book-recommendations

[stuck breach]

some of them are doable

[proud osprey]

I haven't had the time to read it, but a friend recommended "An introduction to Gödel's theorems"

The ebook is free https://www.logicmatters.net/igt/

[grim wolf]

I haven’t and I agree that they are really hard (I’m not good enough to solve them either lol)

[lyric storm]

any recs for a quick overview of galois theory to prepare for a reading using Marcus' number fields?

I've had previous exposure to galois theory, but forgotten most of it

[full cairn]

Maybe Milne's course notes? https://www.jmilne.org/math/CourseNotes/FT.pdf Dunno if it qualifies as a quick overview, but I think it's a pretty decent intro to the subject

[dry ridge]

can i ask for both?

[fading mango]

Any books useful for Computer Science undergraduate course? I'm interested in learning discrete math, linear algebra, graph theory, etc.

Would be nice to have anything else useful that's math-related (or none math-related) too.

Preferably, free. But recommendations you think are worth the money would be ok too.

I have been looking through 'search' but there seems to be a lot which makes it harder to know which one I should use

[regal perch]

Anyone know how i can get the art and craft of problem solving Paul Z. Phyisical book under 50 bucks

[gray gazelle]

Are you taking CS too?

[normal crystal]

MIT OCW Math for CS uses a free textbook they wrote
their OCW LA class uses Strang's paid textbook, but there are true free LA books

[tulip blade]

Idk what your background is but some recs: introduction to graph theory by douglas west (nice intro that covers some cool topics in cs and optimization), algorithms by jeff erickson (intro algorithms book), introduction to theoretical cs by boaz barak ( nice set of notes that is basically a book on intro tcs)

[vital bane]

Yea, intution \neq rigor

intution, rigor, computation are all very interconnected

only focusing on one thing is what leads to your downfall

[tawny spruce]

anyone got any suggestions for math books in regards to set theory or number theory?
I’ve been reading Naive Set Theory by Paul Halmos and I loved it so far. I know the book suggested Hausdorffs set theory and Axiomatic set theory by Suppes.
I’m open to other suggestions for topics as well but I’ve been loving learning about set theory so would like to get something lined up for afterwards.

[tender river]

there is this https://4chan-science.fandom.com/wiki/Recommended_material

[last cipher]

any good linear algebra book after a computational course in linear algebra?

Something more in theory

was thinking lang's linear algebra

[tender river]

https://linear.axler.net/

[vital bane]

Linear Algebra by Friedberg Insel Spence

[signal mountain]

i would be highly surprised if there was software specifically for this

many people have created graphics to show this though

https://github.com/TalalAlrawajfeh/mathematics-roadmap/?tab=readme-ov-file
here's the most comprehensive one ive seen

i would say its over-specialised

its basically just a flowchart or graph and plenty of software exists to create those

anyhow the issue with these roadmaps is that theres some subjectivity to the order
for example some people say you should do point-set topology before analysis, others argue the other way around
some say you should do a course in proof-writing before analysis others say just learn it through analysis
to list a couple of the common ones ive seen talked about here

[vital bane]

That seems pointless

[graceful moon]

I’m possibly misunderstanding what you’re looking for but obsidianMD will generate a dependency graph based on how your notes link together

It’s not open source and IOS only though

[vital bane]

just learn whatever you find fun spend time in college, meet new people

[heady ember]

So, TikZ and PGFPlots.

[vital bane]

visualizing Forcing in Tikz when

[heady ember]

I shall singlehandedly implement true 3D vector graphics in tex

[livid lintel]

Hmmm, Isn't Obsidian available on all devices?

[graceful moon]

Potentially, I don’t use it myself but I thought it was IOS only

[livid lintel]

Since I use it on Windows and my Android phone

[graceful moon]

Not IOS only then it would seem

[livid lintel]

Logseq is kind of like Obsidian, and it has graph views too, and is open source.

[remote vortex]

I mean, no one uses TikZ without being forced to...

[vital bane]

poor grass, being forced to use TikZ

I wonder who's behind this

[livid lintel]

The TikZ devil, obviously

[heady ember]

https://tenor.com/view/im-outta-here-gif-20990964

[stray veldt]

i know someone who offers to tikz your diagrams and then asks for coauthor based on that

[dapper root]

Grift

🫡

[graceful moon]

Worth

[fickle lake]

ummm may i reccomend bungou stray dogs

🆗🆗🆗👌👌👌 it's really good books

many of them

many of books

very good 🧛🆗🆗🆗🆗🆗

[vital bane]

https://tenor.com/view/breaking-bad-funny-wtf-wth-jesse-gif-17336046

[sleek vale]

Hello everyone, I am looking for any online website, where I can find the pdf of this geometry book "Geometry, ancient and modern”, J.R. Silvester, 2001, Oxford University. Press pdf"

I wanted to read it for my geometry class but I can't really find it anywhere and it's quite expensive

[fading mango]

im still in final year of sixth form and a levels coming soon, but im taking a gap year before university

i hated my predicted grades so i never applied to university yet

my real grades should turn out better

as im putting a lot ofwork in

[fading mango]

are they all free

[tulip blade]

you should be able to find them online

[foggy quest]

libgen dot is?

[full cairn]

Isn't that copyrighted? I don't think you should share that here

[molten gulch]

<@&268886789983436800> piracy

[remote knoll]

Please don't post pirated materials here

We don't want to get on the wrong side of discord TOS

[molten gulch]

we also reported the user's message to discord

fwiw

[remote knoll]

Dude

[molten gulch]

<@&268886789983436800> again

oh-

OOPS

[remote knoll]

Do it again and I ban you

[molten gulch]

FWIW they've done it a few diff times over the last few days too

[remote knoll]

This is the first time a mod has talked with them about it?

[molten gulch]

I'm unsure

I believe they've been told off in the past but idk if for piracyposting

[remote knoll]

Oh, someone else timed them out

Thanks doot

[split portal]

The only ticket we have for them is me muting them right now.

So if they were warned before today it was informally.

[graceful moon]

...

[molten gulch]

Well, we tried to, it did not get sent because the message was deleted before the report could be sent and therefore just threw an error

so ig they're safe for now

we don't want this place to get nuked

[tender cobalt]

https://www.amazon.com/Math-History-Long-Form-Mathematics-Textbook/dp/B0F4YHW1XL

became no 1 seller the moment it dropped

[pine tundra]

<@&268886789983436800>

[zinc sundial]

whay

[zealous coyote]

Mind explaining the problem?

[pine tundra]

I thought it was a scam sorry

[zealous coyote]

OK

[pine tundra]

My bad

[zinc sundial]

scamazon

[split portal]

Amazon links do look a little sketchy lmao

[split portal]

I don't think it takes much to get amazon best seller status.

[normal crystal]

there are so many subcategories
"Top 10 Books Dooter Once Mentioned On A Sunday"

[rigid trail]

thats good

no such thing as too much

[full cairn]

If you're just copying the book, or if you end up focusing more on the actual writing rather than thinking, then I would argue it's too much

Btw, this discussion would fit well in #study-discussion

[fading mango]

whatever works for you works for you

although im not sure how much you overdo it, so maybe you should try speed up a bit

even though some people may not take notes, personally i find it helps me to write stuff down and it helps me process the information than just reading

[green mirage]

Any textbook recommendations for self studying logic and discrete maths especially nonclassical logic; more than just a passing mention. I'm thinking of printing the open logic project

[tall idol]

Hello! I want to study maths for the local college admission exams in my country. I DL'ed a list of math topics they ask me to study and ran it thru Google Translate then uploaded it to Pastebin, so could someone please recommend me some books to study each of these? 🙏
https://pastebin.com/t4J2FT0h

[green mirage]

Yes, 995 pages. 70 euros so kinda expensive

Looking for alternatives before I do that

[oak tide]

What level of math are you looking for algebra algebra 2 college level calculus statistics

Geometry even you need to give a specific category

[remote sparrow]

#book-recommendations message

https://www.amazon.com/Gödels-Theorem-Torkel-Franzén/dp/1568812388

https://www.logicmatters.net/tyl/

[tender cobalt]

https://www.youtube.com/watch?v=0N3IxPYHc6Q&ab_channel=MathematicalAdventures

[thorn jolt]

Anyone know of any good books on logic

[naive lava]

use your library

[remote knoll]

My hobby is going to used bookstores to pick up math textbooks on the cheap. You can normally get them for between $5 and $30 no matter the subject.

The problem is having enough shelf space

[vital bane]

new mod?

hello new mod

[remote knoll]

Hello!

[vital bane]

Buff Bezos

[remote knoll]

If I were Jeff bezos I'd just pay full price lol.

[heady ember]

Insert wait a minute, who are you meme

[native breach]

Me too, though the selection around me tends to be fairly old ( pre 2000)

[tall idol]

did you check the list? I wanna study middle and high school math

[tall idol]

flat geometry I think

[native cradle]

Any recds on introductory opeator theory books

I've done one sem of LA, until calc 3

[vital bane]

Don't you need functional analysis for operator theory?

[native cradle]

I'm doing it next sem

idk

[vital bane]

oh you mean you're doing functional analysis next sem?

[native cradle]

A prof is taking it with teh only pre-req being a course in LA

no

operator theory

[vital bane]

interesting

[old notch]

hello what's a good book for self studying on complex analysis?

[molten gulch]

What maths have you studied previously

[old notch]

calc 1 thru 4, linear algebra, real analysis and a little bit of topology

[native cradle]

what is calc 4

[grand thistle]

stein and shakarchi

is standard

[old notch]

it's vector calculus i think

[native cradle]

Any reccs for what a first year should study over the summer

[old notch]

or maybe just calc 1 -3

[native cradle]

maths

planning to do AA, LA2, RA1 anf 2

anything else

[old notch]

thanks

[native cradle]

would differential geo be a bad idea

[grand thistle]

no

[native cradle]

reccs?

[molten gulch]

Have you taken real analysis and topology?

[grand thistle]

books like guillemin and pollack or tu's intro to manifolds explicitly state that it only requires linalg analysis and maybe some basic topological notions

[native cradle]

topo no, will be taking RA next sem

[grand thistle]

the topology you learn in real analysis will probably be enough tbh

[molten gulch]

I mean shouldn't you also have an idea of seperation axioms, what a hausdorff space is, etc...?

[native cradle]

hmm, expensivs stuff, and open source reccs

,w 4000 INR to USD

[grand thistle]

true but u can kinda wing it it'll be hard tho

[native cradle]

,w 4000 INR to USD

[hasty eagle]

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[native cradle]

I'd rather not pirate

[molten gulch]

Discussing piracy is discouraged here <@&268886789983436800>

[native cradle]

Would spivak's manifolrds be a bad idea

[grand thistle]

chill 😭 i'm just talking about like their local library

[native cradle]

my uni library may have it

I'll check

[grand thistle]

calculus on manifolds?

is a p good idea ngl

you will not need much topology for that

[native cradle]

Just It's relatively affordable too

[grand thistle]

and it sets you up for more serious differential geometry

yeah good idea

[native cradle]

at 13 USD

[native cradle]

thanks, will get it

for algebra I have artin, Judson, and allufi

good combo?

[grand thistle]

sounds good

though you won't need any algebra for calculus on manifolds

[native cradle]

for RA I'mma use Abbott , Spivak and Rudin( or is this too much)

[native cradle]

Need it for my core courses next year

[grand thistle]

ah ok

[grand thistle]

sounds good too

[native cradle]

for LA, I suppose Axler works?

I used it to self study LA 1

[grand thistle]

tbh i like just sticking w one book

but it's totally fine and up to u

[native cradle]

hmm, which ones do you suggest

for Aa and RA

for LA, I'll stick to axler, yeah

[grand thistle]

i used rudin and it was not that bad

hard for sure but not impossible

[native cradle]

hmm, I was considering spivak or abbott actually

which one would be better

I have all 3

Also why am I doing this now when I have a calc 2 exam tomorrow

[grand thistle]

just try them all out and see what u like

[molten gulch]

Go revise for your calc exam and think about analysis later /suggestion

[native cradle]

,ti

[hasty eagle]

The current time for math_rocks is 10:27 PM (IST) on Mon, 28/04/2025.

[native cradle]

I'm mostly ready tbh

will wind down now, sleep and revise tomorrow morning

exam is only at 2

[grand thistle]

good luck

[rigid trail]

someone save me from rudin

[molten gulch]

We have a meeting in 30 mins we should really peint out the documents we need for yet the printers on campus are so fucking annoying

[rigid trail]

😭🙏

[grand thistle]

which chapter

[rigid trail]

i'll check but its stone weierstrass theorem

[grand thistle]

oh that one

[rigid trail]

i am unable to understand proof

[grand thistle]

that proof was pretty hard i remember

[rigid trail]

the math isnt mathing

also,

Let $\mathscr{B}$ be the uniform closure of an algebra $\mathscr{A}$ of bounded functions. Then $\mathscr{B}$ is a uniformly closed algebra.

[hasty eagle]

qiu

[rigid trail]

im sorry WHAT

[vital bane]

not if you're doing abstract manifolds

[vital bane]

Abbott

[rigid trail]

abbott is so easy in comparison man

i think it good

[vital bane]

Abbott is so beautiful in comparison

[rigid trail]

rudin is death

hell

idk which ring of hell but it's one of the worse ones

[vital bane]

Half of Rudin exercises are similar to ones in Abbott

one is not necessarily more difficult

[rigid trail]

and can someone clarify on wth this is saying 😭

[vital bane]

they're just different

[rigid trail]

the language is a lot harder

[vital bane]

Stone-weierstrass moment?

[rigid trail]

i feel

[rigid trail]

yeah i think it generalized stone weieristrass or smth

[vital bane]

it's not "harder" it's just poorly written

[rigid trail]

i dont get it tho

[rigid trail]

both.

😔

[vital bane]

uniform closure just means that you're considering closure with respect to uniform convergence

[vital bane]

nah it's just a bad book to self-study from

[digital pumice]

I liked Tao for self study

[merry sphinx]

it does cover more adv topics

[vital bane]

Tao is also pretty good I hear

[rigid trail]

i think i get that, but "be the uniform closure of an algebra" vs "is a uniformly closed algebra" feels the same to me 😭

[vital bane]

Like differential forms?

[merry sphinx]

nah just in c1-8

[rigid trail]

i would do tao, but once i power through rudin i wont need any other intro analysis books so

[vital bane]

is that really worth the lack of exposition? when you can properly learn analysis in R, and use that experience to generalize it to different spaces?

[rigid trail]

and rudin is mandaroty for my course 😔

[merry sphinx]

im pretty sure youre just letting B be A + the limits of all uniform conv seqs in A

i think lebl is the easier to read rudin

[vital bane]

lebl?

I think Rudin is good as a problems book and a reference book

[rigid trail]

?

isnt that uniform closure

[vital bane]

yes

[rigid trail]

whats the difference

didnt answer my qu still 😭

[merry sphinx]

i mean, you dont understand why this is true?

[vital bane]

"closure of a space is closed"

[rigid trail]

i understand why it is true, but the language is weird

[rigid trail]

yeah is it just that 😭

[vital bane]

yes

[rigid trail]

bruh

[merry sphinx]

yeah

[rigid trail]

sky is bule

fine

okay thanks ig 💀

[vital bane]

The sky is a uniform closure of a banach algebra

[rigid trail]

pls spare me

i have enough issues

[digital pumice]

Anyone got any Lebesgue integration book recommendations?

[merry sphinx]

folland

cohn also nice

[vital bane]

What about Axler

[merry sphinx]

havent looked at it properly

[digital pumice]

Thank you!

[remote knoll]

Please take care with being too specific about methods of piracy, we don't want to run up against Discord TOS.

[native cradle]

AXLER MENTIONED!!!

[sand path]

What’s the difference between kunen’s foundation of mathematics and his set theory text ?

[torn blade]

yeah no shit, its in the name

[remote vortex]

And yet a function that can be integrated isn't necessarily integrable

[merry sphinx]

lnx moment

[remote sparrow]

scroll up

[fresh skiff]

#book-recommendations message

Credit goes to sour drop

[thin kernel]

Axler is a great introduction

[tall idol]

is it a faux pas to bump msgs

[unborn jackal]

has anyone read "Stochastic Calculus of Variations in Mathematical Finance"?

[molten gulch]

Generally it is discouraged to do so in any chatroom

[unborn jackal]

nvm i havent done enough analysis yet

[molten gulch]

Openstax has a ton of textbooks at this level available for free, khan academy has videos, also look into paul's online math notes

[tall idol]

understood, won't do it again

[molten gulch]

But people do it here a lot anyway and we're no authority on this server or on online etiquette, so uh...just don't break the rules ig

[tall idol]

i just realized you're not a moderator 🤦‍♀️

i feel so silly rn

sorry, i'm new to the server

[molten gulch]

Lol you're fine, mods have a bright blue or bright pink role colour

[still panther]

yeah mods have neon bright colors to indicate danger

[shut mesa]

I am looking for resources on the teaching of math

[tall idol]

ya i wanna get a book

[silk patrol]

I've been working through https://www.amazon.co.uk/No-bullshit-guide-math-physics/dp/0992001005 and liking it

Might be a bit above middleschool level

[torn blade]

complex analysis books which are as good as / better than stein shakarchi ?

in your opinion ofc

[merry sphinx]

whats wrong with SS?

[full cairn]

I like Asmar and Grafakos for complex analysis, but I haven't read SS, so dunno if it's better

[remote sparrow]

well a lot of things is an understatement for the schutzstaffel

[cunning elk]

LMFAO

[dim pendant]

Kind of hard to compare books on the same subject with similar philosophy. Just acquire a handful of options and move between them as your comprehension requires.

Visual Complex Analysis is a classic, Alfhors or whatever is nice for a direct, down and dirty approach, and Conway has a boring but highly readable text for those who need the practice working with analytical reasoning

I say just stick with Stein, again, until you hit a wall and need to look elsewhere. Also can ask here for help and whatnot.

[rigid trail]

Asked in #math-discussion but it prob better to ask here. Recommendations for starting in PDE's? More inclined towards theory, i do not care as much about physics/other applications. I have ODEs course done and will finish basic analysis (baby rudin) soon

[dim pendant]

If you're interested in going as far as you can, "Some Nonlinear Problems in Riemannian Geometry" is a great read if you're willing to refine and add onto your familiarity with manifolds (especially since it is considered the weakest point of Baby Rudin)

It does some basic differential geometry and walks you through some relatively recent developments in research in the area of the title

[rigid trail]

Okay I will give it a look, thanks

[trail hemlock]

@jovial parrot is

[livid lintel]

You're going to summon a bunch of child prodigies

[dim pendant]

Yeah, I'm one of them and I solved the collatz conjecture

[marble solar]

I'd say Conway is much better than just being highly readable or dry, but it's actually the most rigorous

It does things carefully and goes to great lengths to set up everything in a tidy system

[marble solar]

I'd say for most people Conway is a great book. It's not my favorite complex text, but it's the best for self-study

[dim pendant]

Yeah I would expect an undergraduate to come away with a lot having studied Conway

And to be honest if you're worried about pace, you're doing yourself a disservice. I like Conway's writing

[timber mesa]

yeah Conway is as good as it gets for a rigorous treatment of complex analysis and it has a bunch of interesting topics aside from what you'll usually see in an undergrad course

[timber mesa]

a recent textbook is https://press.princeton.edu/books/hardcover/9780691207582/a-course-in-complex-analysis

which also I think fits the bill for "interesting topics"

[vital bane]

Have you ever checked out Gamelin? How does that compare with conway?

[marble solar]

Haven't read gamelin

[jovial parrot]

Hi bb

[gray gazelle]

or just someone with an interest in math 🤷‍♂️

[wise imp]

chat put me onto some number theory books, like ones for just getting into it

[karmic plover]

Guys can you recommend a good calculus book for a beginner (that has decent knowledge in high school calc like until diff eqs)

[rigid trail]

spivak

[karmic plover]

The 2008 version?

[tribal crow]

probably

[karmic plover]

Or the 1971 version?

[tribal crow]

the newest one is likely what they meant

Spivak isn't really a calculus book though

it's somewhere between a calculus book and a real analysis book

so it's quite hard if you don't already have some experience with proving statements

but it's well written, and has good problems

[karmic plover]

I really don't have any experience so I am very much of a beginner

Thanks let me see If I can get my hands on it

I can thanks a lot guys

[rigid trail]

There is also Khan academy

Honestly probably best for basic calculus

Just my opinion, but there is no point in getting a textbook for basic calculus since there are soooo many free resources online

[vital bane]

This

Just watch Khan academy, grind some calculus problems and then start doing analysis

[rigid trail]

hop on rudin (don't)

[vital bane]

Rudin should be used after you learn analysis

[rigid trail]

Tell that to my prof bruh

I'm getting slaughtered

[vital bane]

I mean for people who are self-learning stuff

[rigid trail]

For anyone 😭

Would not wish it on my worst enemy

Idk from which ring of hell it's from but it needs to go back

Except the exercises, those are worthy enough to remain in the world

[karmic plover]

I got rudin's principles of math analysis and was completely bewildered

Till date other than solving about 2 problems I have made 0 progress with the book

[slender cargo]

Just choose a different book. Easy solution!

[silver stirrup]

Just finished a course in mathematical analysis and linear algebra (math 295,296) at UofM, and I was wondering if there were any good books that I could use to kinda review the class

I never took notes

And the first textbook (spivak) is quite long, and I quite dislike the linear algebra textbook (Hoffman and kunze)

Additionally, how many proofs should I have memorized?

[fresh skiff]

What i guess it's nice one. I will use it for revising LA

[fresh skiff]

None !!

[silver stirrup]

Really?

Funadamental theorem of algebra?

[molten gulch]

Eh there's some clever ones you should know the arguments for imo

[silver stirrup]

Spectral theorem?

L hospitals rule?

[molten gulch]

There's at-least six known ways to prove this, pick your poison

[silver stirrup]

We learned the l’ambert or smth way

[fresh skiff]

Knowing the technique is something different from remembering the proof? Isn't it? (Idk but seems different things)

[silver stirrup]

Circle is compact or smth, so you just show minimum of polynomial is 0, or smth, I didn’t really pay attention

[fresh skiff]

I haven't seen such proofs why😵‍💫

[molten gulch]

For some yes

[silver stirrup]

It doesn’t require much knowledge, really just compactness

We got it from a section in Hubbard vector calculus, linear algebra, and smth book

But yeah like stuff like l hospital and chain rule

[fresh skiff]

https://sites.lsa.umich.edu/kesmith/teaching/math-295-honors-mathematics-i/
Did you guys use this one?

[silver stirrup]

Yup

[fresh skiff]

Wow

I will visit it (since my uni is full shit so i have to visit other universities pages)

[silver stirrup]

Although we have a different instructor, who will also be different next year

[fresh skiff]

Oh, probably i found an old web

[silver stirrup]

Yeah

Current professor is Sarah Koch

It’ll be Stephen debacker next yr

[fresh skiff]

Ah interesting.

I saw her web and the course link, but it requires students id or id from uni lol

Well seems interesting. Unfortunately we don't have good teachers (teachers with knowledge of pure maths) at our uni ah

Thank you sharing course codes i found the webs haha

[fresh skiff]

For linear algebra i used FIS (Fridberg) for selfstudy it was amazing. But think maybe not for revision i am not sure
For analysis, we all recommend rudin and Abbott
I hope someone will confirm if either these books will be suitable for you

[ocean basin]

can anyone suggest me on P vs NP problem since trying to understand its concept

[proud osprey]

Scott Aaronson has a paper explaining the current state of the problem

https://www.scottaaronson.com/papers/pnp.pdf

[ocean basin]

ty

[silver stirrup]

I feel like abbot doesn’t cover as much

Like it doesn’t do nearly as much topology

Like we dont really normally prove IVt and EVt, they are just corollary’s of the fact that continuous functions preserve connectedness and compactness

[proud osprey]

imo it makes sense to first cover IVT and EVT first as purely real analytical theorems

and then come back around later and show it's actually topology underneath

[tender river]

https://www.amazon.com/Second-Course-Linear-Algebra/dp/0471626023 and i like lax's textbook a lot too

did you mean you used spivak for your analysis course?

if so then a really appropriate text at that level is https://classicalrealanalysis.info/documents/TBB-AllChapters-Landscape.pdf although on the bulkier side, it does mark the skippable sections that have no impact on the rest of the chapter text and has lots of exercises and problems

[vital bane]

!??! Abbott covers as much topology as ANY intro nalysis book like Tao, Rudin or Cummings

[vital bane]

?!?! Abbott provides 2 proofs of IVT

they are just corollary’s of the fact that continuous functions preserve connectedness and compactness

Which generalizes far more easily

[silver stirrup]

Iirc when I looked at abbot the topology part was just what is open, closed, and compact for specifically real numbers

[vital bane]

what does that even mean everything is actually topology underneath, there's no "pure real analysis" there will always be topological considerations

[vital bane]

and perfect sets and connected sets

[silver stirrup]

Oh damn yeah I don’t remember

[vital bane]

this is what is covered in almost every intro analysis book lmao

[silver stirrup]

I’ll take another look

[vital bane]

were you expecting point set topology?

that isn't covered in most intro analysis books

[silver stirrup]

Well ok here’s what we covered with topology

All the stuff mentioned before

Some stuff about Hausdorff spaces

Cut points or smth (just homeomorphism things)

R^n is sequentially compact

Path connectedness stuff

I might be forgetting stuff cuz most of this is first semester

Oh also just like what is a topology definitions

*definition

And that’s probably it?

[tender river]

so you meant spivaks calculus on manifolds and not calculus ?

[silver stirrup]

Nope just normal calculus

[tender river]

wut

[silver stirrup]

We did a bunch of stuff outside the book

[tender river]

none of these things are covered in that

oh ok

[silver stirrup]

Yeah

Like we also learned some really basic group theory to show certain results

Like log product rule

[tender river]

brucknor thompson covers about all of these things

[silver stirrup]

Yeah I saw table of contents and it seemed to match basically everything we did

[tender river]

amann escher is another book that covers and uses a bunch of algebra stuff

[fresh skiff]

Well i believe you will like Abbott's exercises

[fresh skiff]

Ah Amann and Escher, well a random question do people try to solve all problems in Amann and Escher?

[tender river]

thats a question for people who try to solve any problems in amannescher in the first place

most people i know dont care about solving every single problem in every book they read so the answer is probably no

[proud osprey]

you can prove IVT either with epsilon-deltas or by first proving that intervals are exactly the connected subspaces of R and then that the image of a connected set is again connected

pedagogically, they're quite different

[vital bane]

Abbott proves IVT in two ways, using 1. Axiom of Completeness 2. Using Nested Interval Property

I think they are both more instructive than epsilons and deltas

besides epsilon-delta stuff is in fact topology in disguise, they are simply open balls

[proud osprey]

yes, I know that

I'm just talking about the pedagogical difference

[vital bane]

fair

[proud osprey]

all the topological stuff was very confusing for me when I first encountered it in Analysis

and yeah maybe epsilon-deltas aren't all that instructive :D

but you gotta work with them in analysis anyway

[fresh skiff]

Oh, so it's like they pick a suitable math book they study, they spend time to get intuition, they solve some exercises problems that they find interesting or some problems for polishing understanding and then move on

[tender river]

normally if ive picked a book to work through i try to solve a majority of the problems during my first run wiht the book and i keep at most only like a couple of other references to supplement the parts that i dont understand and i try to select the exercises from those books as well. for example while studying linear algebra from morton curtis i must have done like 97% of the problems from each section in that book and i only left the ones that were immediately obvious just from reading the problem text or a computation that i didnt wanna bother with at the time. i had axler on the side to solve additional exercises occasionally. similarly while studying dummit and foote i mustve attempted about 90% of the problems on the first run of which i might have had success with about like 65-75% or something on the first try

if you only did a handful of the problems from every chapter while working through a book then i dont think thats sufficient to move on at that point. you might move to studying a different subject but youd still want to continue reviewing more problems from that subject on the side and make sure youve got everything down pat

[vague kiln]

depends on the number of problems but unless you have one of those gigantic 1000 page calculus textbooks i absolutely agree

[keen vale]

what do you all think about Elementary Linear Algebra by Anton and Rorres?

[tender cobalt]

???? what

Not as much as rudin

Rudin legit goes over metric spaces

Abbott sticks to R not even R^n as well

Pugh also goes over homeomorphisms along with metric spaces (i think rudin too)

[vital bane]

lol metric topology is the same in any metric space

R or (X, d)

so in fact they cover the same concepts

you literally replace |x - y| with d(x, y)

[vital bane]

he doesn't have to🗿that's the whole point, everything before differential calculus and integral calculus generalize trivially to general metric spaces

for proper coverage of differential and integral calculus in R^n it's wise to choose a separate book like Hubbard or Shifrin

[tender cobalt]

ye i did shifrin

[vital bane]

based

and Rudin doesn't cover the Henstock-Kurzweil integral whereas Abbott does🗿

[tender cobalt]

[vital bane]

try it!

though of course there is more to said about metric spaces than what's covered in Abbott, which would be useful for functional analysis and other stuff

[tender cobalt]

But different inequalities when workin with R^n :/

[vital bane]

such as?

[tender cobalt]

i forgot but theres the /sqrt(n) thing

[vital bane]

what

[tender cobalt]

wait

ok nvm its the examples and proofs that are different

[tender cobalt]

yes

just replace d(x, y) with norm from normed VS

haha

[vital bane]

🗿

[naive lava]

Functional analysis in a nutshell

[civic timber]

😭

[iron pulsar]

@silent roost have you considered reading brotopia ?

[fierce coral]

Bro why? 😭

[pale mica]

the page is gone o.o

[fresh skiff]

Berkeley university student wow

[cunning elk]

?????????

what

famous for sure

but calling it "definitive" seems like a massive stretch

[remote sparrow]

https://www.amazon.com/Introduction-Real-Analysis-Textbooks-Mathematics/dp/0367486881

found out about this book, seems interesting

examples are worked out in detail and there are hints and solutions to selected problems in the back

maybe on the dry side

[vital bane]

💀

[tender cobalt]

imo the channel is good for starting out to self study math

[vital bane]

This server is better

[tender cobalt]

true

[opaque flax]

hey guys

i m fucked up in inverse trigonometry

[fresh skiff]

Ah your name (it means stars in my language)

[iron pulsar]

interesting. i like to read about power.

i'm considering reading one of Ruha Benjamin's books next.
what have you been reading lately?

[wanton tide]

I am 2nd year engineering student wanting to taste some pure math classes would Introduction to Real Analysis byJiří Lebl be a great book for an intro to real analysis?

[median edge]

what are the pre-reqs for math made difficult

[pine tundra]

Huh?

[normal crystal]

it's an old book that does as the title suggests

[gray gazelle]

My class used Rudin and my contempories used Petrovich, I think the latter is a great beginners book

[shrewd ember]

Anyone have any good recommendations for applied diffusion mapping, and similar non-linear dimensional reduction?

[kindred sequoia]

Math

[last cipher]

so like

summary?

[rigid trail]

I do know

He does not belong

[oblique sequoia]

I'm self learning math and I'm stuck on inequalities with modulus and greatest integer function, any place where I can get a proper explanation and a few practice problems that clears things out?

[trail hemlock]

i think this might be a response to a viewer email

he always does this clickbaity stuff

and i mean he’s hella clixkbsity snd the ai thing is deplorable, but his content isn’t without value

[normal crystal]

yea
sometimes it has negative value

[stiff crow]

Is it better to start Linear Algebra or Real Analysis after multivariable calc?

[molten gulch]

Imo should've done linear alongside multivar

[stiff crow]

I mean I did do learn the basics, vectors, dot product and cross product, I understand what they are for and how they work, matrices etc but I think there’s a lot more in linear algebra than just those so I was just wondering if I should read a linear algebra book or if I should just go to real analysis

[molten gulch]

Yes there is quite a bit more to it

[hybrid salmon]

hi does anyone know any good books o ncoilguns and magnetic fields for coilguns? Thanksss in advance

[rigid trail]

Just click "Do Not Recommend Channel"

That's what I did

Hate his videos. I am a hater

Treating math content likes it's low effort gym motivational content bruh

What did I do 😭

Okay I'll try not to worry about someone hating me even more than hating Math Sorcerer

😨

[stiff crow]

Yeah I was wondering what else, because I learned through Stewart’s calculus

So you can just assume I know everything related to linear algebra there was covered there

[wide jewel]

NOOOO

[sharp goblet]

some good book in axiomatic set theory?
good problems?

[wicked fractal]

Wasn't bro advocating for math? What happened?

[wicked fractal]

You can try Abbott. If it is too boring you can jump into Rudin

[thorn cloak]

The funniest thing is when city tutor math made a video calling him out

Math tuber drama

[molten gulch]

LOOOOL

for AI books or-

[thorn cloak]

Yeah

https://youtu.be/rPMmLUpluu4?si=Bi7Pkei-QIHva7-n

[wide jewel]

Math sorcerer my fucking goat

[vital bane]

I didn't watch it

[vital bane]

stop hating, learn to simply not care🗿

[rigid trail]

Normally I don't care, until people bring him up again 😭

[mortal ore]

We already do

And it's served to be harmful (as romanticization does)

[vital bane]

We should romanticize romance

[heavy vault]

What do you guys think are the prerequisites for "lectures on the curry Howard isomorphism"

Js like an intro logic textbook?

Will the friendly one by Leary leave me prepared enough

[tender river]

Enderton is standard

and another book i liked was goldreis classic set theory although its organization is a bit weird

[naive lava]

how deep you wanna go?

[heady ember]

Enderton mention spotted

[terse linden]

math youtube beef is crazy bro 😭

[ancient vine]

Διαγωνισμοί μαθηματικων Σωτήρης Ε

[pure cradle]

What is wrong in giving valuable advice?

[mortal ore]

It can barely even be counted as beef

Math Sorcerer just uncontroversially sucks ass

[thorn cloak]

Honestly I kinda liked his old videos where he would do book reviews. But then he just started making like the same "just study hard; don't need to be a genius" "how to be a genius" videos. AI books sealed the deal

[normal crystal]

he never did decent book reviews imo
it was always the shopping haul format for used math books

[dim sierra]

yeah lol it was pretty stupid

[half void]

On the daily too bruh 💀 and the fitness videos

[sterile wave]

1m digits of p i

[rain wren]

wait what ai thing?

[exotic lake]

hi! i want to self-study differential geometry and i'm wondering if anyone has any book/problem set recommendations? ♡

[digital pumice]

I liked Tu supplemented with (John) Lee

[exotic lake]

thank you!

[thorn cloak]

he made like math history books and stuff using ai

Like all of it from the actual content to cover

[normal crystal]

nah man, treat the guy with the respect he deserves
he's out there writing nonstop, hand drawing covers 24 hours a day
barely stopping just to do some pushups and squats
so that we can be enriched by the 100+ books he published in a week

[dim pendant]

Is anyone aware of any books which try to teach a highly popular area of pure math (e.g. algebra, differential geometry, etc.) by developing the theory directly out of motivating example(s), rather than your typical (1) definition, (2) simple results chasing the definition (3) different types of the object (4) other results, (5) theorem, (6) repeat?

More concretely, I've been quite curious of Borcherds's claim that the right way to learn e.g. Lie group theory, is to study a couple of interesting Lie groups in detail, rather than start with the axiomatic details and take a walk through the major results

[remote knoll]

Borcherds's lecture series for group theory on YouTube (perhaps unsurprisingly) takes this approach, by studying small finite groups in detail via starting from small groups and expanding to larger ones as the larger orders introduce complications. He then introduced theorems motivated by these problems to address them each in turn.

But this isn't a book, and I don't believe he has written a book following his lecture series

[lyric cove]

hello anyone here knows a good book about mathematical proofs? i'm freshmen at uni and i would like to know more about mathematical proofs

[heavy vault]

Bump

[rigid trail]

I don't think you really need any prereqs

[heavy vault]

I mean surely you'd need to know some like basic logic no?

[plucky lantern]

How to think like a mathematician was what I had It's pre good

Plus a lot of old editions with not a lot of changes so you can pick em up for cheap\

[rigid trail]

It discusses logic

[remote sparrow]

@solemn rover

[lyric storm]

what are the pre reqs for donaldson's book on 4 manifolds? is any diff top needed, or would basic riemannian geo suffice?

[solemn rover]

I'd say it's pretty middle-of-the-road? Like it's not so gentle as to be handwavy, it's certainly rigorous, but it's not overwhelmingly technical either

Proof theory is a pretty technical subject so for a proof theory book it's gentle

Just start reading it and ping me if you have questions 🙂

[sand path]

How does Enderton’s Elements of Set Theory compare to Kunen’s Foundation of Mathematics ?

First Set Theory Book

[heavy vault]

Oo ok tysm!

Should those go in foundations channel

[bleak wave]

I saw what you did

[mystic peak]

favorite pop math books just for fun?
stuff similar to GEB which im working through now (which ik is more philosophy but still pretty interesting)

[rigid trail]

For your own safety I would not ask for pop math here

jk

What's GEB ?

[gray gazelle]

John Lee is pretty good

i think its better than Tu but idk

[gray gazelle]

quanta magazine?

[mystic peak]

hm maybe pop math was a bad way of putting it

[gray gazelle]

its not a book but they prob have some cool math and science stuff there

[mystic peak]

im pretty good at math at the undergrad level, but looking for some math-related book i can read this summer, just for fun

[gray gazelle]

would you mind being more specific?

if i had to read one book tho, i would pick categories for the working mathematician by mac lane

having knowledge in category theory is a must in order to learn further advanced math

and category theory can be fun

[plucky lantern]

Does anyone have any recommendation for graph theory practice questions?
I'm using Diestel's graph theory and there is a distinct lack of any sort of hint or answer

[remote sparrow]

it's not a must for more analytic fields like pdes and probability

bit of an overstatement

but it's very useful or even essential for fields that rely heavily on algebra

[vital bane]

yea category theory is useful iff you want to learn advanced algebraic stuff like algebraic topology, algebraic geometry, homological algebra etc.

if you are doing analysis or geometry or differential topology, then you won't need it

[heavy vault]

@solemn rover honestly the first chapter of the curry-howard stuff seems like pretty over my head rn it's just a bunch of like unfamiliar definitions and terminology do you think theres helpful background

i dont really know any logic beyond like basic propositional stuff so would it help to study that first somewhere thru some book?

[gray gazelle]

yeah but pure math was in my mind when i was giving that recommendation

[remote sparrow]

PDEs and probability are pretty theoretical

[vital bane]

Basically all of analysis

[mortal ore]

i was recommended a category theoretic textbook on topology as my first topology text

idk what to think about that

[vital bane]

was it the one by Tae Danae Bradley?

[mortal ore]

lemme check

[mortal ore]

seems to be from szymik

i have no background in categories though so i doubt this would be a good decision frankly

[remote sparrow]

https://www.amazon.com/Introduction-Enumerative-Combinatorics-Mathematics-Applications/dp/1032302704

[vital bane]

Is this it?

[vital bane]

[remote sparrow]

FYI there is a new edition of this book that was released earlier this year

[mortal ore]

i tried munkres and got bored

[remote sparrow]

a lot of people say that

[vital bane]

Munkres is fun imo

[mortal ore]

it felt the same as trying lang's undergrad algebra book

i switched to armstrong and i liked the opening

[cunning elk]

spivak for single variable

st*wart is horrible

if you actually want any sort of rigor

https://www.amazon.com/review/R2IADID8E966E8

^ perhaps the most elegant takedown of stewart i've ever read

did you know that he built some stupid ass mansion with all the money he got from price gouging the shit out of his shitass textbook?

textbook industrial complex

[gray gazelle]

eh i see them as a field of applied math

[gray gazelle]

lee has a topological manifolds book, some people use that instead of munkres

[remote sparrow]

the reason we even have analysis as a field is because of calculus, which was obviously motivated by physical problems (but of course grew to have a life of its own). almost all of analysis developed side-by-side with some real-world motivation. your orientation to pdes and probability implies that you essentially dismiss all of analysis as applied math

[graceful moon]

Point set topology is just kinda boring imo, but it’s useful. Learning it can feel extremely dry at times

[remote sparrow]

https://www.youtube.com/watch?v=1js2PSD1BdA

[naive lava]

okay, so, I'm about to finish Aluffi's algebra in a few days, and then I will need to move on to other subjects, in which order should I read this, or what is the logical next step?

Currently also reading Rotman's algebraic topology

Bott and Tu, Milnor's Topology from a differential point of view, Kobayashi Nomizu and Griffiths and Harris are the books I need to put in order

I also might consider changing kobayashi nomizu with something more suitable for someone that has an idea of stuff but not learnt it mathematically

my prof reccomended me to read Lee's whole series and then read Steenrod's fiber bundles

which if i skip the 1st book

Still a whole lot of pages

and tbh i won't need half of it

okay maybe this would be a more suitable question for the physics server

[gray gazelle]

👍

[flat plaza]

Thoughts on Vector Calculus by Baxandall & Liebeck?

[grand thistle]

how much of aluffi? cover to cover?

[vital bane]

Atiyah Macdonald/Matsumura -> Hartshorne

[real marsh]

Hartshorne ❌
The red book ✅

[naive lava]

yep

[naive lava]

Im NOT planning on committing suicide but thanks

[grand thistle]

oh cool which sections would u say were ur fav

[vital bane]

"the last section, so that I could be done with this book"

[naive lava]

I hate all the math that exists

[naive lava]

yeah lmao

[naive lava]

except alg top and alg geo those seem cool

[vital bane]

Dogu is a certified physicist

[grand thistle]

LMAO

[naive lava]

hopefully a math phy in 3 4 years

[last cipher]

Real Analysis I books?

[grand thistle]

would u say the last two chapters are worth reading

[naive lava]

8 is definietly worth it

idk about 9

I js need fundamental gropus tbh

[grand thistle]

cool cool

[naive lava]

so homological algebra is an overkill

[grand thistle]

also, how important do u think getting all the categorical notions down is throughout the book

im on chapter 3 and im kinda struggling w the category theory but i like the actual alg exercises

[naive lava]

I chose this book because i wanna learn about both cat theo and algebra

and again, I don't exactly know how common these stuff are in math community

but i heard that cat theo pov is getting more and more popular troughout the math community

so it might be worth it

but those categorical things will catch up to you if you don't understand them later

[grand thistle]

alright makes sense, thanks!

[gray gazelle]

bro wants algebraic geometry

[gray gazelle]

is this actually a good path to learn algebraic geometry though?

i feel like its way too advanced and accelerated

[vital bane]

I don't really know I was just memeing

right now I'm just going through

[gray gazelle]

ooooo, thats a good book for graduate algebra

ive read allufi

tbf i didnt gain much from reading it though

but i am planning to learn commutative algebra in the summer

[fresh skiff]

ppl are talking about algebra and algebraic geo

well i missed the conversation

[gray gazelle]

Its fine

Atiyah macdonald is a small book

Harthshrone assumed you know classical ag

So maybe try to find some articles online or some books that discuss older shit

And then harthshrone

[mossy flume]

a good first text is Fulton's Algebraic Curves and/or the Gathmann notes

as far as commutative algebra I prefer this text: https://dspace.mit.edu/bitstream/handle/1721.1/116075.2/WWCM.pdf?sequence=6&isAllowed=y

it is a strict superset of Atiyah Macdonald

but this has complete solutions as needed, great for self study (just don't be tempted to look too early)

and IMO the exposition is nicer

[fervent obsidian]

what book you recomended for algebraic geometry modern :¿

[mossy flume]

Gortz and Wedhorn

[vital bane]

mathematicians: We are very rigorous and very serious
also mathematicians:

[gray gazelle]

oh yeah i should learn that after doing commutative algebra

[vital bane]

What about Vakil?

[gray gazelle]

👍

[gray gazelle]

You can do both

You dont need to treat math as completionist

But stuff will show up and u might be confused ig

[gray gazelle]

nice i rly appreciate the rec but this is too long 😭

[mossy flume]

Oh so true

[normal crystal]

relevant to all of you in this previous chat
https://www.youtube.com/playlist?list=PLArBKNfJxuulCCX0z_n5JJcvZrX9ej8uq

[mortal ore]

How is a source being too long a problem

[gray gazelle]

idk if i will be able to finish it in the summer

[mortal ore]

Just read a chunk of it

[gray gazelle]

yeah, ig i dont have to read all of it

[remote sparrow]

how is this too long

half the book is just solutions

mf looked at the page count and didn't check the toc

[gray gazelle]

what is expected to know before reading rudin?

[remote sparrow]

in principle, knowing how to read and write proofs

[normal crystal]

the YouTube playlist was for recent Fields Academy Shared Graduate Course: Modern Algebraic Geometry
since I distinctly feel nobody will look

[remote sparrow]

in practice, it's wise to have instructor guidance or prior experience with analysis

[gray gazelle]

im gonna be continue reading proof writing transition to advanced mathematics book

is it solid

[remote sparrow]

yeah

[gray gazelle]

i have done like epsilon delta proofs and riemann sum to integral stuff

is that somewhat there

not really all analysis course

may be i can read bartle

or smth

[remote sparrow]

bartle is good

there's plenty of good analysis books out there

[gray gazelle]

so i need to get down the proofs writing and bartle in theory would be all good to start reading rudin

[remote sparrow]

sure

[gray gazelle]

alright thank you !

[normal crystal]

Jay Cummings has his Analysis book
I saw on his site he's releasing videos for it in the fall semester when he teaches
he also just released a Math History book, which is why I was looking

[remote sparrow]

yeah i heard about that math history book

nice to know he's planning to make videos for his book too!

[normal crystal]

he said he's adding slides for the Math History book when he teaches with it in the fall semester
why he's not also recording those, idk

[gray gazelle]

oh i didnt notice that

[vital bane]

Knowing analysis because that book sure as hell won't teach you

it's not

there's just a vocal minority recommending it

and it depends on your use case

I mean depending on whether you're self-learning or you're learning analysis from a university class

Axler measure theory or Axler LA?

and which Spivak?

Calculus or Calculus on Manifolds?

[gray jungle]

to me there is mainly two situations where its better than the other books
1: you have a strong math background from doing other stuff or 2: you are in a class where the instructor supplements it.

I only recommend rudin as a "exercise book" or if i know someone is really strong already, since it demands a lot of effort from the reader to keep track

abott seems like a better option overall, or tao if you're also new to proof based math.

And i mean my problem with rudin isnt even the conciseness, its that the book structure feels really weird, if you are doing RA for the first time you wont be doing it on metric spaces, so chapter 2 which is the "good chapter" just feels extremely unmotivated unless you just already have a good grasp of things on the real line already.

and the same thing with chapter 6 where you work with the reimann-steiljits when you havent picked up the intuition for the normal integral

chapter 5 and most of 7 i think are extremely good tho

just that the progression of the rest of the book feels out of place, might as well do real analysis on R and just dip into metric space topology later as a topology course with analysis flavour

[vital bane]

[golden salmon]

I agree with not using Rudin upfront. I like Rudin but it's not a good first book. the proofs are a bit 'show-offy' in that yes they're concise and that's nice, but it doesn't make you sit down and think about the structure any more than a more explicit exposition (imo).

The metric space comment is very appropriate: Rudin works better as a 'second' 'hard' maths book. By which I mean you've already had some exposure to how mathematicians normally write. This is why he's good as a second visit to the subject.

One (weird, but workable) way you could work in Rudin is go Munkres -> PMA Rudin -> RCA Rudin -> FA Rudin. That's.... Sure that's a choice But then you're missing out on better books imo.

[vital bane]

also there's barely any exposition

it's good as a problems book/reference book

[golden salmon]

Another insane pairing is Schramm Real Analysis + Rudin Real Analysis

that'd work but just.... lol

[vital bane]

I've never heard of Schramm, what's that like?

[golden salmon]

Exposition heavy!

its about 350 pages and the proofs are fine

The focus is on intuition rather than going super in depth

which to me feels like its the 'right' introduction to RA

but it would definitely need a 'mean' supplement like rudin to feel complete

(no pun intended)

[vital bane]

exactly, there's no need to learn everything at once, having a strong base is what's important, after that you can go however deep you want to go into the subject

[golden salmon]

yeah I think you basically know when the switch flips in your head and you no longer want exposition

There's probably a more elegant way to word it but every time I get to the point where 'aight cool its exercises time' its totally unconscious

[vital bane]

I mean you always want exposition at any level to actually...learn the subject , it's just at a higher level now

I hear good things about Zorich from @remote sparrow

I use textbooks as the main source

maybe sometimes lectures as a supplement

[heady ember]

If you use a math book like a reference list of theorems and exercises, Rudin is a fine choice.

I always read my books like that --- proving everything myself and finding intuition myself --- so I haven't really had many gripes with Baby Rudin.

[vital bane]

1

[vital bane]

meanwhile grass: also using schroder

if you only used Rudin you'd have gripes with it

I'm doing this now

I'm on section 6.5 of Abbott

I will get back to it

[heady ember]

Not exactly. Schroder was decently challenging when I started using it, so doing Rudin then might have resulted in me being slapped too hard. But, especially nowadays, I don't really use Schroder for clarifications. I use the same way as I do Rudin. The extra-pedantic nature of Schroder has been more an annoyance than helpful, in fact. Also, Baby Rudin covers and uses metric spaces quite heavily; I had no gripes with its coverage at all. In fact, I loved my time learning about metric spaces, even though I read nothing about them in Schroder (aside from R under the Euclidean metric).

[vital bane]

That's what I mean, you have to first get your basics straight, before you jump into the deep end

[vital bane]

and about the metric spaces, they're not too hard half the time it's just replacing |x - y| with d(x, y)

[heady ember]

Eh, I wouldn't refer to using baby Rudin as jumping into the deep end.

[vital bane]

I would refer to it as that due to the lack of exposition

[heady ember]

I would be inclined to disagree. Stuff like compactness, Baire's theorem, etc goes beyond such a mere generalisation.

[vital bane]

They are all identical on R and on a metric space

I've done those using Abbott

also Baire's theorem based

[heady ember]

Well, try playing with equivalent notions compactness and you'll find that working with R can be misleading/doesn't give you the full picture.

[vital bane]

simply change the metric!

[heady ember]

Namely, complete + bounded is not equivalent to compactness.

[vital bane]

you don't need all of Rudin for that lol

[heady ember]

I never claimed that.

[vital bane]

so you've abandoned Schroder now?

[heady ember]

Stop shitting on Rudin or I'll shit on D&F

[vital bane]

that's the neat thing, I don't have to

[vital bane]

or are you gonna do both?

[heady ember]

No but I have accomplished what I want with it. It lands firmly in the category of secondary reference now.

When I do measure theory, I'll be doing it from another book, for instance.

[vital bane]

Rudin RCA

[heady ember]

How about no.

[vital bane]

I thought you liked learning from a big list of definitions and theorems 😔

[heady ember]

That's essentially how I read math books, sure.

[vital bane]

I actually haven't decided my own measure theory path, I'm just focusing on algebra rn, and after that I'll finish Abbott

[heady ember]

But that doesn't mean I'll go with a book that has a large amount of mixed options on it, just because its terse

I'll probably go with the book by Dietmar Soloman (can't rmb his name exactly) rec'ed by James

[vital bane]

is it the ETH Zurich thing?

[heady ember]

Yeah

[vital bane]

oh nice

yea that looked cool

I think I'll probably do what ari is doing

Folland + Cohn

[heady ember]

Traitor

You should follow me

You swore to form a measure theory reading group with me, yet now you abandom me

[vital bane]

Who says you can't have a reading group where different people follow different books

that's just more diversity!

Depends, I'll just do Tong notes + Spivak CoM

reading guys* 🗿

I actually first learnt multivariable calc from Khan academy

it's dope

[heady ember]

L take

Real men learn multivariate integration via measure theory

I don't need to fight someone who has already lost.

[vital bane]

real men stop wasting time on discord and do math 😔 time to go chat, goodbye

[remote sparrow]

https://press.princeton.edu/

there is currently a 50% off sitewide sale

[heady ember]

[remote sparrow]

[vital bane]

Sour Drop™️ can buy it for you and ship it to you for free

[silk vault]

hi i'd like some practice material recommendations to go with

professor leonard's lectures

[remote sparrow]

for what subject

[silk vault]

broadly? mathematics
narrow? im relearning everything so starting with algebra

i suppose a recommendation for proofwriting would be welcome as well

[rough umbra]

Abstract algebra? Or like precalculus?

[stable flicker]

Does the discount apply to this

[rough umbra]

If the latter, maybe khan academy? If the former, maybe Jacobson 1 or Dummit & Foote

[silk vault]

precalc

[rough umbra]

I think proofwriting is smth u can pick up as u learn intro analysis or algebra by reading and doing. Something like D&F or Abbot

[rough umbra]

then i think ppl like khan academy

[silk vault]

i see. someone also recommended me book of proofs and how to prove it

[rough umbra]

Velleman?

[vital bane]

Dummit and Foote mentioned

[rough umbra]

TRUE

[vital bane]

The GOAT 🗣️🔥🔥🔥

[rough umbra]

Jacobson >

Icl

[silk vault]

first one is by Hammack and second one by Velleman, yes

[rough umbra]

If you wanna do that first, it could def help

I just think u could also pick it up by doing like an intro course in elementary set theory or elementary number theory

[silk vault]

you have to watch their lessons first before practising still right

[rough umbra]

like how most unis teach it in an intro to discrete math type course

[rough umbra]

idk, havent used it sorry

I think it's the most popular intro to abstract algebra

[vital bane]

because it's based

and it will never give you up

or let you down

or run around

and desert you

[silk vault]

NOOOOOOO

[rough umbra]

my personal fav

[remote sparrow]

it covers a lot, so for instructors, it makes for a flexible reference that can be adapted to lots of courses

[vital bane]

and you can take it to grad school as well

(it only has like intro grad stuff but still it's a good reference)

So much stuff to learn! Isn't it exciting!

Did you do the exercises?

[rough umbra]

Then thats a perfectly reasonable pace i think

[tender cobalt]

Jacobson I mentioned

[drowsy nacelle]

what is usually the difference between like "nth printing" and "nth edition" for math texts?

if it's possible to answer that in any generality

ig i've usually thought of it as like, new printings maybe fix errata and improve formatting stuff but don't revise the actual content of it like editions do

is that more or less it

[remote sparrow]

https://mitp-content-server.mit.edu/books/content/sectbyfn/books_pres_0/11599/e4-bugs.html

there's a pretty concise explanation on the CLRS errata page

[drowsy nacelle]

I’ll check it out thank you

[remote sparrow]

sometimes errata don't get fixed beyond a certain printing number (see long-standing textbooks like conway's Functions of One Complex Variable or folland's Real Analysis: Modern Techniques and Their Applications)

[drowsy nacelle]

Ah yeah I’ve def seen a lot of books that have errata but only a couple really old reprintings if any

[gray gazelle]

Good books on algebra and trigonometry. I am ok with basic algebra and arithmetic, but i have a really weak foundation on functions ect... any book recs?

[rough umbra]

What do ppl recommend between Folland and Bass for measure theory?

[gray jungle]

As i understand, Bass is less of a systematic book on MT and more focused on helping you pass qualifying exams and practising proofs, so its quite different in spirit from folland which does teach MT systematically.

[desert quest]

I recommend Folland

[gray jungle]

so depends on what you want really, if you're trying to learn measure theory Folland is quite terse without a instructor, if you feel confident you can use it tho, its still a great book.

if you want a nicer approach see Roydens real analysis book.

My personal recommendation is the notes by DA Salamon.

[rough umbra]

Ah I see, thank you

[rough umbra]

I'll check them out, thanks so much :)

[remote sparrow]

haven't really looked at royden before since i heard about the numerous errors in the 4th edition, and i've mostly stuck to axler, but the 5th edition seems pretty nice; i would assume most of the errata in the 4th edition have been fixed in the 5th edition

https://faculty.etsu.edu/gardnerr/gardner.htm

also there's a guy that made lectures for royden

any specific things you like about royden?

[gray jungle]

It does have problems, but its exposition is pretty classical and really friendly, i like the structure of the book and how its accessible to anyone with basic RA

I agree with the main critique that doing R alone is not "efficient" but its also a valid gentle approach.

I like the proofs and exercise style too, overall a good read if you're careful with the typos and errors

[mystic peak]

https://press.princeton.edu/

psa: princeton university press is 50% off. I copped a hardcover copy of The Princeton Companion to Mathematics for like 50 bucks, great deal.

also has great books in like every subject you could be interested in

[remote sparrow]

https://www.rxddit.com/r/math/comments/17k9xf9/measure_theory_textbook/

[vital bane]

How did no one mention

[remote sparrow]

they're probably all old-heads that took measure theory a long time ago

[vital bane]

They learned measure theory from Henri Lebesgue

[gray jungle]

S&S still has probably the best written chapter (to my knowledge) on differentiation

to be expected given steins field of work

with that being said its a topic thats usually covered after a fair bit of MT has been done

[marble solar]

Yeah, where Stein and Shakarchi lacks in the abstract measure, it more than makes up for it in chapters 3, 4, and 5

[silk vault]

i have settled with using openstax to practise

[rigid trail]

my uni has a pretty good math library, i go there to read if I'm just curious to check out smth

But for courses I buy textbook

[normal crystal]

are you standing at the checkout desk

[meager isle]

Can anyone recommend me a book to start on string theory? I have a background on Differential Geometry and Manifold Theory. Thank youuu

[golden salmon]

I'm not a string theorist but the bits I've read of String Theory and M-Theory: A Modern Introduction by Becker, Becker and Schwarz were really nice

[dreamy robin]

For Olympiad Combinatorics, which book is good? PHP, I.E. ,Dirichlet etc. and basic ones too covered in depth

[desert quest]

Olympiad combinatorics is mostly intuition which you gain from doing problems

[rain wren]

I liked lee way more than tu

but lee got a major humpback at the start whereas tu's learning curve is way gentler (that mofo defines AN EQUIVALENCE RELATION)

highly encourage checking out both and seeing which one you prefer

[exotic lake]

thank you! i have acquired both books now ♡

[exotic lake]

sounds like a nice read for my brain, which got deep-fried by physics for the past two years

[rain wren]

oh you do physics?

tu is definitely a more suitable option I think

I'm pretty sure that book was written with physicists in mind whereas lee was catering specifically to future geometers

[remote sparrow]

if you're curious about curves and surfaces, tapp is really nice

although most arguments in R^3 don't generalize well

they're neat

[exotic lake]

unfortunately

[rain wren]

my condolences

[exotic lake]

ty, i'll check both of them out! so far tu reads quite nicely

[exotic lake]

i'll look for tapp too! ty

[remote sparrow]

o, pressley and do carmo are other good choices for curves and surfaces (do carmo has also written more advanced books on differential geometry)

[exotic lake]

real (cubed)

[remote sparrow]

pressley has solutions in the back

[exotic lake]

that's always neat

[remote sparrow]

do carmo has hints and answers to some of the problems

[digital pumice]

I studied physics and love Tu

[exotic lake]

found all of them now! ty for your help everyone ♡

i'm going to have a fun summer

[brazen grove]

intuitive calculus of variations book with derivation of formulas too for applied maths

should have max coverage aswell

applied functional analysis

[remote sparrow]

https://tenor.com/view/i-saw-what-you-deleted-cat-gif-25407007

@rain wren

[rain wren]

I had forgotten quantum mechanics was a thing :3

and like

pdes

[gray gazelle]

Do any of you guys have good books for basic functions, trigonometry and algebra? Thanks in advance

[fresh skiff]

any calculus book will work i guess

[pearl moat]

I haven’t gone through these books personally, but have heard great things about them (by Dolciani):

• https://www.amazon.com/Modern-Algebra-Trigonometry-Structure-Method/dp/0395142563
• https://www.amazon.com/Modern-Algebra-Structure-Method-Book/dp/0395142555/ref=mp_s_a_1_1?crid=1R1EH1U3N2YJX&dib=eyJ2IjoiMSJ9.Ni4dOSZzY55tI4EFAD9xOKGehi1teESacXRHlK9u0bJC78AJhMt6wqmX-fhJWAAZiBBj4zC2QsIocUpiELx-9OXQohSAoKrwPMHODO-C2emAaS0JSwxkagNBn662uVQcZxzBaVYV1A_2eFFy9dhgdU9Pt4mkj-YJvO01FT-hN-Mbh94HIHfdy89S6GR_v5RtZQVU1bUPLLhaOfJ7UeTRaQ.QXQ3yU8Oof73Z44zp5WJYZbju3D5sgBlEruN204fGE4&dib_tag=se&keywords=modern+algebra+dolciani&qid=1746363548&sprefix=modern+algebra+dolciani%2Caps%2C108&sr=8-1
• https://www.amazon.com/Practical-Algebra-Self-Teaching-Guide-Second/dp/0471530123/ref=cm_cr_arp_d_product_top?ie=UTF8
• https://www.amazon.com/Modern-Introductory-Analysis-Mary-Dolciani/dp/0395286972

follows recommendations from the following videos: https://youtu.be/SQtOZGfmZlE?si=o2tR-2VnQs8KpW0H

https://youtu.be/usLkuFlmNew?si=OeKQuV_Kn0pRYbYR

[lyric storm]

any good recommendations for learning about homogenous spaces and principal bundles?

[gray gazelle]

Thank you so much, thanks 😊

[pearl moat]

Np! These are a bit more rigorous than your usual algebra/pre-calc texts, but I am certain that after going through them, you will have a very solid understanding of the material

[gray gazelle]

That's what I am ready looking for, I am prepping for the things I am gonna study, and my math is not that strong so I struggle with problem solving.

[sharp latch]

I’m also looking for this so I’ll bump it

[vital bane]

Radon-Nikodym?

[vital bane]

El Psy Congroo

[neat prism]

I can help

[gray gazelle]

How can you help me 😊 I am currently doing stats and calculus in school, but I don't have a good grip on pre calc.

[neat prism]

Like?

[gray gazelle]

Like I got a really bad grade when in came to functions and trig. Never really understood them.

But trig especially, and I never learnt trigonometric functions

[neat prism]

Try from basics

Is ncert available in your country

[gray gazelle]

Ncert?

I searched it up, is it a website for education?

[neat prism]

It's a publication... Yeah.. There's a website also

[gray gazelle]

Ok, is there a specific book that i should study

[neat prism]

Check dm

[red wraith]

I have book recommendations
How to die in 101 ways