book-recommendations

[remote sparrow]

e.g. conway

[marble solar]

What are you learning analysis for?

What interests you?

If you haven't learned any complex yet, then it's a good time to learn complex analysis. If you've learned real & complex, then it's a good time to look at PDEs

[placid canopy]

ah right, and thanks for the specific rec!

[placid canopy]

thinking about this since our professor had introduced hilbert spaces (not on the test) to motivate potentially functional analysis

[trail hemlock]

i took a brief glance at kolmogorov's FA book and it seems to be nice as well

[placid canopy]

i'm still a sophomore, so i'm still unsure but i'd say real was my favorite class so far in undergrad

[placid canopy]

complex seems to be a good angle though, especially for scratching that analysis itch!

[sharp latch]

I liked Perfect Rigor by Masha Gessen and The Man Who Knew Only Numbers by Paul Hoffman. In general, biographies of mathematicians will cover lots of historical context for their lives as well as the work they did but in abstract easily digestible terms

[main cedar]

hi all, i just finished highschool recently and am looking to self-stduy before uni starts

i was wondering if anyone recommends any textbooks for complex numbers that is not too verbose. I noticed that my uni course doesn't seem to contain much of complex analysis (if any) and I am not really motivated to continue with uni after undergrad

if important, my highschool covered basics of complex numbers although it is more heavy flavoured in geometry and polynomials

[opal flicker]

any good books / free lecture playlists on mathematical logic?

[main cedar]

what level

or if there is an emphasis on a topic

'logic' is really broad and vague so it might be hard to find what u are looking for specifically

[opal flicker]

I'm in high-school but I'm interested in how a formal system is constructed, a rigorous definition of a proof, incompleteness theorem and some model theory

I've self taught myself some abstract maths so I'd say early undergrad level

some of the questions I want an answer of would be how zfc works as it is, since it requires definition of quantifies but it is at the same time an axiom

maybe something about compatability consistency and decidability as well

that would be grand

[main cedar]

im not much help sry, axiomatic maths is not something ive studied really

[opal flicker]

np

[main cedar]

although more rigorous proofs and maths of that nature tends to be taught hand-in-hand with most undergrad math and i think its only post grad that u deal with the latter

[opal flicker]

I see

[open merlin]

#book-recommendations message

there's a bunch of suggestions in this pinned message

[opal flicker]

I'll have a look

ty

[wise crater]

read peter smith's books on Godel's theorem

they're pretty accessible

[vital bane]

not even close I mean if you're just reading through it and not doing any of the exercises...then probably? but that's not entirely useful

doing exercises is where 70% of the learning happens

[celest bear]

True

How about 2-3 months then

[vital bane]

sure that's doable if you're spending 4 hours a day

[celest bear]

I got the free time

[vital bane]

lucky you

[celest bear]

Yeah I’m an introvert

It’s go to the gym

Study

Sleep

Repeat

[vital bane]

you should also hang out with friends sometimes, or study with friends

good friends are hard to come by these days

[tender cobalt]

i lost friends thanks to maths

[celest bear]

Yeah

There’s not really anyone I know in my class

I would prefer to study alone

[tender cobalt]

Same

I study alone mainly because no one else is interested in the things I study

[celest bear]

Exactly

[tender cobalt]

I'm a highschooler so

[celest bear]

Everyone’s just doing the hw

I got my own textbook

[tender cobalt]

No one else is interested to know whats linear algebra lol

or even theoretical bits of calculus

[celest bear]

Ooh I would love to learn linear

But I wanna get calc done first

[molten gulch]

Analysis and Algebra are very fun

[molten gulch]

The lack of interest by highschools in more undergraduate level mathematics irks me

[celest bear]

And what’s weird is my school has one calc class with a good chunk of students

But none of them seem interested to pursue a career in math

[molten gulch]

calc is useful for other fields too

physics, chem, CS, etc...

[celest bear]

Yeah

But for some it’s not worth the effort I guess

[molten gulch]

our school offered multivar calc and one kid finished that in 9th grade, a lot of people just clowned on him for "being such a nerd"

[tender cobalt]

no one likes math

[tender cobalt]

😭

I'm in 9th grade and I'm studying spivak calculus after learning non rigorous calculus

am i a weirdo

[rigid trail]

Bruh

They're just jealous

[tender cobalt]

Facts

[celest bear]

That’s sad

Math is underrated

[tender cobalt]

everyone is like

I wnana be physicist when i grow up

I wanna be engineer

I wanna be doctor

I wanna be scientist

but no one says I wanna be a mathematician

[rigid trail]

I want to be a mathematician

[celest bear]

It’s all about money these days

[tender cobalt]

lol even so they don't self study it still

Self studying something that interests you is really uncommon

they grind valorant fortnite minecraft whatever

i grind maths 💪

each math chapter is a level to me or a quest

[celest bear]

Literally the only hard part is consistency

[tender cobalt]

a math subject is like a questline

[rigid trail]

I doomscroll nlab 😤

[molten gulch]

no

[celest bear]

I think once I finish integration, I’ll find another book for linear algebra

Or number theory

[tender cobalt]

what book are you using to learn calculus

[celest bear]

Thomas’ calculus

https://a.co/d/gDVh7Uy

[tender cobalt]

Awesome

[main cedar]

tbh the friends point is fairly important

friendships in earlier stages of our lives tend ot be more pure

theres no motivations in befriend another besides just being friensd

[tender cobalt]

idk why i lost all friends at the end of the year

lonely 17yo

[main cedar]

as u move on to other parts in life where money and there are things to gain or lose, friendships become harder to distinguish

between friendships built on the idea that "I can benefit from this friendship in X ways" and just "i want to be friends"

[tender cobalt]

i guess the latter only happens for kids

for late teenagers, i dont think that applies most of the time

[main cedar]

'most'

it only becomes harder later on

[tender cobalt]

well i have had friends who benefitted from me since i was 12-13

[main cedar]

i think now is as good as ever of a time to build some authentic friends

anyhow, i dont mean to be rude but this is digressing from the channel

[tender cobalt]

right

[main cedar]

(my fualt for starting it)

[tender cobalt]

maybe #chill

[crimson mural]

hi

[cyan valve]

Is there a good reference to learn about dg algebras?

[native cradle]

can I have a Multi var calc book recommendations

something between stewart and shifrin preferibly

Or would shifrin be ideal

I want for instance something that actually explains the double derivate test for multivariable functions

[molten gulch]

I think second derivative tests work the same as for single var functions

[wise crater]

its up to the hessian

and positive definiteness

[devout mica]

Can Somebody give me a recommendation of a book thats about topology or set theory or calculus? One of the three, i'd appreciate it ,thanks

[wise crater]

Munkres is the go to for point set topology

[devout mica]

Can you send me an Amazon link?

[native cradle]

so which book is that?

[wise crater]

not a book thats just a construction you use to do the 2nd derivative test

[vital bane]

shifrin does

[wise crater]

im trying to think you'll have to gice me a bit

[native cradle]

Yeah,I know, but shifrin introduces toplogy on R^n, I'm still doing the topology of R

[vital bane]

it's literally the same bro

[native cradle]

I see

okay

will use shifrin then

[vital bane]

even topology of general metric spaces is basically the exact same as topology of R

as in if you know how it works on R, you know how it works on general metric spaces

All the properties of open sets, closed sets, connected sets and compact sets generalize easily

[native cradle]

I see

thanks

[vital bane]

which books are you using for analysis?

Abbott?

[native cradle]

yea

I'm still in chapter 1

I forgot that I haven't started toplogy yet

oops

[tender cobalt]

I'm in spivak's chapter 1

and getting cooked

[fresh skiff]

Interesting i am using Abbott as well

[remote sparrow]

gamelin

[remote sparrow]

#book-recommendations message

https://youtube.com/playlist?list=PLjJhPCaCziSRSUtQiTA_yx5TJ76G_EqUJ

https://youtube.com/playlist?list=PLjJhPCaCziSQyON7NLc8Ac8ibdm6_iDQf

https://ocw.metu.edu.tr/course/view.php?id=270

[opal flicker]

no offense but this guy doesn't explain things well

it looks like he's reading off a book in particular endertons

[remote sparrow]

you can look at one of the books i've listed instead

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

[hidden wharf]

Hi, I would like to hear an advice on what should I read. So, I have two books for linear algebra one is Linear Algebra Done Right and the other one is The Elementary Linear Algebra by Howard Anton, what should I read if I've just finished reading How to Prove It?

[wise crater]

Anton is pretty milquetoast, not very proof heavy from what i remember. Plenty of exercises

never done Axler

Ive heard theres more proofs, determinant is defined more generally (Axler famously hates the determinant)

[tender cobalt]

I have not finished axler but i see lots of proofs in the exercises

well its mostly proofs

[hidden wharf]

Yeah, I know, but I've read the introduction to Axler's and it says that if you are a student then it is probably your second exposure to the topic, so I immediately thought that this book is for more advanced users

What would you say?

[wise crater]

My school revised LA curriculum a few times over my time there, by the time I graduated and I think they ironed out the kinks

Axler was in the pure math course on LA, and they used a more computationally heavy book than Anton for the gen sci req, cant remember the name

maybe it was anton

[molten gulch]

We had a computational book in linear 1 here and linear 2 generally follows friedberg or axler

[wise crater]

i dont think anton is a complete treatment by any means, i felt like i came away from my degree with a lot of holes i had to fill on my own time

[hidden wharf]

The problem is that I'm not even in the university yet, I finished calculus then I finished How to Prove it and now I'm thinking whats next

[tender cobalt]

Linear Algebra Done Right: Calls itself a second course (meaning theory at the expense of computations), but it's self-contained and has rather gentle prose. Works over R and C. Anti-determinant, which in previous editions led to stupid choices. 4th edition is much better (I'd still change some stuff, but it's no longer unhinged), and now it's one of the few books that does multilinear algebra properly rather than just doing the minimum needed to define determinants.

it would seem the book is pretty much self contained

[tender cobalt]

but it depends how do you want to learn math

do you want to learn theory or just computations?

[hidden wharf]

theory

[tender cobalt]

then go for linear algebra done right

it's full of theory

and since you learnt how to write proofs

you'll be fine

[hidden wharf]

Ok, thank you very much

[tender cobalt]

https://www.youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmSinFV0wEir2Vw

the author has this playlist on youtube to accompany the book

if youre into videos then these will come in handy

[clever tiger]

Currently going over Algebra 1 independently before starting Algebra 2 and I'm not sure exactly what I should know and what topics are most important to have a good understanding of. Anyone know any free books, or strategies to relearn and remember the material (I understand it easily but forget it easily too).

[normal crystal]

you can look at OpenStax textbooks or Khan Academy

[clever tiger]

Not a huge fan of khan but ill try openstax, heard of it before. thanks

[timber mesa]

please don't spam links in the server, especially not in this channel

[willow merlin]

which reasource explains orthogonal projections for newbies?

[molten gulch]

most linear algebra textbooks

[tribal crow]

most linear algebra books would have a section dedicated to orthogonal projections, methinks

[willow merlin]

I never understand it, I will keep reading I guess, linear algebra sucks

[molten gulch]

The only way to understand is to do problem sets

[graceful moon]

If you honestly just google orthogonal projection any one of the pictures that appear should give you a pretty good idea of what it is, it’s a very geometric idea

[willow merlin]

I am trying to do the orthogonal projection of a point onto a line

[remote sparrow]

@shadow river @trail hemlock @heady ember heads up, bought a "Like New" copy of Set Theory by jech from amazon for about a 45% discount from the list price, but it's print on demand slop

[heady ember]

Print it out yourself and thread bind it yourself

I printed out a copy of Cartan's Differential Calculus and I'm planning to bind it when I recover from my flu.

[trail hemlock]

of course it is smh

i got a copy of rotman from springer and it’s also the same

[remote sparrow]

i went for the softcover of his AT

honestly softcovers are better if you get a POD

[heady ember]

POD?

[molten gulch]

print on demand, I assume

[remote sparrow]

print on demand

[heady ember]

I see

[shadow river]

nice, i definitely didn't get 45% off my copy lol!

[remote sparrow]

how's the binding on yours though

mine is glued

[shadow river]

i don't think so, it folds pretty nice

[remote sparrow]

mind sending a picture?

wait when did you buy your copy anyway, and from where?

was it new or used?

[open merlin]

Anyone got any history of math books they particularly enjoyed?

[shadow river]

i got it on amazon, it was new but probably printed on demand. i'll send a pic when im at home

[remote sparrow]

[remote vortex]

All sets, all the time

[sharp latch]

Where did you learn to bind books?

[remote sparrow]

https://www.reddit.com/r/bookbinding/

here is a pretty good starting point

[timber mesa]

book binding

[trail hemlock]

is that bad or good? i don’t get it lol

[remote sparrow]

the glue is cracked in four places

it's normal but it sucks

[trail hemlock]

oh 😭

springer used might be the way to go

all my badly bound low quality books are the new springer ones

[remote sparrow]

well i bought a used book

i mean it said "like new" but it's kind of a gamble

[trail hemlock]

lol

[loud cradle]

you have to go back more than a decade if you want reliable quality from springer, they had already started the print-on-demand crap by the early 2010s

[heady ember]

I found an online tutorial. I followed it yet though

There are some neat online tools that can help you convert a normal PDF to one arranged in signatures, for binding.

[remote sparrow]

the book was first published 2002 but i got unlucky

[tender cobalt]

I buy books from a service who print the book out for me and puts desired binding like softcover or hardcover

spivak calculus costed like 6.70$ hardcover lol

[remote sparrow]

lulu?

[tender cobalt]

no

its some book store in my country (Bangladesh)

[remote sparrow]

yeah that tracks

[normal crystal]

in the US, 6.70 hardly gets you the cover

[karmic wave]

is anyone (in turkey) or ( turkish)?

if so is there any book/source suggestions?

[earnest wolf]

imagine getting US salary and living in Bangladesh

u will be considered a god

it's also what europeans sometimes aim for [getting a remote job in the US while spending it in their home country]

because buying power per buck in eu >> in the US

but salaries are 5ĥìț

[rigid flint]

are there any good books on learning about series? im currently going through the book (Almost) Impossible Integrals, Series and Sums, and im struggling with the series and sums part.

[tender cobalt]

although with the spivak calculus that i bought from them there are some issues with the order of the pages cuz they probably printed it from the pdf found online which has the issues

[tender cobalt]

yea

3000$ per month here is considered rich

[devout mica]

would you guys say this book is good or you have any book you would recommend over this one https://www.amazon.es/Real-Analysis-Long-Form-Mathematics-Textbook/dp/1077254547/ref=bmx_dp_ke1c7pso_d_sccl_3_1/258-6643433-7816722?pd_rd_w=OHLSJ&content-id=amzn1.sym.674a7df6-bf6f-4380-ba5f-567588ae00ee&pf_rd_p=674a7df6-bf6f-4380-ba5f-567588ae00ee&pf_rd_r=PK1XKYB7MAA6KS5Z4T5Y&pd_rd_wg=9wglQ&pd_rd_r=9943266b-8fa4-4475-8ec1-2a73a2bc3f99&pd_rd_i=1077254547&psc=1

[earnest wolf]

I read bits of it, and it seemed extremely friendly

especially if u don't have that much mathematical maturity (ie haven't taken a bunch of proof-based classes before)

there isn't one holy book tho

I'd recommend reading motivation in Cummings' book and filling in the details with other ones

Check out Abbott also — it's very very good for self studying

[vital bane]

Do you have a printer?

also I hope you get well soon

[spiral patio]

Good vector calculus book?

[tender cobalt]

multivariable as well ?

[spiral patio]

Yea

[tender cobalt]

do you want rigorous

or just a book with the computations and formulas

[tender cobalt]

you could go for Stewart's calculus or Thomas' calculus (a bit more theoretical than stewart) in that case

[spiral patio]

Not rigorous im in engineering

[tender cobalt]

^

[spiral patio]

Ah ok thanks very very much!!

[vital bane]

http://www.damtp.cam.ac.uk/user/tong/vc.html

Also check out these

very useful for physics/engineering students

[molten gulch]

We still look over these occasionally because while we generally prefer a "maths" view of what this stuff looks like, sources like this are helpful for us to just quickly check on for something if we need be

[autumn fox]

any recommendations for more advanced linear algebra textbook?

[molten gulch]

We liked friedberg and axler for proof based linear (assuming this is NOT what you mean) but if you want to go further than that I guess there's like roman's advanced linear algebra (only glanced at this) and I think most books like Lang would have a section on Multilinear Algebra and Module theory if that's more your interest

[autumn fox]

yeah my library has access to roman's book so i'll start with that if it's decent
especially the chapter about metric vector spaces and bilinear forms seems like it would be useful for what i'm after

[tender cobalt]

i own axlers book and romans book

none of which i have even read

idk why do i have romans book i havent even finished axler

but the last chapter in romans book umbral calculus, its funny

[upper garnet]

I have thisssss

[tender cobalt]

which

[upper garnet]

Stewarts 8th edition early transcendentals

[tender cobalt]

ah I see

[weary bison]

Hello! Why was the channel that collated book recommendations archived? Also I vaguely remember that the reviews also got put on a website, but does anyone have that link if that site is still extant?

[trail hemlock]

https://mathematics.gg/books
it’s it the channel description for future reference

[remote sparrow]

bump

[heady ember]

No but my mum's office does. The paper and ink seem to be of high quality too

[heady ember]

Thanks

[earnest wolf]

btw, why weren't the nicks of the authors who wrote the reviews mentioned on the website?

[trail hemlock]

lol good point

[oblique hatch]

What’s a good book for arithmetic dynamics, for someone who know like a first (slightly more applied) course on dynamical systems, and a fair amount of number theory?

[covert portal]

whats a good book for quantum algebra

[shadow river]

as in quantum groups, free probability, etc?

teo banica has a new book on the subject, I've only heard good things but I haven't read it

[daring lake]

just had a look

how did he write so many books wow

[weary bison]

Thank you very much!

Incidentally, do y'all have recommendations for books on the history of math and the philosophy of math? For the former, I'm looking for books centered around the 20th century and maybe one or two centuries earlier, and for both, I'm interested in books on the Crisis in Foundations and its aftermath

[tidal sonnet]

Anyone could recommend a few for beginners getting into pre-algebra? I’ve collected a few sources and want to compare, the recommendations here, thank you.

[trail hemlock]

aops prealgebra is my fav, khan academy is great as well

[tidal sonnet]

I’m sort of skeptical towards Khan Academy, recently I watched a video about how it ruined stem majors, because it’s main focus was the step-by-step, and that it doesn’t solve actual problems that you’re just watch another person doing it. That’s what they said though, Idk what’s your take?

[trail hemlock]

out of curiosity, can u send the video?

my take on that is, well khan academy does focus on you solving actual problems. it has short quizzes after every unit, and a big unit test at the end of each topic

idk what a step-by-step focus means, but imo its useful for students to kinda see how someone tackles a problem and understands how to look at a problem before solving on their own

[tidal sonnet]

Alright, let me find the video, also I looked at the books you suggested and glad that it included like a beginner test to see if I am ready to take on it

[heady ember]

If one merely looks at the solution, without attempting it themselves beforehand, then its their own fault imo.

The resources are there. How one chooses to use said resources is up to themselves.

[trail hemlock]

reminds me of this from Lee's preface

[heady ember]

Skill issue

I do not extract joy from seeing solutions, only from finding my own. So, I face no such temptation

[tidal sonnet]

https://youtu.be/o2HBrGURofY?si=bW_7ooPIXQKlEoX9

[trail hemlock]

ight bro 🤓 🤓

[trail hemlock]

its notable that he doesnt like people looking at solutions or step-by-step, but he sells an "The Ultimate Crash Course for Calculus 1 & 2" with "Step-by-Step Solutions and Formula Guides for Common Calculus Exam Questions"

[tidal sonnet]

True, can’t afford it tho

[trail hemlock]

that is a SCAM 🙏 hes selling what u can get for free (legally) from a calc textbook like calculus made easy

[tidal sonnet]

Lol I know, but he made good points at least

[tidal sonnet]

That being said, the textbook you suggested is their another book you could suggest less than it, my math skills are definitely not where it should be at a college level, but now it’s holiday for us, I am taking this time to learn before our next semester on Calculus

[trail hemlock]

for calc, or for precalc or lower?

[tidal sonnet]

That I do not know it just says Calculus

From previous math subjects we tackled on basic college math, statistics, physics, probability theory, and discrete math

[trail hemlock]

well there is a nice list of general stuff u should know before calc here:
https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ap-ab-about/a/ap-calc-prerequisites

u can use the relevant khan academy lessons, or u can go through an algebra skills workbook (just search up algebra II workbook) and do problems in the categories that khan academy lists

[tidal sonnet]

Alright I’ll look into it thank you for the info, could I contact you someday regarding the progress?

[trail hemlock]

u can send ur questions in #calculus and i will respond if im there

[tidal sonnet]

Alright thank you once again

[fresh skiff]

i wish i read it few mintues ago, i just gave up and looked the solution and my reaction was exactly same as lee mentioned damn

[trail hemlock]

yeah i was abt to look a problem up a few days ago, but the solution just occured to me and i was like damn

it was a proof of arzela ascoli iirc

[fresh skiff]

interesting

[gentle jasper]

Could anyone recommend a relatively terse classical mechanics textbook? I’ve worked through Susskind’s TM book, and it was very good, but it’s obviously missing my details, p-sets, etc.

So many classical mechanics books are 1200 page monsters. And I don’t think many people have 1200 pages of interesting things to say, though I may be wrong.

Preferably something that’s just “hey, you know the math already, let’s just work on the physics and do a lot of applications.”

[tender cobalt]

which book topological manifold or smooth manifold

[tender cobalt]

I like "An Introduction To Mechanics" by Daniel Kleppner, the exercises are hard af but it's a math heavy book, although focused mostly on Newtonian mechanics

im by no means an expert in this , this is just what i like and my opinion , im a beginner in mechanics

[agile ermine]

can anyone recommend a book that really breaks down mathematical concepts preferably from scratch? (i'm a university student)
it feels as though my curriculum had us memorize formulas without a fundamental understanding of why they were derived in the first place. feel free to give any suggestion, but it'd be preferable if you could also mention books that really break down concepts which are elaborated more in calc + lin alg later on :))

feel free to recommend any resources other than books that could be of use too (especially for self-studying)^^

[tender cobalt]

Michael spivak for calculus

everything is proved in the book

[fresh skiff]

Topological manifolds

[agile ermine]

thank you so much!

[oblique hatch]

I’m going to try Silverman Arithmetic of Dynamical Systems
It seems to be pretty much what I’m looking for

[covert portal]

oh ty

[shadow river]

he's a brilliant guy! his cohort of mathematicians (french mathematicians working on quantum stuff since the early 2000/late 90s) are all super talented

[hallow belfry]

Can someone suggest me a rigorous book for a second course on odes? I took a course in undergrad but it didn’t go very deep on the proofs and in general it wasn’t very rigorous

[mortal creek]

Does anyone have any good books for a complete introduction to Boolean algebra? Im self-learning comp sci ATM
Books arent necessary though, any resource will do

[stoic hamlet]

Arnol’d has a nice book on ODEs

[karmic thorn]

Gerald Teschl, Ordinary Differential Equations and Dynamical Systems

Arnold's book is great too

[formal bronze]

Differential Equations and Dynamical Systems, Perko

[remote sparrow]

https://www.rxddit.com/r/math/comments/1hd5x0h/publishers_that_still_produce_high_quality_print/

[formal parcel]

I am currently reading book of proof and I want to have a book along side it that really covers discrete mathematics well. anyone have reccomendations?

[tame tree]

@wary pier do you have any words on spivak vs munkres for calculus on manifolds

[willow merlin]

any book on game theory?

[remote sparrow]

are you still doing hubbard

[tame tree]

i occasionally refer to it now and then

but it's treatment of stuff wasn't the best fit for me

i've benefitted more from learning topology more abstractly first and then going to R^n

[remote sparrow]

[tame tree]

Thanks

Is something like Lee a natural continuation after spivak

how are the exercises in folland

[molten gulch]

TTeppa, sorry if this is paritally out of the blue, but what (point set) topology book did you use?

We looked through Lee but like...idk how to feel about him omitting stuff like separation axioms, metrization lemmas, infinite tychonoff theorem, etc...

we get fully why he did it but like...idk

[tame tree]

you will assuredly learn topology by reading munkres

idk if it'll be exciting, but you will learn topology

[molten gulch]

yeah

[surreal token]

Is the Stewart calculus book good?

[molten gulch]

Go read what other people have said about it in this channel

[rigid trail]

go straight to getting an analysis book 🗿

[molten gulch]

Sure but I believe that they'd also want some computational practice

[rigid trail]

Exercises in analysis books + online problem sets for more basic calculus stuff probably suffices

[tribal crow]

I wonder if I’ll be harmed by not knowing these

[dapper root]

I think Stewart is fine

[trail hemlock]

i did a (notably short) point set book before lee and i think it works out well in terms of both maturity and understanding the material

i also look at willard to fill some stuff in for the first 4 chapters, and for later chapters rotman has material from time to time

[graceful moon]

Can point set topology ever be exciting?

[marble solar]

The weird spaces you can come up with are kind of fun

[graceful moon]

Maybe I’ve just never seen an exciting treatment but to me at least it’s essentially just a prerequisite to do more interesting stuff and all of the proofs are exceedingly dull

[marble solar]

Also examples/counter examples are fun to play with

But point set topology tends to be on the dry side

[graceful moon]

Yeah maybe that’s just a matter of taste, I personally find the weird pathological counterexamples to be neat as an idea in and of themselves but eh it’s not exactly thrilling I guess

[marble solar]

When you try to draw pictures & figure them out for yourself, it's actually pretty engaging

But when in a class a lot of the time it's beating them into your head

[graceful moon]

Topology is so useful that I don’t mind it, but it’s never been a course where I’ve come across a result or proof that got me at all excited

[molten gulch]

I see, my eventual goals are to go through hatcher or bredon and lee's ISM before moving onto more complex stuff (complex manifolds at some point), so would ITM be enough or a fuller treatment like munkres or willard or dugundji or whatever?

[trail hemlock]

thats my goal too, but im not qualified at all to answer

[graceful moon]

Yeah that’s a very good point, it’s potentially soured by my experience of oh you forgot about the polish name space under the weird topology, breaks the result that works basically every other time!

Anyway this is off topic, but yeah I just tend to feel that point set is somewhat inherently dry so maybe a more terse treatment is best to just get it done and move onto more interesting stuff

[trail hemlock]

for a terse treatment i used conway

hes such a silly guy 🥺 sometimes half a page wil just be a paragraph abt the life of some mathematician

[molten gulch]

but yeah fwiw, if anyone has a good rec for this, pls do share (and please justify)

Do not reply ping, we'll check this later, we're very tired and going off to bed in a bit

[solemn rock]

hi, can someone suggest me a good book as an introduction to differential equations?

i was suggested Futher mathematics for economic analysis(Sydsaeter), by a friend (cause i´m an econ major), is it a good book ?

[marble solar]

Boyce & DiPrima is pretty good

I can't comment on economics

[solemn rock]

ok, thanks 😉

[fresh skiff]

Does one need a first course in number theory for Abstract algebra?

[formal bronze]

No

[fresh skiff]

I saw ch 0 of D&F was about basics of number theory. So it's more than enough for the book?

[formal bronze]

Yes, to the best of my knowledge

[fresh skiff]

Gotcha

Thank you

[tender cobalt]

Any algebra book recommendations? How's Artin compared to Lang for starting out?

[slender cargo]

I've gotten up to ring theory of D&F, and yes it's enough

[fresh skiff]

cool

thank you

[ember slate]

I am a cs student and would like to learn linear algebra thoroughly, should i use Gilbert strangs mit ocw lectures in conjunction with his book which from the outside seems to be focused on the applied side or should i follow a typical (proof based) book?

[mellow surge]

use strang if you want more proofs use linear algebra by friedberg, insel and spence

[tender cobalt]

I think friedberg, insel, and spence is also has lots of computation alongside with proofs

[mellow surge]

that is true it has a nice combination of both but if you focusing purely on applications strang is better

[tender cobalt]

yeah

[tender cobalt]

guys hows loomis sternberg advanced calculus

[civic python]

I have only covered the first like 3 chapters

[civic python]

I think it’s a cool book

I like their take on differentials

I feel like you can trust the authors to give you a thorough treatment of the material

[tender cobalt]

what prereq did you have? @civic python

[daring lake]

its just stuff like modulo which you should pick up even if you don't go through that chapter

[formal parcel]

I am currently reading book of proof and I want to have a book along side it that really covers discrete mathematics well. anyone have reccomendations?

[upbeat vine]

I recently came across the book “Glimpses of Soliton Theory” 2nd Edition. It looks quite good for KdV at the first glance as it tries to develop intuitiion for ODEs and PDEs and even goes back to very first principle like equivalence of functions and the later chapters cover till Pseudo Diff operators. Has anybody used it?

[weary bison]

Bump

[fresh skiff]

ah yes, i have studied when i was studying proof writing

[gilded turtle]

can anyone suggest me resources to learn euclidian geometry

[civic python]

I had completed a course in multivariable calculus and self studied the first 5 chapters of bb rudin.

[tender cobalt]

non rigorous multivariable calculus ?

[ember ruin]

I found this optimization playlist to be helpful
https://www.youtube.com/playlist?list=PL-DDW8QIRjNOVxrU2efygBw0xADVOgpmw

[civic python]

Ye

[umbral spade]

What are some good books for probability and stats?

[patent valve]

i'm looking for a good book that contains affine and euclidian geometry with solved exercices

[tender cobalt]

Any classical mechanics or maybe fluid mechanics book targetted for someone who knows the math but not physics? Like Mathematical approach

or maybe a continuum mechanics book

[wise crater]

im looking for an optics book in the same vein, tried hecht but he's obnoxious with the exposition

[tender cobalt]

maybe try a waves book first

[wise crater]

lmfao i've studied my fair share of waves

[tender cobalt]

oo

[karmic thorn]

Marsden has books on both

[tender cobalt]

name?

[karmic thorn]

Foundations of Mechanics is the book on mechanics, very geometric approach to classical mechanics

I forgot the title for the fluids book but "marsden fluid mechanics" should suffice to get search results

[tender cobalt]

i found A Mathematical Introduction to Fluid Mechanics

[karmic thorn]

That's the one, yes

[tender cobalt]

Is there any other books

[karmic thorn]

Arnol'd, Mathematical Methods of Classical Mechanics

[tender cobalt]

Doesn't that book go over like math topics

[terse lynx]

hi does any one know this book anylase 5éme edition skowokski 1993

[orchid bridge]

Im learning about difference sets right now and my prof told me to go read up on representation theory, below is from the text im using. Does anyone have any recommendation? im looking for something as minimal as possible, I just want to be able to at least understand what the text below is saying, right now i don't even know what a group algebra is.

"The difference set will be interpreted as an element in the group algebra K[G] where J( is some field. Let us assume that the characteristic of the field and the group order are relatively prime. Then it is well known that the group algebra is semi-simple, which means that the algebra can be decomposed as an algebra into simple algebras (which are algebras without non-trivial two-sided ideals). The reader is refered to any good text book on algebra for proofs of the facts that we will use throughout this monograph"

[karmic thorn]

Well, I was under the impression that it also addressed the mechanics part

Otherwise I don't understand your request either

[tender cobalt]

I mean like learning classical mechanics without physics prereq and understanding it mathematically

[tender cobalt]

So it does cover classical mechanics?

[mossy flume]

Maybe check out Fulton-Harris or Serre's text

[orchid bridge]

thank you, going through fulton-haris right now, im missing alot of gaps even from chapter 1 but i think i should be able to fill them in as I go

[mossy flume]

what gaps?

iirc it just starts at the basics of rep theory

[orchid bridge]

just small things here and there, i don't know what a cokernel of a vector space is for example, i didn't even know you could take quotients of vector spaces actually

[mossy flume]

Have you never seen quotients of algebraic structures before?

like of a group, ring, etc

[orchid bridge]

oh i have, just never seen it in the case of a vector space

[mossy flume]

I mean it's what you expect then lol

[orchid bridge]

but thats what i mean by i can fill them in as i go

[tribal crow]

@fossil nest any thoughts?

[fresh moat]

I know this has probably been asked already but does anyone have recommendations for a substitute for AoPS’s lack of an intermediate number theory book? There is a class for it in two months but I want to learn some before then

could be books, websites, videos, etc i want good theory and good problems, hopefully in one

[marsh ingot]

Sources about M-harmonic functions?

[earnest wolf]

for anyone interested in upenn's software foundations – there seems to be some video lectures about it as well:

https://youtube.com/playlist?list=PLre5AT9JnKShFK9l9HYzkZugkJSsXioFs&si=0-xON2KoHMw9S0V-

[dim pendant]

Hahaha

[normal crystal]

a lavender infused, calming meditation on formal methods

[hollow shore]

looking for a discrete math book that isn't as full of bloat like Rosen or Epp

[latent shadow]

I once had a common core book say that 0 is a positive number and a teacher told me that 1 is prime 💀

[spice stag]

what does bloat mean in this case ? how is rosen bloated 👀 ?

[spice stag]

thats nothing my teacher was confused whether 0 can divide a prime number or not

[stray veldt]

0 is positive in france, 1 being prime or not is a convention (though not being prime is the better one)

[upper plover]

Why is 0 not negative?

[wise crater]

2nd derivative test

[quick hornet]

in french, 0 is positif and négatif

in english we typically say that 0 is neither positive nor negative

but in some sources (especially those translated from french), the "0 is both" convention is used

its ultimately arbitrary, just a question of whether you use >/< or ≥/≤

[keen vale]

///<

[devout mica]

I dont think there are any known discord Servers about engineering so i'll ask Here, do you Guys recommend any book that IS about Materials? And the Tests

Hardness

Impact

[quaint arch]

We have to take a mandatory course on mechanics (, tho I am majoring in Mathematics). Can someone suggest some good books that I may follow to have a clear understanding of it?

Side note: I am not at all good in physics. I feel horrible while studying physics coz I think the way physics books delves into concepts is highly unrigorous. (I know that I might be wrong, but that's just my opinion).

For a better glimpse into the matter, our syllabus consists of:

Co-planar forces. Astatic equilibrium. Friction. Equilibrium of a particle on a rough curve. Virtual work. Forces in three dimensions. General conditions of equilibrium. Centre of gravity for different bodies. Stable and unstable equilibrium.
Simple Harmonic Motion. Velocities and accelerations in Cartesian, polar, and intrinsic coordinates. Equations of motion referred to a set of rotating axes. Central forces. Stability of nearly circular orbits. Motion of a projectile in a resisting medium. Stability of nearly circular orbits. Motion under the inverse square law. Slightly disturbed orbits. Motion of artificial satellites. Motion of a particle in three dimensions. Motion on a smooth sphere, cone, and on any surface of revolution.
Degrees of freedom. Moments and products of inertia. Momental Ellipsoid. Principal axes. D'Alembert's Principle. Motion about a fixed axis. Compound pendulum. Motion of a rigid body in two dimensions under finite and impulsive forces. Conservation of momentum and energy.

---

This is our syllabus.

[deep epoch]

kleppner and kolenkow might be up your alley

morin/taylor classical mech might also be helpful to look at

[rich sun]

What about https://discord.gg/fYkvJNQ

[fresh skiff]

Amann and eschar

[rose dirge]

Any opinions on using Towards Higher Mathematics by Richard Earl for highschool students?

[dim pendant]

It looks fine for someone who is very solid with their algebra and calculus but I even having skimmed some of the contents, it doesn't feel especially great a presentation

I quite liked this book

Mathematical Proofs: A Transition to Advanced Mathematics by Gary Chartrand (2013-11-01) https://a.co/d/i4bLmq4

The chapter on sets is exceptionally well paced, and then you can try to read something harder, like an analysis book, to learn proofs. Like speed run it though, don't spend 100s of pages reading through the details.

[fresh moat]

.

[fresh moat]

anyone?

[hidden wharf]

What is the best rigorous multivariable calculus book?

[tribal crow]

what do you mean by "best"?

[vague granite]

mont? idk i never looked at it

but its famous

[hidden wharf]

I mean the best one you have ever come across.

The one which covers almost all useful material and also has sufficient number of examples and exercises.

For pure math

[terse lynx]

Hi does any one of you know this book analyse 5éme edition skowokoski

[fresh moat]

hmm. im not sure

i migt just use michael penn + brilliant + some outside problems honestly

[vague granite]

book >> yt imo

or like honestly pick up a college nt book

same stuff

[fresh moat]

yeah its a decent book, but i think the videos are honestly better.

[vague granite]

idk what ur aiming for tho

[fresh moat]

what recommendations for that then?

[fresh moat]

to learn more nt, but not nt that requires so much background knowledge. so some competition-style stuf fbut also more than that

[vague granite]

i meant ur comp goals

are u tryna aime

cuz like amc nt is not that deep but aime nt is more deep

usamo nt is even deeper

[severe gust]

Is Calculus Made Easy by P. Thompson a great recommendation for Calculus book in general or just for starter? Is there any thought for someone that has been reading this book?

Or is there any good recommendation Calculus book for self-study?

[upper plover]

I just went at it with Rudin.

I'm kidding.

I mean, I used Calculus by James Stewart, and it worked fine for me (though I honestly wish I just studied Set Theory and done Real Analysis...)

[fresh moat]

I kinda hate the Stewart calculus

[floral lantern]

Oh nah

Bro popped in for comp math

[floral lantern]

I like AoPS’s calculus book as well

It’s a really good book that mixes some key theory with hard problems

[floral lantern]

I mean most mvc books aren’t rigorous, but as I understand Hubbard and Hubbard is a good book

[vague granite]

lmao 😭

[trail hemlock]

what the hell

[trail hemlock]

folland's MVC is a good one

i used it with spivak's CoM (i stopped using munkres cuz it sucks) and its really good

.

[floral lantern]

nerd

I'm using munkres in my topo class next year

[trail hemlock]

munkres anaysis on manifolds

his topology book is like melatonin bro 🙏 i use willard and lee

[floral lantern]

💀

melatonin is a crazy comparison

[trail hemlock]

oh speaking of nerd, how was your primes interview

[floral lantern]

uh

I got completely broiled

he pulled a problem out of etingof's rep theory book

and it was bad

I'm just not getting in

[trail hemlock]

wait do u pick the topic?

[floral lantern]

no

[trail hemlock]

💀 💀

[floral lantern]

I put down "know basic lie/rep theory for physics" on my app

and he pulled out etingof's book 😭

I learned the basics for physics bro

not this shit

[trail hemlock]

if i got an analysis problem i would be ok ... anything else i would be COOKED 🙏 😭

[floral lantern]

tbf it was a long ass question anyways

some ppl didn't even get math

and nobody got the depth I did

💀

[trail hemlock]

u will prob be graded ok

[floral lantern]

they got like basic algebra and shit

💀

[trail hemlock]

💀

[hearty steppe]

Is there any functional analysis book on the level of Kreyzig or a bit easier?

Figured I’d ask before I go looking through my collection again cuz I dont Remember if I asked

[tender river]

eberhard zeidler applied fa with applications to math phys

[trail hemlock]

@floral lantern oh i just rememberd this, your analysis book is written by the same guy who has these notes: https://math.okstate.edu/people/lebl/uw522-s12/
this guy is awesome

[floral lantern]

Yeah nice guy

[hearty steppe]

Cool what about Variational methods/calculus of variations?

[hearty steppe]

Anyone familiar with this? https://link.springer.com/book/10.1007/978-3-662-05062-0

[alpine ridge]

Can anyone recommend a book for differential equations? Just finished calculus 2 but it only covers the basics of differential equations

[tender cobalt]

The one by Dennis G Zill is a popular choice

[alpine ridge]

Got it, thanks

[tender cobalt]

loomis is harder than rudin???

[valid coral]

What do yall think about Herstein's Abstract Algebra vs Dummit and Foote

Tried reading Dummit and Foote and that shit is really dry, it was like eating stale bread

[fresh skiff]

ch4 folland (set point topology), is it a self contained chapter?

[hearty steppe]

there are two books?

[tender cobalt]

Folland advanced calculus?

[timber mesa]

Herstein is obviously narrower in scope but probably more pedagogic

when I learnt abstract alg I didn't really follow one book just handpicked stuff from notes and stuff I read

[tender cobalt]

Other one is on PDEs i think

[remote sparrow]

https://www.amazon.com/Real-Analysis-Modern-Techniques-Applications/dp/0471317160

[hearty steppe]

One of the best books I ever worked through 👍

[hearty steppe]

Oh ok have you also checked that out? Took a glimpse of the first course book and the exposition and presentation is fantastic

[valid coral]

thanks, i'll prob use both then

[timid delta]

I'm thinking about getting Stephen Abbott Understanding Analysis, any thoughts?

[valid coral]

I think the book is pretty good. I used it as a supplement for my real analysis class, because the given book was pretty trash.

You'll eventually have to move on to Analysis on metric spaces in which Rudin or Analysis II by Tao will be better

[timid delta]

Does it have a lot of exercises?

[valid coral]

yeah it has a bit and theyre good

but if you need more than just look at another book online, Abbott's book is good solely on its explanations

[timid delta]

Thanks:)

[obtuse hawk]

lp[

[fresh skiff]

No. Folland real analysis

[fresh skiff]

Also hard one

[fresh skiff]

It's a friendly book.
Abbott contains three types of problems (easy, medium and hard) and a good number of problems as well.

[hearty steppe]

I plan on working through his Fourier analysis book at some point since I enjoyed his real analysis text so much

[fresh skiff]

abbott?

[hearty steppe]

Folland

[fresh skiff]

oh gotcha

[hearty steppe]

Abbott is good but that’s for people who don’t have much exposure to rigorous math

[fresh skiff]

agree

i tried to read folland, but stuck badly

[proper iron]

Can someone suggest a book on quant finance, I'm a beginner and know intermediate lvl maths

[willow merlin]

which book covers cyclotomic polynomials? I am trying to factor 2^15 -1

[sudden kindle]

Dummit and foote

[tender cobalt]

nah I only saw the first course book. Awesome youre liking it. PDEs are a later thing, i think you'd use some other book for it , im not sure about PDEs

[tender cobalt]

Is it rigorous

[fresh skiff]

yes

its measure theory book in actually

[tender cobalt]

ive started working through folland advanced calculus yesterday

[fresh skiff]

cool

[tender cobalt]

oh

[slender cargo]

er.. don't you need to work through single variable real analysis first?

[tender cobalt]

well this book isnt really an analysis book

its more of a multivariable calculus book

[slender cargo]

eh I think it uses a fair amount of material from real analysis, even if it's named calculus

[tender cobalt]

yea but its kept to a minimum

[slender cargo]

I guess it's not entirely necessary

[tender cobalt]

in the preface author said the prereq is just single variable calculus

[slender cargo]

Ah yeah, I'm reading it. He tried to keep the "foundations of analysis" to a bare minimum

[tender cobalt]

yep

[slender cargo]

Seems you're right

[tender cobalt]

so maybe its a spivak for multivariable???

[slender cargo]

I guess so. I think of Spivak's Calculus as a real analysis book though

[tender cobalt]

doesnt cover metric spaces though

or any topological notion

[slender cargo]

Doesn't need to in a first course imo

[fresh skiff]

some people use baby rudin as first course in analysis

[tender cobalt]

cool thing is he covers some fourier series as well xd

@slender cargo have you seen courants introduction to calculus and analysis vol 2

[slender cargo]

I have not, but I hear his stuff is good

[wide geode]

anyone have book recom for intergral

calculus

[tender cobalt]

advanced or like beginner

[wide geode]

both

[tender cobalt]

james stewart or thomas calculus is good

if you want harder and theoretical, then michael spivak

[rose dirge]

Spivak

[hearty steppe]

I’m kinda always sort of thinking about PDEs in my own way

Speaking of which idk if there are PDE book recs that aren’t too rigor heavy

[desert tusk]

Is there a fun book on symmetry groups of various geometric objects?

Stuff like hyperbolic tilings and other more exotic objects

[wise crater]

Trees by Serre is the classical example

Theres also counterintuitivelt word processing on groups by D B epstein, Cannon, Holt, Levy, Paterson and Thurston

[desert tusk]

Alright thx a lot

Do you like one more than the other?

[wise crater]

Word processing on groups is a lot less terse than Trees

Trees will also require a good amount of algebraic topology iirc

[mellow wren]

trees is like 150 pages but it's one of the deepest books I've ever read it's horribly dense

[wise crater]

The former tho is primarily on the result that there exists a quadratic time algorithm for the word problem in finitely generated groups of a certain variety

[mellow wren]

serre isn't an amazing writer imho so the exposition is kind of meh

[wise crater]

yeah its schizo tier definitely

[torn blade]

whats some interesting pure maths i can learn if im a bit burnt out of analysis/algebra/topology atm

[wise crater]

combinatorial game theory!

Look up winning plays for your mathematical games by erlenkamp and conway

[desert tusk]

oh also, is this book related to basse-serre theory? i know that subject was in a syllabus of one of my classes next semester

[wise crater]

that's correct!

its the foundational text in that series of study

afaik anyway

[marsh ingot]

Rest

[wise crater]

weakling^

[desert tusk]

pretty cool, ill have to check it out then

[torn blade]

never

[wise crater]

enjoy the rabbithole

[desert tusk]

ill prob look at both books tbh

yeah thx lol

have to do something while im on break

[marsh ingot]

I just know my limits

[marsh ingot]

Number theory

[wise crater]

we're not in the analysis channel bub those qont help you here

[marsh ingot]

I wasnt joking but ok

[sudden kindle]

Maybe try some recreational math

[next maple]

set theory

[torn blade]

what does this entail?

[sudden kindle]

There are some books by Martin gardner

[wise crater]

oh theres also knights and knaves proofs

I like Smullyans compilations, he gets real brainy by the end of some of his books

oh god that username

[still panther]

🙂

game theory, graph theory and set theory are pretty far from analysis and algebra, maybe one of those

[wise crater]

i mean if its Nash game theory its pretty close to analysis

[still panther]

formal automata theory makes for a pretty light reading

the proofs and concepts are usually short and intuitive

lattice theory is a cornerstone of math that is rarely included in the curriculum

[sudden kindle]

Its hard to stay away from algebra, analysis and topology because they are so fundamental

[marsh ingot]

Idk if recommend measure theory

[fresh skiff]

Hi alex

[surreal token]

any book recs on linear algebra?

[tribal crow]

how rigourous of a book do you want?

[surreal token]

not so much, i heard i can start linear algebra in the same time as calculus so an easier book would be nice

[tribal crow]

Strang or Anton might be good picks

[surreal token]

ok thanks higher

ur so cool

[marsh ingot]

Hiiii

[severe kernel]

A Trans man walks into a gay bar

It's a super good read

[fresh skiff]

Is it math related?

[severe kernel]

No not at all it's about kissing dudes

[surreal token]

added.

[fresh skiff]

Then i believe it doesn't belong here

[tribal crow]

well no, this channel allows non math books to be recommended and discussed too

sometimes there'll be people asking for e.g. children's stories

or thrillers

or whatever else

[hearty steppe]

General Relativity for babies

[grim ore]

i recommend the velveteen rabbit, my favourite story as a child

[tribal crow]

[heady ember]

You sniped me! ||(By five hours)||

[fresh skiff]

Oh i thought this is particularly for math books. Thank you for informing me this

[weary fox]

anyone know of a good book focusing heavily on (nonstandard) models of arithmetic?

[remote sparrow]

try asking in #foundations as well

[trail hemlock]

found sour drop on yt

https://youtu.be/NtMVw1HnbYs?si=yp9Pxmgv6kDHSbt5

[pseudo forge]

thinking about taking a second course in linear algebra (Axler i think) after taking an initial one that went through Anton. How useful would this be? (not a math major, but interested in fields around math)

[fresh skiff]

major you should take a look at fridberg

axler is nice and well writtern but determinant free book

[pseudo forge]

hmm why is it determinant free?

[fresh skiff]

idk why axler choose it to be determinant free

[pseudo forge]

ok thanks , it seems better than hoffman kunze

[real zenith]

Can someone please suggest me a good book/resource to study Runge Kutta methods, very funadmentally and in great detail? Would be great if it also mentions any suggestions on programming the different models of RK, like RK 7, 8 or higher in Python.
But, primarily I want to understand the method, the derivation of the formula, and it's application in real life problems.

[pseudo forge]

a whole book on it?

you’re probably looking for chapters from select books

[real zenith]

yeah, I just need the content

[pseudo forge]

hmm prob good to see some ode and num anal books

try sacco and saleri’s numerical mathematics

[real zenith]

Alright, Thank you.

[remote sparrow]

it's not determinant-free

it's covered at the end

[fresh skiff]

Oh

Sorry for incorrect information@pseudo forge

[trail hemlock]

is there a reason why chapter 9 of baby rudin and onward are not good?

ive heard that his differnetial form coverage isnt great, but would love specifics. darq brought this up and i just remembered it lol

because from a learning perspective, they seem to have more details and examples than the first 8 chapters, which is nice

[loud cradle]

9 and a half hours!

[trail hemlock]

and thats just part 1

but i watched some of it, and god damn that guy knows so much stuff

[loud cradle]

the guy has to be committed to that house, imagine trying to relocate

[trail hemlock]

[heady ember]

Have you seen my book, btw

[remote sparrow]

yes

[heady ember]

What do you think

[tender cobalt]

awesome

[vital bane]

Grass' book: Linear algebra is left as an exercise to the reader, coming up with exercises is left as an exercise to the reader

[daring lake]

linear algebra is trivial

[fresh skiff]

i am a non trivial guy

[heady ember]

Thanks

[severe kernel]

Reverie by Ryan La Sala

It's a very good book

(are you starting to see a trend with my recc.)

oh and the The Tea Dragon Society Box Set, its a cute read

[gray gazelle]

What's ye book?

[heady ember]

#1059828221887135774 message

[gray gazelle]

W

[thorny robin]

I am a student in Romania and here we do not study maths like in the US. I do want to go to harvard and study CS but for that i have to take a few years and learn more topics that are studied in the US high school's. What books can you guys recomment me to buy to help me with this.

[rain hound]

So he could do a development in a more functional analysis style. Determinants don’t make much sense in infinite dimensions!

I think he did a damn good job. This book is the best precursor to functional analysis.

oh oops intended to reply to @pseudo forge

[pseudo forge]

interesting, so i should take axler over friedberg?

what doors do each of them open

[rain hound]

My suggestion is read Linear Algebra Done Wrong by Treil and Linear Algebra Done Right by Axler both. They’re both free on each others’ website. And together both provide the conventional treatment, and the interesting novel treatment that generalizes well.

You can read them concurrently or Treil first.

[pseudo forge]

whats the difference between the two?

and why did the author name his book la done wrong ..?

[rain hound]

This was done to spite Axler lol

[rain hound]

Treil does a more concrete approach using bases and determinants heavily, moreover it does linear algebra exclusively over R.

Axler does a more abstract approach, more basis independent, that more readily generalizes to infinite dimensions. He proves theorems for both R and C, with notation that readily suggests generalizations to arbitrary fields.

[fresh skiff]

thats fine hehe

[old elk]

Books to learn homological algebra for the first time ?

[remote sparrow]

pretty good

[remote sparrow]

rotman or weibel

[oblique hatch]

What’s a good source to learn about perverse sheaves?

[whole hedge]

yo all

what is a good differential equations textbook?

ode

[dense plover]

looking for a book/notes on commutative algebra sufficient to make a start on algebraic geometry (was looking at vakil but recommendations for this would be appreciated too)

[rain oracle]

hi gang! What's the best diffy Q book?

of 2024

[rain oracle]

i asked the same question lol

Beginner Level (Introductory)
"Elementary Differential Equations and Boundary Value Problems" by Boyce & DiPrima

Widely used in undergraduate courses.
Clear explanations, real-world applications, and a balanced approach between theory and practice.


"Differential Equations with Applications and Historical Notes" by George F. Simmons

Provides historical context and intuitive explanations.
Good for understanding the "why" behind methods and applications.

This is what chatgpt said

[remote sparrow]

how about eisenbud

[dense plover]

all of it?

would something like reid or atiyah be insufficient?

[remote sparrow]

just a subset

you don't need all of it

[remote sparrow]

reid maybe, but atiyah mcdonald should be fine too

[dense plover]

thanks

[trail hemlock]

this is comical

[heady ember]

Thanks!

[heady ember]

https://tenor.com/view/indian-phahaha-gif-27058287

If I write a book, I'll leave the bookbinding as an exercise for the reader.

[trail hemlock]

i watched that vid u send and i might acc try it

[heady ember]

Dew it

[trail hemlock]

do u mind if i ask u questions as they come up?

[heady ember]

You don't need to buy anything, you can just cobble shit together and it works

[heady ember]

Sure

[trail hemlock]

(or is it an exercise to the binder )

[heady ember]

I slapped three pieces of cardboard together for the hardcover and it works.

I used this same tactic for my two preceding (slot-in) hardcovers (which I made to protect my softcovers).

[heady ember]

Well, I guess you need glue. But you can use your mucus

[trail hemlock]

i’d like to have a nice cover on it, can i like buy that

[heady ember]

"Just make it yourself, you fuckin' casual" - A casual.

[coarse lintel]

I want to research abstract algebra and number theory. What books should I read.

[stray veldt]

https://link.springer.com/book/10.1007/978-3-030-98931-6

[tender cobalt]

Is the Art and Craft of Problem Solving by Paul Zeitz a good book for preparing for math olympiad

[vital bane]

wait LADW by Treil only does LA over R? not even over C?

that's kinda weird

I can understand not doing LA over arbitrary fields and only focusing on R and C

but focusing on only R is weird

[vital bane]

Lmfaooo bro wtfff

more like the master of lack of exposition

[trail hemlock]

bro idk 😭😭

[queen badge]

hi there, how do axler and friedberg/insel/spence's linear algebra textbooks compare to each other?

[vital bane]

I would suggest FIS (Friedberg Insel Spence) over Axler

because FIS is a more traditional treatment of LA over Axler

Axler hates determinants (for some reason, I haven't read his "down with the det" post)

some people think it makes LA more elegant, but it just makes it more clunky imo

I'm talking about the "determinant free" approach presented in Axler

Actually I think Axler is looking at Linear Algebra from the perspective of an analyst

so he's trying to do stuff that would generalize to an infinite dimensional setting maybe

either way that's unecessary for an introductory LA book

[queen badge]

I'm mostly asking about abstract linear algebra, the teacher taught Axler for the regular class 15 years ago and FIS for the honors class next semester, so I was curious how they would compare from that (i.e. 2nd course) perspective lol

[vital bane]

ye ye I'm also talking about abstract linear algebra presented in FIS and Axler

But I'm not sure what you mean by "compare to each other", in what sense?

[tender cobalt]

FIS is more comprehensive than Axler

[queen badge]

I was being more vague, i.e "compare to each other" as in "I don't actually know what could be compared so hopefully my non-specificity will lead the person who answers to give their own criteria"

[tender cobalt]

I suggest you read both and see what suits you then

this applies to most math books, there are a lot of books to learn from and they have the same content, it just depends on personal taste which one fits you more

[vital bane]

I wouldn't say "it just depends on personal taste"

there are good books and there are bad books

I'm not saying Axler is a bad book, I'm just saying FIS is better for a first exposure to abstract linear algebra

Axler = 6/10
FIS = 8/10

[tender cobalt]

that depends on personal taste again

theres no difference in contents

[vital bane]

The quality of exposition can vary significantly

that's not personal taste

and the presentation of content matters, which also is different from personal taste

the determinant free approach presented in Axler is clunky, which you could say is a personal taste

but I would disagree

[tender cobalt]

there are also people who argue differential forms approach is better than typical multivariable calculus course

many people suggest the traditional course is better and differential forms approach isnt good as first approach

but the other day i saw someone who is actually finding differential forms approach "easier" and more intuitive than the traditional course

[tender cobalt]

in the end of finishing the book

one knows the same content from axler as they would from FIS

just "differently"

[vital bane]

that difference matters imo

at least in my case it does

I'm speaking as someone who has gone through Axler

in 4th ed Axler has included multilinear forms

[tender cobalt]

well whatever book suits you is good

both are standard

[vital bane]

I'm not sure FIS has those

[tender cobalt]

the 3rd edition is widely used

[tender cobalt]

yea fis dont

[vital bane]

I see

[tender cobalt]

i didnt go through 4th edition of axler

[vital bane]

well anyway most LA courses don't cover multilinear forms

[tender cobalt]

i went through 3rd

yeah

[vital bane]

same

[tender cobalt]

But the main difference between FIS and axler is that

I find axler more terse

and fis more comprehensive

fis also has balance between computation and proofs

while axler puts emphasis on proofs

Like Axler is more on pure mathematics side

Axler also has mad hard exercises

Goated thing to do is combine both books

finish every singles exercises from both books

Then upon finishing both

you are gonna be a linear algebra monster

you can transition into insane books like roman's one

easily

[empty mortar]

This was how I was taught linear algebra first semester - done wrong + done right together

[tawny crater]

Axler has some very strange proofs where he will not use determinants for the life of him otherwise very cool imo

[weary bison]

Any recommendations on books about the history of mathematics?

[gray gazelle]

Hello. I am interested in buying a book beyond school level. Not something advanced, but in detail. One option I am considering is Abstract Algebra. But I would like a few more recommendations beforehand. Thanks.

[dense plover]

oh, i didnt know there a book channel, well anyways, i wanna buy a book on graph theory, not for academic performance but because i just wanna study for the sake of it, its fun, so what are some cool books? 🙂 , i did try searching on yt but i didnt find much

[molten gulch]

We've read bits of diestel, liked what we've seen so far

[dense plover]

alright 👍

[wise crater]

perhaps try baby rudin :^) for a more serious answer of something beyond secondary school you could try spivak's calculus, or if you want a specifc algebra text thats beginner friendly, Judson is free

[dense plover]

so, i found lectures on the book, as a minor i cant afford a book THAT pricey, dollars are more expensive in my country ,(PPP)

[gray gazelle]

I really need something beginner friendly... thanks for the recommendations, I'll add that to the options

[dense plover]

so guess ill see them, thanks 🙂

[limpid bear]

you can read diestel for free though iirc, it's on his page

https://diestel-graph-theory.com/basic.html?

[dense plover]

i looked it up a few places, then i found the authors channel where he has lectures of the book

[dense plover]

ohh, alright, thanks !

[limpid bear]

yeah the yt is a recent addition

[wise crater]

spivak's calculus book is a pretty good intro to the sort of single variable calculus that you would find outside of highschool

[dense plover]

being a recent addition, maybe it has more relevant topics?

well anyways, thanks 🙂

[limpid bear]

well the book was updated recently

[dense plover]

oh the website, it make me buy the ebook for 16 euro, i as a minor cant afford that much rn after already buying linear algebra by gilbert

[limpid bear]

the videos and the book are more complementary, videos emphasizing different stuff than the book

[gray gazelle]

Alright, I'll try

[limpid bear]

at least that's what he affirms, it's not like I watched the playlist fully

[wise crater]

pirate it

authors get no money anyway

[dense plover]

eh

[molten gulch]

<@&268886789983436800> advocacy of piracy

[wise crater]

Fuck off tcc

[tender river]

https://youtube.com/playlist?list=PLu06QHBZ8gasqV0bgYx6D63UzV8k454cE&si=9jYXvprLos_pPuqw yt graph theory course, the disclaimer also has link to notes and i think also to assignments??

[dense plover]

alr, ive saved it!

[vital bane]

Understanding Analysis by Stephen Abbott is perfect for that

[stray veldt]

advocating piracy is not against discord rules

you just cant provide pirated content or links to it

[vital bane]

done wrong + done right = the entirety of human knowledge on LA

[gray gazelle]

I see... Thanks for the recommendation

Why is the paperback more expensive than hardcover...

[gray gazelle]

Can you tell me a bit about it

[stray veldt]

me when i obtain the entirety of human knowledge

[remote vortex]

I still hope someone ends up publishing "Linear Algebra Done"

[molten gulch]

I mean, what would a book like that need to cover? Rings, Fields, VS'es, Modules, Operators, Matrices, Gaussian Elimination, Finite and Infinite Dimensional Spaces, Linear Maps/Homomorphisms, Endomorphisms, A bit of Polynomials, Eigenvalues and Eigenvectors, Cayley Hamilton, Rank Nullity, Inner Products, Multilinear Algebra?

Is that all?

[rich sun]

Wew Linear Algebra Done Soon Tbh

[molten gulch]

LMAOOOOOOOOOOOOOOOOOOOOOOOOOO

[remote vortex]

Linear Algebra: Don't

[normal crystal]

there is a playlist from 2021 for the same course on his channel too, I was just looking

[elfin scarab]

Linear Algebra Done Okayish

[gray gazelle]

I recomend the many mysteries of the finkel family

[tropic nacelle]

SF is better than LA

(Special functions)

[molten gulch]

san francisco is also better than LA

[urban light]

The Pinter abstract algebra book is pretty cheap. Alternatively you could get a book like A Transition to Advanced Mathematics by Smith/Eggen. If you do that get an older edition so it doesn't cost so much.

[remote sparrow]

linear algebra is a good choice. intro-to-proofs books are good, too.

[stiff tulip]

From Brezis, Conway, and Rudin Functional Analysis, what are the reasons for picking any particular one

[gray gazelle]

anyone have any good recommendations for an open textbook on physics c mechanics ?

if there's also a cheap online one that's a good resource i'll take it as well

[normal crystal]

Openstax has a general/university physics textbook
or you can look for older editions of the popular textbooks

[gray gazelle]

already tried looking on openstax, they don't have a physics c book 😞

will try looking for some older variants though, much appreciated

if you find anything else lmk 🙏

[normal crystal]

it won't be called "AP physics c"
you can use their University Physics for calc based physics

[gray gazelle]

you are so right

much appreciated

[heady ember]

You can always sail the seven seas

[gray gazelle]

I see... thanks :) 👍

[gray gazelle]

Thank you too

[gentle jasper]

I want to ask about Lang’s UG Algebra and Dummit and Foote.

They seem pedagogically different in order. For example, Lang’s 2nd chapter is on Mappings. Is there a reason that this interlude is included, but excluded in D&F? Lang also goes into Rings much, much earlier.

I’m not exactly sure what my question is.

Two undergraduate algebra books, two very different organizations and timings. What are the pedogogical differences/intents and the difference in learning outcomes?

[plucky rose]

I am really enjoying Statistics [Henry E. Klugh] (1970 - first edition I suppose?). It’s writing style is extraordinarily good and well suited for being read by first years. Amazingly easy to read and understand. It’s supposed to be a book for psych students but I just write that off as a statistics book with applications in it.

[formal parcel]

Currently learning discrete mathematics and proofs and logic really interests me. Does anyone have any good logic textbooks that would be great for a somewhat beginner?

[craggy river]

Heyy, I'm currently working my way through Basic Mathematics by Serge Lang and I was wondering if it's a good start? I hope to pursue another degree in STEM (currently pursuing a CompSci degree) but I haven't quite decided between Mathematics, Physics or something related to biochem

[rigid trail]

decide on mathematics

🗿

[plucky rose]

Discrete Mathematics with Application [Susanna S. Epp]

[sterile pelican]

Depends I would say personally Velleman's How to Prove It is a great book to learn proofs and logic. Been through all of it myself, and I also did Susanna Epp's book but I am not exactly fond of it since I didn't inherently learn proofs from there

[formal parcel]

Already reading

[formal parcel]

I’m looking for one very mainly on logic. I’m reading two proof books already

[sterile pelican]

That can greatly depend Hodges book on Mathematical Logic is what I am actively doing, and you can do it after doing proofs, but I don't think this qualifies as something "beginner friendly"

[remote sparrow]

@sturdy shore what's your experience with zakeri's complex analysis book? can you also speak to the quality of the binding as well?

https://mastodon.social/@princetonupress/109858840052570122

https://x.com/PrincetonUPress/status/1754505232334110794

Princeton University Press @princetonupress.bsky.s (@PrincetonUPres...

Enjoy 75% off select titles!

Visit our website to explore our Book Lover Sale now through February 26, worldwide. Select titles and editions have been marked down with code 75OFF at checkout: https://t.co/BuueQUy9i9

What will you read first? #ReadUP

Twitter · Feb 5, 2024, 2:00 PM

also note that PUP has done a 75% off sale on select titles for two consecutive years now

some textbooks were on sale then, including zakeri's

https://press.princeton.edu/sale/flash-sale-faq

there will also be another 50% off sitewide sale coming in spring next year

so save your money if you're interested in any PUP titles

[sturdy shore]

I haven't used it yet, am actually gonna use it soon

as I will be taking a complex analysis course

quality of binding seems fine? But I don't actually know how to evaluate that

[remote sparrow]

can you share some pictures when you can?

[sturdy shore]

yeah, later today or tomorrow

you can remind me if I haven't done so by tmrw

[gray gazelle]

Can I use Apostol's Calculus book if I haven't touched math for over 6+ years? (Only know up to algebra)

[fresh skiff]

I think yes

[remote sparrow]

@sage python also a pdf for zakeri's complex analysis book is out there if you have the time to evaluate it

[analog lava]

is there a differential topology textbooks that assumes algebraic topology and is quick?\

[heady ember]

Oh really? I never managed to find it!

The seven seas I sailed. Treasure I found not.

[remote sparrow]

yeah i've been periodically checking too

[heady ember]

Could you dm me the goods?

[remote sparrow]

yeah the file was uploaded on november 28th

[hearty steppe]

Anyone familiar with this? https://books.google.com/books?id=RfhTDwAAQBAJ&pg=PA1&source=kp_read_button&hl=en&newbks=1&newbks_redir=0&gboemv=1#v=onepage&q&f=false

[full cairn]

I've just discovered that I really like Artin's Algebra and considering getting a hard copy, but I already have 3 other books covering introductory algebra 🙁 Anyone else have lots of books covering the same topic?

[remote sparrow]

sure. #advanced-lounge message

[full cairn]

Jeez, that's quite the collection! and you have two copies of Linear Algebra Done Right?

[remote sparrow]

the third and fourth edition; i got the third edition a few years before the fourth edition came out

[full cairn]

I see. That's an inspiring bookshelf, I guess I shouldn't be so hesitant to buy books

btw, did you get any of those on discount? I've tried to look for used books, but it's hard to find in my area

[remote sparrow]

many are used. a good number are new, but mainly from affordable publishers like dover. some were discards from my community college library. there is a guy that sells random books every now and then on campus.

i did get some books from last year's springer sale

[full cairn]

Ah, the springer sale is a good tip! Seems like there's a sale right now: https://link.springer.com/shop/springernature/study-sale-mathematics/en-eu/

[remote sparrow]

it's not that good

it's just 30% off compared to last year's 50%

also i'd generally suggest getting softcovers over hardcovers, as they're at least easier to open

axler is the one weird exception but your experience may differ

for example his LADR may be bound nicely like his third edition or it may not, like mine

but his MIRA is good

[full cairn]

I see I kind of like hard covers, as they feel sturdier, but mostly for the thinner books, for the really thick ones I find softcover works better

[remote sparrow]

i do like hardcovers too, but the binding is often just glue, which of course isn't as sturdy as a book whose pages are sewn together

with that said, i'm still generally biased to purchasing hardcovers when possible, as they can be put in my backpack

i put softcovers in my bag as little as possible

[remote sparrow]

another reason for buying used is if your book was made before the 2000s, you can expect the physical construction of the book to be of higher quality

[full cairn]

Yeah, that's a good point

[full cairn]

Interesting, didn't know that. I guess they've started using cheaper production methods now?

[remote sparrow]

yeah