book-recommendations

[tribal crow]

I'm personally interested in learning more about classical mechanics and general relativity, but that's just me

[torn blade]

i think i should start with mechanics right? i was kinda lying when i said i didnt do any physics cause i did mechanics & further mechanics in high school

and i liked that because it was basically all maths and hardly any physics :]

[tribal crow]

mechanics isn't a bad place to start

you could probably start there, or with E&M, or with QM

it's kind of your choice imo

[torn blade]

E&M?

[tribal crow]

electricity/magnetism

lots and lots of vector calculus

[torn blade]

oooo ok

[tribal crow]

thing is, I feel like whatever subfields of math interest you the most will have a nonzero impact on what subfields of physics interest you the most

if you're into geometry (like me), then classical mechanics and general relativity are attractive

and so on for other subfields c:

[torn blade]

linear algebra, abstract algebra, topology, getting into some algebraic topology... the first of these is obviously used extensively, maybe the other 3 too, but idt id necessarily wanna look into a field of physics just because it uses them tbh

ive heard some representation theory knowledge is good?

[tribal crow]

probably, though perhaps not immediately

I should say at this time that my words aren’t gospel, and others may disagree

[torn blade]

helpful nonetheless

[tribal crow]

I do agree with this final assessment though

you should probably sweep a little broadly to get a taste for what’s out there, before settling on smth specific

unless you happen to find something that’s so engaging you can’t let go

[torn blade]

okayy thank you

[tribal crow]

ig this takes quite a lot of time though

it’s not dissimilar to mathematics in that sense though

[pliant wadi]

Statistical mechanics and QM if you lean more towards the analysis side. If geometry, then GR is an interesting place to jump in or you can start with electrodynamics.

Oh and ofc, considering your background non-linear dynamics would prolly be the best! There's a book by Hilborn: Chaos and Nonlinear Dynamics. Though it takes more of a chatty approach to things at times, it's definitely more mathematical than strogatz which is generally the more popular and introductory choice in a physics course. A downside might be being unable to find a good copy of the book. It's hard to come by.

Oh and if you are feeling particularly out there, jump into the world of Quantum Dynamics. 🔥

Solid state physics is a solid choice too and from there you can get into condensed matter. (You'd need some electrodynamics and QM as well here ig). There's some interesting work by W. Anderson 'on absence of Diffusion on certain random lattices', studying quasi-periodic models, etc.

There's some interesting bit of analysis that you come across in astrophysics - Like use of minkowski functionals, hadwiger's thm, shapefinders, etc. Naturally Cosmology is an area of interest from a mathematical perspective along similar lines.

And ofc my favourite, there's: Quantum Topology!

Source: Courses I have taken; Espionage missions to physics dept seminars/poster presentations in search for free food.

[rocky sphinx]

Comprehensive math is fun book to read my grandpa gave me volume 2 and i don’t feel like studying when reading it

It’s mostly how to measure area and space of random shapes and other subjects

[silk cosmos]

how to get good at combinatorics problems?

[wise crater]

count really high

[silk cosmos]

i have knowledge of a level statistics and not much else

and struggled with interview combinatorics problem

[silk cosmos]

time is essential for me

i have to solve it in 7.5 minutes

1 problem divided into 3 mini problems

[dawn shoal]

Can you really go into QM without any prior knowledge of classical mechanics?

[native cradle]

Can y'all suggest a nice book on algebra

for an undergraduate course

would Judson. be a good option?

[mossy flume]

I like Artin alot

Dummit and Foote seems to be standard but I don't like it lol (I think it's far too dry)

I've heard good things about Judson though but I've never looked at it

[native cradle]

Is it similar in style to LADR

was hoping for something like that

[fresh skiff]

Wdym by DRY?
I have seen this bunch of times.

[remote vortex]

I don't know whom you're asking and in what context, but in programming it's the principle of "Don't Repeat Yourself", i.e. avoid writing two separate pieces of code that do the same thing.

[fresh skiff]

I was asking in this context

[remote vortex]

Ah, the capitalization threw me off.

[fresh skiff]

Lmao

I should use italic rather than Capital

[remote vortex]

I would describe a mathematical text as "dry" if it was just statements of definitions and theorems and the text of proofs, without any commentary or personality.

[fresh skiff]

Oh unlike Abbott who talks with the reader

[mossy flume]

yea D&F was just alot of

Theorem
Proof
Lemma
Proof
Lemma
Proof
Lemma
Proof
Example
Example
Example
Theorem
Proof

repeat ad nauseum

just bleh

great reference text

but for actually learning, I don't like it

Artin I feel does a better job talking to the reader and motivating things

[fresh skiff]

Oh interesting. I will start algebra soon once read analysis and MT

But many people like D and F

Maybe as a reference, I am not sure.

[small perch]

leng, aluffi are my favorite books

[fresh skiff]

Do you mean Lang?

[small perch]

oh, really

yeah

[fresh skiff]

Lang Algebra 3rd edition?

[small perch]

yeah

[fresh skiff]

It's graduate level book
I haven't even taken first course

[small perch]

But it can be too much for your course, but book is pretty module one and you can just skip a lot and you will still understand

[small perch]

Oh, it's actually good for first reading

Depends on how much algebra means to you though, but I don't know if there are more basic texts

Aluffi has another book for people who are new to algebra

Aluffi Algebra Notes from the Underground

[fresh skiff]

Yeah. But algebra by Lang for first reading looks horrible tbh

[open merlin]

I've been working through this & really enjoying it so far ^_^
The exercises are probably on the easy side tho (Since I can do them 😆)

[tender river]

you can try using artin, theres a server full of people working through artin as well

[native cradle]

Cool

thanks!

[tribal crow]

ehh, sure?

I don’t really see what’s stopping you

[dawn shoal]

I know close to nothing about physics, but I assumed there would be some prerequisites, just like you should know linear algebra to get into multivariate analysis

If there's none, then that's really nice

[pliant wadi]

I mean, there is! But it's not that much of a big deal. You need bits and pieces of a lot of things but they can be easily learnt over a short period of time.

For a complete newcomer, Griffiths's book is a good one.

It's readable, it's complete, the problems are nice and it covers a good deal of ground.

No kidding, it almost reads like a good novel.

[steel cloud]

Any idea about Kalpansky's set theory and metric space?

[dawn shoal]

https://en.wikipedia.org/wiki/Introduction_to_Quantum_Mechanics_(book)
This one?

[pliant wadi]

Yea but I used a newer edition ig

[pliant wadi]

Yea we used it for our set theory + proof writing course

Is that what you need it for

[dawn shoal]

Thanks! When I have more free time, I'll give it a go!

[pliant wadi]

super! :)

[pliant wadi]

'cause it's good and all as an intro text, but there are better texts out there imho

Both for metric spaces and set theory

But yea it's very concise

[steel cloud]

I need for metric space

[pliant wadi]

What all courses have you taken so far

Are you planning to take topology, is that what it's for?

[steel cloud]

Abstract algebra and topology and analysis I already done Carothers but now I want to revise metric space

[pliant wadi]

Ohh then

Simmons

Is a good one

[steel cloud]

Bit isn't for topology?

[pliant wadi]

The chapter for metric spaces is good

[steel cloud]

What about Searcoid?

Or Conway?

[pliant wadi]

Oh I own that book! A tad elaborate for a review. But it's a good one, yes.

[pliant wadi]

This idk about

Hmm is it the same guy with the complex analysis book

That's more well-known ig

[timber mesa]

I like Searcoid's metric space book

has some unusual (counter)examples and bits like distinct notions equivalence of metrics, which aren't often mentioned elsewhere

[steel cloud]

Okay, is there any metric space problem book?

If anyone is interested why don't you make a review on metric space books?

[timber mesa]

that one does have a bunch of exercises iirc, also most problem books in pointset topology will have a chapter on metric spaces

[pliant wadi]

The exercises in Simmons are nice

[steel cloud]

Okay

[steel cloud]

I will follow that

Also there is one Surinder Pal's metric space

[pliant wadi]

no idea

[steel cloud]

Okay thank you

[pliant wadi]

Mention not!

[noble swan]

hi

what book would you guys reccomend for an introduction in number theory ?

[remote sparrow]

o'searcoid has solutions to many problems in the back, and there's a full solutions manual online

[remote sparrow]

#book-recommendations message

[noble swan]

thank you so much

[grim delta]

Any good books for someone starting with geometry - trigonometry?

[timber mesa]

there's one by Skokowski, it's decent I've taught with it

I also liked Lehmann's Analytic Geometry but that book's old and somehow it's easier to find the Spanish version than the original one }

[graceful moon]

Magnus' Metric Spaces book is really nice

[drowsy nacelle]

Question

Is there a list anywhere here of like top tier math books overall irrespective of the area they’re in

Like just very well written ones in any area

I’ve seen the topic specific lists but I guess what I’m asking is slightly different than just like the aggregate of those lists cause “best books for xyz topic” is less exclusive than ones that just stand out among books in general although some would probably coincide

Maybe could’ve phrased this better but yeah

[molten gulch]

I'd assume it's a bit subjective but if there is a big list of common favourites, I'd like to see this too

[graceful moon]

Dami has a list of quite a few books in various subjects pinned in this channel

[drowsy nacelle]

Yeah those are part of the ones I was referring to here

[drowsy nacelle]

.

[nova crane]

any good books for geometry in texas

[tribal crow]

why is Texas important?

[remote sparrow]

there might be curricular standards specific to texas

[tribal crow]

I see

[bright epoch]

You need a big textbook

[trail hemlock]

Khan academy has a list of videos that align with TEKS
https://www.khanacademy.org/standards/TEKS.Math
and the most popular TEKS geometry book is this one: https://www.amazon.com/Geometry-Texas-Student-Mcgraw-Hill/dp/0021392552
which seems to be pretty cheap if u buy used

u can always jus buy a regular geometry book, I like aops geometry but there are a lot of other recs here. teks is not different enough from other standards where I would justify buying a whole seperate book

[steel cloud]

Okay thank you

[steel cloud]

Okay thank you

[heady ember]

Otherwise the IRS will come for you

Texas ~ Taxes

[grim delta]

Can you specify the name?. I am self-taught and would like to learn geometry and trigonometry now that I am finishing pre-calculus.

[vital bane]

Texas is non-euclidean

[tender cobalt]

I'm learning calculus from michael spivak book, what would be the followup book for multivariable calculus?

any standard proof based multivariable calculus book like spivak?

[cedar rain]

Spivak wrote one on multivariable calculus called Calculus on Manifolds.

[open merlin]

Shifrin's multivariable mathematics probably?

[remote sparrow]

hubbard is also a good choice

[trail hemlock]

folland also has a nice book

[tender cobalt]

Thanks I'll check them all out

[tender cobalt]

Since I'd like a bit of applications as well, I'm considering either one of Hubbard, Shifrin, And Folland, which one would you guys suggest? (I don't have strong background in linear algebra)

just read Shifrin's preface, it asks for the reader to have finished a course in single variable calculus with Spivak's text

[tender cobalt]

Maybe I'm going to consider either shifrin or folland

Actually hubbard looks promising too

I'm having hard time deciding lol

Shifrin and Folland's books seems to reference Hubbard's one

[vital bane]

Shifrin has lectures based on his book on youtube

[tender cobalt]

Just saw it

[vital bane]

https://www.youtube.com/playlist?list=PL5I-Eyk8l9FHdJUd9UujGcvumjCFPHbrd

[tender cobalt]

Do you think it'd be a good idea to start on that without any prior multivariable calculus knowledge

With just spivak level calculus knowledge

[vital bane]

yes, it's an introductory course

You can also check out

https://www.khanacademy.org/math/multivariable-calculus

and

http://www.damtp.cam.ac.uk/user/tong/vc.html

[honest bluff]

Does anyone have good book suggestions for getting imo level

[heady ember]

Normally one might do analysis on just R^n. But, if you want to do it more generally on normed spaces, you can check out

• Henri Cartan Differential Calculus
• Coleman Rodney Calculus on Normed Vector Spaces

[stiff grail]

I heard spivak calculus more into real analysis
is this true?

[trail hemlock]

yes

[stiff grail]

so even if Ik calculus should I read it?

or do its multi var book?

[trail hemlock]

i may not be caught up with the convo, whats your end goal?

[floral lantern]

hi blackbeard

did u apply for primes

[trail hemlock]

marlins i dont wanna talk abt it dude

ask amukh

[floral lantern]

huh

ok

sorry mb didn't know

[trail hemlock]

wait im kidding lol

[floral lantern]

💀

did u get interview

[trail hemlock]

no my teachers didnt submit their recs

[floral lantern]

bruh

💀

that's such ass holy shit

that sucks

[stiff grail]

like I was wondering since I need to get sm insights on real analysis
I was wondering should I read it (I alr know cal)
or read its multivar book (which i know little abt the topic)

[trail hemlock]

its not all lost, i found a local professor who does research into stuff that im intereted in, so im meeting with him fairly often

[floral lantern]

oh super cool

any new results or anything yet?

my physics stuff is getting close to getting basic new stuff but there's so much bullshit physics

[trail hemlock]

if you already know calc, you might wanna jump right into real analysis. Spivak's Calc can offer you something in terms of mathematical maturity, but honestly its not a strict prerequisite for real analysis. I assume u meant calc from a book like Thomas or Larson, so consider reading

• Tao's Analysis 1
• Abbott's Understanding Analysis
• N. L. Carothers Real Analysis
  since they are fairly gentle. real analysis does not require or even deal with multivariable calculus. if you do want some nice multicalc books, follow the conversation from [this ](#book-recommendations message) point

[stiff grail]

alrighty thank you

[floral lantern]

Tao's book builds up a lot of basic math as well (constructions of integers, rationals, reals, sets)

[stiff grail]

Tao's Analysis meaning by terence tao?

[floral lantern]

yes

[stiff grail]

holy shit

[trail hemlock]

marlins what is this brokie emoji use not ⬆️

[grand thistle]

just read rudin

[floral lantern]

that would be my recommendation if you don't have formal proof experience

[floral lantern]

nerd

how are college apps

[trail hemlock]

yeah who uses rudin

smh

[floral lantern]

idk my school uses a fucking open source book

💀

[molten gulch]

I don't think this is a great idea if someone doesn't already have some mathematical maturity

[grand thistle]

brown comes out in 17 hrs lmfaooo

[floral lantern]

LMAOO

[grand thistle]

scared as shit

[floral lantern]

ik princeton came out alr

and stuff

cornell?

I think

but gl

you'll make it in

[grand thistle]

thanks lmao

[grand thistle]

i was joking

[floral lantern]

I got my PRIMES interview email today so I felt the reckoning of god as well

[trail hemlock]

👀 congrats

[grand thistle]

oh shit u got this bruh

[floral lantern]

I need to lock in I think I'm cooked for interview

💀

[stiff grail]

after this real analysis I can finally start physik lmao

[floral lantern]

I got a russian dude who moved here last year

[floral lantern]

???

what

[stiff grail]

yea

[floral lantern]

analysis isn't a prereq for physics or anything

[grand thistle]

why do u want real analysis for physics

[floral lantern]

it's not even really helpful until you get into deep theoretical stuff or PDEs

[trail hemlock]

bros reading Spivak's Physics for Mathematicians or sum 🙏

[floral lantern]

if you want advanced math for physics, linear and abstract algebra are key

especially linear algebra for QM

and a little bit of representation theory but that's advanced stuff

[grand thistle]

or i guess diff geo for mechanics

[floral lantern]

well I mean yes but that's definitively grad school stuff

[stiff grail]

so I need LA, PDES for physik only?

[floral lantern]

not even really PDEs

you need to know LA

and basic ODEs

for basic physics

[stiff grail]

oh then I can start

[floral lantern]

if you go down the theoretical route you will need to do a lot of group theory/rep theory/lie theory

but yeah

[stiff grail]

ohh

[floral lantern]

LA/ODEs will take you through an entire undergrad curriculum

lol

[stiff grail]

damn

[floral lantern]

analysis is almost not relevant at all unless you look at the functional analysis formalism of QFT

[stiff grail]

any specific book you know?

[floral lantern]

for what subject?

and at what level

[grand thistle]

you likely won't be using heine borel or smth in your mechanics class

[trail hemlock]

😔 u dont gotta remind me man

[floral lantern]

wdym likely 😭

[stiff grail]

mechanics and electro magnetism
ug level only
But should start from basic

[floral lantern]

ok

so at the first year level?

[grand thistle]

e&m just make sure ur multivariable calc is good

[stiff grail]

yes

[floral lantern]

or have you seen some mech/e&m in high school

ok

the best books are David Morin's book

[trail hemlock]

marlins dont say morin or sum 💀

[stiff grail]

little

[stiff grail]

oh?

[floral lantern]

huh

morin is still probably best

classical mechanics is his mech book

purcell and morin is the e&m book

mech you can kind of do whatever

but purcell and morin is the definitive best e&m book for getting good at it at the first year level

[stiff grail]

david morin right?

https://davidmorin.physics.fas.harvard.edu/books/

found it

[floral lantern]

yes

[stiff grail]

thank youu

[floral lantern]

the books are hard and will take you a long time to work through

but super good

[stiff grail]

alrighty thanks

[trail hemlock]

same vibes

[stiff grail]

hahaha

[vital bane]

Best classical mechanics book: John Taylor

Best Electrodynamics book: D.J. Griffiths

I mean of course Morin and Purcell are great too

it's just Taylor and Griffiths are my personal favorites so I have a bias towards them

[novel hound]

Saw this on reddit: Springer discount: Code HOL30 for 30% off all books/ebooks until December 31st, 2024.

[trail hemlock]

ily if this works

YO

[novel hound]

I was hoping for more, 50% would have been nice 😢

[trail hemlock]

springer still greedy but we get what we get

[floral lantern]

to be fair, these are upper division books

fantastic books (especially Griffiths)

[trail hemlock]

@jovial parrot how is de carmo for you

[jovial parrot]

It’s chill

I didn’t work on it for a bit cuz of school

And stuff

But it was chill last time I checked

[vital bane]

I mean... anyone with calculus and some linear algebra knowledge can get started with these tbh

Like they cover all the necessary prereqs to get started

[floral lantern]

I mean, yeah. But, the background from first-year courses is imo necessary to interpret all the complex stuff in generality. I know prior exposure is assumed specifically for Griffiths (idk about Taylor).

[trail hemlock]

ok

thanks

[median iron]

Why are they considered upper division?

Those books are right after a hs course in Physics

[formal bronze]

Griffiths is a first semester book

[floral lantern]

Most universities only use those for upper div classes, even the very prestigious ones

The first E&M courses at mit and Harvard use Purcell and Morin iirc

[trail hemlock]

forgot to ask, which one?

[formal bronze]

I see

[floral lantern]

Jiri lebl’s book or something

See jirka.org

I’ve heard it’s a mid book

The open source algebra book (Judson) I think is pretty good

[trail hemlock]

oh this looks aight

carothers remains my favorite so far (including rudin)

[floral lantern]

Judson is a great AbsAlg book imo pretty clear exposition

Exercises don’t have enough computation though

Which is a huge problem

[trail hemlock]

i meant the real analysis text

ohh judson looks cool

[remote sparrow]

bro is not doing the sagemath exercises/projects

i get it'd be a hassle tho

[floral lantern]

True but like I mean there’s value to handheld concrete stuff

[remote sparrow]

trying small examples by hand before writing the code is common practice

[floral lantern]

Fair enough

[tender cobalt]

still having hard time deciding between shifrin, folland, and hubbard

ima just start with one of them and just swtich to other if i have hard time reading one

[quasi haven]

Any good book for Proof for engineers who are non-math?

[tender cobalt]

update: im loving shifrin's lectures, maybe ill follow through shifrin's book

[tender cobalt]

there's this really nice proof writing book for beginners by Jay Cummings

[quasi haven]

can a non-math guy like me understand it?

I mean I dont know the landuage of math

[tender cobalt]

yea

just knowing basic math is enough

[quasi haven]

math guys use a lot of symbols which I call language of math

I dont understand them

[tender cobalt]

yeah the book covers them too

[quasi haven]

okay

[tender cobalt]

this dude is a legend

i never understood vector projections much until i saw his video

[heavy sentinel]

Whats a good text or notes for rep theory of Lie groups? I want to properly understand the relation between weyl groups and simple lie algebras

[stray veldt]

is that not in fulton-harris?

thats the standard book

[flint tusk]

Squid Game

[vital bane]

not necessarily, i had no trouble going through griffiths without prior exposure to basic stuff

Besided you can jist watch some lectures on the more basic stuff if you really want to

Griffiths starts out from coulomb's law, i.e the literal starting point of EM

and he has an entire chapter dedicated to reviewing Vector Calc

[tender cobalt]

you can just skim through multivariable calculus part from a book like Stewart's and read through griffiths without any issues tbh

I guess griffith's notation is a bit weird which makes it harder to read for some people

[vital bane]

physics notation🗿

[analog spade]

What do you guys think about Edgar Allan Poe - The Masque of the Red Death?

I'm about to start reading it

[vital bane]

I've heard of Edgar Allan Poe a few times

I heard he was a Poet

ba dum tssh

[daring lake]

You are so based

His works are in my to read

if i can get through fucking Ulysses

[restive falcon]

what

don't ping me randomly please

[gray gazelle]

Your famous

[restive falcon]

wait why would i know about history of maths?

[gray gazelle]

Your a genius

[restive falcon]

<@&268886789983436800> slur used by becoming

then don't ping random people and call them slurs

[split portal]

Is the issue a slur? Or just them stereotyping ppl?

[restive falcon]

the word i called them out on is a slur

[split portal]

Okay, thanks for making it obvious that you aren't participating in good faith here. You can come back in three months. In the future you should be more considerate of other users.

Huh, the mute didn't work at first. You can dm @marble steeple

[elfin scarab]

Boy minus girl

[covert vector]

hello! does anyone have any recommendations for physics mechanics textbooks (preferably ones that go into lagrangian mechanics and beyond, etc what would come in a mechanics II course in college) if there are no options for a book with both good supplementary writing And good exercises, good exercises are prioritized

[keen pebble]

taylor classical mechanics

[brisk ice]

Anyone know anything that is relevant to tomography and tomographic reconstruction? Maybe some sort of data processing kind of thing. Like how algorithm for something like a CT scan works.

[autumn fiber]

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

[snow valley]

Is Sheldon axler linear algebra a good intro to proof based math

[rigid trail]

It's a linear algebra book

[snow valley]

So is it, or it wouldn't be wise to start with that

[timber mesa]

well it's a linear algebra book first and foremost, I don't think any particular care is made about explaining what proofs are or something

there's Hammack's Book of Proof which you can read the first few chapters of (or directly skip to Part II) to get the hang of it https://richardhammack.github.io/BookOfProof/

[timber mesa]

still, it's a decently written book and people like it for a good reason

[snow valley]

What topics should I focus on just the proofs part?

[timber mesa]

from Hammack's book, yes probably

the first part is there if you don't know what sets and propositional logic are, the part about proofs then builds from that

[rigid trail]

I have sheldon axler and it does not handhold you teaching you how proofs work

granted, the proofs arent too crazy

[snow valley]

If I'm self studying how would I know if my answers are right , is there a place to take a quiz or something,

[timber mesa]

yeah some people say LA is a good place to start with proofs precisely because the proofs aren't too crazy

linear maps and vector spaces are about the nicest behaving structure there is

[rigid trail]

i like discrete math as an introduction to proofs but that's probably only because that was my experience lol

[timber mesa]

for many things you can use the searchbar on e.g. https://math.stackexchange.com

or in the case of Hammack there's solutions in the back

idk if Axler has this but it's such a commonly used book you'll probably find solutions in the Internet

as a last resort you can just ask people here

in a help channel, or #linear-algebra and #proofs-and-logic for the respective topics

[snow valley]

If I decide to try the axler book should I do all the exercises at the end before starting a new topic

[timber mesa]

personally I don't think that's a good way to work through textbooks

[rigid trail]

i think it's good to pick out a few that seem interesting

[timber mesa]

yeah that

sometimes it might even be fine to skip things you don't fully understand and come back to them later

[rigid trail]

or if you arent confident (of your understanding)

good to do basic problems on said topic

Sometimes i glance through all of the problems and try to think of an approach to solving each but not actually doing the work of solving them

i think that's useful too

speaking about math books in general ofc

[snow valley]

Like for example there was an exercise in the book like,

Show a+b=b+a for a,b in F^n it only made sense because axler showed how to prove it but for other exercises they don't tell you.

[dense patio]

It is a bit of a dangerous approach when you end up almost never doing the work though

[rigid trail]

yeah i pick out interesting problems to work through then just glance at the rest usually

idk i'm too lazy to actually do them all

[snow valley]

It's sort of like I know what I need to do but don't know how to execute it or start it.

[dense patio]

Understandable! I just avoid actually writing things down way too much - so for me doing more is the direction to go 😅

[rigid trail]

Yeah often I have to humble myself enough to actually do some problems lol

[dense patio]

Oof, relatable

[gray gazelle]

anyone have good book for calculus i am in highschool

[steady lily]

You can try openstax, see if it's good for you

[gray gazelle]

its free right @steady lily

[steady lily]

Yes

[steady lily]

They also have books for other subjects

[gray gazelle]

thx @steady lily

[vague dagger]

i liked stewart, should probably be able to find a pdf online

[chrome verge]

Did u check internet archive or ocean of pdf ??

I get it from there

[gray gazelle]

sure

[heady ember]

The seven seas is a pathway to many materials... Some would consider unnatural...

[harsh apex]

Any good book to study calculus of variation ?

[slim bramble]

Shrifin's book along with his lectures. lectures are really helpful if you're self studying.

[untold eagle]

can I have some opinion on the Art of Problem solving

algebra precisly

[quasi haven]

Any good book recommendations for Analysis?

[earnest wolf]

Abbott

[formal bronze]

Rudin

[earnest wolf]

this one when one already knows analysis

his exposition to the subject sucks

[tender cobalt]

Yeah Abbot's book is great

[tender cobalt]

I heard Rudin's book is doesn't really go into the motivation behind the proofs lol

[formal bronze]

Rudin is the book usually used for a first course in analysis at my uni

[tender cobalt]

I guess if you're taking a uni course then the lectures will guide you through

for the intuition that the book lacks

[remote vortex]

Yeah, Rudin as a course textbook (i.e. presumably supported by lectures and other guided forms of learning) is still not a great choice, but not necessarily an actively harmful one.

Rudin for self-learning analysis for the first time is a very inadvisable option for the majority of people asking that question.

(although there is a sizeable contingent of such people for whom Rudin does work)

There is the joke (which I make myself) that it's a textbook for people who already know analysis, but at any rate, it's a textbook for people who are already comfortable with reading high-level, concise (not to say terse) mathematical texts.

Abbott is a much more solid pick if the question is just "what's a good book for analysis" without any further information.

If you find Abbott too verbose, slow-paced and boring (some people do), then yeah, Rudin

Honorary shout-out to Fichtenholz (sadly unavailable in English), who makes Abbott look terse

[earnest wolf]

isn't it available in English?
I think I even read some bits of it

altho my memory could be playing tricks on me and in reality I read it in one of the 3 slavic languages that I know

[remote vortex]

To be clear, I mean his three-volume textbook on differential and integral calculus; some of his other works might have been translated, but last I checked that one was not

https://shop.elsevier.com/books/the-fundamentals-of-mathematical-analysis/sneddon/978-0-08-013473-4

This one does seem to exist in English, but I have no experience with that one (although presumably the style will be similar since it's the same author)

[earnest wolf]

yeah, I also had those 3 volumes in mind

[remote vortex]

It does exist in German, wasn't that your native language?

Maybe that's why you're sure you've read it?

[paper tangle]

Oh I also had to ask recommendations on a good set of analysis lecture notes, with ample excercises(and even better if they have solutions) (by analysis I mean includes measure theory and functional analysis)

Freely available online

[remote vortex]

It has been translated into several languages, including German, Polish, Chinese, Vietnamese, and Persian. However, no English translation has been completed yet.
^ That's what Wikipedia syas

[earnest wolf]

Nah, I'm not German
but at this point I don't have a native language lol

[remote vortex]

Apologies for the mistake!

Either way, if you do find it in English, it will be great news

[hasty sluice]

Is it ok to self study a math book if I can't find its solution manual?

[stray veldt]

yes

most math books do not have solution manuals in fact

[hasty sluice]

But how do I know if I solve a problem correctly?

[pulsar lantern]

Practice learning how the techniques works by proving (or attempting to prove) the theorems or work the examples that are worked out first and understand them well before doing the exercises.
Eventually you will reach a point of knowing that your proof or computation is (basically) correct from its logic. But failing that you can also post "verify my proof" questions or plug things into a calculator or computer system if necessary.

[heady ember]

I know Chinese

[earnest wolf]

typeset ur solution with latex or typst and post it here, on reddit, or as a last resort — math.stackexchange.com

but stackexchange is very toxic to anyone who doesn't know how to answer their own question

they have so many great posts with hundreds of upvotes [indicating people wanted to know the answer] while the mods closed many of those for BS reasons

or the passive-agressive replies just to show off and farm some points...

[molten gulch]

They have strict guidelines, if you don't want your question closed, then you shouldn't post any questions that are open ended, styled like homework problems, meta content, or just questions that may have already been duplicated. IMO it's the job of the OP to check via tags AND keywords whether something similar has been done before prior to asking, as if anything, asking twice does just use up people's time

Sometimes the way they close questions is definitely up for debate, but much less than many of the "obvious" cases in my opinion

those are clear cut

[earnest wolf]

I'm telling how my experience was with it

if you are happy about it — good for u

I had a post when the passive aggressive comments / answers weren't even touching the meat of the question(!)

so, u do u ig, but I hate it

[molten gulch]

Okay in the cases where the answers did not even answer the OP's question or provide sources, that is an issue. But in cases where people are duplicating, trolling, or posting homework problems (explicitly stating this as it's against SE TOS), I actually do believe that a bit of chiding is needed, because they should really go just read their book and (if their friends and professor are good), ask them

[earnest wolf]

it wasn't math.SE, but another SE site

the funniest part is that people sometimes justify their downvotes as "I was not interested in the question"

so because u were not interested to answer it, the OP has their posting rights suspended / stripped away

[tropic nacelle]

no, that is not how downvotes are used

downvotes mean that the question doesn't meet SE's quality standards

[earnest wolf]

this was not a guess
I have seen people justifying their downvites this way in comments, and those comments in turn had a lot of upvotes

[tropic nacelle]

link?

[earnest wolf]

I mean, that's a fair question

but it was such a long time ago, that I don't remember much: neither the question itself nor usenames

so sry, I'd love to, but I just don't remember

[merry coral]

any good introduction to measure theory?

[earnest wolf]

in my case it was also the case that

1. people downvoted because they didn't bother to read more than one paragraph and see what the question was about

2. and the "answer" that was most upvoted contained no useful information regarding the question(s).

they even went as far as asking in comments other users how they could improve the answer, without checking first if that's what the OP needed

sorry for the rant btw

[empty quartz]

Any recommendations for a book that gives an overview or introduction to mathematical modeling? Two I've considered so far are: An Introduction to Mathematical Modeling by Edward Bender and Introduction to the Foundations of Applied Mathematics by Mark Holmes. Would either of those be good to read?

[gray gazelle]

Hi! Does anyone have a Calculus I pdf, containing all the main theorems, proofs, definitions? Like a super summarized calculus for someone who already passed all calculus stuff, to remember everything

[molten gulch]

paul's math notes should probably be good

[gray gazelle]

Thank you very much

[quasi haven]

Any nice discrete math book for non-math students?

[earnest wolf]

• what's ur major
• what's the approximate curriculum of ur discrete math class

the second question is because each institution / lecturer includes vastly different topics

afaik, at least in eu

[quasi haven]

Major is Electrical Engineering

Curriculum is none. I'm reading as hobby

[earnest wolf]

so, discrete math is usually a mix of different disciplines

in my case for example, it was (is) ZFC set theory, combinatorics, graphs/automatons/Turing Machines etc

and it might be better to find resources for each part separately

if u r reading as a hobby — try to narrow down just by a tiny bit what exactly interests u in discrete math. see for example some online curriculums and topics they include

and then search / ask again resources for the topics u chose

[quasi haven]

I'm more interested in the logic, combinatorics and graphs (I never studied graphs)

[normal crystal]

Epp - Discrete Math

[earnest wolf]

For graphs, I'd recommend seeing video lectures from this and this courses (the second one is more advanced)

watch specifically the ones abt graphs. like lectures about breath-first search, depth-first search, shortest paths, bellman-ford, dijkstra, minimum spanning tree, max flow / min cuts

[quasi haven]

Thank you

[quasi haven]

I'll look at it as well

[normal crystal]

those courses both presuppose you took MIT's version of a Discrete Math class, Math for CS

[earnest wolf]

I mean.... I think it was just some high-school algebra

[quasi haven]

So I need to watch math for CS first?

[normal crystal]

if you want to follow the MIT algorithms courses
I would recommend doing their Math for CS or any Discrete Math course/text first
since that was your original request anyway

[earnest wolf]

ok, so this is their prerequisites:

6.042J Mathematics for Computer Science: Basic knowledge of discrete mathematics: set theory, relations and logic, combinatorics, proofs, recursion, number theory, graph theory, and probability

for graphs out of all those set theory wasn't needed (naive understanding was sufficient), relations and logic also wasn't needed for the lectures I mentioned and so on

Basically they explain everything along the way as far as I remember

[earnest wolf]

if u know how to do proofs then I'd say no

those prereqs aren't 'hard' prereqs

either way, u can just watch a lecture and see if you can follow it

[normal crystal]

on the plus side
their Math for CS has a free pdf text, multiple lectures on MIT OCW and OLL
Epp is a friendlier intro to Discrete Math

[remote sparrow]

https://measure.axler.net

[sharp juniper]

Hello,
I like to self study as a hobby, and I like to have a physical text when I can
Any good recommendations that I can put on a xmas list?
I’m interested in intro texts to things like algebraic geometry, commutative algebra, Fourier analysis, or something like a second course in number theory

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-642-37956-7

https://link.springer.com/book/10.1007/978-3-642-38010-5

https://link.springer.com/book/10.1007/978-1-4612-5350-1

https://www.amazon.com/Undergraduate-Commutative-Algebra-Mathematical-Society/dp/0521458897

https://link.springer.com/book/10.1007/978-3-031-56500-7

https://www.amazon.com/Fourier-Analysis-Introduction-Princeton-Lectures/dp/069111384X

https://link.springer.com/book/10.1007/978-1-4757-2103-4

these are all standard references

[loud cradle]

^ fyi, this is new book that is separate from his two-volume reference

from the preface

[sharp juniper]

thank you!

[trail hemlock]

i can attest to the fact that this is GREAT as a compliment to stein

[cyan geyser]

Any recommendations for practice books that start from scratch? I feel completely lost and nebulous about math and want to build a solid foundation.

[trail hemlock]

for stuff like alg1 and alg2, khan academy is your best bet for practice problems

[trail hemlock]

has anyone here read one-dimensional man by herbert marcuse? it seems interesting, but i am not familiar with the Frankfurt school enough to know a good starting point

[remote sparrow]

it says it's by herbert marcuse?

[trail hemlock]

oh im reading off a website and i read it wrong, whoops

💀

[sudden kindle]

Whats a good book for Riemannian geometry?

[vast leaf]

Algebraic Geometry by Hartshorne maybe?

[sharp juniper]

I know it’s the classic but I wondered if there were more intro oriented texts
because AFAIK it needs commutative alg and I haven’t covered that yet

[vast jackal]

yes

[vast jackal]

discrete math probably

also linear algebra, and calculus

[north nexus]

Do u guys also recommend lecture notes

I am looking for lecture notes and problem sets that are freely available online

[torn blade]

i really like https://dec41.user.srcf.net/notes/

has notes and alot of Cambridge’s maths courses

[mellow wren]

there's a book by Lee

it's considered like a sequel to smooth manifolds

I think it's just called Riemannian geometry

[empty quartz]

Any recommendations for a book that gives an overview or introduction to mathematical modeling? Two I've considered so far are: An Introduction to Mathematical Modeling by Edward Bender and Introduction to the Foundations of Applied Mathematics by Mark Holmes. Would either of those be good to read?

[fresh skiff]

oh wow these are nice

[tender cobalt]

does anyone know any video lecture series based on michael spivak's calculus

[fresh skiff]

and useful

thank you

[torn blade]

np! :)

[quasi haven]

Is there any possibility of getting Cambridge math video lectures?

[gray gazelle]

@quasi haven

Can you send me a DM?

Is there any books all about physics that I can read for free? 😭

[torn blade]

not that im aware of

[vast torrent]

University Physics?

[normal crystal]

there's a guy on YouTube doing his own lectures based on the Cambridge notes above
I think he's finishing Vector Calc rn and he already did the Part 1a Michaelmas term courses

[gray gazelle]

Yes

Or General physics

Anything

[normal crystal]

openstax has a survey textbook
all their books are free

[balmy elm]

@gray gazelle https://physics.stackexchange.com/questions/6157/list-of-freely-available-physics-books

[vast leaf]

I've heard Aluffi is good

[molten gulch]

aluffi doesn't cover alg geo

[fresh skiff]

for alg geo consider Hartshone

[harsh apex]

By Calculus of Variation I meant Euler - La grange ' s equation. I can not find that in the book. Can you provide me with necessary for links ? I might be looking at the wrong book.

[vast leaf]

For commutative algebra.

[molten gulch]

ahhhhh

[north nexus]

Thank you kind soul

[deep epoch]

Gathmann has some notes i enjoyed reading from

https://agag-gathmann.math.rptu.de/en/notes.php

[mossy flume]

Yea read the Gathmann notes

[trim kayak]

What is the best way to read through a Calculus textbook to learn concepts just for fun? I know a little about the basics, but that's about it. Any suggestions or tips are helpful.

[marsh ingot]

For fun?

[trim kayak]

Yeah, for fun. Don't laugh at me.

[brave burrow]

Is there a better way to read a book other than reading it?

[humble spire]

Do khan academy instead then

[trim kayak]

I'm wondering about the text I have, not Khan Academy

[humble spire]

What text do you have?

[trim kayak]

Stewart's Calculus with Early Transcendentals (8th Edition)

[humble spire]

Have u done precalc?

[trim kayak]

Yeah, but it was years ago. I need to review a little of that too.

[vast leaf]

Read through it and most importantly solve the exercises in the back to make sure you understand it.

If you find yourself missing some prerequisite knowledge try to learn that by googling or asking a friend instead of skipping and moving on.

[vast leaf]

You're in the right place lol

[daring silo]

Why is this book so expensive?
https://www.amazon.com/Algebra-Chapter-Graduate-Studies-Mathematics/dp/0821847813

[paper tangle]

Because GSM is like 🤑

[trail hemlock]

LMAO i saw this allufi is tweaking or sum 😭

they have the audacity to charge shipping on top of it

[remote vortex]

Evergreen

[trail hemlock]

cheapest GTM after the discount bruh

[remote vortex]

The discord rules prevent me from condoning piracy.

That said, it's not the author's fault

The academic publishing industry (and I mean both textbooks and journals) is deeply rotten and Aluffi sees a tiny amount of that price, if any.

[subtle violet]

wow that's a new record. highest i ever saw was some decrepit set theory book for $1500

[balmy elm]

LIterally so exploitative how puBlishers GENerative most of their revenue by stealing from the writers themselves

[remote sparrow]

https://bookstore.ams.org/gsm-104

no hardcover?

[daring silo]

Is it the handbook of set theory?

[paper tangle]

I got alluffi printed in like less than a dollar

Wait no like 5 dollars

Less than 5 dollars

[remote sparrow]

you can have it printed with lulu

[remote sparrow]

i think ams has stopped producing hardcovers altogether

[paper tangle]

Yeah they do like originals

[trail hemlock]

yeah ive seen this for like rudin's books as well

[paper tangle]

And the only thing they lack is the smell

[daring silo]

https://www.amazon.com/Handbook-Set-Theory-Matthew-Foreman/dp/1402048432

[subtle violet]

nah, it was some book about large cardinals: https://a.co/d/8bOCd9t
probably not the fair price though tbh

[dim sierra]

What’s lulu?

[subtle violet]

i think that same listing for $1600 has been up there for a year lmao

[paper tangle]

https://www.lulu.com/

[remote sparrow]

a printing service

[dim sierra]

cheap?

[trail hemlock]

my only gripe with lulu is that the books are so damn hard to like keep propped open

[remote sparrow]

it's marketed to self-publishing authors

[paper tangle]

Yeah

[remote sparrow]

yeah

[dim sierra]

like for hardcovers?

[trail hemlock]

softcovers

[subtle violet]

wow $670 to buy a freaking EBOOK

and $800 for the hardback/paperback variants

[remote sparrow]

that's pretty much every perfect bound paperback

that isn't bound in signatures

[paper tangle]

Have it printed in 2 sets

I did that with mine

[trail hemlock]

should i get it bound a different way?

[dim sierra]

Does lulu do hardcovers

[trail hemlock]

yes

[paper tangle]

Yeah

[dim sierra]

y not do that then

[trail hemlock]

more money 😔

[dim sierra]

lmao true

[remote sparrow]

it won't open better anyway

i presume the binding is the exact same as the paperback; the cover is just different

[trail hemlock]

i jus put one end of the book on a clipboard and stretch it out like a medival torture device

its crude but it works

[paper tangle]

Oh also I believe B5 is a better size than A4for these books

A4 IS ENORMOUS

[dim sierra]

facts

[trail hemlock]

i usually jus do the same size as amazon lists for the real book

[paper tangle]

Smort

I had to learn the hard way

Now my dummit is enormous

I can drop it from a height and it can kill someone

[remote sparrow]

i have the real dummit and i don't regret having it

[paper tangle]

Based

The only real thing I have is misery

[remote sparrow]

https://tenor.com/view/oh-the-misery-oh-the-misery-everybody-wants-to-be-my-enemy-gif-25368312

[paper tangle]

Omg gatto 🥰

[rigid trail]

ummm why isi t $800

may i inquire

[subtle violet]

uhhhh hmm now it's redirecting me to a different book

it was a book about large cardinals listed for $1600

but it was a single used copy

[rigid trail]

do people really buy a single math book for that much

[subtle violet]

i don't think so

[normal crystal]

from my personal experience
those absurd listings seem like they are algorithmically priced
I have a hard time believing someone will actually pay the price they ask for sometimes
especially if it's like 10x or more what it was within a month

[severe gust]

Some people do especially collector, but me? I would rather buy other copy of It for several bucks or check the PDF. They are hella expensive for some reason, one of the reason is limited

But if you respect the author and not poor, you would buy the original

[remote sparrow]

has nothing to do with respecting the author

they often receive little, if any, of the revenue from textbooks

[severe gust]

Are you sure because i'm talking about illegal copy of the books?

[remote sparrow]

the purchase of original copies rarely benefits the author financially

[severe gust]

Ooh alright then

[daring lake]

at that stage i would rather start my own printing press

[loud cradle]

and yet sometimes... https://www.fastcompany.com/3052267/the-house-that-calculus-built

[hasty marsh]

I love pirating

[hollow shore]

Raskolnikov (Math Student Edition)

[severe plank]

I am looking for a concise book recommendation on abstract algebra, specifically covering groups, rings, and fields, including finite fields.

[remote sparrow]

judson

https://judsonbooks.org/aata/

#book-recommendations message

other books you may consider

[fresh skiff]

are these recommedations good for learning algebra in deep?

[remote sparrow]

they make good first courses

[fresh skiff]

i see,

i am hoping to start one of the book soon

[earnest wolf]

how do Chapter0 and Notes from the underground by Aluffi compare?

surprisingly googling that question didn't give anything

[remote sparrow]

notes from the underground does rings first and omits category theory, though there are gentle nods to it

it also has solutions to a good number of problems in the back

[formal parcel]

I need a good calculus 1 and 2 practice book that goes over most problems.

[solar pasture]

are there any free digital pdf copies of math books?

[wise crater]

many, just gotta look hard enough on the open sea matey

[hearty pollen]

any recs for linear algebra done over commutative rings with identity

[tender cobalt]

i think Advanced Linear Algebra by steve roman

[tender cobalt]

you can look up a free solution manual of any popular calculus text

you can just search james stewart calculus solutions and you will find solutions to all of the exercises listed there

[hearty pollen]

tysm

[vocal shuttle]

so like is this place only for maths book recommendations

or any book

[molten gulch]

Check the channel description

[vocal shuttle]

oh sorry i dont use discord a lot

[molten gulch]

You're fine

[undone finch]

Anything for combinatorial group theory or geometric group theory?

[wise crater]

for a terse example ofnthe latter that is kind of foundational, Trees by Serre is pretty nice, and theres a lot of companion lectures on youtube to enhance your self study experience

The exercises can be pretty involved from the get, try to phase in prior chapter's questions while reading at a modest pace

[old elk]

http://www.supermath.info/

[tender cobalt]

is spivak THE GREATEST calculus book

[fresh skiff]

Wdym by greatest?

[tender cobalt]

theory, rigor, depth, intuition, content

[wise crater]

spivak is pretty good but i cant understand how there could be a greatest calc text

a lot of directions you can take something foundational

[tender cobalt]

well "greatest" is an exaggerration ofc

but everyone talks about it being so good

[slender cargo]

Yes. I haven't done an in-depth study, but as someone who is very fond of that book, yes

[tender cobalt]

Is there any similar books

in spivak's book, i see him suggest Courant

[slender cargo]

Apostal's Calculus and Courant's book as well

Spivak seems to be the most popular though for Honors Calculus courses

[tender cobalt]

Apostol takes a historic approach right

[slender cargo]

I hear he does integrals first

[tender cobalt]

yeah

[slender cargo]

Ted Shifrin of University of Georgia strongly recommends Spivak's book though, because he thinks the problems are way better in Spivak's book

[tender cobalt]

Yeah

[slender cargo]

The other nice thing about Spivak's book is that it has a full solutions manual (maybe not so great if you're an instructor)

[tender cobalt]

I was finding a rigorous multivariable calculus book, someone suggested Shifrin's book in this server then I saw in his preface to learn calculus with spivaks book

interestingly spivak's book also suggests shifrin's book

as follow up

[tender cobalt]

i wonder if i should get it

[slender cargo]

I hear Shifrin's book is good. My class used Edwards Advanced Calculus of Several Variables. If I were self studying though... I think I'd now just go for Spivak's Calculus on Manifolds, or Advanced Calculus through Differential Forms since that book seems really cool

[tender cobalt]

Though Edwards book doesnt cover generalized stokes theorem does it?

[slender cargo]

It does

[tender cobalt]

Ohh

Is edwards book good

[slender cargo]

I liked it enough but I thought the material was a slog to get through. I now kind of wish we used Spivak's much shorter and terser treatment

The proofs in Edwards book were unwieldy to me. That book made me uh appreciate more concise books in general

[tender cobalt]

looking through many books I kinda found shifrin's one better

well i didnt read it properly yet

but i watched some shifrins lectures

and he seems really good at explaining

so i reckon his book must be really good as well

[tender cobalt]

hows the advanced calculus a differential form aproach book

[slender cargo]

Starts with differential forms, which is really cool. I haven't used it though so can't really say more

[tender cobalt]

sounds real fun

[tawny crater]

Looking for proof technique texts like how to prove it

I'm teaching a newbie class

[trim hawk]

Hello, I need a book teaching undergrad math and another one with exercises or maybe a place where I can find any math problems please and thank you :)

[normal crystal]

https://richardhammack.github.io/BookOfProof/

[remote sparrow]

#book-recommendations message

[normal crystal]

one book won't cover all of undergrad math and I'm guessing based on how you asked, you probably don't have a good idea what that would include
you can start with OpenStax for free precalc/calc books

[trim hawk]

I would like to start with calculus and linear algebra. Maybe some discrete math

[surreal heart]

if you're prepared for calculus (don't rush into it) then Spivak's book is very popular for self-studying, and Stewart's book is very popular for classes (would also be a very good choice to study), there are a myriad of quality books to choose from though. what's important is that you pick one, stick to it, and learn calculus

[remote sparrow]

spivak and stewart have different audiences in mind

spivak does proofs. stewart includes some proofs for completeness, but problems that require proof are not the main focus

[surreal heart]

that's a good point. you should consider how formal/rigorous you want to be. it's normal to start with a computation-heavy perspective and build understanding later but really it just depends on what your goals are

[trim hawk]

I would love to learn how to think in math too if there is such books

my goals are to learn, study and understand advanced math

oh well Ill follow this github https://github.com/ossu/math

[trail hemlock]

ossu is a really nice resource

[earnest wolf]

TIL there is ossu for math as well

I only knew abt the one for CS

[severe sequoia]

Hi, is there any recommendation book/paper that explain the math behind bidirectional GRU method?

[zealous bear]

Book for geometry (basic of it.)?

[steel cloud]

Which one is good for multivariate? Analysis on manifold by Munkres or Wendell Fleming or any other recommendations?

I have done a point set topology and analysis I and II

[marsh ingot]

There is one called Calculus on manifolds too

[zealous current]

Hi, is Calculus by Jean-Marie Monier good for pre-university student?

[steel cloud]

I am not sure which book should be good for me for multivariate? Someone suggested Spivak but I don't want to do a calculation, what about analysis on manifold by Munkres?

[tender cobalt]

Spivak on Manifolds is solid

its proof based

[tender cobalt]

I'm not sure of that book, what's your background?

[tender cobalt]

Schaum's Outlines of Geometry is good

[steel cloud]

Okay thank you ❤️

[trail hemlock]

spivak is good if you can do the exercises with minimal exposition. a lot of material comes from the exercises exclusively

a analysis on manifolds is the same content with more teaching and explanations

[steel cloud]

Okay thank you

[tender cobalt]

what is typical book after lets say spivak calculus and spivak calculus on manifolds

[tender cobalt]

hows pugh's book as follow up for abbot's

[dim sierra]

Probably learn topology somewhere and then Lee Intro to Smooth Manifolds

[dim sierra]

I guess it’s fine to learn some multivariable stuff but you’ll be revisiting a bunch of stuff so it seems inefficient

[tender cobalt]

so what about pugh's book instead of abbot

[tender cobalt]

hmm

[tender river]

things like measure theory and topology and stuff

stuff that spivaks book leads into like diffgeo or whatever

[dim sierra]

I really like Abbott’s book so I wouldn’t recommend that

I think Pugh is harder and Abbott is just very well written

[covert temple]

hello guys i want to learn maths behind machine learning so i just bought the introduction to linear algebra of gilbert strang, is it a good book for beginners (i'm 15)

[bright epoch]

yeah it's a good book for beginners

[covert temple]

ok ty

[flat plaza]

Is Zorich too ‘advanced’ for freshmen(or even sophomores)?

[plain barn]

does anyone know if paul halmos' book on measure theory is as complete as folland's?

I really like halmos and his way of writing and stuff but I'm kinda worried picking an ancient book will lack too much

[tribal crow]

it depends entirely on your background

saying that one is a freshman doesn't mean anything in general

[earnest wolf]

there's a saying that pugh's book is rudin but with pictures

[formal parcel]

Best books for introducing to proofs

[molten gulch]

velleman or hammack are p. good

[formal parcel]

Opinion on jay cummings proofs? I just found this right after typing the question but I’ll check out the ones you recommended

[molten gulch]

Haven't looked into it

[formal parcel]

It’s pretty new I think.

[earnest wolf]

I mean, does ur ❌ mean "there isn't such a saying" or "I don't agree with it [the saying]"?

[tribal crow]

probably the latter

[marble solar]

Pugh's text is a lot more than just Rudin with pictures

[trail hemlock]

i read through it, its really good

u cant go wrong with any of those 3, just pick the one u like the most tbh

[tender cobalt]

It's solid

It also has memes

[tender cobalt]

Hmmm

[marble solar]

I'm a huge fan of Pugh's analysis book

If I had the pleasure of teaching undergraduate analysis, then I'd teach out of that book

[oak flower]

I strongly reccomend Munkres over Spivak unless you have someone to discuss the content with. From my personal experience, Spivak skips a lot of nontrivial steps. Sometimes he also uses properties of constructions that he didn't mention in the theorem statement. Although, Spivak does have some really pretty proofs. I think it would be good for a 2nd read rather than an intro.

[alpine girder]

does anyone know about this book containing every single math concept?

im trying to find it everywhere

it was like a Smithsonian book I think and the cover was white

[livid lintel]

That stuff doesn't exist

It's impossible to do so

[alpine girder]

istfg

I have read through the pages

[marble solar]

well do you know all of math?

[alpine girder]

well nit every concept but almost everything

[livid lintel]

Still no

[alpine girder]

no this was when I was like 8 I didnt understand polynomials back then

omfg I found it

[tender cobalt]

go for pugh or abott

[heady ember]

Or Schroder

[steel cloud]

Yes now I am following Analysis on manifold by Munkres and Tom Apostol second volume

[cedar rain]

Munkres book is basically Spivak’s book but much better

[vocal egret]

Accidentally stumbled on "A BRIEF COURSE IN ANALYTIC GEOMETRY" by Yefimov, and I was wondering if I should buy it... I mean, this book is antique and out-of-print, so I don't know if I should.

[tender cobalt]

if you wanna buy it for its antique value

go for it if you feel like it

[vocal egret]

oki then, thx :3

[earnest wolf]

math u study at school is arithmetic mostly

that isn't what people in a math discord server have in mind when they think of math

[final swallow]

Princeton's companion to mathematics comes to my mind as the closest answer

Math is too broad and wide for all of it to fit in a 1000 page book anyway

[tender cobalt]

What do you mean by "everything" though

Can you remember what topics were they?

[tender cobalt]

He probably means like an algebra + trigonometry book or something

[earnest wolf]

are there any {upper undergrad, grad} {books, lecture notes, video lectures} that give a high level overview of topics related to foundations?

like proof theory, model theory, etc

and also looking for anything of the same vibe but in theoretical-compsci: (homotopy) type theory, formal verification etc

[rigid trail]

i really like "type theory and formal proof" nederpelt/geuvers

working through it rn

for proof theory specifically i have takeuti

also v good

[earnest wolf]

@rigid trail, by any chance, can you comment anything about this one?

saw some redditor recommended it. haven't read from that author before, so..

[celest bear]

Thoughts on using this book to self study calculus? https://a.co/d/fG9KvRQ

[rigid trail]

i havent seen this so i can't comment much

i'll look at a (cough) pdf

you could too ( 🏴‍☠️ )

[earnest wolf]

I mean, I downloaded it a few secs before :))
but it isn't like I can quickly determine whether

1. the author gives reasonable exposition
2. gives a lot of insights and intuition, instead of just dry presentation
   etc

[tender cobalt]

That book is solid for learning calculus

I learnt calculus from it

[rigid trail]

Looks pretty good first impression

[tender cobalt]

I would say its way better than James Stewart's calculus

[rigid trail]

👍

i'll read through it too

it does seem good

[celest bear]

Really?

I also have this book

For calculus questions

[tender cobalt]

Ye it proves a lot of the things and has good intuition

[celest bear]

https://a.co/d/atGAePE

This gives a lot of questions

[celest bear]

How many pages should I do per day?

[hasty sluice]

Could someone recommend books that includes random vector?

[tender cobalt]

You can do a section per day

[hasty sluice]

I don't quite understand my current textbook and need to save final exam.

[tender cobalt]

or two sections

[earnest wolf]

what exactly do u mean?

randomized algorithms, probability, ...?

[celest bear]

A section?

I haven’t really opened the book in a while

But I wanna start

[hasty sluice]

There's a chapter called random vectors(about probability)

[tender cobalt]

Yup

[celest bear]

I can do that

But doesn’t each section have like 50+ problems

Just to memorize one concept

They really tryna torture me

[tender cobalt]

well dont do all problems

i just do like 5- 10

[celest bear]

I’ll probably do more than that

Cuz I like doing math problems for fun I guess

Got nothing better to do

[tender cobalt]

however much you liek 😄

[marble solar]

It depends on your background. If you've done spivak's calculus, go for pugh

If you haven't done spivak's calculus, go for abbott

[tender cobalt]

whats the difference between abbott and spivak

[celest bear]

Alright

How long should it take to finish the book

From start to finish

[exotic lion]

Need any german math teacher,expert etc. pls i am stuck at one topic and i Write my exam at friday 😭😭

[remote sparrow]

#book-recommendations message

[fiery hamlet]

+1

[tender cobalt]

6 months is a good estimate

[tender cobalt]

+1?

[fiery hamlet]

like I'm wondering what the difference is too

[tender cobalt]

well maybe Abbott has some "analysis" stuff

like fourier series

not in depth though

Guys how's Zorich for studying some analysis?

Compared to Pugh

[clever tiger]

Not quite asking about books but does anyone know of somewhere (free) that has like thousands of practice problems for all algebra 1 topics. Im currently a freshman in HS and hoping get to calculus 3 by senior year. I have the time and motivation but I have no clue where to go to get a better knowledge of algebra 1 before starting algebra 2.

Sorry if this is a little off topic, figured it is close enough to books and not your typical help question.

[dim sierra]

Alcumus on AoPS has lots of practice problems

You can also open the introductory algebra 1 textbook from OpenStax and do problems from there

[clever tiger]

Thanks, Ill check those out

[celest bear]

6 months…

That’s kinda long

[normal idol]

hey professors

OHHHH

[remote sparrow]

https://web.archive.org/web/20240416105855/https://www.mi.fu-berlin.de/archive/raut/logic3/hint.pdf

rautenberg has solution hints and full solutions

it's not my first choice for an introduction though

[remote sparrow]

@torn crypt @sturdy shore

these two liked it

[sturdy shore]

yes

great book imo

[earnest wolf]

btw, do you have any preference out of those?
maybe highlight at least two great ones, exposition- and content-wise, if you can

I just struggle to find a lot of free time atm, so it's a bit hard to skim thru all of them

[earnest wolf]

here's what I'm looking for (just in case u didn't see, altho u probably did)

[remote sparrow]

i think leary and kristiansen and westerstahl have the best exposition

[willow merlin]

is there any book with solved exercises on modular arithmetic

or simple examples for newbies with 0 mathematical maturity

[foggy quest]

K. Rosen's discrete math book must have some

[willow merlin]

ok thank you

[turbid jackal]

are there any good books for practicing things from calc 1 and 2? like maybe just a bunch of practice problems

[torn crypt]

I have no specific comments on it, I think there’s some issues with the specific writing structure in how he presents some stuff when evaluating from a POV I know, but I don’t think it’s bad

It’s not perfect but it’s effective I think

I think it would be good for a course, but with a course is a bit different that going entirely on your own, as I do worry there’s a few possible confusions/doubts that could arise in self-study

[stiff grail]

hi

what book should I start to go through fourier series

thanks

[limber lava]

Any good books for 10th grade math

N 11th basic math

Like the book has both of them

[remote sparrow]

https://www.amazon.com/gp/customer-reviews/R24AKR3DDYGA5T/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=3030331423

Great author, very well written. This book is so loved we made it into a cake, so all could eat those formulas!

what a fun review

[tender cobalt]

well the book is about 1300 pages with like 19 chapters

if you can finish 1 chapter per day then i guess it will take you 19 days

[crude sage]

I looked at this and thought "I didn't know that they had that in hard cover!!"

[remote vortex]

they have it in fondant cover!

[keen orbit]

Why is it not recommended to study multivariable from baby rudin

So what's bad about the chapters 9→11 in this book

[tender cobalt]

i'm having hard time deciding between abbott and pugh

coming from spivak

[tender cobalt]

how about both?

[timber mesa]

they cover different things don't they

[tender cobalt]

yea

abott doesnt include multivariable

pugh does

[timber mesa]

I don't think you really need Abbott coming from Spivak though it is a nice book

Pugh is a decent intro to metric spaces and multivariable

[tender cobalt]

thanks

ima get pugh then

[dusk lion]

Hello 🙂

Is the book 'Measurement' by Paul Lockhart worth considering for getting the ball rolling?

[keen orbit]

Ohhh ok tysm

[wise crater]

i suggest it to highschoolers or people who havent invested time in mathematics in a while

i think it is pretty good at getting someone with motivation interested

[dusk lion]

I'm not a complete beginner mathematically as I've some background in philosophy and computing, but I am really not very good at the more traditional formal study methods. I've redone a fair amount of the very early years on khan academy and need to get back to it to get further on with the pre university calculus and algebra, I am quite self motivated but do wander all over the place when it comes to subjects. I was wondering if this might be a good way to channel that into math more effectively.

I was blown away by how much looking at the very early stuff helped me with basic algebra, all kinds of things that I really should have been noticing first time round at school, but just didn't.

Perhaps it could be worth a shot.

[wise crater]

i mean, if you want a slower paced course in geometry, its a good book

but if you want something more rigorous, start with a book of proofs

How to solve it by Polya is also enjoyable but is less directly "math" and more philosophy of math

[dusk lion]

Thank you for the pointer, I will make a note of the title and take a look at that also.

I'll likely prefer to take the more traditional mathematics approach eventually, I've bought a copy of Rodger Penrose's 'Fashion Faith And Fantasy' and am kind of thinking of using that as a bit of guide, being keen on physics/cosmology too.

If Measurement is a way of 'tricking' me into that, it could be ideal. I get really emotional about math and find the use of symbols quite destrating untill I've internalised the ideas behind them.

[wise crater]

yeah, read measurement then

first 30 or so pages just kinda sets the vibe

[dusk lion]

Thanks for you input, I'll take the plunge and order a copy. I've heard good things from someone already; With confirmation here too, that settles it.

[vast leaf]

Representations and Characters of Groups by Liebeck is pretty good

[remote sparrow]

it's always been sold as a hardcover though?

[remote vortex]

I've only ever seen the PDF

[loud zephyr]

I've started learning set theory from Charles C. Pinter's A book of set theory. it looks amazing so far. anyone know this book?

[ornate saddle]

Pugh sounded mike tuah.

[crude sage]

I wonder why considering it is freely and legally available as a pdf

[remote sparrow]

people like physical books?

[crude sage]

True. I've looked for it at the library but questioned why they would have bothered to acquire it

[tender sun]

What about A Beautiful Mind by Sylvia Nasar. It's about a mathematician but also has some history

it touches a lot on personal life of the dude, but once you get into the maths it is fascinating

hope you enjoy

[celest bear]

Now we’re talking

1 textbook in 19 days is doable

I think..

[mossy flume]

Has anyone ever checked out this commutative algebra text: https://dspace.mit.edu/bitstream/handle/1721.1/116075.2/WWCM.pdf

A Term of Commutative Algebra by Altman and Kleiman

I was thinking about self studying some commutative algebra from it (as opposed to A-M)

just because this seems to have all the exercises from A-M + more. ALso, from what little I've read of this and A-M, I find this text to be much less terse than A-M

Just curious if people think this text is worth looking at over A-M or if they have a better recommendation for a "tour" of commutative algebra

I just need enough commutative algebra to do algebraic geometry which I guess really means enough commutative algebra to be able to pick up stuff later on as I need it

[marble solar]

Rare time I can comment on Algebra, it's cleaner than Atiyah

When I was taking Algebraic Curves & Commutative Rings, this was a very good reference

[pallid quail]

i was trying to get into the subject, i will try to pick it up

[tender cobalt]

Its gonna be hard af lol

If all you do is memorize formulas

Then u can do it

Its math not biology or chemistry

[placid canopy]

any recs on any analysis texts? just finished a real analysis course, we ended on MCT, DTC, fatou's, and very briefly hilbert spaces

[trail hemlock]

#book-recommendations message

personally i have bass, snd i like it and stein a lot

[remote sparrow]

you may want to look at some dedicated functional analysis textbooks as well