book-recommendations

[quasi sonnet]

the course is multivariable calc but i just read tao to see what it was about

[trail hemlock]

quick question

im reading through munkres analysis on manifolds

the linear algebra review section is genuinley boring me to dead

i may perish

is it alr if i skip the chapter? like the conventions and whatnot will be the same as another LA text (i used lang)

[remote sparrow]

a review section is just that: for review. if you do not need it, at least skim through it to fix notation and skip it. you can refer back to it as necessary

[trail hemlock]

ok perfect

im gonna skip to the metric space and compact space stuff

analysis my beloved 😋

[gray gazelle]

I have LADR as a first approach ,what books should be my next reading guys I need help

[remote sparrow]

maybe hoffman-kunze

[trail hemlock]

ive seen enough. give him Roman

[small perch]

thanks for idea for how to skip chapters

[gray gazelle]

thanks

[distant schooner]

@frigid comet hello ! I hope you are doing good. As you are doing research in the field of semiclassical analysis, I had a question. I would like to do a work group in the field of quantum chaos (e.g dealing with things like quantum unique ergodicity conjecture). Do you know any book dealing with those kinds of topics ? The more geometric oriented, the better !

(this message is also oriented to anyone who know the field obviously, I mentionned him because I know that he is doing research in semiclassical analysis)

[vocal egret]

any1 got books to learn about am-gm for an olympiad?

[timber mesa]

I think "The Art and Craft of Problem Solving" is a good starting point for Olympiad-type problems, and another one I like is "The Cauchy-Schwarz Master Class" -- this one is about inequalities in general

and iirc includes a chapter and maybe more focusing on AM-GM

[vocal egret]

I checked them out, they seems very complete for the basics and essentials

I checked and the constraint questions can optionally be solved using lagrange multipliers, not sure if that's tru tho...

[timber mesa]

probably true, Lagrange multipliers are just a way to solve constrained optimization problems in general

any problem that is like, optimize a function f(x) assuming that g(x)=0, where x is some vector in R^n

and that f, g are C^1

[vocal egret]

It seems to require the basics of real analysis 😦

[timber mesa]

yeah, it's a theorem in multivariable calculus

[vocal egret]

gonna go with AM-GM or Schwarz method instead, seems nice

[timber mesa]

still, if you know derivatives it's not that hard to apply

[vocal egret]

I found the symbols used to be a bit confusing

I gotta revise more

[timber mesa]

I know some problems of this sort can be cheesed with Lagrange multipliers lol

but go with what you're more comfy with ofc

[vocal egret]

I checked and it seems like I need to be more comfy with more complex derivatives than I'm used to. But it feels more straightforward compared to AM-GM

gonna go with lagrange then. Is there usually this kind of topic in Thomas' calculus book?

[timber mesa]

I think not, Thomas is about calculus of functions of one variable

you'll find that in Stewart

[normal crystal]

that's false
they both have multiple editions
but the full versions cover comparable material through multivariable

[vocal egret]

thx for the info

[grim delta]

Any good book for a starter on geometry?

[stuck zephyr]

what geometry?

[grim delta]

basic geometry?

euclidean

[glad rampart]

i liked AoPS's geometry book

[grim delta]

https://artofproblemsolving.com/store/book/intro-geometry

This one?

[stuck zephyr]

there is a free book on openstax.com

[glad rampart]

yes

[grim delta]

I think i'll stick to this one

thank you both

🙂

[compact jolt]

Are there any good books that you would recommend for prepping for Putnam?

[hushed panther]

I'm in my 4th yr of retaking my gcses and i am super unconfident and iv had alotttt of gaps in my knowledge. Does anyone recommend any good books to revise maths gcse uk under the AQA exam board. my exams have been so differnet i did AQA EXEL City of Guilds and now im back to AQA. does anybody recommend anything that could help me?

[golden salmon]

1. do as many problem sets as you can. If a problem is taking more than 15 minutes total, read the answer, understand it, then try again
2. discuss stuff you learn and stuff you are enjoying/not enjoying with peers. try explain stuff to them if they're interested, and summarise for yourself when you do
3. Read the syllabus, regularly check against it to make sure you are making progress. Google suggests this is your syllabus https://www.gov.uk/government/publications/gcse-mathematics-subject-content-and-assessment-objectives

[oblique hatch]

The spec is this
https://filestore.aqa.org.uk/resources/mathematics/specifications/AQA-8300-SP-2015.PDF
The govt document just says what all boards have to test, not necessarily what they do

[final sluice]

what do you guys think of munkres for alg top? (in topology textbook that's reference for point set)

[undone trellis]

hello
can you recommend me good books for calculus 3 ( it covers series, integrals and functions defined by integrals)

[molten gulch]

thomas' calculus

[steel cloud]

How many chapters of Rudin should I do ? And after that what can I do ?

[oblique hatch]

What’s your goals?

[steel cloud]

I don't know how to say that ?

I want knowledge and intuition

I completed the first 5 chapters of rudin, now I am thinking what I do now ?

I want to complete the Riemann integral part

[oblique hatch]

If you’re essentially just reading it for the sake of reading it, then (assuming you mean baby Rudin) first 5 chapters is up to Riemann integration?
If you’re enjoying it, then why not try to finish?

[steel cloud]

And sequence of functions as metric approach

[steel cloud]

Finish up to chapter 11? Someone said that after chapter 8 it is not good

[remote sparrow]

no one ever goes past chapter 8

[marble solar]

The usually is the first 8 or 9 chapters. Chapter 9 is ok. Just focus on getting through Rudin. Once you're through that then you can see what you're interested

[misty wyvern]

In my opinion the first 8 chapters are undergrad analysis content. After that you can just go to Papa Rudin

[steel cloud]

Okay thank you

[steel cloud]

Okay thank you

[static prism]

never got a chance to take complex variables or complex analysis in my undergrad, so now i'm a 2nd year phd student who knows nothing about complex analysis. might jump into the grad sequence this year, but i'd like to at least skim something on complex variables/basic complex analysis so i don't go in completely blind.

anything that potentially touches on complex dynamics would be welcome as well. one thing is i don't really know much topology either.

[hallow oriole]

stein and shakarchi is purportedly canonical for ug ca

[gray jungle]

I like the 2nd half of rudin RCA personally

[deep epoch]

on top of the usual CA books above (i also like Bak and Newman, Freitag and Busam, Brown and Churchill too) , i also have enjoyed skimming through some parts of Needham's book as well as Wegert's book as supplement for some intuition as well

[remote sparrow]

dami has a pinned message for complex analysis

as far as complex dynamics, according to a review for zakeri, it does cover complex dynamics

@sudden kindle

gamelin is one of the more gentle texts

definitely thumbs up

conway is very precise and detailed

marshall has a power-series first approach

bak and newman also has a power-series first approach, but because it's also explicitly designed for undergraduates, it sorta shies away from the geometric and topological aspects compared to marshall

some people dislike a specific expositional choice in stein-shakarchi (the notion of "toy contours"), but it seems people here agree its exercises are good. according to @marble solar there's an exercise that shows toy contours are not a problem

there's definitely a bias to analytic number theory

[static prism]

in stein?

[deep epoch]

yea

[static prism]

might be good for me. i'm interested in number theory

[deep epoch]

Freitag-Busam is also number theory-biased so that might be of some interest too

[static prism]

alright cool. i'm starting with stein-shikarchi for now but i'll check out those other texts. thank you @deep epoch @remote sparrow @hallow oriole @gray jungle

[molten gulch]

Jumping off this slightly, would brown and churchill be appropriate for someone who has completed a course in calculus and is familiar with the notions of complex numbers but not much beyond that?

[remote sparrow]

yes

[sudden kindle]

Zakeri Complex Analysis is the best complex analysis book

[modern sphinx]

My course used Zakeri's book. It's very nice, but has a VERY rapid start; it's clearly aimed at an audience that already has some complex analysis background. I think Cauchy's Integral Formula is very much in play by section 1.4, in the first 30 pages or so. But yeah, it clearly has an eye towards dynamics

(To be a bit more explicit: Zakeri's book is now one of my favorites, and the book I always use as a reference. It's GREAT, though I do wish it had more analytic number theory. But I know some folks in my course who did not have a strong complex analysis background basically floundered and sank.)

[marble solar]

I have a copy you can take a look at

[molten gulch]

well we have a new plan for winter break...maybe :3

[novel hound]

Yep. Churchill and Brown preface: "The classes using
the book have consisted mainly of seniors concentrating in mathematics, engineering,
or one of the physical sciences. Before taking the course, the students have completed at
least a three-term calculus sequence and a first course in ordinary differential equations".

And, the ODE knowledge required is very minimal.

[crimson leaf]

I highly recommend Conways complex analysis book as well it's very good and does not require much than basic undergrad analysis maybe not even that tbh

[molten gulch]

Oh nice, we haven't done anything with ODE's before but this might be nice to get a taste of what CA is like before we go through a more proof based book a-la stein or freitag

bc we've wanted to see what the fuss is all about

[novel hound]

It should be perfect for this purpose. The exercises are also easy, mostly computational. The main theorems and proofs are all there, but it's a very gentle intro.

[serene merlin]

Any recommendations for generating functions? I am currently exploring these from Concrete Mathematics

[remote sparrow]

generatingfunctionology by Herbert Wilf

https://www2.math.upenn.edu/~wilf/DownldGF.html

[quasi sonnet]

what are some recommendations for multivariable?

[limber fern]

Are there some introductory books for mathematical modeling? Maybe even dynamical systems or scientific computing

[azure lark]

The scope of topics you mention is very vast

For basics you might wanna start with Kincaid and Cheney's Numerical Analysis

Then theres Strogatz for Dynamical systems

you might wanna also look at Enns and McGuire's : Computer Algebra Recipes An Advanced Guide to Scientific Modeling

but thats more application based than theoretical

If you are into fluid simulations, then theres Robert Bridson's book which is somewhat on elementary level, and R. J. Leveque for a deeper dive into the same

[upper flint]

hey everyone, I need a recommendation for a single variable calculus textbook, specifically the sort of stuff you would learn in the first semester of an undergraduate course. I'm looking for something that's quite compact and proof light, but rich in examples and exercises. I mostly know the theory but I still need a lot of practice

[keen knoll]

Any good book reccomendations on Lie theory? Preferably under $100

[slate mural]

"Introduction to Lie Algebras and Representation Theory" by James E. Humphreys" its aroudn 50$

its clear too

[keen knoll]

Amazing! I’ll check it out. Thanks!

[slate mural]

its a classic introduction to lie thoery

[slate mural]

yw 😄

[keen knoll]

Have you read it?

[slate mural]

yeah

its like introductory to intermediate

[keen knoll]

Oh ok!

[slate mural]

@keen knoll also, what level are you looking for?

[keen knoll]

I’m only learning about this now. I’m actually a physics-guy. An introductory book would be great

[slate mural]

you a beginner?

[keen knoll]

In Lie theory, yes.

[slate mural]

"Lectures on Lie Groups and Lie Algebras" by Roger Carter is a introductory tho aroudn 40$

i have all those

i love lie thoery

[keen knoll]

There’s certain fields in mathematics that I haven’t covered — one of them being Lie theory.

[slate mural]

ouh i usually feel excited when learning new topics

[slate mural]

you'll love it, trust me

anyways, those are the two options

[keen knoll]

Yup! I’ll check them out 🙂 Thanks again

[slate mural]

yeah dw ping me when you need help w lie thoery or anything in general

[keen knoll]

I hope to ask you some questions regarding Lie theory if I’m stuck on something

[slate mural]

sure i dont mind

[keen knoll]

Nice!

Which level are you at? PhD in math?

Just wondering…

[slate mural]

yeah

but i mostly love learning

so

[keen knoll]

Cool!

Same here

[slate mural]

love that

[vocal egret]

I am so cooked

[lilac venture]

I’ve felt that way too!

[remote sparrow]

hubbard or shifrin

i guess since you've read a good amount of tao, munkres and spivak might also be accessible to you too

you can also look at Advanced Calculus by buck or Advanced Calculus of Several Variables by edwards

[quasi sonnet]

thanks 🙏

[foggy quest]

https://mtaylor.web.unc.edu/notes/lie-groups-and-representation-theory/

[keen knoll]

Beautiful! Appreciate the help

[remote sparrow]

Has anyone here read The Axiom of Choice by Jech? Is it worth reading?

@still panther

[tight patrol]

its nota a book about math but i really liked percy jackson series

[hexed lark]

Any good book recommendations on number theory and combinatorics? Ik its a broad field best way i could specify would be that I need them to prep for hmmt

[vocal egret]

Is Titu Andreescu's Mathematical Olympiad Challenges good? I feel like I'm missing lots of topics cuz I just started learning, so not sure which.

[gray gazelle]

Any book that helps me to improve my problem-solving skills?I usually give up on problems that are harder to me and I want to improve that

[gilded shuttle]

AOPS

[hallow oriole]

I usually give up on problems that are harder to me and I want to improve that
then don't give up on the problems; a new book won't help you on that unless your real issue is attempting problems you don't have the prerequisites or mathematical maturity for

[willow merlin]

if you have to go to desert island which linear algebra book you grab

[abstract copper]

I think linear algebra would be the least of your concerns

[willow merlin]

real analisis maybe?

[remote knoll]

The biggest one, and hope that I can digest paper.

Maybe grab a chemistry book to see if it has any hints about converting cellulose to glucose.

[willow merlin]

no with desert island I meant something like rapa nui or Maldives or bermudas

[remote knoll]

They have internet in those places though

[willow merlin]

which algebra book you recommend for grasping the basics doe

[remote knoll]

I learned linear algebra from lightly edited, and lightly corrected for errors, notes from my professor bound and sold as a textbook for a king's ransom, and I would not recommend using that particular resource.

Probably http://joshua.smcvt.edu/linearalgebra/

[normal crystal]

which one

[foggy quest]

Read one book from beginning to end. I used https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/linalg.pdf chapters 1,2,3, so I know it is good.

[still panther]

on my list, but im getting through big jech atm

[remote knoll]

I don't even remember his name anymore. It was 2002 in Georgia Tech.

[normal crystal]

GT has that Interactive Linear Algebra now
in addition to whatever else they use

[remote knoll]

The book from 2002 from what I remember was bound in a robin egg blue cover, paperback

It was about 250 pages. But that could be off by as much as -50/+100 or so

Long time ago, and I didn't keep the book because it was the worst.

[grim karma]

The theory of everything and the general theory of relativity (didnt read this one but u have it)

[floral oxide]

isn't that physics

[gray gazelle]

switching books will not help it's the commitment to it... maybe change your habit or something, make a strategy, make new ways..

[gray gazelle]

you don't need prerequisites you just need to think hard about the problem but if he really doesn't know things about it like law of.... then i guess he needs to review his prerequisites

[wanton pendant]

What are some books just for amc10/12 and aime

Currently doing volume 2 aops

I can probably score 114+

I usually get like 120ish on past amc10s

I calc error around 1-3 questions and I’m not sure how to not have that happen

Also I’m a little slow

[lapis sundial]

Hm I mean these are major topics in commutative algebra so any good commutative algebra textbook. In particular I like Atiyah-Macdonald, but Eisenbud's book is also very good for this

[vocal egret]

Does "the art and craft of problem solving" complement "problem-solving strategies" well?

[subtle violet]

sounds like a question for @fossil nest

[shut frigate]

guys is there any book introduced topological vector space?

[remote sparrow]

presumably functional analysis textbooks would cover them

@gray jungle

it might also be covered in a text used for a year-long course in graduate real analysis, e.g. folland

[abstract copper]

Not part of axler

Rudin functional analysis, Langs, ...

[tawny crater]

"Concrete mathematics" is nice

Youll also be king (or queen) of summing things after reading that book

[warm nest]

summing as in 1+1=2?

[rain wren]

how deep do you want to go?

the only reference I know is like

gramps rudin

james would prolly recc that but it may or may not be a good recc depending on your goals/background

[remote vortex]

Yeah, I think Rudin's FA is a solid pick (mark the date; I'm recommending Rudin to someone), although ideally you'd have already had some familiarity with normed vector spaces

But also I don't have much experience with the available FA textbooks, since I've learned the subject from materials that were in Polish, and I haven't taught enough of it to develop a broad overview.

Rudin's FA is still a Rudin book, but considering FA is an advanced subject either way, the Rudin style is more reasonable.

[tulip hearth]

Any question practice books on Vector Calculus and such?
(from ground up ofc)

[shadow bay]

Guys what are some good textbooks for trigonometry?

[trail hemlock]

???

[molten gulch]

Idk of any practice books but textbook wise

Thomas
Shifrin
Hubbard and hubbard

All 3 probs have qns for each chapter

[reef escarp]

Does anyone know the pre requisites of artin's algebra?

[molten gulch]

The ability to write proofs

AFAIK familiarity with a bit of linear algebra can be useful but is not req'd

[reef escarp]

only ever done basic analysis proofs

is that enough?

[molten gulch]

Should be fine

I'd also wait for other ppl to chime in a bit

[gray gazelle]

Hey, what would be a good source of supplementary exercises for Martin Isaacs' Algebra, a graduate course? I'm stuck on the chapter about nilpotent/solvable groups, subnormal series etc. Looking for good problems (but less challenging than Isaacs') that I can develop intuition on

I enjoy pretty much everything about this book, if anyone has worked through it, please share some advice

[daring lake]

Yeah, that should be enough. Artin starts with matrices and determinants iirc, so should be fundamental if you have some experience with math rigor.

[rain wren]

blackbeard trying to not make everything sexual challenge (impossible)

[rain wren]

I would think so

if you have any trouble just ask for help her on the server

[tardy cave]

can anyone recommend me a free pdf for linear algebra?

i'm trying to get started with machine leanring

[candid bluff]

Does someone know a really good book on statistics?
Fyi I am doing a masters degree in Financial and Actuarial Mathematics. So I do know some stuff about stochastics and probability theory. The book therefore shouldn't be just about basics

[rain wren]

the first part of hubbard and hubbard is really good

there is some extra multi var stuff in there

but you'll need it for machine learning too so

[tardy cave]

alright thank you very much

[rain wren]

the book is called "linear algebra, vector calculus and differential forms"

[tardy cave]

okay i'll look into it

i just found about lay lay mcdonald

how is it compared to the one you just suggested? if you know

[rain wren]

haven't heard of it tbh

all I can say is that hubbard leans heavily into applications but remains fully rigorous (proof based)

[tardy cave]

i like that type of teaching so i'll consider it, thanks

[molten gulch]

Linear algebra done right by axler

Linear algebra done wrong by treil

Linear algbra by hefferon

[molten gulch]

V. Frequent book here in US unis, very computational

[tardy cave]

thanks mate

the titles are pretty interesting lol

[dapper root]

Linear Algebra done maybe okay idk don’t ask me

[molten gulch]

Lmao

[molten gulch]

Treil's book was a callout on axler afaik

Hence the name

[gray gazelle]

Any good books on convex optimization?

[stable flicker]

I'd read this if you write it

[stable flicker]

just use Nemirovski's stuff? Quite available online.
If you want more math the springer stuff should work

Can't remember the name off the top of my head

Ok found them. For analysis I recommend anything by Hiriart-Urruty, or the one by Bauschke

[tardy cave]

lmaoo

[rain wren]

boyd is really really good

pretty much a standard reference kekw

it's also literally called "convex optimizaiton"

[stable flicker]

Intro yes. Deeper no

[rain wren]

that's what people are usually here for so

¯_(ツ)_/¯

[molten gulch]

What'd you say is a deeper book on convex

[stable flicker]

..

There's also even more mathy stuff, those would focus or go around Milman

I'm not remotely into math so I have no opinions on those books

[gray gazelle]

What books would you recommend for going through the history of mathematics alongside looking at the actual mathematics itself

[timber mesa]

Stillwell's Mathematics and its history, and for a slightly more vintage rec Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov and Lavrent'ev

[fossil nest]

stillwell is an amazing expositor

[remote sparrow]

#book-recommendations message

#book-recommendations message

[crude skiff]

Are their any pdfs online you'd recommend reading for a person starting to get into maths

[vital bane]

by Chmonkey™️

[molten gulch]

what subjects are you/will you be studying

[crude skiff]

Not sure I just wanna have a well rounded view on mathematics icl

But i am interested in computer science

so perhaps linear algebra

[molten gulch]

Proofs, number theory, graph theory, combinatorics, linear algebra, basic analysis, theory of computation

[crude skiff]

Ye

[tender river]

http://web.archive.org/web/20190421073943/www.math.hawaii.edu/~pavel/Aluffi_notes.pdf

[crude skiff]

thanks 🙂

[gray gazelle]

Thanks for the optimization recommendations. One more though: any recommendations for functional analysis?

[molten gulch]

Conway, Brezis, Rudin, Stein, Kreyszig

All the FA books I know I've seen mentioned in this chat before

[finite crane]

Brezis is barely a functional analysis book
it doesn't even teach you about distributions

conway is decent

[marble solar]

I'd say Stein isn't really a functional analysis book

[remote sparrow]

what's your favorite functional analysis textbook

[finite crane]

it's a balancing act between needs and time

if you could read all of Yoshida you would be a god

but usually people just need the basics and the specialized stuff can be learned later, so Conway is okay

if you allow series, well Barry Simon

but then that is truly overkill

[marble solar]

I've heard great things about Peter Lax' book

But haven't taken functional

[finite crane]

some special topics like sectorial operators are actually quite useful for PDEs, and not a lot of functional analysis books touch them

[rose raven]

https://link.springer.com/book/10.1007/978-3-662-03278-7

Did any one read this?

[wraith sandal]

book for first intro to algebra?

im thinking of using hersteins for group theory but im not sure

[marble solar]

A book of abstract algebra by pinter is good

Although casual

[wraith sandal]

thanks im going to check it out

[cold tusk]

What’s the math prerequisite for someone wanting to read “The Art Of Computer Programming”?

[vocal egret]

any1 have a good resource material for fixed point and moving point? This is the first time I see this kind of topic

[livid lintel]

https://www.reddit.com/r/math/comments/18t5xhq/how_can_i_best_prepare_to_read_knuths_the_art_of/ This might help

[mystic orbit]

what

brezis is definitely a functional analysis book

distributions aren't what I would call strictly functional analysis territory either nor super necessary for an introduction

[mystic orbit]

brezis is really good and does a lot of convex analysis stuff

[heady ember]

Hi Dar3

[mystic orbit]

which isn't super relevant to convex optimization but it is super important for calculus of variations

if you're into that

[finite crane]

The opposite. Distributions are crucial foundations for PDEs and Schwartz kernel theorem and microlocal analysis (wavefront set) and harmonic analysis (Fourier on tempered distributions)

its TVS topology is purely a crowning achievement of functional analysis. The study of TVS is func analysis. Schwartz literally got the Fields medal for that.

Any func analysis book that doesn't teach distributions is like a topology book that doesn't teach compactness and Tychonoff

[gray gazelle]

Where do I get Roman's advanced linear algebra in pdf/dujv that isn't typeset like ass

Anyone got actual scan of the second edition?

[finite crane]

Maybe be careful with the rules

[gray gazelle]

Okay

[lusty elk]

I've got the third edition

can DM if u want :)

[gray jungle]

Lax is incredible, another great read is taos blog posts in epsilon of room

[remote sparrow]

i don't think roman had good diagram-making skills

i'm pretty sure he made them in microsoft word as far as i can tell from my copy

[lusty elk]

yeah that's true...

[fossil nest]

now that’s what we call an instant turn off

[signal mountain]

looking at third edition it doesnt seem too bad tbf

or maybe i just didnt look hard enough haha

[mystic orbit]

well, first off, functional analysis isn't merely a tool box for pders to use, second off, not even evans does distribution stuff, a book written specifically to treat introductory pde theory

I think missing out on introducing distrubution theory barely disqualifies a book from being a functional analysis book

nor from being a good book for that matter

[finite crane]

sure if you believe in that yardstick
I went to a math camp in undergrad for fluids and even physicists were confidently talking about differentiating non-continuous functions with distributions and I had to ask them what it meant

[mystic orbit]

like, I'm not saying distributions stuff isn't important, I'm saying that brezis not having distributions in doesn't make it a bad book 😭

I personally love brezis

[finite crane]

mildly embarrassing but that was the first time I even heard of distributions

[mystic orbit]

prolly my favourite math book thus far

[gray jungle]

I mean i think there is level to functional analysis since its a big subject for there to be a "FA book"

brezis is intro FA, rudin is 2nd read FA, other advanced references exist

I agree that distribution theory should be included, but for what it does, its pretty good

I'd even consider epsilon of room to be a FA book

just depends on how you define it

for me functional analysis starts with normed and hilbert spaces

But i personally prefare distribution theory in its own book, allows to showcase more PDE applications rather than just present this abstract theory on its own

[finite crane]

I read grandpa rudin
it has zero motivation behind its definition of topology of distributions
I think Conway does a more illuminating job since he clarifies a bit about the inductive limit nature of it

[remote vortex]

Well yeah, Rudin doesn't really do "motivation"

[finite crane]

the more that time passes and the more I see how others try to explain it I realize Rudin just does the bare minimum job of explaining anything

[remote vortex]

If that.

I maintain that Rudin's books are best seen as reference material for people who already broadly know what's going on and why.

(and that they are excellent when viewed in this light)

[finite crane]

I did fine with Rudin via trying to prove everything myself and from that I picked up some of the intuition but Conway would probably have shortened that trip

[gray jungle]

Yeah i think rudin is just a pleasant read if you have the motivation and insight going in. (graduate book meme)

Granpa rudin is one of my favorite references for tools i need from abstract FA, chapters 1-4 and 10-11-12-13 are really well written in terms of just the math imo

[finite crane]

it's certainly concise for reference

[cold tusk]

Hows polyas "how to solve it" book? Generally highly regarded or?

[near jewel]

Are there any other publisher than Springer that does science (math, physics, computer science, etc.)?

[molten gulch]

oxford, cambridge

[gray gazelle]

Wiley

[near jewel]

[buoyant halo]

What a book road map for pdes research

[sudden kindle]

Id really like to learn complex analysis in several variables. Does anyone have any book recommendations?

[hallow oriole]

im also interested in this

[gentle arrow]

@finite crane is there a quick and dirty book for multivar analysis that you know

i need it for first part of evans

[remote sparrow]

maybe spivak calc on manifolds

[finite crane]

honestly I picked up the formalism from learning diff geo. In practice Stokes theorem is mainly for integration by parts

[gentle arrow]

so should i read uhh

something like bott&tu?

[finite crane]

$$ \int_M \partial_i T^{ij} = \int_{\partial M} n_i T^{ij$$

[hasty eagle]

Delerik_taylorpilled
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[finite crane]

that's basically Stokes' theorem on tensors written in abstract index notation. easily extends to tensors with more index slots

n is outwards normal vector field on the boundary

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

[gentle arrow]

so just this

[finite crane]

to be honest with you before I learned rigorous diff geo I just picked up quick and dirty diff geo formalism including abstract index notation from Robert Wald's "General relativity"
That's a book for physicists. But that's ok since we just care for the formalism

you just need to know how to do integration by parts

a worked out example is $$ \int_M f \mathrm{div} u= \int_M f \nabla_i u^i = \int_{\partial M} f n_i u^i - \int_{M} (\nabla_i f) u^i = \int_{\partial M} f n \cdot u - \int_{M} (\nabla f) \cdot u $$

[hasty eagle]

Delerik_taylorpilled

[finite crane]

where f is scalar field and u is vector field

evans basically does a lot of things that really come from diff geo thinking, like partition of unity, coordinate chart, and Stokes theorem / integration by parts

I think you will have a more comfortable time with Evans after you know Stokes theorem / integration by parts in diff geo, and that specific part doesn't require a lot of diff geo machinery

@gentle arrow I think you can read Spivak calculus on manifolds as suggested above for the math bits (it will teach you basic diff geo along the way)
for practical calculations you can pick up abstract index notation from Wald later. it really simplifies vector calculus and integration by parts

well Evans just works on simple flat domain so you won't even need most of the power of the abstract index notation. it's just something that working PDE analysts know and use

[gray gazelle]

I have 11 months to study precalculus until I go to uni. I am considering 3 books - Openstax, stewart or blitzer.

Any suggestion? My college algebra is okaish, know some basic trig on the right triangle as well. Looking for an “easy” book to self study.

Also, these books normally only have solutions to odd numbered exercises. Will I be missing too much if I only do the odd exercises?

[hallow oriole]

you can just do khanacademy for precalc

i will say - the concepts of calculus are not difficult

the main barrier to people doing well in calc is lack of good algebra skills

[gray gazelle]

I have done a few khan academy courses and I prefer a textbook.

I kind of lose my focus a lot when watching videos and I feel that khan academy exercises are a bit superficial most of the times

[remote sparrow]

if you are thinking of buying stewart, you don't have to buy the newest edition

[gray gazelle]

When I used khan academy for algebra, whenever I grabbed some exam exercises, the gap in difficulty was too big imo

[remote sparrow]

old editions have basically the same content as the newest edition, but are often much cheaper

you can also ask for your school to lend you one of their precalculus textbooks

that's what my mom did for me

she had me study ahead over summers

[gray gazelle]

I am from Portugal, we dont really have precalculus here

We have yearly textbooks

Grade 10, 11, 12

[remote sparrow]

but have you covered algebra and trig? usually precalculus goes over algebra and trig again, plus they start talking about functions

[gray gazelle]

I have covered functions, missing exponential and log functions

Know right triangle trig

Only

Since I have almost 1 year, I will prob just go through a pre calc book

[remote sparrow]

you can use whatever is cheapest for you

[buoyant halo]

anyeone familiar with Olver's PDEs?

https://www.chegg.com/homework-help/introduction-to-partial-differential-equations-0th-edition-solutions-9783319020983

I found this on Chegg

is chegg okay for higher math,

or is it AI generated garbage

[hollow peak]

I think I used it for studying Lie's method of symmetries in PDE?

It was really good for that topic

I might be thinking of a different book

[rapid sigil]

Does anyone know of any useful resources for metric spaces

[foggy quest]

https://link.springer.com/book/10.1007/978-981-19-7284-3 and https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/anal1v.pdf

[remote sparrow]

#book-recommendations message

[wheat trout]

Hi all. This semester it is my first time TAing a precalculus course targeted at nonmath major freshmen, from social science, biology, etc. One student asked me where he could find more real-life examples other than from the textbook for concepts like polynomial, power and logarithmic functions. I checked Khan academy and found out that they focus more on math. Where could I find more real-life examples and applications? Thanks in advance.

The course itself is a remedial algebra course.

I do not want to make up some examples using random numbers as I assume real numbers are somehow more convincing.

[ashen ruin]

I'm looking for a geo book, i wanna study the affine geo and euclidienne geo also euclidienne plane and it would be better if it was in English

[shadow bay]

Trigonometry by Israel Gelfand and Mark Saul
Precalculus by James Stewart, Lothar Redlin and Saleem Watson
Trigonometry by GB Thomas and R L Finney
Advanced Trigonometry by CV Durrell and A Robson
Schaum’s outline of trigonometry by Robert E Moyer and Frank Ayres

or SL Loney?

vote please, i want to learn trigonometry completely...

[open flint]

I am in 11th and SL Loney is extremely popular here
like i havent heard about the other names you have mentioned
but ik a lot of guys who do SL Loney along with the course

[pale scarab]

If it's your first time learning it I think gelfands book is solid. All his books are top notch imo.

[mystic orbit]

I got the perfect reference for you bud

Multivariable Mathematics - Linear Algebra, Multivariable Calculus, and Manifolds

by shinfrin

altho, to be completely honest, you should just blackbox the result and work with it a bunch

it's essentially FTC

and even the proof would boild down to just that + fubini

stokes is important because of its applications, its proof isn't particularly illuminating

I made the mistake last year of trying to understand it fully before tackling evans

obvioulsy you can come back to it later

[vital bane]

Hell yea

Shiffrin da goat

[rain wren]

is that the same dude?

[vital bane]

Ted Shiffrin

[rain wren]

coz my book definitely says shinfrin and I've heard of shiffrin before

[vital bane]

Lmao what

[vital bane]

my bad it's only one f

you do mean this book right?

[rain wren]

nah, theodore

[rain wren]

yes

[vital bane]

mfw shinfrin

[vital bane]

Ted is a common abbreviation of Theodore

@gentle arrow but yea Shifrin's book is based, he also has a lecture series following this book on youtube

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

these zoomers think cameras in 2014 were a blurry mess

[timber mesa]

blud talking about 2014 like its ancient history

[rain wren]

is it not?

I hadn't gained consciousness yet

[open merlin]

there should be an option to filter out everyone <25yo so i stop feeling old

maybe they should add this option to the rest of the internet/ real world

[stone lance]

Hi, I am looking for an avanced group theory book. I am mainly interested in finite groups and their structures or generaly computational group theory

[near jewel]

When reading science textbooks, is it normal/average to read 10mins per page？

[slender wasp]

According to Axler "If you zip through a page in less than an hour, you are probably going too fast". But obviously this is a function of what you are reading and how much you know about it. Review or simple stuff will go fast. Advanced terse stuff can go as slow as you need to be...

[gray gazelle]

good book for vectors & 3-d geometry for grade 12?

[molten gulch]

the first 1-2 chapters of any linear algebra textbook should work fine

[tribal crow]

not any, but many

I don’t think e.g. Axler talks much about that stuff, if any at all

[molten gulch]

oh yeah fair

[remote sparrow]

blud betraying hubbard

also i'm not sure if shifrin and quick belong together

he's already done a good amount of schroeder and rudin

[stark turret]

i’m reading milne’s “group theory” right now and i think it’s pretty good

[mystic orbit]

I mean, I literally used it lmfao

You just skip to chapter 7 (?)

And cat bread has the background to follow along

[remote sparrow]

@slender cargo how are you finding Advanced Calculus of Several Variables by edwards?

[slender cargo]

uh

I'm not sure how to feel about it atm

Some of the material on, say, manifolds, feels like it's not a good first exposure to that stuff. But then, I don't know how to compare to other books. I've been keeping up with it somewhat fine, but I've been investing a lot of time on the course material

We are going to cover the Implicit and Inverse Function Theorems soon, so I am looking forward to that.

(it's at least a relatively cheap book, and I know Michael Spivak recommended it alongside Shifrin's book)

[remote sparrow]

i can loan you my copies of hubbard and buck next week if you're interested. i don't have shifrin, so you'll have to look at a pdf online

[slender cargo]

I'll consider that, thanks!

I'm probably fine continuing with just this book

[remote sparrow]

average #book-recommendations math book pathway

[molten gulch]

sour what the fuck

I love this

it's so amazingly cursed

[tender river]

@fossil arch theres just the right book for you

[gray gazelle]

Hello! I am studying telecomunications engineering first year and I want to learn more about complex numbers and complex analysis (We have only seen them superficially without mathematical demonstrations). What books do you recommend? (If they are in Spanish, even better)

[ashen blade]

Hi guys, im trying to get deeper in math on my own, i really want to read a book that talks about calculus. Any good suggestions that are for beginners too?

[open merlin]

Might be completely wrong, but maybe Calculus With Applications by Lax & Terrell?
Haven't read it myself but I've been looking at the multivariable one they've written, to brush up on that

3blue1brown's series of videos on calculus is pretty good

[ashen blade]

why math books are so expensive😭

[open merlin]

there was like a 40% autumn discount on until.... 2 days ago, woops

[ashen blade]

going to cry myself to sleep thinking about the price of that book...

[remote sparrow]

you can look at stewart. old editions can be super cheap

[ashen blade]

Thanks!

wow, youre right. old editions are super cheap!

[pale scarab]

https://openstax.org/subjects/math

Has free textbooks that are solid especially for a first time book.

[remote sparrow]

@mystic orbit since you used both hubbard and shifrin, which do you ultimately prefer

#discussion message

@narrow fiber what do you suggest for a first course in linalg and vector calc?

@novel iris have you ever looked at shifrin?

[drowsy thicket]

Woah Shifrin!

He used to talk in MSE's chat a lot (probably still does)

[remote sparrow]

https://www.reddit.com/r/math/comments/ri9ly9/are_there_still_math_publishers_that_care_about/

[marble solar]

My copy of Marshall's Complex Analysis is beautifully printed

Stein and Shakarchi never had a good print, but all of Spivak's books are printed well

[flat ermine]

Anybody have any good recs for books that cover Combinatorics and Graph Theory really well, with optionally some good Game Theory?

[trail hemlock]

THE ENGINEERING ONE HELP

[remote sparrow]

i think spivak's printing quality is worse now according to an amazon reviewer

his publishing company was absorbed by hindustan books

[marble solar]

Oh that is unfortunate

[trail hemlock]

is that the same people that print tao's analysis books?

[remote sparrow]

both springer and hindustan books sell tao's books

[trail hemlock]

ugg i cant attach imahes, but "Hindustan Book Agency" is hte one I have

print quality is ehh

[remote sparrow]

but it was cheap right?

[trail hemlock]

oh yeah

[gray gazelle]

wtf

[gray gazelle]

is fomin’s book on calculus of variations too hard with some with basic diff eq and multivariable calculus knowledge do you need analysis for the 1st two chapters and the Euler Lagrange equation

[remote sparrow]

you unequivocally need analysis

[gray gazelle]

fck

so like my understanding is that if u don’t have analysis u won’t be understanding variational calculus at depth but what if u want a basic idea where do you from there

analysis or linear algebra

[remote sparrow]

real analysis

[gray gazelle]

so is it sort of counter intuitive to study calculus of variations without analysis but what if you want to focus on Euler Lagrange for a model

for a physical system

liek maybe a two body problem or pendulum

something like that

I think Taylor mechanics will save me

[remote sparrow]

you can look at Calculus of Variations with Applications to Physics & Engineering by weinstock if you like

it's a less rigorous take

still, i'd recommend studying some real analysis beforehand

[novel hound]

probably a maths for physics type book like Boas, Arfken or the one Sour mentions above.

[vital bane]

Lmfao I'm saving this

[trail hemlock]

its pin worthy

[tribal crow]

LOL

[vital bane]

Visual Complex Analysis by Tristan Needham

[hallow oriole]

for a while my answer has been to somehow legally acquire the ebook after which it is legal to use a book printing and binding service to fulfill your needs

[gray gazelle]

I mean I’m just looking for a project for a intro ODE class so it doesn’t have to be crazy

not at this level

[vital bane]

I mean if you wanted a completely mathematically rigorous approach to calculus of variations doesn't one need functional analysis?

[gray gazelle]

im in my first yr at uni with minimal knowledge so i dont expect it to be completely rigorous with the little time i have

to do the project it’s just gonna be on using ODEs for modeling

i can probably consider more rigorous approaches after this class and when i finally study real analysis in next yr

im scared i made my prof overthink it by even mentioning it cuz i approached him for the project but i want to focus on its application i.e. in lagrangian mechanics

[vital bane]

oh yea i wasn't talking about rigorous approach in relation to your project

[gray gazelle]

not the rigorous theory i have

[vital bane]

I was about to mention this

[gray gazelle]

it has *!

ya someone in the physics and math department at my uni recommended it

to focus on chapter 7-8

to model keplers laws and problem using lagrangian mechanics

[vital bane]

you mean chapter 6 and 7

[vital bane]

oh okay never mind then

6 is variational calc, 7 is lagrangian mech, 8 is orbital mech I think

[gray gazelle]

just models

he told me not to worry too much about the theory at this level

he made me a latex doc with the basic ideas without and the proofs

like the action the lagrangian

the variations principle

[vital bane]

If you know newtonian mechanics and have worked with kinetic and potential energies and conservation of energy you shouldn't have too much problem with the theory part of it

[gray gazelle]

but my prof could possibly introduce variational calc to me at a very basic level probably not for the project but for my interest when i study it in lot depth in the future

he said he has grad textbooks but he said I could just do the beginning

[gray gazelle]

ya i can catch up quickly

[vital bane]

good luck with the project mate

[gray gazelle]

i looked through the Taylor chapters they don’t look insane to me and I know partial derivatives

[gray gazelle]

thanks

u study ohysics ?

[vital bane]

I study physics and mathematics, but recently I've paused my physics studying to focus on master's program entrance exams

[vital bane]

make sure you know the multivariable chain rule as well

[gray gazelle]

oh ya I need to review that my stupid multivar calc prof basically skipped it cuz he just wanted to focus sm on interpreting derivatives

i have to self study anyways cuz he sucks

[vital bane]

khan academy is pretty good for multivar calc

[gray gazelle]

grant Sanderson did the series right

[vital bane]

https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/multivariable-chain-rule/v/multivariable-chain-rule

[gray gazelle]

im using Stewart as well

[vital bane]

yup

but also Sal Khan did a few videos

[gray gazelle]

oh nice

also prof Leonard but his stuff is long as hell

[vital bane]

along with this I would also recommend learning about the Total Derivative (i.e basically the Jacobian) https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/jacobian/v/jacobian-prerequisite-knowledge it's useful when doing lagrangian stuff, or anything relating to multivariable function composition

[gray gazelle]

Okii thank you

OH YEAH

[remote sparrow]

gelfand and fomin is an older book

https://www.reddit.com/r/math/s/edR6OQLwlR

[livid lintel]

People really are sleeping on iPads, imagine a textbook but it's just 10,000+ textbooks condensed in a lightweight device that you can carry everywhere, scribble things on it with redo, undo, highlight and even crop a question to do in a new page. It's just so convenient.

Not to mention the instantaneous jump between pages and multi-tab stuff for reading textbooks and its supplementary materials at the same time.

For me iPad has goodnotes which is a huge game-changer

[remote sparrow]

i was considering getting an e-ink tablet at one point

i don't take notes

[livid lintel]

and the Apple pen thingie is really good as well

I see

[vital bane]

you can lasso all the cows running across the screen

[livid lintel]

I see

[vital bane]

I guess I should get a samsung tablet

[livid lintel]

For me I just feel like it's smoother, the lines are more connected and it's more intuitive with how hard I press.

I have, from my friend's tablet but It's been like 3 weeks.

I like the apple pencil because it feels like pen-ish, like dragging smooth strokes is really easy with apple pencil.

I don't really know the edition or anything like that but it comes with my iPad

I think I got scammed 😭 In my country it's like 700 dollars

I'm currently living in Thailand

I see

[toxic willow]

I wonder whether Spivak Calculus will be reprinted. It's hard to find a new book😭

[remote sparrow]

it's still being sold?

it's just the binding isn't as high quality as when spivak was still alive

[toxic willow]

I can find used one on amazon and anabook

[remote sparrow]

i'd recommend buying used for sure

even if the copy is somewhat beat up

i don't buy "acceptable" quality books

just good and up

[trail hemlock]

my copy of spivak's calc is so bad

[toxic willow]

The edges of Spivak Calculus got damaged during international delivery🥺

[remote sparrow]

what happened

[trail hemlock]

the printing is like

a calm piece of dogwater

[remote sparrow]

yeah that can happen

[trail hemlock]

i cant send a pic cuz apparently us peasants dont hv image perms

[remote sparrow]

you need the "Active" or greater role

or emeritus

https://tenor.com/view/discord-no-image-perms-image-perms-image-perm-flex-gif-25321823

[toxic willow]

Maybe a link of image?

[trail hemlock]

yeah i had active before. im basically a romanov if u think abt it

[remote sparrow]

just turn off perma-studying for one sec

and send in #chill

[trail hemlock]

turn off perm study?

its on for a year i fear

[remote sparrow]

idk upload to imgur

you can still send links here

[trail hemlock]

i dont care enough tbh

[trail hemlock]

check #calculus

[novel hound]

The biggest annoyance I have with pdfs is if I need to refer to a previous theorem or chapter then I have to scroll around. And, with e-ink it would be even slower. On comp, I can open same pdf on two different browsers so I can keep one on the current chapter and move around in the other one. But, I wonder how ppl deal with this esp on tablets.

[tribal crow]

I just open the same pdf in multiple tabs

sometimes I have 5 tabs for the same pdf

[tribal crow]

I mean that's basically all you can do

[novel hound]

it's possible to do in ipad/android tablets? sorry I haven't used tablets!

[tribal crow]

I usually have one "primary" tab for wherever I am in a chapter, or whatever problem I'm working on, and then my other tabs are just there to scroll around

[tribal crow]

ah, I was talking about computers

I'm not sure about mobile

on mobile that seems super annoying to deal with

[novel hound]

ok yeah that I do anyway. I use different browsers, I could use different tabs I guess... not much different. yeah on mobile is what I was asking how people deal with this.

[tribal crow]

in that case, I'll let someone else answer

[novel hound]

I edited tabs to tablets 😛 sorry for the confusion!

[livid lintel]

For me it's just keeping a tab for normal reading and another tab for navigation, this is especially easier when the pdf you're reading has hyperlinks

[umbral field]

if you use a browser for pdf viewing there's nothing stopping you from opening the same file in multiple tabs just like you can have multiple tabs of a website (this applies both to computer and mobile)

[livid lintel]

That's what I basically do on an iPad

[novel hound]

so the default pdf app in ipad allows you to open the same pdf multiple times in different tabs and it is fairly convenient to switch around?

[novel hound]

ah ok I guess I could do the same thing in tablets, hmm wonder why I didn't think about it 😂

[brave burrow]

Yeah. You can even do split screen in your browser

One for reading and one for scrolling stuff

[livid lintel]

No, but you can open multiple instances of apps in an iPad

I also use goodnotes which allows opening many tabs simultaneously

[hallow oriole]

there r pdf readers that let you mark spaces to come back to

fe sumatrapdf will let you save pages of a book to favorites, add searchable annotations, etc etc

[gray gazelle]

Thank you!

[bold prism]

books on linalg, real analysis and number theory that are easy to learn from?

[vital bane]

You can't beat Understanding Analysis by Stephen Abbott when it comes to being easy to learn from

for Linear Algebra I would recommend Fridberg Insel and Spence

[bold prism]

can you provide a link to these?

thank you!

[vital bane]

and for number theory... I do know a really good book but I don't really have a book that's easy to learn from

[vital bane]

Link to download?

that's illegal yk

[bold prism]

yeah or a amazon one

[bold prism]

ill give it try

[timber mesa]

we can't allow direct links to pirated content -- #rules

but honestly libgen has everything

[vital bane]

yea I'm not gonna tell you to go to libgen, type in the name of the book and then click download

because I'm a good citizen

[vital bane]

An Introduction to the Theory of Numbers by Niven, Zuckerman and Montgomery, it's a great book but I would recommend first finishing real analysis before you start this book as it requires mathematical maturity

[bold prism]

tyyyyy tehe

[bold prism]

wait real quick, whats the best order to learn real analysis, num theory and lin alg

anyones input would be appreciated

[vital bane]

real and lin alg you can do either one first it doesn't matter, neither of them are a pre-req for each other

you can even do them simultaneously

[bold prism]

oooo i might

[vital bane]

for number theory, it also doesn't matter but it depends on the book

Like the book I suggested starts from the very basics but assumes you've already seen pure math and proofs before

but I'm sure you can find a good elementary number theory book that a beginner can use to learn

honestly number theory is the most unintuitive field of math for me 😵‍💫

[bold prism]

wait, pure math??? im only a first year uni student

[vital bane]

But I will conquer it in time

[bold prism]

what are easy to learn proofs and pure math books before i attempt the core stuff

[vital bane]

Understanding Analysis by Stephen Abbott

that's the book I learnt proofs from

it teaches you how to write proofs along with teaching you analysis

[bold prism]

perfect.

[vital bane]

pedagogical masterpiece

[timber mesa]

one I like a lot that's also free is Hammack's Book of Proof https://www.people.vcu.edu/~rhammack/BookOfProof/

it's where I first learnt about math proofs and just mathematical thinking in general

[bold prism]

ill give it a read too

[timber mesa]

follows a "proofs course" type approach by teaching you set theory, logic and combinatorics first

and then showing you how those are applied in reasoning about e.g. basic number theory or calc proofs

[bold prism]

Ooooo

wait

https://www.simonmarais.org/uploads/8/2/3/5/82358688/smmc2023_paper_a.pdf

would u say this contains num theory

lin alg and real analysis?

[vital bane]

it certainly does contain real analysis and set theory

if you're looking to prepare for competition math, then you should pick up some math olympiad books

they have a lot of tricks and stuff that's useful for math competitions

[bold prism]

can u recommend me some please

easy to read ones

[frosty dust]

Challenge and Thrill of Pre-College Mathematics by Krishnamurthy and Pranesachar

[bold prism]

thank u

[formal parcel]

I have 0 knowledge of set theory and want to enter with elementary set theory. Any good book recommendations?

Also off topic but any good linear algebra book reccomendations.

[tender river]

try endertons elements of set theory

[abstract trellis]

Goldrei dereks book on set theory

[celest estuary]

Review on
Functional Analysis, Sobolev Spaces, and Calculus of Variations by p pedregal??

Anyone

[last pond]

read the 1 million digits of pi

[hollow shore]

do you guys know of any course pages following Burton's ENT (7th ed) text?

[frosty dust]

Trust me brother, I have tried to find the same when I was studying NT from that book and could not find any.

[hollow shore]

I found this https://people.math.wisc.edu/~nboston/580.html

6th ed tho

altho i think the problems are mostly the same

[frosty dust]

Why don't you try George Andrews' book?
Or, Hardy's Theory of Numbers?

[hollow shore]

our class follows this one

[frosty dust]

I see.

[hollow shore]

are these more rigorous?

[frosty dust]

Yep

People do say that Hardy's book is a bit on the primitive side. Though I never felt that way.

[frosty dust]

You could also check out Challenge and Thrill of Pre-College Mathematics

[frosty dust]

It's NT section is pretty solid

[frosty dust]

Basically Olympiad lvl

[hollow shore]

my CMI/ISI prep trauma would come back 😭

[frosty dust]

Tell me about it

Which college you at bro?

[hollow shore]

well i am almost done with my ug

[frosty dust]

I see.

You wouldn't happen to be in DU by any chance would you?

[hollow shore]

no

[frosty dust]

I see

[hollow shore]

I wish

DU would have been great

[frosty dust]

BTW, I should call you bhaiya

I am a first year

[hollow shore]

[frosty dust]

What's that mate?

[molten gulch]

I almost responded to this in urdu

[frosty dust]

I said 'Bhaiya' not 'Onii-chan'

[hollow shore]

chill

[molten gulch]

🤦‍♀️

[hollow shore]

which college?

[frosty dust]

Sri Guru Tegh Bahadur Khalsa College, University of Delhi (North Campus)

[hollow shore]

nice

you are in north

[frosty dust]

Yup

[hollow shore]

good luck man

you can do better

[frosty dust]

Thank you brother

[hollow shore]

btw how is st stephen's for math?

[frosty dust]

I suppose 'tis the Best

[frosty dust]

Seeing that the Cut-off did not come down in the seat allocation rounds.

[frosty dust]

What do ya wanna do after UG?

[hollow shore]

I am unsure

[frosty dust]

Sama here brother

[hollow shore]

Along the lines of Math/CS

[frosty dust]

Along the lines of Mathematics for me too

[frosty dust]

Prolly focus on pure mathematics, if I do decide to go for Masters

[hollow shore]

I have heard that the course pressure in DU is not that much

[frosty dust]

I cannot say much on that subject as it has not been that long for me.

[frosty dust]

I did speak to the seniors though and they did gave me the impression that they were pretty chill and not to worried about their course.
And the senior I spoke to had a CGPA of 8.6

[frosty dust]

So, it's a reliable source of info.

[hollow shore]

I mean, compared to the flagship research institutes I suppose it is very frugal. If one is self-motivated, they can acheive a lot by self studying.

[frosty dust]

True enough

DU is well connected, though
My college will be hosting the International Conference of Mathematical Sciences and their Applications 2024

[hollow shore]

Can I add you?

I don't know many people in DU

[frosty dust]

Yup sure thing bro

[frosty dust]

Or should I really call you Onii-chan?

[hollow shore]

💀

James is fine

[frosty dust]

Right then.
You in Delhi James?

[hollow shore]

nah

[frosty dust]

I see

[hollow shore]

I gtg. Mid term tomorrow.

bye

[frosty dust]

Holy smokes.
Alright then bye.

[gray gazelle]

can someone give good books for having a strong foundation in maths?

[gray gazelle]

What’re your goals in studying math

The definition of “foundation” varies by extent of what you wanna know

[gray gazelle]

Well, to be honest I haven’t decided any

i just want to study mathematics but i don’t know which book to start with

What’s your background?

In math

high school student 😭

I am in high school rn

[gray gazelle]

Well, that varies country by country and program by program. What’s the last thing you studied?

[gray gazelle]

A lot of trignometry

[gray gazelle]

Then you may be interested in studying some algebra or pre calculus

Which is available online freely on Khan academy

Once you’ve finished algebra or pre calculus and have a solid foundation in these topics, you can start learning calculus

[gray gazelle]

ohh cool

tysmo

[novel iris]

my god what a throwback

i've never read shifrin

but I loved Hubbard

it was a very influential book for me

my experience with it was a nontrivial contributor to my ultimately going into math rather than physics haha

[hollow peak]

Complex cobordism spectrum detected

[keen pebble]

Best book on abstract linear algebra problems starting from vector spaces and subspaces

?

[gray gazelle]

ohh alr tysm

[gray gazelle]

Linear Algebra Done Right

by Axler

starts off w/ Vector Spaces and is rather abstract

[keen pebble]

alternatives?

[gray gazelle]

Friedberg, I guess, but I haven't read the book

why do you want an alternative, if I may ask?

[keen pebble]

i wanted new problems

but anyway thanks

[tribal crow]

FIS, Treil, Lax, Halmos, etc

all are great sources

[remote sparrow]

you can also look at van brunt's The Calculus of Variations

[umbral pivot]

Anyone know of any good books for someone who has a familiarity in stats but needs a refresher on it?

I am trying to learn some ML stuff, but I feel like my background in prob-stats is a bit lacking right now

[remote sparrow]

wackerly, mendenhall, and scheaffer

[umbral pivot]

Bet, I'll check these out

[remote sparrow]

it's just one book

those are the authors

[umbral pivot]

Ohhh I thought those were multiple authors

for diff books

[mystic orbit]

I love artin

[remote sparrow]

@rain wren

@mystic orbit

[mystic orbit]

uhhh

I dunno if I can give a fair comparison

I saw very different parts at very different times in my math journey lmao

[gray gazelle]

thanks

[mystic orbit]

the only think I could notice is the extremely calculatory nature of shifrin

which I don't think is a bad thing, especially for the parts I was reading on

I feel like doing a buncho calculations on the incredible concrete setting in shifrin helps build intuiton

(manifolds are defined to just be the image of a diffeo with a full-rank jacobian or some shit)

[remote sparrow]

for the purposes of discord search, can you change every instance of "shinfrin" to "shifrin" so that future readers can see your messages pop up?

[mystic orbit]

isn't he called shinfrin?

[remote sparrow]

no

https://math.franklin.uga.edu/directory/people/theodore-shifrin

[mystic orbit]

that's what my book cover says

huh

[remote sparrow]

is yours a paperback or a hardback

[mystic orbit]

no clue

it's a pdf

[remote sparrow]

well it doesn't matter since even the international edition has it spelled correctly

[remote sparrow]

anyway, how do you feel this compares to the approach of hubbard?

[mystic orbit]

at any rate, I like both, maybe shifrin is a bit more suited as a reference

coz hubbard often gets lost in tangents lmfao

[mystic orbit]

as I said, I haven't read the corresponding parts from hubbard

[remote sparrow]

👍

[mystic orbit]

international - {usa}

ig that makes coz the us is always national

everything else is internatiional

[remote sparrow]

[remote sparrow]

fun fact, it is 100% legal to buy international editions of books in the U.S. as per a supreme court ruling

https://www.npr.org/sections/thetwo-way/2013/03/19/174757355/supreme-court-oks-discounted-resale-of-gray-market-goods

[gray gazelle]

This is more about history but anyway. Any books of Albert Einstein and his life during second great war?

[sonic aspen]

Hey guys, does anyone have good recommendations for a book for differential equations? Thank you.

[sonic aspen]

Einstein: His Life and Universe" by Walter Isaacson seems like it might help, unless you're looking for his math during ww2.

[trail hemlock]

darq add me 🥺

[marble solar]

Boyce & DiPrima is an excellent book. Just get an early edition

[remote sparrow]

@vital bane something that's been bugging me for a while is that you spell "shifrin" as "shiffrin"

there's only supposed to be one "f"

your opinion on shifrin will be easier to find via discord search if you spell his name correctly

[cold tusk]

Any book recommendations for developing mathematical thinking? I know it will take a long time but I want to know how I can start developing my mind for it, currently working through algebra at school and I’m learning it quite fast and I think I might have a knack for math that I never knew of, but then again it’s algebra not real analysis or topology.

[remote sparrow]

abstract algebra?

[cold tusk]

College

[remote sparrow]

#book-recommendations message

[sonic aspen]

Hey sorry again, anyone have any good beginner's chess book recommendation (or should I just use Chess.com)?

[foggy quest]

"Introduction to Differential Equations" here: https://mtaylor.web.unc.edu/notes/math-524-second-semester-ode/

[foggy quest]

https://mtaylor.web.unc.edu/notes/linear-algebra-notes/ is good

[cold tusk]

Would you say working an hour a day for the book of proofs is substantial? Instead of working day 6 hours one day a week

[remote sparrow]

spreading out work is a good idea in general

[hallow oriole]

also, time taken will just vary per person

[cold tusk]

Okay appreciate you, decided to go with book of proof because it’s free and pdf is nice

[hallow oriole]

there's no "set time" to do maths, just go at your own pace

[cold tusk]

Well I mean setting an amount of time to make sure I do a little maths everyday,, a little something everyday goes a long way

[hallow oriole]

oh, sure, that's fine

[cold tusk]

Even if just 30 minutes of doing exercises!

[cold tusk]

Would you suggest doing all the exercises after each section or just the odd / even numbers

[hallow oriole]

if you are just beginning math do all the exercises

[cold tusk]

Okay I will do, I’m a computer science major though I’m in community college and eager to learn discrete maths / math for computer science before I go to UNI, I won’t learn discrete for 2 years so if I can develop the intuition for it early and have a head start for be it, I enjoy math I’m just not very “good” or experienced in it as I am with programming and general computer science concepts, I also want a PhD in computer science so math is a need not a nice to have

[left canyon]

everyone says what the sigma but no one says hows the sigma😢😢

[trail hemlock]

exactly, for instance 3am on a school night is when I find I do most of my best work

[strange sentinel]

This is so real though

[stark turret]

any gre practice book reccs?

[uncut zealot]

One of my precalculus students sent me a YouTube video about using Peano's axioms to prove 1+1=2, and seems interested in learning more. I sent them the natural number game, and also said that I'd try and find a book to send along. Any recommendations for anything covering foundations-y topics, accessible to someone with literally no math background at all?

[hallow oriole]

book of proof!

[strange sentinel]

As valley says, something to teach you proofs, and then maybe Enderton's Elements of Set Theory or similar?

[trail hemlock]

cummings intro to proof book?

[hallow oriole]

maybe not enderton after book of proofs

probably something a bit easier

like halmos naive set theory

also hi arti!

[uncut zealot]

I feel like even halmos might be a bit much, but I guess if I recommend the student read book of proof first.

[trail hemlock]

arti is post graduate math now? good shit

[uncut zealot]

The issue is I also don't want to just dump a massive reading list on this kid

[trail hemlock]

wait zorn why not use cummings book? it’s very gentle

[hallow oriole]

damnnnnnnn

i should apply too

what're the reqs again

[uncut zealot]

Haven't read it.

[hallow oriole]

if halmos is too much abbott should be readable after book of proof and will probably seem a lot more concrete

after the student has established real analysis some foundations stuff will be a lot easier to motivate

[uncut zealot]

Sorry, I again want to clarify, this student is in precalculus.

[hallow oriole]

oh, damn

nvm 😭

i think book of proof into halmos is the best bet then

[uncut zealot]

I'm thinking, like, an expository paper on peano arithmetic written for a motivated highschooler or very early undergrads, or for a "math for non-math people" style course.

[normal crystal]

Zorn, do they even want a textbook
a pop sci math book thats decent might be where they are for now

[uncut zealot]

I don't know much in the way of popsci math books, but yeah, that might also be suitable.

[hallow oriole]

what good pop math books are there at precalc level?

[uncut zealot]

I don't think the student really has anything specific in mind beyond, like, "hey I heard about this cool thing, any recs for further reading?"

[hallow oriole]

the only "good" pop math books i can think of are not properly understandable at that level

[tawny copper]

Why don't give them something they might not understand?

(This is a genuine question, I'm not a teacher)

[uncut zealot]

A lot of kids in a university precalculus course have had bad experiences with math before, and don't feel confident doing it. If one of my students (a) found something in math on their own, (b) was motivated enough to reach out and ask me about it, I don't want to scare them off.

I want to encourage and motivate this student to learn more, not scare them off with "Hey, you thought you found something cool? Fuck you you know nothing".

[tawny copper]

I think it's possible that students can be braver than what some teachers sometimes think, but idk

[uncut zealot]

It's possible, and if there's nothing gentler out there I'll do Hammack + Halmos.

[hallow oriole]

hammack is as gentle as you can get imo

[uncut zealot]

But at the same time, I'm not giving a precalculus student Abbott.

[uncut zealot]

Hammack is super gentle. The issue is that it's a 400 page book that doesn't cover what they said they wanted to learn more about; it's a 400 page book that's a prerequisite for reading a different book about the thing that they said they were interested in, and no matter how gentle the book is, that can seem pretty fucking daunting.

[hallow oriole]

hmmmmmm

okay yeah fair point

the best solution is individual meetings but i’d be surprised if you (or any marh grad student) had the time for that

[tawny copper]

It doesn't take a lot of time to deal with the Peano axioms, they should use it as a bridge to learn more. Maybe the student is interested more broadly in the foundations of arithmetic

[uncut zealot]

Yeah, the plan is ultimately use it as a bridge to get the kid motivated to learn more about math.

[strange sentinel]

Have been for roughly 2 months, yeah

[strange sentinel]

Kind of unclear; I just listed a bunch of finite model theory papers I'd read and they gave it to me

[uncut zealot]

Hmm... I think with me having already sent the natural number game, they can see quickly how their "silly question" about numbers leads into needing formal methods of proof, which should hopefully motivate Hammack enough?

[trail hemlock]

cool :)

[tawny copper]

Given that they sent you a video about 1+1=2 you could respond with a video about Godel incompleteness 😝

I don't know of any particularly good videos on this topic, but I always like the numberphile videos

Idk what that thumb is btw

[uncut zealot]

It's thumbrat

[trail hemlock]

thumbrat???

[tawny copper]

I didn't mean to click it, idk how it ended up there

[strange sentinel]

All the pop math about the incompleteness theorems is pretty garbage

[trail hemlock]

oh god not pop math

[strange sentinel]

Like there is good pop math but not on that topic

[uncut zealot]

There are math theorems that might be both TRUE AND NOT TRUE AT ONCE! spooky!

[trail hemlock]

im on a crusade in my scool to fight against pop math

im don quixote in this bitch tbh

the comp math people are ... you know

[tawny copper]

I remember the numberphile video only talking about the math. I don't think it's garbage lol

[trail hemlock]

the only numberphile-esque channel that I know of (in the sense of quality of production), that actually talks about math, is "The Bright side of mathematics"

[broken meadow]

Consider: Mathologer

[trail hemlock]

🤦‍♀️

forgot abt him

[remote sparrow]

#book-recommendations message

[strange sentinel]

Mendelson rec is a good one

[uncut zealot]

Thanks. I'll send over one of these books, I think.

[remote sparrow]

feel free to let me know how it goes

[hallow oriole]

wait reading research level papers is enough for postgrad???

also mendelson topology book is so good i hate munkres

[hallow oriole]

i might actually get it then

i thought you had to actually be doing research

i also think the only good pop math book i’ve ever read is chaos by james gleick but if yall got other recs im down

[trail hemlock]

any reason why?

i referenced munkres on occasion when i read a pst book, it was quite good

[hallow oriole]

oh yeah it's a great reference

[mystic orbit]

?

Where

[trail hemlock]

oh good heavens

on discord

[mystic orbit]

like, as a friend?

you cou'dve sent an invite

also, shouldn't you be asleep

[hallow oriole]

lmao

[trail hemlock]

,ti

mayhaps...

[hasty eagle]

The current time for blackbeard4198 is 02:38 AM (CDT) on Mon, 30/09/2024.

[remote sparrow]

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

@tough egret are you the amazon customer that reviewed this

[tough egret]

No, but I tried leaving a review that basically stated the same things. It unfortunately was refused because it was written in English but I bought it on Amazon France.

But yeah, this book is 100% worth its price

[molten gulch]

morning chat

it's 07:00 here

[tough egret]

It has hints for most exercises

And there’s a ton of them

[remote sparrow]

it's 900+ pages

i'd say that's a fair price

[molten gulch]

On top of that, most springer and just maths textbooks are decently expensive

[vital bane]

yea I don't know where I picked that up

my bad

[remote sparrow]

all good

[ruby seal]

Anyone knows about some book that goes over basic group, ring and field theory (with some Galois theory in it) kind of fast? I've already seen these topics but I need some sort of review which doesn't require me to re-read Dummit and Foote.

[tough egret]

What’s « fast »?

[ruby seal]

A book that's mostly an overview and doesn't dive too deep in the details preferably

Maybe some lecture notes

Which usually are a shorter read

[near jewel]

Are there any good books for advanced calculus? I looked through Buck’s Advanced calculus, and it seems like a lot of the things are already contained in basic calculus, like calculus 1 2 3 4.

[near jewel]

Or is advanced calculus just real analysis?

[vital bane]

I think lecture notes is what you're looking for

instead of a book