book-recommendations

[dapper root]

and like different things happened each time I swear

It's non-deterministic

[quick hornet]

believe it or not, ive never played it

so i have no clue what you were doing wrong

but uh

get good scrub

[dapper root]

Yeah 😔

[modern stone]

programming conventions type beat

[karmic thorn]

This definition was sourced from nlab

[quick hornet]

yeah thats bona fide nlab lmao

[gray gazelle]

tfw #book-recommendations turns into #anime-recommendations

lain is the only good anime smh

[misty wyvern]

nlab needs an article on anime

[shut kestrel]

hello everyone

[halcyon hornet]

Hello fellow evolutionized monkey.

[modern stone]

Return back to monke

🐒

[gray gazelle]

#chill

[green estuary]

Any suggestions?

[karmic thorn]

Mathematics and its History by Stillwell is a great read

[green estuary]

Thanks!

[grim pivot]

What are y’all’s thoughts on Categories and Sheaves by Kashiwara and Schapira

[solemn rover]

haven't spent much time with it but it seems fine. the explicit use of universes is a bit intimidating at first. keeping track of all that is a bit intimidating

i have used it as a reference once or twice and there are some cool theorems in there.

i should really go back and read more of it. it seems pretty interesting

they seem to be mostly interested in developing it for the sake of homological algebra and applications to geometry, so that's the focus

i have heard their other book "Sheaves on Manifolds" is a bit easier and more accessible

[grim pivot]

I appreciate the insight!

[solemn rover]

it's dense and technical. idk if there's much of a way around that. personally i don't mind it. their notation is also like, not super standard, but in a good way, it's well chosen for communicating efficiently but it has a bit of a learning curve? my memory's blanking here so i'm kind of just filling in gaps with possibly spurious information lol

[atomic hound]

Hey man, thank you very much for the information!!!You are the Guy!

[solemn rover]

not sure if this is sarcastic but really hilbert systems are covered at least in passing in dozens of books. Elliott Mendelson's "Introduction to Mathematical Logic" is one, just for the sake of giving you a name. A hilbert-style proof system for predicate logic is covered in chapter 2.3.

The deductive system presented in Enderton's "A mathematical introduction to logic" is also a Hilbert system from what i can tell

The book "Basic proof theory" by Troelstra will introduce Hilbert style systems and prove their equivalence to natural deduction and gentzen type systems. this is good for the sake of seeing a complete, explicit definition

but they are not studied much in the book beyond that. Hilbert style systems are not important to structural proof theory

[gray gazelle]

Diligent, do you have any recommendations for modal theory?

[solemn rover]

do you mean model theory?

not making fun of you, there is such a thing as modal logic

[gray gazelle]

Yes, I made a typo

Sorry ‘bout that

[solemn rover]

I learned model theory out of the books by Tent and Ziegler ("A Course in Model theory") and Marker ("Model theory: an introduction"). both are fine. the book by Marker has typos. i haven't studied model theory in a long time and i'm out of touch.

Other than that I think you want to see a book at some point that treats things using infinitary logic, like L_{omega_1, omega}, and see Scott's isomorphism theorem. I can't remember off the top of my head what books do things this way.
Other good references

• Chang and Keisler
• Hodges, "A shorter model theory"
• Poizat (I used this as a reference when I was struggling with the omitting types theorem. i found his proof, if not easy, at least easier to read and understand.)

[gray gazelle]

Thank you!

[gray gazelle]

Do you have any recommendations on modal logic as well?

[solemn rover]

no

😢

[gray gazelle]

Thank you!

[sudden kayak]

book recos for statistics that focuses on election statistics?

[junior merlin]

Nate silver's book the signal and the noise is a good casual book on prediction

[pure dome]

Hi, me and a few friends are interested in studying category theory, so far ive been recommended
-Categories for the working mathematician - Saunders Mac Lane
-Category theory in context - Emily Riehl
So i was wondering which one is better to get started, thanks 🙂

[quick hornet]

both are fine texts. how much algebra do you know? are you comfortable with the basics of homological algebra?

[pure dome]

only know the basics of abstract algebra, so group theory rings and modules

also im taking a course on topology that will cover some notions of homology by the end of the course

[sudden kindle]

Book on Sieve methods https://www.ams.org/books/coll/057/coll057-endmatter.pdf

Opera de Cribro by John Friedlander and Henryk Iwaniec

[gray gazelle]

[loud rampart]

Can anyone suggest a book on elementary number theory (I want to be perfect with my theorems)

[karmic thorn]

@loud rampart

[loud rampart]

Ty :)

[halcyon hornet]

Any recommendations for Quadratic Optimization(using Inequalities)?

[gray gazelle]

help

#❓how-to-get-help

[sudden kindle]

This is suppposed to be a down-to-earth concrete introduction to algberaic topology:

https://link.springer.com/book/10.1007/978-1-4612-4180-5?page=2#toc

Algebraic Topology - A First Course by William Fulton

[marble solar]

Can confirm, I've read a lot of that book

Pre-reqs are like calc 3

Fultons texts in general are very good

[remote nova]

How neat

[modern stone]

Really?!

This seems to good to be real

[crimson pagoda]

no its not

[marble solar]

That's where you're wrong bucko

I spent a semester course on fulton's algebraic curves

Those problems are intense

[thin hollow]

Calc textbook

That actually teaches

Something that provides harder examples of derivatives more than OGCt

[analog pollen]

Spivak

[gray gazelle]

harder examples of derivatives

come up with your own

write down the most genuinely disgusting function you can think of and try to differentiate it

[analog pollen]

Checking your answer by differentiating after integrating sqrt(tanx) 💀💀

[manic fox]

painful advice by tterra

[inner token]

Now that I'm in grad school I whine like a baby Everytime I need to do integration by parts

Who wants hard derivatives. Symbolaaaaab

[strange wedge]

I just passed out from high school. And would start college with CS major. Which books to start with for college algebra and Discrete Mathematics?

[karmic thorn]

"College algebra" is very vague and depends upon your syllabus, for discrete math Rosen's book seems to be recommended a lot.

[broken meadow]

rosens book is okay i felt

[strange wedge]

I mean Linear Algebra and Number Theory

[karmic thorn]

Hmmm, perhaps for a first course in linear algebra which takes a matrices-first approach, Strang's book or Lay's Linear Algebra and its Applications might be fine. For elementary number theory, several recommendations are present in the pinned messages.

This

[gloomy palm]

I’m using David Lay linear alg book rn for my course

[solemn rover]

I used that book in my first linear algebra class

[jolly quarry]

hey when do we learn linear algebra

[dapper root]

Whenever u want to

[loud rampart]

Lmao

[velvet briar]

@jolly quarry
Usually first year uni

[atomic heron]

I do NOT recommend Partial Differential Equations: An Accessible Route through THeory and Applications by Andras Vasy

it is not accessible at all

[jolly quarry]

thx

[slim coyote]

Hi

Please recommend me a book on combinatorics. I have no math background.

[livid ermine]

a walk thru combinatorics miklos bona

[slim coyote]

@broken dragon thanks

[slim peak]

What is your level ? The book seems to be adressed to 3rd ou 4th year students

[atomic heron]

3rd grade

[slim peak]

You just started it right ?

[atomic heron]

Started what

[slim peak]

Your 3rd grade year

[atomic heron]

Yea

[slim peak]

That's why it is not acessible for you right now

wait until the next semester or the end of the year depending on the Lecture you had

[atomic heron]

wait with what

[slim peak]

To see that "Partial Differential Equations: An Accessible Route through Theory and Applications" is indeed accessible

[atomic heron]

oh ok

Don't think I'm gonna take anymore maths courses though

And just focus on DL

[slim peak]

You are not a Math student ?

so just give up, the book won't be of any use for you

[atomic heron]

I am not

Not gonna give up though lol

[solemn rover]

yeah i'm focusing on DL and DN

[sudden kindle]

Focusing on DN is good

[atomic heron]

deez nuts

[gray gazelle]

Someone please suggest a good discrete math book for computer science?

[grim pivot]

Is that infinitely large napkin book any good if you want to actually learn a topic, or is it just kind of a survey/beginning points on different topics in math

[gray gazelle]

I am looking for something that would help me develop computational thinking and logic~

oooh i dunno about this book~ infinitely large napkin book

[grim pivot]

Haha my question was unrelated to yours. Sorry about the confusion!

[stray veldt]

the latter

its written for competition math kids who want to know what topic X is kinda about

[gray gazelle]

also yes I'm kind of a beginner in cs

[gray gazelle]

oh not competitive stuff as of now

[stray veldt]

again, this was about napkin

if you want a discrete math book, try Rosen?

it has a lot of content, but you can pick and choose what you need

[gray gazelle]

oooh okk lemme look up for this

[jolly zinc]

Does anyone have good graduate-level instructional material on spectral theory and generalized Fourier analysis? I’m not totally sure what I’m looking for, but I think that I want to use something along the lines of this paper in my research (though i am not specifically working with fractals): https://arxiv.org/abs/math/0606349

I’m familiar with the content in the first half-ish of Rudin’s Analysis on Groups, but it’s been over five years since I’ve done much serious in that vein.

[fathom elk]

Is there a math body of knowledge? Like the SWEBOK? Or like a list of topics in math and a list of textbooks covering each topic?

[quick hornet]

Is there a math body of knowledge? Like the SWEBOK?
no
Or like a list of topics in math
kinda, the AMS subject classification
and a list of textbooks covering each topic?
no (but there are many lists of textbooks if you restrict your scope to undergrad level)

https://mathscinet.ams.org/mathscinet/msc/pdfs/classifications2020.pdf

[slim peak]

For Spectral Theory, you can look at C.Cheverry and NRaymond's book called A Guide to Spectral Theory, Springer Birkhauser, 2021.
About General Fourier Analysis it depends what you mean more precisely : Fourier Analysis, Harmonic Analysis, in an Euclidean setting ? On Groups ? On Lie Groups ?

[misty wyvern]

I'm still not clear what Fourier analysis on groups, as a field, is about.

[sage python]

Did someone say Fourier analysis on groups?

[slim peak]

Use unitary representation of Groups, then use the given morphisms to build a Fourier transform using the existing Haar Measure

[sage python]

teafortwo basically the idea is that you sorta notice that in the case of Euclidean space or the torus

That Fourier transform has an interpretation via rep theory/functional analysis

[misty wyvern]

Yes

Fourier analysis to decompose spaces and regularize things

[sage python]

Namely it's decomposing the regular representation of G on L^2(G)

[misty wyvern]

L^2(G) with the Haar measure?

[slim peak]

yes

[sage python]

Yeah

[misty wyvern]

like anatole said

Ok

[slim peak]

when you have G, you can construct its dual ^G

[sage python]

In general, if you give me some locally compact abelian group G, you construct the dual group as Anatole said, both objects have a measure

[slim peak]

You can construct a Natural isomorphism

which is unitary

Called the Fourier Transform

[sage python]

R dual is R and S^1 dual is Z

So that's why you think about the Fourier transform on R as L^2(R) to L^2(R)

And why Fourier decomposition on the circle spits out a sequence of coefficients which will be in l^2

[slim peak]

sending L²(G) to L²(^G)

[misty wyvern]

Ohhh, I get it.

So what does the general Fourier transform look like

[slim peak]

Things becomes more clear on finite groups or somewhat but it is overkill af

[misty wyvern]

brb

[sage python]

L^2(G) -> L^2(\hat{G})

[slim peak]

In general the is no fully explicit formulas except for some explicit groups, but even in those cases formulas are quite unpleasant

[misty wyvern]

So the natural isomorphism isn't constructive?

[slim peak]

"constructive"

[sage python]

There is a formula for sure

But the problem is like

DO you have a nice description of the elements of the dual group?

[slim peak]

$f(g) = \int_{\hat{G}} F(f)(\chi) \chi(g) ~\dd\mu(\chi)$

[sage python]

Ugh I hate that you use upright d

[hasty eagle]

Anatole

[sage python]

😦

[slim peak]

\mu must be the "dual measure"

[sage python]

Prob should define the Fourier transform first lol

[slim peak]

But nothing more explicit than the above formula

I just wrote the inversion formula

but you can guess the usual formula

[misty wyvern]

So the dual group here is the Pontryagin dual

[slim peak]

Even for nice groups it is kind a pain in the ass to explicit things

[sage python]

But yeah basically in the case of R, every character is of the form e^{2pi i a x} for some a

[hasty eagle]

Sloth King Daminark

[broken meadow]

@leaden grotto can you not

[misty wyvern]

Is Rudin the man to read about this or is there a more general resource for someone familiar with harmonic analysis

Or barebones introduced

[sage python]

I have a small physical book by Loomis that I bought for like, $5

[slim peak]

here he identified charaters with their representation a in R

[sage python]

Folland Abstract Harmonic Analysis is a thing

[misty wyvern]

kay

[sage python]

I'd wager if only based on typesetting that it's more modern than Rudin

[misty wyvern]

[sage python]

But yeah this is in the case of abelian groups fwiw

[slim peak]

Thangavelu for the specific case of the Heisenberg Group

[sage python]

Because then irreps are just characters

[slim peak]

and the link with microlocal analysis and Pseudo Differential Calculus is made

[sage python]

In the non-abelian case things are tricky. The dual is no longer automatically itself a group and representations can't necessarily decompose into characters

If you assume the group is compact then you still do have something nice called Peter-Weyl

[slim peak]

There is some generalized Characters and we can still perform stufff

[slim peak]

Fourier Series Only

❤️

[sage python]

Which says a unitary rep of a compact group on a Hilbert space still splits as a Hilbert space direct sum of finite dim irreps

[slim peak]

So this is what people who do "non commutative Lp spaces" are looking at

Not only

[misty wyvern]

Why is every book in this topic published last century

Folland is the newest, I'll pick it up. Thanks for the rec.

Or rather I'll sail the high seas to find a copy

[marble solar]

a lot of it has fallen out of flavor within the analyst community

Decoupling has been gaining traction by a lot, recent progress on the collatz conjecture

And there's been recent progress on navier stokes (or so I'm told)

So people are chasing down other things like that than harmonic analysis stuff

[misty wyvern]

The recent progress on the Navier-Stokes as far as I know is basically pure harmonic analysis-derived regularity, I'd be interested if you knew where to find these representation-like structures.

[marble solar]

I have a copy of Stein's Mammoth

But I don't think it represents where people are pushing Analysis nowadays

It's just a reference tome

[slim peak]

If there is I do not know either, about representation theory link to Navier-Stokes, but for pure Euclidean Harmonic Analysis technics, P.G. Lemarié-Rieusset wrote 2 books that reviews regularity properties (Existence-Uniqueness theorem) of Navier-Stokes Equations using pure Harmonic Analysis.

[misty wyvern]

Yeah, I'm looking through Lemarie-Rieusset for anything rep theoryish

But all I see are inequalities

[marble solar]

I'll be more involved in Harmonic Analysis hopefully next year

[slim peak]

Stein's Books are really important

they are the foundations of all the modern PDEs

[marble solar]

Is there value in learning computational PDEs

outside of industry

Like does it actually help develop a sense for the theory

[slim peak]

Absolutely not in my opinion

But maybe I'm wrong

[marble solar]

I'll just take them for employability reasons then

lol

[slim peak]

It is more about proving nice Theorems about fucntional analytic properties of Sobolev and related spaces.

It provides nice and easier proofs than the first ones given 20 years earlier

And some new results

[marble solar]

I took a course on Sobolev Spaces, Regularity Theory, and Semi-Group Dynamics

I was following along till we got to semi-groups

[slim peak]

:(

[marble solar]

This was holy shit 2 years ago now

[slim peak]

Gagliardo-Nirenberg-Sobolev inequalities are equivalent to the decay of the Heat Semigroup

That's sad you dropped at the most interesting part

it is even true for Abstract semigroups

on abstract Lp Spaces

whose Sobolev Spaces are just domains of a Fractional Power of the generator

[marble solar]

I did my final project in there on semi-group dynamics

[slim peak]

Nice

[marble solar]

I didn't understand most of it, some paper by Liggett

[slim peak]

More precisely ?

[marble solar]

lemme find the paper

[slim peak]

If it is about Nonlinear semigroups then stay away from me Satan

[slim peak]

Phantom ping ?

[sage python]

So sad 😦

[foggy relic]

what is a good book to learn introductory automata theory

at undergrad level

im looking for a book that also has a good chunk on languages

[misty wyvern]

Hopcroft and Ullman

[foggy relic]

can it be understood by someone with 0 background in the subject?

[misty wyvern]

Do you know what a proof is?

If so it's accessible to you.

Proofs, set language, propositional logic

[foggy relic]

i meant for someone who dosent know any automate theory

but i do know those so i think i can do it

thanks for the req

[remote nova]

Don't worry about if you're "prepared" for it

just jump into the book, and if you're not, come back here 😌

[karmic thorn]

@foggy relic MIT came out with its "Theory of Computation" course video lectures on YouTube as well. The lecture notes/assignments are available on their website. Sipser's book is the one they are using.

[foggy relic]

can you please send the link for it? thx for letting me know 😄

[karmic thorn]

https://youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY

[foggy relic]

i think i'll do sispers book b/c of those videos & its what the instructor of my class recommended

[karmic thorn]

https://ocw.mit.edu/courses/mathematics/18-404j-theory-of-computation-fall-2020/index.htm

Here's the course webpage

[foggy relic]

https://tenor.com/view/leonardo-dicaprio-thank-you-cheers-smile-gif-17045602

[hearty steppe]

Seems like measure theory is probably a good time investment

Not quite there yet but I think I’ll prioritize it when I am

[gray gazelle]

measure theory

[broken meadow]

📏

[manic fox]

feet

[broken meadow]

ruler

its a RULER

[gray gazelle]

[broken meadow]

oh it says straight ruler

📐

i guess to contrast with this one

[crystal lion]

why is there a straight ruler but not a gay one

homophobic much

[jolly zinc]

I’m familiar with the theory for L^2(G) where G is locally compact and abelian. However the paper I link to discusses a generalization of the notion of Fourier analysis that appears to apply to a great many other spaces by transferring interest from a LCA group to a measure that has certain properties (which the Haar measure meets). Like I said, I’m not totally sure what I’m looking for but I found this paper and I can tell I want whatever it is that bridges the gap between Analysis on Groups and this paper.

I’ve also read most of Folland, but it doesn’t go much beyond compact and locally compact abelian groups.

[jolly zinc]

It’s possible I’m looking for pedagogical materials on “Fourier Frames” but I’m not sure what those are exactly 🤣

[misty wyvern]

They will literally never stop naming things after Fourier.

[narrow talon]

Anyone know of a slim ODE reference? I took a course on them a while back but forgot everything and now need them to calculate expectations pretty regularly but don’t want to deal with a chatty textbook

[karmic thorn]

Some users here shill Viorel Barbu's Differential Equations

[still saddle]

Is there a website like goodreads but for academic papers, except for the writing reviews part? Like you know get recommendations based on what you have read etc.

[junior merlin]

arxiv sanity is useful, doesn't hqve reviews though and its for ai stuff

sounds like what researchgate is supposed to be

[still saddle]

Thanks, this totally slipped my mind. I keep forgetting to make an account there.

[slim peak]

MathScinet for reviews

SciHub, Arxiv, HAL etc... for papers

[still saddle]

Thanks

I just checked research gate, it looks like i need an institution or company account to access it. I dont have either.

[slim peak]

Oh you are no longer an University student ?

[still saddle]

yeah pandemic kinda made me quit.

will reapply next year

[slim peak]

Difficult to access thos website, especially Mathscinet, without an Institution

[still saddle]

Thanks anyway, scihub generates recommendations?

[slim peak]

Non of the websites I gave you has recommandations

Except Research gate.

[still saddle]

oh okay. Thanks.

[proper moss]

Anyone knows how long it take in general for a MyCopy to dispatch from Springer?

[slim peak]

it depends on your country

to me one week and a half almost 2weeks

Sent from Germany to France

[sleek python]

What is MyCopy

Is it like libgen

[slim peak]

I bought one a week ago, I will tell you when I will receive it

[slim peak]

Absolutely not

[sleek python]

Oh wait nvm it's for a physical copy. Who knew people really bought books

[slim peak]

If your Institution (University) has suscribed for some books, if you log into the website using your Institution you are able to purchase physical copies of books for 25$

[sleek python]

You almost made me run to springer and purchase physical copies massively

[slim peak]

The counterpart is that you cannot resold your MyCopy Books

[sleek python]

Ew

[proper moss]

Well I had an order placed last week, I hope it arrives by end of this month. Anyway thanks for the info!

[slim peak]

they are specific books printed from the pdf version with a identification number and a banner is printed on the cover

[slim peak]

np

I have almost all the books needed for my PhD

Thanks to the mycopy Program

[orchid musk]

wait this mycopy sounds amazing. how do you use it?

[quick hornet]

does your school give springer access?

mycopy is a way to get a physical springer book shipped to you if you already have digital springer access

i think its like $25

[orchid musk]

i can log on and 9/10 times a math book is available in pdf from the springer website

[quick hornet]

then yeah you probably have access

https://www.springer.com/authors/book+authors?SGWID=0-154102-12-768604-0

[orchid musk]

thx

[inland elm]

i'm deciding between herstein's abstract algebra and herstein's topics in algebra as an intro to algebra

should i prioritize the former

[forest sleet]

btw springer author token and professional society discounts should apply to mycopy, so you can get mycopy for noticeably less than $25 with those

[past ice]

kind of a weird request, but does anyone know of an intro to multivariable calc that assumes knowledge of measure theory? I'm kind of thinking of Folland's sections on change of variables and polar coordinates, but much expanded.

[dense wren]

Is Hartshorne a good text to self study algebraic geo? If not what’s a good alternative

[marble solar]

You should start w/ Fulton's Algebraic Curves

Then choose between The Rising Sea or Hartshorne

[halcyon hornet]

What are some good books for Multivariable Calculus? Does Stewart's book has Multivariable Calculus?

[rugged bobcat]

Any good books that make you love math?

[halcyon hornet]

Yeah, many.

[gray gazelle]

calculus 4 ed by michael spivak

[halcyon hornet]

Aight cool.

Where is it damn not on Amazon.

[gray gazelle]

stewart doesn't help me comprehend

[halcyon hornet]

And Thomas?

[gray gazelle]

idk i've never read one

[halcyon hornet]

Great book fam!

WTF $800 for a Thomas Trains book?

[gray gazelle]

I think she meant calculus on manifolds

[broken meadow]

she

[gray gazelle]

yes

Sorry I automatically type that.

thanks for reminding them to change the address

that's okay

[halcyon hornet]

Does not Thomas cover like both?

Single and Multi Variable.

[broken meadow]

thomas does

[halcyon hornet]

Cool.

What is so good in Spivak. And why is it not available in Amazon or such online for a reasonable price?

[gray gazelle]

the way the author explained, and it offers proves

[halcyon hornet]

@gray gazelle can I DM?

[gray gazelle]

go ahead

20 mins

[obtuse ibex]

Could anyone please suggest me good book for the history of mathematics

Mathematics and it's history by John stillwell is good ?

[analog pollen]

spivak has good and hard problems

[analog pollen]

stewart has multivariable too yes

[gray gazelle]

metal literally has told you

[gray jungle]

i'm looking for a book to rework on linear algebra more rigorously and theoretically any recommendations?

for context i have not taken bilinear algebra and euclidean spaces yet just linear algebra this is sorta me preparing for that

[halcyon hornet]

I forgot.

Why is Thomas not considered so good then?

[gray gazelle]

Thomas is bloat.

and so is every other intro calculus book

[halcyon hornet]

Spivak too?

[gray gazelle]

Spivak is good

but that is more on the theoretical side

and not the "grind these weird integrals" which is what is done in engineering

[halcyon hornet]

Oh.

[solemn rover]

the answer to this question depends on your background imo

You need a lot of commutative algebra background to make sense of hartshorne at all. Beyond that, I don't find it very readable or accessible as a first introduction to sheaves and cohomology.

It took me a long time before I was knowledgeable enough about general geometry, homological algebra and commutative algebra before I was able to appreciate it.

Vakil's book "The Rising Sea" is more self contained as far as commutative algebra goes.

[analog pollen]

ye so i think it depends in what you are interested

for example if you like pure math and stuff go for spivak

but if you want to study physics or something i would use stewart

[halcyon hornet]

And Thomas?

[analog pollen]

haven't read that book

but they are the same ig

[halcyon hornet]

No?

[analog pollen]

i like stewart

[analog pollen]

what no/

?

[halcyon hornet]

Thomas is different.

[analog pollen]

meh

basically the same

as some one said

[halcyon hornet]

Same with what?

[analog pollen]

it's just grinding the integrals and stuff

[analog pollen]

as stewart

[halcyon hornet]

Oh alright.

[analog pollen]

what do you want to persue?

physics or math

[halcyon hornet]

Pure Math and Pure Physics.

Not engineering ever.

[analog pollen]

what is pure physics

theoretical physics?

[halcyon hornet]

Well yes.

[analog pollen]

think spivak is fine

but like i don't know if you'll manage well with stewart if you want to learn like pure math

cuz i have no experience in that

but i think if you like pure math go for spivak

[halcyon hornet]

It is costly af.

Can I DM?

[analog pollen]

sure\

[analog pollen]

you can find a pdf

[dense wren]

My understanding was for rising sea you need to be well versed in commutative algebra/algebra - it also seems like a much friendlier book with hartshorne so I think I’d go with that one

[solemn rover]

Any course in algebraic geometry will involve substantial amounts of commutative algebra. The rising sea definitely uses lots of commutative algebra but imo you need way less of it to make sense of the book. On the other hand we can also say that if you know a shitload of commutative algebra going in, you'll find it a much easier read.

[modern stone]

Burn Math Class and Reinvent Mathematics for Yourself, by Jason Wilkes
Gödel, Escher, Bach, by Douglas Hoftstadter

@solemn rover what would you recommend for an intro book to logic?

[solemn rover]

Sure.

What kind of background do you have with regards to this stuff?

[modern stone]

more or less 0

[solemn rover]

Ok. but you're like, mathematically sophisticated, you read and write proofs ok

There's a pinned reading list on logic in this channel I wrote last week.

I think I recommended

• A mathematical introduction to logic by Enderton

• Mathematical logic by Ebbinghaus, Flum, Thomas

• The Foundations of Mathematics, Kunen
• Computability and Logic, Boolos

All of these are pretty general introductions that cover things which belong to mathematical logic generally.

[modern stone]

thanks a lot

What do you think about Peter Smith’s book on logic?

[solemn rover]

Well, peter smith's "Teach yourself logic" study guide is great, i appreciate the list of recommendations. But I have no idea about his logic books. I haven't looked at any of them.

What's it called

[modern stone]

Intro to Formal Logic

[solemn rover]

Ok. I found it. Give me a minute to flip through it

Huh. Uh, I don't think I would recommend this book, based on the table of contents. It's too niche to serve as a general introduction. You want something much broader. For a 400 page book this doesn't cover very much imo.

Philosophers are interested in much different content

i think like

this is an introduction to predicate logic which is meant to be sufficiently rich that it would give you some stuff to chew on with regards to translating informal arguments in mathematics or philosophy into predicate logic

but idk i don't htink you need this kind of explicit walkthrough as to truth functions and tautologies

idk.

You'll get something out of it

Maybe somebody else can comment on what exactly his motivations are on the book and you can decide based on that. I just have different interests than this guy, it's a matter of what you want to get out of it. Maybe read the preface to get a sense of what the point is

(It's aimed at philosophy students)

[gray jungle]

sorry to repost my question again
i'm looking for a book to rework on linear algebra
for context i have not taken bilinear algebra and euclidean spaces yet just linear algebra this is sorta me preparing for that i dont have the best grasp on it yet especially theory wise
and i would prefare something not too long
tried to search logs and seen some criticism towards axler which was the 1st option on google why so? what are my options here

[late hawk]

do you all, know a book or material, with good questions, that will make me learn Calculus fast?

[gray gazelle]

spivak's

go speedrun it

[late hawk]

I heard a friend say about it.

ohh

spivak is bettrr than stewart?

[gray gazelle]

yes

[late hawk]

more easy?

in theory

[gray gazelle]

why don't you have a look first

in order to develop thought on it?

[late hawk]

Because I am in High School Math

I dont understand anything of calc

no base or knowledge

I will study calculus after unit circle

[gray jungle]

heard tom apostol is good cant confirm it

[late hawk]

oh

[gray jungle]

dont think its a good idea to rush calc tho

[late hawk]

At least in my exam, it needs Limits (easy) and Derivatives and Differential Integral Calculus (hardest thing in my exam)

calculus 1

It is much things, or it is possible learn fast? At least in 3 months. After it I will train other exams

[gray gazelle]

I learned it in a month or so for my summer class.

Basic calculus at least not spivak level.

[late hawk]

oh

[heady kiln]

Hey all, ive already asked this on #geometry-and-trigonometry

But im looking for a resource to learn trigonometry from scratch

[modern stone]

@solemn rover should I begin with Enderton or with Ebbinghaus?

[solemn rover]

I think Enderton is a little bit easier to read.
I think a lot of this stuff is a bit dry and boring. I don't love any of it. One alternative I would encourage you to find a topic in logic that you really want to learn about, and start reading about it, and use these general books as a reference when you need them to make sense of the concepts. Personally some of my favorite books are on really niche topics!

One of my all time favorite books is Kolmogorov Complexity by Li and Vitanyi

a bit niche but with ties to computability theory/Turing machines, physics, information theory, machine learning, the philosophical problem of induction

all kinds of great shit

[novel obsidian]

when it comes to getting better at IMO esque problems are there any NT, problem solving and proof books that would help a complete beginner in that type of math?

[pulsar geode]

any recs for learning topology? background of cs, analysis, linalg, abstract algebra, and discrete

[gray gazelle]

i think just some real analysis (knowing what a metric space is is good)

[solemn rover]

Eh, I don't recommend this approach

Yeah. I would say some experience with epsilon-delta arguments in real analysis is valuable.

[modern stone]

Is there a good book to get an intuition for topology?

[gray jungle]

so on previous topic i made some research and found 4 interesting books for linear algebra
1-axler - linear algebra done right
2-hoffman and kunze - linear algebra
3-Friedberg - linear algebra
4-paul hamous - Finite-dimensional vector spaces
which one would be your choice if you are restudying a previously direct LA course (i can use most LA stuff but i dont understand them nor can i prove them properly and i want to get a better grasp before my multilinear course 2 months from now )

[prisma snow]

Lmao, it's Hoffman not Hoofman just btw

[gray jungle]

[prisma snow]

And probably 2 or 3

[broken meadow]

3 to me is very introductory

[prisma snow]

Probably 2 then 🙃

[broken meadow]

i would not read it if you already know some linear algebra (instead you may opt to treat it as a reference text even)

i havent read 4 or 2 or 1 tho

i just know that 3 is an introductory text

[prisma snow]

I haven't read any of them, don't let that hold you back on opining

[gray jungle]

well i heard good feedback on hoffman kunze so might as well

axler has a lot of critique on his approach and ide rather not find out why

[prisma snow]

If you already know determinants it would be weird to follow a book that explicitly tries to ignore them imo

[gray gazelle]

“The” introductory book is Munkres’s

[modern stone]

but does it also provide a good intuition for top?

[gray gazelle]

I like the linear algebra book by cooperstein.

https://www.routledge.com/Advanced-Linear-Algebra/Cooperstein/p/book/9781482248845 currently reading it now. It might be more to you alley.

[languid plover]

How do I determine my level of math education and subsequently a book to buy?

[gray jungle]

this actually looks pretty neat
does anyone have previous experience with it?

[slim peak]

You can probably find some exercises on the Internet for every grade

do almost all possible until you cannot perform more than 70% of a whole bunch of exercise of the associated grade

[languid plover]

I'm looking to learn the MacLaurin Series, (more) Integration Techniques, and Differential Equations

[slim peak]

This should tell you that your level is barely

[languid plover]

Ok will do soon

[languid plover]

Any recommendations based off this alone? Ofc I am down to learn more than this, by the way, I just wanted to list some of what I intend to learn

[slim peak]

for Computations/Calculations books, Schaum's old series seems good to me, but maybe some people will disagree

[languid plover]

What do you mean by Computations? Is that under Calculus?

[slim peak]

I can't really

say

just look at Schaum's Outline of Theory and Problems of Differential and Integral Calculus

I don't know books about especially Taylor series

[languid plover]

Thanks nevertheless, I will check it out

[manic fox]

alwaysthemore

[carmine echo]

Hey, I'm an undergrad math student that has Physics class that's kinda easy

So I need some book to do in free time to make it a bit harder

And possibly understand physics even better than I'm supposed to at my course..

(I don't have any previous knowledge in physics, but my course is easy)

[sleek python]

Do you want maths books or physics books?

[carmine echo]

Well both

[gray gazelle]

What sort of physics course are you taking?

[grim pivot]

Any good books on probability theory? My class's book (Probability & Statistics by Degroot) feels like it was written for a second year. I'd love a much deeper dive into the topic

[grim pivot]

Oog maybe that’s an area I should avoid

[wheat prism]

whats ur background

probability theory can be really deep if you want

[grim pivot]

I’m in my last year as a math undergrad and I feel like I have a good amount of mathematical maturity. I’ve only really dipped my toe into real analysis tho if it requires a good amount of fluency in that

[wheat prism]

Loeves probability is mostly self contained

so i'd recommend that

[grim pivot]

1977. Nice

That book looks like just what I was looking for. Thanks!

[wheat prism]

you're welcome

[grim pivot]

Ngl the slant on that A is gonna be hard to get used to

[wheat prism]

lol

maybe there are some newer prints of it

[quick hornet]

damn, sick limbo skills

[manic fox]

michael jackson A

[graceful gorge]

Any suggestions for introductory number theory books?

[quick hornet]

do you know any abstract algebra?

like, if a book defined things in terms of ideals of a ring, would you be able to parse that?

(its not a problem if not, just changes the recommendations)

[graceful gorge]

No, I don’t know any abstract algebra

[solemn musk]

anyone know a good book for multivarible calc/calc 3, preferably one thats pretty rigorous

[grim pivot]

I’ve heard “Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach” is pretty rigorous and self contained. But this is second hand

[solemn musk]

alright, thank you for the rec!

[gloomy palm]

Thomas’s Calculus Transcendentals @solemn musk

[solemn musk]

thank you!

[gloomy palm]

you can find it online

[grave blaze]

Hello, I'm a highschool senior (Grade 12) looking for a intro to abstract algebra book and a number theory book. Any recommendations?

[marble solar]

Pinter A book of abstract algebra

[grave blaze]

i've seen dummit and foote being recommended on reddit? is it too high level?

[dapper root]

It depends

It’s really up to the person, if you’ve never seen proofs it might be rough but idk if that’s necessarily a bad thing

[still saddle]

Artin's algebra

[slim peak]

Very good book, I recommend it to you

(just kidding)

[grave blaze]

bruh hahahah

thank you anyway!

[still saddle]

also Alan F Beardon's Algebra and Geometry is a great first book

[reef axle]

Mathematical Circles (The Russian Experience) nice puzzle questions for free time. Recommended

[desert copper]

I’m nearly done with Calc 3 and I want to do differential equations next

What book would you recommend?

[kind dock]

ordinary DE? i did Morris book before
they say #multivariable-calculus message paul is good too

[desert copper]

I think so

idk what is usually covered in differential equations classes and whether they include partials

Oh and also linear algebra (asked about this before but got so many differing opinions that I got confused)

[kind dock]

yeah there are lots of LA books, you could check them and see what works best, it really comes to preference
some do Strang book, some LADR, i did Hoffman a bit and then moved to Friedberg

well
I'm working A First Course in Abstract Algebra Fraleigh book, my instructor also teaches from this book
just compared 8th gen with 7th and looks like the changes were a lot kinda
do they contain same materials and not much changed (or perhaps reduced), or should i get older version? my tutor teaches way older one

[still saddle]

a great book which does linear algebra and differential equations together is Hirsh & Smale's "Differential Equations, Dynamical systems & Linear Algebra"

[analog pollen]

Schaum's lin alg

also it's pretty cheap so that's a plus

[gray jungle]

i started working with hoffman/kunze and i really like it so far might be worth checking out i do have LA background tho so freidberg might be better if its your 1st time

[ember lake]

Any good group theory problem books? I'm just starting a course on it, plus I'm not a math student, so not tooo hard

[ember hearth]

Any general mathematics book recommendations(which you really liked), i am feeling bored after completing flatland,lost in math,what is maths and all that.

?

[gray gazelle]

#books-old

[gray gazelle]

Fermat's last theorem by Simon Singh

[ember hearth]

Read that

[gray gazelle]

I see

differential geometry by michael spivak

Polya's How to solve it is a good one

[ember hearth]

Lets take it as a challenge

[broken meadow]

lol

[ember hearth]

I will learn differential geometry to not get bored

Thanks

[gray gazelle]

You could learn Algebraic Topology too

hatcher: "am i a joke to you?"

You would definitely not be bored

[ember hearth]

Suggest me the best one

[gray gazelle]

Su and Starbird

[ember hearth]

Ok thanks

[gray gazelle]

Lmao

real analysis and complex analysis by papa rudin

[broken meadow]

el father

rudin

[gray gazelle]

make sure to do the computations

they will keep you on your toes and help you develop your quads

[grim pivot]

I’m really loving the pace of Tu’s introduction to manifolds but im not sure if that can be called a diff geo book

[viscid shadow]

Hi all, my first post here. I'm sorry if I am interrupting. Figured I'd ask my question in the channel as it seemed most appropriate: I am starting my next math course starring Vector Calculus covering topics up to and including Surface Integrals. The same course also stars Fourier Series covering up to DFT and FFT. Does anyone have any recommendation for preparing myself for these topics by covering some pre requisites by review. I have only 2 weeks to prepare for this.

Those are the main topics covered in this course aside from some computer aided math which i am relatively comfortable with

if anyone has any recommendations for books or resources to both prepare myself for these topics and also to study alongside to get a good understanding of these topics.

i would greatly appreciate it

[ember hearth]

Ok thanks

[gray gazelle]

correct, it is not a diffgeo book

in the same way lee's ism is not a diff geo book

[kind dock]

sorry, you have any idea about my problem?
i want to squire a physical copy and prices are the same here. i personally think newer version of books are better since are refined, but again the tutor teaches from an older version. i checked the preface but didn't make so much sense to me since i don't know the material

[modern stone]

what do you think about infinitely large napkin?

[kind dock]

also i don't have access to the digital material
am i missing stuff? did they move stuff away from the book?

[slate quarry]

Hi, guys, I'm looking for a good introduction to philosophy of mathematics, any recommendations?

[languid plover]

Hi! Any book recommendations for someone looking to deepen their calculus knowledge? I'm particularly interested in the Maclaurin Series and differential equations

[analog pollen]

Spivak

[languid plover]

I googled Spivak but I'm not sure what I'm supposed to be looking at

[analog pollen]

Wdym, his book is just called ‘calculus’

[quick hornet]

I don't think Spivak has any diff eq content?

It certainly has Taylor series though

[languid plover]

Oh I didn't realise Spivak was an author

[analog pollen]

No diff eqs no

[languid plover]

Oh damn

Ok I'll check out what it does have though

[analog pollen]

For diff eqs use a seperate book

But ODE’s won’t be more than plug and chug

So learning it in dept is kinda far fetched imo

[quick hornet]

To be clear, Spivak is meant to be a proofsy take on calculus

So it's perhaps a different perspective from what you've seen

[quick hornet]

This only really applies to ODEs

[analog pollen]

I meant that yes

[quick hornet]

PDEs can be plug and chug for the first course but they have a very deep theory beyond that

[gray jungle]

i dont think im educated enough on that to answer your problem

[kind dock]

oh ty🙏

[misty wyvern]

Stop doing proofs

start plugging and chugging

[analog pollen]

Agree with both

[gray gazelle]

Fraleigh old editions are just as great

I have the 5th edition still a wonder

You can check a newer edition from the library but I dont think its worth sending way more over it

[kind dock]

My tutor is using third edition
I have this bias that newer versions are refined and organized the stuff for best intuition and understanding(not all, some are made for profit and exercise change however this is not the case here). Here in 8th edition they added a new guy and moved lots of stuff here and there, and looks like they moved some theorems to exercises and added some other stuff (some sections are cool like encryption, then again if it dilutes the main material then it would not worth it)

I can use the 8th edition but check the 3rd to see if I be missing anything. But a friend of mine is using 7th edition and the deciding makes it hard (I think changes in 3-4-5-6-7 be minimal compared to 8th, I could take any perhaps but gotta compare 3 with 7)

Unless 8th edition is made simpler/worse cause they revised most chapters (including their names and contents, some contents moved from later parts to newer parts, some diagrams missing, some newer stuff)

The whole thing gets harder because I want to get one physical copy (assuming they all have same price)
Perhaps physical copy for this book isn't a good idea (then again, I can ask which one to get physical and which to just look from)

[still saddle]

Can someone suggest a good, preferably short, introduction to random matrices?

[still saddle]

thanks, after googling him I found his video lectures

https://www.math.uni-sb.de/ag/speicher/web_video/zmws1920/lec1.html in case someone wants to have a look

oh thanks again

[gray gazelle]

Buy an order used copy (best condition-price ratio) youll save 100 bucks and just reference a recent edition from the library

Trust me if you want a good math physical library youll have to save where you can

And besides Fraleigh cant change that much to make spending way more worth it

Get a 5th or 6th edition

[manic fox]

fralee

[slim peak]

what does mean "plug and chug" ?

[dapper root]

Just like

you learn algorithms or formulas

and you pass the class by plugging numbers into them

and then chugging along a computation

[slim peak]

okay so just basic computation stuff as learned in Highschool ?

[dapper root]

yeah but the focus is just on

here is magic formula

rather than like

proofs or why stuff works or anything

so I guess yeah HS

but also beginning university

[slim peak]

Yeah yeah I got it

[dapper root]

[slim peak]

Thanks a lot

I kinda hate this kind of Maths, I'm glad I had a teacher that hated it oo during my last HS year

But people hated us so much, him for its abstract non-sens lecture, and me to loving it

[manic fox]

lolol

[gray gazelle]

If it were me you couldnt sit at the kool kids table after that

[slim peak]

I don't really mind about it, since I was not that much present at my highschool lectures, I rather prefered to go out, watch anime, play video games.

[regal wasp]

Is there a good supplement for Hoffman’s Linear Algebra? It’s so dry. I’ve already done Axler.

[kind dock]

their price is same here (its print)
i don't think even international ed exists here
(so 7th and 8th, or the ed they have around would all cost around 9$)

i do all my books digital but some feel good for better understanding (math books especially, i like physical CS books too and i gotta get some but then again i prefer some of them to be digital (the digital editions got some nice fonts for screen))

[hearty steppe]

Hoffman is more of a second look at formal linear algebra exposure. I hear the Friedberg et al book is good but i haven’t checked Out their more formal book

Don’t use the elementary linear algebra book they made. That is more plug and chug easy linear algebra stuff you’ll mostly learn in a first or second discrete math course. You want to go with the book titled “Linear Algebra”.

[gray gazelle]

Well if its cheap who cares then lel

For me unfortunately that option isnt common occurence

[gray gazelle]

Uhhh based mgtow?

[gray jungle]

https://www.springer.com/gp/book/9781846283697 is this a good book (to study metric spaces obviously)

[gray gazelle]

Hmmm no idea but Ill definitely try to check it out

Since Im doing course stuff on metric spaces

[timber mesa]

I've read it, I think it's a great reference but the chapter order is a bit weird

then again there aren't many books specifically about metric spaces, the other one I know is in Portuguese (E. Lima's Espaços Métricos)

[gray gazelle]

Based Lages Lima enjoyer

Only one I know as well

[kind dock]

so

A. im not biased and new editions are good (when they actually make a change)?

B. i won't miss out materials?

[gray gazelle]

If its cheap why not get a new pristine copy?

You can also google about differences between editions

[sudden girder]

is there a linear algebra book like axler but for a first exposure to linear algebra? i.e. theoretical based but doesn't assume you taken an engineering version of the class prior

[grand osprey]

I think you can go for axler itself if you have had some exposure in writing mathematical proofs

[sudden girder]

okay, good to know. thanks

[gray jungle]

friedberg's

[analog pollen]

maybe this is not like axler but i really like the schaum's oultine book

linear algebra

[gray gazelle]

Freedmountain, Incel and Spensive

Idk jokes

[mellow wren]

Recommendations for introductory algebraic geometry texts?

[winged mauve]

Really weird question. Is there a book that kind of babies you through calculus?

[gray jungle]

depends on what kind of calculus if its proof based calc spivak is your best option regardless
if its just calc any book will do fine tbh

[grim pivot]

Hitchhikers guide to calculus by Spivak isn’t rigorous by any means but its looks nice to get an intuitive grasp of what’s going on

[winged mauve]

Thank you.

[winged mauve]

Thank you, as well.

[regal wasp]

Good supplement to Munkres analysis on manifolds?

[gray gazelle]

spivak calculus on manifolds

it's the exact same content but not verbose

[winged mauve]

Sounds like Spivak is a pretty good author, then?

[gray gazelle]

yes

[regal wasp]

Good supplement on spivak calculus on manifolds?

[marble solar]

Hrmm, my professors notes are really good on it

But it's not available

[regal wasp]

Thanks I guess

[marble solar]

I'm thinking

[crystal lion]

moonbears is teasing us

[sleek python]

Give us your notes

[fossil badge]

seconding this
I'm convinced there aren't any

[marble solar]

Algebraic Curves by Fulton

[fluid bay]

Neither hartshorne nor vakil assume any prior exposure to algebraic geometry

[slate quarry]

Hi, guys, I'm looking for a good introduction to philosophy of mathematics, any recommendations?

[quick hornet]

stewart shapiro's thinking about mathematics

[slate quarry]

Thanks, I shall check that out!

[finite gale]

Recommendations for p-adic analysis that have detail but also not too advanced? (I.e. more than gouvea but less than robert?)

[foggy relic]

is this the same as the regular edition? https://www.amazon.com/gp/product/8131525295/ref=ppx_yo_dt_b_asin_title_o00_s00?ie=UTF8&psc=1

I just purchased it since its literally 10x cheaper

[somber pendant]

Has anyone read GTM 95, Probability 1? Is it any good?

[timber mesa]

Alain Robert's A course in p-adic analysis perhaps? I've never read anything beyond Gouvêa but I know a prof who does non-archimedean analysis and likes this book

it's

[finite gale]

I specifically said less than robert..

[timber mesa]

ah didn't read that part sorry

honestly Robert's seems to fit the bill for "detail but also not too advanced" and there aren't many more books of the subject, that I'm aware of

[finite gale]

I guess I'll try robert's some more

thanks anyway!

[modern stone]

Elliptic Tales

[covert heron]

any advanced calculus book?

[marble solar]

Calculus on Manifolds

[covert heron]

thanks

[tulip blade]

How is the number theory book by ireland and rosen?

[stray veldt]

good

it requires a bit of an abstract algebra background though

[tulip blade]

Is an undergrad course in algebra using dummit and foote enough algebra?

Groups, rings, fields some galois theory

[broken meadow]

wdym by enough

oh

for the above

lol

oops

idk

[pale scarab]

It is pretty much the standard reference book for algebra. I think its a little wordy but the exercises are excellent though

I think lang is necessary if you want a more modern concise approach or want to do research in the area but those exercises are brutal.

[tulip blade]

I meant enough to read the number theory book I mentioned above.

[manic cape]

yeah it's fine

you don't even need all of it to jump into it tbh

[finite gale]

Which lang book?

[regal wasp]

Sad to witness

this Artin disrespect

Lang is only used in grad courses as a reference text iirc

[languid plover]

book recc for diff eq?

[misty wyvern]

Looking for a good pedagogical resource to "reteach" undergrads vector calculus to supplement a late-undergrad PDEs course for math majors.

I do not want to get into differential form technica, we're not working on manifolds. It has to be fully Euclidean.

For reference right now I'm thinking of just running through an undergrad math methods in physics treatment of vector analysis but I'm curious if anyone has a different opinion.

[manic cape]

This is primarily a computation oriented course then?

[sage python]

You could do differential forms just on R^n in principle

[misty wyvern]

This is primarily a computation oriented course then?

Yes

You could do differential forms just on R^n in principle

[livid ermine]

have anyone read the "a course in combinatorics" by van lint and wilson?

is it suitable as a first course in combinatorics or how much background do you need?

[slim peak]

My pdf file named TeaForTwo's interest contains basic notations, and a good variant of stokes formula, if yrrc.

[misty wyvern]

That I do, let me take a look at it again

thanks for writing that up by the way, that's legendary

I also took a look at the Mitrea Taylor volumes on the Hodge Laplacian but it was too specific and technical for me to read and get general insight into my problem. My brain is too smoll

[slim peak]

no proof, but just notations and some papers where it is used for pdes and a riemmanian geometry.

[slim peak]

lol it deals with the riemannian setting

in its full generality with low regularity metrics

it's completely aweful

[misty wyvern]

Yeah, I'm basically not concerned with the Riemannian setting with bad metrics -- for now, at least. I need the geometric toolkit to actually deal with singular boundaries in R^d, but this is unrelated to my pedagogical problem of educating undergrads.

The generality is useful for the boundaries, and I am looking at locally shit behavior on said boundaries that need higher regularity structures to renormalize.

[slim peak]

yes but really unreadable

[misty wyvern]

Everything Taylor wr ites is unreadable

One of the benefits of SPDEs is you never leave R^d except in special forays into nice Riemannian spaces with easy processes.

Mainly because everyone is too scared to do it otherwise

[hearty steppe]

I am going to check out Finite-Dimensional Vector Spaces by Halmos. Not sure if there’s anything other people would recommend

[marble solar]

I think that's a fine book

Just be weary, especially if you get the first edition

"linear manifolds"

[hearty steppe]

Why be weary

[marble solar]

Oh, some of the terminology is outdated

But that's ok

[hearty steppe]

Oh

[marble solar]

linear manifold just means vector space

etc.

[brittle breach]

How is "Rings of Continuous Functions" by Gillman ?

[dapper root]

[marble solar]

Halmos was an interesting dude

[past ice]

Linear Algebra and its Applications by Lax (not the one by Lay!) is super underrated. Don't be put off by the word "applications." It's a pure math book.

[manic fox]

lmfao holy shit

[hearty steppe]

Lax? I may have heard of that one

Yea I have I’ll give that a look too

[solemn rover]

Lax has a functional analysis textbook too. Someone I know told me it was good.

The person was of absolutely atrocious moral character. Downright evil.

Just wanted to point that out. If that influences your opinion on their book recommendations, so be it.

It's probably a fine book

[marble solar]

I think Lax is pretty good

I don't believe objective morality exists

[karmic thorn]

You didn't get a good copy

The problem with Lax is that it's not clear at all who the intended audience is

Because it seems Lax almost assumes you know everything already? Then why did you write a book on LA?

I mean

I don't think it does the job

In terms of content

[gusty smelt]

Idk why but I have seen many ppl fit the former

[karmic thorn]

Yohan just continue to read it

And you'll probably see what I mean

A certain copy of Jacobson's Basic Algebra is also floating around with similar OCR formatting

[sleek python]

dye your hair blue to protest against this book

[solemn rover]

Buddy you haven't met the guy I'm talking about.

[marble solar]

You are correct

I haven't

[solemn rover]

reminds me of that George Orwell piece.

"Politics and the English Language"

[modern stone]

Based. No need to make terminology fancier than it needs to be

[broken meadow]

this is some percy grainger shit

mf wanted to use english in his music

thats why we have stuff like HAMMERINGLY in some parts of his music

[modern stone]

Where is the passage from?

[livid ermine]

how based is that lmao

[solemn rover]

this is from Peter Lax's textbook on Linear Algebra which was being discussed in the channel shortly before

[sage python]

So my take on that notation thing is

I am fine with saying "f maps X onto Y" but I don't like "f is onto"

[analog pollen]

Any good book for point set topology, I only have a background in lin alg

And some set theory

[sage python]

In particular I'm guessing you haven't seen much analysis yet?

[analog pollen]

Nope

[sage python]

Or at least proof-based calculus?

Point-set in principle can be done with nothing but it's a little bit weird to do it without having seen some analysis because a lot of it is like

We have a notion of continuity in R/R^n/metric spaces that we know and love

How do we go from that setting to more general settings, what survives, what needs to change, etc

Without that underlying idea of what these ideas are "supposed" to mean it'll be somewhat bizarre

Munkres is the default but to me it spends more time on point-set than anyone should really be spending on it lol

[analog pollen]

Should I acc learn analysis then, like I’m a physics major lol

Or can I just manage perfectly without it

[sage python]

I mean you can manage without analysis, I just think point-set topology in particular makes a little more sense with than without

If you at least have some intuitive idea of continuity check this out: https://pi.math.cornell.edu/~hatcher/Top/TopNotes.pdf

[analog pollen]

Ok thanks!

[analog pollen]

I’ll look at it

[weary meadow]

if you are beginning, Art of Problem Solving is good for beginning competition math

[gray gazelle]

any recommendations on getting a thorough understanding of finite automata, regex and regular languages in a rigorous manner? I'm in a particularly challenging course that uses a book that feels a bit too condensed and messy (Miruoka's Concise Guide to Computation Theory)

I'm open to lectures or books

[hearty steppe]

Some members of my analysis study group have benefitted immensely from reading Munkres along with baby Rudin starting from chapter 2 of baby rudin of course

[cursive orbit]

sipser

[foggy relic]

MIT also made a lecture series based on sipsers book

https://youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY

someone here sent it to me

[astral cloud]

A good book connecting combinatorics and topology without too many prerequisites?

[misty wyvern]

Sipser is cool.

[gray gazelle]

Anyone have a recommendation or guide on Endogenity and new methods to work with Endogenity? Eg. Instrument Variables

[tulip blade]

•S. Kolins. “Topological Methods in Combinatorics.” Course notes, Spring 2010. http://www.math.cornell.edu/ eranevo/homepage/TopMethNotes-1Sam.pdf
•M. de Longueville. A Course in Topological Combinatorics.
•J. Matousek. Using the Borsuk-Ulam theorem. Lectures on topological methods in com- binatorics and geometry.

[hearty steppe]

Oh shit those look like solid recommendations

[remote ginkgo]

Introductory PDEs primer need a quick fast book not some thick tome

Pls

[remote ginkgo]

I will point out that munkres does not even talk about analysis in his analysis book.

That book is an advanced calculus book, roughly equivalent to spivak's calculus on manifolds

So i'm not sure how it would help with learning real analysis

[hearty steppe]

I been asking so many times again and again about Diff Eq recs good luck. People keep recommending Evans

[remote ginkgo]

For PDEs?

[hearty steppe]

Like ODEs and PDEs but I have been trying to find a good book that introduces Diff Eqs rigorously but not demanding too much background

[remote ginkgo]

Computation of ODE solutions is hard to write a book about

Google 'ODE practice problems' and learn from paul's online math notes as needed to solve them

[hearty steppe]

Meh sounds like plug and chug stuff

[remote ginkgo]

You make me need the world's largest cigarette

And i don't even smoke

[lament sage]

any recommended books for basic numerical analysis? we'll mostly be going through root finding methods, interpolation, integrals and ode's

[hearty steppe]

What lol

[remote ginkgo]

Uwaterloo has a good set of notes online for this topic

[lament sage]

as far as I can tell we'll be skimming over the material since we only have like, two months left lmao

[lament sage]

lemme see, thanks!

[remote ginkgo]

I think it's on their mechanical engineering site, google it

Uwaterloo num'rical analysis

[hearty steppe]

Idk maybe I need to look at Boyce DePrima again but I don’t remember it being rigorous and neither Nagel Saff Snider. Not bad books but it’s like just more elementary calculus stuff

[remote ginkgo]

Computing diff eqs is literally just elementary calculus

[hearty steppe]

Use this formula to solve these problems that really just involve basic algebra

[remote ginkgo]

Yes, that's what diff eqs are

[hearty steppe]

I thought there was more to it than that

Like with analysis

And algebra

[remote ginkgo]

Not in a first course in ODEs.

[hearty steppe]

And geometry

Oh

So what do you recommend

[remote ginkgo]

What i told you already

[hearty steppe]

Just Paul’s notes?

[remote ginkgo]

Yep

[hearty steppe]

I think I’m just gona man up and read Evans as soon as I can fuck it

[remote ginkgo]

Waste of time

[hearty steppe]

Why

[remote ginkgo]

Books have endless prose for no reason

500 pages where a single sentence would suffice

All of them are like that

[hearty steppe]

lol

What you mean

[remote ginkgo]

The pertinent information is a needle in a haystack in computational ODE books

It's an absolute bunglefuck of timewasting

[hearty steppe]

What about like theoretical Diff Eq stuff

[remote ginkgo]

That's fine

It's for a second course in ODEs though

[hearty steppe]

I don’t even know what books are out there tho

[remote ginkgo]

It only discusses existence and uniqueness of solutions

[hearty steppe]

Oh

[remote ginkgo]

That's really all there is in diff eq theory

[hearty steppe]

Eh well is there anything else worth checking out in that arena

[remote ginkgo]

Yes, after you learn to compute basic solutions

Olver has a good book on applications of lie groups to diff eqs

[hearty steppe]

Ahh I get it. Like with linear algebra, learn the basic computations before the theory

[remote ginkgo]

Yep

[hearty steppe]

Got you

I think I might be ready then cuz the books I was working thru didn’t seem to teach me much of anything

[remote ginkgo]

Can you find the general solution of a second order diff eq

Linear

Non homogeneous

[hearty steppe]

I’ll have to look up some problems to work thru and get back to you. I think that’s where I got to

Like actually that’s exactly where I left off

[remote ginkgo]

Did you learn the method of variation of parameters

And solution by laplace transforms

If so then you can move on

[hearty steppe]

Oh I got a little bored before I got there but I’m pretty much right there actually

[remote ginkgo]

You should master those though

[hearty steppe]

The books I was working thru are just so dry plug and chug problems

[remote ginkgo]

And solution of bernoulli diff eqs

[hearty steppe]

Ye I remember those

Those were kinda interesting ish

[remote ginkgo]

Ok master var of params and laplace transforms

Thru pauls math notes

[hearty steppe]

Ok

That doesn’t sound like it will take very long

[remote ginkgo]

It's easy

[hearty steppe]

You should start studying systems

[remote ginkgo]

It's just one undergrad engineering class

[hearty steppe]

If you haven’t

[remote ginkgo]

I know everything already

[hearty steppe]

Like dynamical systems

[remote ginkgo]

I'm taking a course in it next semester

[gray gazelle]

im looking for an algebra book with longer equations

[dapper root]

Bury ebil

[gray gazelle]

[distant gorge]

Anyone would recommend a book for chaos theory?

also maybe knot theory

[forest sleet]

The Knot Book by Colin Adams is good if you haven't taken algebraic topology

for chaos theory maybe try Strogatz Nonlinear dynamics and chaos

[gray gazelle]

Taylor’s Classical Mechanics has a good chapter to introduce folks.

Goldstein (same title) also has one in his third edition.

[marble solar]

Knots & Links by Rolfsen is good

[covert heron]

any trigonometry book pls

with trig calculus

advanced trig

[atomic venture]

Is Calculus by Gilbert Strang good for starters?

[gray jungle]

gilbert is a bit informal but its pretty good for starters and self study
depends on why you are learning calculus
if you are leading into more proof based path spivak might be a better option or even tom apostol
but honestly if you are new to calc khan acad/youtube might be worth more than a book
heard stewart is good resource as well

again
depends on how much calculus you are willing to know and how much you already know and whats your level atm

[atomic venture]

I can't define my level, because I studied in Russian system. I just intuitively decided to start from calculus. We have been learning algebra for last 3 years at school.

[gray jungle]

take a look at gilberts book and see if you can understand it
use online recourses to aid you

i cant judge your level but you'll know when you start working on it

[atomic venture]

Can you also recommend some high school level algebra 1-2 textbooks. I guess I'll have to review something while starting with calculus.

[modern stone]

@atomic venture I recommend the book “Burn Math Class and Reinvent Mathematics for Yourself” by Jason Wilkes, if you are a complete beginner to calculus. The book only assumes a knowledge of elementary arithmetic

https://cdn.discordapp.com/attachments/834359595597561866/839893445497978890/466002601-Burn-Math-Class-And-Reinvent-Mathematics-for-Yourself-2016-epub.pdf

^here’s a pdf if you are interested

[atomic venture]

Thanks

[analog pollen]

I like stewart

Dont review all that algebra

You’ll learn/review it already while doing calculus

[glad prairie]

If you did want a book, consider using something like Gelfand's Algebra. Easy to find free pdfs online if you look it up. It's a classic book which has a more conversational style and focuses a little more on proving things than on computing things. The problems are more fun that way IMO!
Ofc you can also just use Khan Academy for the topics you need to refresh, that is free and very high quality.

[craggy agate]

Any recommendations for a beginner book/textbook for self studying Linear Algebra and later on intermediate level?

[sudden kindle]

axler

[craggy agate]

Thanks

[tulip blade]

Friedberg, insel, spence @craggy agate

[gray jungle]

maybe not biginner level but i think hoffman kunze is such a good book im working thorough it atm its concise with simple exercises after each section rather full chapter
a helpful thing you can do is keep something like friedberg for reference as you walk through it to help digest some ideas
i like to think of it as the rudin of LA ,great book for math/phy majors
if you are only interested in computational level LA then gilbert strange might be more worthwhile alongside his free lectures

idk about axler but i know he is also 2nd course ish with an unusual approach to det

[craggy agate]

I'll take a look at all of these that everyone mentioned. I've been wanting to start studying LA for a while now but never really made the effort. I'll definitely spend the time to read through and understand them

[craggy agate]

Yeah, in his intro to the book he already mentioned that determinants won't be used until the end of the book in order to better understand the existence of eigenvalues

Again, thanks everyone

[pale scarab]

I like gelfands trig book but if you are just looming for hard problems look at contest prep books.

[remote nova]

Friedberg actually has decent exercises

Sometimes Axler doesn't make a whole lot of sense

I third the suggestion

[foggy relic]

based

[sharp latch]

I used to be team axler but after reading friedburg I am not

[celest dust]

Can anyone recommend me books of number theory for beginners?

[karmic thorn]

has a comprehensive list, along with the message right above

[low perch]

is there any such list for multivariable calculus?

[karmic thorn]

The recommendations seem standard, Thomas/Stewart/Khan Academy/MIT OCW for more introductory stuff, Hubbard and Hubbard if you have some more background, and Spivak's Calculus on Manifolds if you have some analysis and linear algebra under your belt