book-recommendations

[foggy relic]

8.2 next

6.3 is more B tier

for ch9 imo 9.3 is S and 9.1/2 are B

or actualy 9.1 B 9.2 A

[fallow cypress]

anyone have any opinions on abbott's understanding analysis?

[sage python]

Abbott has positive opinions of it

Also Eric you strike me as well beyond that book tbh

[fallow cypress]

yeah I just read the first chapter, and I figured

Lol

I just need it for a course

[sage python]

Tell your department to let you skip that course

[fallow cypress]

nah it's a grad course

[sage python]

What

[fallow cypress]

I assume we're going beyond abbott

[sage python]

Abbott is like

Low level undergrad

Send me the topics list

[fallow cypress]

yea it surprised me too that he was using that book

okay one sec

[vital bane]

yea abbott is for students who've never seen proof based math before

but it's really good though

[sage python]

It's basically Spivak Calculus iirc

[vital bane]

for them

[fallow cypress]

I wonder if he just chose it because it's free online 🤔

dami can I dm it to you

[sage python]

Sure

You don't need all all of Rudin but might as well

[vital bane]

wouldnt graduate level analysis be like measure theory or functional analysis or harmonic analysis or something lol

[sage python]

4 needs the first 3 I think

[hearty steppe]

Hey any book recs on Ergodic Theory? Not too heavy on the pure math but engages in the capacity to apply to areas like computer science theory, biology, and theoretical physics ?

Like I said I might just stick with the books I got but not sure if there is more focus on where Ergodic theory goes

[queen chasm]

Any calculus for beginners book recommendations? I'm looking for a book that can make you invent/explore calculus by yourself. Also it would be nice if the book had a sense of humor or wasn't just a collection of formulas and knowledge

[stone beacon]

Is it possible to read a 200 page book in 1 day?

[unique ice]

allegedly yes. I tend to fall asleep though when I read so.. I don’t see myself being able to do that..

[still panther]

depends on what you mean by read and on the level of the material

if its completely new material and you want to get even a not-surface level understanding, then definitely no

for me i think its a very good pace if I can cover 20 pages a day of new material

[livid ermine]

If you could do that and have deep understanding you could get a mathematics phd in like 1 month

[stone beacon]

are there any good reading tips to stay concentrated?

I have to finish this book in 2 weeks

[livid ermine]

if you're just talking about a novel or something like that, then you could read a 500 page book in 1 day without that much issue

[livid ermine]

which book is it?

[stone beacon]

The road to winter

[livid ermine]

young adult fiction, dystopian fiction

💀

[still panther]

oh

[livid ermine]

you are fucked m8

Good luck

[still panther]

in that case just read it, you can read it in an afternoon

[livid ermine]

read papa rudin first

[stone beacon]

I hate reading but its only 200 pages

how do i love reading

[stone beacon]

How can i enjoy to read'

[unique ice]

You need to meditate, regularly, every day.

[oblique hatch]

Does anyone have any recommendations for a good introductory book on Lie algebras focusing a bit more on the representation theory of them?

[livid ermine]

Have you looked at the brian hall: "lie groups, lie algebras and representation theory"?

[oblique hatch]

I don't really have access to an academic library, and £80 is a bit much

and a quick google search doesn't yield a pdf version

[grand thistle]

||there is the (lib)rary which is (gen)erous||

[queen chasm]

:?

[inland dawn]

Did you check the ones in #books-old ?

[queen chasm]

Oh... right, thanks

[split basin]

have you looked at "Representation Theory" by Fulton & Harris?

[sage python]

Also Humphreys

[hollow shore]

um re-iterating the same thing in the book is fool's errand tbh

I kinda tried that and it ended up killing a lots of time. What I would say is that you should write down important theorems or results and write the down the proofs from examples and exercises as fleshing it out on paper is really helpful. Just don't sit down and write exposition a lot, just trimm it to the bare minimum.

if it helps you and doesn't make you time inefficient then sure

[hearty steppe]

Being time efficient is the struggle seriously

The heck does that even mean anymore?

You can kill so much time trying to 100% a math book or trying to solve math proof based problems over your head even though you understand the content of the chapter (to the extent you need to understand it for your own purposes)

If I had all the time in the world to work through the first 7 chapters of baby rudin, I totally friggin would but I don’t. And my studies don’t revolve around just pure math but the application of theoretical math to computing and physics related areas at the moment

I don’t think it’s necessarily naughty to try to get through a book chapter by chapter as long as you understand it and only focus on exercises or example problems that are relevant to how your applying what your learning (the application part is tricky because that depends on what your doing, but I don’t think it’s entirely dishonest if your not a mathematician but your going through a math book for insight for your work)

You can’t learn everything but you can learn about anything.

[heady ember]

Yeah unfortunately we have limited time

So much math, so little time

[hearty steppe]

So much everything ad infinitum. Now we have people trying to say it can’t all possibly be infinite can it? That’s not what math or science is saying now isn’t that something?

Even if there are boundaries, we can minimize to an infinitesimal approximation in many cases where we know we never have an exact answer for a computation. (So really infinity doesn’t matter as much as convergence)

Now science is trying to understand what emergence is, because that’s what you get with converging and diverging behavior at scale and processes compounding eachother on top of some state spaces (the enumerable yet irreducible outcomes of compounding state spaces are what interests me in Rulial spaces)

[gray gazelle]

[gray gazelle]

How do you become a helper, I'd love to help some people with their math

[sand frost]

Ask ModMail, but you don't need to be a helper to help

[gray gazelle]

Someone please suggest me maths Olympiad book of imo level..

[devout sphinx]

Can someone suggest me a really elementary category theory book/articles or whatever that build up to something i can use later

https://arxiv.org/abs/1612.09375

in particular is this good enough

actually nvm I solved my own question

but to give some context to what I'm asking I'm talking an abstract algebra course and the prof keeps talking about categorical properties and later he wants to start homological algebra/prepare us for taking that course later

[solemn rover]

This is probably a good starting point, yeah.

[foggy relic]

Aluffi

and the link you sent is also good

[gray gazelle]

Any particularly good book for nonlinear optimization?

[gray gazelle]

Can someone suggest a good book for probability n statistics

I need to do all types of distributions - binomial, normal, geometric, hypergeometric, x^2, t, F n Poisson.

[gray gazelle]

For that Wikipedia could be sufficient

[gray gazelle]

😭

That’s a good thing though

No need to read a book

[misty wyvern]

Grimmet and Stirzaker if you must read a book.

[midnight peak]

Wikipedia is insanely good

[fierce hedge]

Is that for the algebra book? The famed one with category theory

[fierce hedge]

You can also try Category Theory by Steve Awoedy. For slightly more matured audience Emily's Category Theory in Context

[ocean mulch]

Introduction to Mathematical Statistics, R. Hogg, J. McKean and A. Craig. Pretty decent imo

[inland dawn]

Just curious - how does it compare against Grimmett?

[ocean mulch]

I've heard of that one too, but never went through it seriously (probably will do next month).

[grand thistle]

i have this book, what are the prerequisites to read it?

is just analysis at the level of baby rudin fine?

or should i learn some multivariable calc before

im planning on reading it after rudin and halmos' finite dim vector spaces

[fierce hedge]

Any topologists here. I have the munkres book and I am thinking of following this UG topology course at University at Buffalo. Are these any good -
https://www.youtube.com/playlist?list=PLoWHl5YajIf6MNTh7Ok024T1JkhZEcYXm

They also have a nice website at https://www.mth527.site/ (with notes and homework)

[gray gazelle]

Thx

[lime sapphire]

Whats the "shtick" with grimmett and stirzaker? Ik grimmett has an intro to prob book but who's the one with stirzaker aimed at?

[hearty steppe]

Oh sweet I’m gona bookmark that @fierce hedge

I don’t need to watch it now but maybe nice reference

[sage python]

Lmao flour I know you're calling me out there

[peak dragon]

what do you think about kuratowski and bourbaki general topology books? ||not looking forward getting any of these rn, I like Munkres, but I just got a neat deal: found Bourbaki TVS hardcover for 32 bucks!|| what about Bourbaki integration?

[fierce hedge]

Link for a giant collection of maths topics (ranging from grade 9 to doctorate level) with notes and textbooks + comments about them -
https://sites.google.com/site/tuloomath/

Can anyone pin this, in case it is helpful for others
Update: It's a bit too comprehensive to be useful

[gray gazelle]

lot of links are broken in that

[drowsy thicket]

If you are on a high school level and want to get into competition math, I think Art of Problem Solving Volume 1 is great, you can look into the table of contents and see what topics it covers, there is also a Volume 2

[fierce hedge]

Just found out about that. Also, for graduate level topics only the links are given without any info

[brittle breach]

Stephen Willard gen top is 20 bucks or less

[peak dragon]

cool, thats a deal. do you have an opinion about the mentioned books?

[gray gazelle]

What is the best book you ever read

[brittle breach]

best book on general topology I have seen, well writing. no manifold stuff though.

[gray gazelle]

For maths or applications of it

[gray gazelle]

Im thinking about this myself and it’s hard to tell lol

[tawny copper]

Evan Chen

[crisp river]

Any good readings on mirror symmetry for I, lacking algebraic geometry knowledge

[split basin]

Matrix Analysis by Rajendra Bhatia

[lapis sundial]

Mann's Doktor Faustus was pretty good

[gray gazelle]

That’s a novel

[lapis sundial]

It's a book though!

[sly field]

I would like to go into competitive math and I would like some books on number theory, algebra etc

That go from literally beginner level to advanced things

[cedar rain]

Good books for Undergrad/ Advanced Undergrad Geometric Measure Theory ?

[sage python]

Doesn't Morgan have a book that's supposed to be pretty good? Might be worth checking out

[cedar rain]

I've took a look at it before. It's not a rigorous introduction to the subject.

There's Fedrer but it's too hard to follow

[gray gazelle]

Try Djokvic then.

[red sentinel]

Oh my god why doesn't discord send me notification when I'm mentioned. Thank you

[still panther]

the sender can toggle mention on response

[vital bane]

,iamnot stu

[hasty eagle]

Removed the studying! role from you.

[wheat geode]

the books here for studyin or overall great books?

i know a ton of the second option

skulduggery pleasent is rlly good

rangers apprentice

spooks series (ik sounds childish but its not)- foundation of the movie called seventh son

[grand thistle]

i like john green

[heady ember]

Grass is green

Ok idk why i said that, felt it was kinda funny somehow (even tho its probably not)

[sand frost]

Does anybody have some good resources about how to accurately draw multivariable or complex functions by hand?

[waxen elbow]

hey ! any linear algebra book recommandation for a 3rd year student ? not a tough one

[heady ember]

[brittle breach]

linear algebra done wrong

[waxen elbow]

Thank you ! Do you have an opinion on Halmos?

[heady ember]

Unfortunately, I haven't really done much L.A. yet so I can't say haha

[vital bane]

you should go see a doctor if that's true

[grand thistle]

i love halmos

assuming you're talking abt his book on finite dim vector spaces

it's one of the best imo

it's a bit difficult and concise though

[vital bane]

is there a book that assumes you know multivariable calculus (in rectangular coords) and does multivariable calculus in just curvilinear coordinates?

like partial derivatives, gradients, total derivative line integrals, green's theorem everything polar, spherical, cylindical, maybe some general curvilinear coords or something?

something rigorous but also a bit computation oriented

is there such a book?

[red sentinel]

I assume you didn't toggle it for example

[still panther]

I did not, yes

[waxen elbow]

i’m talking about this one ! i think i’m not that great at LA, i wanna get better and not skipping important things. do you think it would be good even if i lack a bit of « mathematical maturity » ? ie writing good proofs

[brittle breach]

sound like you talking about some diff geo type stuff.

[waxen elbow]

(i have a copy of Roman’s advanced LA and i think it’s too hard for me atm)

[grand thistle]

to be honest i think you should just try it, it may seem a bit unmotivated at first but if you can go through the first few parts, it's really not that bad

[brittle breach]

Spivak calculus on manifolds
do Carmo deff geo of curve and surfaces
these two might be what you looking for

[vital bane]

not differential geometry

just stuff in R^n

but

using different coordinate systems

calculus of functions from R^n -> R^m just using different coordinate systems

[grand thistle]

i find a lot of beauty in the book because it doesn't hide the abstract algebra part of it, such as including quotients and talking about dual space a lot

but imo, it might be better to try an easier book with more motivation like hoffman kunze at first

[waxen elbow]

so the path would be Hoffman > Halmos > Roman ?

[vital bane]

roman as in "advanced linear algebra" by steven roman?

[grand thistle]

im not even sure if it includes gaussian elimination

[sage python]

Hoffman-Kunze and Halmos are at similar levels

Doing both is prob pointless. Roman will have a decent bit of overlap with them but then go much much higher

[vital bane]

like tensor products of hilbert spaces or something

[waxen elbow]

yup

[grand thistle]

id say do halmos if you've already seen LA before, hoffman kunze if it's ur first time

[waxen elbow]

i’ve seen LA, basic vector spaces and linear operators + diagonalisation stuff, a bit about determinants too

(im in Cs/stats major, so i lack a bit of rigour)

[vital bane]

if you want to learn about them then go ahead, nothing's stopping you

[grand thistle]

i mean theres nothing stopping you like neamesis said

im also in high school

and id say i read college level books

[vital bane]

based

probably yea

if it's stuff like vector arithmetic and matrix vector multiplication and stuff

depends on what you mean by that

[grand thistle]

i mean for the class itself you definitely dont need one

but if u wanna learn it urself

then that's ur choice

[vital bane]

like there's lin alg books based more on computation which includes vector arithmetic and matrix multiplication along with more advanced stuff

and there's books that cover abstract lin alg

[grand thistle]

try like strang's lin alg

[vital bane]

yea gilbert strang's lin alg book

[grand thistle]

that's pretty computation based iirc

[vital bane]

lol depends on what you wanna learn

if you just wanna learn enough stuff for your class, then that's okay, if you wanna learn more, you can do that too!

you can if you wanted to

[surreal phoenix]

just read your school's textbook

[grand thistle]

pov learning from rudin for an ap calc class

[vital bane]

i bet you can find it online

[surreal phoenix]

try to find it online

[vital bane]

sniped

[surreal phoenix]

Damn it.....

[vital bane]

then just use the first few pages of gilbert strangs book

[grand thistle]

i mean strang is much more approachable than rudin, a high schooler can easily read strang

[vital bane]

also yk khan academy as you previously sugested

[surreal phoenix]

mfw I spend 6 months getting through rudin for ap calc and my test asks for the derivative of x^2 instead of the proof for BW

would be kinda based tho

[vital bane]

Lol stop fumbling about what resources you wanna use, just pick one and get started learning, you can always switch to another resource

https://www.khanacademy.org/math/linear-algebra

go

learn

[grand thistle]

😭 when i use an epsilon N proof in my algebra 2 class to prove that a graph has an asymptote and my teacher asks wtf im doing

any concise books on group/ring/field theory?

most abs alg books i've seen drag it out through like at least 400+ pages

[vital bane]

[grand thistle]

i've already done a bit of group theory, and will be doing field theory in the next few weeks in my online class

[grand thistle]

already tried, hated it

[vital bane]

Lmao

[grand thistle]

it was boring af

im looking at like

lang

and it looks perfect

in the length and organization

but

it might be a bit too hard

[surreal phoenix]

how about that aluffi doe

[grand thistle]

categories 🤢

but

aluffi looks good

just again, a bit too long for what i need

because once i finish halmos and rudin, im planning on moving onto either complex analysis or multivariable analysis

[smoky zephyr]

concise

[grand thistle]

exactly

reading dnf felt like reading the dictionary

sure it had everything, but then it also had everything

got bored after chapter 3

[vital bane]

but that's the fun!!

at least for me I wanna learn everything

but alas, one lifetime is not enough

[smoky zephyr]

just become a computer

easy

[vital bane]

ah yes of course, let me just plug that old usb cable into my skull

[sage python]

@drowsy thicket what counts as high school or college or etc level is more a you thing tbh

If you think you're having fun and you're ready

Shoot

If it turns out to be too hard you can take it easier

[hazy elk]

Artin? (Just do the first 2 group theory chaps and the first ring theory chap and then you can probably read most other parts of the book according to your liking)

I mean not really concise but I would think that any more conciseness would affect the pedagogy for an intro level book.

[devout sphinx]

you could probably just do with lecture notes then

https://www.ams.org/open-math-notes/omn-advanced-search

Idk i've always felt that my favorite algebra books are huge

at least 500 pages

[pliant stream]

Larry Grove Algebra is extremely concise

[gray gazelle]

I mean after BSc + MSc in math one has probably seen most fundamental things

Everything else is niche

Almost

[gray gazelle]

Assuming you didn’t take bullshit electives

[pliant stream]

Even 4 years of undergrad you'll have seen all basic stuff

[gray gazelle]

Nah not necessarily

[inner token]

Anyone able to review "Algebra" by Lang? It's at my library

[analog roost]

What are the best differential equations books?

That offer some advanced concepts

and have some clear proofs

[mystic orbit]

is that illegal?

[main void]

i think the analysis in #books is quite fair, if you're incredibly methodical when reading it might be a good book for you, but if you're not, or if it's your first encounter with abstract algebra i definitively would not recommend it.

It is incredibly dense and, as a first encounter to new concepts, a bit too much so.
I once tried learning about field extensions from it and it was definitively rough

its great as a reference or to read up on topics though

[mystic orbit]

I think most advanced differential equations books are split into ODEs and PDEs

[analog roost]

yeah

[mystic orbit]

you can see the recommendations in #books

[fickle whale]

Has anyone read Tenenbaum and Pollard ODE?

[mystic orbit]

@analog roost I just remembered you need the advanced role to #books but you can get that from #get-advanced-access

[slim wind]

Hi everyone! Can anyone recommend a book about how mathematics naturally develops from the ground up (from basic arithmetic and geometry)? I'm not talking about foundations or set theory.

And I'm not really asking for a textbook recommendation.

[mystic orbit]

principia

[slim wind]

Hehe.

[vital bane]

yes, but i wanna become an expert in every field of math, but sadly that's impossible

extremely impossible

[fickle whale]

I don't think that's impossible

but you won't be young when you get there

[vital bane]

I mean if you had perfect memory and could learn a thousand times faster than the average mathematician and could live for 10,000 years then yea maybe it's possible

math is literally so frickin huge

like insanely huge

[fickle whale]

yeah and?

[vital bane]

and you need all that to learn everything

[fickle whale]

many subjects simplify comprehending eachother

and experts typically still don't know everything in a field

the difficulty all hinges on your definitions of the fields, and being an expert

but I think for most reasonable definitions of either, it's achievable

[inner token]

@main void thanks, it's my second pass at AA. Artin is available PDF but I like carrying a physical book

[fickle whale]

it'll take dedication, and it will have to be a specific goal, but I think it's achievable

[vital bane]

true

[fickle whale]

but this isn't book-recs

[main void]

Eh i dont think lang ever is a book you want to actively learn from, dummit and foote or some book with a more specialised subject will make quite a big difference imo

Also, maybe other people may disagree with me, but lang is not made to be read linearly

[fallow cypress]

I think he put a chart of which orders you can read it in in the preface

[gray gazelle]

It’s even almost impossible to be an expert in a single field

Gotta be at least a professor / researcher for that pretty much

[brittle breach]

I think it's more from the top down and a bunch of guessing.
Polya's books "Mathematics and plausible reasoning" might be a good resource for that

he is in a video on YouTube where he gives a demonstration

[slim wind]

Thank you for the suggestion! Much appreciated, I will check it out.

From the book's description, it may just fit the bill.

[solemn rover]

I once heard somebody say that David Hilbert was the last great mathematician who was able to contribute substantially to every major field of math

Since Hilbert, mathematics has simply exploded in every dimension, each field branching into subfields which become fields in their own right

So yeah it's been like 100 years since it was possible to learn all of math.

[lament sage]

Any recommendations on books related to mathematical finance?

I know a fair bit of probability theory

[formal tinsel]

what are some good books for modern econometrics?

[grave thorn]

For a "rigorous introduction" all books in red are good (they all assume measure theory)

Imo Etheridge is the best out of all of them

Shreve 2 is an option but he spends too much on some topics, too little on others

[analog lava]

yo DCT fan

check out advanced anal please

have a question

[distant jolt]

So, I am in a freshman in HS but I have been really invested in math over the years and somehow I got to a position where I am helping AP Calculus BC students get ready for their AP Exam, so I was wondering, are there any books for basic analysis courses?

I figure that is sort of the "next step" in terms of math classes

[foggy relic]

do you know basic proofs

i would do that first

[distant jolt]

Basic proofs as in how to construct one?

[foggy relic]

yeah

have you just proved stuff before, although easy proofs

[distant jolt]

Uhm, I know the basics of it because of my Geo class

[foggy relic]

thats a bit different (assuming 2 column proofs)

but the logic is somewhat similar

i think you should try reading a proofs book first but you might just want to jump into analysis and see if you can do it

[distant jolt]

I can understand proofs fine typically as long as I know the notation

Its the making of the proof that kind of concerns me

[foggy relic]

sure, than try reading Schroder's concise intro to analysis and see if its too hard

[distant jolt]

Okay I'll check it out!

[grave thorn]

imo Rudin > Schroder plus Rudin is available online while Schroder isn't

[loud cradle]

everything's available online if you look hard enough 😁

neither is available online legally afaik

[heady ember]

Dami: What the f- did you just say

[heady ember]

zlib

[grave thorn]

Rudin is bad at measure theory and intro diff geo

But other than that

Its very good and concise

[heady ember]

Yes

[grave thorn]

Rudin chapter 10 is bad because he doesn't want to scare people w/ the word "manifold"

Or "tensor product"

[foggy relic]

schroder is online

i have a pdf

rudin has no pictures

which is bad

[loud cradle]

many math books have no pictures, it's not inherently bad

[grave thorn]

From my personal experience pictures add more confusion than not adding them - however I understand there are people who benefit from them

The whole "topology is when donut coffee cup" is a worse way of explaining to a real analysis student: "topology is a generalization of metric space theory; it allows one to define continuity/convergence/etc in arbitrary spaces

[remote ginkgo]

topology is pregeometric

@grave thorn have u read sternberg lectures on differential geometry

[remote ginkgo]

big rudin good

[grave thorn]

No I've done only a very small amount of diff geo

[queen zenith]

Hi guys, I'm just starting calculus and wanted a book to test and learn concepts while doing it.

Would highly appreciate if you could recommend one with most scenerio or real life based examples.

[primal mica]

Sounds like a physics book to me

(May be substantially biased)

[grave thorn]

Physics 🤮🤢🤢🤮

[lime sapphire]

Are spivak's diff geo volumes worth going through whether it be in undergrad or post grad 💀

They seem a bit overkill

[queen zenith]

I'm studying for finance actually

Just want some practice problems to solve while I go through the course

[fierce hedge]

There's a book by Robert B Ash which is pretty short and has hints and answers of all exercises.
Same for Knapp but his book is pretty comprehensive just like Rotman's

[hearty sluice]

algebra + concise = lang

algebra + concise + decent, different question

[fierce hedge]

Lang is recommended if you hate yourself or wanna kill someone's motivation

Drier than yo mom's ...

[grand thistle]

hey this looks exactly like what i’m looking for, thanks

organized like lang, but not lang

[vital bane]

man hilbert was something else

[gray gazelle]

Von Neumann

[gray gazelle]

Hmm but is this good and relevant? Aside from all the computer driven stuff math and physics are pretty much stuck since about 70-100 years. Researching some super niche topic to the bottom isn’t really useful (yet, it could be useful in some years or decades)

No big new things except all the computer and numerical stuff (whose foundations are old too)

[livid ermine]

???

I can see the argument for physics being "stuck" due to the memes about new theories of physics not making testable predictions, although I think that is much too simple

but for math I can't possibly see how you can say its stuck for the last 70-100 years..

Grothendiecks work was done in the 60s and 70s, no?

[gray gazelle]

Ah yea forgot about about that dude

But for physics it’s kinda true

Most advancements in the past years were experimental proofs of old theories and some useless string theory bs

[primal mica]

Nothing has changed in any field if you choose to be ignorant of it

[last anchor]

We landed on the moon 53 years ago

I'd hardly call that physics being stuck

[primal mica]

But plenty of large advancements in the field of physics have taken place. Yes old theories have been tested and new theories are untested, but how do you test something not yet hypothesized?

Also: Quantum Chromodynamics, Topological Quantum Field Theory, Electronics, Plasmonics, etc etc

[vital bane]

I think they mean "if literally ground breaking work that completely changes the entire field isn't being done, then the field is stuck"

[primal mica]

Graphene kind of changed the game. I think those are the most cited physicists of all time and that was 2010 they got their Nobel prize or something like that.

It’d kind of be like saying nothing big has happened in medicine since penicillin. :P

[gray gazelle]

That was engineering

[last anchor]

Surely not all engineering

Who figured out when to launch the rocket and how to get back to earth

[gray gazelle]

Lol

[vital bane]

astrodynamics ftw

[solemn rover]

That's an overly charitable interpretation. Karkess has it right. They just haven't studied any math which was produced in the past 70 years and are not really aware of the developments and they choose to take this as evidence that nothing really substantial has happened.

Mindboggling take but there you go.

[vital bane]

If you ask me that's kind of ignorant

no offense stagger, I'm just saying, if I was unaware of something's existence I would ask and search around and not assume it doesn't exist (maybe you did do that and didn't find anything, lol I shouldn't assume you didn't)

[still panther]

nothing happened in biology since we invented dna im pretty sure

[gray gazelle]

All good, of course advancements have happened, otherwise research output would be zero and it obviously isn’t.
I was just tryna say that not much fundamental and ‘world changing’ stuff has happened since the big minds of physics and maths have passed away

Engineering probably made the biggest advancements in the last 40 years because of the increase in power of computers and simulations

[sage python]

Wait we invented DNA? Means at least one other thing happened

Namely we manipulated all life so that it must be deeply tied to this newly invented "DNA"

Impressive we have that much power

[vital bane]

Yes humanity has insane amounts of power but it's all locked behind a huge wall of stupidity

[dapper root]

I can unlock it for $99.99 for you

[gray gazelle]

Buy my course

[vital bane]

just 3 installments of $99.99 over the course of 3 months, and you can get it unlocked too!

[gray gazelle]

But no download only web content

[mystic orbit]

how about learning the basics of every field?

[keen marten]

i need some book recommendations on Karnaugh maps

[fickle whale]

A lot happened in the 60s and 70s for math

[solemn rover]

maybe look at books on 'digital logic'

[hasty echo]

@solemn rover best book on vft

[solemn rover]

Essays on Marx's Theory of Value, by I. I. Rubin

is VFT = "value form theory"

[hasty echo]

yes

[solemn rover]

because that's what i got out of it

ok

nice

[hasty echo]

have you read postone

[solemn rover]

no i got a bit into it and got distracted by other things. i signed up for a summer reading group and made it through like three zoom calls before dropping out

[hasty echo]

lmao

the coolest thing in vft rn is søren mau's mute compulsion imo

i strongly recommend it

[solemn rover]

Thank you for the recommendation

I can't remember if I've heard of this before

I don't think so

[hasty echo]

he made quite an impression on a libertarian think tank here

[solemn rover]

Unexpected, but cool

[hasty echo]

they were not pleased

[solemn rover]

lmfao

I don't know waht i expected

[hasty echo]

he implied that they would be "done away with" one day in an interview

and the leader of it (CEPOS) said it was the "scariest thing he's heard in 16 years" or something

so søren thought that was hilarious and then took that quote and put it on his backcover for the book

[solemn rover]

Hahahaha

[hasty echo]

no but it's really a great book

he revives a kind of 'corporeal analysis' or analysis of the body

in marx

[solemn rover]

Yeah, I understand you're serious

[hasty echo]

it's really interesting in the discussion of ecology

and the relation between nature and man as such

[solemn rover]

Oh, I see.

[hasty echo]

since in the 'bodily' exposition neither man nor nature present as 'realms'

[solemn rover]

Ok. You're losing me but my interest is piqued

[hasty echo]

i dont really know how to put it into words but it's really a simple text im just bad at explaining

i just hoped to lure you in a bit

[solemn rover]

It's alright. I need somebody to takl to me about it once in a while so i don't get sucked into math and forget about all the other shit

actually right now i'm brushing up on some dry technical stuff to see if i can get a cushy software development job somewhere

databases and shit

[hasty echo]

ah

that pays well i hear

i translated a small selected portion of it a while ago for a friend, most of it is from the thesis he wrote initially though

[gray gazelle]

can yall recommend or give me some tips and resources on how can I improve my speed and accuracy on solving multiplication, addition, subtraction and division😭🙏🏽

[tawny crater]

Another point is that most recent developments are way too technical to reach the common crowd

[hasty echo]

what was this in response to

[hollow shell]

You wont believe this,

Practice!!

[gray gazelle]

Just practice those often

I remember one of my math profs he struggled with those too

[gray jungle]

and my english professor struggles with the alphabet

[tawny crater]

The "there was no major developments in math/physics" discussion

[hasty echo]

oh

[tawny crater]

It feels as though even if one practices those forever hell never be as fast as someone who practiced them as a child

My father had USSR education with a lot of memorizing multiplication and he still at 50 busts out immediate calculations for two-low three digit multiplications

[gray gazelle]

Damn

Possible

I suck ass at head calculations too

[grand thistle]

anyone know of some very condensed notes on multivariable calculus (that are still readable) for someone who's going to skim through them and speedrun multi for complex analysis?

also they should be fairly rigorous

i'm looking for something like this on multivariable calc

[pliant stream]

Why should notes be different than a textbook?

[grand thistle]

textbooks are also fine, just need them to be concise

[pliant stream]

Try Apostol Calculus Vol. 2

[grand thistle]

that's a bit too long i think

im not looking for complete mastery, ill review all these concepts rigorously later in like spivak com or smth

but i need like the fundamentals to read stein and shakarchi comp analysis

[pliant stream]

Perhaps you can just watch 18.02 on 2x speed

That’s how I learned calculus lol

[grand thistle]

hey i found some decent ones

looks pretty ok

decently short too

don't need all that stuff on green's thm stokes' thm differential forms so ill prob use like a bit more than half of it

[waxen elbow]

hey boys, do have any recommandation about a measure theory / probability book ? something not suuuper long

[lusty perch]

Guys ping me and tell me the best calc book, i just finished algebra 2 and stuff...

I come from a background of basic math by serge lang

Currently im mostly considering spivaks, or thomas calc book

[brittle breach]

abbott understanding analysis,

[lusty perch]

Would i be able to understand that right after algebra 2?

And does it teach calc?

Sorry if i sound dum

[brittle breach]

yes, not for a calc test though

[lusty perch]

So its a pure math rigirous book that teaches calc, and even ppl who know upto algebra 2 can learn from it?

[brittle breach]

yep

[lusty perch]

Kk ty

[distant jolt]

Damn I stumbled through it and got somewhere but I am really strugglin. I am grasping the concepts but not the specifics

it is infact too hard

[pliant stream]

You don’t want to learn calculus from an analysis book

You won’t end up learning calculus

[foggy relic]

Hmm

I would learn linear algebra then

Do something like treil

This will also build up your maturity

[pliant stream]

Id just read Strichartz

Everyone has a hard time reading analysis book initially

Mit has video lectures on analysis I think it should be 18.100

[distant jolt]

I've gotten to like the start of the naturals and integers or whatever comes after supremum and infimum

but I have had very heavy nudging in the right direction for the excersizes

[foggy relic]

What wyatt red so far isn’t really analysis

That chapter is like what is N what is principle of induction etc

[distant jolt]

Its mainly the proofing part that I am struggling with

I can understand what I am reading, but i can't put that to use in a proof typically

I get to the answer, but i often overcomplicate or completely get stuck

[pliant stream]

Yeah that’s pretty typical

It doesn’t necessarily mean give up and try something easier though. If you just keep working through, it will get better

[brittle breach]

abbot is also pretty good, for intro to proof and analysis

see if you like his style better

[lusty perch]

Oh i c, someone said the same in the main chat

[distant jolt]

I can visibly see how I would prove the first excersizes much better than I could with Shroder's. Now, I am asking "How do I do this" instead of "What do I do" which I think is a big step for me

[soft dust]

Hey guys, I've been studying math privately for a couple of years so I got a good understanding of some simple and some complex topics, was learning the stuff that I needed for quant finance. I'm gonna start my bachelor in math this september and just wanna repeat analysis 1 and lin alg 1. What are some good books for a very brief overview that don't go deep into great details?

[sage python]

Try "Abstract Linear Algebra" by Morton Curtis if you want something efficient/repeat

[soft dust]

Thank you 👍

[sage python]

Oh yeah I forgot about analysis. Baby Rudin might be good for that

[devout hollow]

Hello, do you any book recommendation on linear algebra for absolute beginners? I do have some single variable, vector, and multivariable calculus background. Not that mathematically mature or accustomed to rigor, though.

[brittle breach]

linear algebra done wrong is good

[grave thorn]

dont read abbott before calc

like that book is slightly easier than baby rudin

so if you havent taken calc

obviously thats not suitable

[lusty perch]

Yea ppl said the same, im gonna read spivaks calc before that book then

[restive falcon]

don't use abbott

especially not after spivak

do sth like royden

or if that's a bit too difficult at least do rudin/browder/apostol

[lusty perch]

Would i be able to do those after smthn like basic math by serge

[restive falcon]

no

[grave thorn]

He wants a calculus book, not an analysis book

[gray jungle]

doesnt royden start with measure theory,that seems like a ruff transition

[lusty perch]

Ye

[restive falcon]

that's folland
I'm not sure abt royden

[restive falcon]

oh then spivak is good

[sage python]

The way to do it is

Spivak Calculus -> Royden

[restive falcon]

yeah

if royden is too hard when you get to it, switch down to one of the options i suggested

[lusty perch]

Oh.. so would this be good...

Basic Math -> spivak calc -> royden -> real analysis

[sage python]

Royden is real analysis

[remote ginkgo]

what about folland tho

[sage python]

Folland requires more background than Spivak, more like Rudin

[grave thorn]

Don't worry about real analysis yet

Like do calc

[lusty perch]

Oh

[azure stone]

Anyone know something for differential geometry?

[grave thorn]

See how it goes

[gray jungle]

the path im familiar with is calculus--> analysis over metric space (similar to rudin)--> measure theory

[azure stone]

For complete beginner

[lusty perch]

Ohh okay, i was confused about what analysis is

[grave thorn]

Analysis is the field of math closest to "calculus": it deals w/ convergence, continuity, etc

[lusty perch]

So imma do..
Spivaks calc, and strengthen all my skills from there. And then look into some other fields,

[lusty perch]

Ohh interesting

[restive falcon]

calculus is really just an accessible part of analysis

[restive falcon]

yeah that seems good

[azure stone]

Exblain

[restive falcon]

calculus is just computations involving limits

[azure stone]

You mean without the rigor?

[restive falcon]

on R^n

[grave thorn]

Am very tempted to say "analysis is the study of vector spaces endowed with some additional structure (eg. measure, topology, etc)"

[lusty perch]

Someone said spivaks calc is hard asf.. and sent me this..

[restive falcon]

i mean it's computational real analysis, so proofs will usually be based more on like
computing an integral

[lusty perch]

Oo, i wish i could learn all that rn lmfao

[restive falcon]

do not take advice from virgin vs chad memes

[grave thorn]

Everyone here (except for the analysts) think analysis is boring lmao

[restive falcon]

I don't

it's cool

[azure stone]

Hmm how do I measure theory

[lusty perch]

Lmfao if u say it that way, then yea ur right lmfao

[restive falcon]

open folland
profit

[azure stone]

And diff geom

[grave thorn]

Do you want measure theory for probability, for other parts of analysis?

[gray jungle]

folland is really good

[grave thorn]

Like what's your goal

[azure stone]

I got all this topics I want learn, but in what order

[azure stone]

Probl both

[timber copper]

What topics

[restive falcon]

then do folland

[restive falcon]

and do proper probability theory afterwards

[grave thorn]

I personally like Stroock's "an introduction to integration theory"

[gray jungle]

here ile make the joke too
chad mt learner for fa vs virgin mt learner for prob

[azure stone]

Topology, measure theory, differential geometry

[timber copper]

Cohn good

[azure stone]

I don't know anything about these

[grave thorn]

Also axler has a good book

[timber copper]

A bit of topology goes a long way for measure theory

[azure stone]

Right so that first?

And differential geometry last

[grave thorn]

I personally think if you want it for probability, no need for Folland. The majority of the book is dedicated to topics that you don't need (eg. the dual of C_c(X) for lch X is not important for probability lmao)

If you want to do stochastic analysis Folland is good

For probability there are books like Jacod and Protter

[azure stone]

I think all the areas I know are very much lacking

So it's bit of where do I begin problem

[grave thorn]

Have you read baby Rudin/similar book

[azure stone]

I've done bit if analysis but not sure if this book goes beyond that

It probably does if I had to guesa

[grave thorn]

What book

[azure stone]

Baby rudin

But no book

[grave thorn]

Up to what chapter

[azure stone]

For the stuff I know

Mostly lecture slides etc..

[gray jungle]

you could start by skimming through baby rudin to get a general idea of what you already know.

[azure stone]

Yeah that sounds good 👍

[brittle breach]

baby rudin

[brittle breach]

why do analysts like analysis

[remote ginkgo]

analysis is fun

im not an analyst

[remote ginkgo]

munkres topology -> big rudin first half -> shlomo sternberg lectures on diff geo

enjoy

thank me later

[brittle breach]

chap 1 to 9 of rudin?

[remote ginkgo]

you need at least to know the standard topology in euclidean spaces before doing lebesgue theory

[remote ginkgo]

honestly chapters 1-2 then switching to royden or folland is fine & is what i did

but you could read the whole real functions part of big rudin it's good

big rudin just has the benefit that it focuses on measurable functions and actually doing integration before it even defines what a measure is

so you get to the meat immediately

btw

measurable functions are defined almost exactly like continuous functions

and measurable sets as well

similar to open sets

but the valid operations change

you even generate borel sigma algebras from topologies

so you really require basic topology first

[brittle breach]

I read 1 2,3 of rudin but only did exercises in 1,

[remote ginkgo]

did it make u happy?

[brittle breach]

yeah

[remote ginkgo]

me 2

i luv u

platonically

(i really love plato)

[brittle breach]

how much of the exercises should I do

[remote ginkgo]

enough so that u get big n strong

[brittle breach]

why shlomo diff geo , first hearing of it

[remote ginkgo]

its perfect

check out list in the blog on the website in my status theres a table of contents there for it

in the Fast Track post

[urban otter]

hey guys anyone take AP Calc AB or BC? If so you guys have any book recommendations?

[keen marten]

any good books on Karnaugh maps?

[solemn rover]

Karnaugh maps are covered in any book on digital logic. I have not studied digital logic in 10 years and I do not remember what book I read at the time but I would really suggest just picking up a digital logic book, flipping to the section on Karnaugh maps, and then reading it.

For example the book "An Introduction to Digital Logic" by Potton covers Karnaugh maps in chapter 4.

[uncut roost]

chill

[solemn rover]

the book " Digital Logic: With an Introduction to Verilog and FPGA-Based Design " by M. Rafiquzzaman, Steven A. McNinch

covers karnaugh maps in chapter 4.

"Digital Principles and Logic Design" by Arijit Saha and Nilotpal Manna also covers it in chapter 4.

[jade monolith]

Hey guys, could someone recommend me a book about Differential Equation?

[tepid prairie]

Ordinary Differential Equations by Morris Tenenbaum and Harry Pollard. (Skip the application chapters.)

[jade monolith]

Thank you

[tepid prairie]

It's good and very easy to understand. The application chapters just take ages to get through since they are so information dense.

[jade monolith]

That's good to know since I'm a starter on that topic xd

[tepid prairie]

You can get through the methods stuff very quick using this book. You'll have a complete understanding too. They're amazing, 🙂

[jade monolith]

Hope to learn a lot in this book, thanks again xd

[heady ember]

Some other ODE resources/books I heard recommended on this server before

[tulip saffron]

do you recommend reading ESL or ISLR?

[south stag]

I think ISLR is a better place to start. Get the ML concepts down first. A lot more math in ESL and more concepts (e.g. EM), of course.

[soft dust]

why do people call this book baby rudin lol https://en.wikipedia.org/wiki/Principles_of_Mathematical_Analysis

[still panther]

cuz its first of the three analysis books by rudin

baby rudin, papa rudin and grandpa rudin

[soft dust]

oooh I see

[sand frost]

Does anyone have any good resources on how to plot complex functions specifically by hand?

[restive falcon]

he has 5 books i swear

[timber mesa]

that, fourier analysis on groups and

[sage python]

Function theory on the unit ball of C^n I think

[pliant stream]

Um he has more books 😦

[shrewd hazel]

Hi guys do you have some recommendations for books like Concrete Mathematics by Knuth but a bit easier

It's going really slow for me so I was hoping for something to ease me into the topics discussed in that book

[halcyon gull]

can someone here recommend a book for having a in-depth read into sproradic groups? And is a undergrad-level knowledge of abstract algebra sufficient, if not which book should i read first?

[karmic scaffold]

Do y’all have any proof theory recs for someone with only one logic course (taking next sem)? If that’s just not a thing that exists I understand too.

[gilded spade]

have any of y'all read GEB: An Eternal Golden Braid by Hofstadter?

[lapis sundial]

I have

I think various others have too

[ripe sail]

any good books about deriving formula/equations?

https://www.youtube.com/watch?v=3tvIxLGe8K4 something like this

[lime sapphire]

Depends on what formulae you want to derive

[ripe sail]

i want a book that covers any formulas

i just want to solidify by basics

hmm

[lime sapphire]

Lang's Basic mathematics.

[ripe sail]

maybe trig identities

[ripe sail]

oh

ive heard about that

ima check that out

[fading wave]

anyone got good free sources for studying multivariable calculus?

Im currently using MIT's videos and problem sets but sometimes I feel like it skips some basic things

[karmic thorn]

Multivariable Calculus by Don Shimamoto is available online for free. I think it's a fine book that tries to cut a middle ground between a computations geared course and one that emphasises theorems-proofs more.

[fading wave]

Thank you! I'll look into it.

[fallow cypress]

yeah

it's p good as an intro to formal manipulation

[solemn rover]

"Formal manipulation" is also what I call it when a bureaucrat screws with my head by telling me I did the paperwork wrong

[inner token]

Is there a gentler intro to topology than munkres?

[timber mesa]

Munkres is about as gentle as you can get while not losing any important content imo

but there's that Topology Without Tears book

decent but mostly focuses on metric topology

[inner token]

I just need a little practice getting started, learning how a basic topology proof goes, etc. I did fine in the first unit of munkres which was all about set theory but now I'm strugglin with basic topology proofs because I'm not familiar at all with how things fit together

I found "Topology without Tears" free so I'll give it a go

[timber mesa]

yeah it's a free book

[vital bane]

This has a lot of useful stuff like, special functions, fourier series, laplace transform, even some stuff about PDEs and non-linear DEs (even a chapter on variational calc)

[fierce hedge]

For practice you can try Elementary Topology - problem textbook. It's more of a workbook but it starts from low and builds up. It also has solutions at the back

[heady ember]

Erh well this might not be exactly gentle but I have heard ppl here reccomend Lee's Introduction To Topological Manifolds as a good intro to topology (non-pointset i think)

[vital bane]

mfw all my topological spaces are locally homoemorphic to R^n

[brittle breach]

baby rudin chapters 2 and 4

well really just ch2

[fallow cypress]

LOL

wtf baby rudin is not gentle

what do you mean

[hazy elk]

Is there a good resource on permutation groups, like something that proves interesting facts about them (Stuff similar to how (12),(12...n) generate Sn (many books do this) but I want some more results and computations. (Like in S_5 how can I find g: g(12345)g^-1 = (a1a2..a5))

[solemn rover]

Another good book on topology is Topology by KLaus Janich

[solemn rover]

if you're struggling with the concepts of topology i really recommend reading a book on analysis preferably one that deals with metric spaces

not necessarily baby rudin but the basic point is that the real numbers are much more concrete than an arbitrary topological space

[fallow cypress]

^

[hazy elk]

I'm not looking at advanced material like representations, maybe a problem book with solutions (for symmetric groups) would suffice

[hearty steppe]

Honestly I would personally suggest skipping going thru a Diff Eq text unless your doing a diff Eq course or what your doing is very specific within the context of the book. But my bout with Diff Eq text books mostly feels unmotivated and lacking in direction.

I feel like I’m grasping a more intuitive understanding of differential equations by learning subjects like dynamical systems theory or differential geometry

And at some point the two subjects play games with each other and we have both a fun and terrifying time

Doesn’t 3B1B have a whole series on diff Eq that can get you up to speed in a matter of hours?

I need to check that out at some point. Im going thru this right now in terms of video series https://youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic

Honestly this whole series is amazing

Covers a ton of stuff

Props to grist for initially sharing it

[drowsy thicket]

Serge Lang's A First Course in Calculus seems to be a great book, you can check its table of contents and see what it covers

[old elk]

guys I'm looking for the best self-taught book to learn group theory and the following topics, Theory of rings and modules, etc...

I want to learn the course alone I haven't seen anything about it I don't know anything, recommend the best book for learning

[gray jungle]

artin alongside the lectures by benedict gross are incredible , its what im using currently altho he does follow the 1st edition so keep that in mind

altho i will say that you might wanna find your exercises elsewhere

artin tend to be a bit routine

[fierce hedge]

Artin if you know wanna know a bit about linear algebra also. Slightly fast paced but good. The standard textbook is Dummit/Foote
Robert B Ash's or knapp best for self study. knapp is more comprehensive

[gray jungle]

otherwise if you use it with the lectures its great

[fierce hedge]

Artin's 2nd edition exercises are pretty good

[old elk]

excuse me, could you tell me the books you just mentioned?

[fierce hedge]

Algebra by Artin, Basic Abstract Algebra by Robert B Ash, Basic Algebra by Knapp

[old elk]

complicated

[sinful cloak]

Does someone know a good book for self learning on differential equations

[fierce hedge]

As in you need simpler books? Then maybe try Pinter or Visual Group Theory. The latter also has YouTube videos and proper webpage.

[old elk]

I tried to be clear, I don't know anything about anything, my advisor turned me down and told me to study the subject well, so I want something for a "child".

:((

[fierce hedge]

Fair enough. Here's the link to the course I was talking about - http://www.math.clemson.edu/~macaule/classes/f22_math4120/
And here's the video playlist - https://youtube.com/playlist?list=PLwV-9DG53NDxU337smpTwm6sef4x-SCLv

[knotty kestrel]

does anyone have a recommendation for a book, course notes or videos that covers lines, planes, curves, & surfaces (generalized dimensions), parametrized vs. implicit representations, etc?

[remote ginkgo]

aluffi chapter 0

[maiden axle]

Do you know of books about analysis on manifolds? Specifically books that contain some or all of the following topics:

Part I. Manifolds and maps

1. Manifolds, submanifolds, tangent bundle, boundary, orientation. 2. Homotopy and applications. Brower's fixed point theorem.
2. Degree of a map as a homotopy invariant.
3. Euler characteristic and vector fields.
4. Lefschetz number, linking number.
   Part II. Differential forms
5. Linear and local theory: exterior product and differential.
6. The Lie derivative.
7. Integration, Stokes theorem.
8. Applications: Linking number and Gauss integral, Gauss-Bonnet theorem for a surface in the 3-space, the residue formula.
9. Degree of a map revisited.
   Part III. Introduction to De Rham cohomology

[sage python]

The fact that you say "degree of a map revisited" suggests to me this is the table of contents of something

That said, I think "From Calculus to Cohomology" might be good

[maiden axle]

Thanks. It is actually a syllabus of a course

[old elk]

this

[heady ember]

Lee's series of 3 books?

[remote ginkgo]

a combination of bott/tu and shifrin's classical diff geo course

[heady ember]

Ah yeah and that too

[remote ginkgo]

actually there might be one book which covers all of what you ask for

and is very concrete/computational

and easy to read

ah it has everything except gauss bonnet stokes theorem

yeah, just do shifrin + bott/tu

[sage python]

I'm less than fond of Shifrin tbh

I love the person

[remote ginkgo]

y

i found his book super easy reading

[sage python]

But the book made me swear off diffgeo for a long time

[remote ginkgo]

huh. interesting

[sage python]

Could be the way I approached it though

[remote ginkgo]

i felt that way about do carmo

i read his book under supervision of one of his doctoral students so i had some guidance in what to focus on

[sage python]

In an analysis bootcamp, we skipped the curves material mostly and jumped to surfaces. But I mainly felt like there was a certain geometric/almost physics intuition I didn't have going in

[remote ginkgo]

shifrin, that is

[remote ginkgo]

oh, yeah. that's a bad idea

the frenet-serret apparatus is pretty neat

also there are other apparati for curves

[sage python]

So yeah idk that kinda very visual geometry just didn't vibe for me

So in our psets I mostly could only do the computations which were annoying. And I didn't care much about the early results in surface theory

Like oh a ruled surface is blah okay cool idc

[remote ginkgo]

actually there is some recent elementary literature on these topics on arxiv

[sage python]

It's v example heavy

[remote ginkgo]

yeah it is

[sage python]

And I couldn't really bring myself to care about those examples

[remote ginkgo]

mhm

[sage python]

Also some of my classmates' presentations were... questionable

[remote ginkgo]

i should say chapter 8 of his multivar maths book is quite good as an intro to integration on manifolds

[sage python]

I came in thinking I was gonna love it because I loved difftop

[remote ginkgo]

what did they present on?

[sage python]

The material. It was a bootcamp so we gave the lectures ourselves

[remote ginkgo]

ah ok

m i l n o r

dont say guillemin pollack

im putting restrictions on what he is able to say

to save me from a heart attack

[sage python]

Milnor and GP are both good

Hirsch is the heavier angle on the stuff

[remote ginkgo]

heavier in what regard

deeper? or more verbose

i havent looked at it

[sage python]

So when I took undergrad difftop our books were Milnor and G&P

I think Milnor is more clear but does less

So if you want eg oriented intersection theory or differential forms you go to G&P

Hirsch is more sophisticated than the other two. So it actually talks about abstract manifolds iirc rather than just submanifolds of R^n, it has a chapter which I think contains moderately tight results in the vein of smooth approximation

I think for the most part people are just content with saying, for closed connected blah blah manifolds you have the tubular neighborhood theorem

Then use Stone-Weierstrass and linear homotopy + project by tubular neighborhood

To get that continuous maps between (adjectives) manifolds are homotopic to smooth ones, maybe mutter that this homotopy can be chosen to restrict to the identity on a closed subset if it was already smooth there

Hirsch I think is way more... idk if I should say careful, because that argument just works, but goes into a lot more detail on this kinda smooth approximation business

[heady ember]

What does G&P stand for?

[sage python]

Guillemin and Pollack

[heady ember]

Ah i see

[sage python]

But yeah then you get stuff in the vein of Bott-Tu and Madsen-Tornehave

Which lean mostly on differential forms and cohomology. That does kinda recover, with heavier technicalities, the intersection theory

[tiny copper]

I have to take multivariable calculus and statistics soon. Could you guys give some book and other resources for these courses

[pliant stream]

Well, we don't exactly know how your statistics class is

So it would be difficult to recommend a suitable book

For context, you're in a math server, and we typically assume math stats when we see stats, which even at the most elementary level, requires a course in multivariable calculus

[vital bane]

multivariable mathematics by ted shiffrin

[tiny copper]

Thanks for the great recommendation, the book looks good and he also has a lecture series to go with it on youtube. Will definitely check it out!

[tiny copper]

Sorry about that I should’ve been more clear

[pliant stream]

not sure if I would read shiffrin which is a pretty niche book and is unlikely to follow your universities course

[tiny copper]

The textbook that they recommend is Probability and Statistics for Engineers and Scientists Ninth Edition by Walpole, Myers, and Ye https://www.amazon.com/Probability-Statistics-Engineers-Scientists-Update/dp/0134115856

I’m not sure what level that would be at though

[pliant stream]

i mean if they recommend it, why not use it?

and it seems like this book would come with online homework, for which you'd need to buy it for an access code

[tiny copper]

I’m using it right now, just looking for other books and resources for support

[pliant stream]

wow that is a stupidly expensive book jeez

[tiny copper]

is the book niche because it strays away from common topics or because it goes into greater depth into some more obscure topics?

[pliant stream]

it goes into more depth than is commonly seen in a calculus 3 course

to be honest, I probably wouldn't use a book to learn calculus 3. I'd just watch lectures

(In particular MIT 18.02)

Like shiffrin discusses contraction mappings, existence of integral, differentiability, linear algebra, etc.

All of these are important to know eventually if you pursue math, but they will never be in your calculus 3 class

[timber mesa]

these are also important to actually prove many of the things you see in calc 3

e.g. using contraction mappings to prove the inverse/implicit function thms.

[pliant stream]

yes, but you don't see the inverse/implicit in calc 3 typically

[timber mesa]

I thought it was typical

well

[pliant stream]

neither mit nor my school (nyu) covers it

[vital bane]

huh true

I guess shiffrin would be a good calc 3 book for a pure math student

[vital bane]

if you don't care about that rigorous stuff and going in depth and stuff, then the MIT lectures and khan academy calc 3 course would be enough

https://www.khanacademy.org/math/multivariable-calculus

that khan academy course is actually really good

[pure swallow]

Is it better to learn multivariable calculus from khan academy or from a book for it?

[heady ember]

Its probably a personal preference

But I'd guess that Khan Academy's exercises aren't too difficult so you might want to supplement it with a book's exercises

[vital bane]

https://tenor.com/view/the-road-to-el-dorado-both-both-is-good-gif-8304204

having explanations from multiple sources is a great thing! if you don't understand the explanation from one source you can look at the other ones until you get it

that doesn't mean you have to finish mutiple different books on the same subject just to study it lol you can follow 1 book and 1 set of lectures but when you're stuck you can try looking at a bunch of different sources

[pure swallow]

right

[vital bane]

no it's not a series on diff eq, it's just like 4 videos that give you taste of what ODEs and PDEs are and solves the DE for shm and the heat equation

[vital bane]

i know right!

you should also check out the one on QM, by fredrick schuler

[hearty steppe]

I mean I feel like that’s extra, besides I feel like dynamical systems theory is the way to go if you want to understand physics as someone who does math

I haven’t spent too much time on my physics books recently because I’m realizing you can use dynamical systems based intuition and structures to piece together classical and quantum mechanics

I’m still gona try to get through them more at some point

[raven fossil]

Hello,Do you have any good books to start number theory?

[maiden axle]

Were you joking about Olver’s book?

[remote ginkgo]

disagree

just read selected topics from shifrin

you dont have to cover all of it

[remote ginkgo]

me funny

but not that funny

[hearty steppe]

Who reads a whole book anymore unless the content is just that good

[remote ginkgo]

me

[pliant stream]

Disagree still

The book is focused on being rigorous. Not what anyone in a calc 3 course cares about

And it's also an absurdly expensive book, when you can pick up stewart for 5 bucks

And don't tell me you can pirate the book. I will die on the hill that hardcopy is superior!

[remote ginkgo]

i have the hard copy

i think it's not really difficult to read due to its rigor

[heady ember]

Just pirate the book and then print it?

[remote ginkgo]

i had already read rudin by the time i got half way through calc 2 though

so i cant really give typical advice

[pliant stream]

Yes so you are clearly not the target audience of calc 3 course!

[remote ginkgo]

why

i had to learn it :p

[pliant stream]

Because people in calc 3 have zero maturity

[remote ginkgo]

i found it much easier to read than stewart or that other one we used

i forget what it was

i think properly i learned calc 3 at work doing engineering computations

and just googling around for notation

lol

[pliant stream]

Besides...no one actually learns calc 3 from a book. They just watch lectures

[remote ginkgo]

yeah, just use khan

he has a good explanation of greens theorem e.g.

[pliant stream]

It's not until much later in your math journey that you begin to read and learn from books

[remote ginkgo]

i guess i agree with you there

well sort of

not really

i think you can certainly start sooner and benefit a lot

but for learning calc 3 yea u can just khan it out

[pliant stream]

For what it's worth, I tried to read apostol's calculus, and I literally could not get anywhere

[remote ginkgo]

i dont find his book readable

[gray jungle]

its not very efficient to use a book for computational calc 3 in general

[pliant stream]

Well the book mostly exists as a problem book

and at under 5 dollars and with a shitload of exerciswa stewart is perfect for that

[remote ginkgo]

i had a physicist yell at me daily to read rudin until i finished it

[gray jungle]

books are great for once you start taking theoretic courses

[remote ginkgo]

that fixed my life

made it all ez mode

maybe he shouldve chosen something other than rudin though

[pliant stream]

I think rudin is great

you do need and want someone to help you out though

[gray jungle]

im in the "dont use rudin for learning but use it as a reference" club

altho i wont start that argument now

[hearty steppe]

Baby rudin is great. I only was able to go through a chapter but man it’s really enlightening how much you learn from one chapter of any of his books. 😂

I’d go through more of it but I have other literature demanding of my time.

Finished half the exercises in it too. Man the exercises are brutal

[pliant stream]

Trube they are definitely much more interesting than exercises found elsewhere

Also I just remembered my analysis instructor completely skipped over anything to do with series lol

[hearty steppe]

I’ve seen Rudin difficulty exercises in other books.

Brin and Stuck’s Intro dynamical systems text has some pretty challenging exercises with wording close to Rudin, maybe not as esoterically worded. But that is part of Rudin’s charm. I like the riddle aspect of making my brain try to think abstractly about maths

[grand thistle]

rudin is fun

chapter 2-3 are i think the hardest chapters

and also the longest

[hearty steppe]

You need to also check out some of the problems in Wald’s General Relativity book

[remote ginkgo]

i found chapters 2-3 easy

[hearty steppe]

It’s a physics book but the problems are interesting and hard

[remote ginkgo]

i think some later ones were harder for me

but then i just got over it and finished the book

[grand thistle]

which ones?

[gray jungle]

i remember chapter 7 being quite ruff to walk through compared to the rest

and i think there is better ways to learn basic topology than a rushed chapter throwing everything at you

[remote ginkgo]

i recall uniform continuity giving me hell (was that 3)?

[grand thistle]

did you do the whole book or 1-8

[grand thistle]

ah that's 4

[remote ginkgo]

also some other things about convergence of sequences of functions

[remote ginkgo]

eventually, the whole thing

[gray jungle]

that is indeed chapter 7

[remote ginkgo]

at the time just 1-8

[hearty steppe]

You know what’s ironic. You finish chapter 1 in baby Rudin and boom your now about to learn about basic topology

Brin and Stuck you finish chapter one and boom, now you learn about topological dynamics. Hah small world isn’t it 😂

[grand thistle]

i hate topology

[remote ginkgo]

i truthfully believe it is better to just read munkres

than rudin

the results of rudin become obvious if you have topology

[gray jungle]

i mean just look at this very obvious proof

[remote ginkgo]

other than integration theory

[hearty steppe]

Read munkres while reading rudin I find an interesting combo

[grand thistle]

i forgot like all the topology i learnt for chapter 3 so i have to review chap 2

[gray jungle]

i second this

[remote ginkgo]

had i read munkres first i'd have had no trouble with rudin

[hearty steppe]

Yea I feel you there.

[remote ginkgo]

i gave a lecture on topology a couple weeks ago

[grand thistle]

why topology so boring tho 😭

[remote ginkgo]

covered 80% of the content of munkres

in 6.5 hours

[grand thistle]

damn

[remote ginkgo]

https://www.youtube.com/watch?v=NSK3FLQRMdE

[gray jungle]

it can be really fun once you get the hang of it

[remote ginkgo]

topology's useful af

[hearty steppe]

Topology is what allows us to make coordinate point associations in any kind of space to begin with before we can even classify it as Euclidean space even

[remote ginkgo]

in particular manifolds are exceedingly useful

you require a bit of topology to define them

[grand thistle]

i hate all this compactness connectedness completeness closed closure c words it feels dry af

[remote ginkgo]

in particular the isomorphism from the topological category is needed

[gray jungle]

it feels dry because you are using rudin

[grand thistle]

that's fair

[remote ginkgo]

@grand thistle part of that is because compactness is an unfortunate accident of the universe

it was supposed to be limit point compactness

a much nicer notion

but when you throw away metrizability

[hearty steppe]

I finished lecture 4 of Schuller like two days ago from that whole Diff geo YouTube series you shared me

[remote ginkgo]

limit point compactness becomes insufficient

[hearty steppe]

Great lecture on topology

[remote ginkgo]

so you need the much shittier notion of compactness via open covers

[grand thistle]

covers

[remote ginkgo]

glad to hear

[grand thistle]

another c word..

[hearty steppe]

https://youtu.be/1wyOoLUjUeI

I am on lecture 5 now

[remote ginkgo]

excellent

i rather liked his first couple of lectures on logic

surprisingly good

also the lectures on bundles will change your life

[hearty steppe]

Oh I thought they were good but didn’t sit through the whole bits for the first couple lectures

[remote ginkgo]

once you get to them

[remote ginkgo]

truly a mistake!

there were highly nonobvious results there

he answered many questions i had from years earlier but never had seen someone explain

[hearty steppe]

He definitely makes a lot of stuff come together in so many ways I wish a book could

[remote ginkgo]

they can, you just have to find the right books

one i do recommend is kobayashi&nomizu

[gray jungle]

tadashi takieda seems to have lectures on topology available on youtube , is anyone familiar with them?

[remote ginkgo]

heard of them, never seen

[gray gazelle]

The Adventures of Huckleberry Finn

[fierce hedge]

I have them saved but haven't watched them. As per description they are more of a geometric approach to topology, with minimal point set topology

[devout sphinx]

I think I watched a video by him on Möbius bands and it was very good

[limber tiger]

Taking intro to abstract algebra in fall. Any book recommendations?