book-recommendations

[restive falcon]

This summer
Starring Charles Chapman Pugh

[hollow peak]

I wouldn't call real analysis "riddled with pathology", that's kind of the point

[gray gazelle]

thats just cuz complex analysis is trivial

[foggy relic]

[restive falcon]

go on
prove the riemann hypothesis

[gray gazelle]

I know this isn't a physics server but can anybody recommend a good physics resource that'll give me a good general overview/knowledge of physics?

[severe rune]

Halliday & Resnick - Fundamentals of Physics is pretty good

[gray gazelle]

awesome, ill note that down, thanks

[thorn canyon]

University physics - freedmen is great too

[gray gazelle]

great, thanks. will note that down too.

[thorn canyon]

:)

[gray gazelle]

☺️

[pale scarab]

The 5th edition in particular has really good problems compared to the newer ones.

[analog horizon]

any good probability theory books

or course

[gray gazelle]

Resnick, A probability path

[analog horizon]

is that book rigourous enough?

[gray gazelle]

yeah

[inner token]

Any suggestions on complex analysis books?

[analog horizon]

ahlfors

[inner token]

Thanks

[analog horizon]

or rudins complex analy booky

[restive falcon]

see pins

[inner token]

Thanks

[gray gazelle]

you re welcome

[gray gazelle]

is there any good math books for year 8/ grade 7 I’m tryna revise to get a higher set in math

[cyan prism]

cambridge textbooks?

idk any other textbooks

lol

i mean u could also review class notes

any good number theory undergraduate books

i know a little number theory from maths olympiad books and problems but idk how much overlap there is with undergraduate nt

[brittle breach]

Hardy and Wright introduction to the theory of numbers

[cyan prism]

thanks

[sudden kayak]

Hello, do guys have a book recommendation for mathematical proof. I'm not looking for a textbook type of book but something that is fun to read yet full of information.

[karmic thorn]

Proof and the Art of Mathematics by Hamkins

[grand wren]

Hi guys, Is it necessary to learn Calculus before Learning Analysis? I really wanna do Tao's Analysis but feel bummed that I would have to go through something like Apostol's Calculus prior to touching Tao's Analysis. I heard Analysis teaches Calc from scratch too.

[sudden kayak]

Thanks! will definitely check it out.

[karmic thorn]

If you have at least done some calculus before (computed limits, derivatives, integrals), you can start learning analysis from any introductory text. That said, Tao's Analysis may be suboptimal, I'll insist on something like Abott's Understanding Analysis instead.

[loud cradle]

In theory, analysis is self-contained, but the motivation may be missing if you haven't already been exposed to calculus. Also, the focus is probably different. In calculus you learn how to differentiate specific functions using the chain rule, etc., and various techniques for integrating specific functions. You don't typically spend much if any time on this in analysis.

[gentle siren]

any good number theory books?

[brittle breach]

no it is not necessary.

and I second Abott's Understanding Analysis

he does go over many of the motivations

[gray gazelle]

theory of numbers

[sick wigeon]

Any suggestions for rigorous numerical analysis books for a math undergrad? (Rigorous in the sense, contains formal proofs for all the algorithms etc)

Is the book by Kincaid and Cheney appropriate?

[slim peak]

@glad prairie May probably know

[sick wigeon]

I just wanna start reading a bit of it to gauge whether i have any interest for it
Just to know whether i like applied math or not😂

[restive falcon]

I'm a bit late but if you want something a bit more fast-paced than abbott, i recommend pugh (or rudin, but rudin is really just pugh without diagrams)

[karmic thorn]

Burden's Numerical Analysis is nice.

[iron granite]

any problem books in calculus/ sources of calc1/2 problems?

[sick wigeon]

Thanks! Will check it

[thorn canyon]

Just wanna confirm, gillbert strang would be good for linear algebra?
Basics

[keen blade]

Thomas' and Stewart's

[iron granite]

Already got thomas, the problems aren't that varied imo.

[frosty girder]

Try pauls notes

Or RD sharma ()

[gray gazelle]

baby rudin has exercises

[iron granite]

Rudin's kinda fking overkill for calc 2, don't you think?

[gray gazelle]

no

[iron granite]

I have the book besides me anyways, lemme see.

Which chapter, btw?

[gray gazelle]

all of them

[gray gazelle]

Why is concrete Mathematics not considered a "true" discrete math book?

[fervent lava]

Probably it doesn't have a propositional logic chapter/section that most discrete math books have.

[polar mango]

Hey guys this is kind of a weird request but i have a trig book that is online provided by the school, is there anyway you know that i can download the book?

[gray gazelle]

your question makes no sense

if its provided by school whats the problem

[polar mango]

yeah the book is has given access to me though a website

[gray gazelle]

what format

[polar mango]

?

wdym what format

[rare sinew]

Would you recommend Undegraduate Analysis by Serge Lang over Calculus by James Stewart?

[restive falcon]

read principles of mathematical analysis by walter rudin
you'll enjoy it

[broken meadow]

huh

[modern stone]

For multivariable calc, is Shifrin a good choice?

[fervent lava]

@ gristbundle have said good things about it.

[slender maple]

I am a fan of gamelin

[sage python]

Gamelin's the best beginner book I'd say

Also someone told me of a book which at a glance might actually be better than Baby Rudin tbh

[gray gazelle]

what book

[sage python]

Browder

[lime sapphire]

Just waiting for all the rudin fans to come at you

[sage python]

Hey I'm a Rudin fan too lol

Except for maybe Browder and maybe Igor Kriz's book

I don't really think any analysis book thus far written holds a candle to Rudin

[gray gazelle]

Any books that really covers how to seutp " differential equaitons" and not just how to solve them?

I am at the point where I know how to solve differential equations but have no clue on how to set the equation up nor its meaning

My textbook and teacher are not helpful in this sense

[slim peak]

What do you mean by "set up" ?

How to get them from physics' laws ?

[gray gazelle]

Essentially yes

[slim peak]

If yes, then check the Introduction of Viorel Barbu's book called "Differential equations"

[gray gazelle]

Will do so, thank you Anatole

[slim peak]

The Introduction contains a list of model from Physics

[gray gazelle]

Sweet!!!!!!1

[sturdy sail]

Are there introductory books/papers which cover the main tools and methods in the Langlands Program?

[fossil arch]

@slim nacelle Sorry to ping, thought you might be able to respond

[split moon]

automorphic normies

[slim nacelle]

yeah, this https://arxiv.org/pdf/1511.04265.pdf

this is a nice book survey of the Langlands program with a focus on the analytic parts of this

so it ends up covering automorphic Eisenstein series and you can get some idea of the spectral decomposition problem for L^2

• fun application of counting black hole solutions

there are other more specific texts for different parts of the Langlands program if you want to learn them in full generality but these can be hard to motivate and hard to read

I don't know of any book that does everything in one place, the thing I linked is the closest thing I know to that

also requires very little background, it starts with p-adic and adelic groups and then covers Tate's thesis

[sturdy sail]

I know Stephen Gelbart has a few books on the Langlands Program which are supposed to be introductory, have you ever read any of them?

Or at least know some opinions on his books?

[sturdy sail]

Oooh

Ok, it looks really promising.

Thanks!

[sage python]

Lol string theory

[gray gazelle]

What is the Langlands Program?

[sudden kindle]

Langlads program is a generalization of class field theory and modularity theorem

[brittle breach]

Class field theory?
Modularity theory?

[sudden kindle]

I don't know either of these things well enough to describe them but basically two L functions are equal

[brittle breach]

what is an L-series in general,
an L-function is the analytic continuation of that correct?

I should be running upon my first L-function soon, so this is cool

[hexed rain]

I still don't really get double categories and topoi

Would really appreciate some very basic stuff for absolutely baby computer programmer nonmathematicians

[prime oak]

whats a good text for multivariate calculus?

[gray gazelle]

advanced calculus by folland

[remote ginkgo]

calculus on manifolds

[runic hatch]

I used Analysis on manifolds by munkres

[gray gazelle]

Any good algorithms/data structures book written in c?

[gray jungle]

langs ok

[dapper root]

WOOOOOO

[south salmon]

Folland

[gray gazelle]

I found that a lot of material covered in rosen's discrete math is also covered in knuth's concrete Mathematics, which one is better should I study?

[gray gazelle]

why not both

[gray gazelle]

does stein and shakarchi II require I?

[round falcon]

@gray gazelle try cengage it's for advance maths

[frosty girder]

[gray gazelle]

please

[rapid cairn]

Would anyone have any recommendations about non Euclidean geometry or other theoretical mathematics?

:3

[gray gazelle]

Other theoretical mathematics?

[gray gazelle]

A way I have to recommend that

Look at Springer books

You can find there books about any math field

[rapid cairn]

Ooo

[gray gazelle]

I already know formal logic, should I skip the sections that go over that?

[gray gazelle]

i feel like my algebraic skills are lacking - any book recommendations?

am in year 13 if that helps

[round falcon]

@gray gazelle try hall & knight

And even Bernard childs higher algebra

[round falcon]

Hall& knight have 3 algebra books higher algebra, elementary algebra, algebra for beginners

[gray gazelle]

ooo ok

ty

ill check em out

[grim narwhal]

Does anyone know where i can find worksheets on high school math like kuta software?

[foggy relic]

@\moderators?

[sudden kindle]

<@&268886789983436800>

Looks like spam

[steel viper]

Hurb

This is probably copyrighted in the first place

[flint forge]

new topology book just dropped

someone tell me if its good

https://urldefense.proofpoint.com/v2/url?u=https-3A__www.worldscientific.com_worldscibooks_10.1142_12586&d=DwICAg&c=-35OiAkTchMrZOngvJPOeA&r=ny9h-hPgaJqQeKPN0N5JcQ&m=cAsi_Tzunuh2eODccvjXX7kRpwkx2OLi01X_Rcfv1yUsTvUpQP71LbYVOTmsETzm&s=yC_LetDE6ZpX2y1tZPJ1JGApn8WozeY_5lqzDvdNpFA&e=

[hearty steppe]

Hey max I started going thru Munkres not long ago

[marble solar]

Are you enjoying it cat man?

[hearty steppe]

Yea I’m gona be doing more Casella and Berger today and tomorrow though

Might sneak a few sections of Munkres in if they’re short enough though. I’m almost done with chapter 1 soon

[modern stone]

What are some good topology books that balance rigour and intuition?

[flint forge]

Hatcher

This is a rant i've given a number of times

but there is no topology textbook that is not rigorous

many people claim that hatcher or other books are "less rigorous" but this is largely nonsensical

[modern stone]

For general topology what would you recommend?

afaik Hatcher is for algebraic top

[marble solar]

Munkres is good

[stone storm]

I’ve been reading Lee’s intro to topological manifolds, and I’ve been liking it quite a bit. It’s basically an intro topology book with intro to manifold theory

[bleak canopy]

hey guys

what up

it's me

how's everyone doing

wait this isn't chill my bad

[smoky zephyr]

oof

[slender maple]

no, there are independent

[hearty sluice]

any complex analysis recommendations?

Im not enjoying Conway's book

[flint forge]

S&S is a common one

[cursive orbit]

this message has some commentary #book-recommendations message

[flint forge]

Stein and Shakarachi if im not making a spelling error

I should try narasimhan

@sage python would i like it

be hoenst

[hearty sluice]

i think ill try narasimhan

at several points in conway ive had the questions: Why arent we just doing this topologically

[sage python]

It's more topological than the others, it does introduce all the basic covering space stuff it needs which might be slow for you

And eventually (perhaps inevitably) it gets into analysis heavy stuff

But it's probably less boring than Conway

Tbh for Max you might just prefer reading Forster or Donaldson Riemann surfaces

[sudden kindle]

This is a book I'm gonna look into

Ch1 is about hyperbolic 3 space

[sage python]

oo

[timber garnet]

http://www.ru.ac.bd/wp-content/uploads/sites/25/2019/03/205_04_Apostol-Mathematical-Analysis-1973.pdf

is this a good book for analysis 1 (course after 'intro to analysis')

this seems like a lot of content

[runic hatch]

I liked it myself, but yeah it’s a lot of content

Analysis in general just kind of has a lot really

I ended up using both Apostol and Rudin for analysis

[timber garnet]

thx ab

[brittle breach]

I prefer Rudin

[brittle breach]

chapters 3 to 9 is topically whats covered

[gray gazelle]

Know any good chess books for Caro Kann

?

[marble solar]

Marshall's

[marble solar]

I think my biggest issue with Stein and Shakarchi Volume 2 is the toy contour business

I'm not a big fan of how it presents that information, but the rest of it is great

[round falcon]

@gray gazelle i think so karpov have written one book on Caro kann

[gray gazelle]

What is a good first book on differential equations

[frosty girder]

apostol? yeah its noice imo, im doing this myself

doing rudin and apostol together seems nice, tho i havent really tried to do any rudin

[timber garnet]

i see why people think analysis 1 is hard now xd

but the content is interesting

[frosty girder]

[frosty girder]

It is!

the proofs arent easy to come up with urself, but the content is 😋

[sick wigeon]

Priestley's book is nice i have heard

[lapis sundial]

personally preferred S&S to priestley by a lot

priestley has bad typesetting and decent number of typos

[sage python]

I'm gonna follow up and say S&S kinda rubs me the wrong way a bit. Toy contours are 🤮 and a lot of ideas are not done topologically when they should be

[brittle breach]

what is good for complex analysis

[sage python]

Gamelin if you're starting, Narasimhan if you're more advanced

And... tbh I wish there was a book at the "I just did Rudin-level analysis" tier, kinda like S&S but with more topology discussion and whatnot

[brittle breach]

me too

[gray jungle]

hear me out
this is your moment to write and publish that book 👀

[restive falcon]

be the change you want to see in the world

[sage python]

Lol maybe I should but it feels like it'd just be a more concise Gamelin

[forest sleet]

I liked the Barry Simon complex analysis book although it assumes a bit more real analysis than normal

But none of those toy contours

rectifiable contours instead

[restive falcon]

still
some people might want that

also you could go a bit deeper into the topological side

[brittle breach]

A lot of books spawn from lectures so maybe you should teach a course on it

[frosty girder]

i want an invitation to those lectures

[graceful lynx]

Any recommendations on linear algebra?

[frosty girder]

friedberg and spencers book is nice

[marble solar]

It's buried in an exercise

That toy contours can be done properly

It's the one thing that turns me off from the book, I think it's an excellent resource for problems though

[graceful lynx]

does anyone have a book recommendation on mathematical notation they found insightful? I find that the math im attempting is unapproachable at times since I cant interpret the actual notation at hand

[stray veldt]

that is odd, books should either introduce notation, have it listed in some appendix, or it is so standard that the notation itself should be the least problem in being able to understand it

that being said, i also dont think such a book exists: notation differs by field and author and probably other things
if its just standard that are literally used everywhere i think there is a glossary on wikipedia

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

(this even has a lot of more niche things now that i look at it)

[subtle mango]

best book for lin alg coming from multivar calc?

[fluid bay]

I don’t think there are any Lin alg books that leverage much multivariable calc knowledge

But my usual rec is linear algebra done wrong by sergei treil

[late plinth]

i like strang

that being said tho

there is very little connection to multi except for maybe projections

and stuff like determinants

[subtle mango]

icic

noted thank u

[gray gazelle]

Good audiobook for a road trip?

[marble solar]

Williamson & Trotter does, and I think so too does Ted Shifrin's text

[fluid bay]

ah okay, nice. There you go @subtle mango

[sick wigeon]

Wait really?

The type setting is good i think 🤔

[frosty girder]

i am using friedberg and spencers book and i like it

[heady ember]

What prerequisites are there for Thomas Jech's Set Theory book, or should I read Enderton's Mathematical Introduction to Logic first as an intro first before trying Thomas Jech's book

[lapis sundial]

Oh well the version i have at least then oops

[zinc iron]

The formal prerequisites are some basic topology and some basic model theory. That being said, Jech serves best as a reference book. There are better introductions to set theory e.g. Kunen.

[heady ember]

Ah I see, so what are some good introductions to set theory (other than the Kunen book you just suggested)? Also, what do you think of Enderton's Mathematical Intro To Logic

[zinc iron]

It depends on what you want to learn in set theory. If you want to learn set theory at the level of what's traditionally a graduate course then Kunen, Jech, Schindler are the books worth looking at (Kunen is the most readable though by a significant margin imo).

If you want something simpler then you can look at Enderton's set theory book or Jech and Hrbacek's book.

[heady ember]

Ohh ok thanks!

[zinc iron]

I've heard that Enderton's intro to logic is good from others, but I've never read it.

[heady ember]

I see

[gray gazelle]

Anyone have opinions on "Chebyshev polynomials" by Rivlin?

Why not use two separate books

I used ahlfors for complex iirc

And for real analysis I used apostol and rudin

Pirate them or borrow from the university library

The rules say "links or files may not be posted"

I didn't post either

Buy international student editions, they're cheaper

Which country are you in?

Oh

Make good friends with someone from mainland China

Aren't there a bunch of math department students from China? One of them can definitely hook you up

Or pirate it and go to a printing shop

[karmic thorn]

You should be able to find cheaper paperback "international editions" for most of the popular/classic textbooks.

[gray gazelle]

In Canada?

always thought those books said "not for sale in north america"

try checking if there are any good dover texts for analysis

those are a lot cheaper

[urban herald]

Can anyone recommend a good book for linear algebra?

[fervent lava]

Friedberg, insel, and Spence linear algebra book or ladw.

[urban herald]

what is ladw?

[fervent lava]

sorry Linear algebra done wrong, it available for free online.

[urban herald]

:0 thanks a lot

[subtle mango]

bless

[crude iris]

Is the art and craft of problem solving a good book to learn beginner graph theory?

[karmic thorn]

I think it should be okay but I wouldn't expect it to cover much in terms of breadth

[timber garnet]

to learn beginner graph theory probably just any intro to combinatorics book should have it

[crude iris]

I tried to learn it from vitaly I voloshin and dienhard diestel and mathematical Olympiad series but couldn't finish even their first chapters

[timber garnet]

https://www.zib.de/groetschel/teaching/WS1314/BondyMurtyGTWA.pdf

skim thru this idk if its any good

my uni uses this one

[karmic thorn]

I'll recommend the relevant sections from Bona's A Walk Through Combinatorics, mostly because I simp for his exposition. 😛

[crude iris]

I want a book which is fun to read and not too hard i.e. I don't want to give up too soon

[half mountain]

you may think its weird or newb, but is there a book for algebraic topology without prerequisite from general topo?? i know there will be a bit of real analysis but must be able to read it after standard algebra courses

[gray gazelle]

Who is insel

[gray jungle]

Arnold J. Insel is one of the authors

he seems to be affiliated with Illinois State University according to researchgate but nothing else on him (that i could find)

[dapper root]

Lol incel

[frosty girder]

[hearty steppe]

If you lack experience with foundations then I think the regular Linear Algebra text by friedberg et al is pretty solid. I find myself going back to it occasionally. The exercises in the text are a bit too easy for me though generally speaking

I think I’ve noticed it’s pretty difficult to 100% a math text. Just find select books of interest that are important to you and focus on completing those exercises overtime

[gray jungle]

this might be an odd question but is there a book with just a very long list of integrals and there answers?

[shy compass]

engineering textbook

[dusky minnow]

Can anyone recommend good resources for learning topology? (with exercises if possible)

[fluid bay]

munkres is solid. So are hatcher's notes on point set topology

these are hatchers notes: https://pi.math.cornell.edu/~hatcher/Top/Topdownloads.html

[dusky minnow]

thanks

[fluid bay]

np

[silent cloak]

Can someone please recommend me good book for stochastic processes

[buoyant spire]

Try the CRC Standard Mathematical Tables and Formulae

[humble bluff]

algebraic or normal

by normal ı mean general

if algebraic

hatcher and j.p may is good

but use both of them

if general

every textbook is really good

[dusky minnow]

what is general topology and algebraic topology?

[humble bluff]

general topology deals with sets while algebraic topology deals with algebra

general topology is the first to go with

if you havent taken a course or read a book on it

[dusky minnow]

alright, thanks

[gray gazelle]

You can find tables of integrals

I'm partial to this: https://en.m.wikipedia.org/wiki/Gradshteyn_and_Ryzhik

[elder cape]

Beside Rudin and Pugh in #books, is there any other book on analysis? I read their descriptions and they seem to be on extreme sides ^^;

[cursive orbit]

abbott and tao are other options you could look at

tao starts from the naturals and constructs the reals before he starts doing any analysis, and that may or may not be your cup of tea

but I'd recommend at least looking at the exercises in Rudin

[elder cape]

And abott?

[cursive orbit]

basically a relatively gentle introduction to analysis

[elder cape]

oh sounds nice

Not much else going for it?

[cursive orbit]

well it's also a good book lol

but it's not really that unique in that it covers a pretty standard set of topics

[elder cape]

So a kinda of a "safe" option

That may be what I am looking for

[hallow knoll]

Is there a book or handout that covers basic/advanced functional equalities well?
Trying to grasp the intuition behind solving them better, so any material would be appreciated!

[slim peak]

Can you give me some example of what you call exactly functional equalities ?

[hallow knoll]

Indeed, Olympiad style functional equations where nice properties are assumed and require tricky substitutions and/or other tools to solve. Here is an example:

[hasty eagle]

peaceGiant

[slim peak]

oh this kind

I cannot help, since I know none of those

[hallow knoll]

No worries, thanks either way

[tawny copper]

Maybe Cristopher G. Small, "Functional equations and how to solve them". The book I think is nice, but is the only one I know of this type

I don't think this type of equations require a lot of theory though

Does someone have Dummit and Foote algebra text in pdf with bookmarks btw? There are pdf available in google, but without bookmarks

[cursive orbit]

There's one on the site comprised of the first 3 letters of liberal and genetics.

[gray gazelle]

Halsey Royden

[tawny copper]

thank you!

[hallow knoll]

Thanks! I'll check it out.

[pallid knoll]

is there a good introductory book on representation theory that someone recommends

[dapper root]

Deadass the intro to rep theory in D&F is pretty good

[pallid knoll]

ah i never read D&F so i'll check it out thanks!

[dapper root]

Swag

[pallid knoll]

faithful matrix 🙏

[balmy phoenix]

does anyone know a good (hopefully free) introduction to proofs?

[sick wigeon]

Any book recommendations on Harmonic analysis?
How's Grafakos?
Is it well written?

I am starting to learn measure theory

After i learn some measure theory, will i be able to read the book directly?

[slim peak]

No, you will need to be familiar with complete metric spaces, and to be more specific Hilbert, and also Banach spaces, then Lp spaces (Banach spaces of measurable functions)

(And some multi var Calculus)

[sage python]

I will probably be using some of Schlag's book

[slim peak]

Grafakos is a very good book but not gentle for an Introduction to Harmonic Analysis

Here is a free book available online

The point of view is fully Euclidean so that it contains no tools for some futher generalization like Non-commutative Harmonic Analysis

[sage python]

😭

[slim peak]

But this is probably, in my opinion, the best Introduction to Harmonic Analysis

[slim peak]

The content is already really heavy

[sage python]

Yeah fair

But 😭

[slim peak]

Non-commutative Harmonic Analysis require a LOT of background, generally "shorts introduction to non-com. HA" is a scam

It is either not short, or not a Intorduction

[sage python]

Haha, so the plan-ish I've got is

Prob either Folland or Deitmar-Echterhoff for the more rep theory side of harmonic analysis

And Schlag for more standard business

[slim peak]

To me a good thing would be to start from euclidean case

Then go on non-com HA on a specific case

like on the Heisenberg group

like Thangavelu

[sage python]

Heisenberg group seems like good shit, at least one prof here's big thing is rep theory of Heisenberg group

And actually it's coming up for me now since I'm learning about something called theta lifting

[slim peak]

That's the point this gives you a bridge between no rep Theory to some rep Theory in a simple case

I was personnally introduced to it by the mean of Pseudo Differential Calculus/Semiclassical Analysis

But I dropped non-com. HA I have already too much to learn/to do in another fields

[sage python]

That's fair yeah. Because of automorphic forms the non-commutative stuff is p central to me :p

[sick wigeon]

Oh i see

Actually i am planning to read Axler fully and then proceed to grafakos

The measure theory text

[gray gazelle]

Evan Chens handouts are a pretty decent group for FEs, other than that I have this book by VK Venkatachala named Functional Equations, you can find that on b-ok.as

Any good coordinate geometry books? I just want to learn most of the theory up to K12/Elementary UG Level with some challenging problems. Something like SL Loney's text (I cant use that)

[sick wigeon]

What do you think about stein and Shakarchi?
Many say it doesn't do certain stuff fully rigorously

As it's not a measure theory based text

And thanks for the PDF!

[slim peak]

I do not recommend Grafakos as a first read on Harmonic Analysis

[gray gazelle]

b-ok.as or libgen.is if you didnt know

[slim peak]

The pdf is a free one available online

hence no need to

[gray gazelle]

but just in case

[slim peak]

Concerning other references, since I'm new to the English world of undergrad/pre grad references, so i can't tell. Mine are essentially French ones, except Rudin.

[sick wigeon]

I see

It's there in the #books channel

[slim peak]

But this is not a measure Thoery book

[sick wigeon]

So you are saying it's better to learn Fourier analysis after measure theory?

And not using the Riemann integral

[slim peak]

I don't get how you can properly defined the Fourier Transform and its proeprties without the Lebesgue integral

You need to do measure Theory and complete Metrics spaces (as Lp spaces) before

[sick wigeon]

I see

But the book claims to do it lol

I don't know

[dapper root]

You can do Fourier Analysis without the Lebesgur integral, I learned some my freshman year using the Darboux integral

[slim peak]

If the review tells true then this book is not appropriate to start on C.Hao lecture notes.

[dapper root]

It wasn’t particularly refined or anything, but you can still get at the ideas

[slim peak]

Oh you prove L² is complete space, the the Fourier Transform is a isometry from L² to it self ?

[dapper root]

You don’t need all that to get at the basics of what the Fourier transform does lol

[slim peak]

The plan here is to check out Harmonic Analysis, which needs very deep properties

[dapper root]

I see

[slim peak]

And I think this the wrong way to be introduced to the Fourier Transform btw

[sick wigeon]

So you are saying if i wanna go deeper into it, a measure theory based approach is "the" way

[slim peak]

There is no other way

[sick wigeon]

And any other way is either non rigorous or too elementary

Right?

[slim peak]

It's even worst

You won't be able to understand a single proof

[sick wigeon]

I see

[slim peak]

Oherwise you'd better do Physics, without proof, just do computations with no rigor

[sick wigeon]

Can i discuss this alone in dm, anatole?

[slim peak]

I'm not comfortable with it

[sick wigeon]

Ok

Sorry

[slim peak]

To me you should check :

1 - Rudin, Real and Complex Analysis, (Chapters 1, 2 + 8 (for Fubini-Lebesgue Theorem)) -> Measure Theory and Integration

2 - Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations (Chapters 4, 5) -> Lp Spaces, and Hilbert Spaces.

3 - Hao, Lecture notes on Harmonic Analysis, the whole thing if you want. -> Harmonic Analysis with all properties of the Fourier Transform in earlier chapters

The order is really important

I think this is best and quicker road map

this gives you less than 350 pages to read

which is pretty honest

this can be achieve in less than 3 months with something like 4hours a week

maybe less

[sick wigeon]

I see

The first 2 are all present in the book i am reading

So i will continue to read

Thanks for the lecture notes!

[slim peak]

np

[gray gazelle]

@slim peak you think I can make it far in math while learning on my own in English?

My studies are actually in french

[slim peak]

The two first books are available in French

[gray gazelle]

I see but that doesn't answer my question, suppose I used rosen's discrete math book can i use that in my studies?

[slim peak]

I don't know that's not how I've done my grad, so i can't tell

[gray gazelle]

I see, thanks

[slim peak]

But until my 3rd Uni year, everything I've done was fully in French

[odd spade]

Do you switch to English for your thesis

[winter hearth]

Where we can get videos or courses on topology

[slim peak]

I did during my last year just before starting my PhD. Every lecture was in English

[odd spade]

oh i see

[misty wyvern]

Anyone have a good book for light reading but otherwise at the graduate math level?

Think "I wanna do math but I'm too lazy to compute anything right now"

[marble solar]

I found historical expositions to be really enlightening

Boyer's History of Calculus

Stillwell's Mathematics and its History

[misty wyvern]

I have almost no interest in science history to be honest.

[marble solar]

RIP

[misty wyvern]

While I do read history, it's mostly annales stuff.

I keep my math and history separate.

[marble solar]

I don't have much then lol

Grad math that's just good for casual browsing

Korner's Fourier Analysis book has interesting applications

If you've read that

Lots of results at a pretty beginner level

Should be pretty light reading for you

If you're at all interested in Topology ~ Thurston has a book on 3 manifolds

and then there's the wild world of 4 manifolds

that are lighter, but still interesting

[marble solar]

Garnett & Marshall's Harmonic Measure isn't overly complicated

But it is interesting

[misty wyvern]

thanks for the rec

[hearty steppe]

You read Munkres

Topology is where math gets to a point where you need to read the standard books

Like it’s just very abstract that just trying to learn it by watching videos and taking an online course does a disservice to understanding what your working with

Munkres has some pedantic wordiness in it at times but it seems quite approachable to me so far. I started studying math rigorously almost 2 years ago

Btw I started Munkres barely a month ago

MAKE sure you go through the entirety of the first chapter. It’s not quite topology yet but trust me. Completing all the exercises is not necessary. You might be able to fly through the first 7 sections like I am

Make sure it’s not the elementary linear algebra book. The one that is titled “linear algebra” is the one you want.

Personally that book is a bit easy for me, but I’m confident you shouldn’t struggle much with it. If your not struggling a lot with the exercises, just pick one or two that are different enough from eachother and before you know it, you might fly through the book too

Lots of redundant exercises in that book, and I think you’ll be able to notice when it gets redundant and you can skip ahead

[balmy phoenix]

anyone know a good book on introduction to proofs?

[smoky zephyr]

book of proof by hammack

it’s what i’m using, i’m almost halfway done and i really like it

[marble solar]

Tell me what you think when you find a PDF or something

and you've read some of it

@misty wyvern https://arxiv.org/pdf/2202.03594.pdf

This packing article by Terry is amusing

[hardy junco]

any books on information theory?

[steel harness]

https://www.amazon.com/dp/B09RFVGKVR

[grand thistle]

how to prove it by velleman

best intro to proofs like ever

taught me the basics to proofs and like rules of inference etc in a week or so

even just reading chapter 1-3

[fervent lava]

Loch's intro proof pdf in #proofs-and-logic pin is also nice. That what I used.

[warm glen]

how about "how to read and do proofs" by volow

has anyone here had experience with it

[solemn rover]

the standard textbook is Thomas and Cover

[fluid bay]

any good texts on operating systems?

[winter hearth]

Thank you
just ispired n dimensions and going to study it
😂

[gray gazelle]

hey guys does anyone have any book recommendation for maths competitions

[hollow shore]

Zeitz's The Art and Craft of Problem Solving is really nice

[gray gazelle]

thx :)

[azure frigate]

+1 for Velleman, it's fantastic

[stray veldt]

-1 for velleman, +1 for aluffi notes

[lime sapphire]

Algebra: Notes from the Underground by Paolo Aluffi ?

[stray veldt]

http://www.math.hawaii.edu/~pavel/Aluffi_notes.pdf

[lime sapphire]

i see

[crude iris]

-1 for aluffi notes, +1 for velleman

[lime sapphire]

also btw i just stumbled upon this at the mention of aluffi, could someone check it out and let me know what they think? it looks like a rather unusual algebra book with rings first then modules and groups and fields after
also seems to cover a tiny bit of category theory?

someone made a rather bold claim on goodreads 👀

will possibly replace... Artin.

[frosty girder]

[stray veldt]

why did aluffi write two undergrad algebra books

[lime sapphire]

perhaps because one of them is a graduate book?

idk

[fluid bay]

I think the category pilled one is intended as a grad text

[stray veldt]

weird

i think giving modules a more prominent role in intro abstract algebra is a good idea

although i wonder how he will draw from a large enough example pool of rings

[odd spade]

Chapter 0 is generally used as a graduate level text IME, yeah

Problem difficulty alone is higher than advanced undergrad books

Or are we not talking about chapter 0

[lime sapphire]

Talking about Algebra: Notes from the Underground by Aluffi

[odd spade]

Oooh

I didnt even know he had other algebra books

Chapter 0 is very good imo

[dapper root]

That one is new!

I think from 2021 or 2020

[odd spade]

maybe i will check it out i think aluffi is a good writer

sometimes a little extravagant but i like the exposition

[stray veldt]

why did he not write chapter 1

[odd spade]

he missed an opportunity

he could have been like jackson pollock

[dapper root]

It does ring theory first

Which is something I think more and more departments are embracing

[dense wren]

Hungerfords undergrad algebra book also does rings first

[marble solar]

Look at the hungerford memer

You ready for your qual berg

[sudden kindle]

I like this too

I did group theory first, but I think ring theory first would be a nice approach to AA

[stray veldt]

my AA class had like an intro chapter that did both rings and groups at the same time and talked about what subobjects and quotients are

[graceful dawn]

Give me some recommendation

[cursive orbit]

For?

[sage python]

I'm not sure what I think about groups first vs rings first

I could see a case both ways

Naively, groups are simpler objects, but a lot of the theory of abelian groups is wrapped up in the theory of modules over a PID

Also ring theory doesn't rely a ton on group theory

I guess some kinda integrated approach might be a good idea tbh

Maybe you focus for a while on this topic or other but you define groups, rings, and fields from the very beginning

And you can talk about quotients in both, etc

[marble solar]

I don't think it matters that much: just don't teach the sylow theorems

[slim peak]

Sylow's are neat

[flint forge]

this seems odd to me but i would be curious to learn why people think its a good idea

lots of theorems are neat but should not be part of curriculum

[slim peak]

Because this a simple, deep, and non-trivial application of Group actions, which have also deep application in other subfields

[marble solar]

I dunno, I think they kinda suck. I found algebraic curves and commutative algebra more interesting

Also applications of algebra in different topological settings

Don't require the sylow theorems

I haven't learned any Galois Theory

So if they're useful there, I wouldn't know

[flint forge]

Sylow theorems would be more reasonable if they took up a much smaller portion of a group theory course

But a lot of schools spend like

[marble solar]

There are other important examples of group actions

[flint forge]

weeks on them and various tricks for like, proving there are only 14 groups of order 43243

[slim peak]

This kind of stuff sucks

[marble solar]

Aren't like Finite Simple groups pretty much all sorted out

[flint forge]

yeah

but they werent when the textbooks were written

and the curricula designed

[slim peak]

Sylow's are useful to prove unicity of simple groupe of order 60

which is A5

(then yes Galois theory)

[marble solar]

See now you're going to the Galois stuff

But for a pleb like me that got filtered by algebra before making it to Galois

[sudden kindle]

Groups are a step up in abstraction than rings imo. This is why ring theory might be more suitable to introduce to undergrads first maybe

[flint forge]

Could you say more

certainly that is literally false

[slim peak]

I did group first, then algebra and ring theory.

[flint forge]

Or I guess not

it is literally true

But its also like, more structure to wrap ones head around

seems like groups are very straightforward

[slim peak]

lemme check out

[sage python]

Sylow theorems could be like

One or two lectures, or even a subset of a pset

And I'd say that's the right way to go about it

[slim peak]

2 lectures is too short but more than 3 or 4 is litterally overkill

[sage python]

PTY: So, groups are less familiar than rings but they are "simpler" in the sense of, fewer axioms going on

I do think a lot about how algebra classes are done should be changed

[split moon]

I think familiarity is a more relevant aspect than simplicity in this sense

[slim peak]

They are also usefull to identify subgroups of GLn(Fp)

[sage python]

Don't agree

Fractal

The problem is that that familiarity doesn't take you far

[split moon]

at least when it comes to the order of teaching

[sage python]

Like, at most you'll be like oo I recognize Euclidean domains

[marble solar]

It's useful for students to be put in something abstract nonsense land so they learn to think via axioms, definitions

and not just examples

[sage python]

And maybe the idea of unique factorization a little bit

But otherwise there's not a ton of intuition that you have that's specific to rings and not groups. And in fact you might be inclined to overapply ideas from Z

To rings where it's not good. Also what Moonbears said

[slim peak]

This kind of stuff is a consequence of Sylow theorems

[marble solar]

Oh cool it's all true

[sage python]

Yup, I don't agree with knocking Sylow completely, it's more important than people realize. But these applications should be emphasized instead of like

Spending time in class being like classify groups of X order

[split moon]

I think undergrad underemphasizes examples
my experience is the opposite problem

people even have difficulty coming up with examples sometimes

[marble solar]

I mean coming up w/ examples is genuinely a difficult thing to do

[sage python]

Algebra is the one subject where I feel examples aren't underemphasized tho

Also like

[sudden kindle]

To me sylow theorems are just used to answer algebra qualifying exam questions

Kol

[sage python]

Eventually students have to learn how to do shit themselves rather than be spoonfed lol

[slim peak]

For a non-trivial abstract Theorem, proving something is good example or counter-example is generally very very long and technical

which is against pedagogy

[sage python]

But yeah I think I'd shift emphasis around a little bit in algebra. Let's say for intro to group theory, quarter long course

I'd probably do

[split moon]

well
I see those two aspects as fairly distinct
working out in full generality facilitates specific things but it does not give them for free
sometimes that coming back from the more sophisticated concepts and tools a ton of work
that comes as a trade off of simple proofs sometimes
I still think both things are important on their own

[slim peak]

Finite group examples are either, trivial, too classical (but you want doable exercises to give to your student at the exam), or very difficult

[sage python]

• Categories
• Monoids, groups, submonoids, subgroups
• Homomorphisms, kernel/image, normal subgroups, quotients
• Isomorphism theorems
• Automorphism groups, group actions and representations (biggest part of it)
• Free groups, adjoint functors, presentations
• Finite groups (Sylow, classification of groups of order blah)
• Solvable and nilpotent groups?

Throughout have examples like cyclic groups, S_n, A_n, D_n, matrix groups,

[odd spade]

imo galois theory and finitely generated groups are the most urgent issues of algebra like that, but it definitely depends on what you are doing

i never use modules or monoids

but people who scale category-geometry-algebra mountain seem to like all that

free groups are really important actually and their introduction felt really sudden to me

[wise umbra]

I would say that modules are more important than Galois theory, if you had to choose
Modules are generalized vector spaces

Of course Galois theory is important as well, and close in spirit to covers and the fundamental group in algebraic topology

[odd spade]

i would say my perspective is biased

if you are doing certain things you would be crazy not to do modules

i stay near group/semigroup stuff

also yeah its further connection with topology and number theory is big

you can avoid galois theory in number theory for a long time technically, i have a book that does this

but i dont think you can do advanced L functions without it

it's actually (extremely) nontrivial to avoid it entirely but in spots it's feasible and even time saving

[balmy phoenix]

this looks great thanks! thanks everyone who +1 velleman looks exactly like what i need thanks

[wise umbra]

Really depends about what you're working on but Galois theory is quite used in number theory 😄

[odd spade]

yeah i think the book i have that does this is by alan baker so

it's pretty cool

it's just a book though, i dont know how far you could take it

[main sonnet]

Recommended books only for problems for abstract algebra? My class is currently going through Herstein's abstract algebra, but I would like some practice problems I can do with solutions

[sudden kindle]

Galois theory is extremely important to number theory

Algebraic number theory is synonymous with galois theory over Q

[odd spade]

yeah i am not suggesting a program of no galois theory number theory haha

quite the contrary, galois theory rules

i say invade every field with galois theory

spread the word of our lord galois

[sudden kindle]

Yes

Its already happened

Thanks to Grothendieck

[odd spade]

🙏

bless

[patent mango]

is there any good books for Mersenne primes?

[quick hornet]

'algebra' meaning?

that term is quite vague at the uni level

#book-recommendations message

there are a ton of options and a lot of people have shockingly strong opinions

LA helps going in but it isnt mandatory for all texts, though i'd at least recommend knowing what a determinant of a matrix is

the only thing you "need" is comfort with proofs

but some books will assume you know LA so you need to make sure your choice doesnt

[frosty girder]

be a chad and do artin, he covers a ton of LA as well

based

i was also doing artin, didnt do too much but i enjoyed what i did 😌

not really ig

i mean, i havent done any amount of maths to properly comment on this
but there isnt an order really, u just do what u like while exploring stuff

[dapper root]

Correct order:
Linear algebra -> abstract algebra -> commutative algebra + homological algebra -> algebraic geometry

Not biased btw

[frosty girder]

truly not biased

whats analysis, i dont know what u are talking about

[frosty girder]

wheres k theory?

[quick hornet]

the last 3 entries

i feel like my presence here makes people think k theory is a lot more prominent than it is

which is bizarre given i never talk about it

[frosty girder]

it does make me think that tbh

[dapper root]

Sorry, I don’t encourage people to learn K theory, I think the world has bough depression in it already

[frosty girder]

i mean it just sounds cool

k theory, m theory (ik they arent exactly related, but still)

[quick hornet]

its a letter

[dapper root]

Yeah Nami like, with how little you talk about K theory I’m surprised ppl know you study it

[frosty girder]

still

[quick hornet]

im not gonna be studying it in 2 months

rip academia

[dapper root]

What?

Are you done with it?

[quick hornet]

didnt get any postdocs

[dapper root]

[quick hornet]

i could try again but nah

[dapper root]

Wtf

[quick hornet]

going into industry instead

[dapper root]

I thought ur thesis was big poggers

[quick hornet]

its good but i only applied to really good postdocs

[frosty girder]

how does stuff after PhD work exactly?

[dapper root]

What’s the like lowest you applied to?

[quick hornet]

because i figured, with how competitive AG faculty positions are, i dont wanna bother unless i get a really good one

[dapper root]

Did you not stray out of like… UMich territory?

[quick hornet]

yeah mich was my lowest lmao

[dapper root]

Couldn’t even get a Mich postdoc even tho they have like 1 billion of those named postdocs

[quick hornet]

i only applied for 4

[dapper root]

Rip

[quick hornet]

f

[dapper root]

Now I am worried

But I still have grad appa to worry about

[quick hornet]

i wouldnt be too scared, i think part of it is that my advisor, while very respected, is more a C*/OA guy than purely K theory

[sage python]

What kinda industry jobs are you going for?

[quick hornet]

so wasnt the best connection to the places i applied

[sage python]

K theory but in finance?

[dapper root]

Where did you end up applying? Princeton, Harvard, IAS…?, Mich?

Idk if you apply for IAS postdocs

[quick hornet]

princeton toronto berkeley mich

toronto weird choice i know since im a student here

but eh

[quick hornet]

dunno, havent started looking really

[dapper root]

Does Toronto send graduates to top tier postdocs with any sort of frequency?

Or is it just the rare one that makes it through

[quick hornet]

still have to actually get my doctorate yknow

[quick hornet]

it does

more than any other canada school i believe

[dapper root]

Gotcha

[quick hornet]

logically i couldve applied for more but honestly like

i was already kinda wavering on academia long term anyway

so i decided to just hail mary it

if i get a real good one then go for it

[dapper root]

Man

[quick hornet]

otherwise settle into a comfy tech job or whatever

way less time commitment for more $

[dapper root]

I know I said this before and Buncho ripped into me a bit but

It’s hard to imagine from where I am rn

Not shooting for a job in academia

[quick hornet]

yeah

[frosty girder]

can you still publish papers if felt like it? or do u have to be a prof or something to do those?

[quick hornet]

(of my phd)

[dapper root]

It feels like I’d be sunk cost fallacying it 2 years into a PhD

Let alone after graduating

[quick hornet]

this is a bit slow which might also contribute to not getting a postdoc

though in my defense i skipped a masters

which is abnormal for a canadian

[sage python]

Wait do they care how long you took to get a PhD?

[quick hornet]

i dunno really

maybe?

[sage python]

I thought that was literally irrelevant data

[dapper root]

Yeah if it’s > 3 years you’re out

[quick hornet]

i bring it up as a possibility

idk for sure whether they account for it

[sage python]

Tbh a less ballsy version of that is my angle Namington. I'm prob gonna gun for like, vaguely top schools

[quick hornet]

in theory, no you dont have to be a prof/affiliated with academia, in practice yes

industry people publishing papers is not really a thing

like they could do it, journals wouldnt reject you just for not having an institution

and a few people have

but its very rare

i certainly dont know of any cases in my subfield

[dapper root]

So true

[frosty girder]

oof

[quick hornet]

4-5 years is the standard in places where youre expected to have a master's first

maybe 3

[rancid ivy]

Do you have a book recommendation for an INTRODUCTION to statistics ?

I say introduction because I want to start

[humble bluff]

I thought you asked for a research level book when you Said “INTRODUCTION”

[rancid ivy]

No, mate I'm in middle school and I'm not C.F Gauss.

[grand thistle]

if i were you id do algebra first

cant do that much with stats without some algebra knowledge

[rancid ivy]

Oh I see, thanks !

[grand thistle]

idk much tho

about stats

maybe you could

from what ive seen ap stats needs only algebra 1 and 2 i think

and college stats needs calc/real analysis and LA

but take what i say with a grain of salt i done probably as much stats as u

[rancid ivy]

everything in math is interesting

[gray relic]

Hey can i get arts of problems solving introductory geometry ?

[sudden kindle]

What books can I learn automorphic forms from?

Daniel Bump's book is pretty rough going

@slim nacelle @sage python

[slim nacelle]

Bump is really the book for learning this properly. If you want a more casual exposure you can try https://arxiv.org/abs/1511.04265

You can skip the physics stuff

[sage python]

Goldfeld-Hundley is easier than Bump

[slim nacelle]

Yeah that’s another good recommendation

[sage python]

If you don't need adelic theory there's also Borel

[slim nacelle]

Lmfao

[sudden kindle]

Automorphic Forms on SL2 (R)?

[rancid ivy]

At this moment, I'm studying all the school math program, so 10th, 11th and 12th-grade, when I finish it what should I study first ?

[frosty girder]

depends on what u wanna do

[brittle breach]

Linear algebra?

Maybe number theory

[rancid ivy]

It's a hard question to ask myself.

[rancid ivy]

Why not.

[frosty girder]

if u are in 8th grade, u dont have to worry about that question for now

[rancid ivy]

Number theory is a good idea.

[frosty girder]

do school maths and decide later

[rancid ivy]

I'm in 9th.

[frosty girder]

Oh, still, my point stands

[brittle breach]

You are late to the party man

[frosty girder]

[brittle breach]

Do you know how to prove stuff

[rancid ivy]

I respect your opinion but I refuse to be so slow in the learning because of school.

[rancid ivy]

What kind of stuff.

[frosty girder]

wdym

i dont mean do it with school

[brittle breach]

Have you proven anything before
A math proof

[rancid ivy]

Helped yes.

But I don't know how to prove.

Didn't learn and I think it's complicated to know where to start, don't you think ?

[brittle breach]

Your are studying calc now correct

[frosty girder]

well if u plan to do maths, u gotta do a lot of proofs

[rancid ivy]

I don't understand

[runic hatch]

you could start with a super gentle intro to uni math

[rancid ivy]

I didn't finish my learning of the math school program but elaborate, what do you mean by gentle intro to uni math ?

[runic hatch]

like maybe How to Prove It by Velleman

[frosty girder]

it basically means learning how to do proofs

[runic hatch]

yeah mostly just this

without needing much prior knowledge

[rancid ivy]

Thank you for the book recommendation.

[runic hatch]

learning how to think mathematically is more important than knowing a list of concepts

[rancid ivy]

For example I could prove that a line is asymptotic to a curve of a function.

Well, it's been a while since I've done it, but I could do it before and I will when I'll finish the math program of school study.

[brittle breach]

I was assuming you did or are doing calculus

[brittle breach]

But I agree with ab knowing how to prove stuff is the gateway to real maths

You could use a book/etc on how to prove things

[rancid ivy]

That'll be after finishing the school thing

But yeah good idea thanks

[rancid ivy]

I did, but really simple, just the basics

[brittle breach]

Or linear algebra or analysis and pick it up as you go, some book teaches both proof and an area were to use proofs

[humble bluff]

I recommend starting math with naive and axiomatic set theory

And after that

Everything about the construction of Numbers up to reals

[subtle mango]

what are good calculus-based physics textbooks for undergrad level (mechanics, electromagnetism, etc)

[rain hound]

The best ones to my knowledge are:
John Taylor Classical Mechanics
David Griffiths Electrodynamics
McIntyre Quantum Mechanics
Schroeder Thermodynamics

And of course supplement with Feynman lectures

[subtle mango]

bless thank you

[rain hound]

Yep, happy to help, a bit of a disclaimer tho, that first and last one are a bit pricy

[subtle mango]

unfortunately as to be expected when buying textbooks

[rain hound]

Yeah it’s regrettable, I looked into some other mechanics books options that are cheaper and there’s legit no other option before grad school level, they just suck (other than Feynman lectures ig)

Not quite physics but you will probably also like James Nearing Math Tools for physics, covers basically all the math you need, and absolutely wonderful exposition

And it’s very cheap LaTeX typeset, open source ftw

[subtle mango]

amen

open source ftw

[rain hound]

I’m looking for a good rigorous beginning graduate complex analysis textbook. I am familiar with computational based complex calculus I should perhaps call it thanks to math methods texts, and I have analysis under my belt after working through Tao. So I’d like something that dives into the theory properly and has good exposition.

[brittle breach]

This

[brittle breach]

Check this out

[gray gazelle]

any good advanced python book ?

[rain hound]

The official documentation would be the best I imagine

[gray gazelle]

i already know that

i need something that is a bit higher level

[rain hound]

Thanks I’ll check them out

[rain hound]

Hmm in that case I’d suggest looking for something more specialized than just a generic advanced python book. For whatever you intend to be doing.

[fervent lava]

Normally if someone wants an advanced programming language book, it would be best to look at the spec instead.

[gray gazelle]

spec ?

[fervent lava]

That depends how far your in your current language. Sorry I meant documentation.

[gray gazelle]

I just want to know enough for data science and manim animations

[fervent lava]

If your comfortable using python right now then refer to your docs. If you want book towards data science and the other thing for python then look towards that instead.

[lime sapphire]

what are some good rings first algebra books other than aluffi's

[karmic thorn]

Rotman

Called Advanced Modern Algebra

[lime sapphire]

is it an introductory text? cus thats what im looking for

[runic hatch]

What approximate level are you at

[lime sapphire]

idk much except for basic LA

[karmic thorn]

Should be accessible, yeah

[vernal steeple]

Hii, i would like to ask if anyone has any resource(website, book) on axiomatic set theory proof questions that have answer to them(undergrade level) smtg like this question thankss

[karmic thorn]

Velleman, How to Prove It

[vernal steeple]

Alritee I'll go search it upp, thankss

[frosty girder]

i almost linked #❓how-to-get-help

[prime oak]

recommendations on good intro to NT books?

[brittle breach]

Serre a course in arithmetic

Or Hardy and Wright

[sudden kindle]

I want to read the 1-2-3 of modular forms by Don Zagier

[slim nacelle]

Yeah that’s a good book

[pale scarab]

Do you feel its necessary to work through a seperate math methods book or just learn as you go? It seems most physics textbooks have a review of the math necessary in the book.

[rain hound]

Learning as you go is completely fine. A math methods textbook is the best companion to have for it though because it’ll give you a fair bit more than a physics textbook will as well as exercises for you to practice and develop comfort and finesse computing and seeing concepts. It’s a lot nicer to be learning physics when you’re only wrapping your head around the physics, and math methods texts make that goal much more feasible. I’d suggest reading both at the same time.

[sudden kindle]

i kinda hate Bump's exposition in Automorphic Forms and Representations

[sage python]

@sudden kindle having not read much of Bump, what in particular do you dislike?

[sudden kindle]

its so technical

doesnt emphasize the important things

i feel like im reading a book in techniques in automorphic forms rather than a book that introduces why i should care about them

[sage python]

I see

I'll be honest you'll get similar vibes from Goldfeld-Hundley

It's easier but there's not much motivation iirc

[sudden kindle]

right now im in the section about converse theorems, and i'm like, why the hell do you want converse theorems?

[sage python]

Hmm

[sage python]

Oh this isn't bad. It's like okay modular forms are of the form sum a_n q^n

If I just manufacture the a_n randomly when is it that a modular form? And the answer is when the L functions have the functional equations you expect

[sudden kindle]

okay so your able to get information about modular forms from just their L functions

cool

also I these twisted modular forms were introduced in the exercises from the previous section and i didnt do those so when i got to this ssection and it all of a sudden talks about modular forms twisted by some dirichlet character im like wtf, idk why you care about these either

[sage python]

Oh that's yeah. Honestly I think a book should make a clear delineation of exercises that need to be solved for the sake of continuity

[sudden kindle]

This is very helpful motivation, thanks

[sage python]

🙂

[slender surge]

Hlo

[halcyon hornet]

Any good and Easy to understand Intuitive Elementary Number theory resources please.

[timber garnet]

Kenneth H. Rosen: Elementary number theory
David M. Burton: Elementary Number Theory
J. H. Silverman: A friendly introduction to number theory

[indigo relic]

I want a book that cover the proof of the area under the graph is computed using the primitive because it still didn't make sense to me

[quick hornet]

this is often taken as a definition of area

but there are others

[indigo relic]

but people didn't define it this way randomly, i mean there's a theory behind it

[quick hornet]

see e.g. https://en.wikipedia.org/wiki/Jordan_measure, in which case the proof is available at https://math.stackexchange.com/questions/2787850/jordan-measure-and-riemann-integral/2788075

i do think jordan measure probably matches your intuition here

the idea is that "area" is defined as the "accuracy limit" of an approximation of the shape by rectangles (whose area is just defined as base * height), and then we can see that, for curves f on the plane, this corresponds to integrating the indicator function on the subset {(x, y) | 0 < y < f(x)} of the x-y plane (flipped if f is negative, im leaving out details)

turns out this becomes the "infinitely many thin rectangles" intuition of the riemann integral

and so we have our correspondence, at least where jordan content is well-defined.

the connection to indefinite integration is now just the fundamental theorem of calculus which any text should cover

[indigo relic]

@quick hornet makes sense man thank you !!!

[outer ledge]

what book should i refer for vector space ?

[covert oxide]

Any good books introducing proofs and how to write them?

[compact owl]

an books particularly related to quadratic residues?

[grand thistle]

How to Prove it, Velleman

[foggy relic]

levesque

[halcyon hornet]

?

[subtle mango]

Fundamentals of Number Theory by LeVeque is what invictus meant i assume

[halcyon hornet]

Oh.

[covert oxide]

Thanks, I’ll have a look on it

[brittle breach]

Serre arithmetic has a nice proof
Hardy and wright's is not too bad either

[outer ledge]

any good references for Olympiad maths?

[frosty girder]

try asking out the olympiad server in #old-network

[foggy relic]

AoPS books

[crude iris]

https://rgtdfg.blogspot.com/2022/02/recommendations-feb-22-version.html

[prime oak]

any recs for books as introduction to category theory?

[outer ledge]

Thanks! I'll check it out

[dull bluff]

Any book recommendations for calc 2?

If you can, can you list some that would be more so about practice problems

Thank you so much

[gray gazelle]

https://tutorial.math.lamar.edu/classes/calcII/calcII.aspx

[plucky edge]

Recommendation for books on undergrad probability and stochastic processes?

[sick wigeon]

People i really need help regarding multivariable analysis
I tried reading Munkres analysis on manifolds
It feels incredibly slow and pedantic and i don't understand it at all
And spivak and Rudin are too terse for me
Can someone recommend a good multivariable analysis text?

[marble solar]

Try like Ted Shifrin's Multivariable Calculus

There's also youtube lectures by Shifrin to go along with them

[foggy relic]

This is a pretty niche book, but I like Aluffi's book Chapter 0 (im still working through it)

[odd spade]

it is a good book for understanding introductory category stuff via algebra, i agree

[sick wigeon]

Cool i will try

[marble solar]

Do you need a link to the youtube series?

The first vid has bad video quality

but the second one on is good

[restive falcon]

I've heard good things about riehl

[marsh cedar]

I recomend

da bibel

and one fish two fish

blue fish

black fish

and dat

[timber mesa]

aside from Velleman which was already mentioned, I really like Hammack's Book of Proof. It's freely available at http://www.people.vcu.edu/~rhammack/BookOfProof/

[fervent lava]

Aluffi’s into proof is nice too. http://www.math.hawaii.edu/~pavel/Aluffi_notes.pdf. Not as long as the other mentioned ones.

[foggy relic]

the man literally includes categories in the prelim chapter

[brittle breach]

I had the same experience with Munkres and I found spivak confusing.
I think Shifrin would be too slow as well ( his prove of the inverse function theorem is just a stretch out version of Rudins.
My strategy was/is to use rudin up to inverse/implesit function theorem then switch to an intro manifolds book.

[fluid bay]

Honestly all of the multi variable analysis the average person needs is in the appendix of lee’s ISM

[runic hatch]

Yeah I found the manifolds section for both Munkres/Spivak to be pretty poor honestly

[gray gazelle]

why

[runic hatch]

Maybe it’s just me, but I found it hard to get a good intuition for it just in the books

[grave goblet]

Hi everyone. Physics Final year undergrad here. I am looking for a good book on spin geometry which is accessible to physics students as well. Could someone suggest me such a book?

[mortal ore]

good textbooks for linalg?

[foggy relic]

what level

strang, triel, axler r good

[mortal ore]

I'm going from calc 2 to multivar

Take that as u will

[foggy relic]

do you have experience with proofs

or nah

[mortal ore]

Mmm

I mean I've proven things before

[foggy relic]

then triel should be fine

[mortal ore]

It's probably more complicated than I think tho

Alright

[foggy relic]

its available as a pdf for free online (legally) so look through the 1st chapter, see if you understand

[mortal ore]

Ok

[foggy relic]

if not, try an easier book

[mortal ore]

Thx

[sick wigeon]

So the thing is i learnt the differentiation part of Munkres well... But no matter how hard I try i can't derive the inverse function theorem and implicit function theorem at one go without looking at the text

Those two theorems are intuitive but still the proof is so lengthy to be lost

[sick wigeon]

Shifrins?

I found it.. thanks

[timber mesa]

yeah it's easy to get lost in trying to prove these two theorems

the best/most elegant way is probably by using Banach's fixed point theorem, dunno if Munkres introduces that at any point in the text

[brittle breach]

Was the same for me

[sick wigeon]

No

Munkres wanted to spoonfeed ppl

[timber mesa]

but I remember e.g. Spivak's proof of inverse fn. thm. in CoM didn't assume that and it was pure hell

[brittle breach]

That was when I decided to slug through rudin

[sick wigeon]

I hate Munkres
I hope his topology book is different atleast

[timber mesa]

I hate his topo book lmao

[brittle breach]

I still haven't done the implicit function theorem as yet

[timber mesa]

you'll find it even more spoonfeed-ey than his multivar book