book-recommendations

[torn rivet]

Enderton “A mathematical introduction to logic” was recommended to me once

[marsh ingot]

I will check it later

[plain barn]

any recommendations for measure theory books

[mystic orbit]

on the contrary

their presence was incredibly entertaining

[daring lake]

Axler, Folland, Rudin

[plain barn]

just specifying: for someone who knows real analysis (basically my knowledge is jay cummings book with some extra generalizations I know with topology and metric spaces) and some basics of general topology

[plain barn]

will look those up

ty

[rain wren]

what do you want from the book more specifically

do you want something light but rigorous? grad level, full generality?

rudin?

[plain barn]

grad level (probably)

[plain barn]

which book from rudin is of measure theory? papa rudin?

[rain wren]

yea

[plain barn]

oh

[rain wren]

then you should check out folland. Be ware it's just a bit less terse than rudin

[vital bane]

Rudin 🤢

[plain barn]

oh hi neamesis

[rain wren]

but it is my favourite on the topic and the one I learnt from the most.

[vital bane]

Hello Gabi

are you gonna do measure theory?

[rain wren]

the exercises are really good, and the exposition is super clear

[plain barn]

I intend to learn it, yeah, it's like one of the topics I look up to to learn

apparently most of the veeery advanced stuff I desire to one day learn have something to do with measure theory

[vital bane]

You could check out "Measure Theory" by Donald L. Cohn (after you're done with it let me know how well the book is written so that I can decide whether to use the book or not )

[plain barn]

btw one question, what are the pre-requisites? cus in the case of rudin apparently the pre-req is baby rudin and I don't really know a lot of stuff from there

[vital bane]

intro analysis is the pre-req

especially sequences and series of functions

and some basic topology of R would be helpful

[rain wren]

just any introduction to analysis would suffice

[plain barn]

like from the end of the chapter on sequence of functions onwards I'm pretty uh, dumb

[rain wren]

you don't need all of baby rudin

[plain barn]

that's great then lol I was reading baby rudin exactly so that I could advance in "analysis"

[rain wren]

just make sure you got up to like

[plain barn]

good I don't need it

[rain wren]

chapter 7

[plain barn]

I just finished reading that chapter today soo

ig I'm fine

[rain wren]

chapter 7 of baby rudin!

[plain barn]

I'll check out papa rudin (again) and folland and axler (this one just because I like how axler writes)

[plain barn]

lmao

oh I also just need the 7 chapters for papa rudin

amazing

[plain barn]

is this the one?

[rain wren]

yep

[plain barn]

ihu

[rain wren]

ihu?

oh, I hate you?

ok

[plain barn]

NO

IHU IS LIKE

IHUUUU

READ IT AS A WORD

it's like

yuppiee

like yahoooo (as said by mario) but without the a

[tender river]

i hear you

[plain barn]

I helicopter you

[analog jasper]

i hausdorff space you

[rain wren]

oh

[rose hazel]

Hello chat, so folland is too expensive to get my hands on , is sheldon's book on measure theory good? if not, any alternatives?

(My goal is speedrunning analysis, and i have done introductory analysis in form of tao 1 and tao 2)

?

[vital bane]

I Heliosphere You

[vital bane]

Sheldon Axler? yes his book on Measure Theory is good

[rose hazel]

how does it compare to say, tao's measure theory book?

[vital bane]

I've never checked out Tao's measure theory book

You could use both

Like

Use Axler as the main thing

and check out Tao's book as a reference while learning from Axler

[rose hazel]

i am quite a big fan of tao's writing, and the book is very affordable so

[vital bane]

yea Tao is awesome

[plain barn]

every book is affordable if you're smart

[rose hazel]

well I like physical books, and unless you are suggesting i do a fine print and custom cover myself, i gotta buy them at market places.

[plain barn]

happens

I'd also enjoy physical books but I study so many random stuff so much that I would not be able to afford them ever in my life

[rose hazel]

i actually still dont know why i buy physical books, i will read a few chapters from them, but then shift to the pdf for most other chapters, because its more convenient when writing notes.

just a collection thing i guess

[tropic nacelle]

what?

[plain barn]

I also enjoy having opennable blocks around me

so I understand

I just love solid things that are parallelepiped shaped

like old cartridges and books

[vital bane]

Never say never

[plain barn]

I didn't say it

I said ever

:)

[vital bane]

"not be able to afford them ever" not + ever = never

[plain barn]

too far

[vital bane]

I use 50% PDFs and 50% physical books

[rose hazel]

or you can just get a kindle

[vital bane]

I think color e-ink tablets are starting to get more popular

kindles also have styluses

[rose hazel]

yeah but kindle is 80$ new here, and i will have to drop 400-500$ on a decent tab (even the Xiaomi one with pen costs 450$)

[vital bane]

also kindles don't use LED screens

They use e-ink screens

[rose hazel]

older generations, especially used are another ball game, though i haven't really ever found any great deals yet.

if i am spending on a tablet, i at least need a OLED screen, which generally bumps up the pricing

i dont live in 'merica

or canada for that matter

[stiff tulip]

How is the remarkable vs ipad debate

[north summit]

Can someone recommend and ODE for first course at the grad level

[rose hazel]

Maybe if i ever have a college hosted trip to 'merica, i will buy one

[stiff tulip]

I placed first in a poker tourney, so i’m thinking of picking one up

[rose hazel]

Generally, samsung used market here is much better than ipad used

[stiff tulip]

We used Gian carlo rota’s book for my ode class

[rose hazel]

s8 plus for like 350$

[north summit]

where?

[stiff tulip]

Uchicago

[vital bane]

oh he has an ODE book? that's pretty cool

[stiff tulip]

Yeah he’s got a book on everything

[vital bane]

Lol

[north summit]

nice

[stiff tulip]

It was an upper level undergrad class, but pretty comparable to a first course grad

Check out the preface see if it’s up to snuff for your purposes

[stiff tulip]

Co authored with birkhoff too

[north summit]

no metric space?

[vital bane]

metric space?

[north summit]

generalized distance function

[vital bane]

No I know what a metric space is, I'm confused why you're asking about metric spaces in the context of ODEs

[uncut grove]

Any book recommendations on college algebra start to finish?

[remote sparrow]

"logic" and social choice theory are normally treated as distinct in math

[remote sparrow]

axler's book is good yeah, but it's less general than folland and the exercises aren't as challenging

i will say that my copy of axler's measure theory is better as a physical product than folland

i'm sure you can find used copies of folland for a decent price if you keep checking

[ornate frost]

then a good introductory book to social choice theory is what i really want (sorry for the mistake, i thought that social choice theory was a part of "logic" within mathematics)

[quartz verge]

List of good mathematical logic books please

[north summit]

picard theorem?

[limber python]

https://www.amazon.fr/Art-Craft-Problem-Solving/dp/0471789011

does anyone know about a book similar to this one that could be translated to french ?

[quartz verge]

why not ask an AI to generate a digital copy in french by feeding it a copy in English?

[limber python]

wowww

is that possible ??

i have it as pdf

[quartz verge]

why not

[limber python]

do you know about one ?

[quartz verge]

https://www.onlinedoctranslator.com/en/translate-english-to-french_en_fr

i havent used this before

im sure claude is powerful enough to do that too

[limber python]

thankss

[remote sparrow]

#book-recommendations message

[quartz verge]

thank you!

[fallow mirage]

Anyone know good resources for learning about waves on surfaces? As in modelling waves travelling on a sphere or something

[quasi haven]

Hi, I couldn't do a math degree but would like to self teach myself atleast at bachelors level.

What are the topics that I need to read in order to cover a bachelors level math major?
I'm an engineer and I know linear algebra, calculus, and probability, vector calculus fairly well although could read them again in "math way"

Any recommendations?

[tender river]

the topics you say you know are algebra and analysis based so you could start with that and build up

linear algebra and analysis are common starting points for many into pure maths

[quasi haven]

What is analysis?

[dapper root]

Calculus but rigorous let’s say

[quasi haven]

I know Complex Number analysis

Okay

[tender river]

study of limits formally, etc etc

[quasi haven]

Yeah I like it

[tender river]

continuity, differentiation, generally maps between normed vector spaces although you can go even more abstract eventually

https://www.amazon.com/Understanding-Analysis-Undergraduate-Texts-Mathematics/dp/1493927116 people here like this book for analysis

[quasi haven]

But the definitions that mathematician use is very unintelligible to me tbh.

I just know the given results and use them to solve a problem statement. Basically not caring the working behind it. That's how I did maths in engineering.

[remote sparrow]

well the best thing you can do is to learn how to read definitions and work with them

https://youtu.be/eGDtW3BZyyE

this electrical engineer did it, and so can you

[quasi haven]

Yes I definitely need the skill to read math definitions

[quasi haven]

Thanks I'll watch it

[sacred sorrel]

what do you guys think about munkres topology book?

[tribal crow]

not a bad book at all

[dim sierra]

its good

[analog lava]

rereading it for the 10th time rn for a course..

amazing textbook

[novel hound]

Math curriculum guide: https://www.susanrigetti.com/math

[vague granite]

does anyone have ode/pde books that assume lin alg?

a ton of the systems stuff seems heavily influenced by that so a book doing lin alg style proofs would be insightful

[real marsh]

how else do you prove the existence and uniqueness theorem

[cursive rivet]

books on how to solve stuff or books on the theory?

basically every book on the theory will assume lin alg, though I can recommend some if you are looking for those

[vague granite]

theory

[vague granite]

my course is on solving but idrk too much about the theory :(

[cursive rivet]

how much real analysis do you have?

[trail hemlock]

has anyone read this book?
https://link.springer.com/book/10.1007/978-1-4684-6254-8
im curious to know the prerequisites, since i really found cw complexes in lee interesting, and i read a paper abt them and it was pretty cool as well

[dim sierra]

Looking at the table of contents you should just read an algebraic topology textbook

[vague granite]

none 😭 but im down to do real analysis if needeed

to get a real view

[rigid flint]

I've recently read through, and completed most of, the book "Inside Interesting Integrals" by Paul J. Nahin, and I was wondering whether there were more books like it.
I'm specifically looking for books about Multivariable Calculus and difficult integrals using things like the Gamma/Beta function and series expansion. But also stuff like Jacobian matrices and other coordinate systems. Cheers!

[light cedar]

hii, im looking for a rigorous book on graph theory, most of the books i have are relatively informal in their definitions

i have noticed that algebraic graph theory tends to be more formal but the books ive encountered arent suited for algorithmic graph theory

diestel's doesnt have that definition-theorem style, it defines things informally

[stray veldt]

this isnt true

just because there are no definition environments doesnt mean its informal

[light cedar]

maybe "organized" is what i mean then

but it is informal just to be clear, ot tends to define things in their geometric interpretation not the combinatorial nature

and its as if it passively mentions voncepts and describes them without dedication

[stray veldt]

can you give an example?

anyways, if you want algorithmic graph theory specifically, there is a book called that by alan gibbons

[light cedar]

im not saying its a bad thing, but i prefer another style

[stray veldt]

and ofc CLRS

its just not true that its informal

[light cedar]

i grabbed 2 examples which i think arent rigorous/formal enough

but i cant upload images here for some reason

[stray veldt]

ping me in #chill with them

[quasi haven]

Some good reads for Complex Analysis?

[grim ore]

Complex Analysis Serge Lang

[quasi haven]

Is it a tough one? Or the popular recommendations to university level students?

[grim ore]

popular, and definitely on like the medium scale of things to read, not too tough but not easy, just right

[open merlin]

there's a bunch of recs in the pinned messages

[grim ore]

If you have taken undergrad real analysis I think that would really be the only prereq for it

[grim ore]

Oh that would be better

[quasi haven]

So I need to do real analysis for complex analysis

Someone recommended book by Abbott for real analysis

I don't know about real analysis

[grim ore]

I think it depends on what text you are using, knowing real analysis for the most part makes complex a bit easier

Like Im reading lang in my freetime and ever so often I bump into something that just makes sense in reals so its easier to follow for the complexes

I guess since R^2n = C^n

[grim ore]

Wouldnt necessarily say its required tho

Some people only do complex analysis in undergrad

[trail hemlock]

yeah maybe i’ll go for rotman or smth. it will cover in the same depth as this right?

[rigid flint]

are there any good books for MVC? i’d consider myself decent at calculus and am interested in learning about jacobian matrices, polar/spherical coordinates and some theorems.

[dim sierra]

Yes, that book doesn’t seem like it’s super deep or anything. CW complexes are super important in any AT textbook so you will learn it well from Rotman or whatever you choose

[vital bane]

well...not equal to, but rather isomorphic as vector spaces over R

[merry canyon]

What is the best Calculus book for self study? Are there any hands on books which help you build understanding. I am right now completing the Essence of Calculus series from 3Blue1Brown, and I just love it. Never thought Calculus could be so fun

[vital bane]

Maybe Thomas' calculus or Stewart

also OpenStax's calculus books are also really fun to go through

https://openstax.org/details/books/calculus-volume-1/

[timber mesa]

Spivak is decent for self-study and one of the standard references, some users are also fond of Abbott's Understanding Analysis since it explains some of the history and intuition behind things

my recommendation is skim through a few and stick with one or two you like

[cursive rivet]

ok so this is a little difficult since the theory will necessarily use some real analysis. a book like Boyce & DiPrima (elementary DEs and boundary value problems) is a standard book on solving things, but has more emphasis on the theory than normal, and is probably the best bet without these sorts of prereqs. a book like https://vmm.math.uci.edu/ODEandCM/ uses linear algebra and some real analysis, but is on the lighter end and you might be able to get by without it

[trail hemlock]

gotcha, thanks a lot

[stiff grail]

please recommend a book that goes with basic and not jargin for differential equations

[misty wyvern]

Annual any fun graduate-level but light math books you guys recommend for bedtime reading question

This one is an oddball but I'll start, Vallis's Atmospheric and Oceanic Fluid Dynamics is very readable for mathematicians and it's fun with lots of pictures

it's at a roughly early graduate level by physics standards, which means an advanced undergrad in math should be able to breeze through it

[dim sierra]

I’ve heard The Wild World of 4 Manifolds is good for this

[vital bane]

Functional Analysis by Walter Rudin

2nd edition

[molten gulch]

That is...not light reading

[wooden tartan]

its a matter of perspective

[misty wyvern]

Already worked through it

[undone finch]

Does anyone have any recommendations on books that develop probability theory and/or information theory using category theoretic methods?

[gray gazelle]

Bro this is a whole textbook

[misty wyvern]

you'll do a page in like a minute

and lots of pictures

[timber mesa]

so 1000 minutes

ngl it does seem interesting but eh

[misty wyvern]

i used it for bedtime reading

[timber mesa]

I'm not sure I'd use any math book for casual reading like this lol, but I like expository articles for that purpose

I really really like Notices of the AMS's What Is... section for that purpose, it's basically very short bits defining a certain mathematical object and where it's used https://www.ams.org/cgi-bin/notices/nxgnotices.pl?fm=gen&cnt=whatis

[trail hemlock]

book-ish question: does springer do 50% off sale during the holidays? i want a book, but i also dont wanna blow 80 bucks if i dont have to

[timber mesa]

right now I think they only have a discount on some e-books, normally they only discount physical books during the Yellow Sale each June or so

[trail hemlock]

yeah, ive seen the 15.99 stuff, sadly doesnt apply to the one i want

[open merlin]

there was a Halloween sale, and an autumn one before that

[trail hemlock]

and im def not waiting until no damn June

[open merlin]

Not sure if sales differ per country tho

[trail hemlock]

im just gonna go down Dami's list until i find the cheapest book

[humble spire]

Can u buy used?

[timber mesa]

and if so I recommend https://www.bookfinder.com

[trail hemlock]

i checked on bookfinder, the cheapest usedis ~55 bucks

[trail hemlock]

bookfinder is the BEST

[timber mesa]

fr

[gray gazelle]

Nah abe books is

[trail hemlock]

bookfinder scrapes abe books and a bunch of other sites

its great

alr i just bought rotman

im so hyped

[mystic tinsel]

Hope this hasn't been asked to death or anything, but I'm currently taking a Real Analysis course based on Otto Forster's book (the course is in German), and I'm looking for something a little more handhold-y which has a greater emphasis on examples.

Sometimes Forster jumps from theorem/result to theorem/result and I was wondering if there was anything that could be used as supplementary material?

I've already heard of Tao and Abbot (though I'm not sure which one to pick from the two)

And Rudin as well, I know that's supposed to be a very challenging text but it was also briefly mentioned in the course description somewhere if I'm not wrong so I'm wondering if maybe pushing through that will really make stuff clear or not?

[graceful moon]

If you want something which holds you hand a bit more Rudin is absolutely the wrong call

Tao and abbot are both amazing books, I say just read a little of both and see who’s still you like more and stick to that one, you really can’t go wrong

And really if you’re just using it as a secondary source to your main book, you can just use either as a reference when you get confused

[mystic tinsel]

Thanks! I'll check them out over the weekend 🙂

I kind of have the same question about Linear Algebra, I have another German book for that but it would be nice to have an English equivalent to supplement it with. It's a proof based course so I'm not looking for anything with a focus on computation.

I've heard of LADR though I heard that determinants are introduced at the very end and if possible I'd like to stick to the "standard" structure that other books would follow. Any other recommendations out there?

[graceful moon]

I personally like Hoffman Kunze, Friedberg Insel and Spence is another common recommendation but I’ve not read that, people seem to like it though

[narrow canyon]

Anyone have any text books for pre uni math that covers pre algebra, algebra and other basics that I can study at home? The bigger and more concise in one book the better

[remote sparrow]

i haven't seen an english translation of forster, but amann and escher might be worth checking out, if not necessarily more handholdy

@stray veldt

[novel hound]

I'm waiting for this too. I have invoices from Dec 13th and Dec 15th last year which shows discounted books for 18.68 Euros. So I plan to wait until Christmas.

[trail hemlock]

i was gonna wait for Christmas but lowkey got greedy

i believe amsco's apush is discounted on christmas, ill prob grab that instead

[novel hound]

I just found this on reddit, posted 7 hours ago: and I checked one Universitext and it was indeed discounted to 15.99 USD. ------ "I just saw an ad this morning about Springer sale. Not sure the discount applied to which series but I had a look around "Compact textbook in mathematics", "Universitext" and "Moscow Lecture", they have a few book which was quite affordable (15.99usd for softcover).

Just want to let people know in case someone want to grab a physical copy like me =))."

yay Gamelin is discounted to 15.99 - I wanted that 😄

[humble spire]

bro i just searched up amsco apush and first link is free pdf on google drive

use online

like save your 25 bucks

[trail hemlock]

i prefer having a physical copy lol

[humble spire]

kk

i do too for all subjects except history though

because control f is truly the peak of technology

[trail hemlock]

knapp had better be discounted ... idk what compelled big bro to price his shit at $125

[trail hemlock]

yeah real lol

i just dont like staring at a screen when i can avoid it

[novel hound]

Freitag Busam is also Universitext therefore 15.99 USD, sweet.

[remote sparrow]

you're better off buying used if it's an old springer; you have a chance to get a book that's bound well

[remote sparrow]

it's on perma-discount on amazon no?

oh wait i'm thinking of advanced algebra

[trail hemlock]

yeah i would, but i cant justify the $57 for a used copy

there is some canadian dude selling for cheaper on amazon, but amazon.ca does not, in fact, ship to Texas

[remote sparrow]

just ask your parents to rent an apartment in canada and fly you out there

[trail hemlock]

perhaps i shall

anything for the buzz (book huzz)

[molten gulch]

I thought the springer price I was was due to my uni subscription lmaoooooo

[trail hemlock]

i need to go to a university that maximizes the books i have access to

[dim sierra]

which state are you in

[trail hemlock]

texas

[dim sierra]

I was gonna say just come to UCLA or Berkeley (and prolly other UCs)

they have math libraries

[brisk gust]

any real analysis text i can go through without a background in calculus?

[loud cradle]

consider a rigorous calculus text like spivak

basically teaches you calculus and elementary analysis in one go

[brisk gust]

Spivak is much less formal than your average analysis textbook, no? also i dont think i will be able to get my hands on a copy of spivak.

[trail hemlock]

i wouldnt say "much less formal", spivak is considerd fairly formal. That said, there is expressly no topology, he prefers to prove theorems in different ways

you can just use spivak -> Tao 1 / Abbott / Rudin / Wtv, but analysis from a very rigirous text without calculus background makes no sense

[brisk gust]

How does spivak compare to apostle, tao or abott?

[loud cradle]

i suggested it because any actual analysis book is going to assume you know calculus, at least in a nonrigorous way

[trail hemlock]

apostle, abbott, and tao assume at least some calculus knowledge, spivak is a good choice because its somewhere in the middle of a calc text and a real analysis text

i also like Honors Calculus by MacCluer for this same purpose (he does some topo for continuity)

[brisk gust]

I understand, but a lot of these books dont actually seem to require much knowledge of calculus, just basic intuition, and build everything from scratch. So i am curious why i cannot pursue say, either tao or abbott.

[brisk gust]

Will check it out

[loud cradle]

no one's saying you can't pursue them, it may work out fine
but it might seem very unmotivated if you haven't seen the concepts before

no harm trying

[novel hound]

I have a thumb rule, if you are pre-undergrad, and have done some calculus and wanna do more analysis type stuff, you should do spivak. If you are first year undergrad you should do Abbott -> Rudin. ymmv

[trail hemlock]

pretty much there is lots of harm with no real gain of trying real analysis without prior calc

[gray gazelle]

Which rudin?

[novel hound]

baby

[brisk gust]

Well, i am not exactly an "undergrad", but i do need to cover at least elementary analysis, number theory, and combinatorics in the next 6 or so months.

going for shorter books saves some time (ignoring me plucking my hair when i dont understand something, that is)

[novel hound]

PSA: Hungerford, Fulton/Harris, Rotman GTMs (Softcover) are 15.99 USD on Springer.

[loud cradle]

is there a full list somewhere?

[novel hound]

There should be but I couldn't find it...

[remote sparrow]

all rotmans?

[novel hound]

The ones on Alg Topology and Intro to Group Theory yes. The one on Homological Algebra no.

[remote sparrow]

cool

i wonder what the difference between his group theory book and his big fat algebra book is

[novel hound]

oh looks like the AMS one is the standard Rotman? I did not know...

[remote sparrow]

well it's a first-year text yeah

but maybe the springer one has more in-depth stuff

[vague granite]

im actually using boyce diprima in my course right now- ill see if i find this better. thanks!

[cerulean steppe]

Introduction to Differential Equations here is great: https://mtaylor.web.unc.edu/notes/math-524-second-semester-ode/ It covers a lot of linear algebra.

[analog rapids]

Wanting to get good foundation in statistics and probability theory for ml, any rec for books or online courses?
I have taken some intro to stat course at college rn but they feel more like plug and chug than something that can really help me understand it

[timber mesa]

check out Mathematics for Machine Learning, it's freely available at https://mml-book.github.io

it only has one chapter on probability and statistics, but it's the necessary concepts with plenty of illustrations examples and exercises

[analog rapids]

I actually read up till vector calculus part in part 1 of that book (have done class on linear algebra and calc before), it feels more like a review/refresher tbh than something I ease into and build from scratch

not sure how to describe it exactly, it feels like they condensed a lotta stuff and as a result it's quite hard to build from nothing

[timber mesa]

yeah I agree that these chapters might serve better as a refresher for people that have seen this before

there's plenty of books in probability, one is A First Course in Probability by Sheldon Ross

[heady ember]

Hi deri

[analog rapids]

o seems like the book is open to public online, I will give it a read

[remote sparrow]

https://link.springer.com/book/10.1007/978-1-4612-0863-1

there are many solutions in the back so while not necessarily the lightest read, at least you won't get too stuck

[gray gazelle]

Only $16 too

[remote sparrow]

https://link.springer.com/book/10.1007/978-1-4612-1005-4

@lean pagoda have you talked about this book before?

[trail hemlock]

i cant believe my favorite book isnt discounted 😔

[timber mesa]

oh the other day I also saw a ridiculous book like that https://link.springer.com/referencework/10.1007/978-3-319-57072-3

ridiculous in size really

I thought some chapters were a decent read

[umbral field]

107 chapters

[timber mesa]

speaking of bedtime reading I also like to read history of math for that purpose https://academic.oup.com/book/53073

some very interesting essays in that one particularly

well, where "bedtime reading" is not literally that but just casual reading related to math

[old elk]

I bought two books, one on topology and one on linear algebra, by Tej and mohammad.

[timber mesa]

i miss the dopamine hit of buying books

[vital bane]

"just one more book bro, im not addicted i swear"

[trail hemlock]

i love (LOVE) the fact that springer has priced conway's <150 page point set topo book at 64 dollars

it makes me so happy to hear

[misty wyvern]

I have another rec for y'all, a physics book that's easy to read for mathematicians and gives you a rough overview of fundamental phys

https://link.springer.com/book/10.1007/978-1-4419-8267-4

im literally bedtime reading it now

NB I have the phys background already but in my totally an expert I'll be a doctor soon opinion it's accessible to the average math grad student

also very light and short

downsides: no pictures 😦

[rigid flint]

Does anyone have any good books on learning Multivariable Calculus?

[trail hemlock]

Hubbard and Hubbard's Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach is really nce

[misty wyvern]

I'm a fan of Hubbard and Hubbard

[rigid flint]

cheers!

[misty wyvern]

if i ever taught vector calc, which i wont allah willing, i would use hubbard and hubbard

[trail hemlock]

folland also has a more difficult advanced calculus book that i really like

[rigid flint]

ive just finished going through most of Inside Interesting Integrals, but it touches on a bit of mvc, so i thought it would be best if i actually sat down and learnt it a bit xD

[heady ember]

Neam be like
Addicted to learning math
Addicted to buying math

[vital bane]

nah I'm too poor for that

[remote sparrow]

me tbh

[remote sparrow]

Probably well-trodden ground for you, but Theory of Complex Functions by remmert has many historical asides

https://link.springer.com/book/10.1007/978-1-4612-1005-4

this book seems interesting

[lean patrol]

thoughts about baby rudin

[loud cradle]

8 authors!

[tribal crow]

most colourful mathematics book name:

[remote sparrow]

it's a compilation of essays that have a unifying theme i think

[vital bane]

bad for an introduction to analysis, good for a review

[lean pagoda]

Apparently I have

Here

[gray gazelle]

I wonder why springer's math books cover are yellow

[crimson swift]

is the book of proofs third edition good for starting maths outside of school?

[crimson swift]

I was planning on getting

I think I will and see how it goes

[crimson swift]

nah I would rather just have a physical copy

just preference

[fresh skiff]

folland only reminds me measure theory

[vital bane]

yes, advanced calculus = measure theory

[minor hearth]

could be worse - several complex variables and complex geometry isn't supported here because "it's just complex calculus"

[trail hemlock]

lol

[tropic nacelle]

have you ever wondered why there's a knight on every single cover though

[vital bane]

it's not a knight

it's a horse

🐴

[dim ether]

Any number theory book recommendations (complete baby in number theory)? i will be doing this alongside analysis, so preferably something not too harsh on the mind. (should cover: prime factorization, modular arithmetic to a decent extent at the least)

[vital bane]

@brisk ice

[tender river]

bros gonna say Burton watch

[dim ether]

why is burton so standard anyway

[tender river]

its the rizz

[vital bane]

https://tenor.com/view/yoda-there-is-another-star-wars-jedi-gif-5140031

But it requires at least a little bit of mathematical maturity

Niven, Zuckerman, Montgomery

really good book

but it's for advanced undergrads

[dim ether]

how much maturity we talking? i would consider myself on the lower end of the ug scale considering i havent even finished elementary analysis

[vital bane]

though anal and algebra aren't strict prerequisties, it helps if you've seen a little bit of those before starting this book

[vital bane]

if you've done like the first two chapters of any anal/alg book then I think you can handle this book

[undone finch]

Two asks, please:

• complex analysis, grad level, introductory
• partial differential equations, grad level, introductory

[vital bane]

grad level or introductory??

[tender river]

first grad course

[dim ether]

i have only done upto cauchy sequences in tao's book, and even that isnt finished yet

[vital bane]

Lol isn't the first 4 chapters of Tao like constructing the reals

[dim ether]

no alg

[undone finch]

right. first grad course

[vital bane]

check this for complex anal #book-recommendations message

[dim ether]

natural axioms + add + mul, set theory axioms + paradox + functions + yada yada, integers + rationals and the 5th is real numbers

which is what i am on

so no "real" real analysis yet

[vital bane]

lol alright then you have some experience with proofs so you should be able to handle

[dim ether]

how harsh it is though

[vital bane]

I mean you can try going through the first chapter of the book and doing some exercises, if it's too hard for you, you can always switch to a different book (since it's not really time wasted, you spent it learning NT)

[dim ether]

i am not looking for something that demands too much time

[vital bane]

it's not harsh at all, it just assumes you have some experience with proofs and pure math

[undone finch]

thank you

[thorn cloak]

My ug pde prof said he uses Evan’s/taylor to teach graduate pdes

[undone finch]

thank you

[brisk ice]

Why am I being pinged. I am taking one elementary number theory course. I'm not the arbiter of number theory books

I haven't even finished the course lol

[vital bane]

I was gonna ask what NT book you were using

i fogor

[brisk ice]

I told you 😭

Or at least told the person when you pinged me

[mystic orbit]

Lol

There are plenty of grad level intros to both lmao

[mystic orbit]

Narasimhan, very fast, very clear, 've been using it for a month and I like it a lot

For PDEs, tried and true, Evans

Tho it will assume a buncho analysis knowledge already

Upto measure theory, some functional analysis for the second part, standard stuff however and those that aren't are in the appendix

[thorn cloak]

I also heard John’s book is very good but haven’t looked at it personally

[gray gazelle]

What are some must have springer books? Any area

Im trying to take advantage of the sale

[gentle jasper]

Could anyone speak on Lang’s “Undergraduate Algebra” book? Is it sort of a “Baby Algebra” compared to his graduate book? I’m trying to decide between the two.

I’ve looked at some others, but Lang seems to present things in a way that work with me, so I’d rather just work through his book.

And could anyone compare its coverage/focus to Dummit and Foote?

[unborn jackal]

i feel like they have a sale every 3 months

idk

[undone finch]

thank you very much

[marble fern]

Hello all

Can someone recommend me a good category theory book?

I'm trying to self-learn all proving-related mathematical fields, like model theory, category theory

What other fields should I learn?

[mystic orbit]

Its called complex analysis in one variable btw

Forgot to mention

[restive falcon]

proof theory?

[restive falcon]

category theory in context by emily riehl is the one i learnt from

[marble fern]

Thank you so much

[marble fern]

If I knew the word for it I'd have googled it

The math fields relating to proving and set theory and logic

[restive falcon]

i mean like

[marble fern]

Y'know what I mean, like model theory and category theory and set theory and stuff

[restive falcon]

proof theory

[marble fern]

Is that a thing?

[restive falcon]

yes

[marble fern]

Oh my god

[restive falcon]

i will say
category theory is kind of the odd one out there

[marble fern]

Words which do not parrain to awakening of an inappropriate kind can't describe how I feel

[marble fern]

Noticed

I can't insert that image

[restive falcon]

it's definitely used within logic

[molten gulch]

#chill for images

[undone finch]

Part of the issue too is that there are multiple fields engaging with those questions.
There's not like a clear essential character that's epitomized by some community.

That's partly stems from the different demands people have for what/isn't a "proof".
Or like what do people want their proofs to be able to do.

[marble fern]

I put it on chill

[restive falcon]

no but like
there is literally an area of mathematics called proof theory which studies proof

[marble fern]

I'm downloading a book

[restive falcon]

sure you can do logic that crosses over between proof and model theory

[undone finch]

Yes, of that I'm aware.
I'm saying that the distinction is not so rigid.
Even calling it "an area of math" is whatever.
But there are multiple disciplines that engage with questions of what is proof.
Proof Theory is obviously related, but does not stand in for all relevant ones.

[restive falcon]

what are these multiple disciplines

[marble fern]

Ok so

[undone finch]

Category Theory
Reverse Mathematics
Meta-Mathematics
Philosophy of Math
Model Theory
Foundational Mathematics
Topos Theory
Homotopy Type Theory

etc

[marble fern]

I looked up model theory on wikipedia

I went to see also

[undone finch]

There are not always hard-and-fast distinctions here.

[marble fern]

I can't show the screenshot but it hasany fields

[marble fern]

I think some of these are more advanced than I am trying to get

I'm just working on something on computer proving

[restive falcon]

ok sure anything to do with logic has some connection with the properties of proof

[restive falcon]

oh you'll need type theory

[marble fern]

Thanks

[restive falcon]

that's kind of what every theorem prover is based on

[undone finch]

I don't think all of what I said necessarily has "anything to do with logic", but I hear you.

[restive falcon]

apart from metamath i think?

[marble fern]

Wait is metamath that axiomatic system equivalent to zfc

I heard it used in busy beaver lower bounds

[undone finch]

To echo what's been actually said though, I think if you're working from Proof Assistants, all of the above has an introductory level that's approachable to someone who understands basic set theory - except maybe model theroy.

So Type Theory would be number one imo.

[marble fern]

I am working on proof assistants

[undone finch]

Which one(s)?

[marble fern]

Currently I'm reading on Z3

[restive falcon]

i mean i think multiple of the things you mentioned don't in and of themselves deal with what a proof is, but are used to study them or something

[marble fern]

But I'm trying to code something else

[restive falcon]

no it's a proof assistant

but yeah the big 2 are very much entirely rooted in type theory

and most of the others

[undone finch]

I'm not sure. I think it's gonna depend on what people need their proofs to do.
For example, Category Theory is very useful at showing what mathematical objects are appropriate for proving certain theorems.
I understand though if people will have a more syntactic treatment and say that Category Theory generally doesn't count.

[restive falcon]

yeah I don't think that counts

[marble fern]

I think I'll go

[restive falcon]

you probably have a better argument for topos theory

[marble fern]

I need to study something

Thanks a lot for everything

[undone finch]

I probably do, but am mostly agnostic on it.
I'm not really realist about any of this.

[restive falcon]

bye

[undone finch]

Take care.

[marble fern]

👋🙏

[restive falcon]

even then like

topoi are not just a logic thing

it'd feel like calling analysis a subbranch of number theory

[marble fern]

Last question

Are proof theory and type theory just smaller than cat theory and model theory?

[undone finch]

No.

The question is a bit ill-posed too.

[restive falcon]

no they're different things

[marble fern]

An introduction to cat theory is 11 times longer than an intro to proof theory

[undone finch]

It's not a containment of topics.
The fields have different goals and histories largely.

[marble fern]

I get it

I mean, as a subject to study

[restive falcon]

all 4 of those are separate fields of study

with connections in between

[undone finch]

There are different texts you can use for Category Theory designed for programmers, software engineers, and computer scientists.
Bartosz has 2 and Awodey's is respectable.

[marble fern]

Smaller as in the number of things to study

[restive falcon]

it probably depends on the text

[undone finch]

I don't really understand the question.
You could study any of these things for decades.
Do you have a particular goal in mind?

[marble fern]

Ok so

[restive falcon]

i think they're mostly all about as old as each other

well

proof theory and model theory are older

[marble fern]

In some course like MIT's analysis

You pick up baby rudin

And achieve a good understanding of real analysis

You wont know all of real analysis

But you'll know some percentage

I want that same percentage

[marble fern]

I think idk I'm a dumby

[restive falcon]

i don't think this is a well defined concept

[undone finch]

I feel that that characterization of "understanding" is really subjective and not necessarily helpful.
Moreover, if one field is more deeply developed than another, then it's easy to sort of be like what appears like a "good understanding" is quite shallow relatively speaking.

Because you have Proof Assistant motivations, maybe it helps to frame your question like that.
Like, what are you wanting to do.

[restive falcon]

like

how are you weighting it

[marble fern]

Makes very much sense

[marble fern]

Idk

[undone finch]

Maybe another question too is like what is the rush?
Are you in any particular hurry and if so to do what exactly?

[marble fern]

You know the dunning Kruger curve

[restive falcon]

"number of results i know", "number of 'significant' results i know"

etc

[restive falcon]

that's fake

[marble fern]

I'm humble, not because I know 30%, but because I know 0%

[marble fern]

Significat

[restive falcon]

still not well defined

[undone finch]

I guess, sticking to math, maybe it'd help if you grounded your goals in terms of specific, quantifiable outcomes.

[restive falcon]

like

[marble fern]

It's an idiom

That's how I take it

[restive falcon]

yeah but like
it's misleading

[undone finch]

So for example, it could be that there's some set of problems typically regarded as elementary.
Maybe then you want to be able to solve those problems.

[marble fern]

Very much smart advice

[marble fern]

You cannot be misled if you don't understand at all

[restive falcon]

the real dunning Kruger curve is a relatively shallow decreasing straight line

[marble fern]

In maths

In other sciences it isn't

[restive falcon]

as in, the difference between your percieved ability and real ability

[restive falcon]

what?

I'm literally telling you the results of the study

that dunning and kruger did

[undone finch]

You may also get better direction in communities that focus on automated theorem proving and the like.
That could look like being able to implement certain proofs, say using Lean or Coq.
It could also be like attending different seminars and being able to understand some amount ( though not always a good metric ).

Maybe there are key papers you want to be able to identify even if you don't understand them.

[marble fern]

What we are doing with dunning Kruger is taking a graph and comparing the number of nodes to the number of connections

If each nose is a piece of info

[restive falcon]

what

that's not what the dunning kruger effect is

[undone finch]

I'm getting the sense things have gotten off topic.
I'm going to take a step back.
Please take care.

[restive falcon]

ok

yes

bye

[marble fern]

Cya

Yeah we are getting off topic

[marble fern]

My point is dunning Kruger isn't well defined

[restive falcon]

it literally is

read the study

[marble fern]

Because not all information has the same topography

Wait lemme explain

[restive falcon]

it's not about knowledge

let's move

to #serious-discussion

[torn blade]

resources for learning about:

• Composition series/Jordan-Holder Theorem
• Sylow Theorems
• Solvable groups
• Nilpotent groups
• Semidirect products

can be one or multiple sources

i know the first 2 and sort of the third but not much of the last 2, just need to recap all of these for uni

[dim sierra]

Dummit and Foote

[heady ember]

Dumb foot

😔

[dim sierra]

It’s such a good textbook holyyyyy

Just so solid

Amazing incredible beautiful fantastic delicious scrumptious is what I would say about that textbook to a freshman

[heady ember]

It yaps so much from what I've heard

[mossy flume]

I do not like D&F

very dry

[old elk]

I am using Basic Abstract Algebra by Jain and Nagpaul.

I learned from someone on youtube this

“Do what you want to do with it:
Theorems
Proof
Examples
Exercises
”

[harsh sphinx]

anyone read "Modern Graph Theory" by Bollobas by any chance?

[stiff tulip]

I have not but I just picked it up to study over the break. I’ll report back in a month in a half how it is. I’m expecting good things, since I loved Bollobas’ functional analysis book

[harsh sphinx]

i wanted to see what prereq's were needed for it?

[stiff tulip]

Essentially none. Graph Theory has one of the benefits that nearly every powerful theorem is a definition or two away. This is also a trade off, since this means that theorems usually require deep mathematical maturity to understand and grasp

[harsh sphinx]

ok cool thanks, just wanted to make sure I didnt need to have advanced abstract algebra or something

[remote sparrow]

look in pins for algebra recs

also advanced modern algebra by rotman is good

[vital bane]

yk tbh I have never heard the term "Grad level intro" I just thought "okay intro = UG, grad level = grad" Also darQ you haven't responded to my ping in #real-complex-analysis

[trail hemlock]

or my ping in the reading group server

[vital bane]

mfw darQ ignores everyone

[trail hemlock]

thinks hes some big shot or smth

forgot his roots

[grim ore]

Personally like ug Hungerford, but thats just what I was exposed to first

Artin is definitely a LOT more in depth

Also ug Hungerford is nothing like the nightmare grad hungerford is greatfully

[vital bane]

D&F is the best algebra book of all time

if you disagree, you're wrong

[dim sierra]

Facts

And Lang is the worst

I regretfully own a copy 😦

[trail hemlock]

if its so bad u should jus donate it to me

[dim sierra]

I’ll trade

What you giving

I can throw in Lang’s complex analysis book in there as well

[trail hemlock]

willard's general topo & spivak CoM 😭

[dim sierra]

I’ll just take the latter

[trail hemlock]

CoM is like 2 pages

front and back

[dim sierra]

?!

[trail hemlock]

ok its like 150 pages

its so small tho

AoM is sm better 😍

[dim sierra]

Lmao

I think both of them

Have terrible treatments

Of differential forms

[trail hemlock]

oh rly? what is a good treatment of differential forms

[vital bane]

Physics books

[trail hemlock]

i like AoM, im on the 2nd last chapter (iirc)

[vital bane]

[dim sierra]

“A Visual Intro to Differential Forms and Calculus on Manifolds”

by Fourtney

It’s goofy af kinda and super slow but

[trail hemlock]

and of course its not discounted by springer rn

[dim sierra]

I think it shows what’s going on

[vital bane]

iirc tristan needham also has a diff geo book

[dim sierra]

Oh yeah that’s prolly good too

I haven’t read it yet

but that guy is goated

[trail hemlock]

i did not like needham's visual complex analysis

some of the pictures were so goofy

[dim sierra]

did you read it before or after learning complex analysis

[trail hemlock]

i like glanced at a couple pages lol

[dim sierra]

bruh

[trail hemlock]

💀

[dim sierra]

💀 indeed

[trail hemlock]

i had apush hw that day 😔

[dim sierra]

lmao how much reading do yall have to do for that

we used to have 30 pages per week

complete torture

[trail hemlock]

we had a 20 page reading quiz today

[vital bane]

I did not like the book

i like glanced at a couple pages lol

[gilded shuttle]

my apush class had 2 homework assignments the entire year

[dim sierra]

A pedestrian discord!

[gilded shuttle]

ap world was the opposite though

[trail hemlock]

yeah unfortunately i am apart of the aforementioned pedestrians in this pedestrian discord server

[grim ore]

becareful who you say that to, I said that once and like 5 people pinged me disagreeing wholeheartedly lmaooo

[grim ore]

I really liked complex by him tho funnily enough

Maybe give another read perhaps

[dim sierra]

yeah I sortta just assumed it would suck after algebra

maybe i will tho now that you say that

[fleet veldt]

hi guys, I'm looking for recommendations for "modern" books about "PDEs" and "probability and statistics"
in PDE i have a book about ODE that has a chapter about PDE but it's not enough for me (the book is "Fundamentals of Differential Equations")
what's important to me is good explanation with an explained question to understand the process

[mystic orbit]

Whar ping 😭

[mystic orbit]

Oh, right, ok

I forgor about yours

[mellow wren]

Evans PDE

It's not an easy book though by any means

You need to know a lot of analysis

Measure theory included

Some functional analysis is also good

[fleet veldt]

so it's not for me

[mellow wren]

Well PDEs are an incredibly difficult topic

[fleet veldt]

i only have calc 1-3 under my belt

[mellow wren]

Idk if there exist any undergraduate books that talk about them in any depth

[fleet veldt]

Here's the syllabus:

1. Introduction, basic concepts, and examples.

2. Linear equations of the first order, characteristic, generalization to quasi-linear equations of the first order.

3. Second-order linear equations: classification.

4. The wave equation in one dimension, d'Alembert solution (infinite section and semi-infinite section), separation of variables/Fourier expansions in a finite section.

5. The heat equation in a finite segment and its solution by separation of variables/Fouria development. Homogeneous and non-homogeneous problems. The maximum principle and the units of the solution. Solution on an infinite segment.

6. Laplace and Poisson equations, Dirichlet and Neumann problems and their solution in a rectangle in a ring and in a circle. The average theorem, the maximum principle and unit theorems. Poisson's formula and Green's functions.

7. Numerical methods for the finite difference model

we've already done 1,2 but i still dont understand ohw to solve quasi-linear PDE

[graceful moon]

You just kinda need to know some more analysis to get anywhere with PDEs beyond the basics

You can go full physics and just blindly plug and chug but (as an ex physics student) it’s not fun, I still don’t understand greens functions to this day

[remote vortex]

I fail to understand why this is not our official slogan

[fleet veldt]

it's in our course so i don't have any time to learn analysis with everything else (I'm on my third semester of electrical engineering degree) we're currently learning harmonic/Fourier analysis but i guess you meant real analysis, right?

[fleet veldt]

unless harmonic analysis is enough?

[graceful moon]

Is this a PDEs course for engineers?

It covers a pretty similar set of stuff to my physics PDEs course I did in my 4th semester, so it is definitely possible with just some Fourier series stuff and no knowledge of analysis, but equally I’m not sure anyone in that course did well or really felt like they learned anything

[vital bane]

you can talk about PDEs in different levels of depth

[vital bane]

I think Strauss' PDE book would suffice for this

"Partial Differential Equations: An Introduction" by Walter Alexander Strauss

[vital bane]

"Pedestrian Discord for Pedestrian Mathematicians"
-Mathcord

[molten gulch]

LMAOOOOOOOOOOOOOOOO

[fleet veldt]

i'll look for it, hope i'll find it

[mellow wren]

I'm pretty pragmatic about it
Always go all the way

[vital bane]

[undone finch]

A grad level intro can make more reasonable assumptions about the reader's mathematical maturity, familiarity with proof techniques, comfort with hard problems, etc. For example, I would not expect a grad level intro to Complex Analysis to have a section explaining how naive set theory works. They could, but it's not high my on my list. I also would not be surprised if said text made some light topological arguments or connections to group theory early on. Say, for example, problems meant to nudge or reveal roots of unity are isomorphic to cyclic groups and also a subgroup of some special rotational groups.

[swift dome]

i want a NT book, well written, easy to read and have bunch of good problems that will help me through

any recs

[vital bane]

Yea I guess it's for people in grad school who haven't seen complex analysis before, but want an introduction to the subject at a higher level

since they already know most of the undergrad math like UG analysis, algebra, topology

[undone finch]

Right. I'm one of those people and also for PDEs. lol.

[vital bane]

tbh PDEs at the grad level is quite an advanced subject requiring functional analysis and stuff

[mellow wren]

I usually recommend Ireland and Rosen's number theory for a good intro
But it's not an easy book by any means
If you don't know basic abstract algebra you'll struggle
Some people call it a graduate text but I've seen it mostly used for UG courses

[marble solar]

Walter Strauss' PDEs

It's an undergrad text

[vital bane]

bruh that's an algebraic NT text innit

not an intro NT text

"A Classical Introduction to Modern Number Theory"

[undone finch]

you've worked through intro grad PDE texts?

[vital bane]

sadly no, not yet 😔 I've only skimmed through them and heard stuff from analysis PhD students here

[mellow wren]

It's an intro NT text

There is a bit of algebraic number theory

But it covers very basic stuff

Like quadratic reciprocity

And basically half the book is like stuff that gauss did

[vital bane]

I see

[mellow wren]

The other half is more iffy ig

[vital bane]

ANT

[mellow wren]

But at UCSD it's used as the intro NT book for undergrads

[vital bane]

"what is this a number theory for ants"

I mean if supplemented with lectures, I'm sure it's good

[rain wren]

light topological arguments
narasimhan proves the general monodromy theorem in the second chapter

almost all of chapter 2 is topology

[vital bane]

Based

[undone finch]

Lol. I don't understand the reason for the emoji. General topology is probably more foundational than complex for many areas...

Even so, I bought Conway first. May check out Narasimhan later.

Honestly, that's been my naive impression so far. I run into complex stuff, but only as it relates to things isomorphic to them or just stuff that's general enough to apply to them.

In more specific cases, yeah they're there. But I don't feel like I'm really doing anything with them besides using them as a namespace for a particular collection of entities that have useful properties for whatever context.

[vital bane]

The emoji is demonstrating the absurd difference between your statement of what is covered and what's actually covered in book

simply: the statement is funny in the given context

[undone finch]

I'm not seeing the difference, but I'll just leave it to people actually studying the material.

[rain wren]

I just think the contrast between "light topological argument" and dedicating an entire chapter to topology kinda funny lol

I meant no offence 😭

[undone finch]

You're fine. We probably have a different frame of reference of what "a light topological argument" is for a graduate introduction to the material.

If they do stuff that's reasonable to find in a 1-3 months study of Munkres ( actually solving problems ), then that's in scope for light topological arguments for me.

[undone finch]

This is probably obscured by ideas on what a "graduate introduction" is supposed to do and whom it's for.

[modern ruin]

do yall have any complex analysis books that you would use to teach to someone who does not have a formal education in math

[marble solar]

I wouldn't teach someone without an education in mathematics complex analysis, before teaching them real analysis

[mystic orbit]

Same kekw

I'll be doing Evans next semester prolly

[undone finch]

I don't know of a text that can do this, but I think it could be done up to an elementary level, say basic geometric transformations of C. So like rotations, maybe some translations, etc.

What would you want such a math book to do? How much assumptions would you make of the reader's knowledge? Do they know what a derivative is and how to find one? What about a sequence and series?

[covert mauve]

are there any books on euclidean geometry that build it from basic axioms and still build geometric intuition? I have never attempted to fix my lack of proper geometric intuition, and it's better to work on it now than later.

[vital bane]

Tristan Needham innit

Visual Complex Analysis

[gray gazelle]

Hello! I am studying geometric series and power series and I am having problems solving exercises. Does anyone have an exercise book or lists on the Internet with solved exercises?

[undone finch]

Khan Academy and Purple Math should have stuff.

[uncut nest]

For real and complex analysis, Whats the census on the books by

• conway
• shilov
• rudin
  I have the first two, Would it be worth it to buy Rudins?

[undone finch]

So many people use Rudin that at least for the math meta, it's probably helpful so to be on the same page as many people.

[rain hound]

If we aren’t looking to first teach a formal education necessary to do complex analysis formally?

I’d just learn complex analysis calculus style out of a math methods book at that point. My favorite undergrad ones are Nearing Mathematical Tools for Physics (free!) and Boas’s book. If they’re an engineer in grad school or something, I’d really recommend the formal treatment, but Arfken and Weber have a good graduate math methods book.

[gray jungle]

i like rudins treatment of CA

might be biased cause thats the book i used

[mystic orbit]

Smay: what's a complex analysis book for people without much math training?
James: papa rudin

[gray jungle]

im replying to catman brotherman

actually i can see the confusion since armadillo was replying to smay lol ma bad

[timber mesa]

i skipped papa rudin and went straight to grandpa

(did about the first half folland instead)

[gray jungle]

follands MT treatment is arguably better

not arguably, its definitely better

i saw a lot of people recommend S&S for CA, which was fine but holy shit i hated chapter 2

[timber mesa]

never liked the writing in SS for some reason

I do have a printout of the measure one somewhere

[gray jungle]

yeah likewise, altho the measure one is actually kinda good

at least on certain topics like differentiations

[timber mesa]

the part about differentiation is good

unsurprising given that it's Stein

[gray jungle]

same wavelenght lol yeah

[mystic orbit]

I also liked the part about differentiation

[mystic orbit]

and you were the one that recced it lmao

[heady ember]

Wait did you do complex before that? Or not at all

[undone finch]

Does anyone have any good resources explaining and developing the Error Function ( https://en.wikipedia.org/wiki/Error_function ) ?
Something like, maybe some history and also just a general treatise of the function, showing where it comes up.
Just something to develop intuitions, becuase the wikipedia page by itself doesn't really do it justice imho.

[timber mesa]

yes way before

conway

[fast trout]

Is this math book recommendations?

[sudden dock]

has anyone read "Calculus with analytic geometry by Burton Rodin". Is it any good? I am in search of a good book for calculus and came to about this one however I can't find much info about it on the interest. If you have read it, please do share your experience.

[vital bane]

conway seems super interesting

I should try that one day

[alpine ridge]

Hello, is there an exercise book that only provide word problems(real life scenario) for calc1-3?? Thanks

[sudden dock]

https://web.pdx.edu/~erdman/CALCULUS/CALCULUS_pdf.pdf
This book has separate chapters for each topics and at the end of each chapter, there are a few problems which might be of your interest.

[alpine ridge]

Perfect! Thanks

[willow merlin]

which reference explains integrating factor first order non homogeneous linear odes for beginners?

I am afraid it wasn't covered in class but is present on the final exam

because the final exam merges two classes together from different professor

so even though it wasn't covered on my class It was covered for the other class

[minor hearth]

you could check the section on Paul's math notes

[graceful moon]

Boyce di Prima & Meade will have a section on it

[gray gazelle]

Whats a good linear algebra book for self studying? Im only looking for theory and proofs.

[foggy quest]

https://mtaylor.web.unc.edu/notes/linear-algebra-notes/, https://www.math.brown.edu/streil/papers/LADW/LADW.html

[heady ember]

With LADW, you DW

[foggy quest]

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

[gray gazelle]

is set theory enough to start reading it or does it have any other prerequisites?

nvm the preface talks about it
thanks

[heady ember]

Damn Taylor's notes seem to cover a lot of cool stuff concisely, at a glance, anyway.

Maybe I should I learnt lin alg from it lol

[fast latch]

LOL

[undone finch]

Ch. 2.1 Boyce and Di Prima

[fluid wave]

someone suggested me to read Hustein and Hoffman-Kunze to learn about linear algebra, I don't have much prior knowledge, any suggestion on how I should go about reading them?

[minor hearth]

Read chunks of it and think about what you read very carefully - if you have some experience with proofs, try doing the middle-of-the-text proofs yourself before they show up. And of course, do as many exercises as you can.

[fluid wave]

I see, my issue is I have some time constraints so I don't think I would be able to give time to both

[still panther]

hoffman-kunze is pretty mild re prerequesties

[foggy quest]

It doesn't have any math prerequisite, but for linear algebra, the more settings you apply it in, the better you understand it.

[remote sparrow]

#book-recommendations message

[undone finch]

Any recommendations on a category theoretic treatment of Linear Algebra? ( Besides Aluffi ).

Could be done ( at first ) locally, looking at Vector Spaces as small Categories. But ideally develops ( eventually ) to the ( locally small ) Category of Vector Space.

[undone finch]

🤔 Alternatively, what about for Differential Geometry?

[velvet forge]

Could someone tell me some resources that can help me train with 'problem solving' (doesn't have to be specific to books)

Ping /reply to the message please

[old elk]

Advanced Linear Algebra with Applications by Mohammad :D

[trim kayak]

Hey everyone. I have basic knowledge of Algebra, Geometry, Trig, and Stats but want to learn more. I really like all 4 of these but I'm not sure if should learn more advanced topics within these subjects or learn something new like Calculus or Linear Algebra.

What would you suggest I do? Should I learn more about these as an intro before moving to something more advanced?

Could you also recommend some preferred textbooks that you suggest I use for learning and practicing problems?

Thanks!! 🙂

[remote sparrow]

calculus will give you an opportunity to apply all your knowledge of algebra and trig

linear algebra is cool too and can be learned independently of calculus in principle, but most textbooks assume you've learned calculus already

[trim kayak]

Interesting. Thanks @remote sparrow

I've taken calc before but its been awhile and it was tough. Don't focus more on Alg, Geo, Trig, or Stats?

[remote sparrow]

try the diagnostic tests in the back of stewart's calculus book

if you can confidently complete them, you're good to go

[trim kayak]

Which edition of Stewart's? I see quite a few books.

[remote sparrow]

i mean even if you only get 70% on the diagnostic tests, i'd still advise just pushing through unless you keep getting tripped up by algebra while learning calculus

[remote sparrow]

i've never looked at editions prior to the 6th edition of early transcendentals

but editions 6, 7, 8, and 9 all have diagnostic tests in the back

[trim kayak]

Are you a math major?

If I cant complete the tests, then start to review the textbook?

[dim pendant]

Advanced doesn't really feel like high school and college math. To a mathematician, "algebra", "geometry", etc. describe very different ways of doing math and look entirely different.

I suggest learning calculus again (just differential calculus and basic integration techniques) and then looking into areas of advanced math on YouTube to see what is interesting.

Calculus itself doesn't end up all that useful for certain flavors of undergraduate courses, but it shows back up through geometry and measure as many students get into grad school.

My general advice is:

• Get an idea of what advanced math is about (applied math, pure math) and what sorts of things people study (differential equations, groups, prime numbers, etc.)
• Assess whether these things are deeply interesting to you.
• Find the shortest path to what you want to learn about.
• Pick up some resources and get off to the races.

Here are some good places to start:

https://www.youtube.com/watch?v=mH0oCDa74tE&ab_channel=3Blue1Brown
https://www.youtube.com/watch?v=AmgkSdhK4K8&ab_channel=3Blue1Brown
https://www.youtube.com/watch?v=MflpyJwhMhQ&t=4s&ab_channel=Aleph0
https://www.youtube.com/watch?v=CwvuZ8aHyH4&t=551s&ab_channel=Aleph0
https://www.youtube.com/watch?v=_bJeKUosqoY&ab_channel=QuantaMagazine
https://www.youtube.com/watch?v=tRaq4aYPzCc&t=738s&ab_channel=Veritasium

[trim kayak]

Thanks!

[remote sparrow]

i'll be a masters student in math next semester if i'm admitted

[stiff grail]

hai

[oak tide]

I recommend Tokyo ghoul as a calculus student

It’s helped me come back from the brink of insanity

[gray gazelle]

Hey, I want someone to recommend me a book about financial mathematics and geometry ( I want to learn it from basics).

[unique coyote]

https://archive.org/details/schaumsoutlineof0000ayre_x3v5/page/n7/mode/2up

i think this is a pretty good book on finance

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

and this is my recommendation for an introduction to geometry

[willow merlin]

Is there any book that covers exterior algebra or hermann grassmans algebra ?

[candid creek]

is there a problem book for real / complex analysis where I can just spam practice problems

for complex analysis, basically just stuff on like cauchy integral theorem, analyticity

residue thm

[molten gulch]

<@&268886789983436800> inappropriate server link

[minor hearth]

that was fast

[molten gulch]

dunno if that as a mod or if the person got scared and deleted the link thinking it'd save their ass

[undone finch]

I don't know how deep into analysis you're looking for, but this might be useful to u

https://jonathanlove.info/qual/

[undone finch]

Study Precalculus, basic Set Theory and Logic, and learn how to prove small things.

Then move onto Calculus 1, 2, 3 and Discrete Mathematics.

[foggy quest]

section 5.3 of https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/linalg.pdf

[earnest wolf]

Guys, are Milewski's category theory video lectures good?

[trim kayak]

Can you recommend any books for those topics?

[oblique current]

Hi, i love math i was wanting to read something about it, can someone recomendme a book?

[earnest wolf]

what about «Princeton companion to mathematics»

[minor hearth]

Proofs from the Book is a tough but beautiful read
I haven't read it myself, but Godel, Escher, Bach is good I hear
Flatland is pretty good

if you want to get into mathematics though, that's a different ballgame that requires knowing what level you're on

[old elk]

I have found that no matter where I run, whenever I change a book it always tells me the same theorem, only the structure of the proof changes, maybe some additional examples, basically being forced to learn what it really is, having many books is not an option.

[oblique current]

Nah, I'm still in high school, I just want to know more about it

[earnest wolf]

then Godel, Escher, Bach will be tough ig

[oblique current]

ty

[restive falcon]

GEB is okay

the way hofstadter writes about mathematics makes it clear he doesn't fully get what like

an isomorphism is

etc

[minor hearth]

I see - that's quite odd

[minor hearth]

You could try reading up on the biographies of famous mathematicians like Galois or Euler - I found it fascinating to see how topics developed with time that way

[oblique current]

maybe, but rn im just trying to understand the next themes than i will see next year in school, so i can do it more easily

[minor hearth]

Ah! That makes sense!

What have you studied so far, and what do you expect to see soon?

[oblique current]

btw here, the school ends like in december 7 and start in march

[oblique current]

really idk, i tryed searching into the public info of the goberment about education but there is only a info about how to say the themes, never naming it

[minor hearth]

odd

well, what grade / year are you in? most schools all over cover comparable topics around the same grades

[oblique current]

3 grade

but here the school system is different

i mean, 3-5 years go to "jardin" then 6-12/13 to "primary" and then 13-18 highschool

im at the mid of highschool rn

[minor hearth]

hmm

[oblique current]

is weird ngl, when u enter highschool u can stay with dudes of 18-19

btw the chat is about books lmao

[minor hearth]

maybe Infinite Powers by Steven Strogatz would be up your alley?

It's a popular book on calculus

haven't read it myself, but it seems to tie in with a topic you will most likely see nearing the end of high school

[oblique current]

i will check it, thanks

[floral lantern]

Recs for a quick intro to Galois theory (enough to read Ireland and Rosen, I guess) - my algebra textbook Judson has what looks like to be a very lackluster treatment, so looking for a different book.

[gray gazelle]

Fields and Galois Theory, Milne

[minor hearth]

I'm going through the text by Rotman - it seems good but doesn't go into detail on the Field theory as much

[trim kayak]

Hey everyone. I have basic knowledge of Algebra, Geometry, Trig, and Stats but want to learn more. I really like all 4 of these but I'm not sure if should learn more advanced topics within these subjects or learn something new like Calculus or Linear Algebra.

What would you suggest I do? Should I learn more about these as an intro before moving to something more advanced?

Could you also recommend some preferred textbooks that you suggest I use for learning and practicing problems?

Thanks!! 🙂

[undone finch]

Idk about Guys.
But yes, they are good.

[earnest wolf]

thanks!

btw, what's wrong with guys?
like, it includes all genders

[old elk]

Are you talking about Galois Theory, I need to study this subject, which introductory books do you recommend?

[undone finch]

@trim kayak @gray gazelle

Any Precalculus text by Pearson or Stewart, whatever is latest or within last 2.

For Discrete Math whatever edition of Kenneth Rosen is latest or within the last 2.

[undone finch]

For Trigonometry or College Alegbra, same vibe

Usual progression is

College Algebra -> Trigonometry -> Pre Calculus -> Calculus

You could reasonably do Discrete Math after Precalculus instead though

[undone finch]

I don't think these arguments are perfect, but they help pump intuition.

https://plato.stanford.edu/entries/feminism-language/#FalsGendNeut

[trim kayak]

Don't focus on topics I already know. Go to Pre-Calc instead?

[undone finch]

idk how well you do or don't know the topics. Math pedagogy is designed so that problems are solved, not just read.

So if you do like 20-30 problems for each PreCalculus section, averaging 90% or more correctness, then I think you're good.

[undone finch]

You could take some college algebra and trigonometry final exams to see how you do. Closed book. Time limit of 45min, or say average of 2min per problem.

[trim kayak]

That's a good idea. Where would you suggest I find some final exams?

[undone finch]

I'm not sure, but try Khan Academy, Purple Math, Schaums, and Paul's Notes.

*You'll want to make sure they come with solutions too.

Alternatively, some Trig and College Algebra books by Pearson may have exams in them.

If you know which problems are in the back of the books, you could make your own exam by doing like some random assortment of problems per chapter. Say, for example, 3 random problems per section

[minor hearth]

as I stated above, I'm going through Rotman's book

so far it seems pretty good

[foggy relic]

Artin

THE Artin

Not the Artin

Lang is also very fast in his coverage of Galois theory

[floral lantern]

Will do - that's the recommendation I got from some other people, so looks like I'm reading artin

[foggy relic]

Not Michael Artin

Emil Artin

His book

[floral lantern]

huh

ok

[trim kayak]

Should I read a chapter at a time, take notes, then practice some problems?

I should start with Stewart's Pre-Calc?

[wet sphinx]

Hi bros. Any book to understand calculus from its roots?

[dim sierra]

Understanding Analysis by Abbott

If you’re wondering why the title doesn’t have calculus it’s cuz the subject dealing with calculus rigorously is called real analysis

[wet sphinx]

thanks mate!

Ill check it out

[dim sierra]

Just be warned tho it’s quite a bit different from calculus you learn in high school

[wet sphinx]

Dont worry bro. Ill put the reps in. NO TRAIN, NO GAINS!

[rigid trail]

Best brief books/online resources to refresh on multivariable? Haven't done calculus in like two years and I'm taking diffeq/real analysis next sem and want to warm up

Also I feel like I may have forgotten stuff so I don't just want to do exercise problems etc

[minor hearth]

you could just speedrun reading Paul's notes

[rigid trail]

Alright I considered that

Will do

[minor hearth]

one thing to keep in mind though is that analysis has a very different flavor

[rigid trail]

Ofc

I just wanna get back into the calculus flow

[molten gulch]

we also read "div grad curl and all that" for multivar

[minor hearth]

ah, I see

if you get time afterwards, it might be in your interest to read some of the analysis materials early

is it a first course in analysis?

[rigid trail]

Yeah but I have done a little bit reading on basic real analysis

[rigid trail]

Is that a book?

[molten gulch]

yes

[rigid trail]

Okay

Thanks

I'll look at Paul's and that

[molten gulch]

but we did that alongside a full calc textbook

so

yeah

[wet sphinx]

maths are hard 😦

[stiff tulip]

What’s a good intro to operator theory after measure theory and intro functional analysis

[hollow peak]

Yosida functional analysis has some good semi group and compact operator theory

Analysis now by Pederson covers spectral theory of compact and unbounded operators in a nice, modern, and sophisticated treatement

It also constructs the functional calculus

And of course, if you're looking for more real stuff, Evans does sobolev spaces and linear PDE operator theory, as does Brezis

[gray jungle]

I second Yosida, good book, ile also add peter lax FA book.

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-319-72326-6

$16 rn

[timber mesa]

there are some nice springer books on sale rn, not many well known ones but still some nice things if you dig in

this one is also at 16 usd, I have a copy already it's good for review and has a ton of exercises https://link.springer.com/book/10.1007/978-3-030-38219-3

[trail hemlock]

(unrelated to anyone's question lol) this book is on sale
https://link.springer.com/book/10.1007/978-1-4612-1007-8
and from what i hear, its really nice

[old elk]

It's functional analysis

[rich sun]

now!

[trail hemlock]

i need darq to voice this over

[shy silo]

any recommendations for analytic number theory?

I feel like Apostol is too 'from the ground up' and makes it boring for me. Specially since I think it has some non-standard notation (?)

[midnight thunder]

recommendations for mathematical philosophy?

[cosmic pagoda]

hi guys, i need to start learning basic trigonometry for optics, any book recomdations ( im a begginer)

[sacred sorrel]

I just want to say here that exists a book called "Calculus in Context" by Kenneth Hoffman et al, that it is very good

and it's free

[trail hemlock]

is that a difference Kenneth Hoffman than the one who write the Linear Algebra text?

[umbral field]

calculus in context - kenneth r. hoffman of hampshire college
linear algebra - kenneth m. hoffman of mit

[trail hemlock]

oh lol

[rose hazel]

Hey chat, my younger brother is prepping for regional olympiads, and I'd like to gift him some books. He is currently just starting calculus, so are there any calculus books focused on improving his problem-solving skills? I know AoPS is one (though i am not completely sure how good for olympiad prep it is), but I'm also looking for other options.

[old elk]

Which introductory book for comutative algebra do you recommend?

[trail hemlock]

the aops calc book is great for olympiads, evan chen's napkin is also worth looking at. in my experience, olympiad calc problems are fairly simple to understand application problems, so any old calc book will do.

[rose hazel]

will go with aops then

[old elk]

[wheat trout]

Atiyah and Macdonald have a book, which is pretty concise and useful. You have to do a lot of exercises in it to understand. Eisenbud has a very long book called commutative algebra with a view towards algebraic geometry, quite comprehensive. Also there is a book called computational commutative algebra, if you are more interested in calculations, like calculate the Grobner basis. I never read it though. Just heard it from friends who is doing computation.

[old elk]

Great, I just downloaded the books that you just mentioned hehehe

[uneven juniper]

i recommend jouney to the west julia lovell translation abridged version

the cover is goated and the book is too

Anthony C.Yu's translation is a bit more what a professor would give you to read

but still good

[rough umbra]

What're the usually recommended texts for arithmetic geometry?

[abstract trellis]

Siegfried Bosch alg geometry and comm algebra, first part is good comm alg intro, a term of commutative algebry by altman kleiman has non-standart approach and many great excercises, all of them have solutions at the end of the book, also Paolo Ferreti recently wrote comm alg book, i havent read it yet though, but heard that its good

[undone finch]

Any recommendations on Proof Theory as well as Computability Texts? Ideally a graduate introduction.

[rigid trail]

What foundation? Type theory?

[undone finch]

I'd take Types, Categories, and/or Sets.

( HoTT and Sheaves are a WIP, so not ready for those yet )

[trim kayak]

Hey everyone. I have basic knowledge of Algebra, Geometry, Trig, and Stats but want to learn more. I really like all 4 of these but I'm not sure if should learn more advanced topics within these subjects or learn something new like Calculus or Linear Algebra.

What would you suggest I do? Should I learn more about these as an intro before moving to something more advanced?

Could you also recommend some preferred textbooks that you suggest I use for learning and practicing problems?

Thanks!! 🙂

[median edge]

what books would u say are good for geometry, (synthetic only)