand things as well as I should

so I want to relearn everything from the beginning as if inventing maths as for time I'm planning on doing this in my free time so its not really an issue and I dont have anything that I need to learn in particular

although I am much more interested in statistics and engineering mathematics

[karmic thorn]

Okay, good. You can start with Khan Academy then, and once you have covered some relevant bits, you can ask again for further directions.

You might want to go through Pre-Algebra, Algebra 1/2, Precalculus units for starters

[neon sky]

hmm my issue with something like khan academy is that the basics are targeted at kids since they are the primary audience

I want something that takes an adult audience into account and moves very quickly through the beginning while still covering everything and going into more complicated topics related to the fundamentals

[karmic thorn]

Perhaps take a look at Basic Mathematics by Serge Lang

[neon sky]

I was taught statistcs through this book but didnt really understand it and ended up failing but then I read the book on my own and retok the exam next year with a week of studying through the book (without help from teachers) and ended up getting an A

[karmic thorn]

Or you could jump right into a Discrete Math book if you have at least seen math before

[neon sky]

issue is I find these books although they teach very well they dont always explain everything sometimes they just give formulas and dont go into how they were derived

and I also want something that starts from the basics to begin with in case I missed anything there

[karmic thorn]

Lang is on the more pure side, it includes a lot of proofs about the results

And would also relay a lot to exercises I guess

@wooden sparrow has worked through it, he has been in a similar situation so he could probably tell about his experience

[neon sky]

not sure thats what I'm looking for then I find that these kinds of books tend to over complicate otherwise simple maths

[karmic thorn]

[wooden sparrow]

@neon skyhow much maths do you know from highschool?

[karmic thorn]

I'm not sure what you're looking for, you want to see where the ideas come from, then you have to use something on the pure side

[neon sky]

its kind of hard to say tbh

[wooden sparrow]

calculus?

trig?

[neon sky]

I've forgotten a lot of stuff

yeah I know calculus and trig

although I'm not as good as I want to be

[wooden sparrow]

My best advice is to take tests in khan academy first.

[neon sky]

to give some more info I just graduated electrical engineering this year

[wooden sparrow]

Why are you learning maths BTW?

competitive stuff? Or do you want to get into undergrad maths?

[wooden sparrow]

Nicee!

alright

[neon sky]

neither

I just want to learn more maths to further myself

[wooden sparrow]

my suggestion, know what you don't know. Take those unit tests on khan academy about the topics from high school

know what you don't know.
this part is where I've wasted half of my time tbh

[neon sky]

Will do

[neon sky]

actually now that I've had a bit of a look at the book it seems to be kind of what I was looking for thx 🙂

[karmic thorn]

[marble karma]

A friend of mine who didn't take math in +2 and studying economics as one of his first year subject is using this book by serge lang to study mathematics from scratch.

[gray gazelle]

Langchads

[gray gazelle]

Landau analysis

[digital lion]

Its ok. Im in a toplogy class in English, but I just wanna read a book in german at the same time as practice

[bronze raven]

Thats ambitous and cool

[native linden]

Hi guys,
I need a book suggestion/tip. I am a CS undergraduate. After a few years of work-ex, I plan to pursue a master's level course in applied mathematics. To that end, I am doing some bridge subjects.
Real Analysis - I have read and solved the exercises of chapters 1-4 from Understanding Analysis, by Stephen Abbott. Currently reading the chapter on derivatives.

I'd like to learn probability theory. Is Protter readable after having done undergrad Analysis at the level of Abbott? [I am planning to read Protter + Feller]

Let me know, what you guys think! 🙂

[dense mantle]

IDK about protter but you should have some measure theory and would recommend topology (particularly, point set topology and an idea about manifolds) as well -- these are generally considered to be the prereq to the end of undergrad/ beginning of grad real analysis, which probability theory is basically a rehash of

some combo of those all is typically taught as like 2nd and 3rd semester of undergrad analysis. Abbott is easy stuff, honestly. You probably don't feel like you've learned anything new

now for myself

in a class using Folland but realizing that it is shit to actually learn from. I recognize that it is a very great reference text, but definitely not for actually learning shit

so, what are the canonical GTM/ etc books such that I might actually learn at a reasonable pace? I picked up Integral, Measure, and Derivative by Shilov and Gurevich, but it's old af

[dense mantle]

just went and skimmed through protter + jacod prob essentials....

thoughts still stand

abbott is not much real analysis

its more of "heres how you prove what you did in calc 1," which is very much just the beginning of analysis. would at least start reading knowing that you're going to need to read other analysis reference texts to piece this all together, probably

the later topics are things that we are covering in a first semester grad course here (that were touched on in the advanced analysis for undergrads; for reference, am at T20 in general and for math, T5 for applied math US university, so we have a decent program for analysis. I understand this to be standard everywhere regardless, so I guess that really doesn't mean much at the end of the day)

[native linden]

@dense mantle , so you recon, I should learn some more measure theory before doing protter? (Btw, I do find some of the exercises in Abbott challenging.)

For measure theory, I had Sheldon Axler's book in mind.

[dense mantle]

the exercises are indeed supposed to make you think. they become easier over time

to be honest

Tao analysis 1 and 2 is probably best bet if you want to actually learn quickly

abbott has good exercises though

the thing i've always hated about analysis is that it feels so much like a means rather than an end (e.g. in fewer words, youll find lots of budding algebraists in algebra classes, but far fewer budding analysts in analysis classes)

Tao also has a good measure theory book. Can be found as pdf online

[native linden]

😄

[dense mantle]

if you actually get all of this done, you won't have to think at all about anything but probability when you're reading

which I suppose is the goal

[dense mantle]

abbott has 0 measure theory... like I said, probability theory is basically measure theory with the words changed out (to be really, really reductionist)

[misty wyvern]

If you're doing an MS in applied math, you'll have the opportunity to take probability with measure theory though it likely won't be required.

[native linden]

The thingie is I was hoping to apply next year October intake. Which means I have about an year to go before my course starts. I have a few other topics that I'd like to devote my time to - applied functional analysis, a first course on PDEs (mostly linear), optimization, numerical analysis. I am just not sure, if I have the bandwidth to do Tao. But, I haven't looked at measure theory by Tao.

[dense mantle]

if you min-max, thats doable, but theres a lot

but like

functional analysis is well beyond your means right now

numerical analysis is also probably beyond your means right now if abbott's stuff is new to you

just read as much as you can

in my experience, planning things out never really goes as.. planned

not the best advice though. if you can stick to a plan, thatd be much better in general

[dense mantle]

also going to second this

measure theory isnt generally expected of undergrads

[native linden]

@dense mantle , thanks a tonne.
I am using this text for applied Functional analysis. Intro to Hilbert Spaces by Debnath, Mikusinski

For numerical analysis, I am using the book an Intro to Numerical analysis by Suli, Mayers

I found both to be accessible.

[misty wyvern]

Might I suggest just working through Stein and Shakarchi if you really want to do the whole set?

[dense mantle]

lol

[native linden]

@dense mantle . they have a course on stochastic calculus, which I wish to take.

[dense mantle]

yeah some complex analysis is usually one of the most glanced over things for apma focused kiddies

yeah bruh

[native linden]

i plan to read off Stoch calc by Schreve, which is more intuition based than proofs.

[dense mantle]

youre making a mistake if you rush through everything. its going to be much easier to be really solid on your analysis + general idea for the rest than to try to be ok on everything

[native linden]

I see.

[dense mantle]

for the most part, this stuff just comes with practice

[native linden]

I agree, I need to think through a bit.

[dense mantle]

like memorizing a bunch of numerical algorithms is a bit of a waste

there are just

so, so, so many

just go peak at Golub's matrix computations. very very thick, granted there are some algorithms in there for which there isnt a faster alternative known atm

nonetheless

your time is best spent focusing on analysis, linear algebra, and pdes

• undergrad stats and probability

[native linden]

@dense mantle , i have done a first course in linear algebra (Axler) - that certainly helps

[dense mantle]

well, yes

but thats only so much

work through the back half of axler again

and then peak through the chapter on matrix analysis in golub

i guarantee there are things you dont know

at least there were things i didnt know

[native linden]

oh yeah for sure

[dense mantle]

my first course was axler as well

[native linden]

i see what you mean

[dense mantle]

youll realize more and more over time how quick you can get through undergrad topics once you get pretty good with math/ learning how to learn math

anyways

this is getting off topic

[native linden]

so bottomline - you don't suggest protter at this point.

[dense mantle]

read more linear algebra (that isnt targeted to early undergrads), read more analysis, read pdes, and get really good with basic stat and probability

i mean you can do it

I just think there are better uses of your time for now

[native linden]

for basic stats and prob - am using Feller (love the examples)

[misty wyvern]

Karatzas and Shreve's rigorous stochastic calculus book is very challenging.

It's my area of expertise and it took a while for me to get comfortable with it.

They have a particular financial math book that you might prefer.

[dense mantle]

hes working on abbott

the single variable book

I don't think rigorous stochastic processes are appropriate for him

not now, at least

[misty wyvern]

That's what I'm saying, Karatzas and Shreve is not my recommendation for anyone except a specialist in stochastic calculus.

[gray jungle]

anything good for self learning metric topology?

[dense mantle]

ah sorry

misunderstood

[misty wyvern]

Metric topology? As in the basic concept or is there a subfield of topology that deals with metrizable topologies?

[gray jungle]

ye the basic concepts of metric and topological spaces

i assume so at least

its my course on my 3rd sem so studying ahead of time

[misty wyvern]

Rudin?

[gray jungle]

i am actually working on baby rudin
but i was hoping for something less compact

[dense mantle]

@misty wyvern sorry to start two convos at once but do you have any particular recs for real analysis? early graduate level. class is using folland but im realizing thats probably best used as a reference rather than textbook purely

[misty wyvern]

If Rudin isn't to your speed then maybe Stein and Shakarchi.

Like Rudin they have several volumes covering various topics in analysis/

And levels.

[native linden]

@dense mantle cheers and thanks again, I'm going to keep you guys posted, on my progress 🙂

[gray gazelle]

Based appreciator of real mathematical languages

[lapis sundial]

sehr basiert

[stray veldt]

just take an algebraic number theory class and read neukirch in the original german

[crystal lion]

teafortwo will take any chance he gets to talk about kartzas shreve

[sudden kayak]

Could you guys recommend me a beginner book for proving. I am kind of overwhelmed to the topic. Preferably starts at Axioms of real numbers

[karmic thorn]

Maybe Elementary Analysis by Ross or Understanding Analysis by Abbott?

[uncut zealot]

Books on proof techniques generally don't start with the axioms for real numbers; that's typically covered in real analysis. For a book on proving things, try something like Hammock's Book of Proof. For analysis, a classic recommendation is Rudin.

[karmic thorn]

If you need something that is still specifically designed for basic proof writing, try How To Prove It or Book of Proof by Hammack

[uncut zealot]

The first course you take where you need to prove things, there will be a steep learning curve. That's just how math works. To get better at proving things, practice is the most important thing.

[gray gazelle]

Landau Analysis

[karmic thorn]

Isn't Landau's Analysis very outdated and dry

[gray gazelle]

Its Landau analysis ok

I dont think I need to elaborate

[gray gazelle]

But you are correct lol

[bitter raptor]

School library sells Lang for 42 bucks

Worth it?

There’s only one copy left so I’d need to decide fast on whether or not it’s worth it or it might get taken

Also they sell SS complex analysis for 120

[gray gazelle]

Sells Lang
That really doesnt narrow it down

[sage kelp]

@native linden Hey, kind of in a similar situation here. I want to gain “math maturity” so my plan was to do analysis & measure theory. Started with Abbott, then switched to Tao. I have found chapters 5 and 6 of Tao somewhat challenging (the exercises, because I see theory is quite straightforward). I’ve been doing analysis since June. I wanted to rush things, but came to realize that I really need to have solid grounds first. And it takes quite the time to achieve that

[dense mantle]

Just read more analysis lol

Its really just how much time you spend with it all...

You would also benefit from reading some basic topology. More important than you might think

[native linden]

Hey @sage kelp, I certainly felt the same. Don't wanna digress - but I have a full-time job, so I have been doing Analysis from Abbott since Jan. I often ask a colleague for a clue, if I am really stuck, or on StackExchange.

That said, the problem sets in both books are nice. And it's worth the hard work. They do make you more proficient at applying the ideas you've learnt.

[sage kelp]

But that’s your advice, right? Like getting solid basics is better than probably reading as many books as one wants, yet not really knowing what’s going on? In the end it takes a lot of time

[sage kelp]

May I ask you, study topology simultaneously with analysis?

[dense mantle]

most undergrad books will introduce you into the topology you actually should know (primarily, point set topology), but it definitely wouldnt hurt

at least, read some before you get into more "advanced" analysis books e.g. Folland

[dense mantle]

yes

especially if this is not something youve done a lot of before... i kind of assume that is the case given you're an econ student(?)

[sage kelp]

Correct

I have been studying on my own this year

[sage kelp]

What's a good very introductory topology book? Munkres seems hard, and I found Waldmann's Topology: An Introduction, but haven't checked it out

[dense mantle]

munkres is the book

if you want to just be lazy

just read the point set topology part of an undergrad analysis book

eg rudin

theres a decent bit of algebra involved with topology, which you really dont need at all

[misty wyvern]

teafortwo will take any chance he gets to talk about kartzas shreve

Everyone should read Karatzas and Shreve. 🙂

[forest sleet]

speaking of Karatzas and Shreve

anyone know where to buy a hardcover one

i only see softcover on springer and amazon

but my uni library has a hard cover 2nd edition so they evidently exist

[solemn rover]

more like Carapaces and Sheaves

[mossy seal]

Is there a textbook for learning category theory, set theory, topology, metric spaces, measure theory, vector/normed/banach/innerproduct/hilbert spaces all at once in a maximally general way with small amount of redundancy, using category theory everywhere? E.g. I want to avoid the situation when I study hilbert spaces without thinking about their topology, and then I learn topology, and then I need to work to connect my knowledge about hilbert spaces with my knowledge of topology. Also, if some property of hilbert spaces holds simply because they are complete metric, then I want to learn it like that, without using the vector structure.

[glad prairie]

This sounds like a very silly way to try to learn functional analysis

But you do you I suppose

My perspective is that functional analysis gets its importance from the specific objects it describes very well, not from the generalities it affords

[sage python]

I wouldn't say there's any one textbook which does that

[gray gazelle]

what is the path to learning math

[sage python]

There's not a single one

[gray gazelle]

what do i do after linear algebra and differentiatl equations

i am also done with vector calc

[sage python]

Are you more into pure or applied math?

[gray gazelle]

both

[sage python]

And how are you with proofs?

[gray gazelle]

i am doing transition to advanced mathematics

[sage python]

Idk that book but I guess it's intro to proofs

So yeah get through this, then your main things to learn are real and complex analysis, algebra, and topology

[gray gazelle]

ok

[sage python]

Exactly why did you think that was worth posting here?

[gray gazelle]

can i be set if i only read rudin's books

[sage python]

Nope

[gray gazelle]

how should i learn real analysis

[sage python]

Rudin's good for real analysis, though you'll wanna focus on chapters 1-8. 9/10 are best learned elsewhere, eg Spivak Calc on Manifolds

11 is measure theory which you'll do after

[gray gazelle]

ok

so which other real analysis books do you recommend

[sage python]

I don't really like any others, I've heard good things about Kriz and Pultr for analysis (also kinda covers you for complex analysis and most of the point-set topology you need) but at least one person says it has too many typos so take that as you will

People like Pugh a lot, I find it awkward/messy

[gray gazelle]

does this mean i can't learn real analysis from one book

[sage python]

Didn't quite say that, those books are alternatives to Rudin rather than followups

[gray gazelle]

ok

i was also wondering

[sage python]

Any one of the three will largely cover you for undergrad-level analysis

[gray gazelle]

am i going to have to do discrete math at some point

[sage python]

Basically assumed this question meant you wanted alternatives

As part of algebra likely, can't hurt to learn it on its own a bit

[gray gazelle]

ok

[sage python]

Don't ask me buddy

[gray gazelle]

after i am done with real analysis what do i do

do more advanced books?

or do complex and algebra

[sage python]

In general i say don't plan too far ahead. Maybe you'll do real analysis and decide chemistry is more fun to you than math or maybe you're not looking much at grad school and need to focus on what you need to learn for jobs

[gray gazelle]

ok

but i am pretty sure math is what i am going to do for the rest of my life

[sage python]

If you continue in math, at least pure, I'd say you should definitely get a solid grasp eventually on real + complex analysis, algebra, and topology

[gray gazelle]

ok

[sage python]

In particular within algebra you'll have a more sophisticated/proofsy approach to content from linear algebra

[gray gazelle]

hmm ok

guess i have a lot to do

[sage python]

As far as applied math goes, I'd wager differential equations, numerical analysis/linear algebra, maybe some applied discrete math are all important?

Anyway yeah just do what's in front of your face

[gray gazelle]

ok thanks for your time

[sage python]

Sure thing fam

[lime plinth]

What are some good contest books for ages 16-18?

[misty wyvern]

imo all mathematicians, applied or pure, should learn the same math as an undergrad. not doing real analysis at all is ridiculous

[sleek python]

At least the first two years of undergrad

With minor differences maybe

[gray gazelle]

Studying maths

I know! Shocker!

[quick hornet]

the same math for all of undergrad is kinda ridiculous

not every math degree is structured to transition into graduate level

[gray gazelle]

Yeah

[quick hornet]

nor should it be

i agree that real analysis should be a requirement though

[gray gazelle]

A lot of my classmates dont care for stuff like topology or functional analysis and more advanced algebra

Just to name a few

They want the 300000 starting

[quick hornet]

then they shouldnt have majored in math

[gray gazelle]

Its a /sci/ meme

[quick hornet]

alas.

[gray gazelle]

But yeah they want to either go to industry or teach hs

No real need

[timber mesa]

pretty old one

[gray gazelle]

A classic nonetheless

[quick hornet]

i avoid /sci/ like the plague

too many trolls trying to start the same old tired racial iq arguments

[timber mesa]

eh it used to be decent before the IQ memery

[quick hornet]

yeah its just imageboard culture to ignore that but

meh

[gray gazelle]

Boards are diluted a lot recently

[quick hornet]

i didnt grow up on imageboards so im not acclimated to it

[timber mesa]

||I did||

[gray gazelle]

Based schwarziana

[quick hornet]

my only 4chan usage is a couple generals in /vg/, unfortunately 99% of /vg/ is utter shit

[gray gazelle]

One day we will all tell tales on how he got those scars

[quick hornet]

and the remainder isnt exactly good

just the only place with a community for the stuff in question

[marble solar]

just ignore those and go to math general threads

[sleek python]

Is that a discord server

[marble karma]

Is it true that one can ask for any kind of literature here ?

[quick hornet]

you can but you probably wont get great recommendations

for non-math stuff

[marble karma]

I am looking for a novel in which the protagonist conquers his fears and achieves his dream

[sleek python]

Harry Potter

[misty wyvern]

Rudin

[marble karma]

[gray gazelle]

yes

even manga recommendations

[marble karma]

Stop there before they ask tentacle hentai manga recommendation

[quick hornet]

cough

[broken meadow]

sneeze

[tawdry orbit]

What is the Prerequisite for spivak calculus?

[broken meadow]

im not aware of any i think

other than like

being solid on precalculus and algebra

and stuff like that

right?

[tawdry orbit]

Finnegans wake.

[tawdry orbit]

Any good textbook that isn’t too long? I know of the stitz and zeager textbook. But I feel it is too long.

[karmic thorn]

Basic Mathematics by Lang isn't too long I guess

Khan Academy works anyway

[tawdry orbit]

Yeah, that seems fine. Thanks.

[modern stone]

What’s good resource (video or book) on linear algebra?

[solemn rover]

3blue1brown videos.

Gilbert strang's youtube lectures on the MIT linear algebra class

[modern stone]

I’ve already watched 3blue1brown series. Do Strang’s lecture cover all one should know about lin alg?

[stray veldt]

"all one should know" is a tall order

[modern stone]

yeah I think “all one should know to have a good enough foundation to continue learning higher maths” is a better way of saying it

[karmic thorn]

It's a good starting point definitely

[gray gazelle]

What are the best mathematics books to introduce myself to set theory and Mathematical logic and concepts

[gray gazelle]

I recommend my books

[gray gazelle]

Which are?

Dispersive pde; tao

should i use abbott or rudin for analysis

Rudin

Then steins harmonic analysis

And hörmanders books

Then my book see above

don't understand

Rudin

what do i do after that

You study more analysis

what books

I said above

Stein then hörmanders and tao

ok

[maiden slate]

4 analysis books?

[gray gazelle]

what do you recommend?

6

help pls

[maiden slate]

that seems a bit overkill. but i haven't learnt analysis

im just learning abbot rn

[gray gazelle]

This is the beginning

[maiden slate]

finished one chapter. so don't ask me lmao

my plan is to go from abbot to visual complex analysis

[gray gazelle]

Complex analysis is a waste of time

[maiden slate]

[stray veldt]

[gray gazelle]

How much does analysis differ from spivak calculus book? I am in chapter 3 and it has been brutal so far. mostly the problems.

[maiden slate]

im only studying analysis so i can learn complex anal and diff geo tbh

[gray gazelle]

Complex analysis is a mined out field

Only use the theorems you need

Black box

[maiden slate]

[gray gazelle]

anybody else have idea on books for real analysis

[uncut zealot]

rudin

[maiden slate]

i just got abbot cause i heard it was the easiest

[gray gazelle]

I can't wait to I finish my analysis studies so I can pack my bag to algebra and stay there.

@uncut zealotwhat do i do after that

[lapis sundial]

Algebra is fun

[uncut zealot]

grandpa rudin

[gray gazelle]

Haha pushing symbols around haha

[maiden slate]

what the hells so great about rudin?

i haven't tried it, but it feels like a cult

[uncut zealot]

Oh it 100% is.

[gray gazelle]

@uncut zealoti can learn real analysis just by reading rudin?

[gray gazelle]

[uncut zealot]

I'm literally just trying to get more initiates because that's how you progress through the heirarchy of the cult.

[stray veldt]

its just that everyone has read rudin and it did a decent job at educating at least a generation of mathematicians

[uncut zealot]

Depends on what you want to do with real analysis honestly. Rudin follows a typical undergraduate real analysis course, though, so you'd learn that.

[gray gazelle]

do you mean principles or mathematical analysis

or real and complex analysis

[uncut zealot]

Principles

[gray gazelle]

ok

[lapis sundial]

I assume you're thinking of high school algebra or smth

[lapis sundial]

Baby Rudin

[gusty smelt]

oh speaking of analysis books

[gray gazelle]

then try explaining me algebraic topology @gray gazelle

[gusty smelt]

anyone got a good recc for functional and/or harmonic, gonna do that soon

[uncut zealot]

baby rudin

[gray gazelle]

Stein for harmonic

Functional do like idk yosida

If you aren't a kiddo

[gusty smelt]

makes sense stein on harmonic

[gray gazelle]

But it doesn't hold hands

can i do funcitonal with rudic

rudin

[gusty smelt]

ill look into yosida

[gray gazelle]

ok

[gusty smelt]

see if its appropriate

[gray gazelle]

yosida is better than rudin for functional?

Weidmann for Hilbert stuff is good

[gray gazelle]

Not if you're new to analysis

[gray gazelle]

no response? ok blocked

so yosida is more advanced?

Yes

ok

Japanese authors are generally less explanatory

You need to put in more work

[uncut zealot]

John what time is it for you

[gusty smelt]

you probably wanna focus on doing rudin 1 first purple, no need to worry about the other things

5:25 am

[gray gazelle]

is folland good

No

ok

I hate folland

[uncut zealot]

Go to bed

[gusty smelt]

I woke up circa midnight its fine

[uncut zealot]

[gray gazelle]

too late for them to go to sleep

[full linden]

Lets form a study group for analysis

[gray gazelle]

ok

sure

[gray gazelle]

you can also do Analysis Now by Pedersen for functional analysis

it's easier than Yosida

[night birch]

hi guys

[gray gazelle]

Hi

[night birch]

hru

[gray gazelle]

I'd tell you but why in this channel?

#chill

this channel is used for asking for book recommendation

[gray jungle]

less of a recommendation more of a question
is Joseph Blitzstein, Jessica Hwang - introduction to probability a good book ? or is there perhaps any better alternatives
and if so what does it do better than it?

[gray gazelle]

Idk I never browsed this book

the one that I like for probability is Resnick

Some people recommend Schilling but that's more for measure theory than probability imo

oh, this book is pretty fresh, first edition is from 2014

[gray gazelle]

looks good, a bit slow, but lot's of explaining, doesn't seem to get into those mathematically interesting parts, but still looks pretty good to me, and includes examples

[gray jungle]

i was skimming through 1st chapter of blitzsteisn and it looks promising i might just work with it
Only issue i have is lack of mathematical detail but its alright
but i'll check out Resnicks and see what happens just to make sure
not too much into measure theory to do schilling

ty ty

[gray gazelle]

oh, Blitzstein, Hwang just seems to try to introduce probability from more intuitive level at the start which is actually how a lot of those books start

I'm sure it'll be slightly more formal later

well, a part of probability is measure theory on finite spaces, but here you also have random variables etc.

so they overlap

besides I think it's a good thing to start a little less informal with probability

doesn't seem to include more advanced things like martingales but it does scratch some theory of stochastic processes

namely, Markov chains

it seems like a really good book, especially if you don't care much about probability and you are some kind of engineering student, for example

if you really want more theory then I recommend Resnick

There's also this book by Billingsley that I really liked as well, but it isn't an introduction, and seems to be a graduate level book

[gray jungle]

pure math
But it is an interesting subject to me so i think ile use blitzstien and keep the other as reference for a different approach
cant say im ready for graduate level proba yet
like you said i think it looks neat just had to make sure

again ty for help ile give some feedback on the book after im done with it

[gray gazelle]

oki

[halcyon hornet]

Book suggestions for Number theory(High School Level mainly).
Especially - "An Introduction to the Theory of Numbers" or "Elementary Number theory by Burton"? Or some other like AoPs Introduction to "Number Theory"?

And Book suggestion for Combinatorics(High School level mainly).
Especially - "Schaums Outline of Theory and Problems of Combinatorics including concepts of Graph Theory" by V. K. Balakrish
Or "APPLIED COMBINATORICS" by ALAN TUCKER?
Or both? Any other recommendations?

And do "Challenges And Thrills of Pre-College Mathematics" and "An Excursion in Mathematics" cover most of Number Theory and Combinatorics of High School level too?

[foggy relic]

can I join?

Ive been meaning to learn analysis

[full linden]

We didn’t create one yet

[gray jungle]

count me in if you do

[foggy relic]

^

which book will you do (if youre gonna do it) @full linden

[full linden]

uh idk, it would be discussed among the members

Well.. People interested in forming a analysis study group, dm me

[uncut cradle]

AOPS

[alpine elk]

Book Suggestion for Numerical Linear Algebraists: Matrix Computations by Golub and Van Loan

[misty wyvern]

That is a good book

Well OK it's as good as a book can get for numerical analysis, which is not good, but it doesn't make me want to kill myself which is always a plus

[gray gazelle]

Any good books on probability theory?

[misty wyvern]

Kallenberg

[gray gazelle]

Above Blitzstein, Hwang was mentioned, also Resnick and the book by Billingsley

[alpine elk]

That's exactly what I think lol. My last one, by Quarteroni, made me want to die

[quasi remnant]

what's a good book for linear algebra, going to mainly use it to self teach

i've done a basic course on linear algebra already where it covered vector space, basis all the way to Gram–Schmidt orthogonalisation

[smoky surge]

Axler

I personally really liked it

[uncut zealot]

I got a pop-up ad for the math book with one of the best names I've seen: https://www.springer.com/us/book/9783540442370?utm_medium=display&utm_source=criteo&utm_campaign=3_fjp8312_product_us&utm_content=us_banner_29012020#otherversion=9783540101031

The book is just called "Trees"

[stone finch]

Does any one have a book recommandation for MSO ?

[misty wyvern]

Does any one have a book recommandation for MSO ?

How to Cook Anything

[karmic thorn]

I was almost about to consult Quarteroni but even skimming through it gave me pain, I settled for Burden-Faires Numerical Analysis which is probably more introductory, but leaps and bounds better written.

[thin hollow]

Books to improve math intuition

For proofs

[misty wyvern]

rudin

[rigid stratus]

Best books for Pre-Algebra?

[gray gazelle]

rudin

[silver herald]

TBH, you aren't exactly wrong though.

[rigid stratus]

?

[marble solar]

Knots and Links by Rolfsen

[gray gazelle]

Any textbook recommended by your school will do

The topic isn't advanced so there shouldn't be any special books for it.... there just wouldn't be anything to write about

[karmic thorn]

Khan Academy is sufficient

[modern stone]

What are some good books to learn Abstract Algebra?

By good I mean a book that also emphasises intuition for the subject

[karmic thorn]

check this out for some standard recommendations.

I'll additionally shill Gallian/Judson/Pinter/Fraleigh/Rotman if you're starting with the subject

[gray gazelle]

bhattacharya

[wise umbra]

Atiyah-Macdonald (for commutative rings), Lang's Algebra

[halcyon hornet]

The 3 messages.

[primal summit]

Gallian

[wise umbra]

(Lang's Algebra might be a bit hard)

[karmic thorn]

I don't get the dislike for Gallian, especially for a first pass

It has a good chunk of problems, some extra topics one wouldn't find in a typical algebra book, even references to a lot of accessible, cool articles relevant to subject matter

[wise umbra]

Also, I really like « A Guide to Groups, Rings, and Fields », written by Fernando Gouvêa but's that's not a textbook, it's like a survey of abstract algebra

So you can appreciate the landscape

[modern stone]

Do they also emphasise intuition?

I would prefer a less rigorous text, but highly intuitive as a first reading rather than a highly rigorous one but very unintuitive

[livid ermine]

I think if you read Atyiah-Macdonald or Lang you would die

[modern stone]

bruh

why?

[livid ermine]

Because he is memeing. Atiyah-macdonald is the canonical text for commutative ring theory, and to read it you'd probably want to have taken at least a couple algebra classes already.

[halcyon hornet]

Uh hello. Anyone any suggestions?

[livid ermine]

Lang is known for being encyclopedic and very difficult to self-study from

[modern stone]

yeah I am a beginner in Abstract Algebra that’s why I was asking

[livid ermine]

idk. maybe bhattacharya like moniker suggested. seems like a decent book

[modern stone]

Are Pinter and Artin a good start?

[livid ermine]

I think pinter is good. It is a lot more elementary than artin

[wise umbra]

Okay so they are not the most suited books for you (actually I like encyclopedic books but I understand that it's not the case for everyone)

[lost trellis]

Suggest me a good book of multivariate calculus for practice purpose.

[gray gazelle]

Lang

[analog pollen]

Stewart has a lot of problems

Is there a differential geometry book that only needs calc, dif eq and Lin alg as prereqs?

And some tensor calc

[karmic thorn]

Do Carmo, maybe?

[analog pollen]

Differential geometry of curves and surfaces?

[karmic thorn]

Yes

[analog pollen]

Ok thanks

I will check it out

[karmic thorn]

Found these on a quick MSE run

[analog pollen]

Thanks

[crystal lion]

what's the best way to think of differential geometry and differential topology as extensions of mvc

diff top is like we're going to prove everything for the general differentiable manifold

but idk what differential geometry is supposed to be

[tranquil ocean]

Differential geometry is also just extending ideas from mvc

And ideas from ODEs

[hollow drum]

Can someone recommend a text book on the history of differential manifolds/differential geometry?

[halcyon hornet]

What are the prerequisites for learning Combinatorics at High School level?

[gray gazelle]

none

you can jump right in

[halcyon hornet]

Cool.

Same for Number Theory it seems.

[gray gazelle]

there is a really good nt text ik for high schoolers

An Invitation to Number Theory by Oystein Ore

@halcyon hornet

[halcyon hornet]

I see.

I plan to use.

Elementary Number Theory by Burton.
An Introduction to the theory of Numbers by Niven.
And AoPs Introduction to Number Theory.

How are these, for general learning and Olympiads @gray gazelle .

[gray gazelle]

these seem nice

[halcyon hornet]

Cool.

[gray gazelle]

the one I recced is a bit beginner friendly which you can use as a first glance

[halcyon hornet]

And my Combinatorics.

Schaums Outline of Theory and Problems of Combinatorics including concepts of Graph Theory by V. K. Balakrishnan.
Later - Applied Combinatorics.
AoPs 2 books on Combinatorics.

Are these great, Orphee?

[gray gazelle]

these seem okay

[halcyon hornet]

Then what seems great?

[gray gazelle]

Bona is good one ik of

[halcyon hornet]

And Geometry -

AoPs Introduction to Geometry.
Euclidean Geometry in Mathematical Olympiads.

What else?

[gray gazelle]

Brualdi is the one I plan to use myself

[halcyon hornet]

AoPs 2 books for Algebra.

And how are these for general beginners -

Thrills and Challenges of Pre-College Mathematics.
An Excursion in Mathematics.

[gray gazelle]

for geometry you can do Kieslev for starters and jump into Coxeter

[gray gazelle]

these are standard comp math books which are really helpful for math entrances in India

[halcyon hornet]

Cool.

And first Thrills.

Then Excursion.

Right?

[gray gazelle]

the order of doing these isn't necessary

pin point what you like and jump right in

[halcyon hornet]

Oh.

And what are the Prerequisites to EGMO?

[halcyon hornet]

Aight, starting with these 2.

Do They cover most material/theory for Olympiad Mathematics?

[soft drift]

9th grade am learning geometry, I want more rigor and/or more dimensions

[analog pollen]

Think the closest to this is like topology or diff geo

[sharp latch]

I would actually recommend Euclidean geometry in mathematical Olympiads

[analog pollen]

Isn’t geometry limited to 3D for a normal geometry book?

[soft drift]

why are we talking about MO

[crystal lion]

extension in what way

[crystal lion]

this is how i think of diff top

surely diff geo has its own motivation in this manner too

[tranquil ocean]

I feel like most diff geo things can be motivated in this manner too. There are some things you can't really do on just a smooth manifold, things that involve distances or angles, that a riemannian manifold allows you to do

[dapper root]

Marvel vs Capcom?

YOU WANNA LEARN HOW TO DO A FUCKIN INFINITE?

[tranquil ocean]

ur so cringe

[dapper root]

Oh god this was #book-recommendations I thought this was a discussion channel

[sharp latch]

Because there are more interesting rigorous problems in that book than a traditional 9th grade geometry class

[soft drift]

what

you mean a book titled "Mathematical Olympiads"?

[sharp latch]

“Euclidean geometry in mathematical Olympiads”

[soft drift]

o

[gray jungle]

so a friend of mine was complaining about
contemporary abstract algebra 7th edition and i was wondering what you guys think of it and what could possibly be a better alternative

[solemn rover]

there are 19 pages of search results for "Gallian" in this channel

did they say what they disliked about it?

gallian is a very friendly book and very hand-holdy but this can be annoying if they want a more sophisticated presentation or one that treats the reader as more mature

[gray gazelle]

um... why don't you see for yourself

[solemn rover]

haha

don't understand what you're saying

To clarify, when I wrote

[gray gazelle]

if you see that someone mentioned the book, and you're asking for opinions, you can check if they had any opinions yourself, no?

[solemn rover]

did they say what they disliked about it?
the pronoun "they" refers to "a friend of mine" in the post by james_ash_

also i am not asking for opinions, i think you're mixing up the authors of the previous posts

[dense wren]

Does stein and shakarchis complex analysis book assume you read the Fourier analysis book first?

[thorny oak]

Naruto manga