book-recommendations

[thorny oak]

amazing books

[solemn rover]

nah they can all be read pretty independently but they do treat the same examples in all the different books from different points of view. so in the complex analysis they'll treat like, the heat equation and they'll make some references to the way they studied the heat equation in the complex analysis book

[gray jungle]

ye it was pretty much overkill
too much examples too little theory
its wayyyy too slow and as you said hand-holdy
any more concise recommendation is preferable

[solemn rover]

so, bottom line, definitely just start reading the complex analysis book if that's what you're interested in, but be prepared

The standard first year graduate textbook in algebra is "Abstract Algebra" by Dummit and Foote. I find it dry but it's pretty thorough, definitely more than enough content for a year of algebra.

[dense wren]

I’ll keep it min mind, thanks!

[solemn rover]

Stein shakarchi is great lol super easy reading

you can cut through it like a hot knife through butter. it's like Lee's topological manifolds just

[crystal lion]

only until recently has #book-recommendations started to shift to pro-gallian

bandwagoners i must say

[broken meadow]

idk what you all say but dummit and foote is not dry

sob

i enjoy reading it

[solemn rover]

Another textbook in algebra is the one by Lang but this is in my opinion pretty brutal. really it's more of a reference for those who already know a good amount of algebra and want to look up detailed treatments of results

[broken meadow]

maybe it gets drier later

[crystal lion]

dummit and foote is drier than a popeyes biscuit

[solemn rover]

lmao

[broken meadow]

lmfao

idk maybe im just too bone headed to understand if something is dry or not

[solemn rover]

i think Dummit and Foote and Lang are the only general abstract algebra references i've ever used, so i don't have too many recs on that front.

[sage python]

I mean if D&F works for you go for it

Just that for me it drags too much lol

[solemn rover]

yeah i definitely do recommend the book by D&F.

[sage python]

I have a long list of recs in the pinned messages

[gray gazelle]

why not add Bhattacharya to this list?

[solemn rover]

a fairly sophisticated treatment of abstract algebra is in the book by Paul Garrett. i haven't read much of it but he develops exterior algebra to give a more conceptual treatment of the proof of Cayley-Hamilton. There's also of course the book by Aluffi, which is famous (infamous?) for developing enough category theory to give a categorical treatment of the standard abstract algebra syllabus

[sage python]

Idk that one Moniker

[gray gazelle]

you can check it out, I think it's good
Markus used it for his course

[solemn rover]

Oh, yeah! a great algebra book is "Basic Algebra" by Nathan Jacobson. Forgot about that but it definitely came in handy when i took algebra

it also treats ultraproducts. 😮

[sage python]

Tbh I think between like

Artin, D&F, Jacobson, Lang

Maybe Knapp

You basically cover everyone

I guess there's room for a more applied algebra book. I know some of the lower level algebra books may have applied emphasis but I feel like applied shouldn't be equated with easy lol

But otherwise yeah I'm pretty sure most other algebra books targeted at a general audience are largely beaten out by one of these. For others you need to be doing something novel/niche (eg Aluffi)

[gray jungle]

artin looks pretty alright imo

[solemn rover]

artin is definitely a well-respected classic, i just didn't bring it up because it's older but that's not a big deal

[quasi remnant]

does anyone know a book where i can learn these stuff

[karmic thorn]

I feel an analysis text? I'm currently consulting Amann-Escher's Analysis, I guess volumes 1 and 2 cover all this and more.

[quick hornet]

its like a really weirdly ordered analysis text

[gray gazelle]

Why do you need Banach fixed point theorem for closed subsets of complete normed spaces, the one for complete metric spaces is easy enough imo (and more general)

[quick hornet]

why is lagrange stuff near the end

why is computing integrals at the end

[quasi remnant]

i don't know

[halcyon hornet]

How to speedrun HS Math in under 1 month?
Books and resources please.

[quasi remnant]

i need to know these stuff for my abroad university

[halcyon hornet]

Ah man I am at the wrong time again.

[quasi remnant]

does analysis i and ii by terrence tao have this stuff?

if you know

[karmic thorn]

I think it is too deficient on problems to be useful here

[quasi remnant]

i've done complex analysis, some fourier series/transform

and analysis i

[prisma snow]

Manan has come arround, antirecommending Tao

I agree. Use anything but Tao

[karmic thorn]

Also, no ODEs, doesn't talk about Taylor expansion in R^n, no Banach Fixed Point Theorem iirc, nothing about Lagrange multipliers, nothing on explicit evaluation of multiple integrals either I'd wager

[quasi remnant]

this was my complex analysis course

[karmic thorn]

You can probably consult any second look into the subject kind of text, try Basic Real Analysis by Knapp or Amann-Escher Analysis 1/2

[sage python]

Amann-Escher seems to be the new thing lol

Tbf it has a very cute picture on the title

[karmic thorn]

😌

The presentation often feels erratic but it gets the job done, that's probably also a translation effect.

[quasi remnant]

@karmic thorn can you tell me whether i have done the stuff on the list if i post the things i have learnt so far?

[karmic thorn]

Umm, sure

[quasi remnant]

i think this is the stuff i learned in my calc course

idk if it can be called analysis i

thats my entire calc course

[karmic thorn]

Hmm, you'd probably still need a primer on basic analysis. Either ways, I feel like you can dive into the two books I recommended above, or a different text that covers real analysis.

[quasi remnant]

i've also done that

plus the complex analysis stuff i posted above

[karmic thorn]

Looks good, all this would certainly help a lot

[quasi remnant]

plus i've done vector calculus and fluid dynamics

so do i at least satisfy some of the stuff or do i need to do some work on analysis i/ii on the books you gave me above

i've got 2-3 weeks to get to satisfy those stuff above

[karmic thorn]

Hmmmm, this could be intense, but goodluck!

[orchid musk]

is there a good book for a second course in geometry? i've taken real analysis, abstract algebra, and abstract linear

[hearty steppe]

Oof I’m on the fluid mechanics chapter of the physics book I’m reading. That seems to be where the difficulty of physics starts to pick up

[gray gazelle]

Recommend Charlie’s ABC book it coveres all the formula’s for the trigiriams

[gray gazelle]

what book is it? I trying to start up my physics again, the way I was taught it during quarantine sucked.

[brittle latch]

is there a book of useful inequalities for analysis

[gray gazelle]

Yes

I recommend H.C. Verma's Concept of Physics.

And another one is D.C. Pandey.

These were the best books I had in Indian entrance preparation.

Anyway, try JEE advance questions, for highschool students.

Many can piss off by seeing the paper.

And Time limit

[coral narwhal]

young and freedman (cat man doo is reading this )
resnick halliday
these are supposed to be the usual intro books for hs but you have other better books for topics like classical mechanics and electrodynamics

[gray gazelle]

does young and freedman feel bloated to you

[coral narwhal]

Jaan Kaalda and Peter Gnadig have good problems in them but they are intended for comp physics

[gray gazelle]

hrk is more readable

[karmic thorn]

Are you looking for something specific like differential geometry, or more generally non-Euclidean geometries?

[gray gazelle]

The Cauchy Schwarz Masterclass is good

[orchid musk]

im looking for something that provides a rigorous treatment of the topics of basic geometry we learn about in HS and beyond, preferably using what i've learned in analysis and algebra

[karmic thorn]

I think Coxeter's Introduction to Geometry might fit the bill

[misty wyvern]

I can second Coxeter. After Coxeter read Rudin.

[karmic thorn]

teafortwo is a Big Rudin agent

[orchid musk]

ill give it a look, thanks!

[polar perch]

Hello, I was wondering if anyone has any book recommendations for rote practice on topics concerning calculus ?

[quick hornet]

mathematics gre prep books?

[halcyon hornet]

What are the prerequisites for "Thrills and Challenges of Pre-College Mathematics"?

[karmic thorn]

Some familiarity with middle school algebra and English language, I guess

[halcyon hornet]

Hush.

There are some people saying that it needs everything till 11-12th grade.

So they are incorrect?

[karmic thorn]

It won't be an easy read for either audiences in general imo, try skimming through some sections to get a feel.

[halcyon hornet]

Well okay.

[verbal river]

I'm looking for a book on proofs. I have taken discrete math earlier in my university career, but my prof merely read the slides throughout the entire course. As a result, I didn't get much out of that course. I'd like to better learn how to write rigorous proofs as well as help me really understand math rather than learning the mechanics of problem solving. The three books recommendations I keep running into are:

• How to Prove it - Daniel Velleman
• Book of Proof - Richard Hammack
• Mathematical proofs: a transition to advanced mathematics - Chartrand, Polimeni, Zhang

Is one better than the others? Which would you recommend?

[stray veldt]

the shortest

[gray gazelle]

That would be book of proof. It about 300 pages, but loch has a pdf intro proof that is 30 pages.

[livid ermine]

velleman is pretty good

[stray veldt]

i really like lochs text!

[royal perch]

good quick primer on discrete probability?

[hearty steppe]

Young and Freedman University physics

It is very surface level tho

But you need that exposure to really get thru physics.

[graceful dawn]

What you guys think of 'Concept of Modern Mathematics' by Ian Stewart?

[gray gazelle]

just use the sticker instead

[frosty girder]

oh yeah there is one sticker as well, i forgot

[gray gazelle]

[frosty girder]

[gray gazelle]

I'm looking for a rigorous book on linear algebra which I can find on pdf by free, like just first or second undergrad year linear algebra topics. Currently I'm using a book meant for engineers, because is the one I found lol, it's good, but not too rigorous on everything. I want to get the fundamentals right. Thanks

[frosty girder]

a good book would be Friedberg Insel Spencer's book

its pretty good imo
i havent completely done it, but its nice still

[polar perch]

Yeah, those’d help

[dense mantle]

what are some of the canon rigorous probability books

something "introductory" --- coming from a decent analysis background; intro graduate level

I just know so little about probability

[misty wyvern]

The canon books are Chung, Billingsley, or Williams, none of which I like.

Do you know measure theory?

[tender egret]

yo

[marble karma]

Dude that book is traumatising for a 10th kid with no experience in oly type math

[quasi remnant]

does anyone know any books that has "Banach fixed point theorem for closed subsets of complete normed spaces. "

[karmic thorn]

Perhaps a graduate analysis textbook?

[karmic thorn]

There's no harm in trying bits and pieces, not to mention that math actually becomes difficult, so you have to get used to it.

[timber mesa]

You'll usually see it proven for complete metric spaces, and a closed subset of a complete normed space is a particular case of that. Royden's Real Analysis has it (chapter 10, 4th ed.) and so does Rudin's Principles of Mathematical Analysis (chapter 9), these two are typical references.

[graceful dawn]

Any recommendation of monthly Math magazine subscription?

[dense mantle]

Late, but yes

In fact, I’m looking for measure theory pre req

[sage python]

It holds for any complete metric space

Oh wait

Someone said already lol

[daring reef]

does anyone know any measure theory books that cover abstract measure theory before going onto more concrete stuff like lebesgue measure? I'm taking a class right now that started off with abstract measure theory, but the textbook we're using assumes prior knowledge of the subject and has almost no exposition

[fluid nebula]

Measure, Integration & Real Analysis - GTM by Sheldon Axler

[daring reef]

ooh i liked his linear algebra book, thank you!

[crude sable]

Books for Fourier Analysis?

[crimson pagoda]

Huybrechts book on Fourier mukai transforms maybe

[crude sable]

@crimson pagoda that's too advanced.

[lament bear]

Hello, everyone. I'd like to get a book recommendation. I've finished Bachelor in General Math about four years ago, forgot most of the stuff, but not all of it. I need to brush up on analysis for several reasons (want to attempt exam to Master's program and to recall statistics course). Can someone recommend a good book for self-studying? I don't have anyone to ask questions about "how to solve that?" and "what is this logical jump in the proof here?", but books I used back in the uni are very much like that...

[crude sable]

for analysis you can look at Abbott 2nd edition, understanding analysis

@lament bear any topic specific book you want?

[lament bear]

Nah, I just want to recall the analysis I studied, no specific topics.

[crude sable]

.

[timber mesa]

Folland and Bartle, too

[gray gazelle]

k so what book would u recommend for linear algebra

[broken meadow]

friedberg

[broken meadow]

stein and shakarchi 1

[lavish parrot]

Why do I learn better from lecture videos than books?

[crude sable]

there's also another book "Linear Algebra" by sheldon Axler you can look into, it's basic tho

[karmic thorn]

Perhaps you engage more with lectures/voice, although at the end of the day you really have to sit down with a book to practice problems and read more details that could be skipped over in lectures.

[hearty steppe]

This

For everything

[stray veldt]

the lecturer lulls you in with their charisma and makes you believe you understand stuff

my undergrad i came back every day after lecture thinking this is easy stuff to do the homework

[hearty steppe]

Well it’s a motivational component as well

[stray veldt]

(it wasn't easy stuff)

[visual zodiac]

I don't recommend to pay for an online additional book content

i.g. the connect platform

[hearty steppe]

I don’t recommend relying on online courses to understand what your learning

[visual zodiac]

I paid like 30 bucks to have access to the Connect platform and oh my god I am so disappointed and the worst thing is that they aren't giving refunds omg

[hearty steppe]

That’s buyers remorse for you. Had that recently when I spent $50 on a set of titanium begleri

[brisk cargo]

Does anyone know a good source of calc 1 problems with solutions?

[junior merlin]

khan academy and blackpenredpen

[marble solar]

Spivak's Calculus with the solutions manual

[brisk cargo]

Yeah, I have Spivak, does anyone happen to have the solutions to its problems?

I noticed they are good but I have found no manual T_T

[marble solar]

There's some in the back of the book

Also there's a solution manual you can purchase with $$$$$

[gray gazelle]

imagine paying for solutions

[marble solar]

🤷‍♂️

Imagine paying for tuition

[brisk cargo]

My college is free hehe

So i have money to spare

[brisk cargo]

Thanks for the advice

[analog pollen]

Maybe you can find solutions on l*bgen

[late plinth]

anyone got a good combo book? i'm tryna place out of my uni's course

through ase

[narrow talon]

My functional course is using Hormander as it’s main reference and I’m having a hard time following the distribution theory. Does anyone know of a good book on distributions at the same level (so excluding Strichartz) that isn’t too long (Rudin and Treves, the latter of which would be my go to otherwise)

[gray gazelle]

You mean combinatorics?

[late plinth]

yeah

i need a book for applied version

[gray gazelle]

Brualdi seems like a standard text. You can try that.

[late plinth]

will look at it thx, also got any recs for intro prob theory?

[gray gazelle]

Sheldon Ross' probability text

[green estuary]

Any good Elementary NT problem book with challenging problems?

[tulip blade]

stein and shakarchi

[crude sable]

yeah that's the book I'm using rn, tx

[robust arrow]

Anyone have recommendations for optimization?

[crude sable]

intro to optimization, chong @robust arrow

[robust arrow]

Ty!

[glad arch]

does anyone have a recommendation for first order logic? similar to the ebbinghaus mathematical logic, but not too much complex

[solemn rover]

a book similar to the one by ebbinghaus is Enderton's "A Mathematical Introduction to Logic"

[karmic thorn]

Also Chiswell/Hodges Mathematical Logic

[sudden kindle]

I highly recommend my prof's complex analysis book for complex analysis

This book should be the new standard

replace Ahlfors with this book

https://press.princeton.edu/books/hardcover/9780691207582/a-course-in-complex-analysis

[karmic thorn]

Oh, the colourful one

[modern stone]

I’ve heard Visual Complex Analysis by Tristan Needham is also very good

[livid ermine]

Its very good but I don't think it can replace more rigorous books like ahlfors, rudin etc

[quasi remnant]

is "understanding analysis" by Stephen Abbot a good choice to use for learning about basic topology

[stray veldt]

it really only talks about the topology of R

[woven spade]

@marble solar Hi Moon bears. I can't see general channel anymore and I had a question about my UC application

Should I put that my country of citizenship is Turkey or the United States?

I have both

[marble solar]

You should put US

[woven spade]

Thank you for responding

Any particular reason?

[marble solar]

Hrm, I think it's more competitive for international applicants

But it's just a conjecture -- I haven't served on any admissions thing at any UC

[woven spade]

Don't admissions want more diversity?

Oh right

[marble solar]

Write in your application essays

[woven spade]

Right

[marble solar]

about your dual citizenship, that'll get you the diversity things you need for the reviewers

[woven spade]

For sure

[marble solar]

I can say that UCLA admissions has like 3 people vote whether or not to admit you

and if all 3 vote yes, then you're in

[woven spade]

all?

[marble solar]

If 2 vote yes, and one votes no you're in a maybe pile. And if 2 or more vote no I think ur application gets tossed

[woven spade]

Interesting

[marble solar]

They have less than 5 minutes to review your entire application

[woven spade]

Yikes

[marble solar]

So put all the important information you want them to remember at the beginning and the end in your essays

[woven spade]

But I also have to like tell a story as well

[marble solar]

Yeah, just give a brief overview of your story in the first paragraph, then tell the story, then summarize the story again

And in the story address challenges/weaknesses/etc.

Man I should charge for admissions counseling

Too bad I despise that industry

I might serve on admissions at my current institution next semester just to see what it's like

[woven spade]

It's really hard

I don't have enough words to tell a nice story

and then reflect

[marble solar]

They spend less than 5 minutes on your story

Just cut things and highlight the important part

It's sad, but true

[woven spade]

Got it

Thanks for response tho I appreciate it

[spiral shuttle]

trying to catch up with real analysis uni courses so i dont have to spend too much energy on them once i have to retake the courses, anyone have recommendations for that? theres 2 courses and the topics stated are more or less real numbers, sets, limit of real function, continuity, derivate, taylors polynomial, riemann integral?

[green estuary]

Any suggestions?

[karmic thorn]

Here's a comprehensive thread @green estuary

[green estuary]

Oh thanks!

[gray gazelle]

maybe terence tao book on analysis.

[karmic thorn]

Too slow, you can go for Abbott's Understanding Analysis

[gray gazelle]

anyone know the link to Loch intro pdf, trying to send it to someone?

[graceful dawn]

How is it?

[gray gazelle]

are you talking to me or someone else?

[graceful dawn]

General.

[spiral shuttle]

thanks, ill keep that in mind, i grabbed A first course in real analysis by Protter, Murray H.; Morrey, Charles B., Jr. for now since it was about the only thing currently at the library

looked ok for my needs from a glance

[karmic thorn]

It should be in the pinned messages

@gray gazelle Here

[gray gazelle]

thanks Manan

[grand osprey]

Hey everybody. I was wondering if Jackobson’s Basic Algebra Vol 1 is a self-contained text for a typical undergraduate course(s) on abstract algebra. Also would love to hear your thoughts and opinions on the text.

[crude sable]

Gallian

[atomic hound]

A good and complete about Predicate Logic?

[gray gazelle]

No

Read Herstein

Or Artin

[grand osprey]

Oh okay. Why not though?

[gray gazelle]

Jacobson is not for a typical undergrad

[grand osprey]

Ah I see. Well I am sorta well versed with the essential bits of group theory. And I think I have the mathematical maturity to read something like jacobson...?

[gray gazelle]

Well I guess it couldnt hurt to check it out for yourself anyway

Its not the end of the world

But defo not an undergrad book

[grand osprey]

Hmm yeah

[sage python]

It's fine for undergrads I think

The good thing is that it explains math in English rather than in symbols

[modern stone]

What do y’all think about logicmatters.com and the logic textbook there?

[karmic thorn]

Isn't it the one by Peter Smith

[modern stone]

https://www.logicmatters.net/ifl/

yes

[karmic thorn]

Ah yes

Well the man himself is controversial but the book might be okay

[modern stone]

bruh

in what sense is he controversial?

[sudden kindle]

Brogic

[karmic thorn]

He's been convicted/alleged of some serious offences for which he was removed from Cambridge iirc

[modern stone]

based?

[karmic thorn]

In particular ||something around child pornography||

[modern stone]

👀

[karmic thorn]

Not really, more like a disgusting creep

[modern stone]

:(((

[karmic thorn]

It's still your call how to receive his work though

His contributions there are probably seperate from his personal life

As an aside, a few recommendations on introductory logic:

1. Ebbinghaus
2. Enderton
3. Chiswell/Hodges
4. Rautenberg (a bit more slick, assumes more math maturity)

[bitter raptor]

There’s also open logic text

[modern stone]

Could you present some of their qualities and defects?

[patent flume]

isnt he just retired

not convicted

of anything

[karmic thorn]

I'm using Chiswell/Hodges and it seems friendly for a self-read (also has solutions/hints to some exercises at the back) but is deficient on content I guess. The first two seem to be canonical choices for introductory mathematical logic courses.

[karmic thorn]

I'm not entirely sure, but he's in shady straits

[gray gazelle]

well if you want to read it, read it. If you find it too difficult when reading, find another book.

[patent flume]

ugh

[prisma snow]

Ew, I didn't know about this. I was looking at his guide to studying logic a while back.

He still is active on his blog

[prisma snow]

Yeah, I didn't care about his book but I thought his guide might be good. I don't think he recommended his own books iirc

[sleek python]

wtf is this story

Good thing there are plenty of books on logic

[prisma snow]

Yeah, I don't have an issue using it, and if I wanted to learn logic, I would still check it out

[silver jasper]

looking for complexity and computability theory resources for a beginner

[marble karma]

Book that combines chess with math

[bronze raven]

What is closure finite weak topology: child abuse

[atomic hound]

What?

[bronze raven]

I'll respost the article from foundations in case anyone reading has no idea what we are talking about. CW: child abuse.

CW: child abuse

jus a corny joke am sorry

[lapis sundial]

😔

[queen rampart]

I'm always semi-confused why it seems nobody has, in some way, managed to produce a list of 20 or so books that have minimal overlap but cover a wide foundation of all areas of maths

[lapis sundial]

I think it'd be relatively easy to do for, say, an undergrad curriculum or at least the start of it, but i see little point in that

[queen rampart]

or because nobody can agree on things I guess

more that take analysis books: half of them include an intro to topology

[lapis sundial]

what's the relevance of this? i don't see how there's rly an alternative to this

[queen rampart]

...I wrote that and then lost my train of thought

[lapis sundial]

oh sure ye

dw

[lapis sundial]

But yeah - I feel like the choice of books can be quite individual and depend on one's own preferences/needs anyway

[queen rampart]

as someone that has spent many years book hopping rather than reading books, so much of the time it feels like either they all overlap in significant ways, or that they implicitly assume familiarity with something

rudin may start from nothing, but it implicitly assumes familiarity with a lot of things

[lapis sundial]

Yeah, it's not designed for a first course

[queen rampart]

but it's not written in such a way that it has "you should know X, Y, and Z"

[lapis sundial]

or at least people don't recommend it for that, i wouldn't

yeah

[gray gazelle]

what does this mean? I trying to have one more thing along with my current study. The book is Advanced Linear Algebra by Bruce Cooperstein, I want to have a solution manual since I am self studying.

"solution manual available upon qualifying course"

[queen rampart]

I presume it means the solution manual is available if you're a teacher

[gray gazelle]

oh well I keep looking for one online, I really liked the contents of this book.

[gray gazelle]

[halcyon hornet]

From the Physics server.

[subtle bobcat]

Does anyone know some book that containts high school theory for polinomials in one variable? By theory I mean theory like Horners scheme and stuff that high school students learn? Normal high school books dont contain theory and proofs of those theorems 😦

[modern stone]

What would you recommend?

[orchid musk]

Is there a specific book that goes over how to think about countable vs uncountable sets? Sets of functions mapping from something to something? Etc. would it just be an analysis book?

Bc abbott skips over this quite quickly and I feel lost on this topic

[stray veldt]

probably in an intro proofs book

maybe check 7.2 of velleman's how to prove it

[broken kettle]

Hi guys, I've just finished by physics undergrad and I'm looking for a good probability textbook

I did some stats in my degree but nothing particularly rigorous so I'm looking for something approachable but still thorough

for context I'm looking to study a Msc in machine learning next year

[astral cloud]

Please recommend a good Introductory book in multivariable calculus with difficult problems

[karmic thorn]

Spivak, Calculus on Manifolds

[gray gazelle]

the correct answer

[gray gazelle]

[silver herald]

[marble solar]

The only correct answer.

[junior merlin]

did you do the exercises? I'm also reading abbott and I got a bit stuck on some of them, but I think I have a pretty good grasp of cardinality now. I'd be happy to help you and reinforce what I've learned aswell

[orchid musk]

ill try working through them again as a second pass, maybe that'll help, thank you though

[hearty steppe]

Ahh your where I’m at. It’s an interesting section. It’s bringing together what is happening with subsets of the real numbers

Well I’m doing the 1.6 exercises atm but yea the whole point of 1.5 and 1.6 is to get you to think about the properties of the subsets of real numbers

Finished 1.5 already

[hearty steppe]

1.6 is just an extension of 1.5 btw. 1.6 has a couple snippets to read but they go along with their own exercise problems in the section

Some people in my study group have suggested I look thru Tao a bit cuz he apparently does a good job going over the peano axioms

[slate ruin]

I’m looking for good books on chaos theory, ODEs, and algebraic topology

[hearty steppe]

Isn’t chaos theory basically dynamic systems?

I’m down for recs on that too. I don’t think I got many from what I remember

[silver herald]

It's a part of dynamical system theory, yes - but not all of it

[broken kettle]

any recommendations for good probability theory books?

[silver herald]

At what level are we looking at? Measure-theoretic probability?

[royal bone]

I am searching math free online book with advanced high school math problems of all kind

[gray gazelle]

sounds like a sat type of questions.

[marble karma]

I am planning to read Spivak ( I know basic calculus that I studied from my school textbooks) is it worth it? Or should I just jump straight into some analysis book ?

[nimble ledge]

Is it a good idea to skip precalculus and go straight to James Stewart's Calculus?

[prisma snow]

If you know and are comfortable with the concepts from precalculus, then you can skip it

If not, you shouldn't

Going into calculus with bad algebra skills can be disasterous

[nimble ledge]

Ok, thanks!

[reef onyx]

ncert

[quartz inlet]

Anyone have any books or PDFs of calculus reviews per section? (Looking specifically for calc 1)

[karmic thorn]

Try Paul's Online Math Notes

[analog pollen]

Yes

Basic knowledge of algebra is fine

Just hs lvl algebra

[fallow rock]

prob. and stats textbook recommendation (intro up to something like Heteroscedasticity) plz

[marble karma]

What's your take on my question ?

I learned some basic calculus from ncert now I am confused whether I should do Spivak calculus or jump to an analysis book

[frosty girder]

[frosty girder]

spivaks calculus would be really good
but it also has a little more than what we have, and by little i mean it has a good load of stuff u probably wont have seen, if u have just done ncert

do some more practice so that u are more comfortable with calc
then u can go head on with it ig

[marble solar]

Definitely worth it

The exercises and problems are super great

Get a reading group to go over it

[frosty girder]

[karmic thorn]

Spivak should be great, as suggested by everyone else.

I bypassed something like Spivak but I think if you're learning on your own, Spivak might feel more accessible than an analysis text

[marble karma]

Okay I will read it

[atomic hound]

Hello, Gentleman, I would like to know a good book on plane geometry. Any recomendation?

A complete one.

[timber mesa]

I liked C. Lehmann's Analytic Geometry

not sure which topics you want to study but that book covers basic stuff like coordinate systems and then lines, conics, higher degree polynomial curves

and then concludes with 3D geometry

it's fairly complete in these topics

[gray gazelle]

I am happy to join one if someone plans to make one. I am currently finishing up chapter 3 problems in spivak.

i want a book for make a new mindset for maths

I go to poor high school and i am a ignorant

But i want to learn about maths

[analog pollen]

Why don’t you start with calculus

What grade are you in?

[gray gazelle]

4 of highschool

[analog pollen]

Huh

Last year?

[gray gazelle]

No

[analog pollen]

Second to last

Yes

[gray gazelle]

in my country we have courses to 6 in the highschool

[analog pollen]

Yes so it’s your second to last year

[gray gazelle]

I am really brillant in others subjects too

[analog pollen]

Anyway

[gray gazelle]

yeah

[analog pollen]

Calculus is a great start

[gray gazelle]

Okey

[analog pollen]

Idk what you want to learn

Pure math or physics.

?

[gray gazelle]

idk

i will discover it

in that moment

[analog pollen]

Start with calculus

[gray gazelle]

Okey

[analog pollen]

Think that is best

Stewart calculus is pretty decent for beginners

[gray gazelle]

Is the base of all no?

[analog pollen]

What?

Oh nvm

[gray gazelle]

Calculus

[analog pollen]

Yes

[gray gazelle]

hahah

[analog pollen]

This I recommend

I just finished it

As you are in 10th

[gray gazelle]

Yes

[misty wyvern]

Never do a single math problen.

Just read the book like a novel

As the common saying goes, math can only be a spectator sport.

[gray gazelle]

read Omniscient Reader's Viewpoint

and Hobbit

[hearty steppe]

Fake news

[tough mason]

whats the most efficient way of reading a stats book
whie taking in alot of info
the book im reading is An Introduction to Multivariate Statistical Analysis summary T. W. ANDERSON

[gray gazelle]

Any sat math book I need good 1

[gray gazelle]

is nagle saff and snider's book good for DE

[analog pollen]

There is no good ODE book

Lol

[radiant wharf]

need suggestions for books on functional equation

i am newbie in functional equations, gonna learn it for olympiads

i have an understanding in modular arithmatic and number theory tho

[karmic thorn]

@radiant wharf I think there's something by Evan Chen on functional equations, uploaded on his webpage

https://web.evanchen.cc/olympiad.html

They're available here

[radiant wharf]

yeh found it

thank you

[karmic thorn]

No worries

[cursive orbit]

just use khanacademy

[gray gazelle]

I need an example book for sat beginners sir

[cursive orbit]

wdym by an example book?

a book with practice tests?

[gray gazelle]

Never mind I've found it sorry to waste ur time Mister. I meant example book which would guide you on the s.a.t for beginners and solve simple questions like practice test basically

[karmic thorn]

Isn't there one that is quite popular (Barron or sth like that)?

[modern stone]

You could begin with Burn Maths Class and Reinvent Mathematics for Yourself by Jason Wilkes

[native linden]

Hi guys, looking for couple of recommendations.
I am getting done with the first pass of Real Analysis from Stephen Abbott's Understanding Analysis.
I have taken a methods course in Ordinary Differential Equations (chapters 1-5, 7) of Kreider, Kuller, Ostberg and Perkins (KKOP)'s An Introduction to Linear Analysis.
I would like to further study -
(i) Functional analysis.
(ii) Applied PDEs and numerically solving these.

[solid prism]

Quick question, is there a good book about the collatz conjecture? I'm more looking for one which is about the history of it or which explains it somewhat simply. I have "The Ultimate Challenge: The 3x+1 problem," but it'd be nice to have one that isn't just academic papers.

The introduction is decent for it, but I was wondering if anyone had other recommendations

[slim peak]

(i) Brezis for F.A. and PDEs;
(ii) Evans, maybe, for "Applied PDEs";

I have no references for numerical PDEs maybe @willow pecan knows some references for numerical.

[willow pecan]

Iserles is a good book

This would be A First Course in the Numerical Analysis of Differential Equations

There's also LeVeque's Numerical Methods for Conservation Laws

There's also Lin and Segel's Mathematics Applied to Deterministic Problems in the Natural Sciences

[native linden]

@slim peak , for PDE, I was looking for more of a methods book. I don't know anything about the elliptic, parabolic and hyperbolic equations.

[slim peak]

I don't really get what you mean by "methods book" ? Just to compute stuff ?

[native linden]

Yes, more on the applied math side of things. I am planning to apply to grad school next year, and the recommended book for PDEs was Farlow.

[split moon]

leveque is op

[native linden]

But Farlow, is an old text, and perhaps I'd like one which is a bit more recent.

[slim peak]

If it is for learning definition, and Methods, Evans is what you are looking for

[native linden]

Seems like a great book for numerics.

[willow pecan]

You might be interested in Fritz John's PDEs book

[native linden]

cool, gotcha

[slim peak]

for people who wants to learn "theoritic" PDEs from the ground with an "applied background" (I mean : starting from an explicit toy model then extrapolate to a whole theory using formulas etc...) Evans is the best as far I know (even if I don't like to do PDEs this way : the book is kind of self-contained and efficient).

[native linden]

how is Kreyszig for FA?

[misty wyvern]

Taylor is the best PDEs theory. I just can't read him past Vol 1.

[timber mesa]

very basic and introductory, good if that's what you're aiming for (e.g. for an undergrad course)

I had such a course based on the first few chapters

[night umbra]

Any recommendations for Linear Algebra books. Need to get good at Matrices especially

[late plinth]

Gilbert strang 8th edition

[slim peak]

That's the point with Taylor's books

[nimble ledge]

Which calculus book out of Spivak, Larson/Edwards, and Stewart, is best if I want to learn physics?

[analog pollen]

Stewart

[gray gazelle]

pls

spivak

just read spivak

[analog pollen]

Schaum’s outline Lin alg is fine

[analog pollen]

You don’t need that for physics lol

Stewart is fine

[gray gazelle]

hopefully

maybe i'll try after my exchange program

what about physics textbook?

[analog pollen]

What?

[gray gazelle]

which one is better between young and freedman; and resnick?

[nimble ledge]

Thanks!

[gray gazelle]

i'm not really into physics

[analog pollen]

Have no idea

[gray gazelle]

thank you for your help, appreciate it

[frosty girder]

i personally think young and freedman is better, i have both of them, and resnick is also really good, but young is just better imo

[gray gazelle]

For ? Your background ?

Generally Resnick & Krane >> Resnick & Walker
Cannot compare Sears-Young / Sears-Young-Freedman with Resnick & Krane. Maybe Resnick & Walker is close.

nah, just trying get into it, for self-learning

[frosty girder]

i just have walker
i had no idea about krane

[gray gazelle]

anyway, thank you for recommendation

5th ed, i suppose

[gray gazelle]

I can only recommend Resnick & Krane since it is the only one I read. I was not a fan of the walker book, since it missed on some stuff that I would have liked.

[analog pollen]

For what course are these books?

[coral narwhal]

hs physics

[analog pollen]

Why does it say university physics tho?

[frosty girder]

they are technically for uni students who are studying in the first year/semester

but they are highly used by highschoolers

[gray gazelle]

walker is like the watered down version of krane

[gray gazelle]

it is more like the bridge between hs and uni physics

[analog pollen]

Ah I see

[gray gazelle]

walker's problems are also repetitive iirc

[analog pollen]

Just use k&k tbh

For intro mech

[frosty girder]

k&k?

[gray gazelle]

isn't it only for mech

the blue and white book

[analog pollen]

Klepper and kolenkow

[gray gazelle]

k&k, great for mech honestly

[frosty girder]

oh

havent heard of that book

[analog pollen]

Yea, only quite challenging problems imo

[analog pollen]

It’s great

[gray gazelle]

k&k is good yeah

also morin

[analog pollen]

Why use this university physics book then?

If you can use k&k, griffiths (EM)

And shankar for example for qm

[gray gazelle]

it fills the gap between hs and uni physics

[analog pollen]

Oh, why does it cover qm tho?

And em

[gray gazelle]

you wouldn't be starting with k&k if you have no idea about basic mechanics

[analog pollen]

I did

Lol

[gray gazelle]

QM? only very basic stuff.

[analog pollen]

I only knew basic hs physics

[halcyon hound]

What is the best thing to say to my math teacher

Can you guys help me lol

[analog pollen]

Ah

[gray gazelle]

Hello hows your day? Good? Thats great to hear

[halcyon hound]

Ehh its for teacher's day

[gray gazelle]

Ah

[gray gazelle]

in "colleges" and advanced classes, such texts are used

[gray gazelle]

Sorry idk, I didnt even know that was a thing tbh

[frosty girder]

it can be used as a refresher, since it has a bunch of topics, it makes it easier to remind urself of some stuff

[gray gazelle]

If you’re looking for an freshman physics text, I’ve generally heard better things about Young and Freedman

[gray gazelle]

K&K is an analytical mech text. You can start with it, but you shouldn’t; you miss things from the intro texts it assumes you’ve covered

[analog pollen]

like what

Can you give me like resources to refresh that stuff

[gray gazelle]

You don’t miss too much; however, you do miss some (an analytical mech book is not going to tell you about static and kinetic friction, for example)

Nor will Griffiths discuss circuits or double slit interference

It’s things like that

[analog pollen]

ahhh i see

[gray gazelle]

I can personally attest to this; I started with Taylor and Griffiths, and there was some material I didn’t know until I took freshman physics probably simply because I missed it

[analog pollen]

is this a major issue when studying further into physics?

[gray gazelle]

It’s definitely not ideal, but I learned quantum mechanics fine enough

[analog pollen]

ok thanks!

[gray gazelle]

I would recommend going back and learning that sort of thing, though

[analog pollen]

yes i will

where can i do that?

any good rescourse?

[gray gazelle]

I’ve heard Young and Freedman is the best for that sort of thing

[analog pollen]

ah ok thanks

no wonder i found k&k quite challenging lol

[gray gazelle]

thank you tesseract

for the recommendation

[royal perch]

Anyone know of a nice introduction to monadic second order logic? I don't even really know what second order logic is in the first place..

[lavish parrot]

Hmm this logic stuff looks really interesting, sorry I can’t help you tho 😂

[misty wyvern]

Surely there's a better calculus book than Stewart for people not interested in math except as a tool for engineering?

For math folk it's Spivak of course, but there are so many calculus students coming out of Stewart classes without knowing multivariate calculus well.

Who're not planning on doing geometry further but still need to learn the material for e.g. mechanical engineering.

[broken meadow]

Thomas?

[misty wyvern]

I'm actually leaning towards not having calculus courses at all and replacing them with math methods courses.

Or at least books.

Math, Math for Physicists, Math for Physicists and Engineers, Math for Everyone Else.

[gray gazelle]

I need to know about the best measure theory books

After studying the Lebesgue integral, I'm interested in that theory

[gray gazelle]

I just recommend Khan Academy and Paul’s Math Notes

I agree, you don’t need Spivak for Calculus I-II. Heck, I learned those from some For Dummies books

[misty wyvern]

Rudin for measure theory, but unironically

Since you're a Gigachad you should be able to handle it

[late plinth]

pauls online math notes is goated

[gray gazelle]

I was going to recommend Rudin ironically, you serious?

[misty wyvern]

Rudin RCA is a good book

[crystal lion]

or baby rudin's treatment of it

(don't use baby rudin for this)

[torpid river]

anyone know where to find the solutions manual for James Stewert Calculus early trancedentals

[foggy relic]

slader is good

i think they charge now though

[torpid river]

yea

i'm not tryna pay lol

[foggy relic]

i remember when i was doing stewart

i found this pdf online that had solutions for the odd problems

[torpid river]

libgen only got it till chapter 11

[foggy relic]

damn

[torpid river]

i need chapter 12

[foggy relic]

i mean u can probably do all of the computation ones on ur own, and if ur not sure ur proof or solution is correct for one of the more difficult ones u can just ask in #calculus

[torpid river]

alr i guess that's what i'll do thanks

if anyone knows please ping me or dm me

[remote nova]

Recently was recommended a really nice introductory text on elliptic curves that I've been loving

if anyone's around, I'd be glad to take literally any suggestions of math textbooks y'all enjoyed

[junior oak]

Hi, guys, has anyone read "Complex functions: an algebraic and geometric viewpoint" by Jones and Singerman? How about it?

[misty wyvern]

I've never read anything

[halcyon hornet]

Intellectually above.

[remote nova]

More like, troll 😂

[halcyon hornet]

He is a PhD student.

[remote nova]

You can't become a PhD student without reading anything lol

[karmic thorn]

Today I'm resuming with Miklos Bona's A Walk Through Combinatorics which is a very nice textbook. 😌

The combinatorial arguments are almost ecstatic sometimes

[remote nova]

Actually had this book in my drive and deleted it because I've made a good effort to stay as far away from combinatorics/number theory/prob/stats as possible 😂

[karmic thorn]

😭

[remote nova]

but it sounds like a lot of people actually like the text, will definitely give it a chance sometime soon

[karmic thorn]

It's a very nice text

Lots of problems have hints/solutions at end of chapter as well

So it doesn't become a frustrating read

Plus Bona is a really good expositor

[remote nova]

I appreciate the recommendation

I've been in this mindset of "pick some area of math and read a thick ass book about it"

and honestly this isn't very motivating by any means

[karmic thorn]

My mode of operation is juggling between 20 books and make progress on none.

It is motivating at the cost of making very sluggish process.

[remote nova]

I just have a lot of holes in my math knowledge, so I kinda just bounce between anything that I can hope to comprehend, and ultimately I get nowhere 😂

[karmic thorn]

I have finally started learning things that are more within my reach/understanding and get the basics before I leap on to the cool stuff.

[remote nova]

Yeah I just can't do that

I got so excited for advanced math that I stopped caring about basic stuff

I haven't studied calc II or linear algebra, but yesterday I described how we transform a line into a sphere using projective coordinates and a "point at infinity" along with the intuition behind the fundamental group of a circle

sometimes it works well, other times it's not so awesome lol

Don't have to wait for fun shit, but most fun shit is a struggle to get through

[karmic thorn]

I'm still learning linear algebra and only recently learnt about calculus-ey stuff like Taylor series

I had this habit of browsing through more advanced stuff as well

[karmic thorn]

True

Basics can be fun too

Just get monotonous sometimes

[remote nova]

Mfw I open Tu's Introduction to Manifolds and can't read chapter 1 section 1 because Idk shit about Taylor series 🗿

[karmic thorn]

I get the feeling

[remote nova]

Agreed. I just think, in general, that calc/linear algebra are so boring

[karmic thorn]

I've astrayed so much from the basics that computational problems scare me a bit

Too used to discarding them ever since I finished HS

[remote nova]

I feel this spiritually

Only difference is that you're doing something right, because you've got the Honorable role, and also I still haven't manned up enough to do calculus and linear algebra 🗿

[karmic thorn]

LA is very clean actually, the matrix plug-chug maybe not, but the theoretical underpinning is nice

[karmic thorn]

Lmfao, Honorable role has nothing to do with mathematical expertise (I got it when I became a moderator).

[remote nova]

I've basically decided that I'm not going to study linear algebra, but I will learn what I need when I come across something in advanced math

[remote nova]

Bruh I thought they gave it to people who were good helpers n whatnot

[karmic thorn]

That's a fair strategy, but tbh you can just sit down with LA and do it.

Use something like Axler if you want good problems

[remote nova]

Even Axler bores me too much 🙄

I just don't find vector spaces interesting

[karmic thorn]

Yeah, that's one of the criteria, it is outlined in #info as well

[remote nova]

same goes for linear maps

[remote nova]

Well there we go 😌

I do find lin alg fun, though, when you're learning it for geometry, or for algebra itself

I think vector spaces are a great way to motivate modules

[karmic thorn]

Vector spaces are very fundamental, and the main results (at least in finite dimensions, that's the only thing I know a bit about) are very intuitive/nice.

[remote nova]

but maybe I'm just a bit naive to have that opinion

Yeah, agreed

it's just kinda like learning complex if you want to be an algebraist

like it comes in handy sometimes, but the necessity to know complex function theory is just absent

no use to invest a ton of time into it, at the moment

[karmic thorn]

If you'll be entering uni anytime soon you can just take classes on these, if not/you're in a different discipline then a study group could help.

[remote nova]

yuhhh actually I'm in my first semester right now

calculus II, taking care of what I need to learn, baby 😌

[karmic thorn]

Yeah good time to get a grasp of the basics I suppose

[remote nova]

😂 Definitely

We should probably get out of this channel 😳

[gray gazelle]

can someone suggest a good algebra book for 12th grade?

including all the topics like PNC, GP, AP, AGP, and you get the idea just all the algebra topics

[frosty girder]

Hall and knight is a very good book

[gray gazelle]

could you send the amazon link for it?

(also is there any other publisher than arihant for it?)

[frosty girder]

i dont think there are other publishers

i have the arihant one

its fine still, but lemme check

[gray gazelle]

oh alirght

[frosty girder]

https://www.amazon.in/Higher-Algebra-2016-H-S-Hall/dp/9351448126/ref=sr_1_5?dchild=1&qid=1633420997&refinements=p_27%3AH.S.+Hall&s=books&sr=1-5

This is one that isnt from arihant

[gray gazelle]

thanks

[frosty girder]

[modern stone]

What do you think about Patrick J Hurtley book on logic?

[frosty girder]

who pingth me

[south gust]

Maths Book For CS

[sudden kayak]

Do you guys have book recommendation that is axiom/proving-related? I hope it isn't textbook type of book, I'd like to read a nonfiction one

[stray veldt]

an introduction to proofs?

[modern stone]

Book of Proof, by Hammack
How to Prove it, by Velleman

[royal perch]

I also feel this omg. every time i see a geometric sequence or series again im like... what... lol

[karmic thorn]

Right

Or problems that require me to enumerate anything

[gray gazelle]

what do you guys think of the linear algebra book from Bruce N. Cooperstein? No much information about it can be found online. table of contents can be found here. https://www.taylorfrancis.com/books/mono/10.1201/b12770/advanced-linear-algebra-bruce-cooperstein

[gray gazelle]

Don't buy this version of the book

They send an old Xerox quality book with poor paper quality

Go through the digital copy of the book available in archive.org

[proven junco]

Real analysis book or introduction to real analysis, more than theory book to practice with exercises ordered from lowest to highest level, is there full demonstrations? The themes, real numbers, sequences, series, topology in R. etc.

[karmic thorn]

Have you tried Understanding Analysis by Abbott?

[sage kelp]

You can also try Real Analysis by Pons. I’m loving that book

[livid ermine]

a walk thru combinatorics is such a nice book

[proven junco]

i have of Aboott

but Pons it is in PDF?

[sage kelp]

What's a good book for an introduction to normed linear spaces?

[fluid bay]

Carothers real analysis is pretty good

At least I think that’s what you might be looking for

A lot of it is metric space theory, but it introduces things like ell_p spaces/norms, bounded linear maps

[grim pivot]

What’s a good book/survey on the different foundations of mathematics?

[dense mantle]

looking for an intro to convex analysis. have measure theory under my belt if that makes a difference/ preferably targeted towards beginning graduate students

https://math.stackexchange.com/questions/276389/convex-analysis-books-and-self-study

?

[gray gazelle]

+1 here , it is awesome.

[smoky sandal]

Looking for algebraic number theory book, any suggestions?

[wise umbra]

The book by Samuel is great

[graceful dawn]

How good is N. Piskunov's Differential and Integral Calc?

[gray gazelle]

Very good

All of my Calc understanding stems from that book

[graceful dawn]

Any missing topics on Volume-1?

[gray gazelle]

Volume-1 ? My text is one single book.

It had whatever I need for my class/course.

[graceful dawn]

There are Volume I and Volume II
12 chapters in Volume I

[gray gazelle]

In my book there are 19 chapters in total.

I think those Vol 1 & 2 separate Integral and Differential Part then.

https://www.amazon.com/Differential-Integral-Calculus-N-Piskunov/dp/B0007JGA6M/ref=sr_1_22?dchild=1&keywords=piskunov&qid=1633515562&sr=8-22

This is the one I use.

[atomic hound]

Hello lovely people, so i would like a good book about Hillbert system. anyone?

[solemn rover]

list of logic textbooks i put together the other day

[solemn rover]

thc campbell you can really just pick up any introduction to logic.

https://math.stackexchange.com/questions/465640/good-book-for-learning-and-practising-axiomatic-logic

[gray gazelle]

Sources for learning python for math?

I know 0 of python, anything is helpful (videos, texts, whatever...)

[gray gazelle]

https://docs.python.org/3/tutorial/index.html

https://docs.scipy.org/doc/

https://matplotlib.org/stable/contents.html

^ this is mostly what you'll need

for scientific computing

also found this book with a quick search

https://hplgit.github.io/primer.html/doc/pub/half/book.pdf

[green estuary]

Any good source on algorithms?

And please can you suggest any math book that would be a fun read, something historical maybe.

[gray gazelle]

Thank you @gray gazelle

[whole rain]

Lol

[slim peak]

"unfornately French"

what's that supposed to mean ?

[prisma snow]

@whole rain ^

Oh it was you

Who posted

LOL

[marble solar]

French people write things that are hard to read

[slim peak]

Is that a real thing ?

[marble solar]

If my one book on philosophy and logic written by a prof at the Sorbonne is anything to go by

Yes it is very real

[slim peak]

Well, I'm aware of it, know. I will keep it in mind when I will recommend some recommendations written by French people

[marble solar]

I mean I like french books because it forces me to practice my french

Which is awful

I've had a hard time finding good books for like PDEs

[slim peak]

Ah okay that's why, translated books are not a big deal right ?

[marble solar]

Yeah

But I mean most native english speakers studying math

Can probably read french math books with just a few verbs, articles, etc.

[slim peak]

In English or in French ?

[marble solar]

in French

I have plenty in English

[slim peak]

Yeah troubles must comes in when you have to read papers written by Lions or Grisvard

[marble solar]

I don't speak french fluently, and I'm not well connected enough with frenchies to know the good books

I'll be in Paris next summer hopefully

[slim peak]

To be honest excepted Brezis, I don't know a single one written in French

[marble solar]

Maybe I'll snag a few books

But even then the english edition of Brezis is better

[slim peak]

"better" if you mean more content, yes

Otherwise the short presentation of the french version seems to be more "easy to read" to me

[marble solar]

Ah more to the point

Less extra material

[slim peak]

Yes, exactly, only the pure essential stuff

[marble solar]

I haven't read either version, I just went off based on what my prof told me

[slim peak]

but less "little corollaries and propositions" that would make some parts more fluent

there are pros and cons

a big cons for the French version is "no exercises"

[wise umbra]

I tried to read Girard's book someday but I don't know much about logic so it was really hard to understand x) and French wasn't the problem haha

[slim peak]

I trust you, lol

[wise umbra]

Btw there is a "Master 2" centered around logic at "Université de Paris" (search "LMFI" on google)

If you are looking for some ressources

[slim peak]

If you are talking to me, I am really far from this field : I am doing Functional and Harmonic Analysis, for PDEs so...

But I heard about the master itslef

[wise umbra]

I was mostly answering to this message (but yeah that wasn't obvious)

[marble solar]

yUh

[slim peak]

Oh, sorry haha

[sage python]

How much PDE does Brezis actually do?

[slim peak]

Are you talking about himself rightnow, or the book(s) he wrote ?

[sage python]

The book (I only know of his FA book)

I know it does some amount of Sobolev space stuff and probably some applications to certain PDE

But it's not gonna cover anywhere near what Evans does, right?

[slim peak]

is FA book goes up to some general considerations like elliptic problem in bounded smooth domains

[slim peak]

Not really it's kind of different

I have both, and approach are not the same

[sage python]

I see

[slim peak]

For evolution equation to talk about the gain of regularity for more regular data, he uses some "deep" results of semigroup theory, and other more "functional analytic technics"

The kind of stuff Evans don't really want to deal with

[sage python]

Gotcha

[slim peak]

and Evans cover a lots of various PDEs but almost only in the L² case

Brezis fewer kind of, but also treat the Lp case

etc...

[sage python]

Okay so that's a bit different than what I expected actually

I thought Brezis was like, pure functional + epsilon of Evans, while Evans was like "Yeah you should mostly know what's up in Brezis before touching this"

It seems more complementary I guess? Example-based vs theory-based

[slim peak]

Kinda, yeah.

Both are two different point of views of PDEs, but there are many more points of view depending on the kind of PDE you want to investigate, but also considering your Maths prerefences. As far as I know I can make something like 8 to 10 main ways to consider PDEs (without talking about numerical PDEs), which can intersect each other.

[sage python]

gomez told me the only way to do pde is microlocal analysis :0

[slim peak]

It is kind a cool way to perform PDEs but Microlocal Analysis allows you to perform PDEs only on Smooth Riemannian manifold, or smooth bounded open set of Rn, which is quite restrictive.

To lower regularity at the boundary some troubles appear

(e.g. Lipschitz boundary)

[frigid comet]

you can do things with boundaries and corners but yeah funny shit like diffraction comes up and problems get much harder technically

[marble solar]

I've done chapters 2, 5, 6, and 7 of Evans

I think Evans does some things really well, but other things it's just a lot of detail without really giving it a whole lot of context

Overall I'm a huge fan of the book though

[misty wyvern]

Haven't read Evans thoroughly, just scanned it

Learned PDEs with Brezis and Taylor separately, in the opposite order which was a mistake

oh also Hormander, he was the OG

[gray gazelle]

Are there any good books on induction, well ordering principle, structural induction etc...?

like comprehensive treatment of induction

[quick hornet]

you wont find a book JUST on induction

since its... not really all that deep?

take the wikipedia articles and just fill in some proofs

and that covers everything that a typical mathematician/computer scientist needs to know

[quick hornet]

books on logic might go into more detail and cover transfinite induction and whatnot, but those are covered as necessary in context (usually for ordinal stuff)

you wont find just a chapter on various versions of induction

[gray gazelle]

Okay

Any recommendations for logic books?

[karmic thorn]

Check the latest pin

[quick hornet]

out of curiosity, why are you interested in induction specifically

[gray gazelle]

It's a huge part of one of my classes

Almost 1/3 of it

[quick hornet]

its a big part of every math class, but very rarely does one need more than the basics

in any case, halmos' naive set theory is a good starting place for logic

section 17 and 18 deal with transfinite induction specifically

but i dont think thisll be relevant to a typical math class

even one that uses a ton of induction

its a pretty specialized technique for set theory

induction is used everywhere but in 99% of cases its kind of the same process each time

[dapper root]

I think seeing transfinite induction exactly once is useful

Also + for Halmos

It’s basically a pamphlet it’s so short and it costs like ten bucks

[quick hornet]

in the sense that, sometimes proving the inductive step is very hard, but it still fundamentally boils down to:
(1) prove a base case, n = m for some minimal m
(2) prove that the inductive hypothesis being true for all k s.t. m ≤ k < n implies it's true for n as well

usually for (2) it suffices to just assume the inductive hypothesis is true for n-1

there isnt really much more you can say about it besides exploring a ton of examples

[round ether]

I need a book magic style fanatasy n stuff

[quick hornet]

and those examples are best shown in the context of your course

[quick hornet]

this is very very very broad.

targeted at kids? teens ("young adults")? adults? what subgenre (high fantasy, realistic fantasy, urban fantasy, etc)? any particular content requirements?

please say "adults", "urban fantasy", and "pictures" respectively

[round ether]

teens high fantasy no pictures

[misty wyvern]

Adults low fantasy coloring book for me

[quick hornet]

can always read tolkien

[misty wyvern]

My favorite YA fic is Pullman's HDM

[quick hornet]

the lotr series is a bit heavier than your percy jacksons or whatever, but approachable for teenagers

[misty wyvern]

actually the only one I like too

[quick hornet]

the hobbit was written for literal children

[round ether]

ah

[quick hornet]

so its no issue

theres A Wrinkle In Time which is more science fantasy and pretty much the only YA book i respect

theres also the Discworld series if you want something comedic

[misty wyvern]

Read Pullman

His Dark Materials

seriously good

[quick hornet]

incredibly disappointed no one got my reference.

if only ange was here.

[dapper root]

I did

I think

Not the specific one but you just wanted to shill for a Visual Novel

[quick hornet]

well yeah thats obvious

[dapper root]

Sadge

[quick hornet]

but that description refers to a pretty specific one

or at least a specific subgenre

[misty wyvern]

I've read through the popular free visual novel uhh

hang on

[dapper root]

Helltaker

[misty wyvern]

Katawa Shoujo

[dapper root]

Oh

[misty wyvern]

It was OK

told me I didn't like VNs, probably

[quick hornet]

KS is a pretty by-the-numbers prototype of a specific genre of vn

("nakiges")

[dapper root]

You should play one with boobies

[quick hornet]

the only weird part of it is that it was written in english lmao

[misty wyvern]

Feel free to rec the Crime and Punishment of VNs then

Yes, I will always rec things to read

[quick hornet]

eh vns are a very tropey genre by nature

[misty wyvern]

Rarely YA fiction except HDM

[quick hornet]

i dont think they have any true masterpieces as much as i enjoy them a lot

[dapper root]

Steins gate

Idk

[quick hornet]

steins;gate is up there

[dapper root]

Steins gate is realllllyyyy popular tho

[quick hornet]

its also a nakige

but less generic of one

because of the sci fi subthemes

[dapper root]

Monster girl quest is a legitimate masterpiece

[misty wyvern]

can I get one fiction where the MC is based and the female lead is insane, and both have enough power to tople earth twice, ty

What if the MC = female lead

[quick hornet]

that sounds like a lot of manga

monogatari?

[misty wyvern]

If you're up to reading some dense stuff consider Jonathan Strange & Mr Norrell, won't be clear who's based or insane or insanely powerful until about 1/2way through the book though.

[sage python]

Oh God I remember some people in another server told me to try katawa shoujo after I finished DDLC

It was

A time

[quick hornet]

the VN id consider closest to a masterpiece would probably be grisaia

[sage python]

It was very sad and yeah the main character is incredibly cringey/pathetic lmao

[quick hornet]

but theres... issues with recommending it

[dapper root]

No there’s not

Just don’t be a coward

[misty wyvern]

I have recently found, as a general anime hater, an anime I'd rank among my top media of all time. It's a shame that diamonds like these are hidden beneath an entire industry of uhhh power fantasies and harem fantasies.

[gray gazelle]

I have recently found, as a general anime hater, an anime I'd rank among my top media of all time. It's a shame that diamonds like these are hidden beneath an entire industry of uhhh power fantasies and harem fantasies.

[dapper root]

I have recently found, as a general anime hater, an anime I'd rank among my top media of all time. It's a shame that diamonds like these are hidden beneath an entire industry of uhhh power fantasies and harem fantasies.

[quick hornet]

well from the totally-not-underage sex scenes to the protagonist thats a blatant asshole misogynist who only gets rewarded for his actions

there are issues

[dapper root]

Yeah

Don’t be a coward

And then no problems

[quick hornet]

i love yuuji despite his assholery though

not as a person

[misty wyvern]

The anime is Haibane Renmei, which I will shill forever. But I get why people don't watch anime. The popular anime are all cringe. Attack on Titan, Something Hero Academia, whatever.

[quick hornet]

but as a protag

[misty wyvern]

All cringe.

[dapper root]

https://youtu.be/35YKD1LxOO8

It’s about angels

Sort of

Just go look it up on Wikipedia or something

[misty wyvern]

Yeah, it's hard to describe.

[quick hornet]

meanwhile, fate/stay night is a masterpiece in the same way star wars is

its kinda schlocky and trashy at times

but it does it really fucking well

if you put up with (or, ideally, get way into) the teenage power fantasy stuff

"anime girl yells random german words while throwing crystals at methed-up hercules" isnt exactly sophisticated art

but goddamnit it works

[misty wyvern]

Haibane Renmei is something IMO that should appear in film school. Spirited Away and Ghost in the Shell are, and I think HR is on that level.

I'm guessing there's a lot of other anime I like out there that I just haven't encountered yet, mostly thanks for AoT being shilled on every anime media site.

[quick hornet]

shonen anime are terrible in general

[dapper root]

Have u watched Lain

[quick hornet]

i moderately like death note

[gray gazelle]

death not

[dapper root]

If not, you should watch Serial Experiments Lain

[gray gazelle]

he gets the life note

[dapper root]

but never mention it to me or I'll start wanting to kill myself

[quick hornet]

but half from the perspective of mocking its pretensions

ill confess to not having watched FMA though

[misty wyvern]

I didn't dig Lain or Texhnolyze as much even though it's the same author as HR.

[dapper root]

weird

[misty wyvern]

Never finished. They weren't cringe though.

[dapper root]

anyway I go bye bye

Try FLCL

[gray gazelle]

it was always #point-set-topology

[quick hornet]

sorry bud

[gray gazelle]

lee is lee

[quick hornet]

that said, ||the vn with the most actual literary merit is easily saya no uta, which is... concerning||

[broken meadow]

i will play that one day

just to

bleak

[quick hornet]

theres subahibi which has fucking wittgenstein as required reading to understand

[dapper root]

I like school days

It is very good

[quick hornet]

as well as cyrano de bergerac

[dapper root]

very literarily important

[quick hornet]

school days is very mediocre and only famous for its bad endings

(which were the only part adapted into the anime, hence the memes)

[dapper root]

It is so good, it has such great writing and charadcter development

[quick hornet]

it also has the weirdest fucking fandiscs

including one whose premise is (nsfw) ||an alternate dimension where all arguments are resolved by strip rock-paper-scissors||

unfortunately, that magnum opus was never translated out of japanese

i wonder why

[dapper root]

I actually played that game

once

I heard about it and found a download

I literally could not understand how the game worked

I read the instructions