book-recommendations

[pliant wadi]

Try Baum's book

It's catered towards undergrads

[gray gazelle]

why did it make you laugh?

[pliant wadi]

Well you see I personally didn't have a very gentle introduction to the subject

[gray gazelle]

munkres?

[pliant wadi]

Nope Munkres' is a saint

In comparison

[remote vortex]

I think the gentlest introduction to point set topology is 1. topology in R, in the context of real analysis, 2. metric topology, 3. general point set topology

But that's a languid path

[pliant wadi]

Oh yea doing metric spaces is recommended+++

Our prof started with general topology

The third example being the Zariski topology

NOT RECOMMENDED

[remote vortex]

I'd definitely be against showing people examples of non-Hausdorff spaces too early on

[pliant wadi]

He started with non-hausdorff spaces only

[remote vortex]

Allow them to develop some intuitions before you shatter them

[pliant wadi]

Then he even proved they are non hausdorff without mentioning the term or why it mattered

[remote vortex]

Oh dear

[pliant wadi]

Apparently he was trying to get the faint hearted to drop out the course

[remote vortex]

Well, if that's the goal, then I find no fault with this approach

I've always been a big softie as a teacher

[pliant wadi]

The problem is he didn't change the approach even after add/drop was over

[pliant wadi]

Funnily nobody dropped out

Ig we just had a penchant for suffering

Though I hear most people did drop out of his algebraic topology course

[remote vortex]

I've heard it builds character

But introducing people to topology with stuff like Zariski sounds like suffering for its own sake

[gray gazelle]

i think it can work if properly motivated

[pliant wadi]

Yea my juniors said they saw him laughing when we were going through our midterms

He'd walk around

Stop, stare, and then laugh

[remote vortex]

Probably, I'm biased towards introducing people into abstract subjects gradually.

Start with something concrete like R/R^n, then some kind of function spaces

[pliant wadi]

You are talking about people who haven't taken even a single course in abstract algebra by then

[remote vortex]

Even on function spaces you can do nonmetrizable topologies, and then you can show them the wonderful world of non-Hausdorff topologies

[gray gazelle]

They surely know what polynomials are. You can motivate topology in terms of semidecidable properties, which makes the zariski topology quite natural

[gray gazelle]

do you have a good digital copy of this? the pdf available has blue highlights in certain places

[gray gazelle]

at least for the K[x] case

[remote vortex]

If I was teaching a general topology course, I'd show some examples of non-Hausdorff spaces at the stage of discussing separation axioms, but I wouldn't focus on them and I'd point out that most of the examples we've been doing so far, are Hausdorff

[pliant wadi]

True, fair enough.

We did eventually get the hang of it.

In the same semester itself.

[pliant wadi]

I do have a good one

I'd DM

[gray gazelle]

thanks

[vital bane]

I saw "Riemann" and got excited thinking you were talking about Riemannian manifolds

But alas! It was just the Riemann integral

also wait what Riemann integral for probability?

[remote vortex]

When you do actual calculations in probability, you end up integrating real-valued functions over intervals in R, most typically

So to get or approximate the actual value, you end up doing Riemann integral

Probably via the FTC

[vital bane]

POV you're a pure mathematician: actual calculuations? 🤢

[remote vortex]

Apparently it's something people do

[gray gazelle]

do probability calculations involve lesbegue integration?

in continuous sample spaces

[vital bane]

Doing calculations with the Lebesgue integral is like doing proofs using the Riemann integral

[remote vortex]

Well, sort of, in that sometimes your result involves limit operations and Lebesgue theory helps you justify the limit passage

But to get the actual, numerical value, you're almost certainly going to use the Riemannian methods.

(including the FTC, so you don't have to literally do the partitions if you can find the antiderivative)

[gray gazelle]

FTC is useful for sure

[remote vortex]

Lebesgue integration is hugely important as a theoretical tool, to prove the validity of various operations

But the actual calculations at the end are going to be more pedestrian

[remote vortex]

Understatement of the week 😄

It's very justifiably called the fundamental theorem

[gray gazelle]

in high school we learned integrals by antiderivative formulas

we didn't know back then it used ftc

[glossy zealot]

Iirc there’s a third type of integral

Darboux or something

[pliant wadi]

Darboux?

Right

Riemann integrals are a more general form of those iirc

[gray gazelle]

Your school didn’t teach ftc?

high school ed is very shitty here

the book probably mentioned it but i don't rembr

we just did what we were taught in class and passed with flying colours

[pliant wadi]

I don't think it's not shitty anywhere

[glossy zealot]

Basically it’s about doing integrals questions using taught techniques

I did not get why it worked back then, but growing old now I get to be more curious of why it works

[vital bane]

FTC moment

[gray gazelle]

Fundamental Theorem of Carla

[vagrant hamlet]

Hi everyone, I'm looking for a good first course on probability.

I want to get to stochastic calculus eventually and tried to read Ioannis Karatzas, Steven E. Shreve - Brownian Motion and Stochastic Calculus, but I realised that I'm not fully comfortable with all the notation of stuff used in probability since I haven't had any probability courses.

I completed a measure theory course and consider myself p fluent with it

Can anyone recommend a quick course that goes through the fundamentals of random stuff using measure theory?

[glossy zealot]

You can take a look at the book by Billingsley, it is a standard probability book for phd student

[vital bane]

@remote vortex would know

[gray gazelle]

https://ocw.mit.edu/courses/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/ I am doing this course on probability rn

it's really good

[crimson leaf]

I thought they were equivalent cause you can construct the Riemann integral using darboux sums

[vital bane]

yea darboux sums are just a different way to do riemann sums

but they're basically the same

[remote vortex]

Not really, it's been a while since I learned and I never taught it

[crimson leaf]

Yeah we kind of did this in measure theory when talking about why we needed something besides Riemann integrals, but he didn't say their name was Darboux sums

[vagrant hamlet]

in analysis we defined riemann sums with nets of tagged partitions

[vital bane]

nets?

[vagrant hamlet]

and the darboux sum is the lim and sup of a partition

but they are equivalent

[remote vortex]

Yeah, the approach with the upper/lower Darboux sums and the Riemann approach with the tagged partitions are very interchangeable.

I often forget which one is called which when I'm in the middle of estimating, but I tend to prefer the Darboux version.

I like working in terms of upper/lower estimates and shrinking the gap

[violet shuttle]

Kallenberg

[vagrant hamlet]

thank

[tawny crater]

textbook so I can see what goes under "applied mathematics"? What are the major problems, areas, techniques, etc...

[steel eagle]

I'm looking for a book on linear algebra or abstract algebra, I have the knowledge from Computer Science's course with some basics and ideas, but I'd like to learn a more pure mathematics approach. I'm also reading Spivak's Calculus (for reference).
I saw the book Advanced Linear Algebra by Steven Roman. Do you recommend this? Or in case I'm missing prior knowledge, what do you recommend?
Thanks

[pliant wadi]

Eh? Fr? We mostly worked with Darboux and our prof just mentioned in the passing that there were some cases where darboux failed where Riemann worked. I just remember it offhand, could be faulty memory. Don't remember if I checked it. My bad then.

[torn crypt]

Semidecidability is very much so not what most students care about

[gray gazelle]

what do they care about?

[torn crypt]

Not logic

I mean dawg I study logic and I still don’t care about this perspective

[gray gazelle]

but its a beautiful 😭

[molten mason]

I feel like that umbrella is too large. It covers anything that's not pure math but uses math. Astronomy, physics, chemistry, biology, oceanography, GPS, radar, 3D graphics, etc.

[molten mason]

I would say Roman is after you've already done abstract algebra and another textbook on Linear Algebra.

Linear Algebra by Friedberg, Insel, and Spence would be a perfect intro to Linear algebra with your background and goals

[gray jungle]

Hoffman and kunze is a good option too

[steel eagle]

Thanks, and after this what would you recommend me on abstract?

[molten mason]

I can't personally because I went the non-traditional route but there's this great review from the pins here

#book-recommendations message

[remote sparrow]

u only need a solid course in real analysis

[torn crypt]

Where is it expounded upon

[gray gazelle]

in my beautiful little mind

[torn crypt]

Pried out

[remote sparrow]

https://press.princeton.edu/books/hardcover/9780691150390/the-princeton-companion-to-applied-mathematics

[dusk wind]

he answered the impossible

[molten mason]

The GOAT

[earnest wolf]

lol, didn't know there was also a book for applied stuff

is it as good as the companion to (pure) math?

[remote sparrow]

idk

probably

[flat marten]

Does anyone have any recommendations for abstract algebra textbooks (in the vein of dummit and foote), but like... Insane? Dummit and foote is starting to feel far too sane for me right now

[violet shuttle]

? wdym by this

I like Lang more than D&F

you could try getting the commutative algebra necessary for Hartshorne and then do Hartshorne

[flat marten]

I mean, strictly ive never done rings, or modules, or fields or whatnot, I got as far as groups in D&F before getting distracted by other maths. But now I'm back it doesn't feel insane enough, if that makes sense. But I will have to study all those thing sooner or later so might aswell get it over with

Idk it's a nebulous question

[elder pendant]

Hungerford?

[earnest wolf]

u mean his undergrad or grad book?

[tribal crow]

probably grad

[violet shuttle]

grad book ofc

[violet shuttle]

mood. mathematical maturity from another branch really helps with everything.

[flat marten]

I went off and read jacobsons lie algebras for Christ's sake like

(BTW good book, highly recommended)

[flat marten]

Looking into this 🤔 🎯

[violet shuttle]

you got distracted from groups by derivatives of groups?

[flat marten]

Pretty much

hungerford just looks like a stripped down grillet

[elder pendant]

Don't know Grillet

Anyways sorry if it's not the right thing, I'm new around here

[molten mason]

Just go through them all and pick what's best for you. They're all fine options. Lang is the just the best option

[hearty aspen]

any recs on basic stochastic calc? and prereqs?

[gray gazelle]

What are your thoughts on Grillet? I’m considering getting it

[maiden glen]

how is the "Princeton Companion to Mathematics"?

[pliant wadi]

Very nicely written articles. A lot of recent topics aren't there tho.

[remote temple]

this

[maiden glen]

Is there a text of equivalent greatness for recent topics?

[pliant wadi]

No idea

If you find it tell me too

[maiden glen]

😒

[whole coral]

Is there a book much more comprehendable than by serge lang's basic mathematics?

I cant seem to understand lang

[knotty dagger]

What resources would be recommended for graphs of algebraic equations?
like nicer theory

..advanced

[molten mason]

Any other Pre-Calc or lower book.

If you need help with that text there's always all the help channels, math discussion, or pre-university channels

[trim kayak]

hey Salagos

[molten mason]

Hello there

[tribal crow]

hey Salagos

[gilded notch]

Are there any good books to get into real analysis with that have only some comprehensive background in basic calculus as a prerequisite?

[rose geyser]

abbott’s understanding analysis

or rudin as a reference/problem book

[cobalt arch]

There is an encyclopedic dictionary of mathematics by the mathematical society of Japan that is two volumes (averaging around 1000 pages each) that I think goes into much more advanced topics although it stops at about 1980 so not anything more recent. You can find many topics there that will then help you find more specialized material. It is older than the princeton companion to mathematics so it might not be suitable for your purposes.

[earnest wolf]

i think almost any first-course real analysis books do not require any calculus

and most of the time the only prerequisite is being comfortable with proofs

[earnest wolf]

here are some other good ones

[pliant wadi]

how's coxeter's introduction to geometry as an undergrad intro to geometry textbook?

[trail hemlock]

jay cummings real analysis book is great 😍😍

[gray gazelle]

how is spivak's book for starting differential geometry?

[gilded notch]

thanks

[weary bison]

@fickle whale Hi I was looking through the server to see if I could find more resources on geometric algebra and Clifford algebras more generally and your name came up. I'm trying to figure out more about what the field around these topics look like. Watched several of sudgylacmoe's videos and read through LAGA by Alan MacDonald, but I guess I'm trying to figure out what's next

Addendum: I think I got through a large part of LAGA but I got lost. But it's been a few years so I'm not sure where I got lost.

I think it was that, unless I missed it, LAGA doesn't go out of its way to describe how the geometric product works for general multivectors that aren't blades, or develop much geometric intuition of non-blade multivectors when I was curious how those would work in a geometric frame. But I also guess that there's a not a great way to visualize those

[vital bane]

@fickle whale you were right

[weary bison]

Some other Lee should make a book on Lee Algebra

[fickle whale]

LMFAOOO

Be on the look out for a William Lee Kingdon

[vital bane]

bruh

[maiden glen]

I'll still use it,

is there any other texts one may suggest that is similar to Forsaken's suggestion and "Princeton companion to mathematics"?

[fickle whale]

There's only one kind of non-blade multivector I find visualizable

The bivector

Well, non-versor that is

[weary bison]

Wait isn't the bivector a blade? Or am I confused?

Also I'm not aware of what a versor is

[fickle whale]

A blade is an exterior product of vectors, a versor is a geometric product of vectors, a k-vector is a sum of k-blades

e12 is the wedge of e1 and e2, so it's a blade

[vital bane]

e12 is a bivector no?

[fickle whale]

1 + e12 is the product of some vectors idfc

So a versor

[gilded notch]

thats the first time ive ever heard the word blade used in mathematics, it really does go deep

[vital bane]

it goes insanely deep

[fickle whale]

Yes

All 2-blades are 2-vectors, not so the inverse

I dare you to factorize e12 + e34

[vital bane]

ah I must be confusing k-blades with k-vectors then

[fickle whale]

K-blades are also called simple k-vectors

We tend to restrict our considerations to blades because they're enough to address the whole algebra via linearity

Or versors because being a product of vectors is also amenable

[vital bane]

You need to create a thread in #groups-rings-fields that is exclusively for goemetric algebra posting

[fickle whale]

Hmmm

[fickle whale]

Ping me in #math-discussion in 8 hours and I'll show you

[weary bison]

Okay in 8 hours is around 6 am for me. Is 10 hours okay?

[neon glacier]

one million digits of pi is...exacly what it sounds like.https://www.youtube.com/watch?v=TXl4q-ZEjvA

[fickle whale]

Yes, that's just the lower bound, when I get off work

[dusk wind]

I was looking for something like this thanks

[novel hound]

You may wanna look at Advanced Engineering Mathematics by Kreyszig.

[maiden glen]

oh yes

thank you

[north flicker]

$ \sum^{n}{i} \sum^{n}{j\ =\ i} \sum^{n}_{k=j}

how to visualize this guys

[tribal crow]

wrong channel

[north flicker]

alr

[tribal crow]

maybe go to #math-discussion

[vagrant hamlet]

Question: Is there a need to go back to relearn linear algebra

[remote sparrow]

you aren't "relearning" linear algebra by reading roman as if you read a book at the exact same level as FIS

[knotty dagger]

any recommendations for algebraic graphs?
like, nicer theory

[shadow hedge]

Hi for real analysis which book should I work though rudin or abbot. I tried to learn the subject before but had to drop out due to difficulty. I now have a little proof experience from the linear algebra course I am taking

I am more inclined towards rudin due to its difficulty and my desire to finally master this course. Would it be a good choice?

[remote sparrow]

are you retaking this course any time soon?

you would likely have more of a head start than your peers using abbott than trying to bang your head getting through rudin

[torn crypt]

@remote sparrow @hallow oriole Proof theory recs?

[hallow oriole]

pretty please w a cherry on top!!

[remote sparrow]

https://www.reddit.com/r/math/comments/1apneml/what_are_good_textbooks_to_learn_proof_theory/

i made a post on this like a month ago

[torn crypt]

Bro knows every book

[hallow oriole]

^^^^

[remote sparrow]

check diligentClerk's reading list and peter smith's guide too

[torn crypt]

Ew Smith

[hallow oriole]

what's wrong w smith?

(idek who that is tbh but)

[remote sparrow]

other books that cover a little bit of proof theory would be avigad's Mathematical Logic and Computation and van dalen's Logic and Structure

[remote sparrow]

https://www.logicmatters.net/

he's the owner of this blog

he's also a sex offender

he was convicted for possessing child pornography

[hallow oriole]

ah

[daring lake]

Just study rudin till you understand how proofs work

[hallow oriole]

ew is right

[torn crypt]

Interesting

[remote sparrow]

https://www.dailymail.co.uk/news/article-2127450/Cambridge-University-allow-child-pornography-don-continue-teaching-lectures.html

[torn crypt]

Goofiest picture

[torn crypt]

Smith was banned from using any computer with internet access

My favorite line

[heady ember]

[remote sparrow]

in case this is not a joke, proof theory has very little to do with knowing how to write down an ordinary proof in mathematics

[daring lake]

yeah that was a joke, hence I marked it out

[torn crypt]

Debatably much to do with math at all, some might argue

[remote sparrow]

https://www.reddit.com/r/math/comments/1tlcn1/proof_theory_book_recommendations/

[shadow hedge]

I will in September so I want to learn by myself before that

Currently I am working through LADR by axler

So will rudin be too difficult to finish in say 3 to 4 months by myself?

[remote sparrow]

most likely

[shadow hedge]

Alright thanks

[graceful moon]

Rudins difficulty mostly comes from its lack of motivation and the fact you have to fill in so many gaps he leaves. If you don’t know much about proofs you’ll have a bad time with Rudin, definitely pick abbot

[heady ember]

There are no additional gaps to fill when you prove everything yourself anyways

[earnest wolf]

interesting. if u buy cheese with holes, do you buy the holes as well? if you buy rudin's book, do you buy the gaps he left as well?

[earnest wolf]

i mean, it's not only abt proof techniques or general familiarity with proofs

ig rudin is a typical example of this — it's a cool book abt analysis only when u know analysis

for example, I think when proving that cauhy products converge he just proves lim sup = 0 and finishes

without explaining why

1. this proves the theorem [we have lim inf = 0 as well, but he didn't even mention it, and it now follows that lim = 0]
2. why can't we do it with the usual limit

btw, is papa rudin that bad as well? (didn't read it)

oh, there is also grandpa rudin lol

[left cloud]

papa rudin

[remote vortex]

I've only read baby and grandpa rudin, and I wouldn't recommend either of them as a book from which to learn

Both are very good reference books and supplementary material.

I often rant about Baby Rudin, but it is a very good book; it's just usually a very bad idea to learn analysis from that book.

If you learn from something else and read Baby Rudin alongside it/afterwards, that's actually a good thing to be doing.

[chrome yacht]

amann-escher and pugh are great rudin alternatives

[remote vortex]

In my opinion Abbott is much easier to learn from; I'd get both books and read Abbott primarily, and once you've done a chapter in Abbott skim Rudin to see what he says about the subject.

Rudin's books also has nice exercises.

Learning just from Rudin is going to be a slow and painful process, especially if you don't have outside help (although you do have this discord, and the #real-complex-analysis channel is active and helpful).

[earnest wolf]

@shadow hedge

btw, Abbott's exercises were also great. Very enlightening I'd say

[remote vortex]

Indeed, they are, and they're made to teach you new stuff.

Which I like, but Rudin is a good supplement for that, his exercises are also good.

In general the more exercises you have access to, the better, doing exercises is hugely important in learning math

[daring lake]

I actually like papa rudin, learnt measure theory from it

[dusk tapir]

Any one knows of a course that followed pugh for analysis (as in to see at what pace they went, what problems they assigned)?
I searched a bit and couldnt find any

[vital bane]

rabbit's advocate?

🐰

[violet shuttle]

rudin explains this earlier in the lim sup and inf chapter, doesn't he? namely that sup and inf exist always, and that lim inf ≤ lim sup, and that equality implies that the common limit is the lim.

It was clear to baby me.

[hallow oriole]

baby xela neq normal ppl

[vital bane]

hindsight is 20/20

[lusty ermine]

books with very few exercises about (linear) algebra, if possible non conventional examples would be fine

[vital bane]

why do you want few exercises?

[lusty ermine]

I already have axlers and the exercises from my algebra class are enough but want to get more info regardless

any recs in mind?

[karmic tangle]

Seems like it, I went through with the order and got billed the appropriate amount

[earnest wolf]

lol, I completed his missing logic in the brackets

and i omitted lim inf and lim sup exist and equal -> lim exists and equals to them, because it was obv ||to me ||

the point is that he neither mentions 1) nor 2), and also forgets abt of what's in the brackets as well

[sage kelp]

What are alternatives to Hubbard and Hubbard for Vector Calculus?

[earnest wolf]

*normed ppl

[earnest wolf]

i mean, if u r saying he didn't have to mention it bc he said that earlier then it's like saying u don't need a proof of FLT after u stated the ZFC axioms

[remote sparrow]

shifrin

[flat marten]

I have officially finished greub, from cover to cover, and I have to say, once you get used to the weird ass notation and the curtness of proofs, it's a beautiful read. 10/10, everyone else is wrong about dual spaces

[dapper root]

wtf is greub

[flat marten]

Greubs linear algebra

[rain stream]

Should I use Linear Algebra Done Right as a first book on the subject?

[remote sparrow]

done what

right or wrong

[rain stream]

Lol, my bad

Done right

[trail hemlock]

😭

[remote sparrow]

you could, but you would be missing stuff like gaussian elimination

[rain stream]

Yeah, but I can complement that by reading a different book later on

I plan to study this on vacation

My motivation for using this book is the fact that it's one of the few proof based linear algebra books I can get atm

[remote sparrow]

by get, do you mean buy?

[rain stream]

Yes. I don't really like reading PDFs

[remote sparrow]

#book-recommendations message

look at meckes and hefferon

[inland seal]

i want to start learning, probably the basic for now, any recommendations?

[heady ember]

Friedberg?

[rain stream]

Not easily accessible in physical format where I'm from

[heady ember]

It was via Amazon for me.

[rain stream]

It seems Linear Algebra Done right is the only proof based book I can buy for a reasonable price

[heady ember]

You don't need to even buy it btw. He has the pdf up on his site so you could print it out if you wanted to save money.

[rain stream]

Super expensive where I'm from

[heady ember]

Even the 5th ed paperback?

that was the cheap one for me

as cheap as it gets (~$30)... i guess

[rain stream]

I'm not from the US

[heady ember]

I'm not either

According to what my copy says, it was printed in India lol

https://www.amazon.com/Linear-Algebra-5th-Stephen-Friedberg/dp/B0B9HBT4XH/ref=tmm_pap_swatch_0?_encoding=UTF8&qid=&sr=

bad thing it its smell isn't great

the paper quality isn't as good as my other two books from Wiley and Dover Publications

[rain stream]

Amazon wasn't listing this book for me

I mean, getting Linear Algebra Done right would still be cheaper I think

Considering shipping costs

[golden salmon]

Shilov's book is a bit weird (it starts from determinants?) but its a good foundation all the same

[remote sparrow]

hefferon is actually the cheapest

there's a print copy available for sale

meckes and axler are about the same price

[rancid hollow]

U can buy it for $0 without even pirating

It's free as a PDF on axler's website

The latest edition

[heady ember]

They want a physical copy.

[rancid hollow]

oh hm

I'm sure there's some website where u can buy for like $10 as long as u don't mind coffee stains

Like how my copy of dummit and Foote came in

I already forgot where I got it from tho

[rain stream]

Some used books are hard to find here. At least for a reasonable price

[rancid hollow]

I think mine was from a Chinese seller

Really wish I could remember

[rain stream]

I can get LADR for a reasonable price on Amazon. I just want to know if it's a good book for someone who wants a challenge using a proof based text

[rancid hollow]

Hmmm depends on you really

You could check the pdf first and then buy the physical copy?

[rain stream]

Alright, Imma give it a try then. If I find it too hard I can always read later on when I acquire more mathematical maturity

[rain stream]

I'll do that

If I like it I'll buy it

[heady ember]

Its good, other than its avoidance of determinants and treatment of characteristic polynomials.

from what I heard

[rancid hollow]

I think the very first section or two had like 1 hard problem considering how early on it is but idr much else that stood out for me personally

It was about proving that if the union of 3 subspaces made a subspace, then one had to contain the other 2

didn't work for F = Z/2Z

Though it points that out

[golden salmon]

oh if you explicitly want difficult then defs do shilov. It's not harder than e.g. a standard groups book but it's harder than the average LA textbook I think https://www.amazon.com/Linear-Algebra-Dover-Books-Mathematics/dp/048663518X

[rain stream]

I want something intermediate

I saw a short from The Math Sorcerer saying LADR has a good mix of easy, medium and difficult problems

Btw, I have a copy of Finite Dimensional Vector Spaces from the 60's

[hallow oriole]

are u currently at a university

if you are, check if your university has a springerlink license

[rain stream]

Yes, I plan on taking linear algebra next semester

But I want to study during the break

[hallow oriole]

if they do, you can legally obtain free pdfs of a large amount of springer books and print them out as long as it's for non-commercial use

[rain stream]

Alright, imma do that

[hallow oriole]

gl!

[rancid hollow]

hmm LADR might be on the harder end if you've never done LA before? It assumes you already know some LA, like knowing how to do Gaussian elimination

[hallow oriole]

remember not to start selling them or anything or you could get in legal trouble

[rancid hollow]

which is p ez but

like some schools do use it for a first semester course but the author himself uses it for a second semester in LA

[rain stream]

I plan on supplementing the stuff I don't know with more introductory textbooks, btw

[rancid hollow]

Alright

[rain stream]

I see. I'm gonna check the PDF version and see how I like it

[rancid hollow]

my first LA class used the LA section of Apostol's 2nd volume of his Calculus series fwiw

it did like LA and then multi in 1 book

I never went to class and got an A+ so it works for self-teaching

[vocal cedar]

Any calc 1 book recommendations? I'm not in uni but I just wanna check what I'm gonna be working with

[vital bane]

You can get a physical copy for 0$ without evene pirating (just break into your nearest math book store and borrow it without permission)

[vital bane]

You don't have to wait until uni to have fun with calc

as for book recommendations...

it depends on what you wanna do

[viral halo]

anyone got a book specified for math techniques?

[vital bane]

math techniques?

[viral halo]

yes

[vital bane]

as in.... proof techniques? induction, direct proof, contrapositive, proof by contradiction?

[viral halo]

like for etc, discrete math u got set theory, logic, trees etc

[vital bane]

Those are topics usually introduced in a discrete math course, yes. I'm still not sure as to what you mean by math techniques

do you want to learn discrete math?

[vital bane]

it depends on what you wanna do, like if you wanna go into non-math fields then "Calculus - Early Trancendentals" by James Stewart is good

as are any other calc 1 books

if you wanna go into math then "Calculus" by Michael Spivak is good

[vocal cedar]

I'm interested in early transcendentals but does it start off with hard topics?

[vital bane]

nope

you can look up the table of contents

it starts off with "what are functions?" and "what are limits?"

[vocal cedar]

Oh that's nice I'm doing that rn lol, I'll definitely check it out thx for the recommendation

[buoyant sedge]

hello guys, i have good knowledge on basic algebra, combinatorics and a little bit of calculus, but i am clueless on what to proceed next, there's just so many things i can start with, like statistics or matrices or vectors or... you get the idea
so what do you guys recommend i continue my learning with now?

[glad rampart]

Linear algebra is insanely useful I’ve heard

[tribal crow]

it is

[buoyant sedge]

its the base for almost everything you'll subsequently study

[glad rampart]

You should learn that then

[buoyant sedge]

yea i already did

like i said

[glad rampart]

You said you haven’t learned matrices or vectors

That’s linear algebra dude

[buoyant sedge]

oh

nvm

ohh

thought it was just linear equations

my bad

then is there any good books i can start with?

[violet shuttle]

most things are linear algebra

[violet shuttle]

yup

[violet shuttle]

I hear good things about Axler, LADR, LADW

[tribal crow]

can I use linear algebra to predict my future

[violet shuttle]

#book-recommendations message

[violet shuttle]

obviously

[buoyant sedge]

dayum

[violet shuttle]

future predictors are some of the most obviously linear algebra things

[buoyant sedge]

thanks 🙏

[swift dome]

not a book specifically, but any online resource from where I can practice problems on number theory( basic + intermediate).

[analog lava]

maybe the art of problem solving or brilliant websites

[glad rampart]

AoPS has alcumus for free but idk how it is with NT

[zenith stone]

compscilib maybe? has number theory practice problems in the discrete course: https://www.compscilib.com/search/discrete-math?onboarding=false#integers (and practice for other courses like lin alg, stats, etc)

[narrow relic]

Wade, Introduction to Analysis has some vector calculus material in the later chapters.

[ruby seal]

So I know some group, ring and field theory and was wondering if anyone knows a book in elementary number theory (I don't know too much number theory, just the basic introduction to proof writing stuff) which uses abstract algebra knowledge to do stuff, as I have heard a lot of number theory is easier to do with knowledge of abstract algebra (a basic example of this is proving the FTA from the fact that Z is a euclidean domain and thus a UFD).

[daring lake]

An Introduction to Theory of Numbers by Niven, Zuckerman and Montgomery

Number theory does use some extent of Groups and Rings (based on how deep you go) so I will say you are good to go

[novel hound]

For an easy intro try Elements of Number Theory by Stillwell and/or Algebraic Number Theory for beginners also by Stillwell. NZM (mentioned above) will be elementary number theory without abstract algebra (although there is a chapter in the last third of the book which touches upon the basics of algebraic number theory). Ireland and Rosen is also elementary number theory with some algebra, but it is probably better done after an elementary number theory course and maybe even some algebraic number theory for the later chapters.

I believe Stillwell is your best option.

[pliant wadi]

what's a good book for undergrad intro into geometry?

Is Coxeter's Intro to geometry a good book?

Do I need commutative algebra

I am studying modules in algebra and euclidean spaces in analysis

[pliant wadi]

I have taken all pre-reqs for these

[remote ginkgo]

what do you mean by geometry

differential geometry and algebraic geometry are completely different things

[pliant wadi]

Yea I know I was just roughly trying to describe my background

[pliant wadi]

That's why I am looking for an introductory text

I haven't done anything particular in geometry since I passed out of highschool. All I have taken are algebra and analysis courses.

[remote ginkgo]

there is no intro to both

you generally have to pick one or the other; they are not similar

[pliant wadi]

Yea I am not looking for differential geometry

Just

Geometry

[remote ginkgo]

oh. then i don't know

[pliant wadi]

Ah alright

Do you have any recs for differential geometry btw

[remote ginkgo]

lots

[pliant wadi]

Ooh give me some

[remote ginkgo]

loring tu - an introduction to manifolds

is a nice one

[pliant wadi]

Nice

[remote ginkgo]

theodore shifrin has a nice book on differential geometry of curves and surfaces

it gives a pretty good background for later, general differential geometry

[pliant wadi]

Oh nice thanks

[gray gazelle]

Hartshorne has a euclidean geometry book called Euclid and Beyond

[pliant wadi]

Thank you

If you don't mind

What's your opinion on Coxeter's intro to geometry

[gray gazelle]

I haven’t read it

[pliant wadi]

Ah ok

[molten mason]

https://link.springer.com/book/10.1007/978-3-031-48906-8

https://link.springer.com/book/10.1007/978-3-031-48910-5

[drowsy thicket]

@molten mason So you're reading Lang's Algebra, right?

Would you say it can work for undergraduate abstract algebra?

[lusty escarp]

Does anyone has a pdf of real analysis by royden 5th edition?

[gray gazelle]

Can I learn Euclidean geometry from these books? I have never studied this.

[slate flare]

umm, our maths education here really sucks (our curriculum is sorta outdated), so i was wondering if there's a good book or website to learn (or get introduced to) advanced maths? i'm not getting into IMO if i just stick to our country's education system.

[molten mason]

I mean any book can work but I agree with Xela that it shouldn't be your first book. Go for it. If it's too much then Lang has an undergraduate version literally named Undergraduate Algebra

[molten mason]

Asking for PDFs is against server rules.

[molten mason]

I don't know how to answer that question. I'm not a geometrist but I want to say yes? You learn Euclidean geometry in school when you're a kid. Those 1000 pages I linked are a continuación of that at the university level. Maybe someone else can chime in.

[old elk]

A book to study differential geometry?

[torn crypt]

Well, piracy is, but PDFs of this one is piracy as not freely available legally

[sage python]

@gray gazelle this is what we should make the kids read to learn multivariable calculus

[gray gazelle]

this looks awesome

what's the book name

[sage python]

Multidimensional Real Analysis

By Duistermaat and Kolk

There is also a volume 2

I haven't actually read it to see how good it is, a friend recommended it as he was learning some, but told me the key thing that he liked was how it treated some differentiation criterion and used that to make some stuff much cleaner

[old elk]

Most of the books are pretty much it depends, it depends on what you are looking for, you could pick another book and say hey, look this explains better integrability in Rn and another one could say hey look this one explains the stoken variety excellently, and so you get the books heh, the hard part is to line up with one book.

[gray gazelle]

yum

[sage python]

Hmmm it might not be that, there was something he said that was a bit of a technical lemma but once you had it, life became very nice

That + the fact it does all this really cool geometric stuff

[rigid barn]

This is more or less what's studied in a German Analysis II course.

[rigid barn]

And this is AnaIII, except integration is done via measure theory.

[sage python]

Yeah the more time goes on the more I start to think the actual strat is

Do some measure theory already in single variable actually

[rigid barn]

One year a mathematical physics professor taught Ana3 and instead of measures they did Stiltjes and gauge integrals, lol

[gray gazelle]

This is where I think Browder’s development is good. Doing measure and then multivariate stuff is more pleasant

[sage python]

This is why I think Browder is basically the replacement for Rudin

Except maybe he should do topology sooner idk

[echo tendon]

https://www.amazon.com/Real-Analysis-Long-Form-Mathematics-Textbook/dp/1077254547/ref=sr_1_3?crid=ZUQKBOFLPRJU&keywords=real+analysis&qid=1706915356&sprefix=real+analysis%2Caps%2C118&sr=8-3

has anyone read this?

[remote sparrow]

yeah it's good

[gray gazelle]

Sorry to ping,
Can you please tell the formal prerequisites for this book

[hollow nova]

I like Jerry Shurman's Multivariable calculus

It's good for a first pass or self study I think

[sage python]

Probably you just need to know single variable calculus well, including some proofs (suprema, delta-epsilon, stuff like that)

[hollow nova]

Actually i'm studying High Dimensional Probability by Vershynin and I can't do any of the exercises, anyone have a recommendation for a book to accompany this one?

[gray gazelle]

Agreed. I don’t love his approach to some of the proofs nor the adhoc introduction of topology, but it’s definitely a good first pass

[hollow nova]

I agree. I just read it for intuition b/c I felt I was lacking a bit

[gray gazelle]

Same

[foggy relic]

mayb the strat is learn topology before analysis

:)

browder is really really good

in terms of topic selection & exposition both

the complete package

[remote sparrow]

thanks for the review nutsoaker

🥜 💦

[foggy relic]

soak your nuts

[foggy fiber]

Anyone have any familiarity with the Life of Fred sets of mathematics texts? I came across a few of them at the library today and from a cursory glance, looks like they're written as novels while still having plenty of examples and questions/answers to learning.

For example: https://www.lifeoffred.uniquemath.com/lof-logic.php

[glad rampart]

I’ve read some of them, I think they work fine enough early on but I really didn’t enjoy anything past prealgebra

[mortal wing]

Any suggestions for good linear algebra, multivariable calculus, real analysis, and proof writing books?

[lusty ermine]

good books for hard questions on recurrence relations, proof based

hard exercises

[quick hornet]

does generatingfunctionology count

[remote sparrow]

https://maa.org/press/maa-reviews/an-introduction-to-category-theory

[trim kayak]

I'm not studying math for a degree or anything but am interested in reading about various math subjects. I'm familiar with Algebra I, Geo, Trig, and some Stats. Is there a specific topic I should read next? Can you recommend some good books to read?

[glad rampart]

A good calculus book maybe?

Heard spivak is good but I haven’t read it personally

[trim kayak]

Hmm okay. I've taken calc before. It was tough. Ill check it out.

[stuck zephyr]

I have found like 3 interesting books but they all seems advanced

[violet shuttle]

some people here have good introductory textbooks for advanced math

like linear algebra, real analysis, algebra

[trim kayak]

Is it weird that I want to read and learn more about various math topics? 🥺

hmm okay thankss

[violet shuttle]

my lad, you are in a math server

i read textbooks for fun. yes it's weird, but you aren't alone

[glad rampart]

I also read textbooks for fun

[trim kayak]

oh okay good. 🙂

[tribal crow]

who doesn't read textbooks for fun here lmao

[stuck zephyr]

I was looking up for some textbook or books for topics I'm doing in calc but I found these three interesting books

1. "Scalar and Asymptotic Scalar Derivatives: Theory and Applications" by George Isac and Sándor Zoltán Németh (Springer, 2008)

2. "Operational Calculus and Related Topics" by A. P. Prudnikov and K.A. Skórnik (Chapman & Hall_CRC, 2006)

3. "Quantum Calculus" by Victor Kac and Pokman Cheung (Springer, 2002)

[trim kayak]

Oohh thanks. Think I should focus on calc then? I've taken calc classes before and they were tough. I still don't really get it. Or should I learn more advanced stuff relating to topics I know such as Geo and Trig?

[glad rampart]

Calc is such a useful tool id recommend learning if you have a good grasp on algebra and trig

[trim kayak]

hmm. what would you recommend @tribal crow

[tribal crow]

of all the people on this server... you ask me??

[trim kayak]

yeahh. why not?!?

[tribal crow]

I'm like, probably the least qualified person you could have picked

[trim kayak]

hmm ok. sowwy

[glad rampart]

I mean she asked me and I’m probably less qualified

[tribal crow]

I guess if you want to learn calculus from here, Stewart's book seems good

I haven't read it myself, but I hear from others that it's a solid intro to calc

[echo tendon]

I have a personal vendetta against those high school style mcgrawhill / pearson textbooks

Ill hate them forever

[trim kayak]

This one? https://www.amazon.com/Calculus-James-Stewart/dp/1285740629

[echo tendon]

Theyre more like math dictionaries than books

verbose for what

[tribal crow]

there are newer editions, but yeah

[echo tendon]

all of that for what

its just bad

[trim kayak]

Oh yeah. I see the 9th edition now. Much more expensive. I wonder how much different it really is from the 8th edition.

[glad rampart]

Probably not very

You could google it though someone’s probably asked before

[trim kayak]

Yeah there is - Reddit

Do you like to take notes as you read a math textbook and work through the problems as you go?

[stuck zephyr]

yes

[violet shuttle]

i write in the book or somewhere else

if somewhere else, that's getting recycled/erased off the white/chalkboard

[stuck zephyr]

I usually write my notes on latex when a reading a book

[violet shuttle]

on latex? why not do it both in latex and on latex?

[stuck zephyr]

I use latex cuz my handwriting is horrible

also latex is hard still like drawing diagrams in tikz

[violet shuttle]

the joke is that you said "on latex"

[stuck zephyr]

I know

[trim kayak]

Makes sense. I really like Stewart's Calc book. I may order that one. I'll keep a notebook for that text only and start going through it. I just don't like notes mixed in with practice problems. I guess I could have two notebooks but that's confusing too. I'm so nerdy 🤓

[gray gazelle]

this is so true

idk about the mcgrawhill ones but the pearson ones are just so dull

[vital bane]

practice problems? you mean exercises in the book?

[gray gazelle]

questions yes

[vital bane]

that makes me rethink my notes because I just have a notebook and I take notes and solve the exercises on it

so it's like notes + solution manual

[trim kayak]

@vital bane Yeah the exercises. I really want to go through a calc text and learn it just for fun. I hope this is a good idea!

[golden salmon]

exercises are fun but I like keeping them separate too

lately I've started the especially problematic combo of doing notes on paper and solving problems in latex

does the church approve? no. will i stop? no.

[vital bane]

It definitely is a good idea! Good luck!

[molten mason]

I normally do quick problem solving or scratch work in a notebook then make it nice and organized on LaTeX. I can't think of the last time I wrote notes for anything. I just read and then do exercises. Any notes I take would be like a formula sheet or simplifing/visualizing something from the text.

Like if I'm in Chapter b and it References something from chapter a I might write it down together on paper just to see why it's referenced or whatever

But then I'll never go back to it, I just move on

[trim kayak]

Any recommendations on topics or specific books? I am familiar with Algebra, Geo, Trig, and some Stats. Sbould I learn more about those or focus on topics I'm not as familiar with such as Calculus. I know its subjective but just want to see what you suggest.

[trim kayak]

Ahh okay. Is Latex easy to use? I don't know anything about it.

[vital bane]

What do you want to learn?

single variable calculus?

[vital bane]

$A^{\text{it is pretty easy to use}}$

[hasty eagle]

Neamesis

[vital bane]

I had to check if it compiled because I've never put text in a superscript

[trim kayak]

Thats pretty cool. I don't know. I really like trig and stats. I wiuld like to learn more about those but also other topics like calc too.

[vital bane]

calculus is amazing

you will absolutely love it

[vital bane]

But yea stewart calculus or thomas calculus or really any introductory calculus book is good. Calculus is one of those subjects which has an abundance of good intro books

Though

if you wanted a more rigorous approach to calculus spivak's "Calculus" would be good

[molten mason]

Takes like an hour to learn

You can google the not so short introduction to latex and just skip down to the math section.

Tons of stuff you can just Google as you need them like font sizes and page layout and what-not.

Howard Anton's Calculus

[molten mason]

Calc involves a lot of Trig
Stats involves a lot of Calc

[molten mason]

You can also pop into #latex-testing and #latex-help

OverLeaf is a website where you can make a free account and play with LaTeX

[trim kayak]

I've taken a few stats classes that didn't seem too calc heavy. Interesting.

Well thanks for the recommendations everyone. Gotta head to bed. Hope to talk more about this soon. I'm sure I'll have more questions.

[heady ember]

VSCode is much better imo, though the set up is a bit more involved.

Keyboard shortcuts and snippets, my beloved.

[molten mason]

I literally went through the process of installing it and setting it up then never used it and opened Overleaf lmao

I do like with overleaf that I can login anywhere like work or my phone and hop in a document.

I'm away from home an order of magnitude more likely than not.

[broken meadow]

porque no los dos

im a fan of using vscode + overleaf + github to sync everything together

[golden salmon]

I'm boomer. I use Kile for latex :)

[heady ember]

What does this mean

,w porque no los dos

[golden salmon]

https://kile.sourceforge.io/

[golden salmon]

"why not both" in spain

[heady ember]

Ye googled it

Aren't git conflicts pretty though

At least that's what I've heard from hearsay

[golden salmon]

yeah but why are you worried about git conflicts?

that's a few steps removed from what you're after

[heady ember]

I see

Never really tried that before

[charred thistle]

books for introductory topology/group theory?

for someone in UG

[golden salmon]

github + git is cool dont get me wrong but a) you should learn how to use the other tools first (as in, use em for a week) and b) git merge conflicts are not that bad and generally are quick to fix. in the nomenclature of git, 'commits' are snapshots of the folder (called a 'repository'). people who make big commits rather than small atomic ones have worse merge conflicts

[golden salmon]

James Munkres' "Topology" is a fave for intro to topology

[slender wasp]

texstudio + github - don't want to rely on a site like overleaf - want a non-corp replacement for github too

[charred thistle]

I have read it

any other book?

[heady ember]

Willard's general topology is well liked by some here

[charred thistle]

ok

[golden salmon]

Not really a standard topology book but https://link.springer.com/book/10.1007/978-3-662-02998-5 is ok

[charred thistle]

any book for complex analysis or real analysis??

[golden salmon]

rudin for both if you are american, amann and escher if you are european, stein and shakarchi if you're australian

(based on my experience with each's curricula)

[charred thistle]

ok

[neon glacier]

https://www.google.com/url?sa=i&url=https%3A%2F%2Fwww.amazon.co.uk%2FOne-Million-Digits-Square-Root%2Fdp%2FB0BQYBTBVK&psig=AOvVaw1KUGS0TtsC_fOUPCMi_xmP&ust=1711359282654000&source=images&cd=vfe&opi=89978449&ved=0CBIQjRxqFwoTCJjKuKTMjIUDFQAAAAAdAAAAABAE

spoirel alert:the 0000 at the end was emotional

[golden salmon]

@marble steeple spam above

[hallow oriole]

ping mods, not modmail

[heady ember]

<@&268886789983436800>

[golden salmon]

modmail is broken then. couldnt message them

[gray gazelle]

Oh gotcha. Is abbott enough?

[vital bane]

really? interesting

[vital bane]

Abbott more than enough for learning rigorous real analysis

he deals with R but you can extend most things to R^n yourself

[gray gazelle]

Wow. Thank you

[golden salmon]

just speaking from personal interactions, but yah

[sage basin]

I loved stein and Shakarchi’s complex analysis

[gray gazelle]

Are these books good for physics olympiad for theory purposes

Resnick Halliday
Physics for engineers and scientists
And university physics

I could also take Feynman lectures but ig it's used by students at bachelor level

Tho anyone here is in discord channel for physics?
Like this is mathematics
So is anyone there in physics

[lusty ermine]

there is a physics server like this one

google is your friend

which book have hard exercises on discrete math? bachelor, proof based learning

[vital bane]

it is in #old-network

[gray gazelle]

sendd pls

[lusty ermine]

.

[vital bane]

Mr. Cow fans be like

[pliant wadi]

oh wow, thanks!

[crimson leaf]

Do people really use rudin for complex? I only see people use Ahlfors and Stein mainly.

[trim kayak]

I really want to grab a math text and just start reading through it and practicing problems

https://tenor.com/view/calculation-math-hangover-allen-zach-galifianakis-gif-6219070

[gray jungle]

its a good book on complex analysis but the spirit of the book is more analytic than a book that touches on number theoretic aspects or geometric aspects like elliptic stuff.

depends on your interests

i learned CA from rudin and i liked it

[trim kayak]

@gray jungle Any recommendations on topics or specific books? I am familiar with Algebra, Geo, Trig, and some Stats. Should I learn more about those or focus on topics I'm not as familiar with such as Calculus. I know its subjective but just want to see what you may suggest.

[gray jungle]

Id recommend a discrete math book, its a very fun domain

Concrete mathematics by Donald Knuth is a good one

[trim kayak]

Oooh thanks. Ill check it out. A few said to focus on calc. I may do that too.

[lusty ermine]

what is the ideal discrete math goto book?

for definitions

[vital bane]

defo

[stuck zephyr]

<@&268886789983436800>

[karmic tangle]

I ordered some books on Springer but iirc I wasn't asked to put in my phone number during the process

do they send the thing to just a nearby post office or will the courier arrive at my door without being able to notify me about the delivery via phone?

[trim kayak]

It will probably get delivered to your address. You should be able to track the package and see when it may be delivered.

[gray gazelle]

@trim kayak https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/

full blown course on calc

no need of buying any books or w/e

[trim kayak]

oh thanks. that looks advanced, but Ill check it out

[gray gazelle]

not that advanced lmao

it's not like you are dealing with epsilons and deltas

[trim kayak]

Hey, calc was hard for me. I can do Algebra, Geo, Trig, and Stats. Calc was a different story 😦

[gray gazelle]

dw you will get used to it

after calc you can start looking at advanced topics

like real analysis

[trim kayak]

I just want something to read through and practice the various problems. I'm not studying it for a degree or anything.

Are you a math major?

[gray gazelle]

yes

this course has problem sets you can try

[trim kayak]

oh okay

thanks

[karmic tangle]

I don't seem to have received a tracking number either

[molten mason]

Springer didn't send me anything for like a solid month or so then I got an invoice finally and thrn a tracking number a few days later then it showed up at my doorstep.

[karmic tangle]

haha

well

I guess I'll have to wait, thanks for sharing that

what was the supposed delivery range you'd gotten when ordering?

[molten mason]

3-5 business days lol

More like 3-5 business weeks

[trim kayak]

Hey Salagos, hows it going?

[crimson leaf]

Yeah everytime I've ordered from Springer they send me tracking info like a day before the package is supposed to arrive not when they get the tracking number

Very annoying

[karmic tangle]

I got 5-14

guess I might get it by autumn

[lusty ermine]

good luck with that

[molten mason]

Another beautiful day on this fine planet. Yourself?

[trim kayak]

Oh pretty good. Spring Break ends today. Nooooo!

[marsh ingot]

Someone know if Les Systèmes Différentiels Extérieurs et leurs Applications Géométriques by Élie Cartan is translated in english?

[plush inlet]

Anyone have a favorite introductory book on analytic number theory?

[stuck zephyr]

@wicked fractal

[fallow cypress]

out of curiosity does anyone have any ergodic theory recs

@sage python

[sage python]

The class on it this semester (which I would've taken if not for the class field theory conflict 😭) is using Einsiedler-Ward, which seems quite good

[fallow cypress]

👀

Wait you still take classes? Did not know that lol

ew, title has number theory?

[sage python]

Yes

[wicked fractal]

Apostol's analytic number theory

Also I would recommend to check other books as well because Apostol sometimes just becomes salty throughout his book

I should make a tier list books for analytic number theory fr

[tribal crow]

you should

[sage python]

My advisor taught a class on that last semester actually

Used "Multiplicative Number Theory" by Davenport

[wicked fractal]

Davenport is a good alternative for Apostol when you feel like Apostol is just ignoring a lot of details

If you are cracked enough you can read the last chapters of Titchmarsh's book on Riemann zeta function

[torn crypt]

There’s EFHN, but it’s operator theory pilled

[fallow cypress]

what's that stand for?

[sage python]

Ergodic FHNtheory

[torn crypt]

The authors initials

“Operator theoretic aspects of ergodic theory”

[torn crypt]

By EFHN

[gray gazelle]

Any recs for sieve methods?

Like selberg sieve etc

[fallow cypress]

I see, I don't know any operator theory yet so that'd probably be difficult lol

[wicked fractal]

I recommend Greaves if you want to hate your life

[gray gazelle]

No thanks I love myself

[torn crypt]

Gimme a sec

[wicked fractal]

Try Murty/Cojocaru

[gray gazelle]

Murty again

[remote ginkgo]

rec books for language learning

[fallow cypress]

what language?

[gray gazelle]

Google

[remote ginkgo]

that is not a book

[gray gazelle]

What language?

[remote ginkgo]

russian spanish chinese(mandarin) germanjapanesefrenchitalian in that preference order

[gray gazelle]

Then @wicked fractal might have better recs

[remote ginkgo]

hm. did u take classes?

[wicked fractal]

I can give a lot for Japanese

[torn crypt]

Delty canonical recommendation list when

[remote ginkgo]

ok my girlfriend might like to have those, pls send

[fallow cypress]

do you know any chinese yet (i.e. heritage speaker)

[remote ginkgo]

(she has family in tokyo, not otaku stuff)

[remote ginkgo]

extraordinarily little

basically zero beyond basic structure of it

[fallow cypress]

okay nvm then I have a book rec but it's for heritage speakers

[wicked fractal]

For Japanese maybe start with JLPT shenanigans in google. Don't stick with JLPT that much because it tends to be very political and it's not that worth it tbh. You can supply it with Maggie sensei website if you want as well. For JLPT I would say focus more on the grammar than the vocab just because the vocab tends to be very political like who the hell is going to use the word "feudalism" in their normal life

[gray gazelle]

wtf is feudalism

[wicked fractal]

LOL

封建制 there u go

[gray gazelle]

I don't even understand this lmao

[wicked fractal]

real

[remote vortex]

A miserable pile of serfs

[lusty ermine]

recommendations for learning to identify recurrence relations

[gray gazelle]

Why you hate Greaves?

[wicked fractal]

I have the same feelings about it the way I do with Hartshorne

very dry

[gray gazelle]

[fallow cypress]

You don't cosplay as a feudal serf?

[remote sparrow]

integrated chinese seems good for beginner to intermediate chinese

minna no nihongo is good for japanese

quartet japanese is specifically for intermediate japanese

[wicked fractal]

gimme chinese recs now

HSK is boring

[remote sparrow]

i'm actually taking chinese 101 rn

the ppts are based off integrated chinese

https://www.cheng-tsui.com/

[crimson leaf]

I wish Davenport had exercises 😦

[remote sparrow]

for spanish i don't know any books besides my high school books. the series we used was Realidades and i thought it was fine. however, Avancemos seems more available on amazon. spanish is really straightforward though. take a look at this book: https://www.amazon.com/Practice-Makes-Perfect-All-One-dp-126428554X/dp/126428554X.

[lusty ermine]

cien años de soledad

[old elk]

jajaja ne

[remote sparrow]

for french, it seems like the series used in high school is Bien dit. these are also very cheap on amazon. you'll have to look up any other textbooks though. there's a complete all-in-one book for french too: https://www.amazon.com/Practice-Makes-Perfect-All-One-dp-1264285612/dp/1264285612

[lusty ermine]

is it bad?

[remote sparrow]

can you elaborate on what "political" means here?

[old elk]

If you want to learn Spanish I could teach you, I am online every day, even if I don't know English je

[remote ginkgo]

hola isomorfismo, soy geogristle

[old elk]

Hola, como estas, Carter?. Soy David.

[remote ginkgo]

comiendo un croissant caliente

[remote sparrow]

 The feudal system consists of the relations of personal domination and servitude constructed on the foundation of the  Germanic community built upon the ruins of the Greek-Roman community. This system can be divided into the two stages: (i) the serfdom system and (ii) the *villein* system. 
 In the system of serfdom, the serfs (labouring individuals) are personally subordinated to the lords, who are the feudal landowners. There are two ways in which serfs relate to the land that constitutes the main means of production. On the peasant holdings, serfs relate to the land as basically means of production belonging to themselves and appropriate products from this land. On the seigniorial domain, meanwhile, serfs relate to the land as something belonging to another person, and the entire product of that land is appropriated by the lord. In the former case, labour is a subjective activity carried out by the serfs themselves to acquire their requisite means of livelihood, whereas in the latter case it is forced labour by means of extra-economic compulsion under the direction of supervisors who embody the will of the lord. Surplus labour is exploited in the latter case in the form of labour rent (corvée) (see Fig. 1.31). 
 With the development of productive power, the serfdom system comes to be reorganised into the villein system. In this system, peasants (villein) relate to the land as basically autonomous owners and appropriate all of the products of the land, with labour being their own subjective activity. However, the lords who personally dominate them use extra-economic compulsion to obtain rent in kind (product rent), and later money rent (see Fig. 1.32).

Source: https://link.springer.com/book/10.1007/978-3-319-65954-1

[old elk]

Super genial, y de donde eres Geogristle ?

[remote ginkgo]

debemos ir a un channel otro

[old elk]

Si claro, como gustes :3

[marsh ingot]

Someone know if Les Systèmes Différentiels Extérieurs et leurs Applications Géométriques by Élie Cartan is translated in english?

[sleek python]

there seems to be a translation: https://www.researchgate.net/publication/260022858_E_Cartan_-_Exterior_Differential_Systems_and_its_Applications_-_Translated_form_French_in_to_English_by_M_Nadjafikhah

[marsh ingot]

Thanks ^^

[sleek python]

Doesn't look like an official translation though so be mindful of that fact when going through the text

[marsh ingot]

At least exist so I will try to find one

[trim kayak]

I found Stewart's Calculus textbook online for a very cheap price. Is it crazy to purchase this textbook to read through and study just for fun when there are a TON of free textbook pdf's online? I really want to buy it but now I'm not sure if I should or not. Thoughts?

[serene merlin]

I prefer to purchase physical copies for studying. I dont think its crazy

[remote ginkgo]

i have spent several thousands of dollars on such things

dont be like me

it is a bad habit

[trim kayak]

I forgot to add that I'm not studying it for a degree or anything. Just for fun.

[remote ginkgo]

same

[serene merlin]

same

[trim kayak]

@remote ginkgo Uh Oh. That's not good. I already have so many books. Ordering another one seems crazy, but I don't do if often. I mostly use the library for novels and things.

hey @serene merlin. What subjects or topics do you like to read about and/or study?

[remote sparrow]

how much is it

the 6th edition can be found in good condition for several dollars

[trim kayak]

$23.00 for the 8th edition of Stewart's Calculus textbook. It's marked as used-like new, so I hope it is. The 9th edition came out a few years later and isn't much different. It's much more expensive too.

[remote sparrow]

that sounds fine

[serene merlin]

I studied statistics in undergrad and masters. I went as far as single variable real analysis formally in math; albeit, it was a pre-req to some statistics course.

Nowadays, I am a hobbyist. I am building a foundation towards modular forms, but I have a lot of learning ahead. I am learning some analytic and algebraic number theory, Cauchy-Schwarz, analysis, rational points on elliptic curves, naive lie theory, and computational topology recently. Also playing catch up on abstract algebra concepts. I would like to learn the works of Riemann manifolds, too

[trim kayak]

Wow. That's really impressive. I've taken various Algebra, Geo, Trig, Calc, and Stats classes. Not sure if I want to learn even more about those or start learning something new. I found a pretty good Calc textbook that I want to get. May start learning more about that.

Do you have alot of physical math textbooks @remote sparrow ?

[remote sparrow]

yeah

[trim kayak]

Oh nice. I have a few math books, several teaching books, and too many novels. 🙂

[vital bane]

novels are good

[vital bane]

You can learn more than what's taught in a degree, when studying for fun

[trim kayak]

Where did everyone go?

[hallow oriole]

if you're studying for fun then i wouldn't recommend a computational textbook tbh

[trim kayak]

What about a textbook that has practice problems throughout the chapter? I think that's a good idea so I can practice what I have read/learned.

[hallow oriole]

i feel like most textbooks will have exercises throughout the chapter, even if they aren't explicitly called 'exercises'

in any case for a calculus book that's proof based i recommend spivak

maybe you can find a cheap copy somewhere

[trim kayak]

I've heard alot about that one. What about Calculus by Stewart?

[hallow oriole]

stewart is much more computational

for self study there's really no need to do computational stuff

[trim kayak]

ohh. now I'm debating that one then

[trail hemlock]

spivak's calculus

😍

[trim kayak]

Not Stewart's?

[trail hemlock]

unless ur insane dont use spivak, its really very difficult. there are pleanty of other good books that arent as computational as stewart. i always liked
Honors Calculus by Charles R. MacCluer
or
Calculus vol 1 with an introduction to linear algebra by Apostol.

but if you are really interested in rigerous problems, spivak is the best. it was my intro to calc so i always rec it

[trim kayak]

Hmm okay thanks. Now I really don't know which one to go with. Have you used or read through Stewart's at all? I was really leaning toward that one.

[trail hemlock]

yep, i had a copyt of stwearts in the past.

[tribal crow]

Spivak is really hard as a first intro lmao

source: it's my first intro

[trail hemlock]

its not a bad book by any means. but its really computational, and you dont learn any theory

in the end, its your choice honestly. people who do sterarts arent doing anything bad, but for higher level math it just helps to learn theory rather than slaving away at computations

[trim kayak]

Just found a pdf of Apostol's Calc Vol 1 with Intro to Linear Algebra. Scrolled through it. It looks tough!

[trail hemlock]

apostol deals with integration before the derivative, which i found a little strange.

[slender cargo]

Are you interested in learning math more rigorously through proofs? Do you even know what that might be? And will you eventually take Calculus in a class format?

[trail hemlock]

its pretty in-depth.

[trim kayak]

Yeah I know what proofs are. No, I don't think I will take another Calc class. I've taken two before.

[grand thistle]

i liked apostol it was fun

[trim kayak]

hi Sean

[slender cargo]

Oh. Just go use a Real Analysis book then.

[grand thistle]

hi

[slender cargo]

You don't need anything like Spivak's Calculus or Apostol.

[trim kayak]

What about Stewart's Calculus?

[slender cargo]

Stewart's Calculus will simply rehash what you learned in your Calculus class that you already took.

[trim kayak]

Oh man. Okay. I know it's mostly subjective, but I'm getting so many different recommendations and just don't know which one to go with. Can you recommend a Real Analysis book?

[grand thistle]

abbott or rudin

[slender cargo]

Abbott's Understanding Analysis is often recommended here and well regarded. Rudin is harder and often not recommended as a first exposure.

I will also vouch for Bartle and Sherbert's Introduction to Analysis. I think that book is good and I have been using it for the class I'm in.

[trail hemlock]

rudin is my first exposure 😓

(im cooked)

(but i love rudin so wtv)

[grand thistle]

same for me

it was alright, i really appreciate his writing style now

[trail hemlock]

chapter 5

the proofs are really elegant and i really enjoy them

but they are too terse sometimes

imo

[grand thistle]

chapter 5 wasn't that bad, i'd say the hardest was chapter 2

[trail hemlock]

100%

[grand thistle]

for me at least

[trail hemlock]

but chapter 2 lowkey made me read "a course in point-set topology" cuz it was the most interesting chapter

chapter 2 was great

[trim kayak]

Thanks guys. Are all of you math majors?

[grand thistle]

i found it to be the most unmotivated tbh

prob cuz he spammed definitions all at once

[trail hemlock]

hs student 😭

[trail hemlock]

yeah but after i did the exercises, it was all very clear

i became enlightened in the ways of point-set topology

(im still fuckin cooked)

[grand thistle]

i mean it's mostly just metric space theory

i feel like it becomes more clear once u just suck it up and just learn point set once and for all

[trail hemlock]

yeah im going through a pst book rn

shit is interesting

af

[tribal crow]

good idea to skip metric space stuff and just run head first into point set?

[grand thistle]

not really, i mean unless ur like this guy and u enjoy point set

it's gonna feel hella

unmotivated and boring tbh

that's why u gotta learn analysis with it

[tribal crow]

well, let's hope I have willpower then

[grand thistle]

my motivation for leraning ps was just learning analysis

[trail hemlock]

r u in hs too?

[tribal crow]

no

[trail hemlock]

or one of those middle school fiends like arti

[tribal crow]

do you not know this yet blackbeard wth

[trail hemlock]

nah idk u

[tribal crow]

I thought you knew I was a 1st year uni student already

[trail hemlock]

oh nah

ur old af

grandpa fr

[tribal crow]

I gotta pick up point-set topology soon

[tribal crow]

is ok

[tribal crow]

fair enough

I have some analysis background

[trail hemlock]

"A course in point-set topoloy" by John B. Conway is the first thing that popped up on springer's website, and its really a great book

[grand thistle]

i feel like point set is something u usually just use as you go along and get better at by using it

[tribal crow]

everything is free if you run fast enough

[tribal crow]

fair enough

I hear that a lot

[trail hemlock]

i forgot i got muted for saying the same thing 😓

[tribal crow]

I feel like you've seen me in discussy a lot though

hmm

[trail hemlock]

idk how old u are type stuff

anyway why are we turning #book-recommendations into #chill

[tribal crow]

right

[swift dome]

need a classic text book for graph theory

[hallow oriole]

diestel

[remote sparrow]

there are many drill exercises in stewart, yes, but there are plenty of nontrivial problems that don't typically get assigned

[harsh surge]

hi

[remote vortex]

I'd recommend doing metric topology (and/or normed vector spaces, if your inclinations run anywhere in that direction) before going full generality; because I feel it's easier to develop intuitions in that way; but it's not an impossible task to learn general topology from the get go

[north flicker]

can anyone help me with the definition of adherence point?

[rustic void]

x is adherent to a set A If for every neighbour N of x there is a point y of A with y in N

[north flicker]

ist like an accumulation point?

[remote vortex]

It can be, but it can also be an element of the set itself.

[tender wyvern]

sounds like it

[remote vortex]

An adherent point is an element of the closure of the set, basically

[tender wyvern]

oh

[remote vortex]

So it can be an isolated point if it's in the set itself

[rustic void]

In the accumulation point definition y must be different from x

[north flicker]

so any x of a set A is an adherence point

[tender wyvern]

i see

[remote vortex]

Yes

Also this is off-topic for this channel, we do have a dedicated #point-set-topology channel

In case you have further questions

[north flicker]

ill speak there , sure

[north flicker]

thanks foru help

[north flicker]

how can i speak there ? i'm not allowed

[remote vortex]

#math-discussion then 🙂

But also https://discord.com/channels/268882317391429632/790023107708583946

[gray gazelle]

HELLO PEOPLE, i was wondering if you can recommend a comprehensible book in differential equations please

[stone lance]

Direct me

[uncut zealot]

I don't know about China, Korea and Japan. I do know that Singapore doesn't have anything that maps neatly onto American ideas of highschool; there's "secondary school" which is for ages 12-16-ish building up to the o levels and "junior college" which is for two years after and builds up to the a levels.
I don't remember any standard textbooks being used. I got notes from class (sometimes photocopies of photocopies that probably originally came from some textbook or another, but mostly original material) and notes from the tuition center I went to (mostly just exercises if I'm remembering correctly) and practice exams.

[daring lake]

You seem to be looking for pre-calc book

https://openstax.org/subjects/math

Though as <zorns_lemon> said, I too just followed my teacher and used notes of whatever they taught at that level.

[uncut zealot]

There was "mathematics" and there was "further mathematics". I knew that sin and cos were trig functions, but I didn't learn about them independently of algebra or geometry or calculus. From my understanding the Singaporean and British systems are nearly identical down to both doing the a levels (but the brits abandoned the o levels a few decades ago in favour of the gcse).

[vital bane]

Depends on what kind of differential equations book you're looking for

the computation focused type of book

or theory focused type of book

[uncut zealot]

It wasn't one subject per semester/year. If you're going to study a level mathematics, you start after you do your o levels and then it's 2 years.

[soft egret]

anyone of you know about the prequesites for "introduction to topological manifolds"?

[tribal crow]

Lee writes them in the preface

the appendices give an idea as to what he's expecting you know

but the group theory stuff isn't relevant until chapter 5 as far as I know

so you don't need to know it until then

[soft egret]

ok, thanks

[tawny solstice]

I’ve been looking between Judson’s and Pinter’s Abstract Algebra book and I don’t know which one I should get. They’re too different

[remote sparrow]

they're both good

judson is more usable as a reference since he doesn't leave as many results as an exercise

pinter is great for learning from though

[tawny solstice]

Okay, thank you

[manic brook]

does anyone know what the labelings next to problems in Enumerative combinatorics mean?

for example some problems are marked [3-]

or [2+]

or [2]

some also have an asterix like [2]*

[remote sparrow]

are you talking about this book?

oh and i just noticed there's a fifth edition now

damn

• means it's harder than average, - means it's easier than average

asterisked problems have a footnote associated with them i think

https://www.amazon.com/Enumerative-Combinatorics-Cambridge-Advanced-Mathematics/dp/1107602629

oh maybe this

stanley was bona's advisor, so i think they adopted the same system

[tawny copper]

It's in the preamble or introduction of the book

It was something like 0 very easy, 1 easy, 2 intermediate, 3 difficult, 4 very difficult, 5 ver very difficult / open

[primal summit]

Trying to learn about algebraic k theory, should I read Milnor's book or the weibel's K book

Or something else

[trim kayak]

I'm such a nerd. On the way home, I passed by a used bookstore. I decided to stop in and look around for a bit. The first section I went to were the math textbooks. 🤓

[lusty ermine]

did you found anything worth sharing

i am planning to go to my local used bookstore

[trim kayak]

I was looking for a few Calc books. Found several but they were so old and outdated. Now that I think about it, even older math books are good. The content doesn't change. Found A LOT of Calc and Stats books. You should!!!

[trail hemlock]

math sorcerer dreamland

[trim kayak]

A used bookstore?

[trail hemlock]

ye

yk the math sorerer? its this math book collector on yt

[trim kayak]

🙂

[violet shuttle]

wdym. older math books are worse

[hallow oriole]

ehhh

in some subjects older math books are just fine

personally tho i don't read textbooks before 1970~ due to lack of latex