book-recommendations

[fresh burrow]

i found a link to what could be it but then god said 404 — File not found.

[scenic kite]

Any book for quantum mechanics?

[slate chasm]

Yeah! I have a list of materials here.

Quantum Mechanics

• Dirac, Principles of Quantum Mechanics
• Shankar, Principles of Quantum Mechanics
• Sakurai, Modern Quantum Mechanics
• Von Neumann's Treaty on Quantum Theory
• Pauling's Quantum Mechanics with Applications to Chemistry
• John David Jackson, Mathematics for Quantum Mechanics
• Valentine Bargmann, On Unitary Ray Representations of Continuous Groups
• Max Planck, The Origin and Development of Quantum Theory
• Heisenberg, Matrix Mechanics
• The Feynman Lectures on Quantum Mechanics
• Leonard L. Schiff, Quantum Mechanics
• Freeman Dyson, Advanced Quantum Mechanics
• E. Wigner, Group Theory and its Applications to Quantum Mechanics
• Hermann Weyl, The Theory of Groups and Quantum Mechanics

[dapper root]

[scenic kite]

Ok. I'm just starting with quantum physics and quantum chemistry out of pure interest, I need to get organized, thank you. Maybe study quantum mechanics first and then physics.

[slate chasm]

But that's not how you start.
Don't disregard mathematical rigor and learn a bit of numerical analysis/programming to be able to apply it, and then learn quantum mechanics well because it will be necessary later.
Oh, and learn the formalism with functions and vectors; they go hand in hand.

[fresh burrow]

found it, it was "an invitation to algebraic geometry" by karen smith

[scenic kite]

oh, okay. Thank you

[slender cargo]

I like to reference this book list from John Baez:
https://math.ucr.edu/home/baez/books.html

Highly opinionated of course, but good to check out. He's a well known professor.

[formal bronze]

Elementary Number Theory by David Burton

[scenic kite]

Okay, thanks

[late plinth]

rosen is nice

this is a good quick reference imo, granted it doesnt go too into depth:
https://crypto.stanford.edu/pbc/notes/numbertheory/

[gray gazelle]

hii can anyone reccomend a very good book for olymoioad mathh NUMBER THEORY well expplained

with exampls

plz

[trail hemlock]

https://www.amazon.com/exec/obidos/ASIN/081763245X/artofproblems-20
https://www.amazon.com/104-Number-Theory-Problems-Training/dp/0817645276/ref=pd_bbs_sr_1?ie=UTF8&s=books&sr=8-1
https://numbertheoryguy.com/publications/olympiad-number-theory-book/
https://drive.google.com/file/d/1BcJTLjQaelZ4w_70oHKyImC2I8zLfyrt/view

[gray gazelle]

thanks

for the effort

[trail hemlock]

i hated studying number theory for olympiad, have fun

I also used part of hardy's "an introduction to the theory of numbers"

[gray gazelle]

yo thanks

[mystic orbit]

I do! Unfortunately it's in a private server and we're currently not inviting any more people in

I'm soryyy

[grim dragon]

I want to teach myself calculus 🙏 😭

[lethal bronze]

I think there is a calculus book published by Dover. I don't remember the name on top of my head, but I heard it is good for autodidacts.

[tame dagger]

Hii Can anyone help me out

Can anyone recommend a good calculus book by a chinese author i heard they are good

[grim dragon]

Thanks

[balmy crown]

Anyone got a discrete math book theyd reccomend?

[stray egret]

.

Am I just too far gone or was this guy not srs

[willow merlin]

I need book for learning euclidian geo from the groundup

with lots of exercises

[maiden glen]

i need an extensive, abundant geometry book concerning foundational geometries (Euclid, plane, solid, line, point, analytic/coordinate, trigonometry.) with exercises.

[nocturne blade]

Hi. Any recommendations for a PDE book? (Hyperbolic and elliptical) I'm coming from a Physics background, and we're not taught in the same way as a Mathematician would, but I'm interested in learning the proper way to do stuff (demonstrations, math language, etc.). If there's a good book plus something that could help me understand it, I'd appreciate it.

[bright epoch]

Idk if you're the same person who asked before, so sorry if this is a repost but: geometry revisited by coxeter

[willow merlin]

best books for real anal

other than rudins

[bright epoch]

I liked Tao's analysis, but I read it after I already knew analysis

other than that, I've heard good things about Abbott, though I haven't read it myself

[warped spoke]

"real anal"

lmao

[bright epoch]

tis what we call it

[narrow relic]

You could check out Bartle and Sherbert, Introduction to Real Analysis.

[willow merlin]

i already ordered it, arrives in two more weeks (used)

[narrow relic]

Oh fantastic! I can give you some tips on which sections to skip, if you like.

It's a great book in my opinion but there are some things I recommend skipping.

[willow merlin]

i feel you hahah

[willow merlin]

like which

is spivak any decent btw?

[narrow relic]

did you order the 4th edition?

[willow merlin]

i heard some of the bartle problems are taken from spivak book

[narrow relic]

which spivak book?

[willow merlin]

3rd

[willow merlin]

single variable I think?

[narrow relic]

Okay. I read the 4th but I'm looking at the table of contents of the 3rd edition.
The key to making the most of this book is ignoring the stuff the authors introduce on something called "gauges". They use it to introduce an integral called the "generalized Riemann integral" which you should ignore.

[umbral herald]

Hi

Does someone have the be smart plus grade 10

[narrow relic]

I went extreme and used another book to learn integration. You might not have to go as far as I did. But I would definitely skip section 5.5. I skipped Chapter 7 (the Riemann integral) completely and learned it from another book, but you might be able to make use of the material here if it doesn't involve the gauge business. I think you should read Chapter 8 and 9 but just ignore anything that mentions gauges (like their proof of Dini's Theorem). Don't read Chapter 10. Don't read Chapter 11 (you can get much better coverage of "topology" from another book).

[umbral herald]

Hello

[willow merlin]

what are you complementing bartle with?

[narrow relic]

and actually by the way, I learned Chapter 8.3 and 8.4 from another book also

[narrow relic]

At that time, I learned the integration material from a book called Introduction to Analysis by Wade

[umbral herald]

Does someone have be smart

Grade 10

[narrow relic]

Once you get to the "topology" section, there are a bunch of different sources you can learn that material from, people here can recommend you all sorts of books for that.

[umbral herald]

Pls does someone have be smart plus grade 10?

I have final exam

And i need to see a question in it

The book

I need to get good grade or i fail math

[narrow relic]

Anyway, I hope this helps you.

[willow merlin]

wade and bartle are the only books you recommend for r. anal. ?

[umbral herald]

Dors someone have be smart plus grade 10 pls

[narrow relic]

For where you are right now, yes.

Also there may be a few typos in Wade, I don't quite remember since I only used it for the integration stuff and for some of the material about functions from R^n to R^m.

@willow merlin Wade errata: https://web.math.utk.edu/~wade/pics/4EDERROR.pdf

@willow merlin another little tip: some people are going to tell you something like Wade isn't good because it's not advanced or prestigious or whatever. ignore them. you can do more "advanced" stuff once you get these basics down.

What's pma?

Also, I'm looking at Wade right now (4th edition). I indeed read Chapter 5 (integrability on R). I also read Chapters 8 through 12

[willow merlin]

got it, ty will try to take. a look

[narrow relic]

You're welcome! Hope things go well.

[narrow relic]

One more thing: skip chapter 10 (metric spaces) in Wade. you can learn that from a better source later. the stuff I'm telling you about is all pre-metric spaces.

it's single variable analysis and how analysis works in R^n with vectors.

[willow merlin]

will do surely, metric spaces and topology are skippable for me

[narrow relic]

Great. That stuff is the "next level".

[slender cargo]

@narrow relic Sorry for asking late. Was just curious why you decided Axler wasn't for you?

(glad you figured that out quickly btw)

[foggy quest]

one variable book here is good (my favorite out of Abbott, Tao, and this book): https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/. Rudin is IMO not suitable for beginner.

[willow merlin]

anal by taylor?

[foggy quest]

ye it's by M Taylor

[foggy quest]

The books by Evans, Folland, and Taylor are good. Taylor's has some differential geometric applications that are very relevant for physics. If you can understand it, it is very good, but as a beginner, the books by Evans and Folland are more readable.

[narrow relic]

Hey @slender cargo! No problem I'm always happy to talk about this stuff.
So, here's the reason: I have a very short fuse for these linear algebra books because I have wasted a lot of time on some of them (e.g. Lax 2nd edition). I didn't like the writing style of Axler right up front. Maybe I'm judging it too quickly.

I think there are issues with Lang and I wanted to switch to something else. I read a few pages of Axler, and also worked through the first few pages of this: https://pabloocal.github.io/web-documents/Teaching/SMATH115AL12023/Linear-Algebra_Paul-Balmer.pdf

I prefer Balmer's style so I'm going with that for now.

[slender cargo]

Fair enough reasons to me. My opinion is that it's not worth going through all that material again if you've gone far enough with it (i.e. with Lang). But if there are serious enough issues with Lang then that makes sense.

Axler's writing style is a bit loose imo

[narrow relic]

Well, I enjoy getting one solid presentation, I'm kind of obsessed with that 😄

[narrow relic]

Yeah. For someone who's never worked through this stuff before it's probably really interesting and fine. He has a great selection of topics in there, the best I've ever seen.

What section are you on now?

[slender cargo]

Section 3.4, isomorphisms and invertibility.

[narrow relic]

Super cool.

[slender cargo]

I took a first course in abstract algebra the term before so this stuff is familiar, but he writes in a way that appeals to someone who hasn't taken such a course yet.

So he defines an isomorphism as simply an invertible linear transformation.

Frankly that presentation would have been a bit confusing to me if I had not taken the algebra course beforehand, but I guess you don't need to fully understand what's going on with an isomorphism at that point.

(quotient spaces, the next chapter, should be easier for me to grasp as a result as well)

[narrow relic]

I see what you mean. Here's Balmer's version: https://a.uguu.se/iqbXBKMr.png

[slender cargo]

I think I would find this confusing also without prior knowledge

I think it's just a tricky topic to talk about without going into too much depth

[narrow relic]

Yeah.

Anyway glad you got back to me on this!

[slender cargo]

Yeah, thanks! It's fun for me also

I want to get up to ch. 9 on determinants before Fall starts, since I'll be taking a course on multivar analysis and differential forms will be presented. We'll see if I can make it.

[narrow relic]

Awesome I hope you can!

[fierce hedge]

These notes by M Taylor are now published as a book right, so is there any reason to study from the notes rather than the book?

[foggy quest]

The notes are the book; I checked, and the published book appears identical to the notes.

[fierce hedge]

Oh I see, usually books expand upon the notes. So, the only reason to use notes is cause it's free?

[foggy quest]

Yeah I guess.

[umbral herald]

Guys

Anyone has be smart plus grade 10 pls

I need to see 5 pages in it

Pls i really need it to study for my final

[golden salmon]

https://www.amazon.com.au/Workbook-Grade-Eran-I-Levin/dp/1495344371 there u go

Unless you're looking for the one by Saieh Hamadieh? That one isn't on Amazon afaik

[covert mauve]

I am looking for something interesting but short to read, any suggestions? any genre works

[broken meadow]

Young Goodman Brown

[wet sentinel]

are there books/resources that has exercises about finding the loci of variable points using complex numbers

so books that have sections about this or any sites/pdfs

[balmy crown]

Anyone got a discrete nath book theyd reccomend?

[bright epoch]

polya's extremal graph theory was quite good

[crystal trellis]

i am looking for a textbook that covers in-depth, but from the ground up, geodesics and related differential geometry. I have background in analysis, linear algebra, and some differential geometry by way of differential forms enough to prove generalized stokes theorem. thanks in advance

[shadow river]

@crystal trellis I like Spivak's writing style in general, so maybe his Differential Geometry volume 1?

I haven't read it so others may have more informed opinions on it

it's online so you can peruse and see if it appeals to what you're looking for

[foggy quest]

There is "Introduction to
Riemannian Manifolds" by J. Lee. There is also "Partial Differential
Equations I" by M. Taylor, where the treatment of the geometry is much briefer, but has lot's of applications to PDE theory.

[paper ferry]

How necessary is the "Linear Transformations" section in Ahlfors (complex analysis) for understanding conformal mappings?

[sage python]

Quite. They're an extremely important example

[crystal trellis]

@shadow river @foggy quest thank you both

[gray gazelle]

anything I should know before delving deep into d&f?

[gray gazelle]

Linear Algebra is helpful, but not necessary

[gray gazelle]

i see

also, is there anything analogous to a d&f but for analysis?

[tender river]

Bucknor thompson?

[nocturne blade]

Thanks!

[gray gazelle]

what is that

can't find it online

oh

bruckner thomson

[languid fossil]

hey does anyone know where I can find if a book has official translations

like an online library or something ?

for example I know that James stewart calculus book has a spanish and french version so I wanted to see if it has another one

for other books too

[willow merlin]

argentina version james stewart?

[deep moat]

Algebra books that're recommended?

[steel cloud]

There are two books on elementary topology a first course textbook in problems and elementary topology problems textbook

What is the difference between it ?

[sudden kindle]

Idk

I used that book to learn topology tho

[bright epoch]

I used Kroom's Principles of Topology and it was a great text

[bright epoch]

what kind of algebra

[steel cloud]

okay, thank you

[steel cloud]

okay

[bright epoch]

not a specific recommendation over other texts you mentioned that I haven't read ofc, just noting that elementary point set topology has a bunch of good texts and you shouldn't expect them to be all that different

[steel cloud]

Okay, thank you

[steel cloud]

Fred H. Croom ?

[bright epoch]

Ye

[versed coral]

any book recommendations for calculus? I am completing a pre-calc book now but i want to start searching for calc books from now.

[daring lake]

Stewart is a simple book (or Thomas or something like that, all are mostly the same)

[versed coral]

I am doing james stewart's pre calc book now

its great but very extensive ig

[daring lake]

Well, I guess that's kinda the exposition you need at the beginning

There will be many basic examples and 100s of problems after every 2 page but you can skip the easy ones

[gray gazelle]

I'm unsure what you mean by this, but I guess either Rudin (as in old-school standard) or something more encyclopedic like the Dieudonne series.

[gray gazelle]

perfect, thank you

[keen orbit]

what are some good youtube university level probability and statistics courses from the ground up which are suitable for engineers

[remote sparrow]

https://stat110.net

[keen orbit]

isnt this a book

oh wait nvm

tysm

[keen orbit]

does it contain statistics too?

[remote sparrow]

no

[keen orbit]

is there some resource for statistics too

videos if possible

[remote sparrow]

https://www.youtube.com/playlist?list=PLLyj1Zd4UWrPZH-fknPLak0tlUpUISBZR

https://www.youtube.com/playlist?list=PLAYxx7zX5F1PIvRju27s4CRAwhSGoxhVg

https://www.youtube.com/playlist?list=PL5LSj-W8URK2VkbA8HCeoyMLr2783GSZN

maybe these could help?

[keen orbit]

tysm

[willow merlin]

what about a course for real analysis, is it available

[remote sparrow]

#book-recommendations message

[willow merlin]

ty!

[remote sparrow]

#latex-testing

[crude sage]

Are there any efficient introductions to mathematical logic aimed at undergrads that cover Godel's Incompleteness theorems?

"Efficient" meaning "not covering much apart from prerequisites to said theorems"

[remote sparrow]

#book-recommendations message

[crude sage]

Thanks!

[crude sage]

Do you keep something like a directory of book recommendations for different subjects? You're always very prepared

[remote sparrow]

no

[crude sage]

All the more impressive I guess

[remote sparrow]

https://www.amazon.com/Mathematical-Analysis-Introduction-Bernd-Schröder/dp/0470107960

https://www.amazon.com/Big-Book-Real-Analysis-Measures/dp/303130831X

https://www.amazon.com/Mathematical-Analysis-Universitext-V-Zorich/dp/366248790X

https://www.amazon.com/Mathematical-Analysis-II-Universitext-Zorich/dp/3662489910

https://www.amazon.com/Analysis-I-Herbert-Amann/dp/3764371536

https://www.amazon.com/Analysis-II-Herbert-Amann/dp/3764374721

https://www.amazon.com/Analysis-III-Herbert-Amann/dp/3764374799

[trail hemlock]

no abbott?

[remote sparrow]

abbott is not like dummit and foote

it's not comprehensive like the other recommendations

[trail hemlock]

im abbott to eat some cookies

[remote sparrow]

what kind of cookies

[trail hemlock]

yummy ones

oh and wb tao? i find analysis I and II to be pretty comprehensive

[remote sparrow]

i don't see stokes' theorem in tao

[arctic crescent]

Book for function analysis and PDEs, they seem pretty interdependent at least PDEs on functional analysis. I have had intro to measure Theory.

[tepid cairn]

I think they're continuous

or smooth

idk

[remote sparrow]

granted johar's book doesn't cover stokes' theorem either

[arctic crescent]

I tried the Brezis but the pacing was at a bit fast for my level.

[remote sparrow]

maybe you'll like conway's book

[arctic crescent]

a first course in functional analysis?

[remote sparrow]

yeah

[arctic crescent]

I'll try

I have had measure theory but I am still noy comfortable using it's concepts on th fly.

I hope the pacing is a bit slow haha

[heady ember]

Schroder is sure to make you Stoked, then.

[willow merlin]

have you guys read A synopsis of elementary results in pure mathematics ?

[granite island]

Any good book for PDE?

[cobalt maple]

Hi, I am looking for a book that will cover the following: Ascoli's theorem, classical Banach spaces, distributions and distributional derivatives, and the ergodic theorem. Any suggestions?

[vagrant rose]

Any good physics book?

[gray jungle]

peter lax functional analysis

[gray gazelle]

better ask in physics discord server, you will find one there #old-network

[radiant oak]

any recommendations on game theory

[deep moat]

Number Theory?

[deep moat]

That's the one that Ramanujan read right?

[steel cloud]

What are opinions on Tao II ?

[native cradle]

Any books suggestions for writing proofs

[modern ruin]

good book

i have a copy of it on my shelf

[tribal crow]

Velleman’s How to Prove It and Hammack’s Book of Proof are the standard recommendations

however, I’m a believer that one can learn proofs along the way with something like linear algebra or real analysis, as opposed to using a dedicated proof writing book to do so

[modern ruin]

once again the mountain says something based

it really depends on how you learn

[steel cloud]

So what is its target ?

[modern ruin]

but if you feel like you need extra practice with proof writing the proof writing books are good

dami about to absolutely own me though

[modern ruin]

i can just share the table of contents with you if you want

have you read analysis I?

[sage python]

Yeah I do agree. I learned it mostly through Spivak

[modern ruin]

BASED

I learned through an introductory open-source abstract algebra textbook (which i have once again forgotten the name of)

[sage python]

I actually like the idea of doing a certain amount of algebra almost before anything else

[modern ruin]

yeah i feel like it was good for my development

as soon as I was done learning the stuff i needed for calculus I just learned some algebra

[tribal crow]

same here - Spivak and FIS ultimately taught me how to write proofs, not Velleman

[sage python]

Like imagine a discrete math class but with an algebra pov on the relevant topics if you feel me

[modern ruin]

yep

@steel cloud https://link.springer.com/book/10.1007/978-981-19-7284-3 this has information about Analysis II TOC

sorry to lnk to spr*nger

[sage python]

So when you study combo there's some chitchat about permutation groups, and when you do number theory you eg give Fermat little theorem as Lagrange, CRT using ideals, show people from the get go that fundamental theorem of arithmetic for both Z and k[t] boils down to ED=>PID=>UFD

[tribal crow]

why the censor on Springer

[modern ruin]

i hate springer

[tribal crow]

is there a specific reason why?

[modern ruin]

no, I'm a charicature of myself.

[sage python]

My instinct is that starting with the needed set theory, induction, defining Z and Q, doing number theory and baby combo using algebra as in the previous message, and then the story of ordered fields/suprema/R

Would be a very good first math major class

[modern ruin]

you could literally use Tao's analysis I as a book, it's literally designed for a class like that.

I love that book so much

except for the algebra part

on second thought, the class that you're dreaming of probably would need multiple references

[sage python]

Some people here recommended this German 3 volume analysis series which I recall as doing stuff like this

Ah it's Amann-Escher I think

[spice stag]

guys i want to study maths but im in a bit of a fix. I can solve the easy ques but i can't solve the tough ques and i don't have any medium ques . what should i do ?

[steel cloud]

Yes but I don't understand how I follow it, is it for good reference?

[steel cloud]

Little bit

[modern ruin]

depends on what you're working on

[modern ruin]

not sure what you mean? I learned analysis from those books, i thought it was fine. I think Tao is a good writer, and obviously you should supplement whatever book you're using by talking to people anyways, and this is a popular enough book that you won't get too much flak for using it

[steel cloud]

I mean people usually suggest Munkres , I don't see anyone who says read Tao II for better insight

[modern ruin]

today i learned that munkres wrote a book other than topology

[steel cloud]

Yes

[ripe prism]

Who's munkres

?

[modern ruin]

he wrote an introductory topology book, probably did some other things

[inner iris]

can anyone recommend me a math book which a highschooler must solve

[ripe prism]

Try solving any junior Olympic books

Did diogenes wrote any book?

[remote sparrow]

http://abstract.ups.edu/

[modern ruin]

yep

[lapis sky]

I used that one too in my first alg course

[tribal crow]

Munkres' Analysis on Manifolds?

that book covers very different topics from Tao II

the two are pretty disjoint

[sage python]

Munkres Analysis on Manifolds is something I've heard a lot of complaints about

[chrome wasp]

What about Edwards adv. calc. A differential form approach? Any opinion?

[sage python]

Idk that one

[tribal crow]

mhm, I've heard a good number of complaints via a select few members of this server alone

[sage python]

Also for a while the analysis class at my undergrad used it second quarter

[tribal crow]

interesting

[rough umbra]

Help me pick a topology book between Munkres, Croom, Morris, and Dugundji pls 🙏

[hot ivy]

Munkres!

[rough umbra]

Can I ask why 👀

[hot ivy]

Because I liked it.

[tribal crow]

I'm pretty sure @sage python has stated before that he dislikes Munkres

as for myself, I can't have an opinion cause I haven't read any of those books yet

[hot ivy]

Jokes aside, I found it beginner friendly with very solid exercises. Haven't read others you mentioned, but Munkres seemed better than what I've seen in other books I looked at.

[sage python]

Munkres is a bit of a yapper

But more crucially, a lot of the material and examples are kinda useless

[0,1]x[0,1] with the dictionary order is just a silly thing to think about

[hot ivy]

It's a great example I think

[sage python]

Really? Feels like it only exists to be a counterexample in point-set topology

[hot ivy]

Exactly!

[sage python]

Yeah idk to me point-set is a tool you engage with because you must, so better to actually engage with "spaces created by God" so to speak

Weak topology on Banach spaces form an actual example of things where lack of metrizability and first countability is something to care about

Contrived bs with ordinals or whatever? Nah

[gray jungle]

okay but fun

[sage python]

Are they fun? Lmao

[cloud hull]

anyone read 1984

[modern ruin]

LMAO

[gray jungle]

i remember ordinals being interesting at the very least

[modern ruin]

i have read part of 1984

[gray jungle]

in order top

[modern ruin]

i put it down for some reason, maybe that'll be on my reading list for the summer

[tribal crow]

I have yet to read 1984

I've read Brave New World though

good book

[sage python]

1984 was fun, I enjoyed it

[gray jungle]

people will have time to suffer with banach spaces in fun anal

[modern ruin]

DEAR algebraists. you CLAIM that there is something called the "zariski topology" but i claim that your entire branch of mathematics is ENTIRELY UNPLATONIC. CHECKMATE.

[gray jungle]

let them enjoy there order topology

[sage python]

You describe ordinals and order topology as fun

And then describe Banach spaces as suffering

[cloud hull]

hm whats the jist of it

[sage python]

This is also such a good term. I need to start describing math as unplatonic and as not created by God

[gray jungle]

technicalities and depth

[fresh skiff]

How is real analysis by carothers? any thought on it (ig its a famous book too but rare)

[gray jungle]

banach spaces still require good muscles to deal with

as opposed to just order topologies

so for a new topology student it makes sense

its in the spirit of general topology one might argue

[sage python]

The spirit of general topology is to exist only as long as is strictly necessary, and then stay out of sight

[gray jungle]

topology hater smh

[sage python]

I like actual (algebraic and differential) topology

[grim sage]

looking for a Differential equations I book any recommendations?

[hot ivy]

ODEs?

[grim sage]

not sure . Here's a quick description of the course "First order differential equations; linear differential equations of second and higher order; methods of undetermined coefficients and variation of parameters; Laplace transforms; power series solutions."

[remote sparrow]

boyce and diprima

#book-recommendations message

also more suggestions

[grim sage]

thank you so much

[gray jungle]

curious, what do you dislike about general topology?

[grim sage]

any tips on how to succeed?

[gray jungle]

a fair amount of people ik had a blast during learning point set

given most of them knew metric spaces beforehand

[sage python]

It's just dull. Every space with these adjectives has those adjectives

[gray jungle]

(which is also a blast)

[remote sparrow]

#foundations message

[sage python]

And to me I don't really give a shit about contrived examples

[remote sparrow]

point being, general topology has to cater to a very diverse audience

[sage python]

Manifolds are good

Function spaces are good

[remote sparrow]

manifolds and function spaces don't seem to appear much in logic

maybe in normal mathematics, but i'll stick with munkres because it's all-purpose

[sage python]

I found metric space topology from Rudin to be 😎

[gray jungle]

isnt that a good thing? it allows someone to go in many directions, someone interested in analysis will try to apply topology to function spaces as mentioned and study compactness, while someone going into geometry might focus more on connectedness etc

but i get that maybe classifying spaces as T1 , hausdorf, LC , 2nd countable etc can be dull on its own

[remote sparrow]

some people have a good idea of what they want to do and thus want more depth into relevant mathematical applications than breadth

[sage python]

I didn't even think Munkres was catered toward logicians, truly I thought the main reason he had his stupid examples instead of actual irl spaces that occur in math and for which you need to think about the topology (eg Zariski, Q_p, weak topology on Banach spaces) is because he can't assume background

[remote sparrow]

i'm not saying it's catered to logicians, but going in-depth on manifold theory seems weird for someone that wants to do logic

a broad intro is what munkres is

[sage python]

So he has to manufacture spaces so that he can show you that hey, there are technically things out there where you need to care about sequence vs net

[gray jungle]

is that really true for someone about to learn topology?

oh you said some

[sage python]

But I don't wanna say weak topology on L^p because you might not know analysis

[gray jungle]

sorry thought i read most

[remote sparrow]

#foundations message

#foundations message

[sage python]

I don't wanna use Zariski as a space which isn't Hausdorff or T_1 because students reading this might not know AG and I'm not gonna teach it to you

[gray jungle]

tbf i first needed pointset beyond metric spaces during a FA course, so its true that you can learn most of what you need during RA

[gray jungle]

yeah thats what i thought as well, given that he also spends a lot of time on just set theory lol

[sage python]

Yeah for point-set, basically unless you're doing hyper specialized stuff like logic, topological dynamics, maybe some operator algebra shenanigans

Then Lee Topological Manifolds, Bredon Topology and Geometry chapter 1, Hatcher's notes maybe, maybe the point-set chapter in analysis books like Folland and Bass

That will cover most of the general point-set that people need. Some will need more but what in particular you'll need depends on you at that point

Logicians might need Stone-Cech, number theorists want profinite spaces, blah blah blah

[gray jungle]

bredon felt a bit too fast for a first course, but i think some university in canada had great notes (ut i think?)

[sage python]

And that you can just pick up on the street

Most of my topology was Rudin for a long time, eventually I glanced through the appendix in Tu Intro to Manifolds which carried me for most of undergrad

Eventually I went through Bredon chapter 1 and soon after forgot most of the details that weren't in Tu anyway since I never had reason to think about the stuff ever again lol

[gray jungle]

if someone dislikes the idea of learning topology that much that they only want to do it for the sake of X then sure

but if you were to recommend a book to someone interested in learning more topology atm

i dont think many books compete with munkres in terms of presentation of general topology (minus some dragging)

at least from my point of view

[sage python]

I still prefer one with irl examples. Like truth be told I think stuff like [0,1]x[0,1] with dictionary order isn't just not my taste but a genuine waste of time

I heard there's Willard as well for the comprehensive approach which is more efficient? But idk it well

Generically I recommend Lee Topological Manifolds

[gray jungle]

its similar to taos analysis book, like sure the book spends a lot of time on building R, but that is one of the books that actually made me interested in math and analysis, its not optimal and munkres isnt either, but they are interesting books for a first course.

[gray jungle]

think i had a fine experience using it as a reference here and there, so id fuck with that

altho now i find myself going more towards kelly and dugundji

[sage python]

I mean does it include silly stuff or is it slow? Like if it just teaches you most of the set theory that you need to know and then talks about number systems and R that isn't too bad. If it's throwing frivolous stuff in there that's another story

[gray jungle]

it takes its time building towards R, but it does it naturally and builds the tools required along the way, all while showing how to reason mathematically and think logically, i think its the best book for someone wanting to get into proof based math on there own

being optimal at the cost of rushing things is ultimately a bad idea

hence why i wouldn't recommend say, rudin or hatchers notes

if you're in undergrad, take your time and digest things

in grad courses i definitely recommend more optimal approaches since you have the muscles to judge what you need to learn and what to ignore

hence why i recommend folland for actual real analysis ( measure theory )

just depends on the audience

and topology is a subject you should take your time digesting imo

given how useful it is

[sage python]

I thought Hatcher's notes were quite gentle

And I found Rudin not too bad for a class either lol

[gray jungle]

gentle, but it felt a bit rushed

[modern ruin]

i like that example

[gray jungle]

with a instructor i agree, its good

my pov was of self studying

[sage python]

It might not even be the worst for that but you should probably already know some proofs

Like after having done the first few chapters of Spivak Calc I started reading Rudin and it was difficult but kinda doable

[rough umbra]

Can I ask what you'd recommend? For someone who's experience so far is being 1 month into calc 3, so only topological space axioms, euclidean topology on R^n, compactness, heine-borel, connectedness, continuity, sequential characterization of compactness, continuous functions between R^n and R^m with the euclidean topology (where we are rn)

[rough umbra]

Is this ok for a beginner?

[rough umbra]

Oh nvm thank you

[rough umbra]

Oh Hrmm, so would you just recommend Munkres

[narrow relic]

There's a book I have read some of by Gamelin and Greene but not done any of the exercises yet so I can't vouch for it. You might want to check it out.

[rough umbra]

I enjoyed Croom’s book. It’s the only point set book I’ve found with the same comprehensiveness of Munkres. But, I found the material much more motivated and example driven. It was a good choice to start with a quick review of analysis and move to metric spaces then abstract those to general topological spaces. I found that much more comprehensible than diving straight into them and presenting metric spaces later.
Hrmmm

[rough umbra]

oh ty

[narrow relic]

The Croom book is good, I've read some of it, but it has some annoying "flaws." I remember his definition of a Hilbert space was dumbed-down (i.e. bad). It's also really pedantic on the metric space stuff, which is good for people who have never seen that material before, but if you've taken an analysis class that uses metric spaces, it came across as a waste of time.
I think it's good for people who 1) have never studied metric spaces ever and 2) don't mind having to re-learn some stuff later like what a Hilbert space really is.

[rough umbra]

A hilbert space is a complete IPS right

[narrow relic]

Since I've learned analysis using metric spaces, the Gamelin and Greene book is pretty good because although it reviews that material in Chapter 1 it doesn't spend a ton of time going over basic examples and extends things in some very useful and neat ways that connects to topology in Chapter 2.

[native cradle]

Thanks

[tribal crow]

do take a look at what I said just below that though!

[narrow relic]

Yeah, an inner product space is a Hilbert space if it's complete with respect to the norm (\vert\vert x \vert\vert = \langle x, x \rangle^{1/2}) (is my understanding)

[hasty eagle]

joesmith1042

[rough umbra]

👍

Also is Topology Without Tears good or just gimmicky

by morris

[narrow relic]

I don't know, I've only read some of Gamelin and Greene and not done any exercises, and Croom and not done any exercises.

[rough umbra]

Lee seems above my level maybe? It says beginning graduate, how true is that?

I just started 2nd year undergrad

[rough umbra]

Ik this stuff wrt topology

Lee looks like I'd need more maybe

[tribal crow]

Lee states the necessary prerequisites needed to read the book in his three appendices

do note that group theory is not needed until Chapter 5 or so though

[tribal crow]

he pretty much only assumes some basic set theory, metric spaces, and linear algebra

some group theory for Chapter 5 onwards

[foggy relic]

best is singer-thorpe chapters 1,2 lowk

like 20 pages minus the intiial set theory fluff

and hits everything

[sage python]

Ah I've heard of Singer Thorpe

[foggy relic]

the book is insane

only flaws are shitty typesetting/notation and no exercises

it gives you brainrot trying to actually read the proofs

only in ohio fr

[rough umbra]

@sage python If my goal were algebraic topology, is there a specific book you'd recommend considering that my general topology knowledge is still weak

[foggy relic]

first 2 chapters of singer thorpe

[rough umbra]

What does it cover past that?

[tribal crow]

perhaps try looking at this book review he made?

#book-recommendations message

[rough umbra]

Oh fantastic

[foggy relic]

algtop, manifolds, etc

de rham cohomology

covering spaces, fundmaental group, simplical complexes for algtop

[foggy relic]

just learn point set fast then read algtop

[rough umbra]

So im prolly overthinking and should just read Munkres right

To start

[foggy relic]

i just said first 2 chapters of singer thorpe

[rough umbra]

Ah wait I misunderstood, ok

Thanks

U answered it for my q abt algtop so i thought it was like in reference to that, my bad

[foggy relic]

i misunderstood your original question actually lol

i thoguht you were asking about a point-set book to read before algtop, not for a algtop book light on point-set

[rough umbra]

Daminable was talking abt how its better to engage with point set in the context of doing more specific topology on specific spaces if I didnt misunderstand so my question was like if there's anything like that for algtop if I havent done much point set yet, but point-set into a dedicate algtop book prolly makes more sense

[steel cloud]

No Topology

[dapper root]

There’s one thing you need to understand. That’s Dami or Daminark, and you need to call him Dummi instead

[hollow shore]

are there any modern alternatives to Rudin out there which is written in a more accessible manner?

[fierce hedge]

Apostol is the first thing that comes to my mind

[sage python]

Lee Intro to Topological Manifolds might be worth a look

[violet sapphire]

What is the best book for me to get better at math?

A book that teaches very math

Every**

[tribal crow]

there is no such book

you'll have to be much more specific about what math you want to learn

with the provided information so far, there is no book anyone can recommend to help you learn "all of math"

[magic spade]

Cummings, Abbott, Tao, Ross, Pugh, Bartle are all considerations which cover different topics with varying levels of accessibility

[violet sapphire]

thanks

[willow merlin]

is there any euclidian geometry book you guys recommend?

[willow merlin]

abbott is real nice, I saw at the beginning that bartle was one of the inspirations, maybe I am mistaken

[remote sparrow]

it is

[remote sparrow]

kiselev

https://www.amazon.com/Classical-Geometry-Euclidean-Transformational-Projective/dp/1118679199

good to do after kiselev or if you already have prior knowledge of euclidean geometry

[willow merlin]

okay, will take a look at them ||either today or tomorrow||, thanks

[maiden glen]

How is Howard E. Campbell's "the structure of arithmetic"?

[spice stag]

highschool level math

[modern ruin]

okay that tells me nothing though

[spice stag]

💀

what more should i add ?

i am studying calculus , algebra , vectors and combinatorics

and coordinate geometry too

[steel cloud]

What about real analysis by Jay Cummings?

[foggy quest]

I like the one variable analysis book from here: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/.

[hollow shore]

Abbott is a better choice imo

[hollow shore]

thanks

ig ill just stick to Rudin itself. Was looking for smth to complement Abbott.

more like reference

[remote sparrow]

bartle and schroeder are good choices

[hollow shore]

hmm

are these more comprehensive?

[remote sparrow]

schroeder is

[hollow shore]

okay I will have a look

[remote sparrow]

https://www.amazon.com/Mathematical-Analysis-Introduction-Bernd-Schröder/dp/0470107960

[hollow shore]

does it cover Metric Spaces by any chance?

[remote sparrow]

yes

[hollow shore]

ah sweet

[remote sparrow]

i have other suggestions for metric spaces too

#book-recommendations message

[hollow shore]

I am all ears

[steel cloud]

I am looking for a second course

[fading mortar]

have you guys heard about Elementary Algebra for Schools?

its a really good practice book till algebra 1

[hollow shore]

I have heard that Amann Escher is good

[fading mortar]

has around 6k questions which will act as a good refresher if u have done high school

[hollow shore]

other recs are Carothers, Pugh, Zorich, etc

grab the PDFs and see which one you click with

[fading mortar]

what ttype Of book is that?

like regarding what topic?

[hollow shore]

Real Analysis

[remote sparrow]

carothers

[chrome wasp]

What do you mean by second course?

[remote sparrow]

maybe do problems from rudin

[fresh skiff]

I am thinking to read a bit of the Carothers book!
(Rn i am on 4th chapter of Abbott)

[remote sparrow]

after that you can read some elementary measure theory books

[hollow shore]

Topology in R

[fresh skiff]

Do you mean after Abbott?

[remote sparrow]

i was talking to Notknow

[hollow shore]

that chapter started with the Cantor Set 💀

[fresh skiff]

I am sorry, my bad.

[fresh skiff]

Are you talking about Abbott?

[hollow shore]

yes

[fresh skiff]

Yes that's interesting. However hard to grip, that's why I skipped all problems which were on cantor's set

[hollow shore]

I plan to resume from that chapter itself

[fresh skiff]

Lol

[steel cloud]

I covered Bartle and Sherbet

[steel cloud]

Yeah I think so but I don't why I am afraid of rudin

[remote sparrow]

rudin has the reputation it does because it's usually an honors student's first ever intro to proofs

it's not unreasonable after going through a book like abbott

[chrome wasp]

Well for start book Sour drop recommended seems good, anyway part one chpt3-9 is same in most books while you do those you might change to something else

[steel cloud]

Sorry, I don't understand

[steel cloud]

So which should I do rudin or Abbott?

[chrome wasp]

Did you finish bartle?

[steel cloud]

Yes

[remote sparrow]

rudin

or you could one of the metric spaces books i mentioned

[chrome wasp]

Does it cover differentiation in R^n

Bartle

[remote sparrow]

i don't think so

[chrome wasp]

Or just on real line

[remote sparrow]

just real line

[steel cloud]

Carothers ?

[steel cloud]

No

[chrome wasp]

Then for start i would suggest Carothers just for Part One

[remote sparrow]

actually there's one chapter on metric spaces and a bit of coverage of topology on the real line but it's late in the book and it's pretty sparse

[remote sparrow]

that's a good choice

[steel cloud]

Its covers metric space

[steel cloud]

Do you have a good quality pdf of it?

[remote sparrow]

i do

you can also find it yourself

[steel cloud]

I found but not good quality

[remote sparrow]

you can preview or download many files, then delete the ones you don't like

[steel cloud]

And should I do the first chapter of rudin?

[remote sparrow]

why only that chapter specifically?

[steel cloud]

I don't know why my annas archive not working

[remote sparrow]

i would skip anything after chapter 8 of rudin though

8 is mostly optional; i don't see special functions come up that much besides the gamma function

[steel cloud]

Because I don't like again and again similar stuff with tricky question

[remote sparrow]

there are solutions manuals online

if you don't like rudin then don't read it

[chrome wasp]

After metric and topological spaces i would recommend some book with differentiation on R^n followed by measure and integration

[steel cloud]

No I didn't mean that

[steel cloud]

Okay, thank you

[remote sparrow]

are you saying there's repeated material in chapter 1 of rudin?

i mean, i guess it's fair that you don't want to do some of that stuff again

[steel cloud]

No actually I read that chapter 2-3 times but when I go for it again I forget how they solve that excercise

[chrome wasp]

I doubt bartle covers it as detailed as Carothers

[remote sparrow]

that's fine

[steel cloud]

Okay, thank you

[remote sparrow]

the cantor set is a pretty important example; you should come to grips with it some time

[chrome wasp]

@steel cloud i havent used this but seems good for what you need
W.Fleming Functions of Several Variables

[gilded olive]

im taking an abstract algebra course that follows d&f next fall. To prepare for that, I want to do some readings beforehand. should i start reading d&f or would it be better if i read gallian first, or any other introductory book? or would it be more efficient to read d&f and skim over gallian after finishing a chapter in d&f?

(do tell me if this question is better suited for the discussions channel and i can move it there)

for context, i took a LA course last semester and that's pretty much all algebra I know

[steel cloud]

I first learnt from Gallain then I moved to Herstein alongwith Dummit and foote

[steel cloud]

Do you have a pdf of it?

[gray gazelle]

https://archive.org/details/takingminutesofm0000gutm_04th/page/200/mode/2up?view=theater&ui=embed&wrapper=false

I need this books pdf

Can I get it pls?

[remote sparrow]

#book-recommendations message

i'd say pinter and judson are great for pre-studying all the concepts in d&f

[gray gazelle]

@remote sparrow can I get taking minutes of meetings books pdf

Or the book where I can read it from

[remote sparrow]

?

taking minutes of meetings?

[gray gazelle]

Yes

[gray gazelle]

If u help me that would be great

[remote sparrow]

enter the search terms "shadow library" in wikipedia

[gray gazelle]

Can u do it for me ,I'm doing another project rn please it would be very helpful

@remote sparrow wtf

what is in there

I'm getting Nazi germany

Anyone having Amazon Kindle premium?

[rough umbra]

thoughts on aluffi's algebra chapter 0?

[spice stag]

is there a roadmap so that i can get to a point that i can solve olmpiad level ques ?

[fading mortar]

not a book but still pretty useful material

https://youtube.com/playlist?list=PLgIi4lM74yW0ChmzTdT1w5ruCnqP0bv3J&si=7XAPIsnLiPE3GxjK

[cobalt maple]

Book recommendations for a grad student wanting to revisit geometry of curves and surfaces after forgetting most of it? I am also currently reading Lee's smooth manifolds

[remote sparrow]

do carmo, o'neill, and tapp are some options

dineen is a really unorthodox book i was assigned

[gray jungle]

@sage python might know

[bright epoch]

you don't need a lot of topology, and there's an appendix with the stuff you might need if you want to look them up

[foggy quest]

You need to know basic things about metric spaces, but for other parts of topology you can learn them as you read.

[foggy quest]

Books http://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/analmv.pdf and books here: https://mtaylor.web.unc.edu/notes/differential-geometry-riemann-surfaces-cr-manifolds-index-theory/ should be good. They are sometimes omitting technical details, but you have Lee's books on smooth manifolds and Riemannian manifolds for those.

[broken pecan]

what is the standard textbook on graduate level game theory? Im reading Essentials of Game Theory- A Concise Multidisciplinary by Kevin Leyton-Brown, Yoav Shoham. But it's very tease

[gray gazelle]

What are your guys thoughts on Polya's how to solve it?

[bright epoch]

I am a big fan but my understanding is that this is an unpopular opinion

[lusty escarp]

I am thinking of purchasing, Lee introduction to smooth manifolds. I have a question, has the errata corrections made it to the book or not? Or I have to follow his list of errata with the book?

[tribal crow]

The corrections have not yet been made

you will have to follow the errata

[lusty escarp]

Atleast, he maintains it though.

[oblique dove]

dm if ur interested in joining an algebraic topology reading group
book: springer algebraic topology by bray, rubinstein-salzedo, butscher

[gray jungle]

@oblique dove can you send me details of the plan? starting time, presentations, commitment etc

really need to properly learn homology, rushed it last time

https://tenor.com/view/dono-wall-talking-wall-bricks-gif-17741481

[lusty escarp]

Is there someone running a Measure theory group also?

[gray jungle]

we are planning one in 1 to 2 months

[junior isle]

Prereqs?

[lusty escarp]

With @vital bane ?

[lusty escarp]

Prereqs is generally a first course in real analysis.

[gray jungle]

set theory and real analysis (especially convergence of sequences of functions ), knowing reimann integration basics helps but isnt necessary

[lusty escarp]

Which book do you plan to use?

[gray jungle]

the plan is most likely folland

chapter 1

parts of 2 and 3

then ch6 7

[gray jungle]

if he finishes abott

[lusty escarp]

I have just started chapter 5 of Abbott.

[gray jungle]

idk which chapter is sequence of functions, but thats the most important imo

[lusty escarp]

Ch-6

[remote sparrow]

you should consider axler too

[gray jungle]

might use it as a reference too, since outside also vouches for it

[oblique dove]

nah none of that is confirmed yet haha just seeing if there's interest

right now its just me and one other person

and according to everyone's schedules id like to make a schedule and commitment plan

[gray jungle]

i do recommend weekly meetings with presentations, it makes these groups survive if everyone commits

[oblique dove]

Yes, like problem presentations rgiht

[gray jungle]

more like topic presentation, but thats interesting too

[scarlet snow]

does someone know of some cheap book that explains calculus from 0 and goes into integral calculus?

[oblique dove]

openstax calc volume 1 and 2 is free online

if you want a hard copy go to ebay and you may find smth like this: https://www.ebay.com/itm/256105675793?epid=92969631&itmmeta=01HZT1373QS1YG6DS6K5S5C7R5&itmprp=enc%3AAQAJAAAA4AE%2F7OlKdD%2F3rtwgfj%2F6nySApo9R27JMSj7DlTrcdVdSWRDYhjtUKx61yBkaTp32KYEXd49--5ffZ%2BZ50m%2BFTrCDd68otXfkEGgFSqR31C5H3jgnexk0Jr8OrQd0w7TmJFIDmpxR5YHqu8J3oRABE4hrfA48yUGVoSMYgacz%2FGSpegov1TnM85U9LcUXiQx4gKu0GPJI22Exiga0KVbMtoyt0S5ucmho24HYNuoRpsohHV%2FAP%2BEIqui%2FMY41qa1F%2BAt%2FwB6OTRDID%2Bmye4pK9YoDyTPVO5LOvWzNwhQ%2BkHdq|tkp%3ABk9SR_rxjMH-Yw

[scarlet snow]

thank you very much

[junior isle]

nooooo thats ch 7 of rudin, im in ch 3

unlikely that i'll get there in time

[gray jungle]

well if you want to

you could do ch4 then jump to 6 and 7

dont think differentiation is a big requirment to do MT

and 2 months is kinda a lot of time

even at moderate pace

[junior isle]

if it is 2 months then i'll have read rudin

im doing 1ch-2weeks

how long will that last?

[gray jungle]

depends on you, if you are grinding you should be done with ch7 by then

[junior isle]

i mean the MT course

[gray jungle]

or you can spend 4 years of your life doing abott like a certain idividual thats definitely not in this server

[gray jungle]

ah, let me check how long ours took

ours went from 18/2/2023 till 24/4/2023

we covered quite a bit of folland

basically all i mentioned earlier + ch5 + some topological groups and haar measure

we had one week where we just spent 1 hour 30 mins on reisz representation proof

so it can be faster

but thats a rough timing

[junior isle]

yeah by then my semester will be just starting so idk how much time i'll have

[gray jungle]

its fine to drop near the end tbh

thats what always happens, half the group disappears

[junior isle]

you're gonna create a server or channel here?

[junior isle]

ikr

[gray jungle]

will probably use a old server

[remote vortex]

If it's just half, then it's a very good result

[sturdy shore]

you'd kill for guaranteed half in these situations

[sly torrent]

Any recommendation for university sophomore-level calculus book?
A long time ago I aced through limits, derivatives and such but then completely failed integrals and diffeqs. So I want to get back to speed, mostly on my own

Not necessarily a book, but some resource

[dapper inlet]

good number theory books?

[oblique dove]

kenneth rosen number theory and apps is good

[remote sparrow]

#book-recommendations message

[remote sparrow]

#book-recommendations message

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

[past tiger]

i am self studying QM and the problems in griffiths book is not a lot and that doesn't make me good at QM, so does any one know any resource that has a lot of QM problems that i can solve?

[remote sparrow]

shankar or townsend

https://www.amazon.com/Mastering-Quantum-Mechanics-Essentials-Applications/dp/026204613X

i heard this is good too from the reviews

many people enjoyed his lectures on mit ocw

[robust geyser]

when someone gives you a list of 6-7 books, are you usually supposed to read all of them, skim the first bit and pick one, or what?

and what about like 2-3 books?

[devout fossil]

any opinions on stoker's differential geometry? (tried reading carmo and barrett but didnt like how they read for some reason)

[remote sparrow]

depends

[robust geyser]

ok let’s say I’m getting to know elementary number theory and I have read burton. Which of the rest of your list should I read/skim/do chapters of?

[remote sparrow]

niven, but also, like, you could move on and do something else?

[robust geyser]

ok so do you recommend moving on or reading niven or either?

[remote sparrow]

your choice

if you complete one book and feel ready to move on, do so

i will say usually people in college courses move on after reading one book, but the beauty of self-study is that that decision is determined entirely by you

[fresh skiff]

I am on chapter 4 of Abbott and it's ch6 (sequence of functions). But two months is a reasonable amount of time.

[glossy zealot]

Gonna be a reading group where everyone is meeting at 3am again

[maiden glen]

I want to learn about systems, such as those that are systems of elementary sets of numbers, i.e. the system of the set of naturals is: $(N, +, \times, 1)$ where i assume the binary operations addition and multiplication are those of which a subset of the set of naturals is closed under, and 1 is the initial element (regarding set of whole numbers) and also i assume to be a number when added to an existing element; yields a successor of the element 1 is involved in a sum with. How do i learn more about systems?

[hasty eagle]

𝓫𝓮𝓬𝓸𝓶𝓲𝓷𝓰

[maiden glen]

where N is the set of naturals

[remote sparrow]

you want to learn about number systems?

[maiden glen]

if that is what they are called, yes

[remote sparrow]

#book-recommendations message

[junior isle]

Also abstract algebra generalizes the notion of number system, so it's worth checking out

[maiden glen]

they're too expensive and i cant find any "yarr harr mateys".

any other suggestions?

[remote sparrow]

mendelson is too expensive?

[maiden glen]

on amazon

[remote sparrow]

?

it's a dover

[maiden glen]

nevermind

[remote sparrow]

https://www.amazon.com/Number-Systems-Foundations-Analysis-Mathematics/dp/0486457923

[maiden glen]

found a yarr harr matey

thank you

[junior isle]

Whats a yarr harr matey

[maiden glen]

pirate

[junior isle]

I have a google drive of yarr harr mateys

[maiden glen]

sometimes a yarr harr matey is a good one

other times.. not really

[remote sparrow]

i found all of them easily

unrelatedly, have you read wikipedia's article about shadow libraries?

[maiden glen]

please give

the ones i foudn were fake

they said harr harr

and not yarr harr

[remote sparrow]

sorry, i can't tell you about it directly here, but i'm happy to discuss this wikipedia article with you: https://en.wikipedia.org/wiki/Shadow_library

[maiden glen]

yes

[remote sparrow]

perhaps you misspelled some of your queries?

[maiden glen]

dm please i need it

[remote sparrow]

or added extra search terms?

[maiden glen]

no.

[junior isle]

I can usually find them by appending the word pdf to name in google

[maiden glen]

which is what i've been doinggg..

i looked through pages

[remote sparrow]

i don't find this very reliable

[maiden glen]

i couldnt find one

[maiden glen]

what is your method

🫗

[junior isle]

Always worked for me

Also important to check files in virustotal

tho it's hard to imagine somebody would contaminate a math book

[remote sparrow]

depends on how popular the book is

[junior isle]

fair

[remote sparrow]

these places run off of user trust

if they lose reputability, then people won't go there

[remote sparrow]

i can only give general advice about refining search queries in less powerful search engines, such as that of your university's library

[maiden glen]

i'm self tutoring

[knotty jewel]

Hi! Excuse me guys, but what proof based books for multivariable calculus do you guys recommend me?

[remote sparrow]

a long time ago, search engines were not as robust as google

[maiden glen]

uhhhhhhhhhhhhhhhhhhh give me your methoddd

[junior isle]

Thats a good question

[remote sparrow]

hubbard or shifrin

[junior isle]

Is there a multivariable followup of rudin?

[remote sparrow]

don't buy hubbard from amazon, it's marked up way more than if you bought it from the publisher

https://www.matrixeditions.com/

[knotty jewel]

Ok, thanks you so much!

[maiden glen]

perchance, may you read your dm

[remote sparrow]

you want a book written like rudin but for multivariable content?

[junior isle]

No, baby rudin as background

[remote sparrow]

you could read Calculus on Manifolds by spivak or Analysis on Manifolds by munkres

[junior isle]

What's the difference between them?

[remote sparrow]

spivak is very concise, munkres elaborates a bit more

spivak has a lot of errata and generally his exercises are considered more challenging

[junior isle]

Ah so spivak is like rudin

[remote sparrow]

i guess

[gray gazelle]

Book for functional equations, something heavily theoretical and concise would be nice

[agile quail]

Oh

[foggy quest]

https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/ is good.

[shadow river]

Multivariable Mathematics by Theodore Shiffrin is good

and the entire course's lectures (taught by the author) is on Youtube

[boreal widget]

what do you guys think about art of problem solvings books

[jade anchor]

Not sure if anyone ever responded to you here, but I quite love it! I am working through it right now after a course in category theory. I'll say having exposure to set theory, logic, and maybe even some prior exposure to category theory and its way of thinking is great. I wouldn't personally pick it up to start my algebraic studies with from scratch -- it's somewhere in the middle I'd say of not quite being right for beginners but would be perfect someone who has some ideas about what a category is, what a group is, and have a solid foundation in understanding equivalence relations. So, I'd call it beginner-ish but still relatively accessible if that is your first exposure to algebra. You might just have to work a fair bit extra hard at the beginning but then it should start flowing. Not sure if these thoughts are helpful but just wanted to share! 😄

[rough umbra]

Tyty

[remote sparrow]

aluffi has also written an algebra book aimed at undergraduates, Algebra: Notes from the Underground

[gray gazelle]

Yo anyone know where I can find a good copy of Polya's how to solve it? I can't find a copy that has good quality

[balmy crown]

Anyone know of any good discrete math books theyd reccomend?

[strange sentinel]

I can DM you one that seems fine

[strange sentinel]

I've heard good things about Discrete Math with Ducks

[analog lantern]

is there any website from where i can download any pdf... actually a website for nerds with all books.... for free...
like i am really in a need so suggest the best one please......???

[tribal crow]

there are several, but we are not permitted to discuss piracy on this server

google "shadow library"

[analog lantern]

ook so where then??

[analog lantern]

ook thanks....

[stray veldt]

plenty of math books at least are also available on university websites

just google the name and "pdf"

[grizzled swan]

<book name> filetype:pdf on the search

[analog lantern]

can anyone recommend me the best book for QUANTUM PHYSICS while i have been reading, one of the best... - The Feynman Lectures on Quantum Physics...

[gray gazelle]

Are you a Physics major?

[analog lantern]

yepp

@gray gazelle umm... yes so do you have any recommendation..??

[gray gazelle]

Oh, no, I have no idea. I was just curious. 😂

[analog lantern]

ook.... not a problem👀

[gray gazelle]

You'll probably have a better luck getting an answer to this in the Physics server which is mentioned in #old-network.

[analog lantern]

ook.... ig

[wispy bison]

have you tried griffiths’ book

[abstract copper]

There are many good QM books but Griffith's is not it

Shankar, Sakurai are good choices (or so I've heard)

I used Griffith's and do not recommend it

[analog lantern]

yeah...... thanks btw... i was currently studying sakurai's book.... so it's great actually....

[analog lantern]

i did... it's good as it has all the values already given in the preface..... not for me.. but for beginners it's good when it's about formula... while let it be its good.. thanks..

[bright epoch]

Sakurai is very good if your linear algebra is strong

[severe gust]

Hey guys, I need great recommendations for pre-calculus. Does anyone have one?

[severe gust]

Discrete mathematics with applications by Susanna S. Epp., this is one of the books that is pretty easy to understand.

[gray gazelle]

are you self-studying or following a course?

[severe gust]

Self studying

[gray gazelle]

Stewart

Does Bredon’s alg top book expect background in point-set topology beyond what is covered in an RA course?

[strange sentinel]

Bredon chapter 1, as so many people say, covers all of the pointset topology most people will ever need

[unborn jackal]

why do people worship gil strang so much? the book (lin alg) is so non rigorous

[bright epoch]

Some people like non rigorous books

[unborn jackal]

it just throws in some random concepts without explaining them

[tribal crow]

as a first introduction to linear algebra, it isn't bad

[unborn jackal]

its like highschool math class

[unborn jackal]

ig

[bright epoch]

I also don't like it tbh, but I think it's just like straightforward and not too dense and goes through the big stuff

So it has broad appeal, because LA is taken by way more people than just mathematicians

[paper tangle]

What books of linear algebra does one like

[bright epoch]

Axler

I'm a big axler stan

[tribal crow]

[bright epoch]

Apologies to the haters

[paper tangle]

It's the standard i guess

[tribal crow]

I like FIS myself

[paper tangle]

Friedberg?

Wait

[tribal crow]

everyone either loves or hates Axler

[paper tangle]

I misspelt

[tribal crow]

I'm not a huge fan myself

[unborn jackal]

i like h&k and i wanted to read the det chapter somewhere else to make sure that i understood everything

[paper tangle]

Isn't dummit and Foote a good linear algebra book 💀

[tribal crow]

HK is good

[paper tangle]

Whats HK

[unborn jackal]

hoffman kunze

[bright epoch]

This is my experience as well

[paper tangle]

Uhh it was used in my coursework

It's decent

[unborn jackal]

its great

[tribal crow]

I feel like it must be a near 50/50 split out of all the people I've asked on this server

[paper tangle]

I prefer abstract algebra books to linear algebra books like i think artin is above everyone

But that's just me

[unborn jackal]

you mean abstract alg?

[paper tangle]

Yeah isn't most linear algebra actually abstract algebra and like if you learn the generalisations then it follows (I guess not)

[unborn jackal]

havent studied it yet

idk

probably if you say so

its used in the definitions of stuff in lin alg

[paper tangle]

Whats you guys opinion on this book
https://books.google.co.in/books/about/Representation_Theory.html?id=vCbHBgAAQBAJ&redir_esc=y

For rep theory

Intro

[bright epoch]

Imo rep theory books really depend on what you're using rep theory for

Like Fulton and Harris was a great text but I'm doing Lie Theory, if you're not then it would be pretty bad

[slender cargo]

I'm going through Axler right now and I like it. If you want more matrix computations then look elsewhere.

[modern ruin]

for what it’s worth i dislike strangs course on it for this reason

not to say that it’s devoid of content, the presentation of it just stresses me out

[tribal crow]

the presentation stresses you out?

how so?

I've not read Strang myself

[slender cargo]

My understanding is that linear algebra follows from module theory, which is covered in abstract algebra. I haven't gotten that far yet though

I think whatever books help you gain intuition is more important than prioritizing a book based on how general the definitions are. That's my (relatively uneducated) hot take. If that's Artin then go with Artin.

I will say that having taken a first course in abstract algebra is helping me with reading Axler, particularly with stuff like quotient spaces.

[maiden glen]

good real analysis books?

[tribal crow]

Abbott, Spivak, Schroder, Tao, Bartle & Sherbert, Apsotol, Rudin...

there's a lot

[maiden glen]

i see.

[maiden glen]

also by tao do you mean terrence tao?

[tribal crow]

correct

though it's Terence, not Terrence

[slender cargo]

Do you know calculus?

[slender cargo]

After going through Bartle's book I now hold Spivak in very high regard. I think it's really well written.

I guess you should use a different book if you know calculus already... but I think you could still make an argument for Spivak.

[maiden glen]

i'm going to use all of them

[slender cargo]

What? lol. No you're not

Just choose one and stick to it

Look at others if you get confused and need another reference.

[tribal crow]

do NOT use all of them!

I was throwing out several books you could choose from!

[slender cargo]

I think for self studying Spivak's Calculus is a great choice. Just choose that one. It has a full answer book and it's been tested by many universities.

[tribal crow]

not telling you to use all

[maiden glen]

I

am going to look through all of them

for reference

and refined understanding

[slender cargo]

Is this for purely self-studying?

[maiden glen]

is his called: "An epsilon of room real analysis"?

[maiden glen]

yes

[slender cargo]

Just choose Spivak's Calculus. That's my very biased take.

[tribal crow]

I meant Tao's Analysis I

[maiden glen]

im sure you know my answer to that bias

[maiden glen]

I see, i downloaded II aswell

[tribal crow]

but I'll let TopDreg shill Spivak

I used Spivak personally

[slender cargo]

(for the love of god don't use Rudin)

[tribal crow]

it's a good book

[maiden glen]

I have rudin too

[slender cargo]

Rudin is a nice reference but I think it would be horrible for self study by itself

All of those books cover the same material at their core. Just some deal with the material in more generality than others

[maiden glen]

reference and refined understanding

[slender cargo]

That's what the problems are for

Just pick a book and start reading.

[maiden glen]

multiple books have multiple problems

[slender cargo]

Perhaps there should be a pin that says "just pick a book and start reading."

[maiden glen]

you may as well have suggested libretexts.org

additionally,

for instance

reading sarge lang's "basic mathematics" and just going only with that restricted scope of foundational algebra, geometry, linear algbera is too little

only reading that book

[slender cargo]

All of the books share similar problems.

You would have vastly diminishing returns doing all of the problems from multiple books.

Doing all of the problems in simply one book is not necessarily a great idea.

[maiden glen]

have you read all of them?

[slender cargo]

His book is more than adequate to get you up to speed for dedicated books on those subjects.

[slender cargo]

I have referenced several of them while studying.

[slender cargo]

Hardly anyone has read all of them, because that's a waste of time.

Once you go through Basic Mathematics, you then pick more advanced books.

[maiden glen]

hm

ok

[slender cargo]

So I take it that you have not gone through calculus?

You just finished Lang's Basic Mathematics?

If the answer is yes, that makes things easy then. Spivak's Calculus is more appropriate than all those other books. Apostol's Calculus is another appropriate choice that some people prefer.

[remote sparrow]

no, think that's measure theory

[maiden glen]

no, i was using it as an example

[maiden glen]

I requested "real analysis" and he suggested a book by the author terence tao, I figured because since that was the only result i had found that was relevant to my query, it was the correct book

i am not familiar with measure theory yet.

[remote sparrow]

he meant Analysis I and Analysis II

[slender cargo]

Just pick the friendliest book for self-study and start reading it. Not every book is good for self-study, imo.

[maiden glen]

I think I have eyes aswell, i would be actively searching for a response if i had come to the conclusion that my original assumption of what he meant was wrong prior to his message.

[maiden glen]

yes, thank you.

[slender cargo]

No need to be a jerk. He was just trying to help.

[tribal crow]

#book-recommendations message

[maiden glen]

I am humbled, thank you all for your hospitality and help and spending your valuable time for helping me.

[maiden glen]

again, i saw that; but again, thank you as i am sincerely appreciative for your help.

[tender river]

ure welcome

[slender cargo]

Now I will get back to fawning over Spivak's Calculus. What a great book.

And it's beautiful.

(sequences being reserved for ch. 24 is an odd choice but that's probably okay)

[sage python]

Yeah it's still doing things in the order of a typical calculus class unfortunately

[sudden kindle]

Nothing like piece of dark chocolate after a flavorful meal

Oops wrong channel

[tribal crow]

I was about to say lol

[sage python]

We don't yet have #bad-takes so idek if there is a correct channel

But also yeah let's not continue this in here

[left pasture]

does anyone know good physics book for university

Sears Semansky
Serway Vuille
Resnick Halliday

that isn't one of those 3

[slender cargo]

Yeah, if a class uses that book for introductory real analysis then it will probably have to spend extra time on that chapter. My impression though is that the book overall is very well written. just imo.

[sage python]

Yeah my calculus class first year of undergrad used it

It's pretty well written but the kinda book that, you like in the moment but then after a while you think back to some of the decisions he makes and you're like what

[slender cargo]

Perhaps I'll have a different perspective after I take more courses. It'll be fun to look back

[trail hemlock]

morin and Griffiths? my physics ug friend always talks abt those.

[willow merlin]

hi, which elementary nt books are well regarded?

[remote sparrow]

#book-recommendations message

[undone pine]

Question about GR and differential geometry.

So I’ve taken a course on differential geometry and I learned about curves, surfaces, tangent spaces, and first fundamental form. Basically first few chapters of pressely’s elementary differential geometry.

For the purpose of GR and natural curiosity, what should I learn next, and what book(s) would you recommend?

I really want to try and understand the math used in GR on a deeper level.

[remote sparrow]

what other math are you familiar with?

[undone pine]

Linear algebra, DEs, ODEs, PDEs( took a mathematical methods course which covered heat equation wave equation, Fourier series, etc), complex analysis, and real analysis ( in bartle, I’ve studied upto but not including the chapter of integration)

[remote sparrow]

you could consider reading either tu's An Introduction to Manifolds or lee's Introduction to Topological Manifolds. you should cover some abstract algebra at some point, possibly concurrently, then read tu's Differential Geometry: Connections, Curvature, and Characteristic Classes

[undone pine]

Yeah I know I need to cover abstract algebra. Any recommendations for that?

I’ll look into the geometry books you’ve told me.

[remote sparrow]

#book-recommendations message

feel free to look through dummit and foote as well

[undone pine]

Thanks

[pliant wadi]

Sort of late but yea thanks for the heads up

[trail hemlock]

currently reading little jech and i wanna read big jech. im looking to learn logic as a prereq and idk how to learn it

basically im very lost

how to learn logic?

[torn crypt]

Just read it

[trail hemlock]

everyone ive ever asked said you need logic

but

since i trust sharp w/ my life

i will

,iamnot dying

[hasty eagle]

Removed the studying! role from you.

[remote sparrow]

#book-recommendations message

also feel free to check out https://logicmatters.net

[trail hemlock]

this feels wrong, but i want to learn the bare minimum as a prereq. i will check the website and those books out, tysm!

[torn crypt]

Jech should cover most of the required logic stuff

[trail hemlock]

yes ty 🫶

[violet shuttle]

look at lees riemannian geometry for the metric and riemann curvature and then use it as a reference if necessary whilst readinf a bkok on Gr

[trail hemlock]

,iamnot dying

[hasty eagle]

Removed the studying! role from you.

[gray gazelle]

hi! I want to do mathematics from beginner to pro for data science and ai ml could someone recommand the roadmap

i used to be good in mathematics but lost the touch to it so if anyone could give me a roadmap it would be really helpful

[gray gazelle]

check #advanced-lounge

[exotic belfry]

what channel is that

if says No Access

[gray gazelle]

that's its description for your concern

Discussion should primarily be about academic life of a mathematician, including (under)graduate students of mathematics and above; this includes relevant mathematics as well as navigating university bureaucracy. (Note that content regarding graduate applications does not belong in this channel, see ⁠graduate-applications)
Think of this channel as a discussion with your advisor and professors, fellow students of mathematics, or colleagues in academia. Do not post content that you would not want your professors/advisor to see.```

I guess when you have undergrad role