book-recommendations

[karmic thorn]

Alternatives exist, you can surf and explore them

[low perch]

alright, thanks!

[modern stone]

Another good recommandation that I’ve heard about is “Div, Curl and All That” by Schey

[gray gazelle]

I love Hubbard^2

[gray gazelle]

hii, i know this is books recommendation but ive figured I'm not really into books and more into lecture videoss so, are there any good lecture recommendations for learning group theory from scratch? do i need to know anything beforehand?

[brittle breach]

When you say "from scratch" you mean you have no prior exposure to groups at all

Or to proof writing

[spiral patio]

best textbook for calculus 1

what is it

i hear the stewart single variable calculus is good

[gray gazelle]

I notice a weird number of math books written by people named spivak

[rain hound]

Hey I’ve been looking for a good abstract algebra text that is both comprehensive, and pedagogical, and is suitable for a first introduction for an (forgive me for my arrogant self-assessment) advanced undergraduate, while also giving good material at a level suitable for graduate work. I thought at first Dummit and Foote was it, and was ready to order it, until I found Aluffi, which seems like a really great way to learn it all from a modern perspective, and as a bonus with some category theory. Do you guys think it suits the purposes I’m looking for? If not, is there a text you think is better?

[solemn rover]

they're both fine but could you tell us what experience you have with algebra

[orchid musk]

i think artin is wonderful for the advanced undergraduate, bit pricey though

[rain hound]

Most of my algebra experience is linear algebra, I’ve worked through most of Axler’s book

[rain hound]

I checked out a pdf of Artin and it is dry and terrible, with no explanations for anything

[solemn rover]

dummit and foote is a standard text for a first year graduate level course. but my lecturer did take about 2 weeks to introduce basic concepts of category theory

dummit and foote is also kind of dry but it's' not the worst thing in the world

[burnt basalt]

can anyone help me

[brittle breach]

I like herstein for the conciseness

[solemn rover]

category theory isn't really like, super important for dealing with the kind of stuff in dummit and foote, so it's not necessary to develop it.

but like, certainly you need at least the language of "universal properties" to talk about the tensor product of modules over a ring

[rain hound]

So am I hearing you would recommend D&F for a first introduction over Aluffi?

[rain hound]

Sorry, thank you for attempting to give a recommendation. That was kind of you, I have nothing against you. I just personally do not like that book, and don’t understand why it’s recommended.

[solemn rover]

really, I don't think it's a big deal. I am just saying that, while it's cool that Aluffi introduces category theory, I don't think it's vital to learn a huge amount of category theory in parallel with group theory, ring theory, etc. The kind of category theory that you're using in these situations is fairly basic, but if you've never seen diagrammatic reasoning before it might be a lot to chew on. If you've talked to people who read Aluffi and loved it and felt that the categorical reasoning added a lot, then by all means listen to them.

[orchid musk]

no problem, i liked the exercises a lot, the exposition is a little scarce i'll admit but to each their own it's fine

it was used in my honors algebra course so i just have a connection with it ig

[rain hound]

Ok I can see that text being a lot more manageable with a prof to guide you through it

I’m self studying completely on my own though

[rain hound]

aight

[solemn rover]

and i guess conversely, it's not like D&F doesn't have any category theory at all, it's just that it only brings in the category theory which is necessary to address the concepts it's dealing with, such as tensor product, ext, tor,...

idk lol i haven't read any of these books. except jacobson and i liked that one a lot

check out jacobson's Basic Algebra vols 1 and 2

idk i took a single semester of abstract algebra, it hasn't been that important to me to learn that stuff. and then i learned commutative algebra out of altman and kleiman

[orchid musk]

i've been trying to read through*** Fabian's Banach Space Theory: The basis for linear and non-linear analysis*** but it's just too dense to learn from. Does anyone have any recommendations for a book on banach spaces? I've done undergraduate real analysis, abstract linear, and abstract algebra.

[sage python]

@rain hound to answer your og question

There's a guy named Richard Borcherds

He seems to have a bunch of YouTube lecture series on advanced undergrad/early grad level math

Check it out to see if he's got group theory and if it's your vibe

[gray gazelle]

WELL ive seen like a very, very quick definition when studying for mathematical phyiscs but nothing proof based

really just wanted to understand group theory

[gray gazelle]

i think i might be ok with that

[gray gazelle]

Gallian :)

[brittle breach]

https://youtube.com/playlist?list=PL8yHsr3EFj51pjBvvCPipgAT3SYpIiIsJ

@gray gazelle he is very good if you can write the proofs your self

meaning you did a lot of math before , he has lie group series as well

https://youtu.be/VdLhQs_y_E8

this is the typical first intro to groups

[gray gazelle]

Eww thats Gross

[brittle breach]

?

[gray gazelle]

Twas a joke using his name

[brittle breach]

i think it all went over my head

[gray gazelle]

Isnt the lecturer's name Benedict Gross?

[brittle breach]

I don't know

[gray gazelle]

Ah I see. Key point was missing from the start

[brittle breach]

yep

[analog pollen]

depends on your future study plans

everything or other?

[prisma snow]

The only two options

[analog pollen]

lol

the most popular options tho

[cursive orbit]

[analog pollen]

okok i changed it

[gray gazelle]

The only two options

[gray jungle]

whats the prerequisites to munkres analysis on manifolds and is the book considered good ?

[gray gazelle]

prereqs are some familiarity with basic metric space / point set concepts, as well as calc 1 and 2 stuff

the book's okay. spivak is more popular

the general opinion is that spivak is better in that it's the same content, but less verbose and with better exercises

[gray jungle]

i assume spivak require the same prereqs for munkres

[gray gazelle]

yes

spivak's treatment of basic topology on R^n is kind of questionable so it's good to know some of that going in

[hearty steppe]

Are you saying he should read Calculus on Manifolds before reading an intro to topology book

[gray gazelle]

[gray jungle]

i think he made it clear i need to know basic topology before spivak

ty for the help ile trust you on the spivak call

[gray gazelle]

spivak uses open rectangles instead of open balls which is kind of weird and really hard to use

at least in that intro section

you could convince yourself they're equivalent and then go read spivak

[gray jungle]

sounds good

[analog pollen]

stfu i changed it lmao

lol

[full linden]

does anyone knows good lecture notes on differential equations and probability?

[analog pollen]

pauls math notes

or somtheing like that

[broken meadow]

dude the open rectangles shit

i cope

[gray gazelle]

Engineering version: https://www.jirka.org/diffyqs/diffyqs.pdf

[marble solar]

I mean bad for topology, good for integration. When I took the course the prof. said we can just open balls if we want for our homework

[gray gazelle]

anyone know good books on galois theory?

[gray gazelle]

References
Suggested literature:

1. A good textbook on general algebra (including Galois theory) is S. Lang, "Algebra"; I especially recommend the 3rd edition (e.g. Springer, Graduate Texts in Mathematics series, 2002) which contains many exercises. The parts V, VI, VII are especially relevant.

2. The source which is probably closest to this course is R. Elkik, "Cours d'algebre", Ellipses, Paris 2002; from there in particular comes the stress we put on the tensor product and base change. It is very concisely written (and in French!); nevertheless meant for students.

3. I also recommend the very nice lecture notes of J. Milne available on his web page

http://www.jmilne.org/math/CourseNotes/ft.html

Read also the last three chapters which contain very interesting and important material not covered in this course.

4. Last but not least, you can look at a very detailed exposition by Ian Stewart, "Galois theory"; the latest edition is the fourth, CRC Press, Taylor and Francis Group, Boca Raton, 2015. It is less ambitious technically than our course, but it has some history in it, as well as some other (than the solvability of equations by radicals, which is the only one discussed in this course) usual applications, e.g. to ruler-and-compass constructions.

https://www.coursera.org/learn/galois/home/welcome

Source of above notes.

thank you wow

[faint spoke]

I recommend using "How To Solve It"

[gray gazelle]

What's a good, mathematically rigorous "intro to tensors" book?

good, mathematically rigorous
open a DG book

what?

differential geometry?

[silver herald]

Yea

[gray gazelle]

isn't there a book just for tensors and stuff related to it?

[quick hornet]

the mathematical formalism of tensors is expressed in the language of differential geometry

[gray gazelle]

what are the prerequisites for differential geometry?

[quick hornet]

well okay

technically a tensor itself is just an element of a tensor product

which is a purely algebraic definition

[gray gazelle]

don't you mean a tensor product space?

[quick hornet]

those are synonyms

[gray gazelle]

ah okay

[glad prairie]

This is so silly

ITS MULTILINEAR ALGEBRA

Not just differential geometry

@gray gazelle If you don't want to learn a bunch of differential geometry to learn about tensors, look at Multilinear Algebra by Greub. It seems to cover all the important stuff and seems to be rigorous.

Assumes linear algebra of course.

This "learn it through DG " stuff is nonsense

[gray gazelle]

thank you

[glad prairie]

I'm sure a pdf can be found somewhere online for free.

[gray gazelle]

i know how to find a free pdf of almost every book 😉

[glad prairie]

Yeah, it's also on springerlink if your uni has access to that and you want to do it legally.

Also good lord I forgot what this book is like but if you want rigor... This very very detailed lol

[gray gazelle]

i do want rigor but wdym?

[glad prairie]

It just gets right into it

[gray gazelle]

oh lol

well that's good i think

[glad prairie]

And like

It doesn't look like it does a lot of hand holding

Rudin vibes

[gray gazelle]

ah well I'm sure i can find other resources(to find a more basic explanation of a certain topic) if i get stuck, or even ask here

sounds like it's a book for graduate students

[tawdry citrus]

Hey people

Im looking for good resources on pdes

I passed a pde course before and have experience solving linear pdes, like laplace equation, wave equation etc

So i would like a good book to pass linear pdes again

And I aim at nonlinear pdes, good books in that area would be good

[glad prairie]

If you know some PDEs already and real analysis / linear algebra, Evans is the standard text.

The second chapter is a pretty in depth study of the common linear PDEs. The third is nonlinear first order ones.

The second half of evans is much more focused on the modern theory of elliptic/parabolic/hyperbolic PDEs, both linear and nonlinear.

[tawdry citrus]

Thanks, Evans seems like a good reference, Ill start reading it.

I have real analysis/linear algebra background like you said, so I should be fine I guess

[slim peak]

I've learned about it through Riemannian geometry, it was kinda smooth to me

I know it depends on people, but just saying "non-sense" is too much for me. It's maybe no the best way to get the biggest overview of ti, but clearly not bad, I think.

[gray gazelle]

Is Bix conics and cubics good?

By good I mean not boring

[glad prairie]

I also learned it through DG... Most people only need it for the DG context. If you're trying to learn it outside the context of geometry, why learn a whole new language around the topic instead of learning the topic itself

I mean if one knows about manifolds and stuff to begin with it's different

For me the context of tensors on manifolds didn't make the concepts any easier, it made it harder for me to parse what was general for tensor algebras and what was specific to the geometric setting.

[slim peak]

Oh, I didn't think about it, good point.

[misty wyvern]

tensors good

[crystal lion]

idt most schools except berkeley offer multilinear algebra as a purely algebraic course

[misty wyvern]

why would you

[grim pivot]

I’m hopping into a manifolds book rn, so would you suggest I take a very quick crash course of multilinear algebra before progressing much further into the section on tensors?

[glad prairie]

no it's fine to learn it through manifolds

but it's just silly to learn about manifolds if you don't want to learn about them from the start

[coarse tulip]

any book recommendations to self study number theory?

[sudden kindle]

@coarse tulip whst math are u familiar with

[coarse tulip]

so far I've taken intro to adv. math, linear algebra, diff eq, num analysis, etc. That's about as far as I've gotten in my undergrad

I'm interested in taking it, but I was going to take my last elective as topology and abstract algebra

[sudden kindle]

So you havnt taken abstract algebra yet

Try Stein Elementary Number theory

[coarse tulip]

thank you! 🙂

[solemn rover]

i have actually spent a bunch of time with this book

not like, reading the whole thing thoroughly

there's some things about differential geometry that are really confusing to me on a conceptual level and so i keep looking at greub to see if i can find nice conceptual explanations of these gadgets

[glad prairie]

It looks more referencey

[solemn rover]

yeah.

that's what i mean

i've been trying to figure out a nice simplicial version of the de Rham complex

[glad prairie]

My point is more "dont read a dg book, read a multilinear algebra book" than "read greub"

[solemn rover]

yeah i wasn't really trying to argue or endorse either way, just saying tangentially

[glad prairie]

I was just stating it to relieve myself of responsibility for this questionable recommendation

[vapid knot]

hey y'all, anyone here read steve roman's advanced linear algebra?

[whole rain]

I've read some of it (not much), it's nice but I remember one exercise that was literally impossible (so impossible that it's one of the 5/6 exercises to which he added an hint in the edition). So get the last edition, if you plan on reading it

[supple folio]

hello, do you have any book recommendations which includes almost all the rules, laws, properties, and lemmas in mathematics?

[sand sentinel]

@supple folio yes textbook grade 1-60 (for legal reasons this is a joke

[vapid knot]

heh, sounds fun 👀 what kind of background did you have going in, if you don't mind?

i've done 4 calc courses, a couple lin alg courses (all uni) and i have some basic knowledge of set theory and some stuff about groups/etc. from elsewhere, but i worry if it's worth my time to chew on without a math major's background

[gray gazelle]

If you want to study it, study it. You don’t have to major in math to do math.

[vapid knot]

ye, it's not exactly pragmatic anyways i just have interest and tangential use for it studying physchem; i moreso meant if it might be better to invest in something thats slightly more intermediate

[gray gazelle]

what linear algebra course did you do?

[whole rain]

Depends on what's worth for you, but if you're just reading it for fun, yeah it's probably worth checking it out, it covers a lot more than what you'd find in your typical linalg course

[vapid knot]

the prelimimary shit is a little bit to remember but i can follow along so far and skimming it it seems advanced but not impossible? but i figured someone whos read it might have advice

[whole rain]

The prerequisites are probably something like being familiar with the abstract-ish way of doing linalg and not just the computational way

[vapid knot]

indeed why i want to read it; i want to take it up a notch

[brittle breach]

did you like it

[whole rain]

Yeah, I'm actually planning on going back reading some parts I didn't read yet soon

[vapid knot]

we spent time in the lin alg courses i did going into lin alg more abstractly (although still only at a 1st and 2nd year undergrad level), so it's not really unfamiliar

all to do with general functions, spaces and relations and such is familiar

[whole rain]

Alright then I'd say it should be readable, but you can't know unless you try

[gray gazelle]

I think your good then.

[vapid knot]

i'll keep reading it then

worst case i drop it i guess anyways, not super pressed

[whole rain]

Also if you're planning on doing theoretical physics, I'm pretty sure most of the "advanced" linalg stuff he covers find some uses there

[vapid knot]

i do physical chemistry

which, depending how far i dive into theory, touches into math and phys above my undergrad chem education

which is why im trynna use my spare time to get a more flushed out background in math and phys areas

also just cuz i like learning about math, and lin alg has always been particularly neat so far

[whole rain]

I see, that's nice !

[whole rain]

(to nuance that a bit, it's probably not an impossible exercise, but it really detonated with the other exercises, which ranged from "not too hard" to "hard-ish", this one was on another level )

(I think we spent the whole afternoon in #groups-rings-fields trying to solve it )

[zealous jetty]

Now im curious, what was the exercise?

[vapid knot]

did you bother doing many of the random proofs in the book yourself, or just doing exercises mainly?

[whole rain]

give me a sec

[vapid knot]

ok not random, i mean just the theorems and such that come along whose proofs arent shown

[whole rain]

https://media.discordapp.net/attachments/496784958430380033/845401757316153426/unknown.png

[solemn rover]

ive heard it's great.

[whole rain]

exercise 23

[whole rain]

Depends, most of the time I already knew it, since this wasn't my first exposition to linalg, but yeah I bothered to atleast sketch in my head the proof of the statements that weren't immediately clear to me

[whole rain]

(I can also share the version with the hint)

@zealous jetty

[zealous jetty]

Doing some thinkeroos

[whole rain]

It doesn't look as hard as it is, tbh. Or maybe I was a dumbo, idk

[vapid knot]

sounds about like my plan for it, was just curiois to see what others do. the completionist in me always feels like doing everything on paper but i'd get tired of it lmao

[whole rain]

I only use paper when I feel the need for it, if I'm convinced I could put the stuff properly on paper, I don't bother doing it

(it's obviously not a fool-proof way of doing things, it sometimes happen that I'm convinced I could do it, and then I try for some reason and I end up struggling, but it works well enough for me )

[whole rain]

This would be literally impossible

[zealous jetty]

Bourbaki

[supple folio]

i though so too. welp. gonna start writing everything i can search and scan on my books so i could review it >< thanks!

[whole rain]

Entire libraries aren't enough to contain even a decent fraction of all the mathematical knowledge we have, let alone a book

Nah Bourbaki doesn't cover that much (and also it's unreadable )

[supple folio]

true tho.

[karmic thorn]

Talk for yourself mortal, I know it all.

[whole rain]

Imagine a guy that would know all the mathematics currently existing

But that would have no creation power

Like, he would be unable to solve any math question by himself, even if it's super easy, if he doesn't already know the answer

How useless would that be ?

[karmic thorn]

Hmmmm

[whole rain]

probably not the right channel, answer in #serious-discussion ig

[karmic thorn]

Right

[rapid token]

Hi any advice for an introductory book on category theory?

[solemn rover]

it would be good to give some information about your background.

Category theory is very abstract. It is easier to understand when it is motivated by examples. So a common recommendation is the book by Emily Riehl, "Categories in Context", which has lots of examples from all over mathematics. But if you do not have this broad experience you will have trouble understanding the examples and a more self contained book will be more appropriate such as the "Handbook of Categorical Algebra" by Borceux.

[dense wren]

Awodey’s book seems nice

[sturdy sail]

I'd like to ask what book do you guys recommend in order to learn classic AG, i.e algebraic varieties and regular functions between them. From what I have noticed, Harthshorne's book is great as an encyclopedia to search through specific results and problems, but not as great as a pedagogical tool to learn algebraic geometry, at least classical algebraic geometry; since I haven't seem so many people dissing over his treatment of schemes and cohomology. I have also heard that the problems in the first chapter are really hard too.

So I'd like to ask for other references to classical AG, but that are easier to use as a book for self studying.

[sage python]

Gathmann

https://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2019/alggeom-2019.pdf

[brisk ice]

Any beginner friendly books on electromagnetism

Probably could ask phyics server but idk 😐

[past ice]

I took a course using Gathmann last year and I thought it was ridiculously hard. Maybe it's because most of the class didn't know that much commutative algebra at the time, but there are lots of things that he says are "obvious" that nobody in the class thought were anywhere close to obvious. This book was a lot more approachable: https://www.springer.com/gp/book/9781848000551

[gray gazelle]

Jackson

[subtle siren]

Why not just MIT OCW E&M notes

[subtle siren]

MIT OCW 8.02 specifically mentions

 Serway, Raymond A., and John W. Jewett. Physics for Scientists and Engineers (with PhysicsNOW and InfoTrac). Belmont, CA: Thomson-Brooks/Cole, 2003. ISBN: 9780534408428.

Tipler, Paul A., and Gene Mosca. Physics for Scientists and Engineers: Extended Version. New York: W.H. Freeman, 2003. ISBN: 9780716743897.

Giancoli, Douglas C. Physics for Scientists and Engineers with Modern Physics. Vol. 2. Upper Saddle River, NJ: Pearson Education, 2007. ISBN: 9780130215192.

Young, Hugh D., and Roger A. Freedman. University Physics with modern Physics. San Francisco, CA: Addison-Wesley, 2003. ISBN: 9780805386844.

Resnick, Robert, David Halliday, and Kenneth S. Krane. Physics. Vol. 2. New York, NY: Wiley, 2001. ISBN: 9780471401940.

and they are very standard undergrad physics books

[analog pollen]

Griffiths

What else

[analog pollen]

Imagine not using griffiths for em

Cringe

[sage python]

Ah I didn't know that book but it looks good. It's kinda in the same vein it seems where it talks about general varieties using sheaves which is good

[gray gazelle]

Purcellchads coming through

[analog pollen]

lol

[wise umbra]

Look at the Daniel Perrin's book "An introduction to algebraic geometry, something like that

[thorn cloak]

Hello! I’m a high school senior going into business but already completed calc bc so I was hoping to find a multivar textbook specifically for applying it to business (if that even exists). If it doesn’t then the best multi var book for I guess just pushing yourself since I’m not planning on taking it in college not going into math. :))

[brisk ice]

like multivariable calculus?

[tulip blade]

Herstein topics in algebra a good book?

My undergrad algebra prof made it sound like it was a level above fraleigh. Is that the case?

[thorn cloak]

Yes

[gray gazelle]

I liked it

can i use vellman's book, how to prove it, as an introduction to formal logic ?

[odd flax]

as someone totally new to measure theory and in dire need of a deeper understanding of it any book suggestions with solved exercises?

I come from a course that's not specialized in maths so gotta develop my critical thinking and justification for answers

[stray veldt]

it's more of an intro to mathematics than an introduction to logic, i.e. it only develops the tools that every mathematician knows
but sure, if you don't know (much) mathematics you have to start somewhere
i personally think its way too long and especially the later chapters are useless
i also think that if you want to learn mathematical logic you should first learn some "actual" mathematics

[stray veldt]

you will not find a book with solved exercises, this is not done in mathematics books as there are many ways to approach and solve the problems so providing solutions is not all that useful; at that point it is also expected of people to be able to check their own solutions

[gray gazelle]

Thanks for the answer!

[stray veldt]

sometimes other people will upload their solutions and you might find them (often on github) when you search for "[book title] [author] solutions"

[gray jungle]

what do you guys think of G polya how to solve it ?

[odd flax]

I feel like in my searches this sums it up perfectly

https://math.stackexchange.com/questions/2458400/reference-request-for-worked-out-problems-in-measure-theory-integration

As someone with no proper background in this themes I feel like I would learn seeing solved exercises so I could apply that in the exercises given by the professor (which have no solution)

[mellow wren]

Griffiths EM is a classic

[brisk ice]

What prior knowledge / math is expected ?

[mellow wren]

Calculus I'd say
It'll give you the run down of all the necessary vector calculus

[subtle wedge]

any good books on Computer Arithmetic ?

[analog lava]

hello guys

how do i learn complex analysis ( for the first time ) where the context is more algebraic or towards geometry ( just for taste and fun for me )

what books

thank you

i know real analysis/measure theory/linear algebra/algebra/topology

[gray jungle]

there is a pin on complex analysis books

[analog lava]

thank you

gamelin it is ig

[thorn cloak]

Hello! I’m a high school senior going into business but already completed calc bc so I was hoping to find a multivar calc textbook specifically for applying it to business (if that even exists). If it doesn’t then the best multi var book for I guess just pushing yourself since I’m not planning on taking it in college not going into math. :))

[analog lava]

stewarts calculus

and read the chapters on multivariable

[thorn cloak]

Thank you

[analog lava]

is stein and shakrachi

the same as lectures in princeton?

are they the same textr

[heady dragon]

Anatomy and Physiology. Learn it, live it, love it.

[sharp latch]

Based read, not a substitute for actually doing math but a nice perspective shift

[karmic thorn]

I think the S&S series is titled "Princeton Lectures in Analysis"?

[broken meadow]

yes

they have a classic deep blue with yellow text on the front

or at least the scan i have is like that

im p sure the newer paperbacks r still blue tho

[karmic thorn]

Yes

I have V2, completely new for 3 years at this point

[mortal cove]

anyone can use it

[marble solar]

I got volumes 1 through 4 baby

[mortal cove]

its very nice

[marble solar]

uhhh <@&268886789983436800> this looks sussy

[mortal cove]

why what happedne

[karmic thorn]

@mortal cove We don't allow sharing of pirated content, or links sharing pirated content.

[mortal cove]

ohok sorry

[karmic thorn]

Discord can crack down on servers for the same, so

[marble solar]

My mum always told me to click on every strange URL on discord

[broken meadow]

do u think it's worth purchasing the four of them

[mortal cove]

sorry guys

[broken meadow]

i am considering

[karmic thorn]

No worries

[marble solar]

The first 3 definitely

[broken meadow]

i am very happy with SS1 so far

wonderful writing

[gray gazelle]

Why?

[marble solar]

The second one isn't as good

[broken meadow]

ah okey

[marble solar]

The third one is amazing

[karmic thorn]

The message was deleted

[marble solar]

The second one is good for the resource of problems

[mortal cove]

also can anyone suggest good books for combinotarics

[gray gazelle]

It contained a drive link of books ig. Nothing promotional.

[marble solar]

I have all four because I did courses that covered 1, 2, and 3

[mortal cove]

which has everything from basic to adavance

[marble solar]

And then when I went into research, volume 4 covered a lot of what I need to know

[karmic thorn]

Pirated ones

[marble solar]

It's also very compact in comparison to Stein's Mammoth of Harmonic Analysis

[karmic thorn]

I will strongly shill A Walk Through Combinatorics by Miklos Bona

[marble solar]

Overall, I think they're worth having all four to see it start to finish

But again I'm an analyst by trade

[mortal cove]

ok thanks

[gray gazelle]

[marble solar]

I've worked through the first 3 extensively. Done most exercises in volume 1, 2, and 3

The fourth one there are particular chapters

That I need to know, and there are others that aren't really related to what I need

I change up what I'm doing once every 3 months

As of now I'm back into Evans PDEs

I'll do this probably through december, then go back to more S&S problems

(Prepare for quals)

[karmic thorn]

Have you read Knapp's Analysis books, MoonBears?

[marble solar]

I've seen copies around

It looks interesting, but it's not something I own

[karmic thorn]

I see

[orchid wyvern]

hi im new here

[karmic thorn]

The problems seem interesting but the exposition is often...very reference like

[marble solar]

The real books I have are Baby Rudin, Papa Rudin, Tao 1 & 2, Pugh, and Spivak's Calculus/Calculus on Manifolds

Complex Books I have are Ahlfors, S&S, and Marshall

I only have one PDE book which is Evans. I'm so far very happy with it

As I am with Marshall's Complex text

But I'm coming at Complex having taken 4 quarters of grad complex already

[karmic thorn]

The analysis books I have are Tao 1/2, Amann-Escher 1/2, Tao's Measure Theory, S&S 2, Robinson's Dynamical Systems (if that counts as analysis at all)

[marble solar]

I couldn't get into Tao's Measure Theory

[karmic thorn]

[marble solar]

It seemed like a worse version of S&S Volume 3

[karmic thorn]

Lmfao

[marble solar]

I'm off to bed, morning lecture at 10

wew

I'm not even prepared

[karmic thorn]

Goodluck, and goodnight

[misty wyvern]

I don't usually wing talks but I did today and it went well

I can only do that for my own field of study

[subtle wedge]

bump

[marble solar]

I teach freshman year pre-college algebra

[simple lava]

book that brings logical challenges to develop logic analysis

[gray gazelle]

Is a book needed to solely to learn DE's? If so, are there any good suggestions ... I also won't mind learning about something called Hilbert space, so a book that has that topic in it (like a calc + LA book) would also be great

and a book which has all that would be perfect

[fluid bay]

Rudins functional analysis:

• Applications to DEs
• calc and linear algebra
• Hilbert spaces

[cyan steeple]

for a first course in manifolds(taugh by a mathematician), which book do you guys recommend? Tu or Lee?

[gray gazelle]

both

lee is just tu but with more topics and depth

tu is more concise, but doesn't cover a lot

though lee can be rather verbose

they complement eachother.

[narrow thorn]

factorise x^2+3+2

[gray gazelle]

#❓how-to-get-help

[sturdy sail]

TTerra, while studying symp geo, I noticed that there's some riemannian geometry stuff I really need to know

And like, I was thinking about using do Carmo's.

But you have said before you don't like it that much.

Any other recommendations?

[gray gazelle]

do carmo's good if you already know RG. lee's book on the subject is great for learning it

what are you doing in symplectic that uses RG?

i don't actually know very many RG books

i have heard good thing about petersen (peterson?)

[sturdy sail]

Ah, not that it is really uses heavy RG. But like, my professor used some results in RG when talking about darboux theorem and Morse's theory.

It's not really necessary, but would be a great tool to have alongside symp geo

[sturdy sail]

Alright, I think I will do Lee's then.

[gray gazelle]

elaborate

[sturdy sail]

Ah, for the darboux theorem. What he basically briefly tried to make sure to us is that we understand in symp geo we don't really have local invariants associated to a symplectic form. Which in contrast to diff geo, a we have local invariants associated to a riemannian metric. And he went on to make these observations more precise.

And he basically spent some time clarifying these differences between riemannian geometry and symp geo.

I am using a book that goes over Morse theory, and there it uses some RG results sometimes.

In any case, these things made me observe that I should at least know some stuff about connections and curvature.

[gray gazelle]

though now im remembering

have fun learning all the equivalent definitions of connection

[serene maple]

Hey im a layman thats interested in doing statistics and combinatorics; not even a maths major 🥴

does anyone know books that would be good as an introduction

like that get into the nitty gritty

rather than what you need to pass the exam

[gray gazelle]

combinatorics
people i trust have said good things about the book "a walk through combinatorics"

[tulip blade]

^^

[dense wren]

has anyone here read or gone through Axler's new measure theory book?

[dense wren]

he has a free pdf of it on his website, it looks pretty nice

[hexed relic]

Hey, do any of you have some decent books on Group Theory? I've sat down to try and learn it several times, but none of the things I've read online have really resonated with me or given me an intuitive approach to it.

Or at least encompassing something similar.

I'm also honestly just looking for something interesting to read, so if you want, just drop a few of your favorite math related books.

[serene maple]

thanks bro

[gray gazelle]

For those who have read principle of mathematical analysis by Walter rudin, how of it would you say differs from spivak calculus? Will spivak cover enough analysis for Sheldon Axler Measure, Integration & Real Analysis

[sage python]

I'm not too familiar with Axler's book but

Royden is well-established as a standard measure theory book

And can be done pretty much right after Spivak

Rudin 1-8 (which is the part of Rudin you should be reading) mostly does stuff like metric topology and uniform convergence over Spivak

But those topics are also done in Royden

At a glance Axler doesn't cover that extra topology stuff so

[gray gazelle]

Thanks for the information about that.

[frigid comet]

royden is more of an analogue to big rudin than little rudin

[prime oak]

any recs for books for problems in LA? im doing serge lang but it doesn't really have that many problems

i mean LA textbooks which have a good amount of good problems

[orchid musk]

is there a book that deals with very mechanical approaches to manipulation of inequalities? i feel like mastering these simple techniques would really help for working with analysis

[frigid comet]

To name a few: Hoffman--Kunze Linear algebra, Axler Linear algebra done right, Halmos Finite dimensional vector spaces.

[prime oak]

ty

[gray gazelle]

Is group theory an essential pre-requisite for Yaglom and Yaglom's Geometric transformations series of books?

[cobalt arch]

Are there any books that construct the most basic structures of mathematics from the grothendieck universe? It would be cool to see a nice exposition which shows how these properties emerge and follow naturally from the axioms. At least how the fundamentals of ZFC set theory can emerge.

[gray jungle]

well idk about "from grothendieck universe part" but i know tao analysis 1 from chp1-5 has good constructions of all basic structures ,operations ,sets and all the good set theory from scratch he even discusses why a universal set would not work through bertrand russell's paradox but idk if thats what you are referencing its also very readable for almost anyone
maybe you are looking for a more specialized book but its alright

[karmic thorn]

Have you abandoned plans to learn linear algebra and analysis

[cobalt arch]

That is good to hear I will check it out

[cobalt arch]

No, not at all

[cobalt arch]

I would like such a book as well if anyone knows because in the context of analysis it is assumed and in the context of elementary algebra well it is too elementary

[cursive orbit]

Check out Cauchy-Schwarz Masterclass

[cobalt arch]

I know this book, is it comprehensive?

At least for a starting point it will be

[scarlet steeple]

Elementary Analysis

By Kenneth ross

[scarlet steeple]

Nah Terrence Taos Analysis book is unreasonably specific

[novel obsidian]

wdym by this?

[scarlet steeple]

50 pages of constructing numbers

Defining them

0+,0++ is how you would define 1 and 2

[novel obsidian]

i mean alright

i was actually planning on reading it for that very reason

[scarlet steeple]

Lool😅

[novel obsidian]

for the giga-rigour

ya get me

[scarlet steeple]

Yeah, I enjoy rigour too but I feel like that was just ridiculous

You still get alot of rigour in elementary Analysis

Its really enjoyable

Alot of examples and practice exercises also

I didn't enjoy rudin either its too hard of a read for a beginner,

[cobalt arch]

Does it contain a solid exposition on inequalities? It seems good but I would like to have that under my belt first. I think the Cauchy-Schwarz Masterclass might do the job for that part actually. I think tao's analysis books subsume both ross and abbott so I don't think I will read those but I will see if I understand tao's analysis book first and then decide .

[scarlet steeple]

Yea absolutely, you start of with some obvious axioms and you continue to expand what you can do with inequalities from there

Prove a couple of cool theorems e.t.c

[gray gazelle]

Is

Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach by John and Barbara Hubbard

a great book for what's in the name, vector calculus?

[gray gazelle]

That the book I plan for multivariable stuff., iirc from table of contents it covers some portion of linear algebra, manifolds topics and differential forms topics is also introduced and all vector calculus stuff done. I remember Tesseract#4843 going through this book in the chat a while back. You can at him for more information.

Here the table of contents. http://pi.math.cornell.edu/~hubbard/tablecontents.pdf

Hubbard also has an incoming sequel to this book he calls advanced calculus, it include 6 more chapters.

[gray gazelle]

well what would you say I should know before diving in?

From talking to a couple guys here before about the book basically a good single variable calculus knowledge.

if I'm going to be honest, all I know is up to integral calc, and some LA

[gray gazelle]

oh that's perfect actually

My goal is LA done right and spivak right now so I am not close to reading the book yet.

well thank you so much for your response 👍

np

also everyone recommends spivak here, is it really that great? Like worth reading through it to maybe warm up on your skills and learn things you might've missed

Spivak is a good read I like it but the exercises are kicking my ass.

That my opinion on reading it.

[gray jungle]

hoffman/kunze >

[gray gazelle]

everyone needs a good ass kicking

[gray gazelle]

wait what, I just looked it up and found a free copy

[gray gazelle]

Are you saying that based on experience or just stating what Daminark says all the time about that book?

[gray jungle]

i am working through it rn

and its pretty damn good

[gray gazelle]

I am enjoying reading LA done right so I am not looking for something else at the moment.

[gray jungle]

eh its down to pref anw

[gray gazelle]

Greub >>>

[uncut zealot]

Is it reasonable for a reading course to try to read all of Munkres Topology in one semester?

[crystal lion]

no way

as a first pass of point set topology?

[solemn musk]

whats a good book for like a first course/look into linear algebra

[cloud bolt]

I just started Beezer because it's free online as a pdf and in website form, heard it recommended a few times

[solemn musk]

alright thank you ill check it out

[gray jungle]

Friedberg, insel, spence is commonly recommend

[sage python]

I endorse that yeah

It's a slightly more modern and slightly gentler Hoffman-Kunze. At least in my experience TAing

[gray gazelle]

Whats a TA? Total Autist?

[quick hornet]

uhh

[novel obsidian]

um

[quick hornet]

thats probably not a good place for your mind to jump to

anyway, teaching assistant

[gray gazelle]

Oh

[prisma snow]

[analog pollen]

all pdfs are free online

lbgn

[cloud bolt]

I've been paying for pdfs this whole time for nothing?

[gray gazelle]

Well behaving ethically is commendable

[tulip blade]

I think selling pdfs for $50+ is unethical.

[sage python]

Discord TOS is such that we are not to endorse libgen and other sites which allow for the distribution of pirated material, so don't recommend it here

[cobalt arch]

I think not telling someone that they are free while knowing yourself is strictly unethical behavior

[sage python]

While I would say it's excessive, and I'm fine with the business myself, but calling that unethical feels like a stress

[gray gazelle]

Yh I agree its too much. My advise is to talk with the authors or editors they give free copies sometimes

But even if that is unethical. Two wrongs dont make a right

I still get from libgen lmao

[cloud bolt]

I was recommending Beezer's book which he hosts online for free, and asks for donations

[gray gazelle]

Only buy what I strictly need or liked

[tulip blade]

Ive never been on lbgen tbh

I just search up book title authors name pdf

And usually some university has it posted online.

[gray gazelle]

This

Plus springer access

[grim pivot]

Reminds me of this email

[junior merlin]

lol

[solemn rover]

lmfao

Pretty funny

[whole rain]

funny and based

[fossil arch]

this professor is valid as fuck

[glad prairie]

Textbook publishing industry is unethical and daminark is an agent of capitalism.

[sage python]

no u

[covert lotus]

Is there any book on physics of color theory and how linear algebra is used in it (also digital implementation)?

[orchid silo]

best book to solve Partial differential equation??

[molten wave]

which one?

there's probably a book for each

[livid ermine]

probably

if 1 semester = 6 months and you dedicate the time you'd normally spend on a course to studying the book, then I think it should be doable.

[prisma snow]

Well, I think most courses typically don't cover the whole book, only the first half

But you can make that your goal, and if you don't reach it, that's okay too, you you would still have learned a lot

[livid ermine]

I think our topology course covered the first 3 chapters, some random other stuff, and then some of the algtop chapters 9 and 10. That is probably a more reasonable goal imo

[misty wyvern]

It took me like 2 years to work through one of the primary textbooks for math phys students

fortunately i started early 😅

it's not a hard book

it's just that core books are made for extended study and reference

[glad prairie]

To solve? If you know real analysis and linear algebra, Evans is the most well regarded PDE book but it's kinda tough and only chapters 2-4 are really about solving PDEs and getting solutions (the later chapters are about proving theorems about PDEs, which is much more fun. There are plenty of theorems in the early chapters too!)
If you need more of an undergrad level textbook, Strauss is not bad. But if you can handle Evans it's the best place to learn from.

[modern stone]

What book would you recommend for someone who wants to learn Analysis? I’ve heard Abbott and Tao are quite good choices

[gray gazelle]

Abbott and Tao are quite good choices.

[gray gazelle]

@gray gazelle

[gray gazelle]

Seconding this

[narrow talon]

If you want to solve them, pick up a book on numerical methods

[regal wasp]

Best book for theory of Fourier transforms?

Including extension to Lebesgue

Oh wait I think I’m thinking of the Princeton one

Stein and sakarchi did a good job

[orchid silo]

thank you

[orchid silo]

thanks for informing

[sage python]

@regal wasp do you already know measure theory?

[misty wyvern]

Solving a PDE is a spook, nobody has ever solved a PDE ever in history

[glad prairie]

I love Strichartz's fourier analysis and distribution theory.

It's so fun

[junior heron]

I love the book.

[pale scarab]

Any good books for the math subject GRE? Or what undergrad classes should I focus on other then calc which I am already doing a lot of problems daily to get quicker. I know speed is a big issue with the test so I am working on that timing myself going through calc problems

[regal wasp]

Yes

[sage python]

Nice, what about functional analysis? I've been recommended Schlag and Muscalu, also Grafakos

[clear plaza]

My calculus course is actually a course in between calculus and introductory mathematical analysis. The suggested textbooks for the course are introductory mathematical analysis for theories introduced. Do anyone have suggestions for textbooks for computation practice?

[karmic thorn]

If you can handle slightly more challenging problems than usual, there's a 3 volume series Problems in Mathematical Analysis by Kaczor-Nowak.

[slim peak]

except Dirichlet Laplacian on the unit disc on C, and the heat equation on the whole space.

[slim peak]

Those are very technical and I didn't continue my reading of Schlag and Muscalu. I read few parts of Grafakos' books, technical but great, really great.

Fourier Analysis by Duoandikoetxea (damn fucking name) god bless this guy (and I'm an atheist !), this book is really great too, short and readable.

What you were talking about is more Functional/Harmonic Analysis than pure Functional Analysis nor properties about deep use of the Fourier Transform

[sage python]

@slim peak I meant more like

"Do you know some functional analysis? If so check out these books"

[clear plaza]

Do you have recommendations for beginners?

[karmic thorn]

There are other "problems in analysis" books that you can look up for, but at that point you might as well just use a regular analysis textbook

[quasi remnant]

anyone know any books which teaches this stuff?

tried linear algebra by insel but didn't really like it

didn't realise how good la by axler was until i can't use it anymore 😦

[whole rain]

why can't you use it anymore @quasi remnant ?

[quasi remnant]

because it doesn't teach schurs normal

or symmetric bilinear forms?

[whole rain]

If you're okay with online-only books, linear algebra done wrong maybe ?

[quasi remnant]

honestly i'll take anything at this point

[whole rain]

Well check out linalg done wrong by Treil, then, it might work for you

It has, I think, everything you're asking for

[quasi remnant]

is this the type of book that i can jump straight into and understand everything

or do i need to do read like the first couple chapters or something to get use to his notation

[whole rain]

The notations are not particularly odd, so I'd say you should be able to follow without reading the first chapters if you already know them

[quasi remnant]

hmm okay, thanks

[gray gazelle]

Hey, any commutative algebra book recommendations that covers and uses intro cat theory stuff?

[subtle siren]

If Khan Academy is adequate for your school needs you can use it. I would recommend finding something that interests you and then studying it out of your interest

[feral onyx]

Any resource recommendation for Classical Mechanics? ( Year 1 - Uni)

[clear plaza]

Introduction to Mechanics by Kleppner

[scarlet steeple]

Has anyone read combinatorics a guided discovery mind dropping a review ?

[sage python]

@quasi remnant to get an idea of what to recommend, what didn't you like about FIS?

[crimson pagoda]

lie groups by daniel bump

[hollow drum]

Is there a good alternative to folland's real analysis?

[sage python]

"Real Analysis for Graduate Students" Bass

[hollow drum]

This actually looks really good thank you lol

[misty wyvern]

I've met Bass

Well after he retired tho

[sage python]

Yeah that's the book my undergrad used for its grad real analysis class

And here they use Folland

[misty wyvern]

I used Folland

where we should've used Rudin

Folland is for the weak

[marble solar]

Stein and Shakarchi volumes 3 and 4

It's not as quick as Folland, but I think it does things more thoroughly

[sage python]

@misty wyvern is Rudin tougher than Folland?

I thought they were fairly similar tbh, just that Rudin had more of a harmonic/complex analysis angle while Folland did more straight up "real analysis"

[misty wyvern]

I remember Rudin being a lot more terse, at the very least.

[sturdy sail]

Any book references that cover matroids?

[gray gazelle]

Can anyone share Springboard book PDF for class 8th ?

[gray gazelle]

Are the Schaun outline books any good?

[gray gazelle]

No

[gray gazelle]

[gray gazelle]

I am 1st grade college student. I am learning English right now but we don't learn anything science related. I know algebra but in Turkish so I have no idea about most terms. Any book recommendations for algebra? I am sure our library has it. I checked and we have more than 20 different algebra books.

[karmic thorn]

"Algebra" has a very broad scope and can range from anywhere between a school book to a graduate text. Can you share your syllabus/curriculum?

[gray gazelle]

Since I am in prep school, I haven't taken a course yet.

There are algebra courses as electives but I don't want to waste my slots.

[karmic thorn]

I see, so you want a book on algebra that you'll eventually see throughout your course?

[gray gazelle]

Nah

[karmic thorn]

Because there's no dedicated algebra course in year 1, and only linear algebra in year 2 as far as I can see

[gray gazelle]

We will see linear algebra

Yes

I want to use my technical electives for organic chemistry

[karmic thorn]

For linear algebra, the book by Friedberg/Insel/Spence is recommended a lot, but since you have a "linear algebra and differential equations" course, you might want to see Strang's Introduction to Linear Algebra first

https://youtube.com/playlist?list=PL221E2BBF13BECF6C

The book is based on this lecture series

You can probably also find notes and problem sets on the MIT website for the same

[gray gazelle]

What about college algebra? I mean I am not sure if I meet the requirements. So I want to study algebra before taking calculus

[karmic thorn]

Hmm, you should go through "precalculus" on Khan Academy

That should be enough preparation

[gray gazelle]

I score 100% though

I did it

[karmic thorn]

On your calculus course?

[gray gazelle]

No

[gray gazelle]

I went through every math course that I though I needed to. But they felt easy

Our univers

[karmic thorn]

That should be enough preparation then

If you want to look ahead in algebra, go for Strang or an introductory abstract algebra textbook.

[gray gazelle]

Alright then. What if I forget things 😦

I will take 101 next autumn

I think College Algebra here is an American term for precalculus

I see then I should be okay

Go through Khan Academy for starters.

In terms of a book, Axler's PreCalculus is good concise book.

[karmic thorn]

Ideally you would not, and the bits you do forget can be reviewed quickly.

[gray gazelle]

Yeah thanks

[gray gazelle]

It was a surprise but our library doesn't have it.

[gray gazelle]

||libgen it||

[gray gazelle]

I prefer books but alright.

[signal tiger]

Understanding Analysis, by Stephen abbott
a good analysis books for beginners

[scarlet steeple]

Id also suggest Elementary Analysis btw

I think its a great book for beginners tbh

[gray gazelle]

I am not a beginner. But I didn't learn in English and I also want to revise

[hearty steppe]

Friedberg Insel Spence made two LA books btw. The one you want is titled Linear Algebra. Just started it middle or last week and I like it. I wish I was exposed to this instead of their elementary linear algebra book but it’s probably good to make sure you are familiar with basic systems computations

[gray gazelle]

I think our library has the normal one

[broken meadow]

yes this is the one

good book

[gray gazelle]

We have 250 (11 lost) different LA books in our library

1500 electronic copies

Biggest library of Turkey, 3rd in Europe

[gray jungle]

11 sacrificed by students

[gray gazelle]

@gray gazelle

[livid ermine]

that book is so good

ch6 is so lovely

linear algebra is made from love

[hearty steppe]

Yea I started going through it last Wednesday. It’s amazing

[novel obsidian]

https://talentdevelop.com/articles/HTBAG.html I found this article on terry tao's blog, I suggest giving it a read, its really motivating

its like 2 pages long

[split knoll]

Book recommendations from me:

• Abstract Algebra Thomas W. Judson (2020 edition).
• Advanced Linear Algebra Roman S. Springer (2008).
• Introduction to Topology Gamelin & Greene (Second edition).
• Algebraic Topology Tammo tom Dieck.

^^ for all who are interested (i really liked them).

[marble solar]

Not even algebra from Richard Elman

Wow

Someone give me the most painless introductory book into Galois Theory

[hearty steppe]

Richard Elman?

[marble solar]

https://www.math.ucla.edu/~rse/algebra_book.pdf

Wow he's at 777 pages

[dense wren]

How is Roman’s book compared to Hoffman&Kunze?

[marble solar]

Roman does stuff over Modules & does in general a much more abstract version

Did you take 115AH berg?

[dense wren]

No

[hollow peak]

rotman

he starts with absolutely no ring theory

[tulip blade]

Richard Borcherds has some lectures online

[strong hornet]

#ask

Do you guys have books recomendation for beginner like me?. I'm really shitty at math. I guess my math level is elementary school.

[pale hawk]

Concepts of modern mathematics by Ian Stewart

[quick hornet]

that wont really... teach you mathematics

its not its purpose

honestly though all elementary-level math textbooks are kinda the same

just go through khan academy till you get stuck

[misty wyvern]

If you liked Stewart you'd like Rudin

[cerulean niche]

Can anyone recommend a good book where I can learn what to do with all these math symbols and what they mean.

[quick hornet]

thats a pretty wide breadth of topics

you wont find it all in one book.

(also, that image's definition of "equation" is... dubious)

[misty wyvern]

lmao more like definitions

Literally who cares about #16

does anyone here want to stan #16, that's the only thing on that sheet I haven't used

also 17 makes me reee so hard

it's just GBM write down GBM

#11 is several equations but it has a single tensorial equation representation

[marble solar]

Maxwell's equations not in tensor form

No dirac equation

No einstein field equations

Nice

[pale hawk]

is that what they asked?

[quick hornet]

usually when i hear "beginner", it implies that theyre trying to, you know

begin the process of learning

which isnt exactly stewarts goal

[pale hawk]

i don't see why Stewart wouldn't be useful in that case

[quick hornet]

i highly doubt anyone comes out of ian stewart able to do more mathematics than they went into it with

knowing more random facts, maybe

[pale hawk]

so

[quick hornet]

having more appreciation for it, sure

but it wont help em pass their trig test

[pale hawk]

they didn't really ask for help passing classes though

it would be strange to ask for just a general book on "math" if they're a student struggling with a particular subject

that's why i recommend stewart to people trying to "get" math

[quick hornet]

¯_(ツ)_/¯

a lot of middle/high schoolers genuinely dont know what to call the math theyre learning

[pale hawk]

that doesn't make sense

[quick hornet]

not to mention people who graduated long ago and want to relearn but have no clue what anything is called

or what order it goes in or whatever

[pale hawk]

i would argue Stewart is good for these people too

[quick hornet]

trust me, a lot of people come in here asking for help with "math 9" or "advanced functions" or whatever

if you ask them "what topic" they might say "solving for x"

[pale hawk]

i believe that but usually there's any indication that it is a math course

obviously this person didn't really leave much information but if they're just asking for a book to help understand "math" as a concept i recommend Stewart

[quick hornet]

i suppose i see your point

[brisk ice]

not a book recommendation but which course should I follow (or are these overrated) https://ocw.mit.edu/courses/physics/8-01sc-classical-mechanics-fall-2016/ or https://ocw.aprende.org/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/

I would say the first course link is more complete in sturctures to fllow and all together. It has its own written mini book but rather than lectures it has like mini lessons and a few problems as you go.

The other one is an actual lecture roughly 1 hour

Here is the book for the OCW first course ( https://openlearninglibrary.mit.edu/courses/course-v1:MITx+8.01.1x+3T2018/courseware/Intro/seq-resources/?activate_block_id=block-v1%3AMITx%2B8.01.1x%2B3T2018%2Btype%40sequential%2Bblock%40seq-resources)

the other course uses this book

https://books.google.com/books/about/Physics.html?id=aRBhAQAACAAJ

Ohanian physics

worse is I have already done like a physics course in Highschool (basically just followed khan academy) but it wasn't taught with a calculus approach. However, I cant recall anything from it really. there were no lectuers in my highschool physics. It was all online and basically just completeing khan academy at my own pace

the first course is edx course : https://openlearninglibrary.mit.edu/courses/course-v1:MITx+8.01.1x+3T2018/course/

[brisk ice]

TLDR which course would you follow out of the two or is there something better? Really want to link the calculas and physics ⛓️ but also want a course that has various demonstrations and can explain well in an intuitive manner

Also yes I understand it is a basic first physics course and I guess isn't something you can exactly mess up (picking either) but I just would like a good structured course and don't wanna backtrack if I decide the other is taught better. Ideally I want to go through (8.01, 8.02, 8.03)

[split knoll]

Hoffman & Kunze is a Good Book aswell, both books have good exercises. But I would say that Romans book is more abstract.

[split knoll]

Yep

[storm hatch]

Do anyone has E book free recomendation for summation?

and also for geometry

[cerulean niche]

Thanks for the recommendations

[signal tiger]

geometry + calculus + quantum mechanics + complex number + information theory + chaos theory + classical mechanics + thermodynamics + fourier analysis
these are the topics that you will find all these formulas

[supple folio]

ayo, do you guys have David Burton's History of Mathematics: An Introduction 5th Edition?

[lament palm]

IDK if I can post it here but
https://b-ok.asia/book/511267/fdc295

support authors if u can

[supple folio]

thank u so muchhhh i just want to check something on the european through the dark ages part ><

[supple folio]

i will, thank you~

[main void]

Any recommendations for. a good complex analysis book?

I was looking at Ruel V. Churchills “Complex variables and applications” and it didn’t go as in depth as I would’ve liked, had the same issue with other recommendations I found on the internet

[gray gazelle]

A lot of people shill Visual Complex Analysis by Needham

[main void]

ginna take a look at it, ty!

[novel obsidian]

has anyone here actually read Lev Tarasov's Calculus: Basic Concepts for High schools?

if so, what was it like?

[sharp latch]

Problem solving through problems by Larson has a chapter on summing series and also one on geometry, you can probably find a pdf somewhere

[sleek python]

Do you guys know any particularly good book about counterexamples on late undergrad level and graduate level topics ? I don't really care about the field, though I'm more interested in probability and all related fields of mathematics.

[gray gazelle]

Perhaps: counterexamples in probability by stoyanov

[sleek python]

Is it good ?

[analog pollen]

Think this one is fine

[gray gazelle]

idk yet just found it today, id say its pretty good but you definitely need to know the subject beforehand

[analog pollen]

If ur not following a book

I like kleppner

[brisk ice]

the one by walter lewin or the other one?

[foggy relic]

in general, if you need a pdf of some kind of textbook/normal book, search it at libgen, b-ok, and zlib

[brisk ice]

[broken nexus]

Are there math books for certain grades?

[gray gazelle]

yes. see this, for example

[broken nexus]

oh yeah, our textbooks

well used to be our textbooks

now we use mathlinks

I love reading

[gray gazelle]

what analysis book should i get

[broken nexus]

idk

[gray gazelle]

thanks

[broken nexus]

your welcome

[storm hatch]

tqqq

[gray jungle]

rudin is the dry standard if you know what you're doing
tao is a less punishing version that helps you build intuition slower
abbott is the easiest one out there from what i heard

[hollow drum]

On the other hand rudin is so old that solutions on line are readily available

Although rudin saw Bourbaki and thought "I wanna be like that when I'm a big boy"

[viral moth]

i tried reading rudin for a self intro to analysis cos i wasnt that aware of how difficult it was

then switched to abbott after realising rudin was a bad idea and that one's a lot nicer

[analog pollen]

Walter lewin is great

iirc the other one is more rigourous of covers more topics

But im not sure

But both are good

[gray gazelle]

answer it is

@gray gazelle

[novel obsidian]

It is

[gray gazelle]

I am blind

I never said anything btw

[wintry quartz]

How would y'all recommend i learn analysis? Like I know some proof writing and i'm decent at calc, which book would y'all recommend

[gray gazelle]

tao's analysis

[prisma snow]

Abbott or Rudin or any book but Tao

[gray jungle]

tao's analysis

[frosty girder]

tao's analysis

[gray jungle]

is there any good supplement to rudins discussion of compactness ?
preferably with some motivation

[cursive orbit]

Rudin gives motivation later, in the form of bolzano-weierstrass, azerla-ascozi, weierstrass approximation, and etc.

[wintry quartz]

Why do you not recommend Tao?

[prisma snow]

It tries to define concepts in nonstandard ways that I think are bad. Half of the book isn't really analysis. It has no exercises, the only exercises are to prove some theorems on your own.

I think it's possible to read the entirety of Tao and not be able to solve a single analysis problem afterwards.

[gray gazelle]

What a bad take.

[prisma snow]

[gray jungle]

terrible take

[severe condor]

I need good books about proof theory,any recommendations?

[wintry quartz]

I’ve tried and seen rudin but for my level rn it’s way too hard ngl

[prisma snow]

Abbott is easier than Tao and Rudin

Try it

[wintry quartz]

This one?

But thank you

[prisma snow]

Yes

[gray jungle]

so here is my take im no expert im currently studying through rudin after doing half of tao
i think tao unlike anyone else shows you why you are doing analysis he does what a 1st book on analysis is meant to provide ,building intuition to basic concepts and building the property to motivate you, sure it doesnt have the good topology and advanced concepts but its meant just as spivaks calculus is "a 1st pass on rigour" only complain i have is the slow pace of the book, but as a 1st pass on analysis its prefarable over rudin which is more of a dry 2nd pass on analysis when you have more mathematical maturity, if you feel confident enough to do rudin go for it but if its your 1st meeting with rigorous mathematics tao is just so sweet

but thats my personal opinion i just like it :3

[wintry quartz]

is tao intimidating?

[coral narwhal]

why don't you give it a read and decide for yourself

[wintry quartz]

yeah i prolly should

Thanks guys

[dark orbit]

yeah, just to reiterate, different books work well for different people (and it's not correlated at all with skill level). the answer with math textbooks is always going to be: "find one that teaches the topic in a way you find accessible."

for the most part that's gonna require some trial and error, which is normal

[sharp latch]

My take on Tao:
-Good for people with only calc knowledge as an introduction to the subject, provides necessary background in countability etc
-Bad for anyone that wants to actually study analysis to a practical level

[misty wyvern]

literally stop reading books, all the math you need is on wiki

and ncatlab

[novel obsidian]

wikipedia: the single most unaccesible place on earth when it comes to mathematics

[rancid vine]

Wikipedia will typically have what you're looking for, but it also has a lot of clutter around the info you're looking for. Especially in undergrad when you don't really know a lot, it can be very scary. It's a decent skill to have, to be able to read math wikipedia pages and figuring out what's considered "clutter" and what isn't.

That being said, I'm still in undergrad

[novel obsidian]

I agree, but books still play a part in actually learning math and getting to the point of actually understanding wiki pages. To demonstrate, I present a thought experiment. Suppose an alien who can understand english and is given the task of using exclusively wikipedia to learn mathematics - how far do they get?

[rancid vine]

oh books are amazing!

I've been (albeit slowly) going through a spectral graph theory textbook in my free time

it's much nicer to go through than wikipedia articles

[novel obsidian]

yeah, which is why i don't think that 'literally stop reading all books' is a good mindset to have for any math student

[rancid vine]

I don't think it's a good mindset in general, regardless of major

I do my best to continue reading books unrelated to math. I've been taking humanities & english courses throughout my degree for that exact reason

[novel obsidian]

i think thats a very healthy habit

[atomic hound]

what would a good book on proof theory?

[atomic hound]

why?

[novel obsidian]

Every article is written in a way that a only a mathematician which already understands the topic and needs a refresher about said topic understands. If you are first seeing a topic it is impossible to understand. It is fully formal (for the most part) and is not condusive to how humans learn.

[atomic hound]

got it

[atomic hound]

can you help me with this?

[atomic hound]

...

[novel obsidian]

no lol

im the wrong person to ask

[stray veldt]

it actually varies a lot

many articles seem to be written for a general audience

then some just seem to be written by grad students who got tired of not being able to easily look up small lists of facts on the internet

sometimes you get both in the same article

[gray gazelle]

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

[stray veldt]

also are you sure you want proof theory and not just intro to proofs

[atomic hound]

well, what would be the difference?

[stray veldt]

proof theory is a branch of mathematical logic, intro proofs is "here is how mathematicians talk and the basics of how to prove stuff"

[atomic hound]

well, the two seems interesting!

well

what would be the goods books on proof writting/intro to proofs?

[stray veldt]

people like velleman's how to prove it (i think some of the later chapters, especially the exercises, are horrible though)

[daring ravine]

Wikipedia math pages are incomprehensible if you’re learning for the first time

[atomic hound]

i gonna look it up.

[atomic hound]

for proof theory, bycuriosity,what would you recommend?

[stray veldt]

not doing it

i have no idea about proof theory

[modern stone]

What about Polya’s “How to prove it” or Hammack’s “Book of Proof”?

I’ve heard they are quite good

[stray veldt]

never really looked at them

polya seems to be less math-y

(my general opinion is that those books are too long, hence i wrote ^)

[novel obsidian]

Polya is about problem solving methods generally

Heralded by many

Tao said polya is how he learned how to problem solve

Take that as you will

[gray gazelle]

#book-recommendations message

I have read this one for proof basics.

[stray veldt]

tao probably read it when he was 6 though

[gray gazelle]

If only my parents gave me math books to read when I was 2 years old.

[novel obsidian]

Oh I'm sure, that man was learning analysis at 11

[split knoll]

Does somebody has a book recommendation for advanced abstract algebra?

[misty wyvern]

Aluffi and nlab

[novel obsidian]

. this (ignore)

[latent ginkgo]

Love

[coral narwhal]

but this is complex analysis ? or did some1 delete their msg?

[novel obsidian]

oh i got the wrong one shit

this one

sry for ping i forgot

[stray veldt]

is any of this advanced abstract algebra though

Lang i guess (partly)

[novel obsidian]

that's what I was thinking

also idk what the word 'advanced' means

its totally subjective

[stray veldt]

i would guess anything beyond a first course

but there are many directions you could take such a class so 🤷

[novel obsidian]

mhm, and i would doubt that a first course would cover all the content in any algebra text

[stray veldt]

i guess a "standard" second course would do field and galois theory (in which case i would recommend morandi)

[atomic hound]

Man, you are the Guy!

[gray gazelle]

michael vey

good book series

[brisk ice]

how do you study 2 books and know if you are making progress?

Like if you are only following one book and you are trying to understand course or subject and then you swap to something else isn't it hard to keep track?

unless the chapters line up well or something

[cursive orbit]

well you could use one primarily and use the other one as a supplement

[pale scarab]

Nlab is really concise but incredibly dense. It is one of the best resources around but to learn from it will likely just end up frustrating you.

[unreal lynx]

The Giver is cool

Hunger Games

Anything Rick Riordan or Rick Riordan Presents

[misty wyvern]

many people incorrectly assume the core of algebra is the study of abstract structures and categorical relations. in truth algebra is about frustration and unreadable esoterica, and nlab is the best at both

[dark orbit]

what do you mean by "making progress"? many of the folks i know specifically select from multiple books in order to get a more complete understanding of a given topic

[brisk ice]

well if you are only study from these books and dont have a direct goal / path

like sure it makes more sense if you are already taking a course

and then you have more books to look at little parts of it or whatever

[dark orbit]

if you are learning math on purpose your goal is at lowest specificity... to learn math. if you don't have more specific goals as a self-learner, that's fine, folks do that all the time, but it's definitely worth some thought

[brisk ice]

well i mean more so like

if I want to learn genernal physics or something

and then you end up deep down the weeds or some really niche thing

are you broading your understanding, sure

but idk I guess depends on goals

[dark orbit]

yep, depends on goals

you know what 'learning' feels like, so as long as you're doing... that (and enjoying it), the only thing I can say is 'keep going'

if you end up in the weeds of a niche topic, so be it

i just finished reading a textbook on fluvial geomorphology. slow going, for someone who's never studied geology. enjoyed every bit of it. next up? lie algebras and racial justice [shrug]

if it takes two books to feel like you've learned a topic, and you find it gratifying to learn, go for it. your progress is your learning. there's no metric for learning based on pages read

[errant sage]

What would be some good real analysis expository notes to accompany Rudin?

[analog pollen]

what diff geo book should i read after munkres? smooth manifolds by lee?

[brittle breach]

it's a nice book it you can learn from, I find Lu "An Introduction to Manifolds" more approachable

@analog pollen

[marble solar]

Spivak's Calculus

[marble solar]

I'm a big fan of...Spivak's Differential geometry

You only really need the first 2 volumes unless you're a mega nerd

[gray gazelle]

*unless you're based

[marble solar]

I mean even if you love spivak

Volume 3 is rough

[analog pollen]

thanks

[analog pollen]

yea fuck i don't have those

learnt analysis from abott and calc from stewart

lol

oh lmfao

nvm

didnt know spivak has 3 volumes on diff geo

[gray gazelle]

5

the first one is your standard intro-manifolds stuff, 2-4 are riemannian geometry, and 5 is vector bundles and characteristic classes

i think

[gray jungle]

im using rudin for metric topology rn and i think its fine to use multiple books for a better understanding
i even use kaplansky set theory and metric spaces to grasp and gain motivate on certain concepts better

[analog pollen]

A i see

[quasi eagle]

hi

[analog pollen]

Hello?

[quasi eagle]

hi

what books would you recomend to me

becuse this is book recommentsdations

pls

[stray veldt]

franz lemmermeyer's quadratic number fields

[quasi eagle]

is that a book

[stray veldt]

yes

this is book recommendations

[quasi eagle]

is it a math book

[gray crystal]

harry potter and the half blood prince

• jk rowling

[quasi eagle]

wasnt jk rowiling assassinated

[gray crystal]

👀

[dense wren]

Do I need another algebra book besides Dummit and Foote & Lang

[marble solar]

Just sell your copy of hungerford

Do you like Elman's book Mr. Berg?

[gray gazelle]

When I saw them for the first time in my unis library my eyes popped

Before you ask theyre fine now. I put them back in

[cloud bolt]

any thoughts on "How to Think Like a Mathematician" by Kevin Houston?

[brisk ice]

do you have a class / course or is this all on your own?

[gray jungle]

my courses in metric topology is next month

[hollow drum]

I wouldn't read it cause it sounds corny

Not to say I'm correct that it is corny tho

[regal wasp]

Anything to recommend on Langlands? I’m familiar with Lang level of Galois cohomology, graduate analysis (complex and real/lebesgue), and some other stuff

[quick hornet]

@slim nacelle i know you technically dont do langlands but im sure you can still hit em with one of your walls

[regal wasp]

Akshay Venkatesh was lecturing on TQFT and langlands and it really piqued my interest

[slim nacelle]

Bump's automorphic forms and representations is the canonical place to start

I also like this book especially if you like some physics motivation https://arxiv.org/pdf/1511.04265.pdf

the latter is more fun to read than Bump, for sure

if you want to go reasonably deep into the story for modular forms and automorphic representations of GL_2 you read Bump and do most of the exercises in there

then there are loads of directions to go after that

[sudden kindle]

I wish there were lectures on Bump's book

[sturdy sail]

Hey, what are some books that cover fourier transforms on locally compact abelian groups?

I suppose some functional analysis books might cover this.

Stuff like Pontryagin duality, Peter-Weyl theorem and so on.

[sudden kindle]

Maybe Bump's Lie Groups but idk

[fringe citrus]

My question, is based on my goals, does anyone have experience with these texts? I'm looking to begin in January, and was going to try to burn through these over the course of November and December to prepare myself. - I'm also looking for a useful math tutor that is good, and has the time. (I can pay as well if needed $)

[frigid comet]

I like Folland's abstract harmonic analysis book for these topics.

[sturdy sail]

I don't actually have much background in analysis

I might take a look tho

[frigid comet]

https://tenor.com/view/what-staring-stare-cat-stare-staring-cat-gif-17697847

[sturdy sail]

I was hoping for something with a more topological flavor

And that is more focused on its applications to lie groups and etc

[frigid comet]

you won't really be able to avoid some amount of analysis in such topics, but yeah idk what would be your preferred text then.

[sturdy sail]

I might take a look at Bump's book then, but I will listen to the analyst here and take a look at Folland's too.

Thanks for the suggestions

[frigid comet]

https://tenor.com/view/cat-cat-standing-cat-stare-stare-bruhcat-gif-22348277

[gusty smelt]

bumps book only does it for compact groups not locally compact, however I'd recommend reading the first 4 chapters because its honestly very beautiful

Got me interested to read harmonic analysis (in the future tho oof)

[sturdy sail]

This seems to be the only way I am going to learn fourier analysis

It looks quite nice, indeed, Bourbaki talks a bit about such topics in their General Topology book.

It talks about topological groups

but doesn't go too further

[gusty smelt]

try reading like the 2 pages of ch 2 of bumps book, it like summarizes the first 4 ch and it will probably get u excited to read it (quick read if you just read upuntil ch 4)

[sturdy sail]

Aight, will take a look at it. Prolly by next year

[sullen delta]

[gray gazelle]

What can you say about Susanna epp's book

Discrete mathematics with applications, the last edition of the series.

[sullen delta]

😳

[tulip blade]

Try kahn academy

[fringe citrus]

Ty

[marble solar]

Have you seen Rudin's "Fourier Analysis on Groups" text?

[gray gazelle]

Im going to attempt to complete its exercises in about 3 weeks time, so I want to know if anyone here read the book once or even is familar with it through a course

The book is Matsamura’s Comm Alg

I want to speed through it, but I am not sure if it is possible. It feels like a smooth read in my opinion

[marble solar]

I don't think speeding through that is a good idea

Usually you want to put things into longer term memory