book-recommendations

[mortal iris]

Tbf that's a failure of the educators and schools and less so the textbooks. Like NCERT is not that bad lol. The intuition is quite decently explained. And graphical problems to do so are quite common too, but the textbook and the boards recommending them tell different stories.

[high stone]

and you end up producing sparkless highschool graduates

[hasty flare]

We're forced to finish learning integration ahead a full year for physics albeit it was preliminary just the basics, but no one in their right mind would know how to take a differential length and setup integrals and perform the integration, if it's not taught rigorously in class.

[mortal iris]

I think this discussion from here on out is better moved to #math-pedagogy or some other appropriate channel. This has veered far from book recs.

[hasty flare]

I don't have access to that

[whole karma]

hey, do you mind if i ask you, where and from what you have learned proofs and logic in mathematics ?

[mortal iris]

If you're an undergrad, you should get the undergrad role instead of pre-uni and you'll have access.

[high stone]

what’s pre-uni math?

[whole karma]

Maybe, the mathematics before university

[high stone]

well technically that’d include high school too

[mortal iris]

And you for sure shouldn't be having the postgrad role, pending as it may be lol.

[high stone]

hat counts as uni?

[mortal iris]

See #info before jumping into channels @whole karma, @hasty flare and @high stone.

[high stone]

I forgot I was a PG…

[grave egret]

thoughts on jänich his books?

[high stone]

opinions on

• “Advanced Engineering Mathematics” by Dennis G Zill
• “Advanced Engineering Mathematics” by Erwin Kreyszig

[mortal iris]

Which ones?

[mortal iris]

Never seen the first, don't like the second. Generally dislike such all-in-one type books (I have like one exception to this that I can recall) but works for the intended audience ig.

[grave egret]

topology and function theory.

I have worked through the first part of munkres and didn't enjoy the book at all (I want to do some point set topology again because I forgot a lot/some of it) and I do also have to learn complex analysis some time in the future.

[high stone]

Why specifically do you dislike the 2nd?

[grave egret]

I can speak german which allows me to read the original versions (I think they were published in german) and I have noticed that they get recommened often.

[mortal iris]

Hand-wavy. Tries to do too much but not well. Perhaps sufficient for engineers, but bad for anyone doing or needing serious math.

[mortal iris]

Can't say much about the German version. I have seen those two books. They are generally nice. But for point set topology idt you can get much better than Munkres. It's one of the rare instances that a gold standard is truly good.

[grave egret]

Could you explain why munkres is viewed as superior? I used it to study (point set) topology because it was the only book people really recommened and to be honest I never really got why. I also looked through a few other books like lee or bredon and both of these seem to cover all the necessary point set topology in their first one or two chapters. I assume that these two books do it more as something like a revision but after going through munkres, I don't really feel like that that would have lead to a worse experience.

But on the other hand I didn't really see (point set) topology as an end in itself (i dont think anyone does?) which might be the reason for my opinion (which may be/probably is uninformed?).

[mortal iris]

Comprehensiveness and level of detail for an introductory book and also gentle writing style I'd say. But taste differs from person to person.

Maybe you can try an inquiry based book like Starbird's if you're revisiting, which covers both PSet and Alg Top.

[molten gulch]

Also, Lee, especially, is intended as "enough point set for diff top and diff geo", as it states (in different wording) in the preface. The first 6(?) chapters quickly cover point set and the rest cover some algebraic topology. It isn't bad as a book for topology if it covers all you need, but that depends on what you want to do with topology. Munkres is good because it covers a lot of topics in a lot of detail

[mortal iris]

It's usually an entry point into other fields. I never did a course on it myself as a physicist and only grabbed what I needed for analysis and later diff geo and also some graph theory when I got to it. Learned some alg top as well somewhere in between.

[molten gulch]

There's a lot that you can use more obscure topological results for. I've seen a few interesting uses on mathoverflow and I know that topology is used quite a bit in logic, but I'm not experienced enough in topology to say much (I'm a CS major)

[grave egret]

I have encountered some topology (basic but I want to brush my topology up anyways) in Eisenbud his commutative algebra.

[molten gulch]

Yeah I think any topo text should have enough to get into eisenbud

[mortal iris]

Honestly good to go with an Inquiry Based book since you've had prior encounters with the subject. Re-learning stuff through Problems will sharpen whatever you should be knowing and also help cover gaps more effectively.

[molten gulch]

There you're dealing with the Zariski topology, right?

[grave egret]

yes

yeah I should probably also learn some more topology and geometry to get a better understanding of lie algebras

[night prism]

Is ‘higher algebra’ still studied in courses? I’ve been reading through some (pretty old) books on it and I felt like it’s so beautiful. Maybe it’s called something else now?

[grave egret]

https://www.math.uni-bonn.de/people/lenz/seminar-HA-25.pdf

https://www.mpim-bonn.mpg.de/hamfc @night prism

[night prism]

Thanks!

[mortal iris]

You from Uni Bonn by any chance?

[grave egret]

in october

but these were the first results that came up when looking for higher algebra

[mortal iris]

Geez. Insane number of coincidences today lol.

Found two ppl from two of the unis I went to

[grave egret]

You went to uni Bonn?

or MPI?

[mortal iris]

Bonn und Köln. Physics

Tho did a number of math courses at Bonn

Side questing max

[grave egret]

How is Physics in Bonn? I haven't heard anything about that so far. I only know that their econ program is also pretty strong

[grave egret]

How are the people in Bonn? I was told that it is really toxic compared to other universities (which I am a bit worried about).

[mortal iris]

Perhaps we should switch to DMs

Off topic this is.

[grave egret]

Yes sure

[mellow wren]

smart to apply in the earlier application cycle

I applied currently and I'm anxiously waiting for the decision

[oblique hatch]

Why Irony no apply in earlier cycle out-of-interest?

[mellow wren]

So I wanted to apply to other unis as well and I wasn't sure if Bonn had a short deadline for accepting offers

So I said I'll apply in the later cycle alongside all the other unis I wanna apply to

[oblique hatch]

mishu see

[desert oriole]

Can't you just accept an offer and then rescind that decision later?

[mellow wren]

I'm not sure and I didn't wanna risk it

risk any issues later on i mean

[desert oriole]

yeah makes sense

good luck on your application

[fluid moon]

best introductory books for theoretical computer science?

[mortal iris]

Sipser's Theory of Computation for sure.

It's a bit of a challenge to read for a complete beginner though, but worth going through right at the start.

[molten gulch]

Sipser by far, very nice to read, a good amount of difficult exercises, quite fun

I liked reading it

[frozen perch]

Love Sipser. Kind of an interesting grab bag of topics, but really good foundational stuff

[ember lark]

any good linalg recommendations

[mortal iris]

I'd also recommend reading GEB aka Gödel, Escher, Bach by Douglas Hofstadter on the long-term. It's rare that I recommend anything pop sciencey, but this one deserves a mention.

[molten gulch]

friedberg

[normal crystal]

https://tenor.com/view/author-book-marketing-book-publishing-book-royalty-youronlinepublicist-gif-26141238

[ember lark]

i cant even false that because it's true (in reply to tcc)

[mortal iris]

FIS or LADW. If you've already seen some computational stuff then LADR or low-key Halmos for a grind.

[remote sparrow]

before you say anything @mortal iris that's the same guy that recommends ladr all the time

[ember lark]

let me check halmos actually

ive heard of it

[mortal iris]

Too late and I just remembered lol. Probably trying to ragebait our resident LADR Skeptic

[ember lark]

wait is it just a problem book

[ember lark]

before i spoke to him: ladr hater
after i spoke to him: ladr skeptic

[molten gulch]

FIS lover vs LADR lover, who wins

(FIS, obviously, Ryan's known as the FIS shill for a reason)

[mortal iris]

Idt GEB struggles or needs a publicist FYI

[mortal iris]

Oh no, it's a lot more chatty than your average problem book even if advertised as such.

[mortal iris]

Just curious. Why is your username what it is?

[ember lark]

i forgot

[mortal iris]

Cos it's an infamous e-print archive

[ember lark]

am aware

[molten gulch]

I believe he set that as response to someone setting their name as ArXiv

[mortal iris]

Vixra papers are quite fun to read sometimes tho. Within a vast majority of brain rot you occasionally find some interesting stuff, even if very sus.

[cunning cobalt]

Some good books for Integral Calculus?

[native cradle]

Oh halmos, uh, used it for a course.

I could be wrong, but not the best for problems.

Excllent for theory no doubt

[night prism]

Finite dimensional vector spaces halmos?

[native cradle]

That's the one I know of

[night prism]

Honestly might be a rough first go

Although I am pretty stupid

[green aurora]

90 percent of this channel seems to be linear algebra book talk

[marble solar]

That's where math begins for everyone. Applied, Pure, Physics, etc., so it's a natural one to focus on

[green aurora]

I began with arithmetic but I guess the starting line is different for everyone....

[vital bane]

I mean you don't see people asking "guys any books on adding numbers?"

[native cradle]

That's called field/group theory 😔

[sick river]

pre-university books for algebra II, trigonometry, geometry and calculus

basically everything pre-university level but at senior high school level pls 🙏

[arctic yew]

... Openstax

[mellow topaz]

For trigonometry I recommend a workbook by Chris McMullen, he has some good techniques, but overall Openstax is a good resource

[native cradle]

for trig I remmeber a russian book

or was it brit

sl loney

[wide patrol]

ygs have reccs for learning addition with numbers above 20?

[arctic yew]

... Youtube videos

[wide patrol]

they go too fast

[arctic yew]

Tfw 0.25x

[wide patrol]

genius

[cunning elk]

count on your fingers hope that helps

[wide patrol]

i dont have more than 20 fingers sadly

[mellow rivet]

Finger sections

https://tenor.com/view/tkt-smart-gif-20642718

[wide patrol]

i shall try it and get back to you

[arctic yew]

Count in binary

,calc 2^20

[hasty eagle]

Result:

1.048576e+6

[rough helm]

any book recomendation before university and after 12th class for physics and maths?

[tender river]

#book-recommendations message you can start with 5. linear algebra

[daring wolf]

my ass be like recommending Lurie's higher algebra

[short fable]

Actual best book after high school: https://www.taylorfrancis.com/books/mono/10.1201/9781315367910/modeling-analysis-stochastic-systems-vidyadhar-kulkarni

[visual delta]

https://scoap3.org/scoap3-books/ Just came here to say that a ton (over 100) of books on quantum mechanics/particle physics/string theory are free and open access. A list is here. Some of the books that are open access are not listed as such on Amazon.

For example, this book is open access, but Amazon has no indication of that
https://www.amazon.com/Relativistic-Quantum-Mechanics-Introduction-Fields/dp/1032565942/
https://www.taylorfrancis.com/books/oa-mono/10.1201/9781003436263/relativistic-quantum-mechanics-luciano-maiani-omar-benhar

Actually it does say it on Amazon but at the end of the description.

https://www.amazon.com/Introduction-Standard-Model-Particle-Physics/dp/100940170X/ This book has it in the description but still says it's $40 to buy the ebook.

[native cradle]

I know I was reccomended Micheal O seceroid for metric spaces earlier.

However my class will appaently use
Introduction to Topology and Modern Analysis by G F Simmons

how different are they in terms of problems

might just be because I'm still in chapter 1, but simmons feels too easy

[last wolf]

If someone replies with a book name to this message I will read it, except if already have.

[ancient ridge]

If u want more challenging problems, specifically on metric topology in real analysis, try baby rudin's Chp 2,3,4, and 7. They are pretty hard in general.

[arctic yew]

Like any type of book?

[last wolf]

Yep

[arctic yew]

Ranging from literature to STEM and everything in between!?

[last wolf]

Yes

[arctic yew]

Try dune then

[last wolf]

Already read it

Horrible

[native cradle]

Society agaisnt the state

[short fable]

High-Dimensional Covariance Matrix Estimation: An Introduction to Random Matrix Theory
https://link.springer.com/book/10.1007/978-3-030-80065-9

[ancient ridge]

Also, if u want more exercises other than baby rudin, u can try the exercises in this math notes. It's my school's lecture notes for 2nd real analysis class, and has many exercises that are different from that of baby rudin and challenging.

[native cradle]

I'm looking at more general metric spaces, thanks!

[native cradle]

tsym!

[last wolf]

That’s a new one, where do I acquire it

[native cradle]

amazon I guess?

JSTOR too if you have access

[native cradle]

one thing

before you read this, will do you some good to read the social contract by rousseau and a bit of bio-power and biopolitics by foucault

[native cradle]

atleast chapter 2 of bio-power and biopoloitics

[last wolf]

Only physical books

[native cradle]

amazon then, yeah

[last wolf]

The book store across from where I live has it

[native cradle]

wow

have fun, I've only read ~1.5 chapters, but it's lovely

[mortal iris]

I'm not referring to his old one on Finite Dim Vector Spaces btw. He has a Linear Algebra Problem Book which is a sequel to that book of sorts and it is excellent, albeit a grind.

[mortal iris]

Nah, that just talks around addition rather than doing it

[mortal iris]

Feynman Lectures. Book of Proof.

[mortal iris]

The Emperor of All Maladies by Siddhartha Mukherjee. Probably one of the most excellent semi-technical books on cancer biology.

[mortal iris]

Lovely to see someone share that opinion lol.

[mortal iris]

This is more so an introductory functional analysis text afaik. Not really sure how it could be used to study metric spaces besides maybe some sections scattered around about things like metrizability and what not.

[native cradle]

There seems to be a chapter on metric spaces

hmm, idk

Thanks! I'll pick up seceroid then

[ancient ridge]

which class r u taking for this? Analysis II or something?

[native cradle]

We have a course called

Metric spaces

[ancient ridge]

what's the syllabus?

[native cradle]

the entire course is about metric spaces

lemme try to get the old syllabus

[mortal iris]

There is but I'd expect that content to be covered in an analysis course already. Not to mention it's quite minimal for a full course.

[native cradle]

Not explicitly , but more or less, yeah

[ancient ridge]

have u learned something like Arzela-AScoli thm, Stone-Weierstrauss thm, Baire category thm, Banach fixed point thm, uniform continuity thm, and etc?

[native cradle]

on a sidenote, it's scary how easy using paypal is 😭

just one click and done

[native cradle]

the first two and uniform continuity thm, yea

[ancient ridge]

hmmm then idk what'd be covered in ur metric space course lmao. I was kinda expecting it to be more focused course on function spaces.

That's what my school does in 2nd real analysis course after chp 1-7 of baby rudin from the 1st real analysis course

[mortal iris]

Which the aforementioned book kinda is.

[native cradle]

I'll ask the instructor for the syllabus then I guess

I had asked a month ago, but guess that was too early?

which tbf it is given that classes only start in august

[silk grove]

how good is the treatment of cat theo and basic homological algebra in jacobson basic alg vol 2

[arctic yew]

I read that as cat theology

[short fable]

[native cradle]

https://tenor.com/view/cat-gif-26735574

[lusty patio]

[last wolf]

Agreed, sadly I finished it

[native cradle]

wot

[last wolf]

Took a little over 3 hours

[native cradle]

how did you read it that fast though

like when I read it I had to look up stuff related to theories of power and all that

[last wolf]

I basically read for a living

[native cradle]

oh fair then

[short fable]

Don't many people read for a living?

[last wolf]

I crunch financial research

[short fable]

Truly exciting work

[last wolf]

Fucking horrible

[short fable]

[last wolf]

Spending a 1/15 of ones life on a plane

[short fable]

I guess you're not going for textbooks

[short fable]

Hey the company pays for it

[last wolf]

I read it already

[last wolf]

And I get the free airline miles

[short fable]

Demian

I think you should spend more time on good books

[native cradle]

was it nice?

[last wolf]

All books are good

[last wolf]

Wonderful

Top 80

[native cradle]

If you liked it, I have a similar suggestion

[mortal iris]

https://tenor.com/view/fastest-book-reader-gif-7696244559719127447

[short fable]

Complete falsehood

[last wolf]

No

[native cradle]

except dune apparently

[mortal iris]

Yeah, like Mein Kampf is good.

[last wolf]

Information and perspectives are valuable no matter the situation

[native cradle]

anthropology in the margins of the state by Veena das is pretty nice too

[last wolf]

Yes, because it’s horrible to read

[last wolf]

I have read that too

In German

[mortal iris]

Pretty sure it's banned there.

[last wolf]

Well yes

[native cradle]

Well, a german translation can still exist right

[mortal iris]

Unless you read the annotated one

[mortal iris]

Yeah but is it good?

[native cradle]

fair enough

[last wolf]

I don’t know what’s going on in the gif

[native cradle]

a friend sent this, any review on it

[mortal iris]

You can find out.

[last wolf]

I think he’s faking it

[mortal iris]

Are you for real rn or did you watch it?

[last wolf]

I skimmed it

[mortal iris]

Yeah. Okay buddy. I believe you.

[native cradle]

wait this waas actually good

I thought it was a real clip

[last wolf]

Didn’t see the end,,, now I realise it’s staged

[mortal iris]

I don't think you even need to be midway to get it.

I'm guessing this is how you read for a living as well

[mortal iris]

There's a few others like this. I remember one where he says his mother died before he was born and then his mother actually appears lol.

[native cradle]

so doof basically

https://youtu.be/gzHRJm-hl2c?si=gZUHV_J_xle6g2Ev

reference

It all began on the day of my actual birth.
Both my parents failed to show up

[mortal iris]

Aye anyways, at the risk of this going into #chill territory let us stop

[molten gulch]

I mean, tbh I've always interpreted this clip as saying that Doof is actually an adopted child

[mortal iris]

Btw this is approximately 1 page per minute given the length of the book. What do you even gain by reading like that even if you could?

Wouldn't you rather let yourself marinate in the thought while reading?

[molten gulch]

<@&268886789983436800>

[night prism]

I have this

[native cradle]

ooh, fun

[native cradle]

I went through it, seems to lack problems?

[night prism]

It approaches it from a fairly advanced perspective

Also, yes, no exercises

[native cradle]

Yea might be an issue for me I guess.
I had asked for reccs here earlier and recieved the same.
Will look at those

[night prism]

Are you looking for an introductory book or something at this level?

[native cradle]

I'm not sure atp. I'll look the course description soon and lyk I guess?

[mortal iris]

If it's for the undergrad ODE course where you're at (230?), I recall the course being underwhelming and mostly redundant with Calc 2. That might change if someone competent were taking the course in your go around. Iirc the only new things you'll see there otherwise are some fairly standard numerical methods and a little bit of Fourier and Laplace transforms in a less than precise manner.

[native cradle]

Ye that's it 😔

It's samit if you know who that is

Oh well, i could self study it properly I guess

[mortal iris]

Yeah I do. No point fishing for a good book unless you plan on studying the subject for your own satisfaction. It's a very weird course they have over there. This and the PDE one if it's still being offered.

[native cradle]

PDE is yes( last time this year)

[native cradle]

Well, looks very applied

[mortal iris]

More than two thirds of this is supposed to be covered in Calc 2 already iirc unless they changed that for yall. The first two main references are rigorous though, but not the last one which is what Samit usually follows afaik.

[native cradle]

we didn't do ODEs at all ( or well beyond HS ODEs) unelss I;m forgetting something

[fickle granite]

Laplace transform mentioned (my goat)

[mortal iris]

I see, then this is valid to do.

[native cradle]

but got it, thanks for the refs

[mortal iris]

Our Calc 2 course contained a lot of ODE theory.

[sacred thicket]

https://people.math.binghamton.edu/malkiewich/spectra_book_draft.pdf nice new textbook on stable homotopy theory

[last wolf]

That might take 2 days to finish

[mortal iris]

I read it in -5 mins. Time turned backwards.

I'm a reading time traveller

[last wolf]

I read a book about time travelling

That was tommorow

[mortal iris]

Please take shit posting to #chill and read everything over there from beginning to end.

[round roost]

How

[night prism]

As in it’d be helpful to know analysis beforehand

[whole karma]

<@&268886789983436800>
Mr beast here too

[ember lark]

death of moderators

[arctic yew]

😹

[ember lark]

make larp larp mod so he can delete mr beasts

https://media.discordapp.net/attachments/1000143691421331626/1496238282365730856/togif-10.gif

[whole karma]

"fellow" lol

[native cradle]

(related to books)

HOW DOES A PUBLISHING HOUSE MAKE THIS MUCH

[arctic yew]

Dont they also host scientific journals

[native cradle]

yes, I think so

[night prism]

My guess (nowadays) would be subscriptions

Also, they have relatively little overhead. People submit their papers (free), they’re refereed (free), and they sell them back to us

[odd cargo]

research paper mill

[mortal iris]

This article offers some insight.

[native cradle]

thanks

[normal crystal]

@mortal iris have you seen these
you would think they're on YouTube but I haven't found them yet
https://web.archive.org/web/20160303194840/https://www.math.hc.keio.ac.jp/coe/videos/spivak2004/

[mortal iris]

Nope. Might as well put them on YT

[normal crystal]

I didn't check all the links but the few I tried worked on wayback
then I would have to play rm files somehow
hopefully they just work on VLC

[trail void]

i think its probably because of the sheer amount of books they produced? 2,7 billion is understandable

[daring wolf]

<@&268886789983436800>

[safe gorge]

what r some of ur fav novels

[bright epoch]

The Rising Sea by Vakil

[daring wolf]

https://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/pubtexts.php

[mortal iris]

Light Novel: Re:Zero by Tappei Nagatsuki.
Standalone Fiction: David Copperfield by Charles Dickens.
Mythology Series: The Kane Chronicles by Rick Riordan.
Mythology Epics: Mahabharata by Ved Vyasa.
High Fantasy: Tolkien's Legendarium.
Biography: The Strangest Man: The Hidden Life of Paul Dirac by Graham Farmello.

[safe gorge]

rick riordan is middle school level literacy no shade

tolkien is good

[safe gorge]

a beautiful book

[bright epoch]

I heard someone bought the movie rights, they're casting Tom Holland as Spec Z

[safe gorge]

hans zimmer should be included too omggg

[mortal iris]

You asked for favourites. I read it in middle school and it was a favourite. It's still good writing for what it's intended to be. Also, Kane Chronicles and Heroes of Olympus were a tad bit more matured than the earlier Percy Jackson series.

[safe gorge]

well out of what u listed tolkien beats it all

[safe gorge]

this was THE series back in grade school omg

[dreamy finch]

Do you guys know of any good online books to study calculus?

[odd cargo]

https://www.cds.caltech.edu/~marsden/volume/Calculus/

[dreamy finch]

tysm

[mortal iris]

I doubt you've read all of the ones I listed. They're all excellent in their own way.

[safe gorge]

considering u listed rick riordan, i doubt ur expertise on literature

well thank u for editing ur message bc the original statement was quite rude

[mortal iris]

You have been nothing but rude in every conversation from the start tbf.

[mortal iris]

I'm not really claiming to be an expert for starters and you can't really go around making claims about what beats out what when you've not read the others.

[safe gorge]

i did not personally ping u for ur advice and if u do not wish to talk to me pls refrain from doing so

[mortal iris]

I never advised you on anything. Smh wtf is wrong with you?

[safe gorge]

i am stating my opinion on the list u replied to me about? apologies if u are offended

[safe gorge]

u responded to my general question when i did not personally ping u, i dont think u should be replying to me if u have a problem with me

[mortal iris]

Like I said in another thread, if you got a problem, take it up in DM. Clearly I'm not the one with the issues.

[golden salmon]

Moving on...

I like a Hero of Our Time and other similar russiaSlop

[safe gorge]

like i said before i do not have an issue, but u r passive aggressive and edit ur rude original messages

[golden salmon]

Pechorin is an innovator in being a fuckass

[safe gorge]

seriously

do u have any good english lit novels

[mortal iris]

There was nothing rude about it (I edited to avoid misinterpreting it as having not read all of the Legendarium which I did not mean) and you've been deliberately trying to offend me for god knows what.

[golden salmon]

My taste is objectively bad but I like wuthering Heights and Odyssey

[safe gorge]

the conversation ends now. move on.

[golden salmon]

Fave translation is Rieu but I like all the ones I've read tbh

[safe gorge]

ooo yes good classics

@golden salmon no shakespeare?

[golden salmon]

Only started reading him recently actually. I liked macbeth but it was waaay above my level

[knotty lava]

hamlet

[mortal iris]

Pete Clark's notes

[safe gorge]

macbeth is rlly good just take ur time on it

[golden salmon]

I got there in the end with a dictionary on hand

[safe gorge]

after awhile, it gets pretty easy reading his writing style in my opinion

[golden salmon]

looking forward to building that proficiency

[safe gorge]

u have time, he has many plays

[dreamy finch]

im tryna be like u guys

[golden salmon]

Oh, the one 'hard' book I can say I read and understand is canterbury tales in middle english

that was fun

[molten gulch]

I find it interesting how we have very similar tastes in this too! I don't usually read light novels, but I do enjoy Dickens' writing a lot, I also somewhat enjoy Dostoyevsky and a few others, same with Riordan and the Mahabharata and Ramayana. I've not had a chance to read all of Tolkien's works yet but I hope to do so at some point

[molten gulch]

Interesting how you found the canterbury tales in middle english to be easier than macbeth in early modern

[golden salmon]

This actually tripped me up too because I picked up Macbeth thinking 'alright Im finally ready!!!'

My best guess is that there are important gaps in my literature education that I'm plugging as I go, and there's a very big one around how shakespeare forms language

[golden salmon]

Dostoyevsky the goat. White Nights sweeps

[molten gulch]

I also quite like Tolstoy's War and Peace, though it is....long

[golden salmon]

Reading that presently!

Love it

[mortal iris]

Mahabharata is honestly my favourite story of all time. Depending on whose translation and what version you read, the style might appear drastically different tho but there's interesting takes on all of them. I think the Dickens thing is probably a result of how popular his books were when our parents were growing up to some degree.

[molten gulch]

I also have a copy of anna karenina lying around that my dad had gotten me several years ago I still need to read

[golden salmon]

solid gift idea

[molten gulch]

Oh true, my dad did get me into reading Dickens about a decade ago (started with Great Expectations, then read David Copperfield, Oliver Twist, A Christmas Carol, and A Tale of Two Cities)

though I think that Great Expectations is my favourite of his works, mainly because it's the one I remember the best

I also quite enjoyed Jules Verne's Around the World in 80 days and Journey to the Centre of the Earth

[safe gorge]

such nostalgic classics

i love how verne was ahead of his time on sea exploration

[molten gulch]

Agreed

[fickle granite]

Yeah I enjoy Dostoevsky a lot as well though I've been slacking on getting through Crime and Punishment

I was using it as reading material while on holiday and it made time fly because I was getting absorbed in it so quickly

[mellow topaz]

Burmese Days by George Orwell pretty much is at the top for me

It has some flaws but it has a great message

[safe gorge]

that’s a pretty good one! i love george orwell’s works

[shell sparrow]

Guys has anyone studied Theory of SPECIAL relativity?

[mortal iris]

Yes, why?

[dusk hemlock]

<@&268886789983436800>

[shell sparrow]

Oh, I wanted to discuss , and along with that, what else are you aware of (like Schrödinger wave equation, or quantum gravity)

[odd cargo]

what was it this time

kai cenat or mr beast

[dusk hemlock]

mr beast

[odd cargo]

was it a link or pictures

[dusk hemlock]

pictures

[mystic orbit]

Was it nuked already?

This mod team is filled with so many fucking sweats

[mortal iris]

Why are you asking for this in #book-recommendations for starters and what do you wanna "discuss"?

[shell sparrow]

Discuss abt potential books* (

[mortal iris]

You can simply ask here.

[molten gulch]

[mortal iris]

I'm confused lol

[tulip aspen]

Welp need a recommendation on probab and stats

[wild grove]

Is trying analysis Terry tao (like following it) a great choice for single variable calc and further study

[brave pebble]

trolling

[mortal iris]

Arguably one of the finest intro courses with tons of problems, a free book and lecture vids. If you want something stronger, Feller's two volume book is great.

[dusk hemlock]

don't do it here though

[brave pebble]

my bad

[dusk hemlock]

do it in #discussion or #chill

it's fine lol

yeah this server's channels are confusing

[mortal iris]

Not really.

[dusk hemlock]

they are for newcomers imo

[brave pebble]

ya not that confusing tbh

[dusk hemlock]

i mean to the extent that all new servers' channels are confusing

this one isn't particularly bad

[mortal iris]

They just (usually) don't bother reading the info or asking anything.

[tulip aspen]

Thanks

[dusk hemlock]

it's generally hard for me to figure out servers even after reading all the info...

[mortal iris]

I think the only slightly confusing ones are the discussion servers.

[dusk hemlock]

well that may be the case for you

[mortal iris]

Everything else is pretty cut and dry.

[dusk hemlock]

but different people are good at different things

[mortal iris]

Feel free to ask ig. You're also in the meta committee.

[dusk hemlock]

yes i am

[dusk hemlock]

^^^^

learning your way around a server may be easy for you but hard for others

[mortal iris]

Fair enough, I agree with that, but asking a question when things are unclear shouldn't require more than typing. Not like anyone will chew you out for doing it in the wrong channel either.

Rigorous server usage

[normal crystal]

speedy, are you telling me you can find new roles that nobody knew about but still get confused by channels

[dusk hemlock]

not anymore

smh i'm still chief rolevestigator of this mathcord

wait we should move to #chill

[wild grove]

Can anybody comment on this

[odd cargo]

i rarely ever see it as a first choice

never read it so i cant say if its a good or bad first choice either

[wild grove]

Then what should I try

Which has rigour

[mortal iris]

Is this your first exposure to single variable calc and rigorous mathematics on the whole?

[wild grove]

Yeah!

[mortal iris]

Usually it is recommended to start off with something more applied and intuitive rather than rigorous for some rather convincing reasons. If that's something you don't want, then consider starting with something that's relatively balanced like Zorich's Mathematical Analysis instead, or alternatively something more limited but pedagogically sound like Pete Clark's Honors Calculus notes. And it would be good do supplement yourself with a book on Proofs like Hammack's and do Linear Algebra (LADW is good) on the side before going to Multivariable Calc.

[wild grove]

Oh like linear algebra doesn't require multi calc? What book do you think is like intuitive?

[wild grove]

Like I am new to these stuff so!

[desert oriole]

no

you can do a lot of algebra without even knowing what a sequence is

[mortal iris]

It's usually the other way round, multivariable calc requires linear algebra.

[desert oriole]

dont you need matrices to define derivatives anyways in multivar

[wild grove]

Do you think I should try zorich's analysis as the first choice

[mortal iris]

Strictly speaking, no. Just so happens that it is often convenient to talk about this stuff in terms of matrix representations at times.

[mortal iris]

You have the physics server tag. Are you a physics student per chance?

[wild grove]

Umm actually no

[mortal iris]

Okay. See if you are completely new to this whole thing with doing math rigorously, Zorich may give you a tough time at the start despite being as detailed and heavily worked out as it is. If you're okay with some initial growing pains, go for it. Otherwise, start with a more traditional text like Piskunov for a first course.

One good thing that I like is that Zorich doesn't shy away from actual applications, mainly in physics while still maintaining a very high level of rigor. It's also probably the most comprehensive book on the subject that doesn't go into Measure Theory if you include Volume 2.

[wild grove]

Like it has pains similar to Olympiad/competition math? If yes would zorich be a nice choice

?

[mortal iris]

Nah. Competition math is of a different style altogether. It will be some, but not much pain (testament to good pedagogy of Zorich) if you're not used to or have not seen much rigorous mathematics. Which is why I suggested supplementing with the Book of Proof and LADW so that you get a good eye in as proofs in Analysis are often much harder for a beginner than proofs in elementary set theory and linear algebra.

[wild grove]

So can I try zorich and LADW?

In parallel?

[mortal iris]

Sure you can, but I recommend starting with Book of Proof first. But if you've already seen enough of things like sets, relations and functions and know a thing or two about writing proofs and logic you can skip it entirely and learn as you go.

[viral dagger]

can some please suggest me a good combinatorics (permutations and combinations) book and calculus book under 5 USD (i'm a indian high school student preparing for entrance exams and I have interest in these particular portion of mathematics but can't spend too much)

[mortal iris]

Why you quoting prices in USD if you're in India lol

This is a great open access combinatorics book if you're willing to use an online version. You should also be able to obtain both of Piskunov's Calculus volumes in around ₹500 via Amazon. If not, you can print out the older internet archive versions on mirtitles.org.

[viral dagger]

I thought its an international server so maybe people don't know what's INR so for convenience, I wrote it in USD and thanks for the recommendation, I appreciate it, would give it a try

[signal current]

Any book recommendations for algebra 2 and pre calc?

[mortal iris]

All the more natural to use your native currency because you're buying in your own country. Prices and even availability vary from place to place and it's not a matter of mere conversion.

PS: India has the largest goddamn population in the world, making the INR the most used currency by population (almost 4 times more than the USD). Even the Euro is more used population-wise than USD.

[mortal iris]

Also, is that best girl Chinatsu Kano on your pfp?

[viral dagger]

oh, ok🤧

[viral dagger]

yupp, do u read blue box?😂

[mortal iris]

Moved to #chill

[still kelp]

hello, i want to self study math from free sources ideally pdfs for printouts, is Precalculus, Mathematics for Calculus 7th ed. good for beginners?

[mortal iris]

There's like a gazillion titles like that with the same material more or less. If you wanna get an opinion really you should specify the author. In any case, they are all mostly the same book with some minor changes. What exactly is your goal in this self-study and present background? Based on that one can recommend alternatives.

[still kelp]

sorry, the author is James Stewart - actually I like maths and want to go really deep to take part in the international math oylmpiad although a lot of it is somewhat irrelevant for my desired profession, Game Dev, I would just want to explore deeper into the subject

[mortal iris]

Stewart's book is not free and probably the last one I'd buy or "get" even if I could. Preparing for the IMO is very different from actually choosing to learn math out of self interest. You'd be well-served with Stitz and Zeager's Precalculus as it's Open Access. If you're gonna buy or "get" a book then Axler has a very nice Precalculus book as well.

[charred cloud]

Books to continue learning linear algebra? I took intro to linear already and this course concluded with complex and orthogonal diagonalization. What’s a good book that picks up where that leaves off?

[cunning elk]

FIS and hoffman/kunze are both pretty standard

[charred cloud]

thx

[cunning elk]

npnp

[tawny cosmos]

A lot also recommend linear algebra done right by Sheldon Axler, i didn't read it myself but i plan to do this summer

[tidal path]

I'm reading that right now as we speak and it's decent as of now

[ember lark]

ladr is great

[wicked fractal]

https://cdn.discordapp.com/attachments/497227343337881640/1494384382910267453/200.gif

[ember lark]

sybau twin

[mortal iris]

Seconded, especially if your first course was primarily calculations.

[remote blaze]

@mortal iris hello bro any suggestions for JEE aspirants

[wicked fractal]

Killuminati in shambles

[remote sparrow]

killuminati gonna have to put "No JEE help" in bio

[remote blaze]

Shambles??

[mortal iris]

Yes. Stop aspiring for exams.

[remote blaze]

Oo

[remote sparrow]

put it in ur server name too

make it "Killuminati (No JEE help)"

[remote blaze]

You guys kinda hate aspirants i think

[remote sparrow]

https://tenor.com/view/squid-game-oh-my-god-bruh-saleswoman-oh-my-god-bruh-gif-2398788864743270124

[mortal iris]

I can say for a fact that I do. Dafuq is an exam (JEE/NEET/NET/JAM/JEST/TIFR GS, etc. whatever) aspirant? The IMO is far more prestigious as a competition. Nobody goes around calling themselves IMO Aspirants as a cultural phenomenon. It's just stupid.

[remote blaze]

Oo

[tame tree]

i am a jam aspirant in the sense that i hope a nice jam sandwich is in my future

[mortal iris]

You're a jam aspirant not a JAM aspirant.

[ember lark]

context, in case you were confused:

[mortal iris]

Dang. Cross channel ragebaiting.

[ember lark]

plz react with an opencry for my troubles

[mortal iris]

What is your rank bro?
This question summarises my hatred for this shit.

[oblique hatch]

Mine is 1

[remote blaze]

Fahhhhhhhh

[mortal iris]

https://tenor.com/view/ichigo-gif-25627343

[ancient ridge]

Good luck with ur JEE 🤞

Those exams look insane and brutal.

[mortal iris]

That they are, especially the second round (Advanced) for which qualification is fairly easy. As much as I respect the sacrifice these students make to clear this, I have far more apathy towards the stupidity of doing so under heavy social and peer pressure.

[normal crystal]

Killuminati the JEEminator

[wicked fractal]

What is your rank bro?

[mortal iris]

That's a very Doofenshmirtz machine name.

[white cradle]

gonna start this off by mentioning How To Prove It by Velleman as a book for anyone who wishes to transition from computational math into proof-based math

[true veldt]

so this channel i guess was gonna be to plan how to use it, or we can just make it up as we go

right now only certain people can use the channel, then when enough posts are collected then we can open it up to everyone

[main flax]

is this a book recc channel? i lik: gallian abstract algebra, robert g bartle analysis, ireland and rosen nt

i'm very glad to witness the birth of a new channel btw

[pale mica]

[main flax]

is this channel already ded, like the #art-discussion

[true veldt]

we'll see, i have a few things to do today. yeah this is supposed to be a book recommendation channel

[main flax]

I suppose this means you should compile a list from time to time and pin it

[true veldt]

the rough idea would be that this would be a channel for people to ask for and talk about book recommendations

and that the channel will eventually be public

maybe in the next few days

[wooden sparrow]

https://openstax.org/details/books/prealgebra-2e
your thoughts on this book?

[quick hornet]

it's hard to go wrong with a prealgebra book.

[wooden sparrow]

okay, I'm just anxious....

[quick hornet]

If you want to learn, spend less time worrying about this and more time doing math

[wooden sparrow]

okay sorry

[main flax]

can someone recommend me a introductory complex analysis book (and explain why) please

[true veldt]

Visual Complex Analysis by Needham has lots of pages but lots of pictures for intuition

@main flax

[main flax]

will check, ty

[civic carbon]

Gamelin is my favorite intro complex analysis book. It goes a lot further than most other intro texts, and has very lucid explanations. Whenever I want to understand something better, that's the first place I look.

I think of Visual Complex Analysis as being a companion to a more classic text on the subject.

[sage python]

Gamelin I've heard very good things about yeah

Been meaning to check it out. Stein-Shakarchi is the standard nowadays and it's very clean, practically bedtime reading, but rubs me the wrong way somehow.

Good if you want some basic analytic NT though

[civic carbon]

Stein and Shakarchi is great, but I would not call it an introduction

and their fixation with the idea that Fourier analysis should come first is... bizarre?

[sage python]

It's odd. If I were them I'd do measure theory first so that I could use it in what comes after

[civic carbon]

haha I'll be honest, I never think about measure theory

but I do agree with them that really, complex analysis should be thought of as mor efundamental than real analysis.

[prime oak]

+1 to that one being in the list

[frigid comet]

Gamelin looks nice, somehow I never opened that one before.

[civic carbon]

haha by coincidence I have it right here on my desk

[frigid comet]

I haven't really needed a complex analysis reference for a while, but have a hard copy of ahlfors, and knopps theory of functions. the latter just because it was amongst things being given away by a retiring prof.

It actually came in handy at some point for some slightly messy stuff relating to perturbations of an analytic family of operators.

but otherwise looked old fashioned in a not fun way. I do like ahlfors though.

[sage python]

I still need to learn the stuff better I feel. I had an undergrad class and know the theorems but it was super super slow, and the grad one did some other stuff but didn't have psets. I wanna learn the topology POV better and do some actual problems lmao

[civic carbon]

I don't think I know what a pset is

[sage python]

Problem set

[civic carbon]

oh haha

I thought it was some component of complex analysis that you viewed as wholly essential that I had never heard of

again, I cannot recommend Miranda highly enough

[sage python]

Oh hah I was actually considering reading Forster with a friend before I got overwhelmed with things to do

Still wanna read, either Miranda/Forster/Donaldson at some point

Though also should like, do more basic complex analysis stuff (basically never computed a contour integral, my undergrad psets were mostly problems related to winding number)

Been thinking of Narasimhan

[civic carbon]

Miranda hammers home a lot of the basic complex analysis stuff while connecting it with geometry of curves

Fulton is, to my recollection, all algebra

[sage python]

Err, Forster is different

https://www.springer.com/us/book/9780387906171

[civic carbon]

oh, nevermind 😛

[sage python]

My impression is that Donaldson is more topology/GGT, Forster is more sheaf cohomology, and Miranda is more AG

[civic carbon]

I can never retain any information about sheaf cohomology. I awlays learn it, understand it, and a month lateri t is like it never happened.

[gray gazelle]

Do you guys have any books that I can use to learn more mathematics that is easy to read and understand? I want to start from one's that require calculations and then slowly transition to theoretical mathematics.
Topics I know : from elementary to high school mathematics including +2, numerical methods (like trapezoidal, Newton - rhapson method), multiple integrals, beta gamma functions, statistical probability (until sampling and some part of hypothesis testing).

[quick hornet]

what do you want to learn?

[gray gazelle]

Not sure about that

But something that dosen't ask me to find many proofs but makes me do more calculations

[quick hornet]

thats still pretty broad

computational diffy eqs maybe?

[gray gazelle]

Computational differential equations?

[quick hornet]

yeah

[gray gazelle]

Okay, so, what is it about?

[quick hornet]

i'll admit i dont have a great reference for that, but someone else may be able to provide

[velvet briar]

Have you done linear algebra yet?

[quick hornet]

differential equations is about - shockingly - solving (and studyin gthe behaviour of) equations involving derivatives (and integrals)

[velvet briar]

Btw differential equations example question
What's the function y(x) that follows this rule:
y' = xy

I have an engineering book which discusses it pretty well

[hollow current]

y' = xy
1/2e^x^2

just an example

[gray gazelle]

I know basic matrix operations like transpotions, finding determinants, inverses, multiplication, cramer's rule and many other things that I can't remember off the top of my head

[velvet briar]

Cool cool, so you know applications of linear algebra. If you wanted to get more proof-based, linear algebra is an amazing place to start, and Axler is a good book

[gray gazelle]

Also, I wish to learn more machine learning, computer vision and embedded so, anything that may be able to further me in those fields will be more than welcome.

And, is there a good book for learning Numerical Methods from that teaches you using a programming language?

[velvet briar]

@gray gazelle
Then honestly, I'd suggest jumping right in. You have the applications you need.

[hollow kayak]

How does Axler compare to Strang?

[calm crane]

most numerical methods book doesnt focus on a specific language and just go over the details of the algorithms i believe
Try picking up some language, it isnt too hard to implement numerical algorithms usually

[gray gazelle]

👍

[sage python]

@hollow kayak Strang has two books: "Introduction to Linear Algebra", and "Linear Algebra and its Applications". Both are more focused on computations/applications, while Axler is more theoretical

Among Strang's two books, the first is kinda lower level compared to the second (which at a glance feels somewhat easier than Axler)

[crude lake]

lol why's this under general

unless this is for math books only

[indigo stone]

A.B.C Maths for Kids - "Teach your kids Maths the fun way!" - E.H Carr

A monumental book in Math pedagogy, innovative and very original.

[gray gazelle]

Book for probability

?

In highschool/low undergrad level maths

Most I've seen require measure theory etc

[gray gazelle]

Also some basic statistics

[mossy flume]

There's a stats class I have to take that only has calc 3 as a prereq. The textbook is Probability and statistical Inference

idk anything about it tho

[cedar tundra]

Hey guys, is there any website which i could get free books? Like economy, business management?

Also for maths

Libgen aurora?

[normal tinsel]

guys which book would you recommend that would blow my mind

I want to get a book that shows the beeauty of math

I do not want a theory book now

[cedar tundra]

Ahh i see thanks!

[normal tinsel]

What would you advice me to read ? Feel free to leave your suggestions

I was thinking about Prime Obsession

[pulsar aurora]

Just watch any of the glorified youtube videos. 😛

[clever stratus]

humble pi?

[cedar tundra]

Aww libgem didn't work....

[pulsar aurora]

i wouldn't know a good book though. I find math to be interesting in its details than the pop-sci kind of materials

[gray gazelle]

@cedar tundra You should try https://arxiv.org

[cedar tundra]

I will try

[prime oak]

lol what

arxiv is not a book sharing resource is it

[cedar tundra]

Yeah its hard to find Malaysian books my friend 😂

Idk

[gray gazelle]

No it is not. it is for articles

Sorry

[cedar tundra]

I see...

Nah its OK

Ok*

[prime oak]

its for scientific papers lol

[gray gazelle]

Yes

[cedar tundra]

Still good

[gray gazelle]

I am sorry. I thought it would answer to his question. I was wrong

[normal tinsel]

Hi @sacred wagon I saw a lot of reviews of that book

Speacially on Calculus by Stewart

They mention that book all the time

[clever stratus]

what about salas hille etgen for calculus

[pulsar aurora]

For calculus, you have to spread around a bit. I think any college level calculus will be sufficient, then for deeper theory, you'd have to sort of read around. Spivak is nearly a meme-level suggestion.

[limpid gazelle]

[slender sphinx]

"Spivak is nearly a meme-level suggestion." 🤔

[civic carbon]

Spivak's calculus book is laugh out loud hilarious.

[pulsar aurora]

A lot of people always suggest it, but I never know if it's actually legit suggestion. That said, I couldn't stick with it. Didn't seem bad, but never had anything else to compare it with back then.

[civic carbon]

I got a copy from Bill McCallum who told me the book was so inspirational to him it was 100% responsible for him becoming a mathematician.

[hearty steppe]

Sweet, this channel is open now!

Spivak is a supplement for analysis as far as I have been reading up on here. I don't think that should be a beginners book to your regular calculus class in American university.

Dami yet to explain why Shilov is so basic for analysis, when it is a hit in the EU

Also can we not suggest shit like libgen in here? That's terrible to put out in the open.

[pulsar aurora]

libgen is hit and miss anyhow. I prefer going to a college campus's library for actual decent materials

Or a used book store

[raw aspen]

One of my favorite books is "Proofs that Really Count"

[hearty steppe]

So can I make some suggestions?

If you want to learn calculus without having to do analysis at the same time (as perhaps learning calculus formulas first may help with leverage later), you have two choices...

https://www.amazon.com/Calculus-Early-Transcendentals-Seventh-Stewart/dp/0538498714

https://www.amazon.com/Calculus-Ron-Larson/dp/1285057090

I have not checked out Spivak or Apostol yet but I think people recommend them based on picking up the rigor involved

[pulsar aurora]

I think Apostol's fine even for beginners if you're willing to slog it.

[hearty steppe]

I barely skimmed thru Spivak, it is very good but I mean, I wouldn't recommend it to someone getting into Calculus after taking a Precalc class

[pulsar aurora]

Apostol puts details in the history and the minute details of calculus.

That said, the one draw-back of Apostol is that he may not reference all techniques to modern day equivalents like Riemann's Sum.

At least, thus far in my study of it

[hearty steppe]

Also I like James Stewart, I completed it (most of it to the point I grasp up to multivar anyway) and I don't think you can go wrong with the sheer amount of exercise problems you can work on to make sure you understand the concepts

[pulsar aurora]

I cannot recommend any proper textbooks. My calc classes had us use Early Transcendentals by Jon Rogawaski, however the edition I have feels a bit over the place, but fairly well paced otherwise. Then I have another that seems better organized and more thorough in proofs without going overboard, but I haven't actually studied much of it.

[civic carbon]

On calc books, my strongest feeling is that Hughes Hallet's multivariable calc text is far better than the other standard options.

[hearty steppe]

Yea I'm skimming thru the contents section of Apostol right now and both books seem great to supplement for real analysis

[pulsar aurora]

Apostol seems more on Geometric analysis though.

WHich I don't mind at all as it helps me visualize what's going on in my skull

[hearty steppe]

Nothing wrong with that though. Geomtrical understanding is important understanding in maths.

[pulsar aurora]

Oh sure. Just stressing the focus from what I understand.

[hearty steppe]

Yea and when you get to integral calculus, your not gona avoid doing geometric series lol

That means the focus of Apostol is pretty much on point

Also man there is quite a bit of material crammed into Apostol compared to other books that gloss over calculus.

Two whole volumes

[pulsar aurora]

Yep. I'm unsure of the quality, but I think it helps me deal with college calculus without feeling the "Just memorize it" notion that people typically have

That said, it goes about it differently. Does the typical set up of basic analytical tools from algebra proofs, summations, and equivalency theorems, then goes into integrals using step functions and upper/lower bound comparisons. THen limits, then differentials. This seems to cause some level of nay-say by some people I have talked to as 'integrals cannot be defined without limits' However, he seems to define them just fine. It may not be Riemann's sums definition directly though. I've yet to study actual integrals in a typical college course however

So, unsure what the main differences, or if Apostol just decided not to reference Riemann at any point

So, it's on my things to think about as I study is, What is the key difference, if any. Which is always a good thing to have

[hearty steppe]

Yea thats the thing when it comes to the transition to advanced mathematics, you start to understand instead of just memorize.

[pulsar aurora]

Yeah, also makes it much more interesting

[civic carbon]

If math were about memorization I never would have made it. I've been teaching calculus for over 10 years, and I still look up trig values on the unit circle.

[valid moth]

lol

smh just approximate with deg 3* taylor poly

lol

[civic carbon]

if one accepts O(1) error, the degree 0 will work

[valid moth]

values range from +-1, so 0 seems like a good approx

[steel viper]

i think spivak as an intro to calc is fine tbh

[velvet briar]

I accept O(0) error

[civic carbon]

I hope you never accidentally encounter a floating point number

[gaunt veldt]

Having done Calc II in stewart, and Calc II in Briggs Calculus, I prefer Briggs @hearty steppe ,

[hearty steppe]

Briggs?

I use Larson for tutoring people at the college I work at and seems almost identical to Stewart

Their classes use Larson anyway

[final kayak]

calculus early transcendentals anyone?

[main flax]

by thomas? its a good book

[blazing dagger]

@tranquil ocean what book is this? The typesetting looks great

[limpid gazelle]

It looks like the Knot Book

[valid moth]

no it does knot

[limpid gazelle]

Yeah it is the knot book

[valid moth]

also

@blazing dagger you're back

[limpid gazelle]

"The Knot Book" by Adams

[blazing dagger]

Harro

Oh I see

[valid moth]

i think you're knot a book

[blazing dagger]

Thanks!

[dreamy lake]

anyone got a good book on probability

[cold lagoon]

i like probability theory from et jaynes

[blazing dagger]

That’s a meme book

Use jacod and protter probability essentials

[steel viper]

all books are meme books

[civic ravine]

any good book on lin alg?

[steel viper]

several

are you looking for something proof based?

[civic ravine]

idk really what im looking for

just a good book for starting?

[blazing dagger]

Klaus Janich linear algebra

[hollow current]

Leslie Hogben in Handbook of Linear Algebra provides a lot of theory

[civic ravine]

thank you both

[calm crane]

is suggesting hoffman kunze for lin alg a terrible idea

[hearty steppe]

Almost Everyone on server seems to suggest that one

[steel viper]

hoffman kunze is good

[gusty smelt]

just learn it from artin smh

[calm crane]

cant react to msgs here ><

[gusty smelt]

(the artin thing was serious btw, if you know some LA already it can be nice)

[bitter raptor]

Book of Proof imo good source when you know absolutely nothing about set theory, proofs, and combinatorics to start learning about them. Like as a high schooler who isnt familiar with the concepts

[calm crane]

tbh i learnt proofs by doing and reading solutions to olympiad problems

[gusty smelt]

same oof

[bitter raptor]

i mean someone who isnt familiar with them probably doesnt spend time doing that

I really mean to introduce those concepts to those who are clueless about them

[hearty steppe]

Artin is abstract algebra tho?

Learn from both?

[calm crane]

learn from jacobson kek has nice modules over pid stuff

[gray gazelle]

Does naive set theory

by halmos

teach set theory for beginners

or for people already familiar wit hthe subject?

[north spire]

for beginners

It has very few exercises so any assertion he makes is something you should prove if you want to make the most of it

[gray gazelle]

What if I don't know proofs yet?

[north spire]

Then, you'll have a fun time working through the book and scratching your head while proving everything he asserts

[gray gazelle]

So basically I should skip the book

[north spire]

That's up to you. It's a basic exposition. If you haven't been exposed to proofs, then you'll be scratching your head with most other sources you use.

Many people here suggest How To Prove It by Velleman as an introduction to proofs. You can use Halmos's text as a supplement.

[gray gazelle]

That seems wise

Thank you

[north spire]

You're welcome

[gray gazelle]

It's open to the public!

[robust kite]

What are some good books for self-studying analysis (especially analysis II)? I've heard some good things about Tao analysis I, but don't know how his analysis II compares

[marble rock]

rudin is golden standanrd

[hearty steppe]

Not in the EU apparently

[marble rock]

what do you guys think of ideals,varieties and alogrithms

AG text

[hearty steppe]

Shilov is standard in EU

AKAIK

[tranquil ocean]

It's alright. I mean, the benefit of the book is that it introduces some AG ideas without much background and is more concrete in the ways it does things

[hearty steppe]

Is it better to go the topology route first and then go AG? Like do Hatcher right

[tranquil ocean]

Uh, no

I feel like you should refrain giving advice about things you don't know

[marble rock]

1 more , how important is having an entire book on galois theory

im getting close to galopis theory now

there is a section for it on df but i can get a book ( first book for me yay ) of ian stewart

section vs book :D?

[tranquil ocean]

The book's cool and introduces AG ideas, but isn't super rigorous and doesn't really teach you a ton I guess. If you're looking to seriously study AG, you should just study commutative algebra and just pick up a real AG book

[marble rock]

yea

[tranquil ocean]

Of course, if you're actually interested in algorithms around AG, this book is great

[civic carbon]

I really love that Stewart's books, but I find the notation in his Galois Theory book awful.

[marble rock]

so for galois stuff

should i get a book or is the section in df

enough

for like average galois theory ig

im not like interested in it idik what it is yet

[civic carbon]

the section in DF is far more than sufficient. It goes in much more depth than Stewart's book

[marble rock]

wow

okay col

ty

[frigid comet]

what was a notational qualm you had with it @civic carbon ?

I can't remember his choices, but I have used that book in the past.

[civic carbon]

he gives names to all the natural embeddings, so there are just functions around everything

e.g. if L is an extension of K, then he'll call the inclusion K to L Gamma

that kind of thing

[valid moth]

$\eta_1, \eta_2, \hdots, \eta_{69}$

[hasty eagle]

Archsys:

[valid moth]

[frigid comet]

Ah I see

[sage python]

@civic carbon damn, that book is 340 pages and covers less than 2 chapters of D&F?

[gray gazelle]

Is there a difference between baby rudin and spivak?

[valid moth]

baby rudin is analysis

spivak is calculus

[sage python]

^

[valid moth]

that being said, spivak is a good bridge into the way of thinking and argumentation in higher math

it's not just any calc book

[gray gazelle]

Can you go from spivak to rudin in that order

[valid moth]

sure

[sage python]

Spivak is a book that you can read with neither calc nor proof background

[gray gazelle]

or do you need some other material inbetween?

@sage python I highly doubt that

[valid moth]

no, it's a good idea even

[sage python]

I effectively did that lol

[valid moth]

dami get on my level

i did calc off of khanacademy when 12 before knowing hs algebra

[gray gazelle]

Spivak assumes you know sequences, proofs and binomial theorem etc which you usually learn in calc class

[valid moth]

yeah unironically i learned hs algebra by doing khanacademy calc

[sage python]

Doesn't assume you know proofs, he covers sequences at the end

And he literally either does binomial theorem in chapter 2 or has it as an extremely easy induction exercise

And literally Spivak was my intro to proofs lmao

[valid moth]

? imagine not having a course in arithmetic as your intro to proofs

[gray gazelle]

I have spivak literally on my hands and he shows sequences and series at page 25 -_- @sage python

So you had 0 knowledge of proof before spivak?

[sage python]

0

[valid moth]

there's this thing called flipping pages

[sage python]

Do you mean finite sequences or something?

Convergence in Spivak is chapter like

Twenty-n

22 I think

[valid moth]

i mean if it's finite you should call it a list

reserve sequences for infinite is cleaner

(imo)

[gray gazelle]

$\sum_{i=1}^n i = 1 + 2 + \cdots + n = \frac{n(n+1)}{2}$

[hasty eagle]

midori:

[gray gazelle]

these

[valid moth]

actually the big brain move is to allow lists to be infinite like Axler

[sage python]

Look on page 24

He literally defines that notation

[gray gazelle]

IN ONE PAGE lol

then

3 pages later

he gives you difficult proofs on it

I mean if you are serious you knew nothing about proofs and series prior to Spivak

I will actually attempt it

[valid moth]

he's series

[gray gazelle]

I just want to know how did you learn to deal witt them?

[sage python]

I had seen like, the notation of a sum in... I don't wanna call it precalc but kinda precalc

But I had only done 1+...+n before

Like, Spivak doesn't do the thing that "Intro to Proofs" books do where they like

Say "Here's how to prove something by induction/contradiction/contrawhatever"

But the thing is he starts you off with the field axioms

And that's literally just like

Only do an algebra manipulation if there's a corresponding axiom. Chapter 2 teaches induction pretty much

And the specific mechanics of writing down a proof is really just logic, like you kinda figure that out as you go

Like okay assume something is false, what happens? This happens. Wait that can't happen though. Guess it couldn't have been false

[blazing dagger]

“Just logic’ Logicians triggered

[gray gazelle]

I see

I will read the book more carefully and give it a second attempt

Last question, how long did it take you to finish it, if you even did? @sage python

[sage python]

So, I was taking a class on it, and alternated between mostly going off lectures, mostly going off the book, and mostly winging it

[true veldt]

keep this channel about books

[sage python]

Tbh mostly winging it and panic reading Spivak since the lectures started off iffy. Eventually I started reading Rudin because I got bored (which is amazing and officially self-contained but actually kinda hard to jump into if you have neither calc nor proofs background. Not impossible but extremely hard)

I guess the lectures did come right out of Spivak so like lol but yeah I was mostly consulting the book directly for chapters 1-12

[tight crag]

archsys there is absolutely induction needed in what you just said

lol

that quick delete

[valid moth]

i didn't delete it

[gray gazelle]

A class is like what, 20 hours work a week?

The book is very tempting and I will attempt it

I gave up first time reading Spivak because I couldn't do the proofs

[sage python]

On the harder weeks maybe close to that, on easier weeks less

But yeah I think the idea is just like, when you're on the field axioms, remember that's all you have to work with

[main flax]

anyone know where i can pirateobtain
Clark Robinson's Dynamical Systems: Stability, Symbolic Dynamics, and Chaos 2nd edition? i tried libgen with no luck

[rocky meadow]

Man I tried reading Spivak when I was a freshmen in college and couldnt get past his introduction

Where he proves the basic algebraic properties lol

It was such a learning curve, getting into that mind set

[main flax]

time to bite the bullet i guess

[gray gazelle]

Do u guys know any book for freaking tough high school problems

for practise

[tranquil ocean]

https://www.imo-official.org/problems.aspx

[gray gazelle]

Not imo zoph

i mean high school level Basically little calc focussed

that is harder than highschool math @tranquil ocean

nd geometry

No i do IMO math

but i need for JEE

I mean like high school enterance exams

I want really cool problems on integration and calculus + coordinate geometry + sequance series + complex numbers stuff

I want book related on them with really good and interesting problems to sove on

[gray gazelle]

@gray gazelle https://www.amazon.com/Challenging-Problems-Algebra-Dover-Mathematics/dp/0486691489

I found this

https://www.amazon.com/Stanford-Mathematics-Problem-Book-Solutions/dp/0486469247

I'm reading spivak

His notation is killing me

the way he writes is melting my brain

Why can't he write i.e. for the trichomtomy law

One of the following is true
for any real number a > b, b < a or a = b

instead he writes

Let P denote the collection of all positive numbers
(i) a = 0,
(ii) a is in the collection of P
(iii) -a is in the collection of P

@sage python explain

[hidden abyss]

[gray gazelle]

?

[blazing dagger]

Old books are weird

That’s why I’m always a bit skeptical of “the classics”

[gray gazelle]

Many people praise and recommend it

It's the "bible of calculus"

[blazing dagger]

People like old books for some reason

[gray gazelle]

No it's specific to spivak only

same way with Lang's Algebra

[blazing dagger]

Even tho there are many newer pedagogically more sound ones

[gray gazelle]

as the bible of abstract algebra

[blazing dagger]

Yeah there are a lot of those

Rudin bible of analysis

[gray gazelle]

exactly

not because of their age i believe because they still get recommended today

lots of other old analysis, calc, algebra books exist too

but are hated

[blazing dagger]

True

Sometimes things just happen

Like memes u know

Ideas

[gray gazelle]

you are right

[blazing dagger]

Things just catch on

[gray gazelle]

I don't understand the hype of this book yet im only on page 13 tbh

but im gonna continue and see

[gray gazelle]

spivak

[steel viper]

is spivak old?

also @gray gazelle he is going to start doing that iirc after he introduces and explains it so like

starting in chapter 2

[calm crane]

@gray gazelle including multiplication and addition that is how you define a ordered field usually

[steel viper]

also is lang's algebra the bible of abstract algebra

like his grad algebra book?

[calm crane]

idk but it is pretty useful sometimes

[steel viper]

I feel like I see it get shit on more often than not lol

[gray gazelle]

@steel viper 1967 lol

@calm crane I just don't like the notation for some reason it seems too detailed or something

[steel viper]

I feel like considering his target audience it makes sense to be detailed and explicit

Maybe not so much for the very first things but later on as things get a bit more complicated I don't see why not

[calm crane]

it just generalizes easier¯_(ツ)_/¯

[steel viper]

Yeah

[calm crane]

but yea it can be confusing at first

[gray gazelle]

i hope you guys are right im really giving this book a chance 😭

[gusty smelt]

also ill add there is no reason to be bashing the old books lol, there is a reason these books are still used after so many years, its cause they are good lol

and different authors will use different notation, having the flexibiity to read all of them is p important

[gray gazelle]

I will be posting my stuff in #calculus

[flint forge]

always bash old books

if its not written in latex its bad

[quick hornet]

rip rudin

[flint forge]

Im shocked no on has latex'ed rudin yet

it would be a service to the community

[gusty smelt]

guess im latexing rudin now

[limpid gazelle]

https://github.com/natestemen/rudin

There's this

But it isn't an exact copy of rudin

It's "a more digestible version of 'Principles of Mathematical Analysis'"

[flint forge]

interesting

[civic carbon]

Marcus was the non-Latex book I was most attached to, but I hear it has been texed now

[gusty smelt]

yeah, the original typesetting of marcus was kinda

really bad

[civic carbon]

haha yeah, really bad is pretty generous

though much better than the Mumford Oda notes hahaha

[gusty smelt]

i have the new version of marcus, its latexed and nice now

[flint forge]

Oh man the worst crime in mathematical history

is that Groups of Homotopy Spheres I is a Kervaire-Milnor paper that is not latex'ed but at least is legible

They never published II

But someone wrote lecture notes to cover what would have been in II

and these lecture notes are quite possibly the worst typeset thing I have ever read

to the point where I just decided to not read them

[civic carbon]

a large group of algebraic geometers were working on a bigger version of the Red Book, but, according to legend, at some point the project fell apart because of... we'll say personality issues with one of the authors. But what was made was so valuealbe people copied what they had, and then these copies would get passed down generation to generation. So my copy is a xeroxed copy of a xeroxed copy of a xeroxed copy of...

But the thing is a mess, like it alternates between typed and handwritten

[flint forge]

lmao

[quick hornet]

i've seen "typeset lecture notes" where the author used | for parentheses () and quotienting / and setminus \

i still dont understand the motivation

doesnt everything ever have parentheses

???????????

[civic carbon]

I really don't like \ for set minus

[flint forge]

apparently the only reason we call bar complexes bar complexes

[quick hornet]

i mean even - would be an improvement

over

A | B

[flint forge]

is that they used to be typeset

with bars

[quick hornet]

yeah because \otimes on typewriters

was lol

it was techcnically possible but you had to like

type an o and then move the page ovver

and type an x

and if you missed it looked ugly as shit

[flint forge]

lol

latex is a great example of how open source software can add insane value without any cost

its kinda crazy

[quick hornet]

this is also where blackboard bold comes from btw

[flint forge]

this is why i support communism

[quick hornet]

people just sort of

rotated chalk on the chalkboard

to bold R and N and stuff

but you cant do that on typewriters

so they just shifted the page slightly and typed again

creating a double-bar effect

nowadays the double-bar has become "standard"

[flint forge]

i fuck w alternative notation for mathbb

like a nice cursive bold? its a nice change in pace

[quick hornet]

$\mathbb{Z}$ is the best looking symbol in all of mathematics and youll never convince me otherwise

[hasty eagle]

Namington:

[quick hornet]

and its almost as fun to write as varphi

[upbeat vine]

And one of the hardest symbol to write using hand

[civic carbon]

the best part about sheafs is getting to write $\mathcal{F}$

[hasty eagle]

zetamath:

[quick hornet]

its not hard to write

just write like

a 7

and then an upside down 7

to make a Z

[upbeat vine]

Yeah but connecting those 7's get so hard 😭

[quick hornet]

like this but connected

[flint forge]

bbZ is easy to write by hand what

i have the hand writing of a toddler

but i can handle bbz

[valid moth]

I actually write it more like

[flint forge]

bad

do it the way namington suggested

[quick hornet]

petition to ban arch

[valid moth]

just wait till i show you how i draw \bQ

[sage python]

\mathbb{Z} but with a dash through it

Also this isn't book-based anymore so let's go back to books

[civic carbon]

the bbZ is the only Z I don't draw slashes through, I think

[sage python]

Also on the earlier discussion of classics/tex'd books: someone needs to either tex Hoffman-Kunze or write an actually good linear algebra book

Preferably the latter because Hoffman-Kunze shows its age for other reasons (e.g. doing systems of linear equations before vector spaces)

[prime oak]

Book recommendations for algebra?

[marble rock]

dummit foote

artin