book-recommendations

[lean pagoda]

Only book of that kind that I'm somewhat familiar with is Velleman's How to Prove It. That one might also be worth a look.

[solemn rover]

yeah this is suposed to be pretty good

i've talked to a postdoc who does this stuff and he says it's a solid resource.

[hearty steppe]

hey is there other sites you guys recommend besides math.stackexchange for finding more books and resources outside this server and getting in touch with different groups, people, etc?

[remote sparrow]

you could try hamkins' Proof and the Art of Mathematics

[sturdy shore]

not sure if they need a 5th book

[zealous coyote]

Pfft, they're already reading 4 so how much damage can a 5th do(!)

[granite ferry]

I'll take a look. Thanks for the recommendation.

[flat sand]

If you think about exploring a solution space, it might have some applications there. Since the rules always seem to take you back down to 1, maybe there is some application that involves ensuring your path is unique, but always returns to 1, given any starting value.

[hearty steppe]

thanks for getting back to me about this. Fortunately I am having an interesting conversation in the DMs with a PhD so a lot of fun is being had 🙂

[dapper oriole]

I really liked Richard Hammack's Book of Proof. But you don't need to buy it, there's a free pdf online https://www.people.vcu.edu/~rhammack/BookOfProof/

[gusty smelt]

yeah true, will fix over the weekend

[pale scarab]

I have read how to solve it, book of proof, and proofs from the book. How to solve it is as nice easy read but it's focus is more so on how to approach solving problems. Itt is worth the read and could be read in one sitting. Book of proof is free online and a nice easy introduction to proof writing. You can go through it pretty quick and it has solutions to odd problems. Proofs from the book is an amazing collection of proofs but many will be hard to decipher at an intro level but it's one of my favorite textbooks I own. How to prove it and an introduction to higher mathematics are slightly more rigorous versions of book of proof that could be worth getting. Though I think after going through book of proof it's best to just get a real textbook and struggle through some proofs. Linear algebra or an analysis textbook I think is a good place to start.

[broken meadow]

dummit and foote is fine :/

oh

i forgot to scroll chat down

bru

[gray gazelle]

Im using khanacademy for multi variable calculus

Would supplements be useful, if so what type of supplements

[remote sparrow]

a workbook i guess

maybe paul's online math notes?

he has a neat cheat sheet

[gray gazelle]

Paul online math

[cinder shore]

Hey folks, what is a good source for learning about free groups with minimal prerequisites? Just upto isomorphism theorems. Our professor jumped to free groups out of the blue.

[hazy elk]

Interesting, is your professor teaching it from (say) Hungerford and Armstrong
(Totally not doxxed)

[normal reef]

problem books reccomendation for undergraduate abstract algebra course?

I don't know about the rest of the world but I'm having an introductory course in abstract algebra during my first year

Does anyone know of a good problem book that doesn't require a lot of theory, just hard problems on introductory material?

[sour saddle]

If anyone wants a random book recomendation Lemony snicket's series of unfortunate events is something I think everyone should read. I watched the show first then read the books which o my part was probably a bad idea but the books are fantatstic.

[sudden dock]

Is the book related to math?

or is it an inspiring book?

[sour saddle]

No it’s just a good book series-

[lone sand]

I need a book to learn linear algebra (open source). Any idea?

[remote sparrow]

pinter's A Book of Abstract Algebra technically is a textbook, but a lot of critical material is left as an exercise. you could use this.

https://math.stackexchange.com/questions/174596/good-problem-book-on-abstract-algebra

this thread seems helpful too

you could also go through old doctoral qualifying exams at your university or others' though the level of the questions asked may vary

[remote sparrow]

https://hefferon.net/linearalgebra/index.html

http://linear.ups.edu/

[sturdy shore]

LADW is free if that is what's meant by open source

[junior isle]

Guys is Thomas calculus a good starting calc book?

[remote sparrow]

maybe, but the praise i've heard for thomas and finney's book were mainly for the older editions. from a few reviews i can remember, they're about as bloated and expensive as mainstream calculus textbooks with regard to their newer editions. i keep stewart handy as a reference and i really did like it when i used it, but perusing through it i can see why people may not like learning from it.

most commercial calculus textbooks are just alright. can't really go wrong with them, but they aren't necessarily the best choice for your particular needs and wants either

[junior isle]

I ordered it on eBay for 8$

[remote sparrow]

eh, i'm sure you'll learn what you need to know from it

[junior isle]

I also have Stewart on pdf

[remote sparrow]

use it as a source of problems to work on

if you don't like the exposition

[heady ember]

You can try

1. Pauls' Online Math Notes
2. Khan Academy (but the complain I have heard is the qns aren't challenging enough)
3. Spivak's Calculus (but perhaps not that great if you're starting out, since the qns are more challenging)

[remote sparrow]

spivak is supposed to be a rigorous introduction to calculus (and could even be considered a basic analysis book). it's an extremely tall order for most people nowadays, though, given that proofs in analysis are pretty tricky for people with little to no background in proofs. velleman's Calculus: A Rigorous First Course might be the better option if you're interested in seeing some rigor but still want the focus to be on what you can do with calculus, rather than building solid foundations for it.

[limpid leaf]

What books should I get for gr9 Ontario

I need help with algebra, i'm not very good with math either

[orchid mortar]

None of these seem open source but I'm wondering if there even is one
Both linked are open source, poggers

[gray gazelle]

I'm obsessed with functions. What are the best texts on the subject of analysis?

[grave thorn]

What level

[gray gazelle]

Idk but I feel like I've almost worn out all the fun I can have with Taylor series

I need more power!!

[grave thorn]

Check Rudin out

[gray gazelle]

thanks will do

[brittle breach]

Fourier analysis Stein Shakarchi

[grave thorn]

Fuck it probability essentials Jacod and Protter

[cinder shore]

Lmao. I wonder who this is.

[keen cipher]

E

E

E

E

EEE

E

EE

[shell valve]

Hey guys

[karmic thorn]

Don't spam

[serene shell]

Any good book for prealgebra

[keen cipher]

1+1 = a2

[karmic thorn]

Probably take a break and don't spam weird messages when you're back

[pure flume]

his brain is just on a different wave length

this will all make sense in 20 years

[sudden dock]

Pacemaker Pre-algebra by Fearon

[serene shell]

Thank you so much bro

[serene shell]

How is art of problem solving pre algebra book? Do you know about it

[sudden dock]

I haven't personally tried it

[serene shell]

Oh are they good tho?

[sudden dock]

as far as I have heard, Art of problem solving books are great

[serene shell]

Oh they can be used as textbook like for learning? Or more useful for practice and solving problems?

[sudden dock]

for practice and solving problems

they are not good If you don't know the topics already

but I am not sure

[serene shell]

Okay and text book suggested is good for learning right?

[sudden dock]

yeah

[serene shell]

Thanks sir

[vagrant zealot]

can anyone suggest me a precalculus book

[versed fable]

can someone suggest me a calculus book (that isnt tarasov calculus)

[gray gazelle]

there are a lot of books on calculus, a simple search in this channel will give you all sorts of recommendations. You are looking for anything particular?

[versed fable]

nope not looking for anything particular
BUT it must not be tarasov calculus

[remote sparrow]

https://4chan-science.fandom.com/wiki/Mathematics

https://github.com/nculwell/MathStudy

@versed fable

#book-recommendations message

[pale scarab]

It's good but if your not familiar with contest type math or trying to learn it for the first time you're going to struggle quite a bit with the problems.

[mild yoke]

Cheap A level pure maths book that explains deeper than a regular A level pure and SM book?

[jade quiver]

Hi I'm new to the server !
I'm a professionnal software-developer, but i'm a self-taught, I was a kind of humanities guy.
Since I have been developing, my interest for math is growing. I want to go through the Algorithm Design Manual, 3rd Edition
Steven Skiena, but my background in mathematics is pretty weak. Do you know some book for people who wants to learn maths for computer science from scratch ?

[cursive orbit]

any introductory-level discrete mathematics book should be pretty accessible and suitable for you rneeds

check out Discrete Mathematics by Rosen

[jade quiver]

@cursive orbit found it:
https://www.amazon.fr/Discrete-Mathematics-Applications-Kenneth-Rosen/dp/1260091996/ref=tmm_pap_swatch_0?_encoding=UTF8&qid=1665870788&sr=8-1#customerReviews
Have you heard about The Algorithm Design Manual ? There is a lot math in it and I'm trying to have solid foundation to understand it

[remote sparrow]

https://www.fm2gp.com/

this book might interest you

it's not a math for CS in general (it's specifically for generic programming, something i'm not an expert in, but which has a wikipedia page), so it might not have as much breadth as a discrete math book, but it seems interesting

it also has pretty low prerequisites

as far as math for CS goes, while discrete math is very necessary, you also said your background in math is weak

let us know if you want recommendations for calculus or earlier

[fluid bay]

as long as you can do algebra (like "solving for x" kind of stuff), I'd start by trying to crack open a discrete math book.

if there are gaps in your knowledge from algebra or earlier, then start with khan academy

[remote sparrow]

for discrete math you won't need to know much calculus or omit a few examples that require it

but later classes will involve calculus

[vocal panther]

Y'all: I'm trying out Abstract Algebra: An Inquiry Based Approach by Jonathan K. Hodge. I'll post a review about half-way through the book

[gray gazelle]

Can someone recommend me the hardest book for the hardest subject?

[vocal panther]

The Princeton Companion to Mathematics

read and understand it through and through

I mean it should be easy

[winter ether]

can i start spivak's calculus book without knowing any analysis, if not whats an easier calculus book to understand the why of calculus and not how

[karmic thorn]

Spivak's Calculus does not assume prior knowledge of calculus/analysis

I think it's probably one of the better books for understanding the why; worth struggling with it a bit

[karmic thorn]

I've heard some of the books written by Shelah are insanely tough reads, sometimes to the point where even people working in the field have to bash their heads with them 😛

[gray gazelle]

Ok I’m going to read all of his books in 2 weeks

Ok only 9 books

,w 9/14

[hasty eagle]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by vertigo♱#3495

[gray gazelle]

I need to read 64.3% of any given book everyday

[heady ember]

Are you trolling

[orchid mortar]

book has basic in it. worth a read, even if only 64.3%

[heady ember]

[gray gazelle]

No. Demon Time.

[gray gazelle]

Pick your poison

[inland elm]

anyone have any good books on tensors? my class is using jeevanjee and supplementing with schaum's but i'm struggling to understand the professor

i don't know if jeevanjee is actually bad or if my professor's teaching style fits me

[gray gazelle]

Tensor Geometry by C. T. J. Dodson and T. Poston

[sudden dock]

What do you do when you get tired of reading one type of book? Do you switch to different type of book? type here means if you were previously reading algebra, you might switch to geometry

[jade quiver]

@remote sparrow thank you so much, feels good to be supported

[gray gazelle]

I do either that or just do something else and come back later

[vital bane]

isnt that just a bad book?

[karmic thorn]

I'm not sure, Shelah also writes books on subjects/topics that are insanely abstract and (presumably) only a handful of people around the world are working on. Maybe the target audience skews the presentation effort too. 🤷‍♂️

[grand thistle]

is it bad to be unfocused when reading textbooks?

i always seem to be jumping around from one textbook to another then returning about like a week or two later

which means like ive read like the first chapter or so of a lot of textbooks

[karmic thorn]

I'm guilty of that too but it kind of is what it is, unless you're following a class and can stick to doing certain parts in line with the lecture at a given time

[willow pecan]

If the goal is to learn math you will eventually need to go past the first chapter of a textbook

[grand thistle]

but i barely manage to retain that information, like im able to recognize certain things and go like "ohh so that's what that textbook was talking about" or smth similar but im never able to remember proofs or put any of it into practice really

hm yeah that makes sense

i usually have one main book (baby rudin as of now) but i sometimes get bored or discouraged because of a hard problem or something and go to other books to get me motivated to study from my main book again

i have fun this way and stay motivated so i guess it isnt that bad

[heady ember]

You can focus on a couple of books at once i suppose

[normal reef]

guys can you please spam problem books for undergraduates?

the hardest they are the better

[karmic thorn]

Problems in Mathematical Analysis, Kaczor-Nowak

[normal reef]

stuff to keep me busy

@karmic thorn thanks

[heady ember]

Don't multipost

[normal reef]

yeah sorry I wanted to delete the other in the wrong channel

[heady ember]

Np

Just take note of it next time

[gray gazelle]

Would you guys recommend basic mathematics by lang or the three books by gelfand or khan academy for someone who needs to cover basic maths?

anyone want to join

[smoky zephyr]

not the channel for this

[subtle mango]

khan by far

[gray gazelle]

Problem books for undergraduate maths?

[main void]

Gonna have to be more specific than that, undergrad math could mean calc 1 or homological algebra afaik

[gray gazelle]

All of that is fine

[main void]

Well you could do problems in Lang’s Algebra ig

It would be really helpful to know what pevel you are at, what subject you want some exercises in, what subjects you want to learn etc

[gray gazelle]

I’ve finished all of math undergrad, just looking for problem books for Putnam

[main void]

Ah I see

I don’t know any specific books for putnam, sorry

[brittle breach]

Putnam and beyond

[cinder trellis]

Does anyone have any thoughts on Spivak's A Comprehensive Introduction to Differential Geometry: Volume I as a good book for differential topology topics?

[forest sleet]

it's differential geometry

although i guess it depends what exactly you mean by diff topology

it has the best covers

[cinder trellis]

I know that since that is rather obvious from the title, but I saw this link (https://www.math.utah.edu/~bestvina/6510/books.pdf) on the web and was curious.

[forest sleet]

it'll do smooth manifolds but I think the topic selection will be different that what you would get in a more specifically differential topology text

some overlap though

[cinder trellis]

Compared to, say, Guillemin-Pollack's Differential Topology, there seems to be quite a bit of overlap. I'm just not sure which is more beneficial to spend my time reading.

[steep badger]

Haven't read Spivak but I'm reading Guillemin-Pollack for a second time. Wouldn't say all the transversality/intersection theory stuff is very related to anything I do.

I saw people really like Lee's smooth manifold/topological manifold. Maybe give that a try? Depends on specifically is there anything you want to cover I guess.

Also Guillemin-Pollack may be appear a bit technical on first reads.

[cinder trellis]

Thank you, Duang. I appreciate the input, Lee’s book sounds interesting.

[plain ravine]

hello, what books would you guys recommend for linear algebra assuming i’ve learnt and understood most of early transcendentals by stewart

[willow pecan]

Friedberg

[remote sparrow]

#book-recommendations message

[tame tree]

thoughts on jumping into analysis before reading something like spivak or apostol?

[glacial crypt]

Should I finish my real analysis book before starting topology?

[glacial crypt]

calculus 4th edition?

[tame tree]

yea their single variable calculus texts

[glacial crypt]

Which analysis book are you looking at

[tame tree]

terry tao's

[glacial crypt]

give it a shot, why not?

[tame tree]

👀 dang everyone giving me hella hope today

[glacial crypt]

I haven't seen analysis 1 but I am using understanding analysis by abbott

could probably have a look at a couple of analysis texts and see which one you like

[heady ember]

You could also try Schroder

[grave thorn]

Depends

[tame tree]

im a bit decided on tao just because i love his writing style so much

it's like im talking with him whenever i read his work

[glacial crypt]

on what?

[sturdy shore]

imo you should see topological concepts in analysis before beginning topology, it will give more intuition behind the concepts

[glacial crypt]

ah

[sage python]

My influence grows

[heady ember]

Yes

I was gonna put " "Use Schroder" - Dami" lol

[tame tree]

why schroder specifically 🤔

[rapid lily]

I looked at that book before (Schröder's book) , but to be honest, it appears to be quite expensive compared to other options. Unless there is some way to get that book at a lower price.

It appears to be quite a good book from its contents.

[heady ember]

Just use a pdf lmao

Then print it out and bind it yourself if you want a hardcopy

[tame tree]

grass 🤫

[heady ember]

Search smt like "from: Dami Schroder"

[tame tree]

lmao

will do

[rapid lily]

Where can I buy a PDF at a good price?

[heady ember]

Basically it seems to be rather beginner friendly while still covering lots of content

[heady ember]

just get it off the internet for free

[rapid lily]

I like that it appears to cover calculus in Banach spaces

To me I am put off books that do not to that

[rapid lily]

I can't do that

[heady ember]

Banana 🍌 spaces

[rapid lily]

Anyway I can use Amann and Escher for free

[heady ember]

Why

[rapid lily]

Through my university

It's not ethical

[heady ember]

Not sure if book publishers are particularly ethical either

In terms of uni texts anyways

[rapid lily]

I like the Dover books

I don't buy many others

And usually that is enough

But some are like 200 or more dollars for a book

That is quite harsh to me

Not dover for others

[heady ember]

Well exactly

Hundreds of dollars for a single book seems rather exorbitant

Some even have poor print quality at that price

[tame tree]

forgive me brother for i must nerd react you

[rapid lily]

The first time I bought maths books, I didn't know what I was doing and bought Baby Rudin for around 100 dollars

And there are printing errors there :/

I like the calculus book by Henri Cartan

[tame tree]

honestly it might just be time for me to suck it up and read spivak or apostol and become a "pro" on single variable calc before moving on

[heady ember]

Nah just get shit on by analysis till we get good

I plan to finish Linear Algebra by FIS and hopefully Enderton's Elements of Set Theory then get slapped by Schroder and Jacobson

[tame tree]

i look forward to the learning but not through the grinding of a bunch of problems

[rapid lily]

That is the important part of maths

[heady ember]

Is there a book / topic you want to work towards slowly?

[tame tree]

ye i understand that

[rapid lily]

But also the hardest

[tame tree]

just terry tao's analysis by next year probably

[heady ember]

The pain and suffering is part of the package

[tame tree]

the advanced topics are cool in math but i recognize that i have to master the stuff i see as """""boring""""" and basics first

would definitely get me a 5 on the ap exam too lmao

[heady ember]

[tame tree]

[heady ember]

One day, I will get to Lee's books

In like 3-4 years hopefully lol

[tame tree]

the time scale of learning math is sometimes 😩

[rapid lily]

If there is a subject you really want to learn, often it's good to try to study that and go back to find about some topic if you need to know that to understand the concepts

Like for example, I tried to learn some functional analysis without knowing any topology and picked up a lot along the way

But you won't have a proper knowledge of topology that way

Then it is easier to go over it quicker after that

I don't know if it is efficient though

[remote sparrow]

If you've read an analysis book, there wouldn't be a need to read Spivak or Apostol.

If you've already done calculus, a lot of Spivak and Apostol will be redundant.

[tame tree]

this day does not stop getting better

:D

[remote sparrow]

It seems like it hits all the main points but it doesn't discuss why analysis is important or how it originates. For a reader lacking context, it may seem like analysis is an exercise in pedantry. Some people might enjoy that but I prefer more discursive books.

[remote sparrow]

Buy used

[remote sparrow]

Don't buy ebooks lol

[tame tree]

terry tao's book come in a very reasonably priced combo on amazon rn

👀

[rapid lily]

Ok thanks

[sage python]

Does it do calc in Banach spaces?

@remote sparrow idk many books which do a very good job at that though

[rapid lily]

Which book?

[sage python]

Analysis origins are very messy, people spent a veeeeery long time doing shit the wrong way before they realized how to do it the right way

Schroder

[rapid lily]

It has a chapter on differentiation in normed vector spaces from the preview

[sage python]

I tend to recommend Schroder nowadays mostly because it gets to some good material toward the end but at the beginning is very gentle. Has a lot of side remarks in the first few chapters that's basically commentary on its proofs

[rapid lily]

Ok I see

[sage python]

Ohhhh tru I mentally assumed it was just differentiation in R^n

Of course a lot of the stuff is pretty similar but that's good that it phrases it as such

[karmic thorn]

Is there a merit to working with such an abstraction on a first go?

[remote sparrow]

I'm not aware of any good inquiry-based analysis texts but given the history of analysis, it would seem it's fertile ground for it. It would be at once a crash course in math history, philosophy, and math. Quite ambitious now that I think about it.

[karmic thorn]

Like Amann-Escher uses metric space and Banach space terminology wherever it can in order to simplify the arguments/do things in greater generality

[sage python]

Manan: So the main complexity between defining a derivative in R^n vs in general normed spaces is that you have to specify in the definition that the derivative in a normed space is an approximation by a continuous linear map

Otherwise it's just that some theorems need "finite dimensional" as a hypothesis

[karmic thorn]

I see

[frozen niche]

should i get ahead of my class with Main Alegebra rn i am in 7th year

Soo what book Should i read on main algebra cus our library has like very smol fonts

[heady ember]

main alg?

I assume you just mean (Abstract) Algebra

Look in pinned

[frozen niche]

yes my class is on pre algebra

[frozen niche]

oki

[heady ember]

nonono

That's highschool algebra

Thought you were talking about AA

In that case Khan Academy I guess

[frozen niche]

yesh i am on junior hs i just graduated elementary last year

[frozen niche]

oooh ok

[smoky spruce]

what's a good book about tensor math for absolute beginner? any recommendations?

[gray gazelle]

https://books.google.pl/books/about/Tensor_Spaces_and_Exterior_Algebra.html?id=bDkf3W65-GwC&redir_esc=y
This is what I read

Lie algebra part was never useful to me personally

The various generalizations of tensor product weren't useful either

But it did help me to see what it is about and how it could be used

And tensor products aren't that much alien to me anymore

Though I'll admit that I don't remember what it means for tensor to be something that acts like a tensor

It talks about cool stuff like Grassmanians which is generally useful

[smoky spruce]

thanks, ill take a look at it

[remote ginkgo]

Goldberg Bishop Tensor Analysis on Manifolds

it's easiest fastest intro

[remote ginkgo]

universal property

[remote ginkgo]

use Sternberg Lectures on Differential Geometry as well

sternberg is harder but u will know everything if u just grind it hard af

u may struggle badly but ignore it

[gray gazelle]

No

[remote ginkgo]

transformation laws

[gray gazelle]

Yes

[remote ginkgo]

silly

[gray gazelle]

I mean. If they don't want to learn it for manifolds then they might try something else. Because it's used in algebra too

But no harm in either I think

[remote ginkgo]

its same thing in either case

manifolds r a special case but the general setup is contained in each book

just ignore stuff on connections & beyond

[foggy relic]

how good at analysis do u need to be for sternberg

[remote ginkgo]

not

it's just linear algebra

• multivar calculus

[hazy elk]

Isn't a tensor just a prototype for a multilinear transformation

[remote ginkgo]

yes

[remote ginkgo]

that's what i was saying here

[hazy elk]

Yes

[foggy relic]

its not too bad to also construct it explicitly

[remote ginkgo]

it's not bad at all

takes just a moment

[weak lake]

any good intro analysis books?

[willow pecan]

Abbott or Pugh

[weak lake]

thank

[solemn rover]

maybe steve roman's book on advanced linear algebra

[hearty steppe]

Sternberg is very rigid but kinda self contained, so not docking it. I just didn’t like his dynamical systems text very much.

[remote ginkgo]

his dynamical systems book is interesting

very specific intent

[gentle arrow]

schroder

[dapper root]

Guy who has used one analysis book

[gentle arrow]

-dami

once i finish schroder im gonna check out abbott for fun

[vital bane]

cat bread you doing anal now?

niceee

finished calc 2?

[gentle arrow]

mostly

[vital bane]

Nice

[gentle arrow]

have to do series but ill do it later

[vital bane]

you do it in anal

how much real analysis have you done?

damn schroder is actually really sick

i mean content wise

i only saw the table of contents

chmonke stop lurking go read algebraic geometry papers

[dapper root]

OOF

[gentle arrow]

im on 2.2

[hearty steppe]

Are there books specifically on the abstraction of eigenstates, eigenvalues, eigenvectors, eigenfunctions, etc

Like general books, I’ll start from order of difficulty and see what I can handle

I could aimlessly look at some of my linear algebra books but probably not that much intuitive info beyond the basics

I think I found some spectral theory books to look at btw

[forest sleet]

Roman advanced linear algebra

[grave thorn]

Has algebraic geometry cured lupus?

[hearty steppe]

I have that book. Awesome

[vital bane]

yes

[left ingot]

is Michael Spivak's Calculus book covers Cal 1 to 3?

[sturdy shore]

no

won't cover multivariable

[remote sparrow]

ah but his calculus on manifolds will

😏

[sturdy shore]

yeah but that book is for a more mature audience, not meant to be a direct follow up to his calculus

[remote sparrow]

yeah i was trolling

on a more serious note a book that's pitched at a much lower level would be loomis and sternberg's Advanced Calculus

🧢

[gray gazelle]

a follow up to spivak calculus is a Linear algebra book

[sturdy shore]

sternberg has the LA to get you started, other books like shifrin do that too

and then you can head directly to a non-elementary LA book for further treatment

same with apostol vol 2 iirc

[remote sparrow]

i was capping on the loomis/sternberg recommendation

unless you're harvard math 55 material

[willow pecan]

Math 50...

[remote sparrow]

i fixed it okay

https://tenor.com/view/crying-emoji-dies-gif-21956120

[willow pecan]

Thinking of cs 50 are you

[eager shoal]

Opinions on "Book of Proof" by Hammack?

[remote sparrow]

it's good

[hallow oriole]

10/10

[remote sparrow]

https://www.youtube.com/watch?v=didXE0HkSC8

https://www.youtube.com/playlist?list=PLO1y6V1SXjjM-1azbCNYq2-A1_7KaioNr

fairly interesting, some reviews aren't very detailed

does give exposure to some less commonly seen books

[dire dagger]

So in the books to begin with I could only find discrete mathematical structures by kolman busby ross to not be expensive

does it contain proof reading and writing aswell?

[vital bane]

shiffrin

[ornate saddle]

I have got two definitions that I more or less have an idea of from my linear algebra knowledge: "complete" and "orthogonal" functions. I need some book recommendation(s) that explicitly define(s) these with examples. Can someone refer me to necessary sources? Thanks in advance.

[rapid lily]

Orthogonal functions may be referring to orthogonality in the sense of an inner product space. You may want to look at books which cover inner product spaces or Hilbert spaces for that. I don't know what would be referred to here as complete functions in this context.

This will often be discussed in the context of something like Fourier series, where an orthonormal basis is frequently used.

Analysis I/II by Amann and Escher will cover this. Another option is Undergraduate Analysis by Lang.

[hearty steppe]

I am gona peak at the linear algebra books I was looking at to see their overview on eigenvalues and go from there. I’ll probably just jump straight into Roman tbh

[ornate saddle]

Gotcha. As I thought. I come from a non-mathematical background, though I have a keen interest in it. This context refers to a solution to plate equation.

As you can see in the equation in 3.14.

[vital bane]

He says you can use it as a first course in linear algebra but already having studied some lin alg would be good

so i dont think you should have a problem with it

[vital bane]

what's ${\nabla}^4$?

[hasty eagle]

Neamesis

[willow pecan]

Laplacian squared

[ornate saddle]

True.

[ornate saddle]

Twice Laplacian.

[vital bane]

Like $e_i \frac{{\partial}^4}{\partial {x_i}^4}$?

[hasty eagle]

Neamesis

[ornate saddle]

Laplacian is a scaler-output operator, though.

It is named biharmonic operator.

[willow pecan]

Biharmonic is also a scalar

[ornate saddle]

Exactly.

[willow pecan]

Anyways why is this in book recommendations

[ornate saddle]

He asked and I replied. I asked my question above, anyway.

[sturdy shore]

shifrin is so good

[vital bane]

i knoww righttt!!

[vital bane]

oh right, lol nvm

[ornate saddle]

Shifrin was good until I met Pavel Grinfeld's tensor book if speaking of goodness.

[remote sparrow]

Discrete math books are supposed to be introductions to proof reading and writing.

[hearty steppe]

I don’t think there are many books as terse as baby rudin

But in terms of graduate level type books, Brin and stuck which sort of starts advanced undergraduate is relatively terse and I’m handling it quite well. That’s a dynamical systems book tho

[rapid lily]

Ok I see. Now I recall that complete refers to a certain property of a collection of functions relating to an inner product space.

Here is its definition: https://mathworld.wolfram.com/CompleteOrthogonalSystem.html

In the book "Banach Spaces of Analytic Functions" by Hoffman, there is a brief introduction to Hilbert spaces which covers all this terminology and shows that some various properties are equivalent to an orthogonal system of functions being complete. However, the rest of the book will most likely not be relevant to what you are looking for.

I believe more is discussed in the context of studying Lebesgue-integrable functions after that. But that is probably more than you need to know for that problem.

[gray gazelle]

They mean orthogonal basis

This is basic Hilbert space theory @rapid lily

https://en.wikipedia.org/wiki/Orthonormal_basis
@ornate saddle

Those books you recommend sound way too advanced and off the topic

[rapid lily]

Thanks. I don't know why I said orthonormal there.

[rapid lily]

Only the part about Hilbert spaces would be useful for that book above. It's only a few pages long, but maybe you don't need much more than that to understand the basics. I agree that most of it is not useful or too advanced though.

[gray gazelle]

I guess people don't actually call it orthogonal basis so that's why. Still, I think the name reflects the meaning

[ornate saddle]

I think that Wolfram link suffices. I am surprised that it did not pop up in my search even though I refer to it for definitions most of the time. Thanks for other sources too, by the way!

[ornate saddle]

Thank you for that link too!

[rapid lily]

You're welcome!

[rapid lily]

Ok I see what you mean.

[remote sparrow]

https://www.maa.org/press/maa-reviews/introduction-to-partial-differential-equations-with-applications

any thoughts on the pde book by zachmanoglou and how it would compare to strauss' pde book?

https://www.maa.org/press/maa-reviews/partial-differential-equations-an-introduction

here's maa's review of strauss' book above

[willow pecan]

It looks pretty similar to strauss

Actually no

It looks similar to Evans

In terms of content covered

There is value in Strauss

Knowing how to separate variables is still fundamental, even if everyone hates it

[remote sparrow]

https://www.math.utah.edu/~treiberg/M5440Texts.html

according to this professor zachmanoglou might actually spend too much time on first-order systems and separation of variables

[willow pecan]

All systems are first order systems in more variables

[placid pollen]

I got filtered hard, what is the prerequisite that would make my experience smoother? I know some topology but maybe I lack advanced multivariable calculus

I don't like that he kinds of defines things but without giving an explicit "Definition 1.1" before every one

[remote ginkgo]

more linear algebra

try shifrin's multivariable mathematics

has manifold calculus + linear algebra galore

easy af, lots of psets

reads like a novel

[placid pollen]

has anyone tried this?

[remote sparrow]

hubbard and hubbard is also a good alternative to shifrin if you want a cheaper book

[remote ginkgo]

this is true

shifrin's students studied hubbard and hubbard 😄

[dire dagger]

It says college algebra prereq

Should bernard and child's higher algebra be enough?

[dapper root]

higher algebra

[remote sparrow]

looks okay

barnard and child seems a fair bit more advanced than the average algebra/trig or precalculus book though, as an older book

probably more stuff than you would need to start working on a fairly modern discrete math book

if you feel like you've got a good handle on algebra already than you can just jump right into any discrete math book

or an intro to proofs book

[hearty steppe]

So spectral theory books focused on Banach algebras, that’s what I’m gona start looking for more specifically

[grave thorn]

why specifically on Banach algebras lmao

like THE hilbert space L2 is not a banach algebra

neither is Lp for p<\infty

[dire dagger]

Oh nice

[hearty steppe]

I’m trying to find a very general angle that won’t make too many assumptions but motivates my interest in understanding how we can make continuous spectra gradient-like projections based off many-body quantum behavior

[grave thorn]

make precise the notion of "continuous spectra gradient projections"

because i dont see what you mean

[hearty steppe]

This may perhaps motivate things a little here https://arxiv.org/abs/1111.2810

[grave thorn]

im not reading a ten page arxiv for this

lol

[hearty steppe]

I think the abstract does an ok job.

At least for a use case

There’s more but I didn’t want to get a lot of examples rather than one I found interesting enough to look at

[forest sleet]

you picked vmm's least favorite subject

[dire dagger]

?

[acoustic crater]

Can anyone recommend a good book about introduction to statistics?

[remote sparrow]

algebra-based or calculus-based

and by statistics, do you mean statistics or are you really talking about probability?

[acoustic crater]

statistics, not just probability

[acoustic crater]

both are fine

[remote sparrow]

Introduction to Probability by Blitzstein and Hwang is available for free on their website along with tons of resources. It is calculus-based. Mathematical Statistics with Applications by Wackerly, Mendenhall, and Scheaffer contains both sections on probability and statistics. It is also calculus-based.

I would recommend getting these books separately, using the former for probability and the latter just for statistics, but if that is too expensive for you, buying only the latter should be fine. Of course there are other channels to obtain ebooks for free. I simply have a preference for and the fortune to have the means to buy physical copies.

[acoustic crater]

splendid, thanks!
Also may I ask about statistical software? The examples, I mean.

[remote sparrow]

Uh, R?

I've never used the R language, frankly. We have a channel for that at #computing-software.

[acoustic crater]

Oops, sorry. Thanks anyway.

[split basin]

i find Rudin's Functional Analysis nice for this and there is also Kaniuth's A Course in Commutative Banach Algebras

[gusty smelt]

if we are speaking of func anal texts, pederson is the best imo.

(i am an operator theorist so im baised lol)

[fluid bay]

i liked "banach algebra techniques in operator theory." Its a short book that assume very little but covers spectral theory and get's into C*-algebras

[gray gazelle]

Pedersen's Analysis Now covers this in its fourth chapter.

I got sniped.

[gusty smelt]

based rakko

[gray gazelle]

It's a great book for someone with a bit of mathematical maturity. The exposition is crystal clear, the proofs are slick, and there are plenty of great exercises. I couldn't recommend it enough.

It's the kind of book you keep going back to.

[gusty smelt]

i agree, its the 2nd best book i have ever read, and it also really is what got me into C* algebras which is what i do now lol

[atomic hemlock]

Any suggestions for a calculus textbook that is less than 400 pages?

[grand thistle]

what’s the best then?

[gusty smelt]

Milnor and stasheff characteristic classes

[grand thistle]

cool

[sage python]

@gusty smelt what do you think of the second volume of Pedersen?

[gusty smelt]

I only know of analysis now and his c star automofhoisms book

Do you mean the latter?

[sage python]

"Analysis Later"

Nah but like that's what the follow-up should be called

[gusty smelt]

Lol maybe if I write a book on c star or we

I’ll do that lol

[orchid mortar]

cool recs, all in all.

[fluid bay]

@gusty smelt yo i hope u don't mind the ping, but I have a question for an operator theorist: idk any fourier theory, but I read that the fourier transform is the gelfand transform on L^1(G) after making appropriate identifications. do u know of any resources that discuss this approach to the fourier transform? Is there such a thing as "fourier theory for the operator theorist"?

[sage python]

@fluid bay you probably want an abstract harmonic analysis books. That'll go into the representation theory but probably do a bit on this story

Folland or Deitmar-Echterhoff

[fluid bay]

thumbing though folland atm. ye, this looks like the kind of thing i was looking for. probably won't start reading this tomorrow or anything () but very cool

ty sloth

[hearty steppe]

You guys give Reddit, stackexchange, and Quora a good run for their money, hope you know that

Everyone kept recommending reed/simon modern physics book but I’ll peak at that too I guess

[fluid bay]

im not sure about the books other recommended, but a caveat of the book i recommended is that it doesn't have any physics terminology, in case that is important to you.

[hearty steppe]

I mean I generally rely on using dynamical systems to get to the physics so, I feel like I pretty much found the more broad sources on that. I prefer leaning more towards the mathematics behind it

Mathematics is like my pair of prescription reality glasses

[hazy elk]

What's a good set of notes for free groups, preferably with a few solved qs?

[vital bane]

what exactly are C* algebras? (some sort of non-commutative ring of operators i pressume?)

[willow pecan]

It's a Banach algebra with some additional involution that behaves nicely

Think complex conjugation, which makes C into a C* algebra

But that is not a book recommendation request so either #math-discussion or #advanced-analysis

[heady ember]

No wonder you decided to latex that eh hehe

[vital bane]

@glad prairie sorry for the ping but perma study please

[willow pecan]

Very book recommendation

[gray gazelle]

hi

[willow pecan]

Hello

[tulip saffron]

hi, does anyone know this concept: zero knowledge proof?

[glad prairie]

For how long?

I'm not always around, just dm modmail next time

[vital bane]

a month

[vital bane]

okay

[gusty smelt]

Harm anal is right, I personally like Deitmer-echteroff

[smoky zephyr]

this is the most cursed use of the abbreviation i’ve seen

[timber copper]

Please do not harm others with anal

[gusty smelt]

i can talk to you about it in some other channel, ping me if you are interested

[willow pecan]

There was some earlier discussion in #math-discussion

[warped cedar]

do fun anal instead

[jade saddle]

Um, Is there an online resource (book or otherwise) to learn linear algebra along with the formal definations? (need not be easy to understand, looking for something akin to a manual for linear algebra)

[willow pecan]

I imagine that any resource will include formal definitions?

[jade saddle]

Not every, I looked on mit open courseware, but what I found was a bunch of lecture notes not particularly easy to navigate and follow

[lime sapphire]

friedberg book?

[jade saddle]

I will check that out

"Linear Algebra, 4th Edition" Thanks! I will practice this for a few months

[gray gazelle]

In uni I never had a fully general LA course, with matrices over PID's and everything. What LA book covers something like that?

[sage python]

If you've already done some basic linear algebra then maybe Roman's up your alley, or Blythe's "Module Theory: An Introduction to Linear Algebra"

[woven cypress]

any calculus workbook recommendation?

[gray gazelle]

Thank you

[woven cypress]

I'd rather like one which is harder and focus more on the quality of questions

[glad stone]

does anyone have a ap calc or ap physics me book recommendation or website recommendation for self studying

[willow pecan]

Khan academy probably

[remote sparrow]

jim hefferon's website links to his linear algebra book with associated resources

[crimson leaf]

Paul's online math notes for calc

[remote sparrow]

https://www.youtube.com/watch?v=didXE0HkSC8

somewhere in the video he mentions two calculus workbooks

[jade saddle]

Jim hefferon's website?

[remote sparrow]

https://hefferon.net/

[jade saddle]

Ah thanks, I will check it out

[sleek python]

Ah yes the end of mathematics

[sturdy shore]

it is a well known fact that mathematics ends with serge lang - algebra

[fallow cypress]

LOL I like how the last book in that video is "Serge Lang – Basic Mathematics"

[vast obsidian]

Is there a good elementary book on statistics (mathematical)?
In highschool the only statistics we did was finding mean value, normal distribution and plotting graphs/bars. What's the next step?

[remote sparrow]

Have you taken calculus already? Also calculus-based stats is supposed to be taken after calculus-based probability.

You could take a conceptual algebra-based stats class but really the most important thing that you'll learn isn't the math itself but statistical literacy.

[vast obsidian]

Why do I need probability ?

[willow pecan]

Because you need probability to do statistics

[vast obsidian]

can u explain why

[sleek python]

Statistics use probability

mean value, normal distribution are probability concepts

[sudden kindle]

Yo

Nt is so cool

◉◡◉

[sterile harness]

Anybody know a place where I can take college math classes online and get a certificate

Like abstract algebra, analysis, etc

[stable dagger]

Look Coursera, they give certificates

[sage kelp]

Looks like he decided to quite update the book list!

[errant heath]

Is there a way to submit book recommendations for this server? I've found a few that I really like but for different subjects in math

[hallow oriole]

throw em in here lol

also there's this

https://forms.gle/Qh3bUZVQP2X9BSAL7

#books-old

[serene shell]

How should I approach maths from scratch to advance? Like pls give me order of books I should read from scratch to advance

Pls

[remote ginkgo]

khan academy

[serene shell]

Oh which course

[remote ginkgo]

all

[serene shell]

And can you suggest me some books as well

[serene shell]

Thank you very much

[remote ginkgo]

serge lang basic mathematics

[serene shell]

Does it contains everything needed

[cedar ridge]

do monographs not have exercises

[gray gazelle]

Some do, some don't

[tiny vale]

Do u guys know any easy to understand calculus books or ebooks??

[halcyon scaffold]

Are there any books that talk about doing set theory in HOL (encoding sets as predicates)

Simple type theory is what I think they are called. I found a paper called “seven virtues of simple type theory” on this topic but it’s too short.

[willow pecan]

If you’ve found a paper you can look through the references for more material

[wispy owl]

Does anyone know of a complete book on logarithmic density?

[sudden dock]

Is Conceptual Physics by Paul G Hewitt good book to self study first year high school physics?

[willow pecan]

This is not the physics server

Do ask your question in the physics server linked in #old-network

[sudden dock]

math 🤝 physics

[woven cypress]

Irodov

It's actually good ngl

[sudden dock]

This book of problems is intended as a textbook for student at higher educational institutions studying advanced course in physics from amazon, I need something for self-study.

[sudden dock]

hewitt?

[woven cypress]

Oh I thought you already had some idea

[sterile harness]

it doesnt have anything good tho

[remote sparrow]

Easy to understand is fairly subjective. It's also hard to make a recommendation given the plethora of calculus books available. Are you having trouble with mainstream recommendations like Stewart? Do you need a workbook? A calculus for dummies book? Could you need something like Paul's Online Math Notes?

[remote sparrow]

The channel description says, "Use this channel to ask for book recommendations. Tends to be mostly math but feel free to ask about other literature (YMMV)."

[willow pecan]

Sure

But they could get people who actually know physics to respond

[gray gazelle]

some people know physics here too
I think once there was a person asking about physics book recommendations before, that said they'd rather ask here, even

[gray gazelle]

I study physics

[gray gazelle]

Does anyone have a recommendation for a first book on mathematical physics?

[forest sleet]

What kind?

Like for qm, stat mech, etc?

There's the 4 volume series by reed Simon though that is more math

Like math you will need in math physics

Of the analysis flavor

For specific physics topics sometimes there's book like "this physics topics for mathematicians"

[gray gazelle]

yeah I meant physics topics for mathematicians, I am now taking a course in E&M and last semester taken a course in Mechanics and haven’t really been able to appreciate the development of the course, a lot of effort is spent trying to develop basic odes / vector calc and almost nothing seems to be (unambiguously) defined. I was hoping for some kind of text which treats e&m (mechanics as well would be nice) sort of axiomatically and includes definitions and proofs to develop the theory

[remote sparrow]

formalism for formalism's sake runs counter to the goals of physics, which is fundamentally rooted in empirical observation. if a mathematical model doesn't adequately describe physical phenomena, then it will be revised or discarded for a better alternative, regardless of mathematical consistency or unambiguousness

if you're learning physics for the first time, i would strongly suggest learning to think like a physicist, rather than trying to bog yourself down in the math

physical postulates and definitions do not come ex nihilo. the axiomatic treatments that you might see in mathematical physics books are the result of centuries of developments in physics. they are very carefully chosen with respect to empirical observation. proofs that result from these postulates and definitions do not matter if the axioms they rely on don't correspond to reality. the ultimate proof comes from the laboratory.

[fluid bay]

I think i see where loganb is coming from tho. In technical subjects outside of math, there often seems to be little imprecisions/abuses of language/definitions/assumptions that interfere with understanding. I don’t see why there couldn’t exist a more “bourbakian” treatment of physics that can still qualify as honest physics for people who prefer to organize their ideas that way

[vast obsidian]

How do you guys finish math books every book is like at least 500 pages ?

[tepid prairie]

I assume most people read them and learn literally nothing.

[lean pagoda]

any universal algebra texts that also cover lawvere theories in addition to the classic set-theoretical presentation?

[forest sleet]

not sure about E&M but for mechanics there is spivak physics for mathematicians, also the short lecture notes http://alpha.math.uga.edu/~shifrin/Spivak_physics.pdf But part of the problem is that even for mechanics, you're going to quickly need more advanced stuff like differential geometry

[gray gazelle]

i can understand this, the problem im seeming to have though is that physicists like to define things through analogy or prove by example and these both leave me with the feeling of being more confused rather than less. In a math class if I cannot rigorously state the definition of something I am studying, I quickly begin to feel uneasy and like there is something I am missing, in physics however you are expected to not know the formal definitions of nearly all the concepts which are routinely calculated. This feels entirely unnecessary though, for instance in mechanics there seems to be real axioms which are assumed (newtons law, the existence of internal frames, etc) from which the entire theory can be derived mathematically

[remote sparrow]

could you provide some examples for your E&M class? as far as axioms for classical E&M go, maxwell's equations would fit the bill. as differential equations, however, they're difficult to solve in general. this is why a lot of attention is paid to special cases and approximations. this trend continues even in graduate school, according to people that have read jackson's Classical Electrodynamics.

[forest sleet]

Fundamentally, the approach in physics is different than in math

You don't start with a set of axioms and see what you can prove

You start with real world phenomena you want to explain

And develop a theory that is consistent with what you see

So at some point you're going to have to accept something as an axiom, "because it gives us the right real world behavior"

For intro mechanics stuff though, the spivak notes I linked might still be helpful

[sage kelp]

https://www.youtube.com/watch?v=didXE0HkSC8

[remote ginkgo]

landau 2 or jackson

for e&m

[viral roost]

axiomatically would be variational calculus on jet bundles

[gray gazelle]

👀

[viral roost]

some of this is in Olver's book on lie groups applied to PDEs

but the actual laws of EM are somewhat more specific

the point of var calc here would be to formulate least action

and it is, as you can expect, somewhat more involved for fields

but Landau carries it out in the relevant case, mathematics books including and beyond Olver talk about the axiomatization

like Atiyah's Yang-Mills theory book and such

it all comes from diff geo

there is very little physics in Griffiths, just multivariable calculus problems with physics terms

on top of Jackson, there is landau 8 which discusses the EM in materials that is mentioned in jackson briefly, relevant to electrical engineering settings

[remote sparrow]

Have you ever looked at Smythe's Static and Dynamic Electricity? It's out of print unfortunately but I heard it's harder than Jackson.

[remote ginkgo]

nope read landau

[tiny vale]

I prefer a calculus book that has an easy explanation on every steps of solving done in a problem

[viral roost]

that sounds like khan academy

[foggy relic]

Pauls online notes is the same thing but objectively better

[remote sparrow]

I'm pretty sure paul's online math notes on calculus can be downloaded as a pdf

[smoky zephyr]

it can

[serene shell]

Thank you so much bro

[tawny jetty]

Anyone know university courses that follow pugh analysis closely for the first couple of chapters? Trying to self-teach.

[glacial crypt]

just learn from rudin

Have you tried understanding analysis by Abbott?

[grand thistle]

has anyone read do carmo's "Differential forms and applications"?

im looking to read it after i learn a bit of multivariable calculus to get acquainted with diff forms

wondering if it's a good book, it looks really good for me because it's concise yet covers a lot

pretty much just looking to do the first 4 chapters

[vast obsidian]

what is a differential form

[gray gazelle]

#diff-geo-diff-top

[hazy elk]

Not always

[grand thistle]

well that's what im tryna figure out from this lmao

[solemn rover]

Life is long. You have time.
If you're enjoying the book, take your time and enjoy it for itself. If you need its contents for something else, figure out what you strictly need and target that.
You probably do have to work through it slowly and in detail to have good retention. On the bright side, perfect retention is rarely required, it's not a sin to read casually / quickly.
Don't spend so much time on one book that you shut out other parts of math and don't progress forward. Mathematics is broad as well as deep.

[woven cypress]

What's the point of the server then?

[zealous coyote]

We do a bit more than just define phrases

[heady ember]

I just felt that it was perhaps a little unnecessary to place that qns there. A google search could have told him what it was and it doesn't really answer the question the person asked previously. If he doesn't have the prereqs to learn it yet, then I don't think people here can really give him a much clearer explaination either.

Of course, he/she could have asked more about diff forms in #diff-geo-diff-top if he/she was having difficulty understanding what they were when reading something like Lee

Hope Im not coming off as an asshole

[gray gazelle]

or just read only the relevant chapters

[remote ginkgo]

throw it out

read chapter 8 of shifrin

it's fast and you will immediately understand what you want

then if you want more read bott&tu

shifrin's book is 'multivariable mathematics'

[grand thistle]

that’s the book i’m reading rn

[remote ginkgo]

do carmo is a tough author

for no good reason

[grand thistle]

just thought that maybe it might not have rigorous enough coverage since it’s meant to be just a multi variable calc book

[remote ginkgo]

everything he has written, shifrin has written something on the same topic easier to read with the same depth

[grand thistle]

ah i see

[remote ginkgo]

it does, it has full proofs

[grand thistle]

hmm i guess i’ll stick w shifrin then

[remote ginkgo]

only exception to this is riemannian geometry, which you can learn from somewhere else anyway

(do carmo's RG book is not good)

[vast obsidian]

every chapter is relevant

[remote ginkgo]

if you want applications, try shifrin's differential geometry of curves and surfaces. the last chapter uses them in surface and curve theory

but bott&tu will give you real practice working with them to compute cohomologies

[grand thistle]

will probability theory ever use any concepts from differential geometry? it’ll probably just be measure theory no?

[remote ginkgo]

it does, a lot

in fact, one example is this

look at the space of normal distributions, parametrized by mu and sigma

this forms a hyperbolic riemannian manifold

[sleek python]

Probability can use concepts from almost any other domain

Depending on what's of interest

[grand thistle]

huh cool

[remote ginkgo]

probability theory takes much from linear algebra as well, and bilinear forms also yield these cone like manifold things

[grand thistle]

so i guess learning just a bit of everything won’t hurt

[remote ginkgo]

well, geometry makes it easy to see what you can even do

if you can get a good, general picture in your head then you automatically have some roadmap

[sleek python]

Tbh there are transversal concepts in all domains of mathematics

Not just probability

[remote ginkgo]

i think geometry probably is the most fruitful study

[grand thistle]

how is bott tu compared to something like lee’s differentiable manifolds?

[remote ginkgo]

totally different text

you should skip lee

and just watch schuller

here let me link

https://www.youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic

the lectures on topological & differentiable manifolds

and basic topology

and then a little about bundles

lee is a reference text and does not really get at the main ideas in proper cadence

the theory is simple

you can literally draw pictures to understand it

as for a textbook on manifolds, if you want extra reading (you shouldnt spend much time here though really) after the 2 shifrin texts, you can look at Tu's intro to manifolds

@grand thistle have you studied tensor algebra/calculus yet

[grand thistle]

no i havent

that’s just like the study of multi linear functions right?

[grand thistle]

cool sounds like a plan

[remote ginkgo]

yes, indeed

it turns out

if you take the tensor algebra over a vector space

and you quotient out the 'anticommutators' of that algebra

you get the exterior algebra over the space

and if you do this over cotangent spaces of a differentiable manifold

you get the differential forms

[grand thistle]

hmm

i have no idea what that means

but sounds interesting

i really wanna learn probability

so what order would you recommend for someone who wants to learn both diff geo and probability?

so many things i wanna learn and such little time

[grand thistle]

from some stuff i’ve read differential forms on R^n are like sums of differentiable elements of the dual space of R^n (probably have this wrong but still) how does this relate to that perspective?

[sleek python]

If you don't know anything about either, then you should learn them separately imo

[heady ember]

To be clear, I have never read Lee (well, I wish to read it one day), but I have heard great reviews about it. So I guess it wouldn't hurt to take a look to see if you like it

[gray gazelle]

not always, in fact I'd argue that a lot of things we read will never be "useful" in the future for some meaning of useful

[remote ginkgo]

you need additional context to say something is a 'differential form' namely it being a wedge product of cotangent vectors

[remote ginkgo]

well, a field of such wedge products over the manifold

[grand thistle]

alright this is a bit over my head now

i guess i’ll go read shifrin til i understand it

[woven cypress]

Nah I get it obviously

[hollow peak]

Bott Tu is explicitly after you've learned the basics of smooth manifolds

It's valuable as a resource for translating a few bedrock ideas in algebraic topology (cech cohomology, spectral sequences, characteristic classes, fiber bundles etc.) into the setting of differentiable manifolds

Would not recommend for learning about smooth manifolds as an introduction

[gray gazelle]

guys

some books on abstract algebra ?? focusing groups and symmetries

pls ❤️

[willow pecan]

Dummitt and Foote

[gray gazelle]

ye i got it

but i wanna smth more :S

[cinder trellis]

Is Advanced Linear Algebra by Roman any good? It seems OK on a first glance, but are there any big issues/cons with it?

[hallow oriole]

@cinder trellis

[foggy relic]

@cinder trellis i like Shilov

(also hi check mutuals lol)

[sage python]

I love that my linear algebra book commentary is so often cited

[sturdy shore]

it is pretty good commentary especially after the update

[foggy relic]

ooh never noticed the update!

[hearty steppe]

What do people think of that 3B1B linear algebra essentials playlist? That might be a good CrashCourse

I just realized it exists 😂

Or I forgot

[foggy relic]

i mean its not something to learn linalg from

[grave thorn]

It's pop math basically

[hearty steppe]

What if someone doesn’t care about refine holing themselves and they just want a refresher on things

[grave thorn]

Also not the best refresher

[hearty steppe]

I’ll just try to skim through various books I was going through to make sure my grasp is more than decent going forward. I don’t feel like I need to twiddle my thumbs in linear algebra land but it’s been a while since I did any stuff with eigenvalues

[sage python]

Depends on what your goal is. I'd say it's the number one most important topic to have solid in straight up math

But if you're using math to some end like bio

Your strat will be to find a math bio book and either learn linear algebra from there or at least look at the topics it references and learn them elsewhere

[hearty steppe]

Yea I feel like I’m fine there. I am not trying to be a mathematician. I am a researcher that applies mathematical concepts to areas mainly geared toward cognitive science, molecular biology, a bit of quantum mechanics, a bit of relativity. A little bit of interesting niches sprinkled around

I found all the books I think I’ll find for learning spectral theory

But I can’t go thru a straight up applied book. I need to go through pure books

[sage python]

Those have different needs I'd wager

[hearty steppe]

That’s the way I learn most is going thru a pure book that motivates concepts well

I’m a weird character when it comes to understanding stuff because of my medical condition

I still go thru certain physics books but I need math books and resources to accompany them

[sage python]

Yeah I mean that's a decent overall take, though if you're at linear algebra then what is specifically an effective strategy for you is probably still tbd

Since that comes very early in the game

[hearty steppe]

Hmm I didn’t really struggle with the texts I was going thru in terms of understanding concepts so I think I’ll just get a feel of where I am at

[sage python]

Oh I'm not saying you did struggle I just mean like

Linear algebra is one of the first topics you see lol

So you might hit later things and be like well the strat needs to change

[hearty steppe]

Exactly

[sage python]

Anyway idk about math bio, again pick up a book on it and find the topics it calls important, then consult another book for those topics

QM and GR... Depends on what you mean by a bit. You probably won't be the first to come up with many new ideas in either, especially new ideas born out of applying math concepts

Since a lot of sophisticated math goes into them already, so the easy stuff has almost surely been done

[hearty steppe]

Yea that’s what I was thinking.

[vital bane]

it's a very good aid to a book

which is what 3b1b literally says

he inuitively explains all the basic lin alg

[languid cypress]

What are some good books for Euclidean geometry and coordinate geometry? I want to learn them asap for physics applications and ipho (Competition level)

I have researched about it and i found out for
Euclidean Geometry: College Geometry - An Introduction to the Modern Geometry of the Triangle and the Circle by Nathan Altshiller-Court

[sudden dock]

Doing seeing and understanding Geometry

[civic canyon]

anything good for like understandinng how to factor polynomials of any degree?

[dapper root]

there's no general method

[willow pecan]

If you want to factor the polynomial to find its roots, there are other ways to do that

[royal gale]

Can someone tell me excelent books to learn Dynamical Systems?

[remote sparrow]

there are two recommendations in #books

[heady ember]

Ehh book prototype

That hasn't been updated or touched in some time already

[willow pecan]

It is currently a work in progress

Progress stalled for a bit but now I am back to bully metal

[heady ember]

[steep badger]

hmmm what kind of dynamical system?

it is a pretty broad subject.

[royal gale]

I want to learn to use in nanobiotechnology, biophysical and biology in general.

[remote sparrow]

https://conwaylife.com/book/

^ seems like a neat book

bonus is that the ebook is free

[royal gale]

Thank u ❤️ @remote sparrow

Can you recommend me other books / topics? I love math, and I really want to use it in biophysics.

[remote sparrow]

no this is not a dynamical systems book

it was a follow-up to a post i made in #chill

#chill message

[royal gale]

I know, it's a kind of fractals? My friend showed to me some videos about it

[steep badger]

Did you check out Strogatz's book on nonlinear dynamics? They are tons of examples and applications in that book, and it is undergrad friendly.

[last panther]

any books to start learning on math logic for a friend who doesn't know how to think mathematically very well?

[remote sparrow]

https://forallx.openlogicproject.org/

maybe this?

[last panther]

thanks ❤️

[remote sparrow]

[slim peak]

this is the smoothest and the most elementary introduction ot differential forms I ever see

Thank you

Nice reference

[gray gazelle]

anyone who’s done a masters in math in Europe, what are the courses you’d typically take in your fourth/fifth year?

[rich sun]

Depends on your specialization

[gray gazelle]

Pure math

Or something more specialised like PDE research?

[rich sun]

Yeah

[rich sun]

For PDE, maybe numerical methods for PDEs (elliptic, parabolic, hyperbolic), Sobolev spaces, continuum mechanics

[obsidian sand]

https://www.amazon.com/Tools-Mathematical-Reasoning-Applied-Undergraduate/dp/1470428997

is this a good book

[rapid lodge]

u can get it for free

don't even need pay for it

but its an online version

nvm

that specific one is not available

[remote ginkgo]

strogatz to begin, then there are two to continue with:
Andronov's Theory of Oscillators
Kuznetsov's Elements of Applied Bifurcation Theory

[gray gazelle]

has anyone read Rotmans introduction to the theory of groups?

[gusty smelt]

Books for dynamics? not interested in like a physical/pde stuff, lets say more topological/geometrical

[willow pecan]

Max would recommend Brin and Stuck I think

Or do you want more ergodic theory

[gusty smelt]

hmm i think this is good, ty

[languid crown]

I'm looking for a book on a niche interesting maths topic, that isn't very complicated, so a pre uni student could understand pretty much everything

hungry for weird maths

I was looking at non-euclidean geometry before, but it gets very complicated sometimes

[willow pecan]

All of math gets very complicated

[loud cradle]

maybe something like generatingfunctionology

[languid crown]

ooh I've heard of generating functions before but don't know anything about them

thanks for the recommendation

[loud cradle]

iirc it requires a bit of calculus but nothing beyond that

[languid crown]

ah I'm good with that

[loud cradle]

freely available from the author as a pdf here: https://www2.math.upenn.edu/~wilf/gfology2.pdf

[crimson leaf]

Yeah requires calculus

R.I.P Dr. Wilf

[loud cradle]

oh man i didn't realize he had died

[crimson leaf]

Yeah about 10 years ago

[loud cradle]

that's nice that his uni has kept his website alive

[crimson leaf]

https://www2.math.upenn.edu/~wilf/gfologyLinked2.pdf here's the link with a table of contents btw

[remote sparrow]

Any modal logic book recs?

[cinder tundra]

any good reccs for an advanced course on linear algebra

[sturdy shore]

check pins

[cinder tundra]

thank you

[gray gazelle]

anyone ever read prinicipia mathematica

[remote sparrow]

which one

[keen orbit]

Hello everyone which book is recommended for self studying linear algebra

[remote sparrow]

for a first or second course

[keen orbit]

I am learning calc rn I am near starting to learn techniques of integration and this will be the first time I read about linear algebra

So i am totally new to linear algebra

[remote sparrow]

#book-recommendations message

[keen orbit]

Is the book linear algebra done right by Sheldon axler considered a good book to self study linear alg?

[remote sparrow]

you can use it for a first course in linear algebra, but axler designed it for use in a second course after you're done working with more matrix computations and earlier introduction of determinants

[keen orbit]

I saw someone on yt recommending it so I want to know

[keen orbit]

Oh ok so it's better not to start with it ??

[remote sparrow]

it will be easier to appreciate if you use it as a second pass through the subject

if you're just self-studying

[keen orbit]

But If I start with it will I miss ideas that the book doesn't include which should be known before knowing the ideas found in the book??

[remote sparrow]

i guess you might miss something? you might miss out on the computational aspects of linear algebra. either way, a typical curriculum requires two passes at the subject.

no book is completely encyclopedic; authors make choices about what to include and what not to for various reasons.

if you've got a fear of missing something out, figure out what you're most worried about missing

[keen orbit]

What I meant is that I want a book that starts from the beginning of the topic

[remote sparrow]

axler is complete in that sense, it's just that his perspective is different.

you should skim through the books i mentioned and axler and see which one is right for you

[willow pecan]

Friedberg

[upper stump]

Need some real good introductory book on abstract algebra

[willow pecan]

Dummitt and Foote

[upper stump]

Mathematical logic & advanced set theory

[willow pecan]

Enderton is a standard logic book I believe

Jech is the standard set theory book I think?

[upper stump]

yeah I have that one

Jech’s

[remote sparrow]

Judson's ebook is free and has a cheap print copy. Pinter's book is a cheap Dover book.

[remote sparrow]

You could use Enderton's set theory book too but i think it's out of print

Nvm elsevier sells a hard copy

Jech's book is graduate level. Hrbacek and Jech's book is undergraduate level.

[lone orbit]

What do you guys think about "Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology" book ?

[sage python]

Is it a historical thing or what?

[gray jungle]

artin book + gross lectures are a great combination, would use something else for exercises.

[lone orbit]

I don't know, the book explains the four classical liberal

and some discovers

"From the time of Plato through the Middle Ages, the quadrivium (plural: quadrivia) was a grouping of four subjects or arts—arithmetic, geometry, music, and astronomy—that formed a second curricular stage following preparatory work in the trivium, consisting of grammar, logic, and rhetoric."

[cursive orbit]

why not use two separate books

[ornate saddle]

Sheldon Axler's Linear Algebra Done Right is quite a fruitful book in terms of readability of his proofs.

[gray gazelle]

Too bad he treats determinants in the most insane way possible.

The book is fantastic as long as you cut out the parts about determinants and the characteristic polynomial and replace it with a more sensible treatment.

[sage python]

Because complex analysis uses ideas from real for the most part.

[remote sparrow]

https://linear.axler.net/

if you're an instructor, you can receive an electronic copy of his upcoming 4th edition to give feedback based on classroom testing, which will also be available as a free ebook

[gray gazelle]

Why did you ping me for this?

I learned linear algebra a long time ago and have no plans to teach it.

[crimson leaf]

I do commend him for making the next edition a free ebook

[heady ember]

Look at Clerk's recs in pinned

[heady ember]

Enderton's Elements of Set Theory is not advanced axiomatic set theory. Its an introductory one.

It only covers the basics like the ZFC axioms, cardinals, ordinals, the Cantor-Schroder-Beinstein theorem, etc. Doesn't cover more advanced stuff like forcing.

[sturdy shore]

imo baby jech is a better book on introductory (axiomatic) set theory to someone that has mathematical maturity

enderton is for true beginner

but idk what the person means by advanced exactly

[heady ember]

Yeah that's rather vague

[remote sparrow]

enderton would make sense if you've never had exposure to something like halmos' Naive Set Theory but have already done some math already

[sturdy shore]

I think if you've done a lot of math it's impossible to not know naive set theory on halmos level, you will pick it up here and there

oh you changed it to some, if youve done like 1-2 proof based course then yeah enderton is still a good option

[heady ember]

I didn't do halmos or pick up any book on naive set theory and I went ahead and did (and am still doing) Enderton

[remote sparrow]

^ right, that's what i said

[heady ember]

I tried Rosen discrete math => Got too bored => Enderton looks cool => Pain but fun :D

[remote sparrow]

my university doesn't offer mathematical logic or axiomatic set theory

[frigid shale]

What was Axler's rationale anyways for absolutely hating determinants?

[sturdy shore]

he has a paper on it

google axler determinants paper

[upper stump]

beyond ZFC stuffs

[sturdy shore]

then kunen is the standard text I believe

[heady ember]

[upper stump]

‘large’ cardinals etc.

[upper stump]

K

[sage python]

@frigid shale he's a functional analyst

[dusk forge]

anyone know any good physics books

Thanks, yea I know it's vague because I don't really know exactly what I want to read but I find physics interesting so I'll check it out

what about a book on light, waves and stuff like that

optical lenses

[hazy elk]

From #books
Topology: A Categorical Approach (Terilla, Bradley, Bryson)
Comfort with Sets and Basic Proof-based mathematics.
This book is quite different from the others on this list, and might best be used in conjunction with one of the others. The book develops basic category theory and point-set topology at the same time, with a different and more modern perspective than point-set is usually introduced. Potentially obscure topological definitions are shown to be very natural and straightforward through their universal properties.

[analog flint]

what are some good resources on several complex variable analysis?

[analog flint]

ah yeah that looks really well laid out, thanks

[wraith shard]

You should try "pilgrims progress" I love that book

[clever owl]

yall should try the ''dairy of a wimpy kid trilogy''

[willow pecan]

[distant cloak]

Does anyone know of any good trig books that can be taken alongside a trig textbook?

[grave thorn]

try trig

[remote ginkgo]

i like how u didnt mention how witten wrote this book

[hazy elk]

Huh..?

[fluid bay]

[remote ginkgo]

one author (the one with the most famous name) is omitted from your list

ik it was copied from somewhere, but still

[fluid bay]

witten didn't write that book

[remote ginkgo]

let me double check

whoa!

then which one am i thinking of

LOL oh it's ISLR that i'm thinking about

nvm sorry

[hazy elk]

Ye lol

[fluid bay]

what is ISLR?

[remote ginkgo]

intro to statistical learning with R

[fluid bay]

damn not even remotely related to topology or category theory

[remote ginkgo]

indeed, that's a wild slip

[sturdy shore]

introduction to topology with category theory

[remote ginkgo]

ye i have both of them

its good

[blazing jetty]

book for set theory

[remote ginkgo]

william lawvere, sets for mathematics

[blazing jetty]

thanks

[sturdy shore]

don't listen to that lol