book-recommendations

[fallow creek]

in engineering its a little more subdued

idk how to describe tho

ill drop a pic

[steel patio]

Oh so you think lol

If you want to expand on those idea you could look into intro to real analysis books

[molten mason]

Also did that person basically just ask for the full math undergrad curriculum worth of books

[fallow creek]

lol literally

[gray gazelle]

I mean yes, I’ve read a real analysis book

But like, to learn trig at the level of a “trig course/book,” you really just need that their a parameterization of the unit circle & euler’s formula, and pretty much everything else follows

[steel patio]

Thought you were the one asking the question wrong my misunderstanding

[fallow creek]

*bc i feel like once you get here then you can get more into vectors

[gray gazelle]

😭😭😭

[fallow creek]

trust

textbooks will do a lot more than u think

i only read like actual literature for more physics/philo type stuff

[molten mason]

Yeah prealgebra, algebra 1, geometry. Algebra 2, trigonometry are separate courses in middle school and some high school

But all 5 of those classes are basically combined in "college math" or "college algebra" course at college-level, which overlaps a lot with pre-calc.

[gray gazelle]

This also varies between schools and between students. I took precalc and calc in high school, but we covered more in those classes because my hs had a lot of students accelerating and such

Or, at least in precalc

[molten mason]

Half of those are like 2nd or 3rd year university subjects.

Tough math books, just the whole AoPS collection. Basic Mathematics by Lang. Ane any calculus book written after 1950.

There's not much else to tell you.

Just go to library or used book store or something and start browsing.

[molten mason]

Yeah

[gray gazelle]

Thanks a lot
Buying a ussr Olympiad book ig

[molten mason]

Those work too

[steel patio]

If you like to compete consider looking at materials related to the Putnam exam. I was never able to take it in college because it was always during my finals week but you can take it as a freshman in college. This is HARD tho. When my friends and I asked our mathematical structures teacher about book reqs, he said “how to prove it” (our class book) and math maturity were sufficient enough

[molten mason]

HARD is an understatement from my understanding lol

[steel patio]

Our real analysis prof told us it’s either the median score is 0 😂

[remote vortex]

Median I can believe

[glad rampart]

Yeah it’s the median

Average would only be 0 if every single person scored 0

[remote vortex]

I've had exams like that...

[gray gazelle]

Richard Feynman topped that putnam ig

[gray gazelle]

Thanks a lot mate, thanks a lot

[earnest wolf]

oh, what subject was it?

I have a class where only 3 out of 200 ppl have a score strictly greater than zero

consistently, for ~3-5 years I think so far

[hearty steppe]

So are there texts/resources that build on learning Lie algebras/lie theory on categories/category theory/topos? One that wouldn’t be too rigorous to approach 🤔

Like not purely theoretical but thinking of application

[glad rampart]

I’ve heard spivak is harder but better if you can handle it

[fallow creek]

stewart is classic

id get both

id read stewart first tho

or j cross reference

as u go

[frank roost]

Hi, I wanted to ask about book recommendations. My course has recently covered intro material in all the symbols, bijections, cardinality, and partitions (quotient sets), equivalence classes, Cantor-Bernstein-Schroder Thereom, etc. My teacher said "There seems to be a lot of interest on epsilon-delta proofs and "stuff that is useful in real analysis". So, we can go in that direction starting next week. This will also give us the opportunity to talk about metric spaces, graphs, and topology."
Is there any books anyone would recommend, something beginner friendly if possible?

[steel patio]

I took a graduate graph theory course that was graded purely on three tests consisting of 5 question and 1 extra credit question. A B+ was 30% and above. To get an A+, it was anything above 80%.

[earnest wolf]

chapter 3 from Understanding Analysis by Abbott?

altho idk how graph theory and eps-delta is connected

[remote vortex]

Yeah, Abbott is solid

And graphs are indeed only tangentially related to analysis (at least at basic level), it's much more discrete mathematics.

[frank roost]

Yea it’s more of a discrete clas

But my prof seems to like to teach stuff that isn’t usually covered

Like we learned about quotient sets, but we didn’t learn about partitions

[earnest wolf]

wait whut

metric spaces [...], topology

anyway

[graceful moon]

They only study the discrete topology

[frank roost]

Maybe I should just wait for lecture — trying to get ahead cause I was falling behind last week.

[sage basin]

what do people here prefer as a text for getting into commutative algebra?

[remote sparrow]

yes

[remote sparrow]

@dapper root

[dapper root]

My favorite is Matsumura commutative ring theory

Undergraduate commutative algebra for a gentler intro

[sage basin]

thanks :DD

[plucky dragon]

oh smart people slide LA .pdf plz

[terse garnet]

Henlo

What a good book on game theory

without using like advanced math

[novel obsidian]

Is there any supplementary text you'd suggest for reid?

[dapper root]

I think it’s fine on its own

[novel obsidian]

I believe in chmonkey

Thank yoy

[dapper root]

At some point you need more, and then you can use Matsumura

[mint haven]

Hi people. Any over-explanatory book for basic math and pre-algebra?

I want things as simple and intuitive as possible.

[terse garnet]

precalculus

stitz and zeager

it has an algebra review

at the end

[molten mason]

What the fuck

[earnest wolf]

was not joking at all.

[molten mason]

What class

[earnest wolf]

the guy just 'checks ur deep understanding'

and theory questions he asks during the oral exam (for all classes we have oral and written exams, where oral usually covers the theory) are never 'by the book'

Like, he tries to see if u get the underlying idea. Why things work the way they work

[earnest wolf]

discrete math

[earnest wolf]

in our case it's ZFC, automata theory and algorithms on graphs

[heady ember]

Did I hear set theory

[torn crypt]

How do so many people falter

[molten mason]

I mean I do that with my students too, but mostly in a way that can improve their score. I try not to be an asshole.

Do people still get decent grades at the end of the term or is that something everyone has to explain when they apply to grad school lol

[trail hemlock]

wait that sounds so cool

i wish we had that

[molten mason]

Say sike right now

[trail hemlock]

anyone read kafka's Metamorphosis ?

someone told me to read but i dont trust this mf

[marble solar]

Kafka's work is very interesting

I've read most of his works, and its been very memorable for me

[trail hemlock]

is it interesting? i dont mind disagreeing with it so long as its interesting

[marble solar]

I think it's interesting. He has a collection of short stories you can try before metamorphosis

Orson Welle's directed a film adaptation of Kafka's "The Trial"

[gray gazelle]

What’s a good introduction to analytic number theory for someone who’s read Ireland & Rosen?

[marble solar]

I did cry reading metamorphosis, it was just a very sad story for me

[tribal crow]

@wicked fractal

[molten mason]

Was required reading in my Writing/English 102 class

[trail hemlock]

i will def check out the short stories and Metamorphosis

thanks

[trail hemlock]

lucky 🥺 my teacher never gives us interesting books

[molten mason]

100% of our readings for those 16 weeks were Kafka. Our instructor had a real boner for him.

It's probably for that reason that I don't care for Kafka, but memorable is a good word.

As is interesting. Very interesting writer.

[trail hemlock]

hmm

sounds interesting ill def check out his work

[marble solar]

Yeah, he seems to have been a very polarizing writer

[molten mason]

We're used to polarizing writers in this channel

[remote sparrow]

@crimson leaf how are you finding conway's Functions of One Complex Variable?

https://home.gwu.edu/~conway/

btw conway has a website

[crimson leaf]

I haven't read as much as I'd like (about to finish up the topology stuff) but it's nice good explanations the problems aren't too hard but aren't too easy at times either. Sadly I got an international Springer edition when I thought I was getting a standard Springer paperback so the print quality is bad. I like how he just goes ahead and proves everything I looked ahead a bit and it seems like you could almost use this as a good analysis review lol. I also like how even when he doesn't prove something it's usually left as an exercise

Oh he also has exercises at the end of sections which I prefer

[lusty ermine]

does all real analysis books talk about relations?

[trail hemlock]

everything reminds me of her 🥺 😭

salgos stop sullying me 😭

[remote sparrow]

all of them talk about functions, which are special cases of relations. hence all real analysis books talk about relations

[quick hornet]

i dont think my real analysis book explicitly "talked about" relations, it just assumed you knew what an equivalence relation et al. was

[stoic nova]

I didn't know you had written a book on 'real analysis', really curious now.

[quick hornet]

i mean the book we used in class lmao

i have not written any books

[civic python]

Baby rudin!

[stoic nova]

Ah, sorry for the misinterpretation

[gray gazelle]

refer a modern discrete math book for that

real analysis books just establish terminology and notation with these basic topics and doesn't really explain it thoroughly enough as it is assumed that you are already familiar with these concepts

[lusty ermine]

why do they do that

[gray gazelle]

The topics that you need to focus is : Set Theory, Relations and Functions, Basic Logic (Propositions, Truth Tables, Logical Operators, Quantifiers, etc), Partial Ordering, Induction, Recursion, etc

[gray gazelle]

they assume that you are already familiar with it

going over these topics shouldn't take much time

I would assume 2 weeks is sufficient

or maybe less

in fact, the definition of convergence uses logical quantifiers

and you need to know how they work

say you wanna negate the definition and find the defn of divergence

in any case, good luck!

[lusty ermine]

im trying

[stray veldt]

relations just appear everywhere in math

you cant talk mathematics without it

[lusty ermine]

didnt knew , sorry i am new to math

[stray veldt]

though you dont need a full book to explain that; the ideas are very simple, the set theory definitions are just a bit obscure

there are "intro proofs" text that teach this

some very long (velleman is popular), some very short (i wrote one myself that is pinned in #proofs-and-logic)

[lusty ermine]

? can. u link me up

[stray veldt]

my favorite one is actually this: https://math.hawaii.edu/~pavel/Aluffi_notes.pdf

its still reasonably short and covers surprisingly advanced concepts already in the later chapters

[lusty ermine]

will read this to supplement my introductory real anal exercises, thx.

[deep nebula]

So, I have completed Serge Lang's Basic Mathematics. am i ready to start calculus? or do i need something else?

and if i am, what book should i start with?

i thought about spivak, but people argue it is too difficult for a first course.

[young lily]

im 6th grade. not that im aroggant but i adapt, or learn fast. is there any book that teaches basic math for 7th-9th grade?

[hallow oriole]

use khanacademy for all the middle school/high school math you dont know, no use getting a book for it

[haughty cypress]

is the book of proof a good book

[molten mason]

If you completed Basic Mathematics, Spivak would be fine.

Remember a lot of people here have done Spivak. There's all the help channels to help you with the exercises of you get stuck. Utilize the #calculus channel if you need a concept explained or need help understanding Spivak

[deep nebula]

thanks!

[slender cargo]

It's fine for a first course. Honors Calculus classes just tend to go fast with the book, which is what makes things difficult.

I personally don't think you need to get Stewart's book if you are using Spivak.

[molten mason]

@deep nebula we have this conversation here every week so you can use the search and find the past convos, but just keep in mind Spivak only covers Calc 1 and Calc 2. You'll have to get another book no matter what for Calc 3

And which book, absolutely does not matter.

If you liked Lang at all, he also has a Calculus book (Calc 1 and 2)
and a multivariable Calculus book (Calc 3)

[molten mason]

Apostol

[earnest wolf]

ig u r

what language do u speak tho? (there is a book I have on mind, but it may not be available in English)

[molten mason]

But why the double ping

Yeah it's 100% worth it but by the time I convince myself to drop $300 on both volumes I'll be in a retirement home lmao

[deep nebula]

I am going to be honest - I am not good at going through multiple math books at once, I will probably pair spivak with lectures (maybe based on Spivak itself, or something like professor leonard's)

yeah... no

[deep nebula]

I dont have any plans on learning multivariable calculus, i am only really doing calculus for the sake of doing it, my main goal is linear algebra.

[deep nebula]

I can only speak english 😦

[molten mason]

You'll get similiar answers in this channel. Calculus is calculus. Taking the derivative of a polynomial hasn't changed. Its the same as it was in 1924 and 1824 and 1724.

All the textbooks are the same. Apostol, Spival, and Kitchen are 3 authors that are rigorous.

Thomas, Stewart, and Anton are 3 authors that are more modern with tons of computations and applied mathematics example like from biology, engineering, etc.

Of course the first 3 authors have tons of problems, and the second 3 authors have some rigor to them if you self-study but not through a school class.

You can literally pick any calc book and you'll end up the same.

If you want a cheap alternative to Apostol and Spivak, Kitchen is $40 through Dover books.

I think Kitchen only covers Calc 1 and 2 though, single variable calc.

Lang has a good multivariable calculus book from what others have said but I haven't gone through it personally so I have no idea.

Also for everyone going through Calc. Use this as a study aid.

https://tutorial.math.lamar.edu/

[deep nebula]

i used it while going through serge lang's book for some extra problems, so fun.

[molten mason]

I have a physical calculus textbook from 1994 by Howard Anton and it's literally the same shit as my 2020 calculus by Stewart.

You can probably go to a used bookstore or thrift store and pick up an old calc book

[molten mason]

Professor Leonard is Bae. I used his YT lectures lol

There's a ton of resources for spivak. You'll be fine.

He needs to hurry up and upload linear algebra. The people are waiting

[covert mauve]

when you realize his last video talking about him coming back was posted a year ago:

[molten mason]

He posted in the comments the new videos should be done by the end of the semester

I think that was October..... lol

[fiery lichen]

@everyone hello

[gray gazelle]

Bumping this question from last night

[tribal crow]

I will ping @wicked fractal once again for his reccs lmao

[wicked fractal]

What do you want to learn regarding analytic number theory?

[gray gazelle]

More on dirichlet series, as well as elliptic functions and modular forms

[wicked fractal]

Have you tried Apostol's first book on analytic number theory? If you have then you probably can start with his second book which has an emphasis on modular forms and Dirichlet series

You don't really need to finish the first book in order to start the second one. The first one glosses over Dirichlet series as well but the second one is more in depth

[gray gazelle]

I have not, but it looks like it has a fair bit of overlap with I & R’s coverage. Is the approach different/are there chapters I could skip over?

[wicked fractal]

Yeah there might be chapters that you can skip over

First chapter for example

I think fifth chapter as well

[gray gazelle]

Cool, thanks

[wicked fractal]

[slender cargo]

If you want rigor and proofs then I think Spivak is the most popular one.

And I know one professor who thinks Spivak has much higher exercise quality than Apostol.

So in my biased recommendation I say go with Spivak

I don't think Thomas is at all needed if you go with Spivak.

Another option though is to just go through Khan Academy's calculus stuff and then pick up an Analysis book. Or use Thomas and then pick up an Analysis book.

A big challenge with Spivak (I'm not sure about Apostol) is that he gives no introduction on proofs. He just throws you in (gently).

[slender cargo]

You don't need both. One is enough. For proofs, here:
https://www.people.vcu.edu/~rhammack/BookOfProof/

If you find Spivak opaque and mysterious at first, but want to keep going with it, then you can look at the above to get a better handle on proofs.

@gray gazelle Can I ask, are you preparing for college, or is this something to do in your own time?

[molten mason]

I looked it up thinking those were key words or topics of the book.

Wow what a title lmao

You'll get all the experience you need with each new class, mostly being Real Analysis.

After/During calculus you can do Linear Algebra. The book by Friedberg, Insel, and Spence is also proof-y and will help you in your developing proof journey

[tribal crow]

what title

[gray gazelle]

“Modular Functions and Dirichlet Series in Number Theory”

[pliant wadi]

Any suggestions for a book on history of algebra or sth

By algebra I mean abstract algebra

[cobalt arch]

There is a history of algebra by van der waerden and modern algebra and the rise of mathematical structures by corry

The former I think is a history of algebra in general but a very good one

[golden orchid]

I have a background in alg top/geo and physics now i want to learn about complex geometry but I haven't taken any complex analysis courses, is there any books that distill the concepts and ease my way to complex manifolds?

[slender cargo]

Oh wow. Okay. Well, have fun!

[queen sail]

yo bois

any coders round here

any good books

bout python

can u tell me 1

I ain't beginner

am c++ mostly

hope to learn another language

messed around a bit

and made a calculaotor

thx

[fallow cypress]

Sorry Discord only allows people who are 13 or older to use it

Oh they already got banned oops

[trail hemlock]

what the hell 12 year old is reading spivak

im cooked

[gray gazelle]

I'm going to start this

any advice on how I should go about it?

my first time approaching anything with proofs

[safe barn]

Any very in depth books on sequences? Like more in depth than real analysis usually covers

[slender cargo]

Just read through the book and do enough problems to feel comfortable with the material. That's it

er I assume you are referring to the Book of Proofs?

[gray gazelle]

yes

[slender cargo]

Are you self studying or in school?

[gray gazelle]

Does your college use book of proofs or do you know any courseware that does?

[gray gazelle]

I will learn it in uni, but I want a bit of a headstart

[slender cargo]

Oh okay

So you will take a class on learning proofs soon

[gray gazelle]

I want to get accustomed to the transition from computational --> proof based

[slender cargo]

I don't really have advice beyond just read the book and do problems.

Do you plan to ever take Number Theory?

(Elementary Number Theory but it's usually just called Number Theory)

[gray gazelle]

hopefully yes

idk if my college offers it

[slender cargo]

Ah okay. Well, just work through the book like normal, yeah.

[gray gazelle]

^ Response to this btw?

[slender cargo]

I never went through the Book of Proof myself. I just linked it because I know it's decent and free.

I learned proofs through a Discrete Math course.

What's important is just getting used to doing proofs in chapters 3 and 4 of the book. Understanding the symbolic logic is nice, but I don't think much in terms of symbolic logic when doing an actual proof.

[heady ember]

Took me a couple hundred to a thousand hours to get somewhat decent (?), and I'm still learning regularly. So, don't be too discouraged if you feel slow.

No second is wasted if you're thinking about math.

[crude sage]

Thanks! I suppose if it's good enough to prepare for GTM lang then it's good enough for me

[junior isle]

I went through it and I think it really helped with my mathematical maturity. I did most of the odd numbered problems and some of the even numbered ones.

[pliant wadi]

thanks!

[stray veldt]

hans wussing is (was :() the main expert on history of algebra

sadly the only translated into english writing i know is https://mitpress.mit.edu/9780262231091/the-genesis-of-the-abstract-group-concept/

there is another book called "4000 years of algebra" which recounts the entire history but im pretty sure its only available in german

[violet shuttle]

vast majority happen in 200 years

[silk plover]

what book should i read as a beginner to math, ive only taken up to geometry in school and i want to learn more before high school

[stray veldt]

you can just follow khan academy

[violet shuttle]

@molten mason you still recommend basic mathematics?

[molten mason]

Always but it depends on the person. I recommend it for adult learners and motivated high schoolers who want to study university-level math one eventually.

OP sounds like a regular middle schooler. Any textbook, khan academy if it suits them.

[rigid forge]

feel like I hate serge lang for having very opinionated thoughts about what should be included and what shouldn't be, but love him for actually introducing things the right way. like, he actually proves the quadratic formula for example, which definitely makes a better mental model compared to my school teachers, because I know it isn't some magic formula and just derived from basic algebra.

[still panther]

well thats more of a deficiency on your teachers' part rather than an advantage for lang

we proved all the formulas in my class for example

[rigid forge]

sure, maybe it is, but proofs are not common at all here. even in my textbooks, most proved theorems/formulas are from geometry rather than algebra.

[molten mason]

Yeah that's fair

[vital bane]

welcome to the math server

[heady ember]

Mfw someone reads Hartshone at 14

[vital bane]

13*

[heady ember]

1

[rigid forge]

opens the book and reads one page there you go, thats me!

[novel sluice]

That's genuinely terrifying

[remote ginkgo]

no its not

its good, good job kid

[remote ginkgo]

only counts if that page is from chapter 2 or later

[gray gazelle]

kids beating adults these days

[chrome abyss]

good book on group theory? id say im pretty much new to the subject

[slender cargo]

What's your goal? Will you be going to college eventually?

Or just for some recreational self study?

[chrome abyss]

im a physics senior, just never got introduced to it formally and im seeing it now in my research and qft studies so i wanna get ahead of it and not be confused when i see it. Also it seems to be very useful just being knowledgable with it

[remote sparrow]

there are many "group theory for physicists" books

but you can always pick up a book intended for math majors

[earnest wolf]

idk abt physicists, but books like «[a mathematical topic] for programmers» are full of šħ||į||ț, unfortunately

or maybe my sample size was too small

[sage basin]

My high school algebra teacher taking a lesson to prove the quadratic formula was the thing in my life that made me care about math as a discipline I think

Most teachers in the US don’t have the time/permission or perhaps even knowledge to do proofs in their lessons but he was like “I have 20 years of experience as a college professor so if they fire me for ‘wasting time’ I’ll just get a job somewhere else”

[lime vessel]

Notice that this algorithm consists of n steps. For each k, the time taken in the kth step is independent of n. Therefore, this algorithm is O(n)

[earnest wolf]

huh?
U mean like independent of n != constant?

[lime vessel]

No like

[earnest wolf]

or at least O(1), if not constant (may differ a little)

[lime vessel]

It's dependent on k

[earnest wolf]

So why on earth when this thought crossed my mind I kindly rejected it as something not important, but now that you wrote it... Yeah

[earnest wolf]

<@&268886789983436800>

afraid to open the link, but looks very sus — those two messages are the only ones he sent on this server

[hallow oriole]

bible-jesus-kulfy-telugu-బిల్-gif

[fallow cypress]

it seems to just be a gif of the bible

@split willow please don't post gifs in this channel, it's for serious discussion of book recommendations

[fossil crescent]

Would it be easier to go through Tao's Analysis books if I complete Spivak's calculus first? Or should I jump straight into them?

[split willow]

It was a gif of the Bible

[split willow]

The Bible is a real serious book dude

[split willow]

Moderators ban this guy!! HE HAS SUS gifs🤓🥸

Reading the Bible will change ur life

[glad rampart]

Does anyone have any suggestions for gay romance novels? Specifically woman and woman

[fallow cypress]

I don't think Spivak is necessary

[remote sparrow]

sure, it would be easier. but tao's analysis books only assume you've taken the regular calculus sequence. so you can jump right into them if you want.

[molten mason]

Not me going through Category Theory for Programmers

[rigid barn]

#advanced-number-theory message

[cobalt maple]

Recommendations for graph theory and combinatorics for a pure math grad student?

[crimson leaf]

Graph theory by Diestel and Emumerative Combinatorics by Stanley

[gray jungle]

diestel book is very good, i 2nd this

[cobalt maple]

Thank you

[quaint wadi]

I'm trying to understand Koszul complexes of algebras, are there any recommendations for this? (Preferably a little hand holdy and concrete)

My ultimate goal is as a computational method for Hochschild cohomology

[rare tundra]

Im trying to start from where i left off at i got done with foundations of alegbra. And i wan to learn all the way from where i left off to trig, caculus and more advanced stuff

my ultimate goal is to get to a really good level of math to make up for what i lost in time any books?

[glad rampart]

I’ve heard good things about langs basic mathematics

[chrome abyss]

what books/subjects touches on slater determinants, im working with hartree fock equations and theyre composed of everything i dont know. So anything helps, i just want to be able to go through the process of deriving and finding their solutions without getting stuck

oh also, i keep seeing a disgusting amount of integrations, whether it be in my books or tryihng to do any research, is there a book that just goes into the many types of integrations/derivatives? One that goes through the problems and gives shortcuts? anything of the sort?>

[acoustic raptor]

Which abstract algebra book is better: Lang or Dummit and Foote?

[next condor]

I'm going to start studying Analysis and I'm torn between using Abbot's book "Understanding Analysis" and Cummings' "Real Analysis: A Long-Form Mathematics Textbook." I've read the first chapter of both books and still can't decide because they both seem great. Does anyone here have a deeper knowledge of both books and could give me a suggestion? Which one would you choose and why?

[daring lake]

I honestly love the way Jay writes. It's informal, witty, but still conveys information he wants to. I haven't read abott but I think both more or less cover the same (looking at the TOC). I don't think you should be missing out much with Jay. If you want, you can just back it up with Bartle or Rudin.

+Jay's book is very cheap too

Although, I have seen many refer Abbott too, I will say it kinda boils down to preference since both are aimed at first time analysis learners.

[normal sandal]

any recommendations for an algebra reference? for context, I'm looking to refresh my algebra knowledge over the summer: I've had first courses in group theory and ring + field theory (no galois theory yet), so I'd like smth that does modules + galois theory and isnt too quick?

also looking to follow a grad algebraic geometry course so w/ my current background could I already look at an alggeo book?

[daring lake]

Dummit & Foote

[vital bane]

Abbott

it teaches you how to write proofs as well

by having you prove stuff yourself by having exercises be basically like guided proofs

[heady ember]

[vital bane]

[short violet]

any books just for to chill and

[slender cargo]

As someone who has had Jay Cummings assigned for a class: I think Abbott is more carefully written (at least in the integration section). Jay Cummings book does have a lot of exposition though, which is neat. I feel like you could use that book with zero knowledge of Calculus. If you feel solid about your Calculus knowledge, then I would lean towards Abbott.

[hasty crown]

funny surname

[next condor]

I'm currently studying calculus using James Stewart's book (I'm at the limits section) because it's more intuitive and user-friendly. However, I'm also looking for an analysis book to solidify my understanding of calculus fundamentals, and it should be beginner-friendly as well. I've already completed Velleman's "How to Prove It," so I feel more confident in writing proofs now. Therefore, I believe I can handle studying an analysis book alongside my current calculus learning. Since I haven't covered all aspects of calculus yet, it might make more sense to start with Jay's book.

[slender cargo]

Then yes, I would go with the Jay Cummings book. You might also consider Spivak's Calculus.

[next condor]

Wouldn't Spivak's book be too formal? I prefer to reserve the rigorous formalism for an analysis textbook and opt for a calculus course that emphasizes intuition and doesn't focus so heavily on strict rigor (considering that the more formal approach developed long after the inception of calculus).

[slender cargo]

Both Spivak and Jay Cummings are as rigorous as one another, and I think Spivak is chatty as well. But yes, the Jay Cummings book is more chatty and has a bunch of dialogue that makes the book appear more friendly.

[next condor]

Oh, okay, I had thought you were suggesting I replace James Stewart with Spivak.

[slender cargo]

I don't think that's a bad suggestion if you want to do the Analysis part right away, which is basically what you are considering doing with picking up Jay Cummings book. If it were me I would just focus on going through Stewart's book first (assuming this is self-study), or I would just go through Spivak's book.

[next condor]

Uhmm, interesting.🤔 So, this could save me time. Yes, I'm learning as a hobby.

[slender cargo]

Yes. And a big reason for why I would consider Spivak is because he has a full solutions manual, where as Jay Cummings does not. His book is also carefully written.

[next condor]

Excellent, I'll look into getting Spivak's book. I came here hoping to make a decision, but now I have another book to consider 😂 . Nonetheless, that's a positive outcome!

Thanks @slender cargo

[slender cargo]

Yep, no problem. If you've already completed Velleman's How to Prove It then I think you'll take the book just fine.

[molten mason]

Abbott has solutions on Quizlet Plus if you're self-study.

[chrome abyss]

what type of book would slatar determinant fall in?

[next condor]

I also found, a few days ago, the book 'Understanding Analysis Solutions' by Ulisse Mini and Jesse Li. By the way, I discovered this wonderful math discord community by reading the preface of this solutions manual. Here is the link: https://www.uli.rocks/understanding-analysis-solutions/main.pdf

[slender cargo]

I like Abbott (I sometimes reference that book for my class) but I don't think it's a good book if you have not gone through Calculus yet. Abbott won't teach you the physical intuition, and some stuff like the Substitution Rule for integrals is left as an exercise, which has its own chapter in Spivak.

[remote sparrow]

Galois Theory by david cox is a good standalone book on galois theory

[remote sparrow]

on cummings' website, hints and solutions to select problems are provided

[sterile remnant]

a mathematics textbook? slater determinants can usually be found in the context of physics books, more specifically quantum mechanics or condensed matter books

[chrome abyss]

oh i seee, ill look for condensed matter book then, thank you

[remote sparrow]

#book-recommendations message

[sterile remnant]

i think the quantum mechanics book by Stephen Gasiorowicz has some things on Slater determinants

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-031-24228-1

[sterile remnant]

As for this previous question, my personal experience is that there's no standard text book on group theory for physicists and most are very difficult to get through because the "group theory" physicists use is actually Lie Groups & Algebras and Representation Theory, which is quite a few steps further after the standard group theory that is typically taught in standard undergraduate mathematics students.

[chrome abyss]

hmmm okay, i will just get through group theory and work my way from there then, dont wanna just skip to the boss

[sterile remnant]

are you interested in theoretical physics

[chrome abyss]

yep

[graceful moon]

Dummit and Foote or Artin are pretty solid for basic group theory, there’s loads of texts that cover the basic well though

(Not Jordan and Jordan though, that book is awful, I got it for £3 and I still feel ripped off)

[sterile remnant]

ill send a few recs in a bit

[molten mason]

Oh nice

[sterile remnant]

@chrome abyss From a physicists POV, I would suggest something like http://abstract.ups.edu/index.html for a quick introduction to abstract algebra (group theory), i.e. chapters 1-6, 9-12 and optionally 13-14 (the rest you can leave and read if required in the future). This specific resource is short, introductory and doesn't go deeper than necessary but is still a mathematical text. After this you'll have some of the prerequisites needed to tackle Lie Groups.

If you're fond of mathematics and interested in theoretical physics, it'll also be useful to learn some basic stuff on topology and smooth manifolds. My suggestion (again, from a physics POV) for a short introduction to topology is chapter 1 of https://books.google.gr/books/about/Topology_and_Geometry_for_Physicists.html?id=TNvCAgAAQBAJ&redir_esc=y

After that, a mathematical resource for smooth manifolds is John M. Lee's "Introduction to Smooth Manifolds" (chapter 1 is most you'll need for now, but most of this book is important for theoretical physics), which also has a chapter defining Lie Groups (chapter 7). After that, you should be able to understand what you're actually dealing with and most textbooks on "group theory for physicists" will not be as scary.

I am not sure about a resource on representation theory but basically all "group theory for physicists" books deal with it.

If you are an undergrad, a good book that utilizes group theory is Jakob Schwichtenberg's "Physics from Symmetry", which essentially construct the full standard model in a classical level (no QFT, although i think it gives a glimpse) and is very eye opening.

Another fun, eye opening book to read is Stillwell's "Naive Lie Theory". This is an undergraduate text in mathematics and you could read most of it even if you're not familiar with topology. It gives a very different perspective compared to other approaches I mentioned, so definitely give it a try!

[remote sparrow]

+1 for judson

pinter is good too

although it's poor as a reference since many things are developed in the exercises

[chrome abyss]

wow, ive added them to my list, they all seem incredible, abstract algebra specifically, that book looks like a pit of knowledge thank you thank you so much, i appreciate this so much!!!

im doing research and i want to branch off into the theory so i need to learn what i am actually telling my program to do, these will surely bring me to the next level once im done with them
(could be a year lol)

[next condor]

Man, are you familiar with Richard Courant's two-volume Differential and Integral Calculus books? Do you have any opinions about them? I bought them at a used bookstore months ago, and I was just checking here; the prices for Spivak's book are way too high for Brazilian standards.

[slender cargo]

I have heard that Richard Courant's books are great and that they compete with Spivak's book. That's about all I know.

[violet shuttle]

how did you know

most people that ask about topology are older than that

and didn't i establish that i a 83 year old 3rd grader?

[mystic orbit]

bruh, that was a year ago

[violet shuttle]

... I'm sorry, diagonalization and determinants before inner products? determinants, perhaps

[mystic orbit]

I don't know what you're referring to, I don't think the kid knew what topology is, I think I said that purely from the way he talked

[violet shuttle]

wait what

no that was just now in my unreads

[mystic orbit]

2023

we're in 2024

[violet shuttle]

what the fuck

it actually just looks like i somehow landed at a year ago

[remote sparrow]

https://www.amazon.com/Calculus-Variable-Dover-Books-Mathematics/dp/0486838064

have a look at this book

it's much cheaper than spivak or apostol

[graceful onyx]

Does anyone have Strang’s 6th ED of Introduction to Linear Algebra, just tryna see how it bares compared to the older, if it’s worth $80

Fairly new so no reviews unfortunately

[gray gazelle]

So howard anton calculus how accurate is the answers and is it a better alternative to stewart

[oblique hatch]

What’s a good book for learning about differential Galois theory?

[magic kite]

Best book for introduction to complex algebra? (Algebra after linear and Calculus)

[hallow oriole]

do u mean abstract algebra?

[molten mason]

It's a good alternative. "Better" is subjective to the reader.

If you're having trouble with an answer being right or wrong you can post in #math-discussion or #calculus

You could probably google and find an errata. Every edition is different.

[gray gazelle]

@molten mason good to know because found it.for 5 dollars 🙂

2nd ed

[molten mason]

Damn mine is 4th and I thought that was old lol

[gray gazelle]

It still have scribbles.and highlights all over plus needed a portable calculus book that wasnt heavy lol

Lang will be my precalculus and anton my calculus

[gray gazelle]

Any good introductory books on the topic of finite automata?

[gray gazelle]

The first chapter of Sipser is pretty good

I see, thank you

[novel hound]

You could check the ToC and preface on the official website: https://math.mit.edu/~gs/linearalgebra/ila6/indexila6.html

[magic kite]

Yes

[gray gazelle]

Are there any good undergrad math textbooks that were just released in recent years (2023-2025)

[stray veldt]

2025 👀

why this restriction?

there are good undergrad math books released most years

[gray gazelle]

I was just asking for a friend

[graceful moon]

I’m dropping the hottest UG maths textbook ever next year just you wait

Magnus Metric spaces is good but I think that came out in 22 so maybe that’s not recent enough for you

But as loch said, I don’t see why when it was published really matters all that much for most topics

[stray veldt]

im sure the notices of the AMS or similar include a review section of recently released books

[gray gazelle]

I see, thank you

[stray veldt]

im reading the notices of the german mathematical society and those always include half a dozen or so reviews of recently released books, many of them for undergrad topics

[karmic thorn]

Looking for a reference on representation theory (of algebras or groups, the latter being preferable) that gets into induced and co-induced representations

Standard books often go over induced representations, but I'd like something that does co-induced representations as well and tries to address the general (functorial) formalism

[rare tundra]

i need a book to teach me stuff all the way from algebra to trig to caculus matrix algebra and stuff any good books?

[gray gazelle]

I doubt one book will cover all of that (at least not well), but multiple certainly will. For elementary algebra and trig, Basic Mathematics by Lang. For calculus, depends on what level of rigor you want, but Stewart is a good (easier) option, and Spivak is a harder one. For linear (“matrix”) algebra, a non-rigorous book would be Strang, whereas Halmos, Axler, or Treil are all good rigorous and comprehensive options

[rare tundra]

the basic math by lang doesent seem to cover trig

[gray gazelle]

Chapter 11 is on trig

[sterile remnant]

"Use this channel to ask for book recommendations. Tends to be mostly math but feel free to ask about other literature (YMMV)"

[sweet ingot]

Yall should read Math Wizo’s books he’s a math author. The only books he has are calculus statistics and algebra. They help you in the beggining but not for advanced stuff like algebra 2 calculus 2

[pulsar pollen]

Books on geometry?

[trail hemlock]

what kind of geometr ?

[sweet ingot]

The cartoon guide to geometry 😭😭😭

[trail hemlock]

oh nah

[pulsar pollen]

Plane geometry

[sweet ingot]

The cartoon guide to geometry 😭😭😭

Ig

[trail hemlock]

no

[sweet ingot]

…

[trail hemlock]

flatland 😭 😭 😭

[trail hemlock]

aops geometry is what i used.

its a little difficult but very fun

[modest owl]

any recs for quantum computing texts

the notes for my course suck so bad

[sage python]

Chuang and Nielsen seems to be the common rec

[hallow oriole]

people seem to proselytize abt that book

i saw someone say the first chapter “taught them the singular true essence of linear algebra” and was “a life-changing experience”

[deep moat]

What're some good geometry books?

that I can find online?

As of the moment, I am referring to AoPs geometry.

[trail hemlock]

aops geometry 😍

[trail hemlock]

"Geometry Revisited" is avaliable online,
for olympiad prep, people sometimes refer to "Geometry: A Comprehensive Course"

[molten mason]

I just saw that today at the store lmfao they have a calculus one too

[trail hemlock]

is it any good?

drop the rec frfr

[tribal crow]

#book-recommendations message

[junior isle]

Advanced Linear Algebra

[trail hemlock]

get him an advanced lin alg book R N!!!!!!

[heady ember]

Roman

[daring lake]

[violet shuttle]

no, over K^n where K might not be ℝ.

[tribal crow]

do you prefer to denote a field by K, or F?

[violet shuttle]

K, k. if extending, E.

K i used to use for the algebraic closure

let K = k^{a}

F seems wrong to me

Probably because it looks like a function

[tribal crow]

fair enough

[violet shuttle]

"the notation should be functorial w.r.t. the ideas!" - lang, referring to
k^{a}
k^{ab}
k^{sep}

k^{norm}?

[bright epoch]

K because of the German

[violet shuttle]

wait what

[stray veldt]

Körper

compare with french corps

the name originates in german, the french translated it correctly, english failed

[bright epoch]

Tbf field kinda works

[stray veldt]

it doesnt fit

the word ring is used to refer to a collection of things/people (compare with crime ring) and the word body is used similarly (think student body)

thats why those names were chosen

so group, ring, body are all in the same spirit

[vital bane]

just use R for fields

because linear algebra is field invariant

[heady ember]

Mf acts like inner products don't exist

[tribal crow]

all inner products look like the dot product anyways

[coarse arrow]

Best introductory graph theory book with difficult problems

[novel obsidian]

I like the name field because it gives the image of being able to frolick freely, similarly, you can do (almost) wahetevrthefuck operaiton you want in a field and you'll be okay.

[wintry cove]

Some recommendations for number theory and math proofs?

[next condor]

I have three books on how to write mathematical proofs, and I'll rank them from best to "worst" in my opinion: "How to Prove It" by Daniel Velleman, "Proffs" by Jay Cummings, and "How to Think Like a Mathematician" by Kevin Houston. Velleman's book changed my life; I always struggled with proofs, and it was only after carefully studying this book that I managed to solve my problems with proofs.

I don't have a lot of experience with Number Theory books. I'm currently studying an introductory book on the subject, but it's only available in Portuguese. I'll leave it to others to assist you with that.

[wintry cove]

Thanks for the advice

Math proof is something I always had struggle with

[trail hemlock]

should i use spivaks calculus on manifolds or munkres analysis on manifolds?

[covert zealot]

Many linear algebra texts sadly cause students to conflate basis vectors with n-tuples. The benefit of Dirac notation is that vectors are properly abstracted so all books covering quantum computing have the benefit of a nice exemplary introduction to linear algebra from an abstract mathematical perspective.

[next condor]

I'm also interested in the answer to this question. 👀

[earnest wolf]

I mean, basis vectors are whatever you want them to be

As long as they are, hm, vectors (we can add them, multiply by a constant etc)

[remote vortex]

And every finitely dimensional vector space over a field F is isomorphic with F^n, so vectors (basis and otherwise) are identifiable with tuples of elements of F

That said I do prefer the approach that generalizes more easily to non-finite dimension, but on the other hand the higher level of abstraction can leave learners lost at sea

[covert zealot]

I think they key points are isomorphic and identifiable, and the key distinction is "not the same". Particular confusions arise when students think about basis change but forget the representations are isomorphic but "not the same" as the vector itself.

[marsh ingot]

Lee intro to topological manifolds then Lee intro to smooth mainfolds

[trail hemlock]

darq alt spotted

is there any reason why?

[marsh ingot]

Ppl usual recommendation plus I read almost the intro to smooth manifolds

[molten mason]

#book-recommendations message

There's also this:
https://maa.org/press/maa-reviews/introduction-to-proof-through-number-theory

[trail hemlock]

ty

[stark turret]

what books on libgen are good for real and complex analysis?

[tribal crow]

er, we can't discuss piracy here

if you want recommendations for RCA, just ask for that instead

[stark turret]

Ah

Can I have a book suggestion for RCA that is 10+ years old and not its most recent edition?

[remote sparrow]

zorich is a good source on multivariable calculus

also hubbard

alternatively you can learn measure theory and then do multivariable calculus

see schroder or browder

#book-recommendations message

[trail hemlock]

yes i wanna do this

sour drop my goat 💯💯💯

[grand thistle]

i mean rudin i guess

[trail hemlock]

except i’ll do em at the same time fuck it

[grand thistle]

folland works too for real analysis

[stark turret]

thanks

[trail hemlock]

ahlfors still recommend or no?

just curious

[grand thistle]

ahlfors is old tho

i mean i guess rudin is also relatively old

idk ive never used ahlfors

but i heard it's good

[trail hemlock]

i’ll prob go folland

[remote sparrow]

you need to specify whether you mean folland's Advanced Calculus or Real Analysis: Modern Techniques and Applications, which is a measure theory book

also the latter book only has two editions

presumably he wants a book that's gone through 5+ editions so he can pick up an older edition for cheap

none of the books suggested meet that criterion

[grand thistle]

wdym

it has 2

rudin rca has 3 editions

idk what ur talking abt cuz

if u want 5+ editions then u probably wanna look at just intro calculus textbooks

i doubt theres many books with that many editions at this level

[gray gazelle]

A book full of algebra questions

[distant spear]

anything similar to Steen & Seebach's counter examples in topology, but for algebraic topology?

[pastel star]

i am in grade 10th please suggest me a beginner book on advance maths

[remote sparrow]

krantz's Real Analysis and Foundations and brown and churchill's Complex Variables and Applications meet these criteria

[sacred goblet]

Rd Sharma

[covert mauve]

Is there a quick guide/ebook/article on getting started with latex? something that covers enough for my math notes.

[native cradle]

SL Loney's plane trignometry is good

[remote sparrow]

https://www.overleaf.com/learn/latex/Learn_LaTeX_in_30_minutes

https://tobi.oetiker.ch/lshort/lshort.pdf

[covert mauve]

thanks

[remote sparrow]

does it have to be prose or can it be a graphic novel, and does it need to primarily focused on romance, or can it be incidental to the plot

[glad rampart]

Hmmm

I’d prefer purely text, and mostly focused on the romance

[molten mason]

Sour Drop really is a humanoid library

[gray gazelle]

can you recommend a book in general research skills , such as literature review , or citations system?

[graceful moon]

The song of Achilles is good but that’s not a gay story though not WLW so maybe of less interest

Worth a read either way imo

[glad rampart]

I’ll look into it

[remote sparrow]

citations systems really vary according to which style your professor or institution requires of you

you can look at style manuals for say, mla, apa, or chicago styles

however for the most part you don't need to read them

instead you can look at something like The Little Seagull Handbook

https://www.amazon.com/Little-Seagull-Handbook-Exercises-Update/dp/0393888967

you can also look through the purdue writing lab

also, ask your local librarian

they are specifically trained for this

some even have masters' degrees in library science

[gray gazelle]

mmmh very interesting , thanks a lot

so , I should look for some writing skills on the topic

[remote sparrow]

there's also a little program for managing citations called zotero

[gray gazelle]

library science , that's about knowing how to find resources such as texts books, etc , right?

[remote sparrow]

i guess

[remote sparrow]

The Little Seagull Handbook gives general tips on how to conduct research

[gray gazelle]

thanks , i will chek it

[covert mauve]

I guess this is a weird thing to ask, but is there a good article on the history of linux? i mean like: how the kernel was originally made, how distros were introduced, how the graphics stack evolved, how we went from x11 to wayland, what de(s)/compositors/window managers came and went.

[patent brook]

Might not be what you asked but I'd like to share it, you might want to watch one of those old Bell Laboratory documentary on UNIX. It details the philosophy behind UNIX and so on, with Ken and Denis present in the vids

It's interesting

[covert mauve]

sounds cool, will check it out, thanks!

[ruby spindle]

Where can i read basic mathematics by lang for free

[dusk wind]

probably the internet

[trail hemlock]

we here at the mathematics discord server do not condone internet piracy of any form (help the DMCA has my whole family hostage)

[rain stream]

Has anyone ever used one of those books written by a committee?

My university's library has a place where you can donate books and take books

I got a precalc book by COMAP: Consortium For Mathematics and Its Applications

[molten mason]

It absolutely amazes me how often people ask for something in here that's the first result on Google.

The same time it takes to ask in here is the same time it takes to just use Google

[rain stream]

I also got a McGraw-Hill Glencoe Geometry book that I got for dirt cheap in a mint condition, but I haven't read it yet, except for some sections

Idk if this is the best chat to have book discussion, since it's a recommendation channel.

[remote sparrow]

i'm pretty sure i used that book in 8th grade

i don't remember much about it but my mom donated it to a library fairly recently

[rain stream]

It's divided into lessons, and it's written by a bunch of people, so it has less personality, I'd say

It's more structured in the sense that the exercises are divided into different sections. It's a bit weird, but I liked it a bit

I saw a teacher on reddit saying he didn't like those committee books, I think

[molten mason]

Yeah it's often college students or recent grads, and often they all write a chapter or portion of a chapter without speaking to each other and then the editor tries to seam it all together.

Fun times.

[rain stream]

They don't seem bad overall. The Glencoe Geometry book was written by a bunch of teachers

And a bunch of people related to math teaching(meaning they're chairmen of whatever related to math at whatever place)

[molten mason]

Before calculus all the books are honestly more or less the same.

Calculus has two major groups. The books within each group are roughly all the same.

It's not until after Calculus that book choice really matters.

[rain stream]

The only problem with this book is that it's analytic geometry

And I wanted the good old euclidian geometry

[harsh smelt]

You should use the Cambridge second edition

it’s General

[rain stream]

I have a plane geometry book that's proof based, this Glencoe one and big and rigorous book on analytic geometry. I think I'm good now lol

[harsh smelt]

ok

[remote sparrow]

https://www.amazon.com/Monstress-Book-One-Marjorie-Liu/dp/1534312323

https://www.amazon.com/Monstress-Book-Two-Marjorie-Liu/dp/1534323147

good graphic novels i read last week

[violet shuttle]

what are they?

also imo even after calculus as long as you chose a book that is "standard" in some sense you'll be fine

[halcyon wasp]

Is Etingof exercises supposed to be difficult

[molten mason]

1. Regular: Anton, Stewart, Thomas
2. Rigor: Spivak, Apostol, Kitchen

[molten mason]

"You'll be fine" yeah I agree with this. I just mean the authors seem more varied in what they include, their approach, their notation, background required, etc

[violet shuttle]

oh duh

[violet shuttle]

yeah the main thing is just "is it TeX'd?", difficulty level, "does the table of contents miss something you want?"

[molten mason]

My flowchart is simple.

Did Lang write a book on it?
Yes: Pick it.
No: Skip the subject. Not important

[violet shuttle]

what if it's a theorem by lang

[halcyon wasp]

Did Lang wrote about algebraic geometry

[molten mason]

Yes

[halcyon wasp]

Oh

Man got everything

[molten mason]

But not in a Lang book?

[violet shuttle]

yup

[molten mason]

Blasphemy

[molten mason]

There's actually one major math topic that he doesn't have any books on. I can't remember off the top of my head but I know I've looked like 3 times lmao

[halcyon wasp]

Let me guess, combinatorics?

[gray gazelle]

Yes, actually

[heady juniper]

I was already helped in another channel determining a way of getting closer to Algebraic Geometry. I don’t want to rush learning advanced topics, just trying to decide the most reasonable book by Lang to continue with. I’ve only finished Basic Mathematics and some of Calculus by Lang.

He has so many different books. Undergraduate Algebra, Algebra, Linear Algebra, Introduction to Linear Algebra, etc.

If I’m sticking with Lang, which I’d like to do, which of these books would be a natural progression? I’d like it to be proofs-based and good foundations overall for undergrad algebra as a stepping stone toward Algebraic Geometry.

Thanks 🙂

[gray gazelle]

Linear algebra is probably the thing you should learn most urgently

[remote sparrow]

the bourbaki group never cared for mathematical logic and axiomatic set theory

[heady juniper]

Thanks!

[molten mason]

Yeah there's:
Introduction to Linear Algebra
Linear Algebra
Undergraduate Algebra
Algebra

Pretty much in that order

[molten mason]

That was one of their main things

Did someone write Analytic Number Theory and then delete it?

[tribal crow]

mhm

wasn't me

[molten mason]

Anyway yes I think that's the correct answer

[tribal crow]

wait but

did Lang write one?

[molten mason]

I've been on a NT rage lately.

He's a fucking number theorist.

Wrote a big book on algebraic number theory. Nothing on analytic

[tribal crow]

Deltoid would not be pleased

[molten mason]

At least Apostol has that covered

[nimble dragon]

Thanks bro appreciate it

[swift musk]

Can anyone suggest a book which covers the following topics

1. Euclidean space, basic topology
2. Limits and continuity for multivariable functions
3. Directional and partial derivatives
4. Taylor’s formula and local extrema
5. Measure theory
6. Multiple integrals
7. Curves, surfaces, hypersurfaces. Lagrange multipliers
8. Vector fields, potentials and line integrals
9. Differential equations and Cauchy problems
10. Linear differential equations – Gauss-Green formulae in R2
11. Gauss-Green formulae in R3 – Stokes formula

[remote vortex]

A book with a chapter on Tuition Free Week might not be easy to find.

[swift musk]

hahaha sorry my bad

[glossy zealot]

That is a lot to be covered in a book?

[still panther]

most "handbooks" in an area are written like that if I understand you correctly

[remote vortex]

I mean it's mostly real analysis in one and more dimensions

[swift musk]

some people are coping up well with it but some like me aren't 🥲

[still panther]

its about 20 topics, each about 50-100 pages or so, each written by an expert in that respective topic

[swift musk]

but yea if someone finds a book which goes through these topics It will be appreciated 🙂

[marsh ingot]

I dont think there is just one book

[swift musk]

damn

[violet shuttle]

... what's a Gauss-Green formula?

[marsh ingot]

I saw it on complex analysis context

Or it was Cauchy-Green...? Mmmm

[gray gazelle]

Browser’s mathematical analysis has pretty good multi variable and measure theory chapters, and covers most of these topics, either directly, or in exercises

[graceful moon]

I presume divergence and greens theorem, I’ve seen the divergence theorem called Guasses theorem

[nimble cliff]

any books with a section / that is dedicated to introducing modular arithmetic? preferably with a BUNCH of practice questions

[gray gazelle]

Ireland & Rosen

[swift musk]

legend thanks

[graceful moon]

Isn’t Ireland Rosen the graduate version?

[violet shuttle]

no, Legendre's work doesn't tend to be covered

[marsh ingot]

Lol

[gray gazelle]

Yes, but there aren’t any prereqs for the first 6 or so chapters

An undergrad can definitely read it

[graceful moon]

Rosen also just has a very basic NT book though, I’m guessing if they’re just looking for modular arithmetic that would be more appropriate

[proper prairie]

I’m working through baby rudin right now, Are there any other books that’s I should read after completing it?

[gray gazelle]

Depends on what you want to do

You can study more real analysis, switch to complex analysis, or topology, or learn some abstract algebra

There are pinned messages in this channel which give recommendations for each

[proper prairie]

I think I’d study more real analysis then move to topology, Thank you so much.

[gray gazelle]

#book-recommendations message

[vast jackal]

How to know the units in dimensional analysis

[graceful moon]

This isn’t really the channel but it’s just algebra, you treat the units as a variable like you would x or y in an algebra problem

[vast jackal]

I'm in 7th grade lololol

Is there any better explanation other than khan's video to teach some 5 minute video for dimensional analysis?

[main hill]

Hello there! Anyone here fan of Leithold?

I have a question regarding his calculus textbooks. Which version do You guys recommend? Are any major (or minor) differences which I need to know about?

[plush inlet]

Anyone have any recs for L-function material that is more introductory than Analytic Number theory by Iwaniec and Kowalski?

[violet shuttle]

It's actually just abstract algebra.

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

you have fundamental basis units

and a dimension matrix that makes new units out of them

since we think of, say, kg meters, we need to take the log to turn this into linear algebra

so q1...qn are n vars in l basis dimensional vars

M a l×n matrix giving a variable in terms of the fundamental vars

e.g. if q1 is kg m^2 then M =
1
2
in the kg, m basis

scaling the basis by \alpha_i will will change the logs of q by -\alpha_i

so log q's - M^T log \alpha's

which is an action of l-dim space on n-dim space

we require that a "physical law" be invariant under this action

and a physical law is one whose kernel is the permissible set of values

[jade rover]

Does anyone have any recommendations for books on pre calculus trigonometry? I have 0 experience with trigonometry

[jade rover]

pls

[valid bluff]

I know you are looking for books, but in all honesty you will learn better using Khan Academy. Though, I have found that Precalculus (5th Ed.) by Stewart, Redlin and Watson is quite good.

[jade rover]

okay

thank you

do you know if the individual trig course of khan academy will cover the same parts of the trig part in the pre calc course

[gray gazelle]

Any recommendations for studying equidistributions? Number theory related.

[wicked fractal]

Yes definitely

https://link.springer.com/book/10.1007/978-1-4020-5404-4

I love this one

I also recommend reading articles and new papers on it

It has the famous Erdos Kac theorem which I found describe as "nontrivial statistical shenanigans"

[rare tundra]

I need to learn everything from algebra 1 and 2 to trig to linear alegebra to calculus to trig to geometry but all the books I’ve gotten recommendations for are just way too advanced they just explain a rule and expect you know know what to do with it the rule is just a number and stuff I need something solid for straight up beginners I also can’t seem to remember anything I have to use it to memorize it

[ruby spindle]

what books other than basic mathematics by lang to prepare for calculus

refresher for everything

[gray gazelle]

Maybe axler precalculus or gelfand algebra. Dont onow the full details, I'm still going through them

[main hill]

I remember somemody mentioning over here some site where You have answers/full step by step solutions to many textbooks? I believe it was a paid site with some membership/subscription options. Does anyone recall what was it?

[gray gazelle]

I know a free one but full of ads

it is called litsolutions

[main hill]

Thanks! Let me try that one!

[remote sparrow]

chegg

[pure briar]

Does anything along the lines of a course that teaches from elementary arithmetic to endgame math exist (with good pedagogy and not cringe)?

[quasi umbra]

https://web.archive.org/web/20140116122708id_/http://www.math.wayne.edu/~isaksen/Expository/carrying.pdf

[pure briar]

This appears amazing so far

[slender cargo]

er... are you trying to find such a book for yourself to learn? or just curious?

[pure briar]

Learn math from the basics, though this definitely presents elementary math in a way that's quite refreshing I must say

[slender cargo]

But you can't understand that article if you're learning from the basics

I don't think any singular course exists that teaches everything to get to "endgame level". Better to just go look at a university's pure math major requirements and then find related books

[pure briar]

If there was a way to have the "learning everything" tag and it exists, then that'd probably be me in some capacity. I'm touching on things from all three levels of math in my current research.

At the same time, my highest level of education from any public school (or "school" in my case) is Geometry and Precalculus.

Quite the hindrance

Bruh I don't have time to look for good courses 😔

ncatlab?

Discrete mathematics, complex analysis. Having just got into complex arithmetic, I can't believe on how much I was missing out. I am now addicted to making sure everything works over the complexes.

Here is my latest Desmos workspace in which I've been doing some research. You can ignore some of the clickbait stuff I have at the bottom there as I just thought the stuff from Wilson's theorem was quite interesting and looked oddly familiar. https://www.desmos.com/calculator/897rcgqwmc

Should hopefully give an idea of what I'm limited by

My whole complex analysis knowledge consists of just learning yesterday about the basics of applying the elementary functions to complexes 😁

Can I not post images in here?

I haven't used differential calculus enough to retain the formula for differentiating polynomials, and I'm saddened by the lack of an equally simple means of finding closed forms for indefinite integrals.

Extend in what sense

as opposed to 3d

Yeah I've heard of quaternions but I'll probably get into that later if at all.

As opposed to mining the ideaspace for more realities

What I'd really like to be able to accomplish is perfect algebraic freedom in closed form and constant time

Well, constant time*

Today I solved $x + y = xy$ and $x + y = \ln x + \ln y$, and thought a bit about $x^2 + 1 = 0 \pmod y$.

[hasty eagle]

Andrew Porter

[slender cargo]

@pure briar If you want to learn more about higher level math then you should look into the common foundational topics - Analysis, Algebra, Topology/Geometry.

There's a reason why these subjects are required of all math graduate students, at every university.

[pure briar]

The issue is filling in the gaps in my knowledge, let alone knowing what those gaps are and where to fill them in.

[slender cargo]

You fill those gaps by starting with books dedicated to the foundational topics.

You have too many gaps right now to even begin addressing any single issue unless it's minor.

So just pick up a foundational book and start reading.

[pure briar]

I hate to sound picky, but is there a set of books/courses that will not torture me with excessive use of analogies like 3b1b and treating things like they exist in a vacuum per the wisdom of public school? Something like Dr. Will Wood perhaps?

[slender cargo]

3b1b is just a popular math Youtube channel to my knowledge. Have you taken Calculus?

[pure briar]

Nope

[gray gazelle]

Basically any actual math text fits these criteria

[pure briar]

Which I've enjoyed reading considerably!

[gray gazelle]

What have you read?

[slender cargo]

Okay, then that's a place to start. You could look into Spivak's Calculus.

[pure briar]

The stuff I've found looking for a way to best approximate $\Gamma(z)$ has been quite interesting, though I need to dig up those papers again (among other things).

[hasty eagle]

Andrew Porter

[pure briar]

I mostly just read stuff on Wolfram Mathworld and browse the OEIS

[slender cargo]

This is not an effective way to learn.

Start with books instead.

[pure briar]

You don't say 😅

[slender cargo]

I assume you will take Calculus at some point through a course?

[pure briar]

Technically I don't. What I understand of it is that it's the analytic continuation of $n!$ to the complexes and that it is the only solution to $f(x+1) = x f(x)$.

[hasty eagle]

Andrew Porter

[gray gazelle]

holomorphic solution*

[pure briar]

Over for me 💀

[gray gazelle]

You should read spivak’s calculus

[pure briar]

Yeah, welllll... I mean I have particular goals in mind, but at the same time I also want to get good at math to not only improve my algorithm finding capacity but just to enjoy it more as well and not have to rely on Wolfram Alpha as a crutch for anything beyond the extent of high school algebra and arithmetic.

iirc a partial derivative is differentiating with respect to one variable when more than one variable is present?

The derivative is very simple conceptually, as is the integral.

Everyone just sucks at explaining it

[gray gazelle]

How would you explain it then?

[pure briar]

The derivative is the slope of the line tangent to a curve at a given point, and the integral is the surface that satisfies the continuous motion of some $f'(t)$ as time increases linearly and is also the area under $f'(t)$

[hasty eagle]

Andrew Porter

[pure briar]

Two sides of the same coin

[gray gazelle]

Is that not the explanation you’ve found elsewhere? Seems fairly standard

[pure briar]

Everyone seems to neglect what I said about the integral.

[gray gazelle]

Also, the latter definition is more accurately called an anti derivative. The integral is (in the one-dimensional case) the area under the graph of f

[pure briar]

Ah

[slender cargo]

I'll just note that all of this is simply an intuitive view of the integral and derivative. If you read a Real Analysis book, you'll actually learn it rigorously!

[pure briar]

Yeah suffice it to say that trying to prove things from first principles is... lengthy

[slender cargo]

If you want to grasp math at the "higher end", there's no way around that.

[pure briar]

I mean nothing I guess. It's just that all the places I've seen it described, everyone relates it to area rather than as the solution to the motion described by a vector over time.

[gray gazelle]

That’s because their talking about a different thing than you

[pure briar]

It would be faster if I had more knowledge of theorems on hand (not to mention would help me in my research considerably perhaps).

[gray gazelle]

What research?

[slender cargo]

You get that knowledge... through books.

[pure briar]

Am a software engineer. I work with plenty of discrete mathematics, usually of the binary variety as you can imagine 🙂

[pure briar]

I just kinda figured things out myself and also used the references as needed to find the stuff that I've found so far, but again, like I said...

[slender cargo]

You work in assembly? Or do you mean, like, if else conditionals?

[pure briar]

I program at any level. I can make a computer do whatever I want given enough time and documentation.

[slender cargo]

Okay... since you have not taken any math beyond precalculus, I assume you got a software engineering job without a computer science degree?

[gray gazelle]

Well, that strategy isn’t going to work if you want to actually understand, for example, the gamma function. Read some books

[pure briar]

My circumstances are unique. I won't get too much into it, but suffice it to say I'm working on a big project that I wouldn't be able to work on if I had a regular 9-5, and correct, I do not have a degree in computer science, or any degrees for that matter.

Mostly software, but I still have to write standard library functions, so both I guess 🙂

Well I need to strengthen my foundation, and I also need to learn a considerable amount to find the closed forms I seek for the algorithms I want.

[slender cargo]

Sorry for prying. I'll just say that I think it would be good to instead of pondering all of these random questions and searching scattered sources, just read some books. And I asked because I was a professional software engineer. I'm definitely not confident enough to say I can program a computer to "do whatever", but sure, I guess with unlimited time one could learn how to program a kernel.

[pure briar]

The closed forms I want in general are those that take a constant number of operations and symbols excepting transcendental functions in themselves, and specifically that those closed forms are as minimal as possible meaning you can't use fewer symbols and operations to represent them in closed form.

These are useful for finding optimal approximations as you can imagine.

[slender cargo]

At least you have the rugged wisdom to read some books.

[pure briar]

Heh, well nice to meet you I guess. You might yet see my project once I release the demo which should be Soon™️ but not necessarily soon.

[slender cargo]

I was an app developer for a bigger company.

[pure briar]

Like I said, I was tortured by public "school" and only gained the appreciation that everyone lacks throughout that time after the fact. Also I have to dedicate all my time to the project and recreation, so I don't have time neither to gamble on shoddy pedagogy that will literally make me cry if it gets too cryptic with analogies and vacuums, nor to do a good job researching what books to read in the first place.

[slender cargo]

This honestly just comes across as gibberish. If you take the time to learn math rigorously, through books or college, maybe it won't be gibberish in the future.

But right now it's undecipherable.

[pure briar]

I'm not entirely sure what I'm saying comes across as gibberish to you.

Definitely every American public school's choice of book ever from 12th grade to below.

[slender cargo]

It's not a well-formulated paragraph mathematically. If I tried to research what you were trying to say with that paragraph, I would be unable to.

[pure briar]

I wasn't trying to say anything mathematically tho...

[slender cargo]

Algorithms are presented mathematically, although with more specialized language.

[pure briar]

Nah, not really; and Physics I Honors was just Algebra II through a textbook and not much else. Yay!

[slender cargo]

If you take courses on algorithms and math, or read a book or two on that stuff, you will learn how to write more precisely on those topics.

[pure briar]

Me and my vocabulary for describing things formally to both fellow academics and enthusiasts like yourself and others on this server, and then to laymen as well, is an uncanny valley equal to Zeta(1).

[slender cargo]

Sorry, I'm having a hard time formulating what I'm trying to say.

[pure briar]

What's a textbook?

Couldn't handle the humor 😔

[slender cargo]

This. I feel like you just want to string together fancy words from math and computer science.

Effectively speaking into a void.

[pure briar]

Honestly? I mean it's late for me, too, but... I'm just trying (badly) to find out what the best resources are in terms of learning for the sake of making progress in those areas of math that I enjoy and are relevant to algorithms research. Like optimal division and multiplication for instance, or computing complex-valued binomial coefficients as a matter of code golfing so I can compute atmospherics in real time without a massive lookup table.

[slender cargo]

If you want to get into algorithms research then consider going for a Computer Science PhD?

That's an entire field that takes a lot of prerequisite knowledge and many years to make a substantial contribution.

[pure briar]

I just figure out all the computer science algorithms myself. That stuff is easy I find compared to making progress in math itself with traditional arithmetic.

[slender cargo]

I don't think it's easy, but okay. And I don't know what you mean by making progress in math with "traditional arithmetic".

[pure briar]

Solving arbitrarily complicated arithmetic equations in closed form, especially Diophantine equations and other discrete arithmetic.

Real analysis is amusingly quite fundamental to discrete arithmetic.

(Of which I lack much knowledge at the moment)

[slender cargo]

These topics take many years of study. That's all I'll say. Go look up a course or a book.

Or go study at a university.

[pure briar]

I'll just see what's in the pins I guess and take the recommendations I've been given here so far.

[slender cargo]

Consider Spivak's Calculus as a first book if you have not studied Calculus.

[pure briar]

I sincerely hope it doesn't tell me the derivative is the instantaneous rate of change on a car spedometer 😒

I will check it out however painful

[slender cargo]

It will give you a rigorous introduction to derivatives, and is also a first exposure to Real Analysis.

[pure briar]

I would just like to make it clear that I trust yours and everyone else's recommendations for me; but I would be lying if I didn't say I have somewhat of an aversion to overcome.

Aight, night.

[gray gazelle]

The wording here makes me think you want a general method for solving diophantine equations. No such method exists (Hilbert’s tenth problem).

[rare tundra]

issue is well they dont exactly work well either khan academy takes 25 minutes to explain a simple term

[trail hemlock]

spivak's calculus is a great introduction to rigerous calculus. also consider apostol's calculus vol1 or Honors Calculus by MacCluer, which are great options

however i will say that spivak has some really nice practice problems

[trail hemlock]

take notes and develop your own intuition for a topic. understand how khan academy explains it, take notes, and explain it to yourself

[rare tundra]

I just can’t focus because the videos take too long to explain the simple stuff I have autism so if it’s something not boring and slow weather than explains the topics I don’t get in slower time I’d do way better

[trail hemlock]

thats just the reason you would takes notes. so you figure out what you are struggling with, and you can rewatch the video or seek out another resource for it

[molten mason]

Youtube has plenty of 1-5 min videos for every math topic or example

[rare tundra]

Mk

[glass kernel]

can anyone recommend me some good books to practice discrete mathmatics

[coral prawn]

Any book recommendations for Complex analysis which doesn't rely too much on results from Real analysis?

[golden salmon]

I'm currently chewing through Brown and Churchill. It's pretty gentle.

[main hill]

Also Demystified and Schaum's books on this topic are quite good and easy to approach.

[coral prawn]

Oooh

cool cool, tks

[lusty escarp]

Erwin Kreyzig engineering mathematics also has a few chapters on complex analysis.

[quasi umbra]

stein and shakarchi

[coral prawn]

Uhhh i think stein and shakarachi relies on a lot of real analysis on the other hand
doesn't it explicitly mention S&S series tries to link teh differnet fields of analysis

[quasi umbra]

fair

[pure briar]

Well I mean that there are still rather simple transcendental relations whose inverses cannot be found in closed form, or are simply not known at this time. As for general method of solving Diophantine equations, I think I might need an elaboration here. Procedure:

1. Be human.
2. solve problem.
   Conclusion: a general method exists for solving all mathematical problems, of which Diophantine equations are a subset.
   Something tells me this isn't what is meant.

There's also the O(n!) methods...

[slender cargo]

Just curious, why do you want to learn Complex Analysis without relying on Real Analysis results?

[graceful moon]

Physicist potentially

[coral prawn]

my friend hates Ranal, finds it boring as hell

they wanna js do CA so I wanna motivate em

[gray gazelle]

“rather simple transcendental relations whose inverse cannot be found in closed form…” could you elaborate on what you mean by “transcendental relations” and by “closed form”?

[coral prawn]

nahhhhhhhhhhhhhhhhhhhhhhh

good guess tho

[slender cargo]

Ah okay... I guess that's a valid reason

Maybe give them the most enjoyable book on Real Analysis

What's a fun book on Real Analysis...

[coral prawn]

exactly it's just... ranal content can be just dry in general to some

[quasi umbra]

first year real analysis is basically applied triangle inequality

[quasi umbra]

depends on ur definition of fun, some ppl find rudin likeable, some ppl hate it

[pure briar]

I mean... https://en.wikipedia.org/wiki/Transcendental_equation

[junior isle]

Jay Cummings' book

He's pretty funny

Compares putin to cauchy

And uses emojis to name equations

[quasi umbra]

LMAO WHAT

i need this book right now

[junior isle]

Real analysis a long form textbook is the name

[pure briar]

Consider that $x + y = \ln x + \ln y$ is a transcendental equation that can be solved in closed form:

[hasty eagle]

Andrew Porter

[junior isle]

It's pretty cheap, 20 bucks

[pure briar]

$x-W_{n}\left(-\frac{e^{x}}{x}\right)=\ln x+\ln\left(\left|-W_{n}\left(-\frac{e^{x}}{x}\right)\right|\right)+i\arctan\left(-W_{n}\left(-\frac{e^{x}}{x}\right)\right)$

[hasty eagle]

Andrew Porter

[gray gazelle]

Wouldn’t closed form typically refers to finite terms of elementary functions?

[pure briar]

No clue lol

This fits my bill for closed form in terms of what I usually look for, however.

[slender cargo]

From looking on Wikipedia, "closed form means if it is formed with constants, variables and a finite set of basic functions connected by arithmetic operations and function composition."

[gray gazelle]

I see

[slender cargo]

So basically if the expression can be reduced to a high school algebraic expression.

[gray gazelle]

Couldn’t you just defined a new function as a solution then

This is equivalent to defining the lambert W function

[pure briar]

Yes, but then you'd have to figure out what that function is to be able to compute its values.

[gray gazelle]

Except that the latter has more use cases

[pure briar]

Not sure what you mean.

[gray gazelle]

You can only approximate them

[slender cargo]

This person has not taken a math class beyond Precalculus or read any book in-depth on math beyond that level.

Just fyi

[gray gazelle]

I see

[pure briar]

Symbols are things. You don't need to numerically approximate everything.

[gray gazelle]

Do you actually understand the process leading to the answer?

[pure briar]

In fact I find the use of numerical approximations everywhere even just for rationals to be cringe

[pure briar]

Bruh, I solved this myself

[gray gazelle]

Tell that to engineers, also imma stop because this isn’t related to book recommendations anymore

[gray gazelle]

You must be able to explain the process of you solving it then, send it in my DM.

[pure briar]

I'm going to be getting into hardware engineering. I'll be sure to tell skill issue to them 😆

[still panther]

[pure briar]

I mean... it's pretty straightforward... move the respective terms involving x and y so that they're both on one side of the equation; take the exponential; realize you have something of the form $z e^z$ and that's it.

[hasty eagle]

Andrew Porter

[gray gazelle]

Blocked, Apparently you can’t follow my instructions.

[pure briar]

Amazing.

[slender cargo]

There is a decent chance this person is trolling.

[pure briar]

Which person are you referring to?

[slender cargo]

You

[gray gazelle]

Ik ik but the conversation isn’t related to the chat so I need to find an excuse to stop it

[slender cargo]

Obviously

And yeah, it's the book channel

Ask this stuff in the math-discussion or some other channel

[pure briar]

There isn't exactly an easy way to just move discussions still but alright

This is it, right? https://archive.org/details/CalculusSpivak

[gray gazelle]

Yes

[pure briar]

Thanks

[coral prawn]

spivak 🔥

[lusty escarp]

At the end, whichever simplest book you take on CA, you will find RA to be there, just not as detailed. Learn RA, it is a prereq for all of proof based mathematics in general.

[coral prawn]

I know, trying to ease my friend into it

[remote sparrow]

Complex Analysis by gamelin and Complex Analysis for Mathematics and Engineering by mathews and howell.

[remote sparrow]

there happen to be videos made by bernd schroder following this book: https://web.archive.org/web/20160613065752/http://www2.latech.edu/~schroder/comp_var_videos.htm

you have to download the videos and slides though

[main hill]

Yeah - it contains a lof of problems but it's good at explaining how to solve them and that builds up your confidence and understanding of the material. I believe that when it comes to teaching the exposure to problems and practice comes before theory.

btw - do we have here folks who read for example Anton's Calculus or Gillett?

[peak ledge]

can anyone recommend any books on conics in euclidean geometry?

[still panther]

is there a book on synthetic geometry aimed at a graduate level? like a speedrun that assumes that the reader has enough maturity to pick up the pace and can appreciate more insight into classical theorems

[molten mason]

Maybe this one?
https://link.springer.com/book/10.1007/978-0-387-22676-7

It's not graduate level but I don't know if graduate level exits....

[still panther]

that looks good, ill check it out, thanks

being able to tell people that i read hartshorne is a nice boon

[molten mason]

Oh wait I think I have one more give me a second

I like these two. They're ~1000 pages combined, so not a speedrun, but they're good books and you can just go to the spots you want.

https://link.springer.com/book/10.1007/978-3-031-48906-8
https://link.springer.com/book/10.1007/978-3-031-48910-5

[still panther]

ooooh looks nice

i love comitting to a 1000page tome i do it all the time (havent finished any yet)

[molten mason]

Yeah tome is an appropriate word lmao

[forest forum]

i am interested in learning number theory beyond elementary number theory was interested to know what books you would recommend to someone beginning analytic number theory. I am looking for a book with very good exercises and clear presentation over anything else. I found a book in my math library by ram m murty and it looks interesting, 500 problems guiding you through the development of analytic number theory IBL style and I was thinking about maybe doing that in a reading course style with a professor next sem, but maybe there is something more efficient i can try

i will be learning some analytic number theory in relation to additive number theory and harmonic analysis this summer for a research thing

[graceful moon]

Apostols analytic number theory is the usual introductory text ive seen recommended. I’ve not got around to working through it myself yet but from a quick skim it seems solid

[forest forum]

looks interesting but im wondering if there was a book intended for use as a graduate textbook

[tribal crow]

@wicked fractal

[wicked fractal]

Ram Murty is good

[quasi umbra]

good book on several complex variables?

rudin vs hormander vs gunning + rossi vs range

[forest forum]

Have you had a chance to go through it?

[wicked fractal]

Yes I did

[forest forum]

how did you end up using the book, and do you have any advice?

[wicked fractal]

Just use it

I obviously didn't only use this book

[forest forum]

is there another book you liked that you used with it?

[coral prawn]

Yay, tks

[rancid bone]

Does anyone have a good recommendation for Calculus 2? Some background: I'm wrapping up Calc 1 and i'd like to take the time over the summer to dip my feet in calc 2 content. Whether your rec is an entire calc 2 textbook or just a textbook that covers beginner to mastery of calc 2 concepts does not matter. Thanks!

[molten mason]

Calc 2 and Calc 1 use the same textbook.

What did you use for Calc 1...?

[tribal crow]

mfw publishers get greedy and split their 1500 page calculus textbooks into two parts so they can sell more money

that was a joke, but I have seen calculus textbooks specifically for calc 1 and calc 2 respectively

so maybe that's why

[molten mason]

Literally Algebra 1 and Algebra 2 lmao

I've seen Calc 1/2 and Calc 3 get split, but not Calc 1 and Calc 2

[hallow oriole]

who tf needs 1500 pages to learn calc anyways

[tribal crow]

I agree, 1500 is too much

*stares at Stewart

I think most of the pages are fluff + other nonsense though

easy way to ramp up the price ig

[loud cradle]

their real money maker isn't even selling the book anymore, it's selling access to the homework system required by most of the universities that use stewart

look at that bargain

[tribal crow]

[molten mason]

At least Stewart is all three calcs

When I got it, it was all 3 terms unlimited time to use

[loud cradle]

ha, looks like you get to pay at least $329 now if you want it for 3 terms

tbh i would have loved this system when I was a calculus TA in the ancient times
grading homework was the worst damn thing
now no human actually does it

[molten mason]

Even the exams are on Cengage

[remote knoll]

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

[gray gazelle]

<@&268886789983436800> Is this allowed?

[mossy shell]

Probably not i can delete it

No need to ping the entire staff

[quick hornet]

it is not

[mossy shell]

My bad

Wont do it again

Is that to like rent that book or is it actually mixed with software or something

Oh its an online textbook bookstore lol

Absurd price

[mossy shell]

Does anyone have good recommendations on beginning statistics

[quick hornet]

whats your math background?

[rancid bone]

Oh ok I didn’t know. I used openstax volume 1

[molten mason]

Oh that makes sense.

I mean Volume 2 is Calc 2 and Volume 3 is Calc 3.

Did you not like OpenStax? I'm a fan of using the same resource for Calc 1 and 2 and then you can supplement with a workbook or speed run through a second textbook.

Paul's Online Notes for important snippets and YouTube channels like Professor Leonard and Brian McLogan for lectures and walkthroughs of specific problems.

[rancid bone]

Yeah I understand the continuation of the openstax books. I didn’t mind openstax v1. Alright then, any good workbooks for practice?

[molten mason]

Schaum's has one "3,000 solved problems in calculus"

[mossy shell]

Algebra 2 is my highest

Also why is this guy allowed to talk about openstax and i cant about yk

[molten mason]

Idk what you're talking about that got deleted. But openstax is a free and legal open-source website, which we haven't linked. It sounds like you linked to a possible illegal paid service?

[mossy shell]

Libgen

[molten mason]

Oh yeah that's illegal af lmfao

[mossy shell]

Mmm ok

[rancid bone]

Have you used this book before?

[gray gazelle]

ive literally downlaoded all my books from there

[molten mason]

Yeah I have it lol when I went through it I remember there being a couple of errors but for thr most part it was pretty solid

[gray gazelle]

how illegal is it on a scale from 1-10

[molten mason]

On this US based discord server and also discord partner, 10

[gray gazelle]

-_-

[molten mason]

Any form of piracy is against this server's rules and can get you banned

[rancid bone]

Awesome, I’ll buy it. Thank you

[molten mason]

As far as what you do on your time with your own computer, no one cares.

[slender cargo]

Hot take: Bartle and Sherbert is the best Real Analysis book at its level. I have no credentials to back this up but I claim this.

[gray gazelle]

Whats the best numerical analysis textbook? I have my final in the month and if I don't Ace it i think ima fail the class 😭

[oblique hatch]

What would be a good source for representation theory of (affine) group schemes?

[valid bluff]

Any good textbook on Existence and Uniqueness Theorems (Picard-Lindelof, Peano, etc)?

[pliant wadi]

I support this hot take. Surely there are better books out there. But as an introductory text, it's a great introduction to University math.

[hearty turret]

what about abbott?

[slender cargo]

Abbott seems really good too, and I've been referencing it for my class sometimes. What Bartle does that Abbott doesn't is it goes over the ordered field axioms on ch. 1, where as Abbott just says "we take the stuff you're used to about the real numbers for granted." And idk I like having things built up explicitly like that.

[remote sparrow]

in chapter 8, there is a project section on dedekind cuts

[slender cargo]

That's at the end though as a project section.

[tribal crow]

how would you compare Bartle to Spivak?

[slender cargo]

Uh.. from what I've read of Spivak, I kinda feel they're similar actually. Bartle includes topology at the end where as Spivak does not, but you could just learn topology elsewhere.

Bartle also puts more emphasis on the Riemann integral where as Spivak sticks to the Darboux integral.