book-recommendations

[past ice]

No, you should be fine. Some small remarks and motivating sections (like in the introduction) might require some knowledge of the prior books but the main material is self-contained. Basically the prereqs are the same as for Folland.

[cursive orbit]

I see, thanks for the recommendation

Any particular reason why you prefer SS to Folland?

[past ice]

Yeah. SS starts more concretely and spends a lot of time building intuition with Lebesgue measure. The order makes more sense to me. And it's much less dry to read.

also idk if this matters to you, but SS is visually much prettier to look at

[halcyon hornet]

Anyone has books to learn Algebra 1, Algebra 2, Geometry and PreCalculus.
Which are not as shallow as KhanAcademy or Something.

[cursive orbit]

I see. If I already have some experience with Lebesgue measure though (I've gone through the construction using the outer measure), would you still recommend SS over Folland?

And personally visuals aren't that big of a factor unless they're particularly atrocious

[gray gazelle]

the construction of the lebesgue measure takes place in the first 10-20 pages of folland

so i feel like the recommendation probably still stands

folland is pretty dry, but it wasn't bad to read when i needed to supplement my profs lectures

[cursive orbit]

Oh I'm planning to self-study, so if Folland is drier than SS, I'll probably go with SS. Thanks for the advice.

[tiny elk]

Hey guys! Does Courant's book "Introduction to Calculus and Analysis" cover Real Analysis as well?

[past ice]

Yeah, SS is still worth reading even if you've seen Lebesgue measure. I don't think Folland is bad, but I just think Stein and Shakarchi is a better, more thoughtfully-written book for the purposes of self-studying. I recommend looking up a sample of each. Also Folland's last 4 or 5 chapters are, to put it kindly, trash.

[cursive orbit]

I see

[halcyon hornet]

?

[past ice]

The Gelfand books are very nice. https://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773

[pale scarab]

What's wrong with khan academy? I feel it's more the appropriate for that level.

[halcyon hornet]

It is too shallow.

[karmic thorn]

Have you worked through it?

I admit the problems are not the most challenging

But at least it can get you started for exploring more challenging problems

[halcyon hornet]

From where though?

[pale scarab]

Just get through khan academy so you can start learning math that isn't so shallow. I feel it teaches that material better than most textbooks for that level of math

[halcyon hornet]

I see. Thanks!

[hasty turret]

I don't think those are seen as real subjects. KA is unironically the least shallow of all the sources available for this

[steel viper]

pauls notes or something idk

[halcyon hornet]

At least I studied Algebra 1 and Algebra basics for it, and it is too shallow.

Like shallower than even the school textbook tbh.

[hasty turret]

https://tutorial.math.lamar.edu/classes/alg/alg.aspx

nvm,This exists

[halcyon hornet]

Anyway are Schaum's Outlines good to use as a supplement?

[halcyon hornet]

Thanks!

[cursive orbit]

I mean what do you want? Formal justifications of all the stuff you learn in algebra?

[halcyon hornet]

Problems which are more challenging, more problems, and basically a bit more advanced.

[cursive orbit]

If that's the case, the first few chapters of Tao's analysis 1 book does a bit of that

Ah

[karmic thorn]

Even though I shill Tao all the time, recommending it to someone learning algebra in school...

[halcyon hornet]

Yeah.

[pale scarab]

You can check out the AOPS books but it doesn't really teach the material any differently. It just has hard problem sets but you can find hard problems looking through old amc/Olympiad tests if thats your goal.

[halcyon hornet]

Exactly.

AoPs is awesome.

[karmic thorn]

That would be interesting though

[halcyon hornet]

AoPs is much more interesting.

And much more deeper.

But those books are really costly.

[karmic thorn]

How would a middle schooler respond to development of natural numbers

[pale scarab]

I have all the books and honestly khan teaches it the same

[halcyon hornet]

I got the PreAlgebra PDF and studied almost all of it, and it was too good.

[cursive orbit]

Yeah tao is a poor recommendation lol

[halcyon hornet]

What all have you studied from KhanAcademy?

@pale scarab I am in 8th grade.

[karmic thorn]

I have almost a million points on Khan

Definitely recommend it for everything up to calculus, feel free to supplement it with any book you like

For calculus in particular the sequence fits with Thomas' Calculus. For algebra, maybe try OpenStax?

[halcyon hornet]

Hey hey can you suggest supplements, that is what I need anyway.

[karmic thorn]

There are also random olympiad math books you can get

[halcyon hornet]

OpenStax is not actually a supplement. It is a textbook used to learn as KhanAcademy teaches.

[pale scarab]

I have gone through all math on there actually but I knew the material already mainly went through it before using it with my students

[karmic thorn]

And you can always browse AoPS website for olympiad problems and solutions

[halcyon hornet]

So I can use KhanAcademy or get printouts of OpenStax.

[halcyon hornet]

From Algebra basics and algebra 1 to Calculus?

Woah.

[halcyon hornet]

Yes sir.

[karmic thorn]

Sure, whatever works. Getting started is more important here. 😂

[halcyon hornet]

Yeah.

@karmic thorn did you learn till Calculus from KhanAcademy?

[karmic thorn]

I've covered a bit of content, yeah

Far from what all Khan has to offer

But I liked the presentation in general

[halcyon hornet]

What all did you learn from there?

Algebra 1, Algebra 2, Geometry?

[karmic thorn]

Mostly calculus, some algebra and adjacent topics too I guess

[halcyon hornet]

Algebra you mean Linear Algebra or Algebra 1 and 2.

[cursive orbit]

I wouldn't use KA for linear algebra

[pale scarab]

Yeah don't get hung up on high school topics get through it so you can start learning more interesting things

[karmic thorn]

Algebra 1/2

[halcyon hornet]

Lol yes.

[halcyon hornet]

Okay then now I have proof that KhanAcademy is really good and I can really trust it.

[halcyon hornet]

Awesome.

[karmic thorn]

It is trustworthy And you are free to learn from other sources too

[halcyon hornet]

But anyway always my first option would be AoPs.

[cursive orbit]

Your goal is to do math comps right?

[karmic thorn]

Russian authors from the last century have lots of nice books with an Olympiad like flavour

[halcyon hornet]

In a few days I'ma ask my dad for AoPs books another time anyway.

[karmic thorn]

You can also check out books by Gardner

More of a recreational math flavour

[halcyon hornet]

It is the clearly the best I have found till now.

Though I do not know how many AoPs books I can get.

[pale scarab]

If want to do math comps really best is to go through lots of old exams which are all online anyways

[halcyon hornet]

Yeah.

Previous exam papers works well when you actually know in a good level how to do that sutff.

[karmic thorn]

You can always ask around here, or in the olympiad server in #old-network .

[halcyon hornet]

Then you can know more about that sutff.

[halcyon hornet]

Yes.

That is the great thing.

You guys help me a lot.

[karmic thorn]

You don't always have to learn from a book first, a lot of problem solving techniques are picked up on the go.

[halcyon hornet]

50,000+ people on a group to help for math is basically really awesome.

[karmic thorn]

But yeah, getting some basics down would certainly be useful.

[halcyon hornet]

Yess.

Again, thanks a lot everyone!

[karmic thorn]

Goodluck!

[halcyon hornet]

Thanks!

[analog pollen]

Who?

Do something usefull instead of troll

[long anchor]

did u speedrun preschool math ?

[hollow current]

hi @long anchor

wotsup

[long anchor]

hello vimes

im just vibing with NT

wbu

[hollow current]

vibing with rust

[long anchor]

wtf use haskell u heathen

[hollow current]

i will

am going to finish rust learning

maybe do couple simple projects

than also renew golang

and sql

and yes haskell

[manic fox]

haskell more like haskhell

[long anchor]

why r u leaning every lang ever

[hollow current]

because stack is huge

and like

i do not learn language

i look at it

see how it is engineered

and try to understand it

[long anchor]

mf thats called learning

[hollow current]

[long anchor]

[hollow current]

i mean i do not try to learn contents of all rust libraries etc.

just to get the nature of language

[long anchor]

did u abandon math

[hollow current]

so my tool stack is not only c++ and java and golang

no i did not

well haven't touched maff for a while

but did not abandon

[long anchor]

ic

do u know the snek language

[hollow current]

no

[long anchor]

damn, what did u even accomplish in life

[hollow current]

It is designed for education and to be able to run with 2 KB of RAM.

2 KB RAM

wow

i have 1 KB RAM

[long anchor]

1KB RAM

oh snek is an actual thing wtf

i meant python

[hollow current]

there is stalin language

[long anchor]

[hollow current]

https://en.wikipedia.org/wiki/Stalin_(Scheme_implementation)

Stalin is intended for production use in generating an optimized executable.

optimized

[manic fox]

mmmm

[hollow current]

The name is a joke: "Stalin brutally optimizes."

[long anchor]

turns out u sort an array by killing off all but one member of the array

[hollow current]

why you leave one member

kill them all

[long anchor]

yeah kill them all

[hollow current]

empty array is vacuously sorted

well and one-element array as well

but empty array requires less memory

[karmic thorn]

Maybe

[long anchor]

[karmic thorn]

Flex

[long anchor]

[ionic marten]

Hi all, i want books on euclidian geometry.. thanks!!

[gray gazelle]

UKMT has a good book on it

https://www.ukmt.org.uk/product/87

this is from the ukmt store

[willow pecan]

[manic fox]

elementary, even

[gray gazelle]

Does someone have any history books recomandstions 🐩

[willow pecan]

What sort of history?

[analog pollen]

Prolly math history books

[split bluff]

has anyone read analysis I by terence tao? if so, would you recommend it to a beginner that is about to finish a single variable calculus book?

[gray gazelle]

@karmic thorn

[karmic thorn]

Was just arguing with Luna about the integration chapter

But yes, I would say Tao is accessible to anyone who has done a first course in calculus.

[gray gazelle]

(manan has read this book)

(i think)

[karmic thorn]

You probably don't even need a lot of mathematical maturity diving in, the starting chapters have loads of proofs written nicely for understanding

Yeah, I'm on the verge of finishing volume 1

[split bluff]

you are? nice

what's your background? i'm a programmer trying to fill some gaps of knowledge

[karmic thorn]

I've only skipped a few bits(last bit of chapter 3, first bit of chapter 4, last bit of chapter 8).

[hasty turret]

Analysis I is mostly fluff

[karmic thorn]

I'm a first year math undergrad, but I started with this book with the same background.

[hasty turret]

You can skip about 60% of the book

[split bluff]

i mean, i'm about to finish reading a single variable calc book, maybe i'll be able to finish it quickly, or maybe i won't

[hasty turret]

No,60% is unnecessary stuff like "what is a function"

[karmic thorn]

You can, but I may or may not advise it, especially if you haven't seen/done proof based maths before. You can skip chapter 3 and some parts of 8 for efficiency, and skip some tedious constructions where you have an idea of working them out, but otherwise its fine. The latter chapters are very efficient.

[hasty turret]

"What if I construct N from peano axioms and make a chapter around it"

"although no one cares about how N is constructed"

[karmic thorn]

Sure, but I'd say the first few chapters are a good substitute for an intro to proofs course.

They have actual meaningful content, and insights which are very useful imo.

[split bluff]

maybe it will be good for me then, i don't have much experience writing proofs, i was actually reading a book of proofs before i started learning calc but didn't finish it

this one

[karmic thorn]

Proof books are boring as hell.

[gray gazelle]

i read the first three chapters of this book before entering university

[karmic thorn]

You can familiarise yourself with basic terminology of sets, functions and relations.

That should suffice.

[karmic thorn]

TTerra set identities researcher arc?

[split bluff]

i did more or less the same, read the first 100-120 pages and then went for calc

[gray gazelle]

having read the proof book helped me be familiar with basic stuff going in but it didn't really help in attaining actual mathematical skill

it was more like

my comfort level was higher

it was less of a shock going in

these things aren't necessary but they do help

[karmic thorn]

Fortunately my HS teacher taught lots of stuff about sets, relations, functions, induction with a good amount of rigour.

[split bluff]

i mean, that's kind of what i'm doing at the moment, filling gaps and learning stuff that useful regardless of the path i take in the future

[karmic thorn]

And then I used to dabble around here asking weird group theory questions from Gallian

[karmic thorn]

Sounds good.

Oh no

Tao denier has arrived

[prisma snow]

I wouldn't say proof books are useless. Like they will help, but I think it would help more to just read some actual math books.

[split bluff]

so, would you advice someone like me to read something else? my background is hs math + programming and calc

i wanted to read one of those discrete math books but i was adviced to learn calc first, which is what i'm doing, i'm almost finished with the book

[prisma snow]

Yeah, calc first is fine

Then discrete math would be fine. It will probably teach you the basic set theory stuff you will need.

Or you could go for Linear Algebra, but you would need to learn the set theory stuff first somewhere

[split bluff]

do you have any recommendations? i have this book called "concrete mathematics" by donald knuth, i got it because it was recommended in many places

but i don't really know why

[hasty turret]

Good problems

[split bluff]

i don't really use much math in my job (i do web development) but i want to use my free time to learn stuff that may help me in the future coding or with cryptography which is something that called my attention and i use a lot in my job (even though i don't really understand the details behind some cryptographic algorithms)

[gray gazelle]

Hello everyone

[prisma snow]

I don't have a discrete math book recc, but I see knuth recommended a lot, so it should be fine @split bluff

[desert blaze]

what did help? currently I enjoy reading stuff like velleman's but even the introductory problems i struggle with

like the one where he asks for factors of something like 2^{32767}-1

he starts by asking for factors of 2^{15}-1 which euler2 assisted me with seeing that this was a difference of cubes

the thing is, immediately after that chapter, there's problems i can do again, like the logic notation stuff.

[velvet briar]

Struggling is okay, getting past struggling means that you're getting better

And these books aren't as easy as you might be used to, which is also okay

I personally got good at proofing just by reading a lot of books that contained stuff about it. This server helped too

[desert blaze]

yea, thanks kay, so like, what i guess i wanna know is

currently, i'm completing assessments and material on time, so i have extra time to study more

i'm studying stuff like lang's basic mathematics that proposes to introduce basic mathematical concepts with the idea of proving

so he'll introduce some power laws, then ask you to prove that if a is a positive even integer, so is a^2

but, i sometimes question whether at this stage i ought to be just continuing with the course material or diverging off in the direction i'm going in with learning proofing for the sake of being a better maths liker.

[velvet briar]

I mean it depends on what you want to do. If you really like proof-based math, read more about that!

[desert blaze]

yeah i really do but i also want to do the thing that is going to help me develop the most in terms of understanding future content

ik it's a dumb question to a certain extent

[velvet briar]

What is "future content" for you?

[desert blaze]

well, i want to continue onto studying for a maths degree, maybe online or not but what i really want to get good at is

well, what you guys would maybe describe as problems about number theory because

i wanna get good at coding

[velvet briar]

Oh kek well then yeah if you want a math degree you'll need to be good at proofs

[desert blaze]

awesome

so pretty much any time spent now on proofs is not wasted at all?

[velvet briar]

I suggest that if you want to know something, look up pdfs for it

[desert blaze]

cool beans, thx so much

[velvet briar]

Or, ask about good books here. People know good sources

[cosmic rivet]

any suggestions for trigonometry books for undergrads?

[quick hornet]

did you not learn it in high school, or are you expecting there to be more trig content than you get in hs?

because there isnt really

theres like complex numbers & fourier transforms & whatnot

[hasty turret]

Doesn't diff geo involve trig

[quick hornet]

which use a lot of trig

but they dont involve new trig content

[quick hornet]

no.

[hasty turret]

Like I remember seeing that modified law of cosines

[whole rain]

guys lol

why are you speaking about diff geo to someone asking for a trig book

[quick hornet]

thats why i ask:

did you not learn it in high school, or are you expecting there to be more trig content than you get in hs?

im not sure what they mean by "trigonometry [...] for undergrads"

[whole rain]

Yh ok

[quick hornet]

i feel like this question is a case of https://xyproblem.info/

they really mean to ask about something else, but its related to trig, so they think some mythical UG-level trig is what they want

[flint forge]

Does anyone have an intro to brin-and-stuck style dynamics

but like

less terse

for an reu mentee

He's also interested in the measure stuff

maybe something focused on like

borel dynamics

Oh cool

Do you know the title

this looks great tysm

[torpid drift]

Hello
so i have these 4 exams and i would like to find a book covering this kind of questions
https://moe.gov.eg/media/brodrbax/math-english-june21-practice.pdf
https://moe.gov.eg/media/3gcha2m5/algebra-english-session1-2021-prac.pdf
https://moe.gov.eg/media/uw1dbwsu/calculus-english-session1-2021-prac.pdf
https://moe.gov.eg/media/f51btj2d/dynamics-english-session1-2021-prac.pdf
any book or website have the same kind of questions would be helpful

[cinder tundra]

What's the best book for someone who is rather new to proofs, going into a bachelor's and trying to tackle a linear algebra book which requires a bit of experience with this.

[willow pecan]

If you go to the top of #books-old there are some recommendations

[cinder tundra]

I'll check it out, thanks

[quaint scroll]

Does anyone know any good resources on Clifford algebra?

[gray gazelle]

clifford the dog?

[quaint scroll]

ye Clifford the bivector

[ripe granite]

https://sites.ualberta.ca/~karpenko/publ/Kniga.pdf

[hard lion]

oh, if you're looking for something that is more about geometry then logic, can I recommend heaths translation of Euclid? He includes a lot of notes about each proposition, as well as describing other formal systems if you want it

[gray gazelle]

Do y'all think I can self-study from Tao's analysis with only a background of Calc 1+2?

@karmic thorn

[cursive orbit]

Yes.

Well, a familiarity with proofs help too

Especially with induction, in the earlier chapters

[timber mesa]

there's better books for analysis but yes

[thorny onyx]

Looking back I think the best route would be starting straight from Logic, a big portion of that book is just set theory. (they call analysis second order arithmetic, after all)

[past ice]

You can self-study Tao with almost no background at all. Just skip the introductory chapter.

[deft hare]

Hello everyone I am trying to self learn abstract algebra just for the love of mathematics I have completed my calculus and some linear algebra(self learned) . Do you have any book recommendations or how should I proceed on learning abstract algebra

[prisma snow]

Yes

Read the books by Rotman.

He has an advanced book at about the level of Dummit and Foote. But he also has an introductory book, and a book focused just on group theory.

[thorny onyx]

I recommend Algebra: Chapter 0 - Paolo Aluffi, which takes an categorical approach from the beginning

[deft hare]

Sorry for not including this. I have no prior background in abstract algebra and other people on the internet ( reddit quora ) say that dummit and Foote is not good for beginners so should I go with dummit and Foote or any other course

[prisma snow]

You can try the introductory book by Rotman then

I never used that one, but I assume it's great based on his other books and I know someone else who is reading it rn

[sage python]

"Dummit and Foote is not good for beginners"
It's fine

I think it's not good in general

But you don't need to know much (if anything) to read it

[karmic thorn]

Absolutely. I don't even know calc 2 tbh, I'm about to finish volume 1 and I think just basic familiarity with calculus suffices. The focus of the book is on more theoretical developments for which it is almost self-contained.

[sage python]

Pretty sure Tao's only prereq (like D&F) is the English language

[karmic thorn]

Yeah hahaha

But he like, revvs up when the heart of the content starts, like he does assume you know at the back of your head what all motivation differentiation and integration have, what the geometric intuition is, etc.

[deft hare]

Ok thank you

[gray gazelle]

what are you using to like grade yourself the practice work?

[karmic thorn]

I ask around on Discord if I'm unsure. As I've done more and more proofs, I can now tell more easily when I'm bluffing with my arguments. Even then, getting your work critiqued is a bit tough when you're studying on your own.

[deft hare]

Hey just a quick question is contemporary abstract algebra by gallion any good for beginners?

[static crest]

d&f is just fine for beginners in terms of difficulty

gallian is if you want to be treated as insultingly stupid

[marble karma]

Guy's do y'all know any spivak equivalent for function of several variables

[formal solstice]

@pliant oasis I am also working through Analysis I by Tao.

@static crest what do you think about Algebra by Artin?

[gray gazelle]

spivaks calculus on manifolds

[crimson slate]

Any suggestions on how to get started with category theory?

[cursive orbit]

Perhaps part of Functions Of Several Real Variables by Paliogiannis and Moskowitz

[karmic thorn]

You pinged the wrong Manan but that's nice 😂

[gray gazelle]

Any precalc book recommendations?

(Not Stewart if possible, I don't like his precalc book)

[orchid agate]

Greetings fellow math nerds. Does anyone have any interesting math book recommendations? Anything will do, just looking to go down a new math adventure.

[gray gazelle]

Try to read a spanish math book if you don't know spanish

Like "Cálculo en una variable" from "Garceta Editorial"

But you have to buy it...

[orchid agate]

Why a Spanish math book?

[gray gazelle]

Because I think you know far more math than me so I may don't have any math book to recommend and as spanish is my native language I thought that I could recommend you a basic math book in spanish

[manic fox]

do applied category theory bro

[gray gazelle]

Which could fit in what you are asking

[orchid agate]

Haha oh okay. Indeed I actually can speak Spanish, but not with pristine fluidity. It would certainly be more challenging to read in Spanish.

[gray gazelle]

Do Stewart calc (complete edition)... doing all the exercises from the book without skipping anyone

[orchid agate]

Yess I hear of category theory. It’s one of the areas I’m eager to delve into. Any book recommendations for category theory?

[orchid agate]

I’ll have a look, thanks!

[gray gazelle]

stewart calc
do all of the exercises

[manic fox]

I don't do much cat theory but riehl's book is gud

as far as ive read, which is not very far

[orchid agate]

Ohh okay awesome, thanks! How far along are you in the book?

[gray gazelle]

Hehehe and to make it a bigger challenge you can't look at any solutions until you finish all of them so then you have to go at Slader to look at everyone of them

You can actually make it a bigger challenge adding the precalc book

Another big challenge would be

Read the whole Springer undergraduate series

And then try to do the math degree without studying

[manic fox]

don't really remember, i was doing cat theory memes for a little bit but before i went on my break

now im looking in to applied math

[cursive orbit]

Ah yes, read the 190 books in there

[sage python]

@manic fox lmao look at this nerd

[manic fox]

I'm looking at him rn

[solemn rover]

Riehl's book on Categories in Context contains many examples from throughout mathematics. There are also books on category theory by Steve Awodey and Tom Leinster.

I learned out of the old book "Categories for the Working Mathematician" by Mac Lane. There is a lot of good stuff in there but I don't recommend it as an introduction.

A very clear and easy to read book is Borceux's Handbook on Categorical Algebra. It is very thorough and complete. But it does not deal with connections between category theory and the rest of mathematics.

[gray gazelle]

[past ice]

If you want to learn pure math don't use Stewart. Go for Spivak.

[past ice]

What's your current background?

[orchid agate]

I claim no expertise in anything, just a young and curious kid who has taken some lengths for self study. I’m comfortable with anything up to MVC, linear algebra, mathematical logic, some order theory and vague nuggets of knowledge from a few other areas.

[hasty turret]

Have you done generatingfunctionology

[past ice]

I see. Murty and Fodden have a pretty recent book on Hilbert's tenth problem that I think you might like https://bookstore.ams.org/stml-88/

[orchid agate]

I had a quick peak of the book. It actually does seem really neat, and covers some things I’m interested in! Thanks for the recommendation 🙂

[orchid agate]

I have not

[hasty turret]

If you ever wondered how to systematically solve reccurence relations, that's a good read

Instead of just "I guess the solution is of the form ... hence it's the complete set of solutions"

[past ice]

No prob. I think it would be a great summer read. Good luck!

[past ice]

so i've had one course in combinatorics 2 yrs ago and i think the takeaway was that generating functions work by means of black magic

[wooden sparrow]

Can anyone suggest me books for LA other than Friedberg, Insel, Spencer?

[gray gazelle]

axler, if you are okay with skipping computational aspects of LA

[wooden sparrow]

Computational aspects?

Also I've never touched AA

New to UG maths

[gray gazelle]

not sure what AA has to do with it. by computational aspects i meant stuff like routine matrix computations

row reductions and all that

[wooden sparrow]

You don't learn that in LA?

[gray gazelle]

you should but axler doesn't really do some of that stuff iirc

i might be talking out my ass so let me check his toc

yeah i ctrl f'd "row reduction" in axler and got zero hits

[wooden sparrow]

Okayy

Well is it useful for in application point of view? Like programming something for computations?

This is the book right?

[gray gazelle]

yup

i don't actually know if row reduction and related stuff is used in computational mathematics

but

[wooden sparrow]

Should I ask Ange?

[broken meadow]

ange probably knows more about linear algebra for computery stuff

[gray gazelle]

i spend time in #linear-algebra and the number of people who are presented with a very basic problem that can be solved by just applying definitions, and then go "do i have to put this in RREF?,"is really shocking

[broken meadow]

rip

[gray gazelle]

yeah ange's type of stuff is what i meant by computational

it's good to know and do a few times but theoretically it's not important. axler just ignores it completely

[wooden sparrow]

Also this book doesn't seem to have that many exercises?

[gray gazelle]

it seems like it has a lot

[wooden sparrow]

Okay my bad

[gray gazelle]

what bits and pieces i've seen of axler i've actually liked

the determinants thing is odd but whatever

axler is the kind of guy who would look in #linear-algebra and write a textbook just to try and get everyone to stop trying to use RREF on everything

[wooden sparrow]

RREF?

[gray gazelle]

row reduced echelon form

it's something you can get by applying elementary operations to a matrix

such operations preserve things you wish to compute and so putting a matrix in RREF can make computations significantly easier

you can tell i haven't used it in a while because i didn't actually tell you any specific use of it

[wooden sparrow]

Nice

[hasty turret]

The best use is probably computing determinants/solving linear equations(Talking about Gaussian in general)

[wooden sparrow]

I heard about this in M2 in engineering. Didn't understand much though

[wooden sparrow]

I just put 4x4 in my casio during that exam

Don't know who even asks for a bigger array than that

[broken meadow]

i remember one use of rref but that's for computing char poly/determinants easier yeah

something about cayley hamilton or something

[gray gazelle]

[broken meadow]

getting a bunch of 1s

somewhere

[karmic thorn]

I've done countless row reductions. I regret wasting my time.

[stark elm]

Any good book recommendations for high school calculus?

[gray gazelle]

hey can anybody recommend me a book on algebra which covers all algebra

lang

[hasty turret]

Bourbaki

[quick hornet]

somehow

i dont think theyre talking about abstract algebra here

though i suppose Lang is technically a correct answer either way

because he has Basic Mathematics for high school algebra

but recommending Basic Mathematics always felt like recommending you eat all rice with chopsticks for the authentic japanese experience

you CAN, and if youre into the authenticity, go for it

but its a bit much

[tulip blade]

Stewart early transcendentals

[sudden kindle]

Is there any book that deals with logic and its applications to number theory ?

I found a book called Logical Number Theory I by Craig Smorynski

[analog pollen]

isn't that just the normal calc book

[tulip blade]

Yes. Why should high school calculus be any different?

Im not sure why stewarts calculus would be inappropriate for a high schooler learning calculus.

[delicate osprey]

shrek

[analog pollen]

i know but maybe he isn't looking for that lol

but i totally agree with you

[delicate osprey]

shrek tentacle

ok

[eager stump]

thoughts on stewart vs larson?

[analog pollen]

im just looking trough larson and im seeing that it doens't cover epsilon delta defintion

also imo it covers topics in a weird order

[delicate osprey]

hey want to know a cool book

harry potter

[eager stump]

oh it has different versions

[eager stump]

mine does

[analog pollen]

oh lmao

but why do you want to know which is better if you already have the larson book

stewart has multivariable tho

[eager stump]

pedagogical reasons i'm just curious as to what people prefer

[analog pollen]

oh

[eager stump]

i honestly didn't like stewart my first time through

[analog pollen]

why not

[eager stump]

but it was a while ago

i think i thought some examples it provided weren't representative enough (this was a while back though). I was probably too green. Also it was a pdf which i think always obfuscates the matter

[manic fox]

do all the exercises in stewart to ascend to godhood

[eager stump]

lmao

[manic fox]

when i did them i actually got to meet zeus

[eager stump]

do all the exercises in tao's analysis and transcend space-time

[manic fox]

pretty swell guy

[analog pollen]

100 exercises per paragraph ☠️

deadly

[eager stump]

😆

thanks for the tips though, i'll see if i can get a second-hand stewart then

[analog pollen]

idk it might depend on the individual

i like it

but i heard some people don't

[eager stump]

i mean, it can have strengths and weaknesses... there's no one-stop shop for calc

[manic fox]

idk bro

pauls online notes are pretty much a one stop shop for the usual calc sequence

[eager stump]

i meant calc in general 😅 , mb wasn't clear

[manic fox]

i mean when we say calculus that's what ur referring to usually, otherwise just do analysis

[eager stump]

fair, touché

[tulip blade]

@analog pollen 🤣why does it matter that stewart has multivariable

It isnt until after all the single variable material. Its not like it starts off with multivariable calculus

They just do the single variable material...

[analog pollen]

its al in a single book was my point lmao

so that's nice

[tulip blade]

Why does that matter?

[analog pollen]

i like that

imo

[tulip blade]

You can buy it without multivariable

[analog pollen]

yes but that's a rip off tho

[eager stump]

guys, but how will the book publishers eat?

[analog pollen]

https://tenor.com/view/very-good-question-accha-sawal-hai-boman-irani-3idiots-gif-21333145

[mint sparrow]

A mathematics manga about the IMO: https://www.mangaupdates.com/series.html?id=156514

[sudden kindle]

If there are some characters who just dont like math competitions, then I might read this manga

[manic fox]

[lyric oyster]

recommend Hammack 3e

[gray gazelle]

Hi guys. What book do you recommend to understand the topic of series of functions? I need to see examples of uniform convergence. The teacher only does theory:(

[sudden kindle]

Uniform convergence?

[narrow talon]

Good (counter)example of uniform convergence is indicator functions of (0,1/n)

[thorny torrent]

geometry and inequalities?

[gray gazelle]

cheeger, ebin, comparison theorems in riemannian geometry

[gray gazelle]

Hey. What is the equivalent of Baby Rudin for linear algebra?

[sudden kindle]

Ebin was my professor

[gray gazelle]

[karmic thorn]

What do you mean by equivalent of Baby Rudin? I think Hoffman-Kunze might fit the bill in terms of being a dry, standard reference which does the job.

[gray gazelle]

I like Rudin as it is both wide and deep, it covers (real) analysis on undergraduate course, and I’m looking for a linear algebra book that I can study along with Rudin

I have taken and passed both analysis and linear algebra courses already, but I feel weak and I need to put in more work in them

[karmic thorn]

You could try Hoffman-Kunze, Friedberg-Insel-Spence, or maybe Axler?

[gray gazelle]

I’ll try the first one, I’ve looked up suggestions online and everyone compares it to Rudin

Thanks

[karmic thorn]

[gray gazelle]

i need very good chemistry regents book for noobs to turn into masters

[solemn rover]

I would like to recommend Algebraic Topology by Edwin Spanier.

[manic fox]

lmao

[clear sail]

recommendation for first measure theory text? hopefully easier to understand & with some lebesgue and probability measure in it as well.

[peak bear]

Hunger games if you haven’t read it yet

[past ice]

Have you ever looked at Peter Lax's book? Don't be afraid that it has the word "applications" in the title. It's one of the most well-balanced texts out there.

[worldly basalt]

Mathematicians are afraid of the word applications

[slim peak]

Here could be why :

Theory : Very cool and smooth 30-40 pages paper that gives a nice result under not so bad assumptions in some abstract setting.

Applications : awful, painful and heavily technical paper, with almost 100 pages, to check the assumptions of the above theoretical paper on a single relevant example.

It's entirely relatable

[gray gazelle]

I’m studying intro to numerical math and I’m dying

[quick hornet]

numbers are well-known to be fatal.

[sharp latch]

This is a fantastic quote

[gray gazelle]

Any good book that covers group and set theory? I'm still in high school so any book that covers the topic from ground 0 would be awesome

[solemn rover]

Someone recently recommended Judson's Abstract Algebra, which is freely available online. I learned algebra out of the book Contemporary Abstract Algebra by Gallian.

For set theory, idk. Maybe the first chapter of Munkres's textbook on topology?

There are lots of books on set theory, Paul Halmos's Naive Set Theory is one that comes to mind

[gray gazelle]

https://www.reddit.com/r/learnmath/comments/34t65n/high_school_can_anyone_suggest_an_introduction_to/

(for set theory)

The embedded hyperlinks don't take you anywhere

read the comments

some person responded with a bunch of books

I have the first book mentioned on that list (Naive set theory by Halmos)

[mint cloud]

I need Calc 3 textbook reccs plz 🥲💞

[gray gazelle]

folland

[mint cloud]

This one?

[clear sail]

.

[karmic thorn]

Some recommendations from a discussion earlier today were Folland, Stein and Shakarchi V3, Rudin RCA, Tao, Axler.

[clear sail]

thanks, thats alot of options

ill go with stein shakarchi cuz i heard of it used in our uni ig

[karmic thorn]

[marble solar]

I'm a huge fan of stein and shakarchi

[gray gazelle]

this might be a wrong question that maybe does not belong in this server? but are there any good java programming books?

nvm, this question fits in this channel, I saw it in the channel description.

[misty wyvern]

Java in a Nutshell by Evans, I guess. But programming in Java is a mistake.

I advise you to resist Java's legacy and switch to Python/C++.

[sharp latch]

C++ and python

[eager stump]

there's no necessary point in this if he's already invested in reasons for learning java

i know more c++ and python than java, but java was what i started with. still a useful language

[eager stump]

in terms of books, it depends on the aim. for algorithms i'd go for something more language agnostic like knuth or the mit press one (name escapes me right now)

[willow pecan]

Tbh books for learning programming languages are not that good

[hearty steppe]

woke answer

[crystal lion]

i’ve never heard of someone learning python from a book

[eager stump]

well here we are lol

you heard something new today

[crystal lion]

well i was trying to emphasize that it’s not very common

you learn to code by coding

[eager stump]

that's one way

[solemn rover]

i learned calc 3 from the book by stewart

[silver kindle]

...

[gray gazelle]

i learned c++ and python in a very funny way

reading 200 pages of a book

without writing a single line

well i wrote stuff in my head but not on a computer

not a good idea tho

[halcyon hornet]

Lmao.

[eager stump]

Hahaha, yea that's the complete other end of the spectrum

[halcyon hornet]

Anyone here has AoPs books?

[gray gazelle]

Maybe you are the computer

[halcyon hornet]

Please reply if anyone has.

[gray gazelle]

xd

[halcyon hornet]

?

[crystal lion]

I do

but I’m not showing y ou

[latent fox]

Any recommendations on books about Number Theory?

[cursive orbit]

Pinned messages has some, iirc

[marble gulch]

Knuth is language agnostic?

[hasty turret]

Yes

He creates his own pseudolang

[marble gulch]

Yeah, that's not language agnostic.

MIX is not my cup of tea.

[cursive orbit]

In that case, no algorithm books are language agnostic because they all need a language to precisely express the algorithm in

[marble gulch]

Exactly.

I want to see an algorithms book based on the lambda calculus.

[flint forge]

computability theory books are language agnostic

unless english counts

[marble gulch]

Well... a lot of books will pick a computational model and use that through-out.

For example, I learned computability from Sipser and he uses Turing machines and does not mention any other equivalent models.

[flint forge]

most computability books dont make much reference to turing machines explicitly

they just use english and vibes

and math notation

[marble gulch]

Computability books that use the lambda calculus are pretty rare.

I've seen mostly TMs or recursive functions.

[flint forge]

i dont see why lambda calculus would be useful

computability people genuinely describe their algos with words most of the time

[marble gulch]

Sure. But there is still a computational model involved.

[eager stump]

Sure, imprecise use of the term. I meant that you could be a cpp or java person and it's the same difference reading those

[brittle latch]

https://media.discordapp.net/attachments/244238376167800832/860481565838409759/Kagamihara_Nadeshiko_CPP.png?width=400&height=225

[willow pecan]

Why did you ping me

[brittle latch]

forgot to turn it off lol, just thought this was funny

[lyric oyster]

Has anyone read Napkin or "An Infinitely Large Napkin"?

[obsidian valley]

[crystal lion]

do yourself a favor and search "napkin" in this server

you'll see how well liked it is among this server

[narrow echo]

yes

[misty wyvern]

Anyone have special topics books they wanna shill? Grad+ level ideally, lightish reading when I'm tired of other topics.

[willow pecan]

Randall LeVeque's Numerical Methods for Conservation Laws

[misty wyvern]

Is this just a finite elements theory book

[willow pecan]

No

[wooden sparrow]

@willow pecan what's your book recommendation for linear algebra for first timers?

[willow pecan]

Friedberg

[lyric oyster]

@wooden sparrow Linear Algebra Done Right

[gray gazelle]

If you just want basic computation, Khan Academy

[gray gazelle]

If you want actual linear algebra, this

[misty wyvern]

what's your book recommendation for linear algebra for first timers?

Wikipedia

[lyric oyster]

Linear Algebra Done Wrong is also good

[wooden sparrow]

I tried it, it seemed a little 'definition, theorem, proof' and nothing else, kinda dry in my opinion

But I heard it's good

[willow pecan]

Ok

[wooden sparrow]

I mean, I read it a bit

Not a lot

Soo

[gray gazelle]

DTP books are great tho

[mint osprey]

Any good book/PDF on Calculus that includes exercices and solutions? (Please ping me for any answer! 😄 )

[woven spade]

#books-old

[mint osprey]

Thank you Tim

[lyric oyster]

@mint osprey Calculus by Spivak

[eager stump]

lmao dark recommendation, great book though

[mint osprey]

Thank you

I found this PDF ( http://teacherpress.ocps.net/cynthiaandrews/files/2013/06/Calculus-9th-Edition-by-Ron-Larson-Bruce-H.-Edwards.pdf ) a few mins ago, lot of exercices so I think I will go with that one but I will take a look at your recommendations

[eager stump]

Larson is ok i have that too. You should follow the links it has listed for more in-depth proofs though

especially the inverse trig functions or e it tends to skimp a little on the foundational stuff

i'm not a fan of theorem by rote

but the exercises aren't bad!

[mint osprey]

Okay thank you! I will take a look at Larson’s book 😄

[mint osprey]

Oh it’s the one I linked in my message right?

[eager stump]

correct, i'm not clicking on it but ron larson is the author yes

[mint osprey]

Great 🙂

[buoyant spire]

I really Like Anton's Calculus: Early Transcendentals

[inner mantle]

I am in alg1 (as of now) should I learn proof writing?

if yes pls suggest books

[eager stump]

alg1? hs? uni?

[cursive orbit]

You'll likely learn it (to some extent) in geometry anyways. It's not necessary for hs math in general though, except geometry. (Usually)

[inner mantle]

ok

[eager stump]

book of proof is great if you've never done any proof writing and you're interested in it, the author offers it for free on his website (hammack)

[inner mantle]

link

[eager stump]

i did not like high school math personally before i became acquainted with cool proofs

https://www.people.vcu.edu/~rhammack/BookOfProof/

[inner mantle]

lel I will learn proof writing for physics'

[eager stump]

i think it's fulfilling, though some people hate proofs

[cursive orbit]

From my experience with high school physics, it's just handwaving

[broken meadow]

small angle approximations

[eager stump]

π = 3

[inner mantle]

??

[eager stump]

it's a physics joke

[inner mantle]

Its not even 22/7

lel

[eager stump]

they just approximate everything

[inner mantle]

yeah

but still physics is lub

[eager stump]

yes if i had an extra lifetime...

i'd do experimental physics

[inner mantle]

I'd do quantum physics :)

Thats why I am doing math

[eager stump]

quantum is cool, yes lol it's one of the reasons i'm doing math too

but from the computing side for me

[inner mantle]

but calc is hard

:(

[eager stump]

i mean hard is good

hard means you get strong tools

[inner mantle]

yes

[eager stump]

and it's also thousands of years of accumulated wisdom

which is cool

archimedes is still as boss today as he was back then

[inner mantle]

I learn some trig from khan academy and maybe soom I will do AP Physics 1

internet sucks

[cursive orbit]

[inner mantle]

On khan academy

[cursive orbit]

I think the stuff in physics 1 can be understood a lot better when you've taken calculus, and at that point you could just jump to physics c

[lyric oyster]

Not if you have a good professor

[inner mantle]

https://www.khanacademy.org/science/high-school-physics/one-dimensional-motion-2/x2a2d643227022488:physics-foundations/a/preparing-to-study-physics @cursive orbit

[lyric oyster]

they'll make you use those kinematics equations

don't -dare- point out that these are derived from analysis

[cursive orbit]

I know the formal prerequisites, but some things that take like 60 minutes explaining if you just know algebra can be explained in about 10 minutes if you know calculus

[inner mantle]

oh ok

btw how much time does it take to cover from geom/trig to calc 3

including alg 2

[cursive orbit]

Depends on the person

[inner mantle]

like average

time

2-3 years?

[cursive orbit]

Including calc 3 and geometry, typically following the schedule of a regular school it would be around 4.5 years.

[inner mantle]

ohk

calc 1 is fine for ap physics 1

?

[cursive orbit]

My recommendation is to jump straight to physics c at that point

Physics C: Mechanics and E&M on-paper can be done with only a calc 1/2 background

However, E&M uses topics from calc 3 so that's quite helpful to have under your belt

[inner mantle]

well ok

[broken meadow]

well

physics C e&m does not strictly use ideas from calc 3

but it helps a lotttt

[lyric oyster]

Maxwell's equations are pretty solidly in the world of analysis.

[inner mantle]

oh k

so what abt physics 1 and 2 after alg2

And Physics C after calc

or precalc/calc1

[rocky hound]

As someone who took AP Physics 1 and 2 and currently self studying C Mechanics, I would say that having done Algebra 2 before going into AP Physics 1 made it easier for me since I was familiar with trig and algebra stuff. For Physics C (at least for mech not sure e/m), you don't have to have completed Calc 1 (I am just gonna say AP here cuz I am more familiar with that term), you don't have to have completed Calculus AB, you could be in it while also doing Physics C, because the calculus required for it is not that intense and is alright. That is just my personal opinion though, could differ from person to person.

[inner mantle]

thats what I thought after trig/geom, alg 2 I can do ap physics 1 and 2 and after pre-calc - calc(1-3) I can do Physics C

Physics mech as well as e/m

[rocky hound]

mhm yeah

[worldly glacier]

Can anyone please share the pdf link of Analytical Conics by Barry Spain?

[gray gazelle]

is it not on l*bgen?

[worldly glacier]

No

[gray gazelle]

sadness

[cursive orbit]

If you have the doi, try s*i-hub

[worldly glacier]

Sorry couldn't understand what you wrote

s*i-hub?

[gray gazelle]

• = c

[worldly glacier]

Oh,understood.Thanks.

It is not there too.🙁

Isn't there any other domain?

[coral narwhal]

it can be borrowed on archive openlibrary

[flint forge]

l*bgen

[gray gazelle]

they checked

[flint forge]

im braindead

[gray gazelle]

it's not there

[flint forge]

sorry

[gray gazelle]

how dare you

[late plinth]

has anyoen have experience with bartle's intro to real anal

and atkinson

intro to num anal?

was debating on to buy a physical copy or not

[frosty girder]

I am in need of a book on calc, with some theory
and a lot of questions, of different varieties and levels
please ping if someone suggests

[gray gazelle]

baby rudin has lots of questions variety and levels

[frosty girder]

what is baby rudin?

rudins book on calculus?

[cursive orbit]

Principles of Mathematical Analysis, by Rudin

[frosty girder]

[coral narwhal]

The book in sticker list

[frosty girder]

?

[frosty girder]

Oh yeah, got it lol

thanks

[hearty steppe]

hey shashwat you goin thru baby rudin too

[frosty girder]

i suppose, yeah

[hearty steppe]

if nyann is cool with it, we can add you to our study group.

[frosty girder]

[gray gazelle]

can i be in the group too ;-, i'm gonna continue read rudin again soon

[marble gulch]

I liked Atkinson's numerical analysis.

[glossy grove]

if you satisfy the axioms

[gray gazelle]

what are the axioms

[glossy grove]

first of all, do you have an inverse?

[gray gazelle]

for what operation?

[glossy grove]

I don't know, what kind of operation is equipped upon you?

[gray gazelle]

i have the very funny operation

i also do this a lot

it's very funny

[livid ermine]

what are the prerequisites for learning about modular forms

[sage python]

Probably some basic complex analysis

Depends on what angle you're gunning at though

[livid ermine]

https://www.reddit.com/r/math/comments/7cicqv/how_hard_to_follow_is_the_proof_of_fermats_last/ this reddit posts says you need modular forms to understand fermat last theorem proof

[sage python]

Oh if you're gunning for FLT you're gonna need approximately a metric fuckton of background lol

It kinda amps up as you go

I think the book you'll wanna read for modular forms is Diamond and Shurman

For that you'll want complex analysis (corollary real analysis) and algebra to start

Eventually you gotta start picking up algebraic number theory and algebraic geometry

And representation theory

[livid ermine]

elliptic curves and modular forms seem intertwined

is it necessary to read about elliptic cuves from a separate resource first?

[sage python]

Not necessarily first

Eventually you'll need both

The basic idea of the proof is

[livid ermine]

concurrently? or does diamonds book introduct elliptic curves itself?

[sage python]

You can do in either order I'd say

Or concurrently

I think DS talks about complex tori a fair bit but idk if it goes into the arithmetic of elliptic curves. I guess the aim is to state modularity so eventually yeah it does

You have objects called elliptic curves, namely you're thinking of solutions to y^2 = ax^3 + bx^2 + cx + d

Where the polynomial in x has no repeated roots

Now the trick is, given an elliptic curve you associate a certain type of object called an L-function

Modular forms also have these L-functions associated to them

If the L-function of an elliptic curve comes out of that of a modular form, you say the elliptic curve is "modular"

(Basically)

Now the strat for FLT is this

Given a non-trivial solution to the Fermat equation, you get an elliptic curve, called a "Frey Curve"

Turns out Frey curves cannot be modular

But uh

All elliptic curves are (this is the statement of modularity theorem)

Wiles proved a special case of this with some help from Taylor, and this case was enough to handle Frey curves

[winged gust]

Ahoy peeps! Would anyone have any decent recommendations for a combinatorics book for someone who wants to engage in some self study of it?

[tulip blade]

A walk through combinatorics.

[livid ermine]

thanks for that explanation

can you explain roughly what an L-function is?

i know basic analysis and algebra

although very little complex analysis

[winged gust]

👀

[winged gust]

This book looks great, it reminds me of "A Book of Abstract Algebra" in that specific topics are explained briefly, then a number of exercises are posed that showcase application of what was explained, then moves along to the next topic, rinse repeat. Seems like the author also goes into a few extra details and explanations. Thanks for the Rec!

[fading ember]

Any good book recommendation for algebra and clac, from basics to intermediate or even advanced, it’s been 2 years since I’m done with high school, would just like to revise and possible learn more as a hobby tough I’ve forgotten everything it seems that’s why I mentioned it being from the basics with a good amount of practice questions

[livid ermine]

langs basic mathematics

contains a lot of questions and gets up right before calc

[fading ember]

@livid ermine thanks I’ll look into it

[gray gazelle]

what do you need to know for tate's thesis?

almost done reading SS fourier analysis

know basic galois theory

[wraith sphinx]

Hello! I am interested in understanding this paper on topology: https://arxiv.org/pdf/1912.11324.pdf Will an introductory topology book be sufficient? I already have familiarity with space groups, point groups, and Laue groups. What do I need to know to understand the terminology and develop a visceral intuition of the named spaces and groups. A group theory textbook as well?

[misty wyvern]

On a scan it looks like an intro book like Munkres should be sufficient.

[near shard]

Take a look at Fourier Analysis on Number Fields by Ramakrishnan and Valenza, its a great introduction to tate's thesis that goes over a lot of the background needed

[wraith sphinx]

@misty wyvern Thank you very much.

[misty wyvern]

Is there a natural sequel to Aluffi's Algebra: Chapter 0?

[gray gazelle]

Algebra: Chapter 1

[hasty turret]

Algebra: Chapter X

X for unknown

[misty wyvern]

Lurie really do be the kinda guy to upload his textbook to arXiv

[karmic thorn]

[livid ermine]

isnt that enough algebra to look at more specialized topics?

maybe read an algebraic topology textbook and youll get to use the algebra you've learnt

[misty wyvern]

I was mostly curious what Aluffi had in mind for an Algebra Chapter 1.

But yes, it's basically more algebra than I've needed in my work anyways.

[livid ermine]

@misty wyvernhave you gone through the entire thing?

[fluid skiff]

How much algebraic number theory is needed to learn general theory of automorphic forms ? Also is there book which teach algebraic number theory through examples?

[near shard]

Marcus's Number Fields has a lot of examples, but you might like Murty's Problems in Algebraic Number Theory

It depends what you mean by the general theory of automorphic forms, the basics don't use that much, if any, algebraic number theory

[misty wyvern]

have you gone through the entire thing?

Never accuse me of reading a book again 😠

[uncut zealot]

Number Fields by Marcus is super accessible to anyone with a little galois theory

[livid ermine]

i've gone through the first 4 chapters and it took me 6 months

[misty wyvern]

My algebra quals class was Dummit and Foote, which I didn't like because they had entire paragraphs of text, so I picked up Aluffi for reference.

I don't think I've actually read a single textbook front to back.

And I literally don't remember learning linear algebra as an independent class at all, I just absorbed linear algebra from various fields.

[obsidian valley]

aluffi is pain

the exercises are very goofy imo

[misty wyvern]

Oh I don't do Aluffi exercises

[livid ermine]

in what way are they goofy?

[misty wyvern]

They're hard.

er than DF at least

[livid ermine]

are they? some people say they're all trivial, other people say they're relatively difficult

i think most of them are quite easy. and then some of them, especially the one with a negation sign are somewhat difficult

[misty wyvern]

Well if Alluffi is trivial then DF is immediate.

[lyric oyster]

Allufi is trivial?

[misty wyvern]

They're not much harder than what many schools would put in a qualifying exam but the standard here is DF

[livid ermine]

i mean, are they? aluffi is literally my first exposure to algebra so i have no reference.

[lyric oyster]

What is a good, but challenging text for a first-course in ODEs?

[misty wyvern]

Arnold?

[livid ermine]

i find they're ~medium hard

[misty wyvern]

VI Arnold's ODE book is probably the only one worth reading for a mathematician.

Otherwise you're better off going into deep theory like Taylor's PDEs

Or alternatively picking up some physics methods book to get the computation skills to solve a bunch

[lyric oyster]

I don't know if I'm big-brained enough for that.

[misty wyvern]

Nobody is big-brained enough for it

[lyric oyster]

I might try Arnol'd

lol @ some person's review of the text "Well differential equaitons [sic] are all about change, and this book changed my life. I read this more than 30 years ago, and all the mathematics I know, I mean really know, I learned from this book. Along with Aristotle's ethics, it is probably the most important book in my life."

[manic fox]

lol

[gray gazelle]

Has anyone read Cassels Local Fields?

My prof suggested it as an option before reading Fourier Analysis on Number Fields but the typesetting is so unappealing lol

[near shard]

You could try Serre's local fields as an alternative, the material of the two books is pretty similar from what I remember

[marble gulch]

Yeah, monospaced math is unappealing...

[gray gazelle]

i think serre's is a lot more algebraic than cassels which has stuff about p-adics, haar measure, and stuff

[cunning kestrel]

Any good book on application of cal?

[manic fox]

california is not very applicable, i'm sorry.

[eager stump]

kek

[nimble isle]

Hey everyone, I just graduated from high school finishing with my highest math class being Calculus 2, and my college is requiring me to learn calculus 3. I going for a pure math major, and I have studied introduction to proofs and bit of linear algebra (mostly computational calculation). I was wondering if their any good textbook that incorporate calculus I, II, III, so I can recap the calculation of 2 and learn for 3. I was going to buy Strang book, but after discussing yesterday with more experience member in the chat, I learn that his books are more computational/applied then proof written. Is it a good idea to still go for Strang book, or is their another book that more efficient for me to study as a person going to in the pure field?

[broken meadow]

start with Friedberg linear algebra, maybe

friedberg is more theoretical

[cursive orbit]

Uhhhh

[broken meadow]

only one chapter involves matrices

[cursive orbit]

Are you asking for a linear algebra book or a calc book?

[broken meadow]

^ this too lol

if you want a proper "calc 3" proof based textbook i think it's calculus over manifolds by spivak

which needs a firm understanding of linear algebra

[cursive orbit]

Because Strang has a calc book too

[gray gazelle]

folland advanced calculus

[broken meadow]

oh

[cursive orbit]

Analysis 1 + Analysis 2 by tao might go over calculus rigorously, but that's probably over the level you're looking for.

[broken meadow]

im dumb they asked for textbook for calc 1,2,3

okay

ignore me

[nimble isle]

cal book

[karmic thorn]

Analysis 1 and 2 is absolutely accessible if you've seen calculus before, and are familiar with the basics of sets, functions, relations.

[cursive orbit]

Anyways I'm pretty sure at most universities "calculus" is going to be mostly computational calculus anyways, and "advanced calculus" or "analysis" or "real variables" is going to be the theoretical side of that.

[nimble isle]

Yea, I have learn little of that from the Book of Proof, By Hammack

So should I just go for analysis book then since cover calculus and it goes deep into proofs?

[cursive orbit]

So CoM or the analysis books by tao might be worse than something like Strang for preparing for calc 3, but it might be better for preparing for a math major

[eager stump]

you know it doesn't hurt. maybe don't expect to fully get everything

especially for major yes

it's got good writing

it won't help you for calc 3 tho like aplhyte said

[hasty turret]

imo the Wikipedia page on LA is more useful than strang

[eager stump]

hahahhaha

[cursive orbit]

Lmao

[eager stump]

the book or the lectures

[hasty turret]

Book

[eager stump]

agreed

[cursive orbit]

I mean Wikipedia is sometimes hard to digedt

[eager stump]

the lectures i like personally, for what they are

[nimble isle]

Alright, so just to confirm, I should check out CoM or the analysis books by tao, they are not cal 3 heavy, but they will help me in the long run.

[crystal lion]

lol CoM is a brutal recommendation for someone who just finished Calc 3

[nimble isle]

I don't even Calc 3 yet, so should I not check out CoM?

[cursive orbit]

CoM seems really concise

Which means it's probably not the best for readability, especially if you don't already know linear algebra

[gray gazelle]

com will eat your ass if you aren't familiar with linear algebra

[crystal lion]

he goes over all of first year linalg in 5 pages

[nimble isle]

Alright, thanks for the recommendation everyone, I probably going to go for Strang to a least get start on Calc 3, and then check out your analysis book once I fully finish both calc 3 and linear algebra.

[broken meadow]

this is true tterra

literally the first set of exercises taught me more about inner product spaces than the whole chapter in friedberg

its lit tho

😼

[storm harness]

😼

[gray gazelle]

[broken meadow]

(this is a joke)

i learned a lot tho when i shared the problems here and u all said interesting things about it

[gray gazelle]

go do 1-10

[broken meadow]

i already did that set

i am on the second segment

reading heine borel rn

took me a few days to digest+ busy

gonna try to hit 14 and 15 tonight

[gray gazelle]

[manic fox]

first time i learned about dual spaces was from a CoM exercise

🧠

[crystal lion]

axler anyone??

[manic fox]

no

[gray gazelle]

determinants!!!!

[manic fox]

if you use or recommend axler i politely request that you eat shit and die

[crystal lion]

gallian and axler both have nice colors

[manic fox]

sully bait

[eager stump]

axler is hot

[manic fox]

more sully bait

[cursive orbit]

I recommend axler

[manic fox]

death calls to you.

[eager stump]

the title is maybe pretentious. but it's not wrong

[manic fox]

oh nooo determinants!!!!

pedagogically horrible!!!

[crystal lion]

exactly

that’s the spirit

[gray gazelle]

[crystal lion]

admittedly axler could have introduced them maybe a little earlier

but it’s still a masterpiece of a book

[cursive orbit]

Axler has those lectures too

[crystal lion]

if you don’t like axler you don’t like math.

enough said

[broken meadow]

https://tenor.com/view/stare-cat-confused-confused-look-serious-gif-16884211

[manic fox]

literally me rn

ty metal

[cursive orbit]

Axler is good

[manic fox]

i am seething rn

[broken meadow]

idk what all this hullabaloo is all about but everyone involved needs to chilllllll

[manic fox]

coping, even

[broken meadow]

its fineeeeeeee

starting first problem in second set for com

it looks hard

will learn much

[gray gazelle]

1-14 is literally just

check that R^n is a topological space

[broken meadow]

jk

it just had a lot of words

looks are deceiving

[crystal lion]

closure on finite intersections

sounds familiar

[gray gazelle]

[manic fox]

sounds wrong

[broken meadow]

the empty set is open right

[crystal lion]

it’s not though

[broken meadow]

moment for dumb questions

[gray gazelle]

yes

[broken meadow]

cus vacuous truth

[crystal lion]

not to melia

[gray gazelle]

it is open

[manic fox]

the empty set is also closed 😎

[broken meadow]

pain

[crystal lion]

is the glass half empty?

[eager stump]

oof

big hitters

[manic fox]

is the glass

[broken meadow]

glass 😋

[eager stump]

the

[manic fox]

is

[manic fox]

true

[crystal lion]

is the discord embed empty or is it just not loading?

[broken meadow]

ok nevermind 14 is weird

maybe i am bad at definitions

or this looks too easy to be true

except im probably gonna struggle with finding a counterexample for infinite intersection case

hmm

ok if i keep working and talking ill move to some other channel

what is this subject

is it not yet topology

[manic fox]

move to #chill