#book-recommendations

1 messages · Page 240 of 1

willow pecan
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你吃饭

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You eat food

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你吃饭了吗?

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Have you eaten food?

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了 signals past tense and 吗 makes it a question

static crest
zealous jetty
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Oui, j'ai mang3 le riz

clever fox
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hey does anyone have any book recommendation for topology!

willow pecan
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Munkres is the standard topology book

storm sleet
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Mendlesons intro to topology is a very easygoing (maybe too easy) Dover Book. I used it to get a basic intuition, then moved to Munkres

gray gazelle
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Munk munk munk

ripe granite
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munkres is popsci for nerds

sudden kindle
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"Standard"

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A lot of standard books are trash

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Ahlfors is trash

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Hartshorne is trash

willow pecan
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Is Munkres trash?

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I've never looked at it

sudden kindle
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Me neither

sage python
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Munkres feels way too long for most people lol

clever fox
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wait i need it to be proof heavy btw

quick hornet
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id be surprised if there was a topology book that WASNT proof heavy

clever fox
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i don't mind it being too long as long as it's good hehhe

quick hornet
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what are you doing in topology if youre not proving things?

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computing standard bounded metrics??

zealous jetty
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learning topology from munkres can be pretty bland I think.. lol

clever fox
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so mendlesons is good right ty i'll look into it!

marble solar
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RIP Miura

timber ravine
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🤔
What about just modern-ish?
Like a Big Hero 6 kind of thing
That's not common?

manic fox
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hi ragh hmmm

willow pecan
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This just in: conversations have context

timber ravine
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Should have thought of that; it's a better example of what I meant

atomic stag
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What was the name of Sivik's book for calculas?

quick hornet
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Calculus

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by michael spivak

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is, im assuming, what youre after

whole rain
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you can also check out the first chapters of lee's topological manifolds, depending on what you're looking for, it may be a nice choice too holoApple

sage python
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Shika's book might be good, without contradicting that I'll toss in my 2 cents: I don't think point-set topology is something to spend too much time on

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Unless you're doing specific things that rely on heavy stuff

whole rain
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these notes are a bit too terse imo

whole rain
sage python
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prepa
Baguette confirmed

clever fox
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so thank u so much for the recs!

whole rain
clever fox
sage python
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Jokes aside good luck

clever fox
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tyty :D

prisma snow
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I would say it's a good choice if you like a looooot of explanations. Like iirc, it even explains like proof techniques

storm harness
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Did you mean to reply to ange hmmCat

prisma snow
whole rain
clever fox
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thanks everyone!! :D

vagrant sedge
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Hi. What are good books on functional analysis and measure theory that have not just theoretical exercises, but also more "computational-style" exercises and also exercises showing applications to other things (like "how to use this theory elsewhere")? Thanks.

prisma snow
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I think kreyszig is kind of an easy FA book with applications but it doesn't use or contain measure theory

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I don't know a good measure theory books with a focus on applications

gray gazelle
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nontheoretical measure theory catThink

prisma snow
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Let me rephrase

old jasper
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any good books on trigonometry?

gray gazelle
vale granite
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Differential geometry books?

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Except T. J. Willmore

gray gazelle
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people seem to recommend Lee a lot

vale granite
past comet
gray gazelle
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NCERT

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Best books

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for any Mathematics problems

frosty girder
hasty turret
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This is high level trolling

raven gulch
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I've been wondering if there is a book with everything about science in general

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Or a site

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I just want to find some organized place with a lot of information

zealous jetty
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w i k i p e d i a

raven gulch
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Except Wikipedia

zealous jetty
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scholarpedia?

hasty turret
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Wikipedia isn't helpful if you want to learn advanced material

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It either doesn't exist or the wikipedia answer is too difficult to understand

raven gulch
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But is there any place with a lot of deep information about mathematics and physics

hasty turret
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nlab?

raven gulch
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Looks nice

karmic thorn
gray gazelle
quick hornet
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i would not recommend any of these (nlab, wiki, planetmath) as a learning source

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theyre not designed to be pedagogically sound or self-contained

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as a compliment to another source, sure

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but youre not gonna find a one-stop place to learn things

gray gazelle
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do any of you know good books for counting and probabiliy?

raven gulch
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That is the problem i don't know what the topics are. I want to have an overview about every kind of math

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So then i could pick topics

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It looks nice

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Thanks

quick hornet
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napkin assumes you already know high school math

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fyi

raven gulch
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I am in high school

hearty steppe
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This looks like something that can be a little helpful for me as well

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Even tho I’m not in high school

frank matrix
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Highschool math is basically just algebra and geometry

vagrant sedge
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Not sure if this the appropriate channel to ask, but is there a "curation" of NPTEL courses? Like a rank of the various better ones for math, physics and engineering out there.

hasty turret
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It's usually better to use other sources compared to NPTEL, except for very specific topics

vagrant sedge
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Hmm ok.

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Is it that bad?

hasty turret
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What topics do you want to learn?

vagrant sedge
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Opps

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no no

hasty turret
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Yea, Balakrishnan is pretty good

vagrant sedge
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wrong link

hasty turret
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as far as I have heard

vagrant sedge
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same professor though

earnest relic
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Anyone have any textbook recommendation to learn about transforming highly nonlinear and complex models into finite-dimensional problems? In particular psudeo-spectral methods.

hearty steppe
vagrant sedge
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@hasty turret btw... sorry to insist on this.. but are the nptel stuff that bad?

hearty steppe
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I think I saw some kind of programming video off nptel that was really bland

gray gazelle
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Plain trigonometry written by nathan o niles is a good book to start learning trigonometry?

gray gazelle
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@vagrant sedge no there just tends to be better alternatives for very mainstream courses

vagrant sedge
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Thank you.

noble kettle
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Hi

hasty turret
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It's usually some guy reading a textbook word to word

karmic thorn
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But yes, most courses offered by NPTEL are...bad.

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The ones being offered recently are improving on a pedagogical level, especially by the younger faculty.

karmic thorn
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Try Manga Guides.

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Hmmmmm

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Pugh's Analysis

gray gazelle
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did someone say tiddies?

karmic thorn
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Yeah, Pugh's Real Mathematical Analysis

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Or in fact

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Gimme a moment

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@fast portal

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There's also a playlist on Knot Theory on YouTube, the animations are very nice.

manic fox
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no, they are knot

karmic thorn
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To be or knot to be

gray gazelle
hasty turret
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Ok?

sudden kindle
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Homotopical Topology

tulip blade
karmic thorn
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I didn't like it that much, the approach didn't click with me.

gray gazelle
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the book is good if used right

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let me tell you, it does not pair well with an analysis class where rigor and proving everything is the norm

karmic thorn
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It's probably more of a book actively used along with a class, not so much for studying on your own.

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Lol

gray gazelle
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i am coping

karmic thorn
gray gazelle
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a month and a half after the end of the course and i am coping stare

karmic thorn
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Archimedean principle proof when

gray gazelle
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i try so hard

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and it keeps coming back to haunt me

marble solar
whole rain
gray gazelle
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the grading policies in this course were...

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extreme, let's say

marble solar
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did you come out ok?

gray gazelle
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yeah i got an A-

whole rain
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Like I don't think it's not rigorous to not prove something you'd be able to prove (I mean, outside of any school context) thinkies

marble solar
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I got shrekt in real analysis

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Two B-'s

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and a C

gray gazelle
marble solar
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Eh it's ok, I got a paper in PDEs

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🤷‍♂️

whole rain
sage python
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Honestly props for not getting traumatized

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I feel like if I did poorly I'd have probably just let it get in my ahead and avoid it

gray gazelle
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hey, any recommendation on a book to teach myself calculus?

hasty turret
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Spivak calculus

gray gazelle
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my background is :
ive completed precalculus and thats it

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oh okay

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ill take a look at it

hasty turret
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:)

gray gazelle
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there isnt much of a big difference between a book and another right?

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like, they are going to teach me the same things

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i assume in different approaches or smthn

sage python
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Spivak Calculus is if you want to have a very rigorous, theoretical treatment of calculus

gray gazelle
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oh maybe thats not exactly what im looking for then

hasty turret
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I guess Thomas might be better

velvet briar
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Most textbooks/youtube will give you a mechanical intro

hasty turret
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Or just watch a YouTube series

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Most highschool books are not worth it

gray gazelle
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i see then

velvet briar
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I wouldn't pass up Khan Academy as he has a curriculum

sage python
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Stewart's the standard for calculus

gray gazelle
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oh yeah i think ill use khan too

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just thought of a book as a complement to khan

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or khan academy as a complement to a book

sage python
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Eh idk if I should recommend Stewart

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Thing is I feel like a lot of calculus books at that level are kinda isomorphic

gray gazelle
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what do you mean by that

sage python
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Like the price difference between Stewart and other books is gonna be wayyyyyy higher than the quality difference

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And there may very well be a cheaper book that's equally good/better

broken meadow
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you shouldnt do stewart if possible

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or any of the other isomorphic ones

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like if you have to do it

gray gazelle
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mentioning piracy is against the rules right

broken meadow
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at least find a pdf somewhere

warm glen
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what ab paul's online notes to learn calc

broken meadow
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somewhere uh

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pauls notes are okay

viral hill
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is apostol one of the isomorphic ones?hmmm

broken meadow
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no

sage python
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Nah Apostol is more like awkward Spivak

warm glen
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ive posted this before but

gray gazelle
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uhh regarding price, lets say i have uhh

warm glen
gray gazelle
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i might do a little bit 🏴‍☠️

sage python
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So the rule here on piracy is, we're not gonna like

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Report you to the cops because we suspect something

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And I don't know how many individuals here care that much

gray gazelle
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ah great

sage python
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But discord TOS is that we don't promote/encourage/engage in illegal behavior

gray gazelle
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Oh yeah i get that

sage python
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So yeah I'm just gonna say about Stewart that I don't think it's so special to be worth the sticker cost. The theorems are the same. If you have some method of acquisition such that the cost is similar between books, be it buying used editions or something more dubious, then I take back my anti-recommendation because I don't know the alternatives

gray gazelle
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oh i see

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lets say that

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all the books cost the same

sage python
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So in that case I'd wager Stewart's probably fine

gray gazelle
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oh great

sage python
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There might be better choices but I imagine if it wasn't one of the better ones it wouldn't become so standard in schools

gray gazelle
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nice

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i dont think my school covers calculus

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well, i hope i can go through 631 pages of math

sage python
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Stewart is like

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3 semesters I think

pseudo forge
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for electrical engineering, calculus 1-3, do you folk recommend Stewart, MIT OCW or Pauls online notes?

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or something else?

storm sleet
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I’ve heard good things about OCW, Paul’s notes are a fantastic supplement in general

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And the above convo recommended Stewart, so I’d opt for that and use the others as supplements as need be

vagrant sedge
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Btw... what do you guys think of Edwin Moise's Calculus book?

sage kelp
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Hello everyone. I would like to know what's your opinion on Abbott's real analysis book. Also, I would like to take advantage and say that I'm looking for a study buddy for real analysis, if anyone is interested

gray gazelle
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Is Gamelin's book good for complex analysis?

gray gazelle
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nice selection of topics, fair number of examples

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the residue integration section in particular is very thorough

sage python
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My impression of Gamelin is that it's the best book for people who don't have a lot of background

gray gazelle
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Thank you! I took a "Complex Variables" course that had no rigor whatsoever

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And would like some proper complex analysis

sage python
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Complex analysis is very cute

gray gazelle
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The only other complex texts I knew of were Alfors and adult Rudin, and I have sufficient fear of God, so I'm not touching those

sage python
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What's your real analysis background?

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Actually I'll just say check pinned messages

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I put a review of complex analysis books

gray gazelle
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Lovely, thank you very much!

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Oh, and you have an algebra one too! That's great

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and I have sufficient fear of God, so I'm not touching those
KEK

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don't worry ahlfors is not as hard as rudin

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ahlfors is alright

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I own baby Rudin
If the baby is that ugly, I don't wanna see the papa

static crest
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ahlfors good

gray gazelle
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my notes r better

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/s

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I'm currently reading through Hubbard^2. I then plan to go to Analysis I/II (Tao), Munkres, Lee (Smooth manifolds), and then Lee (Riemann)
I'll squeeze complex and algebra in there somehow

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lee riemannian manifolds stareFlushed

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Is that a bad choice?

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no not at all

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i really like that book

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I want to learn diff geo (and math in general, lol).
I've been doing physics up until now, but I'd like to know what in the fresh hell I'm actually doing

gray gazelle
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Is it good if I try to self study linear algebra from Friedberg book?

willow pecan
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Sure

craggy imp
sage python
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Hard disagree

gray gazelle
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Hmmm, I was afraid that if I choose those, I'll have a harder transition when I want to move to a more applicative based side

sage python
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Axler thinks about char poly and determinants like a moron

craggy imp
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You dont like it?

willow pecan
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I don’t either

sage python
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It's probably good exposition in the first part

craggy imp
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To be fair i didnt read the last bit

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I liked all of what i read, which was most of it

gray gazelle
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I just heard Friedberg has balance between pure math and application math kind idk

viral hill
gray gazelle
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So that's why I ask here to make sure o.o

willow pecan
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Yes Friedberg is a fine book

gray gazelle
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friedberg is nice

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i like it

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Okay thanks 😄

sage python
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But like he says char poly is given by, complexify, upper triangularize, product of t-diag

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Which is so stupid

craggy imp
craggy imp
sage python
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Friedberg seems good, I partially used Hoffman-Kunze which is old school but good

gray gazelle
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the alternative is just defining a determinant stare

sage python
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Oh oh

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Yeah just define determinants conceptually

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Computationally and using exterior products

gray gazelle
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so good

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axler fanboys in shambles

willow pecan
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Product of eigenvalues

sage python
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Ehhhhhhhhhh

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I don't like the idea of passing to a larger field when you can just work in the field

willow pecan
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Real matrices have real eigenvalues

sage python
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Uhhhhhhhhhhhh

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Wait you're trolling right?

willow pecan
sage python
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This isn't helping me figure out whether you're trolling or not lol

gray gazelle
sage python
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I'll assume you are

willow pecan
craggy imp
gray gazelle
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By the way, the friedberg book itself is self-contained right?

(means I don't need anything outside high school math, probably requiring some experience in proof writing, which I have).

craggy imp
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Yeah would just require high school algebra

gray gazelle
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Okay 😮

craggy imp
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The proof writing you pick up as you go

manic fox
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le algebraic closure of a field has arrived

gray gazelle
hasty turret
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You can skip a significant portion of Tao and still be fine,I think

gray gazelle
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Duly noted. I've gone through the construction of the natural numbers already

manic fox
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you can skip all of tao and you will be fine

gray gazelle
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What would you recommend instead?

manic fox
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i just wanted to take a jab at tao opencry

gray gazelle
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Fair OMEGALUL
I thought you were going to recommend baby Rudin to me, had some heart palpitations there

manic fox
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i think just read around and see what u like best

gray gazelle
manic fox
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catshrug everyone is very different

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hmmCat so ppl learn diff and with diff approaches

gray gazelle
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I actually like Rudin, but I'd like to use it as a supplement

manic fox
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go for it 😌

craggy imp
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Didnt get it for my life

hasty turret
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Same for R,you just assume R exists and has the least upper bound property

gray gazelle
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Fair

manic fox
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i mean u can construct them definitely hmmm

small garden
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what's a good way to access research papers? (in compliance with rule 7 lol) I know that I can get them from my university but mine isn't that great so they probably won't have really niche stuff

hybrid sparrowBOT
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Rule 7

When asking for help, do not insist on getting just the answer; we are here to help you learn, not cheat. Likewise, if you are providing help to others, try your best to explain and elaborate instead of simply giving away the answer.

storm harness
quick hornet
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arxiv

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assuming they were published in the last couple decades

gray gazelle
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hello!
i am applying to ug computing in 2022.
i'll be grateful to get some recs for sequences and series.

small garden
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oh what

golden bear
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Are these two books good to review before I head to grad school? I never took Undergrad abstract algebra

quick hornet
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wow stillwell is a bizarre text

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in any case, that isnt sufficient if youre going to actually do any algebra in grad school

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very minimal commutative algebra exposure

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also very little rep theory (van der waerden only has 1 small chapter on rep theory and its in volume 2)

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that said, if you managed to get into graduate school without any algebra, then you probably wont be doing any algebra in grad school

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so i guess thats not a concern

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in which case, probably sufficient although if youre doing analysis/topology id still recommend doing a bit more if possiblee

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wait, what do you mean by review?

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do you mean you learned abstract algebra but never took a formal course?

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in that case my advice changes

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(and you probably wont need stillwell at all)

golden bear
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I NEVER took a formal course.

quick hornet
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but you did learn the content before?

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if so then the van der waerden series should be fine

golden bear
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No

quick hornet
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then what do you mean by review?

golden bear
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My transcript does not have abstract algebra

golden bear
quick hornet
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perhaps we're using different definitions

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how are you defining "review"?

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I assumed this definition:

view or inspect for a second time or again.
"all slides were then reviewed by one pathologist"

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i see no other definition in google dictionary that seems to fit your intention

golden bear
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I think of review as a short introduction of the material. So that way I can have some knowledge of the terms and such.

quick hornet
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perhaps you meant "overview"?

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in that case, then sure

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the VDW series can be skimmed for a solid overview

golden bear
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Overview sounds good

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what chapters should I focus on? I was thinking of the first four

quick hornet
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i dont know anything about stillwell

golden bear
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alright

quick hornet
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besides its table of contents being screwey

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what are you going to be doing in grad school?

golden bear
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What about van der waerden?

quick hornet
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its a classic but is pedagogically dated

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i wouldnt consider it a good source for a first learner

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but if you just want a reference text to understand the definitions and common problems we care about

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its fine

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(its intended for grad students who already have a bit of familiarity with algebra)

golden bear
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I'm going for a masters in math and the program I am going to offers complex and algebra this Fall.

quick hornet
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pure math, id take it?

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in that case, my recommendation would be as much as possible

golden bear
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the program is mix with applied and pure

quick hornet
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but at least the first 5 chapters

golden bear
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They going to teach stats

quick hornet
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exept maybe omit chapter 4

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its not crucial if you already know rigorous LA

golden bear
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StillWall the first five chapters?

quick hornet
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VDW

golden bear
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oh

quick hornet
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you can also probably skip chapter 1

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id also recommend reading chapter 7

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the others arent crucial

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but 2, 3, 5, 7, familiarity with vector spaces

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are what id consider the core algebraic backbone of an upper undergrad/early masters student

gray gazelle
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What subject u talking of?

quick hornet
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van der waerdens algebra

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(copy-pasted from amazon preview, not piracy, dont nuke me discord admins)

gray gazelle
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Is that similar to contents of algebra by lang

quick hornet
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like the first half of lang

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ish

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van der waerden comes in 2 parts and they only have pt 1

golden bear
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is chapter 4 good if you forgot about LA?

gray gazelle
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Someone recommended me algebra by Lang when I said i wanted to refresh my algebra, but I meant hs algebra

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Lol

quick hornet
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sure, it can be a good refresher

golden bear
quick hornet
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up to like 4.5

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the tensor stuff is low priority

golden bear
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what about 6?

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chapter 6

quick hornet
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not high priority, mostly buildup to galois theory

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knowing stuff like what a root of unity is is certainly a good idea though

golden bear
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SO I have Chapter 1, 2,3, 4 (up to 4.5), 5 and 7

quick hornet
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(an nth root of unity is a solution to z^n = 1; there exist precisely n in ℂ for each n)

golden bear
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I will learn that in complex

gray gazelle
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Why don't u read it all

quick hornet
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again, thats what id consider the minimum working knowledge

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if you can do more, do more

gray gazelle
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No harm in learning all of it

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The more u learn the better

golden bear
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Also, health is important too.

gray gazelle
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U have a deadline?

golden bear
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I don't have a deadline

gray gazelle
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Then just go at it slowly and take break days

golden bear
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Yea, I am starting like June 6

gray gazelle
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Do u have to kno it by a certain date

golden bear
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Not really. It would be nice to get to 4.5 by July 26 or so

gray gazelle
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Then take ur time and learn it all

left crown
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Can someone recommend me a good trigonometry book?

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I am in the 9th grade from Romania(( choose the hardest type of math that I could

gray gazelle
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Search this channel with "in:book-recommendations trigonometry book"

crude iris
narrow talon
#

Is there a set of lectures available online for grad PDEs? Just to follow along with Evans

craggy imp
narrow talon
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just basic existence, uniqueness, and regularity results of elliptic and parabolic PDEs

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I like Brezis a lot and have read enough to not be somewhat comfortable with Sobolev spaces but that’s all

slim peak
narrow talon
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Sure, sounds a bit more advanced than basic PDE theory but Ill trust your rec

slim peak
#

You don't need other stuff than basics of semigroup theory, and basic Sobolev Spaces knowledge. Notice also the above book deals with semigroup theory almost from scratch using accretive sesquilinear forms (then later in the book it is given some sufficients conditions to extends the involved semigroup on Lp using almost full abstract Functional Analysis arguments)

narrow talon
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👍 thanks! That’ll probably be most useful for me then

hearty steppe
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After a quick skim through Chen’s Napkin it would be hard for me to recommend it to high schoolers. Maybe gifted high schoolers that maybe did some Olympiad but if you don’t fall into that category, save yourself from using it as first exposure. Seems like a good reference read or something to reflect back on after learning a bit of modern algebra

narrow talon
slim peak
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libgen

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probably

narrow talon
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Weird, I searched the text name and found nothing, but searching the author worked. My bad pacman

analog pollen
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Any recommendations for a book on diff eq and linear algebra?

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That are good

gray gazelle
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hirsch smale

warm glen
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the explanations in both are pretty easy to follow

vagrant sedge
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Hi. I have taken a first course in linear algebra (twice actually) using Hoffman & Kunze. I was looking for a material good for self-study that would serve as a course after that which was focused on preparing for a more numerical methods/analysis and optimization sort of use of linear algebra. Any recommendations? I have "Matrix Analysis" by Horn and Johnson in mind. What do you guys think?

willow pecan
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For numerical linear algebra, I would suggest either Demmel or Trefethen and Bau

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These are the two standard texts on the subject

warm glen
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has anyone read "geometric approach to differential forms" by bachman

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it seems cool

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and has very few prereqs

pale scarab
#

Any good math blogs to check out that are not geared at professional mathematicians? I know tao is quite popular but many of his posts go way over my head

manic fox
#

good question actually thonk

broken meadow
#

undergraduate math blog when

vapid scroll
remote ginkgo
#

but honestly

#

i have to recommend shifrin's multivariable mathematics or spivak's calc on manifolds for a more complete intro to the subject

#

bachman is a really good primer though

warm glen
#

nice that's cool

#

ty for the info

#

i been looking for stuff like bachman that i could self study without too much stress over the summer

pale scarab
broken meadow
#

lolialgebra

#

what

#

scary

livid ermine
#

Have anyone read the book Combinatorics and Graph Theory by Harris?

#

Is it any good as an undergrad combinatorics book?

buoyant eagle
#

Can anybody recommend a book on dynamical systems? I'm a researcher in epidemiological applications of agent-based network models and I have a degree in math, but I've never so much as opened a book on dynamical systems.

#

In return I offer this

#

I'd be interested in both theoretical and applied approaches. Bonus points if it includes graph dynamics.

willow pecan
#

Strogatz has a book on nonlinear dynamics

sudden kindle
#

Ah the memes

obsidian valley
#

what is the best book to learn do Carmo content from

#

is it do Carmo

#

or shifrin

#

or osmething else

#

tteppa fone

gray gazelle
#

curves and surfaces, or riemannian geometry?

gray gazelle
#

Any good books on numerical analysis?

willow pecan
#

What sort of numerical analysis?

#

If you want numerical linear algebra, either Demmel or Trefethen and Bau

#

For ODEs/PDEs, Iserles has a book

#

LeVeque has a few as well

obsidian valley
#

I was told I can waive the pre-req for geometric analysis & relativity

#

but i need to get some diff geo knowledge

gray gazelle
#

(If you know of any general introductions, though, please do tell)

willow pecan
#

I don't know of any good general introductions

sage python
#

@obsidian valley waive the curves/surfaces prereq for those two? I mean just do the book the class uses probably

obsidian valley
#

No sorry it's one course

#

called Geometric Analysis & Relativity

sage python
#

Ah

obsidian valley
#

the pre-req book is do Carmo

#

but I have a choice

sage python
#

Honestly my impression is that it's the correct™️ book for that content lol

obsidian valley
#

so I'm wondering if something does do Carmo better

sage python
#

I don't like Shifrin

obsidian valley
#

hm okay I think I will use do Carmo

sage python
#

There might be others but it seems do Carmo is common and I dislike the one alternative I know so yeah lol

last cloud
#

Hello people, I just started delving into Machine Learning. Any recommendations for Linear Algebra books which will be relevant ?

willow pecan
#

You should first learn linear algebra with Friedberg's book

#

Then you should learn numerical linear algebra with either Demmel or Trefethen and Bau

buoyant eagle
last cloud
#

How is Sheldon Axler's book ?

buoyant eagle
#

beautiful

#

Both aesthetically and pedagogically imo

willow pecan
#

Axler is not that good

last cloud
willow pecan
#

The presentation of characteristic polynomials and determinants is lacking

gray gazelle
#

"lacking"

#

you can be honest

willow pecan
hasty turret
#

Axler also causally assumes choice

willow pecan
#

Casually

#

Choice is not a big deal in applied subjects

buoyant eagle
#

I should add the caveat that when I read math books I'll read multiple on a subject using a hub and spoke type model- one friendly and readable book to give motivation to the subject and foundational knowledge (hub) and others for different perspectives and coverage. Once I move through a topic in the hub book it makes all the other (potentially less readable) books much easier. So in that context Axler is a good "hub" for LA imo.

hasty turret
#

True

willow pecan
#

Because unless you're doing QM, everything is finite dimensional

quick hornet
#

choice doesnt matter in applied subjects because the cases where you need choice never arise

#

and choice just makes theorems for those cases line up with theorems for more finitary cases

#

so it only really cleans up theorem statements

#

with no real downside

#

choice doesnt matter in pure subjects because everyone accepts it anyway

#

so who cares

#

its coconsistent with zf and thats enough for me

sage python
#

Even if you're doing QM aren't you gonna likely stick to separable Hilbert spaces?

#

Anyway for the most part nobody really cares about choice. I honestly don't buy the philosophical problems people have with it even in general, and regardless in any reasonable applied setting there's no real question lol

#

Problem with Axler is that he teaches you how to think about char polys and determinants like a moron

quick hornet
#

the philosophical objections are valid since its a weird axiom relative to the ZF ones

#

so its at least worth thinking about

#

the philosophical consensus is almost overwhelingly "yeah its fine" unless you also reject like

#

the axiom of infinity or LEM

sage python
#

Or I guess I don't mean on a logical level so much as... idk surprising things are true in life yeah?

#

And I'd wager that choice is sorta "obviously true" and makes a lot of things work

quick hornet
#

which seems to me like a reasonable interpretation

#

choice is worth thinking about

#

but when you think about it

sage python
#

The bizarre consequences then just become facts of life

quick hornet
#

its not that weird

#

cartesian products of nonempty sets ARE nonempty, mom

sage python
#

Well when I say "buy the philosophical problems" I don't mean "Shut up and accept it" so much as

#

If you end up disagreeing with it I will give you a lot of side-eye

quick hornet
#

i maintain that the real problem with choice is actually power set

sage python
#

Sleeps_irl

quick hornet
#

and you should weaken power set before choice

#

fixes literally all the counterintuitive shit

#

alas

sage python
#

I mean life has counterintuitive shit lmao. Like I guess Banach-Tarski is the most commonly cited thing right?

#

To me it's just... yeah R is a big and very fucky set

#

So big that SO(3) contains a copy of the free group

willow pecan
#

Reals don't exist

#

Only rationals

sage python
#

Tbh you could prob make a case that thanks to Planck length or something, R isn't really a "physical" object, and so Banach-Tarski isn't a physical phenomenon

#

Back on topic though: yeah don't use Axler, not because of choice since that's not a problem, but because char poly and determinant

#

Friedberg is probably the correct intro to linear algebra nowadays tbh. I like Hoffman-Kunze but it's old school

smoky surge
#

i liked axler slightlyembarrassed

#

it was the second time i went through LA though

static crest
#

axler kekw

gray gazelle
#

Best calc 1 and calc 2 book?

static crest
#

spivak

gray gazelle
#

thx

tulip blade
# gray gazelle thx

uh Spivak is good but it is mostly proof-based and requires a decent amount of maturity.

storm sleet
#

Best introduction to module theory?

gray gazelle
flint forge
#

define best

tulip blade
#

There is no best calc book. It is the best for SOME people but for others it would be a horrible choice. Why are you learning calc and what are you goals @gray gazelle

flint forge
#

spivak is the best book for a potential math major for sure

gray gazelle
#

Something with all the topics and necessary info to have a good understanding of calculus. Preferably better than the average calc student

flint forge
#

but idk if its the best if all you want is to compute integrals quickly

#

yeah it depends on what you wanna understand

#

like if the “why” matters

gray gazelle
#

Simply put I wanna kno more calc than my peers who r also taking calc 1 and calc 2

flint forge
#

spivak

tulip blade
#

Then try stewarts book

flint forge
#

spivak is a solid choice but thats a not great motivation hahaha

broken meadow
#

what is "more"

#

lmao

#

like

tulip blade
#

Something like transcendentals

flint forge
#

lmao

broken meadow
#

do you want to know how to compute more integrals or

gray gazelle
#

I mean i wanna know all calc 1 and 2 b4 I move on

flint forge
#

just learn a bunch of dumb set theory and you can flex nonsense

gray gazelle
#

I just mean I wanna do well in my calc class

broken meadow
#

become a hs category theorist

#

or ug

flint forge
#

yeah spivak is a good choice but honestly

broken meadow
#

whatever

flint forge
#

basically any textbook

#

will be fine

#

for hs

#

like if you can do all the problems

gray gazelle
#

And I wanna understand calc well

flint forge
#

in any standard calc book

#

youll be fine

broken meadow
#

when i was practicing calculus the textbook i did practice problems from was stewarts calc book (any of them)

tulip blade
#

Spivak would be very difficult. Most ppl ik who used it already took a discrete math class

broken meadow
#

i went to the section labeled "problems plus"

#

it was nice

karmic thorn
#

The problem sets from MIT OCW's single variable calculus course are very good.

gray gazelle
#

I just meant I wanna know it and understand it well

flint forge
#

i think you are too worried about book choice

gray gazelle
#

Better than the average person

flint forge
#

if you pick a book and hate it

#

then whatever find a new one

#

but youll be fine w basically any choice

broken meadow
#

im not really sure you know what you want well enough to determine if a certain book is more fitting for you than another

gray gazelle
#

I heard Courant is also good

broken meadow
#

because "better understanding" is vague

#

like spivak will help you understand some theory better is what i hear

gray gazelle
#

I took calc but I still feel like i don't fully understand it

#

I took ap calc

sage python
#

I mean the problem is "being good" is vague

flint forge
#

then do spivak

sage python
#

You can be an integral monster

#

Or you can know the theory

broken meadow
#

right if you've already taken ap calc i see no reason to do stewart

sage python
#

If you wanna know the theory then Spivak is the objectively correct answer

broken meadow
#

you're not going to learn anything new

#

go with spivak then like max suggested

gray gazelle
sage python
#

If you're more interested in computations but really getting good at them then... honestly any calc book works. Stewart at its sticker price isn't worth it. Tbh it's more at that point about practice problems than books

gray gazelle
#

Is there a book u prefer

#

Some books would have better problems tho or even more problems

flint forge
#

spivak for theory , lots of problems for computations

#

from various books

#

just prte them

#

shoot

tulip blade
#

Just use spivaks calculus on manifolds

flint forge
#

p*rate

tulip blade
#

\s

broken meadow
#

yes

#

i mean

#

No!

sage python
#

You can find problems online. Stewart if you can get a used copy or [REDACTED FOR TOS] is probably good but no calc book is worth $200 lmao

broken meadow
#

i can't condone piracy here

#

!

flint forge
#

who said piracy

broken meadow
#

i mean uh

flint forge
#

i meant parote

broken meadow
#

parote.

flint forge
#

porate*

sage python
#

How dare you

broken meadow
#

yes you should keep that as a secret

gray gazelle
#

I guess for problems I can just find different books and do those problems

tulip blade
#

@lucid yew

sage python
#

Yup

#

So if you wanna get good at problem solving do that

gray gazelle
#

But for theory spivak is good

flint forge
#

i will also say that like

sage python
#

Exactly

flint forge
#

honestly

#

youre probably a bit too anxious about this

gray gazelle
#

Alr thx

broken meadow
#

breathe

flint forge
#

unless ur training for an integral bee or something

#

calc 1/2 isnt that scary if you like math and are willing to do the work

gray gazelle
flint forge
#

Well

#

i suck at calc

#

and i am accepted for a phd

#

so

gray gazelle
#

Really?

flint forge
#

youll be fjne

#

fine*

tulip blade
#

Calc is dum

sage python
#

Linear algebra, on the other hand...

broken meadow
#

i never did spivak and no one cares how well i understood calc 1/2 material

#

well

tulip blade
#

Spivak is kinda like baby analusis

sage python
#

Metal prove the mean value theorem right now or I'll make you do a backflip

broken meadow
#

at least that's what i perceive

#

uhhh

gray gazelle
#

I didn't understand trig well so I had tuff time with calc regarding those sections,, so I don't wanna have any issues with not understanding calc well

broken meadow
#

rolles theoem but u do cute subtraction

gray gazelle
#

I also didn't understand some specific advanced algebra topics

broken meadow
#

idk 💀

#

im gonna learn all these things in real analysis right

sage python
#

Honestly there's a pretty easy flowchart for how to prove things

broken meadow
#

oh i was responding to daminark earlier human

sage python
#

The key point is intermediate and extreme value theorems

flint forge
#
  1. ask your advisor
#
  1. give up
gray gazelle
#

Is analysis the same thing as calc? I looked it up and it said it includes differentiation, integration, series, etc..

sage python
#

That takes either some pain or some topology

#

But once you know that it's like

broken meadow
#

it is not the same

flint forge
sage python
#

So there aren't clearly defined boundaries here

tulip blade
#

We know what it is

sage python
#

Some people say calculus is just analysis without proofs

broken meadow
#

well that kinda makes sense but like even then analysis has so many things you won't see in a calc class

sage python
#

To me analysis is a broad subject, calculus is the part that's concerned with computations of derivatives and integrals

flint forge
#

yeah it goes further

flint forge
#

turns out if you dont spend months calculating convoluted integrals

#

you can actually learn

#

some math

gray gazelle
#

Could someone just skip calc and do analysis?

flint forge
#

yeah

tulip blade
#

Yea

flint forge
#

it would be hard

flint forge
#

but doable in theory

tulip blade
#

Just use spivak

sage python
#

Depends on your definitions, to me calculus is part of analysis. So at some point in an analysis class, if it's self-contained

golden bear
golden bear
gray gazelle
#

Calc is more like a warm up

#

Analysis is the actual run

flint forge
#

sure

tulip blade
#

If theyre interested in analysis spivak isnt a bad choice. They have computational problems too

sage python
#

You'll learn theorems like product/chain/quotient rule, u-sub, etc

gray gazelle
#

I kno how to do those

sage python
#

That will come up in a self-contained analysis class and I'd consider that to be "calculus content"

flint forge
#

nah

golden bear
#

Assuming you're a high schooler @gray gazelle ?

flint forge
#

dami

#

these are broke ass defns

golden bear
#

9th?

flint forge
#

analysis is a matter of perspective not material imo

gray gazelle
#

Dam no

#

12

#

They don't teach calc at 9th here

#

You'd have to test out of classes or self study for that

flint forge
#

almost no one learns calc that young

#

dw

golden bear
#

Usually on this server, you have 6th graders do analysis

flint forge
#

thats so false

sage python
#

Usually?

gray gazelle
#

Fr

broken meadow
#

jesus calculus in the 9th grade

sage python
#

There's like

flint forge
#

and also perpetuates an already unhealthy narrative

tulip blade
#

Theyre joking

sage python
#

< 5 people here who know calc in 9th grade

flint forge
#

that causes young people here to have pointless an iety

flint forge
# tulip blade Theyre joking

these jokes have genuinely caused hs kids on here to be worried about only being 2 years ahead of their peers lol

gray gazelle
#

Yea when I was younger and i read about terence tao I thought u had to be like him to be a mathematician lol

golden bear
#

But in the USA. to get into college. you have to start taking rigorous courses in middle school

broken meadow
#

no

#

that's just wrong

sage python
#

That's kinda bullshit lmao

sage python
#

I learned calculus poorly in high school and only learned it well in college

tulip blade
#

I never took calc in high school

flint forge
#

killerwhale you should stop talking about things you dont know anything about

#

its not good to misinform young ppl

broken meadow
#

im in college??? i didnt think of math at all until the last year of highschool and honestly i could have just left it at that

sage python
#

Like when I took the calculus placement exam in college I only placed out of one quarter of calculus

flint forge
#

i never took anything past ap calc in ha

#

hs

gray gazelle
#

Yea i've learned calc poorly as well so I'm going to spend some time strengthening it during the summer

golden bear
sage python
#

Aka I knew differentiation well enough but not integration

broken meadow
#

???

sage python
#

And I went to a pretty good school, did well while there

golden bear
gray gazelle
#

no one could possibly be interested in math, ever

flint forge
#

lmao

#

so cynical

broken meadow
#

that seems like a really unsound generalization

#

lmfao

sage python
#

Killer's just full of shit lmao

gray gazelle
golden bear
#

nah

sage python
#

Yeah human I'm sure your progress is just fine

flint forge
#

u r embarassing urself @golden bear

#

@gray gazelle ur chillin

gray gazelle
#

Thx

tulip blade
#

Yea human never mentioned proofs we mentioned spivak tbh

sage python
#

Again I didn't know the definition of the integral until college lol

#

I thought it was just antiderivative evaluated at endpoints

flint forge
#

lol

broken meadow
#

it be liek that

golden bear
gray gazelle
#

I don't remember the definition either but isn't it just the area under the curve

sage python
#

Oh no

#

Yeah you're probably gonna be trash lmfao

gray gazelle
#

i bought nitro so htat means i can sully bomb

flint forge
gray gazelle
#

Dam 🤣

broken meadow
#

you are free to sullybomb

sage python
#

Speaking of TAing

golden bear
sage python
#

That's good

flint forge
#

I dont see how thats related

#

so do I

manic fox
gray gazelle
manic fox
#

society if

broken meadow
#

this is rich coming from someone who is feeding anxiety inducing nonsense

flint forge
#

i care more about most things than math

sage python
#

Wait all mentally healthy people assume that high schoolers learning proof-based math is virtue signaling

gray gazelle
#

Health is important becuz it can keep ur brain healthy and able to do math

sage python
#

Max this is common knowledge

flint forge
#

shoo

#

shoot

karmic thorn
manic fox
sage python
#

They take Basic Algebra in middle school

broken meadow
#

im taking algebra 1 this fall i must be horribly behind opencry

tulip blade
karmic thorn
flint forge
#

my goal is to be

gray gazelle
#

i took multivariable analysis in my second year of schooling, catch up guys!!!!

flint forge
#

a B+ TA

#

like

#

i wont be the best

manic fox
flint forge
#

or even that good

golden bear
#

Even if I am a bad TA. The only difference between TA and a student is has to grade. TA are still students and will have bad days. Unless you are uncomfortable with that then maybe TA isn't going to be good for you

manic fox
#

yes bro

sage python
#

All of UChicago's undergrad course titles are so condescending

manic fox
#

people under 18 doing proofs is just virtue signaling

sage python
#

"Basic Complex Variables"
"Probability for those who don't know how to wipe their ass"

gray gazelle
#

Couldn't anyone theoretically learn calc very early if they know the prerequisites?

#

And even other math

karmic thorn
sage python
#

In principle

tulip blade
sage python
#

I think when you learn calculus is largely random in a way

manic fox
#

yeah but like ive found u need to have maturity otherwise to do some stuff thonk

sage python
#

Like some people look it up on Google young and are like :0 this is dank

willow pecan
#

r2t2 simps for discord

sage python
#

And get into it

flint forge
#

i tried to self teach young

sage python
#

Other people just stumble upon it when they take a class on it

flint forge
#

but got bored

golden bear
#

The rush to calculus is real in high school. Why rush to calculus?

manic fox
#

like you only begin appreciating things once you spend a little longer with the defns n stuff pepega

flint forge
#

in my defense

gray gazelle
#

If my school didn't spend so much time reteaching previous years and teaching stuff that didn't take long I'm sure everyone could've learned calc in 10th instead of 12th

manic fox
flint forge
#

calc is boring

sage python
#

Killer depends on what you mean by "why"

#

Why do students rush? Why does education frontload calculus?

flint forge
#

rush to calc is commonly frowned upon here and discussed in #math-pedagogy

manic fox
#

i have that channel muted

gray gazelle
#

By reteaching I mean they spend a month teaching content from previous year

manic fox
#

😌

sage python
#

Students tend to rush to calculus because either they just like math and that's the standard accelerated math path

tulip blade
#

My school disnt offer ap calc we only had higher topos theory instead

sage python
#

Or they're told that to get into a good college they need to have AP everything

manic fox
#

math path

#

mathpath not to be confused with matpat

golden bear
#

They rush because they think is a good approach into getting top schools. Every school thinks taking calculus 1 in high school will prepare them

flint forge
#

lurie should do a stint at a highschool

#

just for the meme

sage python
#

Which is an unfortunate phenomenon but it happens

manic fox
#

tfw knowing how to differentiate polynomials = good indicator of success

sage python
#

A lot of people in the calc classes I TA did some kind of AP in high school

willow pecan
#

Calculus is also useful in a lot of science and engineering disciplines

sage python
#

Now I actually thought AP was kinda pathetic because it's like, you're taking Calc 1 which is supposed to correspond to AB Calculus

#

And yet you're having a hard time

manic fox
#

killer u know what you should do

broken meadow
#

yeah i mean it makes sense that they want to learn calculus cus of stuff like physics and chem maybe

#

but like

manic fox
#

consider some tteppa

gray gazelle
#

First semester of ap calc was pretty ez

broken meadow
#

idk maybe they should focus on teaching the regular math correclty before rushing kids to calc

#

halfassedly

karmic thorn
#

The same is true of linear algebra, and surprisingly it doesn't see the same enthusiasm.

tulip blade
#

I rushed to do calc bc i thouught it was the end all be all

golden bear
#

High school calculus $\neq$ college calculus

manic fox
#

wtf ted is mod

hasty eagleBOT
#

KillerWhale2498

sage python
#

Tbf UW's calc class is non-trivial but yeah I thought AP was just lol. Then I looked at some free response questions from the AP exam and tbh they don't seem like the worst

tulip blade
#

Then i stopped once i learned other math existed

karmic thorn
manic fox
#

cringe moderation team

sage python
#

Manan: I have actually said I'd rather frontload linear algebra than calculus

karmic thorn
#

I agree.

broken meadow
#

ap linear algebra when

flint forge
#

i would frontload stats

manic fox
#

ap category theory pepega

karmic thorn
#

Why so?

flint forge
#

more important to have a vaguely data literate society

broken meadow
#

i also think stats is honestly more worthwhile

tulip blade
#

I would frontload machine learning and data science

flint forge
#

than linalg

manic fox
tulip blade
#

Jk thats cringe

broken meadow
#

statistical thinking is so important nowadays

manic fox
#

stats is a pain

tulip blade
#

Id front load combinatorics tbh

manic fox
#

if you do it wrong it's going to like

#

🤮

broken meadow
#

at least for stuff on the news and all

manic fox
#

be terrible

karmic thorn
#

I'm currently taking stats and the subject is super interesting, but it is already assuming a theory-heavy calculus/analysis background.

flint forge
#

like being able to understand expected value, basic probability, how to read graphs and look for manipulation in fitting

broken meadow
#

its scary how much data is presented oddly

golden bear
sage python
#

MaxJ that's true, I guess I mean that I think linear algebra should be the default "I want to accelerate in math" choice

flint forge
#

are all wayyyyy more important

#

than linalg

#

for most pol

manic fox
broken meadow
#

right dami

sage python
#

While data literacy should be more "basic high school graduation requirement"

broken meadow
#

right

flint forge
#

sure

#

fuck it kill precalc and calc do both

broken meadow
#

lol

manic fox
karmic thorn
sage python
#

I have no clue what precalc entails but tbh sure

broken meadow
#

precalc is just like

#

polynomials and trig

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or something

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idk

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i didn't learn anything in precalc

golden bear
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Algebra is everything.

broken meadow
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end me

tulip blade
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Precalc is galois theory

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Polynomials and stuff

flint forge
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precalc is commonly described as preparing you for the algebraic/analytic manipulations youll need in calc

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but without any reason to it

broken meadow
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oh yeah

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conic sections

sage python
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That sounds boring lol

broken meadow
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why did i even learn conic sections

flint forge
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it sucks

flint forge
broken meadow
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literally only used conic sections for obscure integrals in calc 3

karmic thorn
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Kindergarteners are combinatorists.

sage python
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My high school math last two years was weird

broken meadow
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WhAT

tulip blade
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Fuck im not taking the gre

broken meadow
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the GRE 😭

tulip blade
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Only general 😎

karmic thorn
sage python
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It was IB Math which had 6 topics

golden bear
flint forge
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metal theres a healthy chance youll never have to

broken meadow
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never have to what

karmic thorn
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Why should I know what the eccentricity of a weird conic section is

tulip blade
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That moment when you switch to cs theory to avoid math subject gre

flint forge
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take the mGRE

golden bear
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2.95 GPA got into a masters with TA. I mean anything can be possible

flint forge
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assuming youre interested in math idk

willow pecan
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Lots of schools are getting rid of gre requirements

broken meadow
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math gre?

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oh

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yeah i heard it was a shitty test

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with like

tulip blade
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Just dont feel like wasting time on it tbh

broken meadow
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integral tricks and nonsense

flint forge
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schools are killing it

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covid helped

broken meadow
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i don't really want to do the mgre

golden bear
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I still need to take the gen GRE if I want to apply to a PhD program

willow pecan
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Michigan probably isn't bringing it back as a requirement

tulip blade
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My friend got into cornell this cycle and he wouldve done horrible on the mgre

sage python
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Some "algebra" (binomial coefficients), "functions" (graph of f(x+a) relative to graph of f(x)), trig, 3D vector geometry, stats, calculus, and an optional topic which your teacher chooses, either more stats, more calculus, discrete math, or "sets, relations, and groups"

tulip blade
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Shows that it doesnt mean a lot

flint forge
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i wouldve had to study a lot for it

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luckily didnt have to

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thanks covid

golden bear