#book-recommendations | Mathematics | Page 245

sage python Jun 21, 2021, 7:11 PM

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~~Corollary Perko is better~~

willow pecan Jun 21, 2021, 7:11 PM

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Daminark is a known troll

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Anyways

sage python Jun 21, 2021, 7:11 PM

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Nah but yeah I've referenced Perko a bit for my analysis class and liked it

willow pecan Jun 21, 2021, 7:11 PM

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The main ODE theorem is Picard-Lindelof/Cauchy-Lipschitz

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There isn't too much else going on

daring reef Jun 21, 2021, 7:32 PM

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Hmm not sure exactly but I think I'm most interested in applications of analysis to diffeqs

willow pecan Jun 21, 2021, 7:32 PM

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Tbh

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PDE stuff depends very little on ODE knowledge

daring reef Jun 21, 2021, 7:33 PM

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Oh interesting

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What topics do you think are relevant then?

willow pecan Jun 21, 2021, 7:35 PM

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Measure theory, functional analysis

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Then it's just pde theory

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Maybe numerical analysis if that's a perspective that interests you

daring reef Jun 21, 2021, 7:36 PM

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Are things like linear systems and existence/uniqueness of ODEs important? I feel like I should at least study those

willow pecan Jun 21, 2021, 7:36 PM

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The existence/uniqueness picture for ODEs is not terribly interesting

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Tbh

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And like

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As long as you know how to turn a higher order ode into a system of first order equations, you'll be fine

daring reef Jun 21, 2021, 7:38 PM

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Oh ok lol

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If I were to study ODEs just for the sake of knowledge do you have an idea of which route to take

willow pecan Jun 21, 2021, 7:38 PM

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Perko probably

daring reef Jun 21, 2021, 7:39 PM

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Cool thanks!

timber mesa Jun 21, 2021, 8:54 PM

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Perko is the useful ODEs imo lol

pure swallow Jun 21, 2021, 9:19 PM

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Can anyone recommend good maths books for grade 11 student?

stray veldt Jun 21, 2021, 9:20 PM

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pure swallow Can anyone recommend good maths books for grade 11 student?

what do you want the book for? school stuff or are you interested in learning more?

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if the former you would have to give some information about your curriculum

pure swallow Jun 21, 2021, 9:20 PM

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I want it for clearing concepts clearly

stray veldt Jun 21, 2021, 9:22 PM

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in general i think khanacademy is pretty good for all thing highschool

pure swallow Jun 21, 2021, 9:22 PM

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Ok ok wait ill show my maths curriculum is sets and relations, then inequalities, trigonometry, permutations and combinations, binomial theorem, complex numbers, lines, circles, parabolas, hyperbolas, ellipse, limits and derivatives, statistics, probability

stray veldt Jun 21, 2021, 9:22 PM

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if it has to be a book maybe serge lang's basic mathematics

pure swallow Jun 21, 2021, 9:22 PM

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And a few others i might hVe missed

pure swallow Jun 21, 2021, 9:23 PM

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stray veldt in general i think khanacademy is pretty good for all thing highschool

I did try khan academy, but isnt it a bit basic, at least for the videos available in my country?

stray veldt Jun 21, 2021, 9:23 PM

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didnt know its limited by countries

pure swallow Jun 21, 2021, 9:24 PM

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I have no idea xd

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This is what i get

stray veldt Jun 21, 2021, 9:24 PM

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are you indian?

pure swallow Jun 21, 2021, 9:24 PM

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Yes

stray veldt Jun 21, 2021, 9:25 PM

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what about https://www.khanacademy.org/math

Khan Academy

Math | Khan Academy

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the order might be different but you can search for topics

pure swallow Jun 21, 2021, 9:26 PM

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Screenshot_2021-06-22-02-55-57-69_bc13efaeea77f75593b4737439aa4ae8.jpg

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Theres also options like this

stray veldt Jun 21, 2021, 9:26 PM

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ye, this is ordered for american school

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but you can probably find some good stuff if you look a bit deeper

pure swallow Jun 21, 2021, 9:27 PM

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But u see like

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When for example

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I find some topics

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Having very little info

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Screenshot_2021-06-22-02-57-49-11_bc13efaeea77f75593b4737439aa4ae8.jpg

stray veldt Jun 21, 2021, 9:28 PM

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i mean ok

daring reef Jun 21, 2021, 9:28 PM

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have you learned calculus?

pure swallow Jun 21, 2021, 9:28 PM

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daring reef have you learned calculus?

Nope...

stray veldt Jun 21, 2021, 9:28 PM

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there are some indian users here

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maybe they can help you

daring reef Jun 21, 2021, 9:29 PM

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i think learning calc might be more interesting then, khan academy has a bunch of stuff for that

stray veldt Jun 21, 2021, 9:29 PM

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most of the stuff you listed would be covered by pre-calc and calc

pure swallow Jun 21, 2021, 9:30 PM

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daring reef i think learning calc might be more interesting then, khan academy has a bunch o...

I do find khan academy explain topics very nicely

stray veldt Jun 21, 2021, 9:30 PM

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with the exception of sets and relations and statistics and probability

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so yes, start with pre-calc and then go to calculus on khan academy

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if its to hard, start at algebra

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if pre-calc is too easy go to calc

pure swallow Jun 21, 2021, 9:30 PM

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Ok ok thanks got it

stray veldt Jun 21, 2021, 9:30 PM

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maybe start at trig actually

daring reef Jun 21, 2021, 9:30 PM

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oh yeah if you havent done precalc yet it'd be better to just start with that

pure swallow Jun 21, 2021, 9:31 PM

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stray veldt maybe start at trig actually

I finished class 11 trig in khan academy

stray veldt Jun 21, 2021, 9:31 PM

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ok, then try pre-calc and calc

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most of the calculus stuff is also in the book i mentioned "basic mathematics" by serge lang

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if you prefer a book (and are fine with english)

pure swallow Jun 21, 2021, 9:31 PM

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Yes im fine with English lmao

pure swallow Jun 21, 2021, 9:32 PM

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stray veldt most of the calculus stuff is also in the book i mentioned "basic mathematics" b...

Ok lemme look it up

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Screenshot_2021-06-22-03-02-31-02_fd1e8ef594b195c55a3bba4818d0ce35.jpg

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This?

stray veldt Jun 21, 2021, 9:33 PM

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ye

pure swallow Jun 21, 2021, 9:33 PM

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Ok will get this, in addition to khan academy

spiral night Jun 21, 2021, 11:18 PM

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does anyone have book recommendations for multivariable calc/diff equations

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would you guys recommend stewart's mvc 8ed

lament sage Jun 22, 2021, 12:00 AM

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Any good statistics books which are more proof-oriented? Currently learning introductory statistics at my university, and while I don't need to know much beyond how and when to use the formulas given, I would like to get a better understanding of the material

marble solar Jun 22, 2021, 12:07 AM

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spiral night does anyone have book recommendations for multivariable calc/diff equations

Uh depends

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For hard stuff apostol is good

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for slightly easier williamson & trotter is good

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For standard stuff, I like Thomas University Calculus

spiral night Jun 22, 2021, 12:30 AM

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alright ill check those out, thank you

karmic thorn Jun 22, 2021, 2:00 AM

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pure swallow Ok will get this, in addition to khan academy

Khan is good enough for the larger part. Complement it with your standard school textbook. Basic Math by Lang is a good book too, it would get you used to some more general ideas as well.

whole rain Jun 22, 2021, 2:57 AM

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@karmic thorn nice role opencry

quick hornet Jun 22, 2021, 2:58 AM

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see #changelog

whole rain Jun 22, 2021, 3:03 AM

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oh, n i c e catFone

wicked nymph Jun 22, 2021, 3:04 AM

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pure swallow I do find khan academy explain topics very nicely

i also use it

pure swallow Jun 22, 2021, 9:21 AM

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wicked nymph i also use it

just curious, r u indian?

alpine wedge Jun 22, 2021, 9:55 AM

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guys pls best book for middle schooler

narrow talon Jun 22, 2021, 9:58 AM

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lament sage Any good statistics books which are more proof-oriented? Currently learning intr...

Wasserman all of statistics is pretty good, especially if you’re going along with a course (by itself it doesn’t quite cover enough details)

hasty turret Jun 22, 2021, 9:58 AM

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Are you 13+?

valid condor Jun 22, 2021, 11:20 AM

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pure swallow

this one is really good ngl

lament sage Jun 22, 2021, 12:09 PM

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narrow talon Wasserman all of statistics is pretty good, especially if you’re going along wit...

Found it, thanks!

prisma snow Jun 22, 2021, 1:54 PM

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Proof of Rotman basedness:

viral moth Jun 22, 2021, 2:12 PM

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any good books for analysis? i know epsilon-delta and def of continuity and a few oddities (so like weierstrass and dirichlet functions) and i have done a few exercises, but i am by far a noob at anal

prisma snow Jun 22, 2021, 2:31 PM

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You could try Rudin

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Tbh, there isn't an analysis book that I really like. Just don't use Tao.

willow pecan Jun 22, 2021, 2:32 PM

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Rudin is not good for intuition and insight

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Abbott is better

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There are lots of analysis books out there

karmic thorn Jun 22, 2021, 2:40 PM

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Don't listen to Luna. Tao is good.

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(In any case, you can try out different books and settle for one which clicks with you.)

willow pecan Jun 22, 2021, 2:40 PM

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Tao is wordy

karmic thorn Jun 22, 2021, 2:41 PM

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Wordy is good, depending on situation.

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Wordiness is precisely what makes it better for beginners who are studying the subject by themselves with minimal help from anywhere else.

hasty turret Jun 22, 2021, 2:42 PM

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Tao could be good

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Just skip 90% of the first book

karmic thorn Jun 22, 2021, 2:42 PM

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Tbh that's true

hasty turret Jun 22, 2021, 2:42 PM

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Most of the first book is literally useless filler

karmic thorn Jun 22, 2021, 2:42 PM

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It picks up steam with chapter 6

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You can skim through 8

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9,10,11 are absolutely cut to the chase

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And then on to volume 2

marble solar Jun 22, 2021, 3:11 PM

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viral moth any good books for analysis? i know epsilon-delta and def of continuity and a fe...

Spivak's calculus

brittle marsh Jun 22, 2021, 3:15 PM

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Opinions on category theory in context by Riehl?

willow pecan Jun 22, 2021, 3:17 PM

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Good I think

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Riehl's pretty popular

stray veldt Jun 22, 2021, 3:38 PM

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its good bcs it requires you to know real math before you can read it

hearty steppe Jun 22, 2021, 4:22 PM

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willow pecan Rudin is not good for intuition and insight

I like Abbott a lot but there is something special about the way Rudin makes you really think about some of the theorems and proofs and really analyze them in detail

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Also there is a couple cool supplementary notes to Rudin out there that makes it not totally overwhelming. Many professors and academics out there spend a lot of time working thru Rudin and posting stuff about it online. Another advantage

On another side note, Abbott seems to follow Rudin a bit and break down some of the ambiguity so I would argue that it’s best to use both books together but go to Abbott when you get stuck in Rudin

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But also Schroder is a good text. Not many people have checked that one out. Classic Abhijeets recommendation

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I would also say that perhaps Abbott sometimes breaks things down too much and makes it misleading to not think much more in depth about each theorem

marble grotto Jun 22, 2021, 4:28 PM

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rudin with these makes it quite readable imo
https://math.berkeley.edu/~gbergman/ug.hndts/06x2+03F_104_q+a.txt

hearty steppe Jun 22, 2021, 4:29 PM

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Oh yea Bergman is great

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Silvia as well

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Like with resources like those notes that those professors took years to craft from Rudin, you have a real Arsenal here

willow pecan Jun 22, 2021, 4:37 PM

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I believe that books should be relatively self contained

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If a book needs all of these supplemental materials, then...

gray gazelle Jun 22, 2021, 4:38 PM

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So I'm fresh out of hs and I wanna learn the analyses right(as in proof based and what not) this summer, and landed on spivaks book, should I read a book on proofs like Vellman's first or can I jump right in?

marble grotto Jun 22, 2021, 4:43 PM

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maybe just start spivak and see if you can follow along

hearty steppe Jun 22, 2021, 4:46 PM

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What’s wrong with supplementary materials

marble solar Jun 22, 2021, 6:16 PM

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gray gazelle So I'm fresh out of hs and I wanna learn the analyses right(as in proof based an...

Just do Spivak's Calculus

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There's enough training wheels to get you going

hearty steppe Jun 22, 2021, 6:50 PM

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I think Spivak Calculus will come in handy for me when I get to the actual calculus parts of rudin. Haven't really fiddled around with Spivak yet besides a quick skim but I already learned elementary calculus up to and including multivar. Also a bit of Diff Eq

lime sapphire Jun 22, 2021, 7:08 PM

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anyone know what website can get me an affordable copy of spivak (i don't live in the US so international shipping is preferred)

marble grotto Jun 22, 2021, 7:10 PM

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i think there's one which has free international shipping

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and the flat cost is free too

lime sapphire Jun 22, 2021, 7:11 PM

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do tell

gray gazelle Jun 22, 2021, 7:19 PM

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there's one that can get you a free pdf

nimble sable Jun 22, 2021, 7:27 PM

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Any recommendations for a book on geometric measure theory?

sage python Jun 22, 2021, 7:44 PM

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The standard is Federer's Geometric Measure Theory

ripe granite Jun 22, 2021, 7:47 PM

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🎾

sage python Jun 22, 2021, 7:47 PM

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Lol

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But yeah that book is... very hard, it seems. I know @polar tulip is working through it I think.

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I was given a free book once which seemed cool, I think by Morgan? And for the more pure/harmonic analysis/fractal side of GMT, there's Mattila

polar tulip Jun 22, 2021, 7:55 PM

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@nimble sable mattila is my rec

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also nobody reads federer, it's a reference

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as someone who briefly tried to actually read it, it sucks

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0/10 would not recommend ever

hearty steppe Jun 22, 2021, 7:58 PM

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sage python The standard is Federer's Geometric Measure Theory

I didn't know Roger Federer was a Mathematician as well as a professional tennis player.

sage python Jun 22, 2021, 7:59 PM

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So I'm pretty sure this is a different Federer

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In fact I learned about the mathematician looooong before the tennis player

tulip blade Jun 22, 2021, 11:49 PM

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hearty steppe What’s wrong with supplementary materials

nothing is wrong with supplementary material but if you need to use a lot of supplementary material then the book probably isnt great pedagogically

halcyon hornet Jun 23, 2021, 4:23 AM

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Hello.
Can I get math book recommendations for math competitions(Math competitions which are up till and including 12th grade)?
Not AoPs as they are very costly.

analog lava Jun 23, 2021, 4:42 AM

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craft of pos

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paul zeits

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classic

halcyon hornet Jun 23, 2021, 4:45 AM

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analog lava craft of pos

What?

analog lava Jun 23, 2021, 4:46 AM

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art and craft of problem solving by paul zeits

halcyon hornet Jun 23, 2021, 4:46 AM

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Okay that.

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But that is like different.

hearty steppe Jun 23, 2021, 4:51 AM

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tulip blade nothing is wrong with supplementary material but if you need to use a lot of sup...

How many math books have you read?

There is a lot of value in having a main book you go through and one or two supplementary texts to help work through it while strategizing your note taking

gray gazelle Jun 23, 2021, 4:53 AM

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halcyon hornet But that is like different.

Zeitz's text is really good for getting into the nitty gritty of problem solving. Also, Polya and Tao are excellent too. But you wanna get some background first and aops is ideal for that.

halcyon hornet Jun 23, 2021, 4:54 AM

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Which one from him?

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Terence Tao.

gray gazelle Jun 23, 2021, 4:54 AM

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solving mathematical problems

halcyon hornet Jun 23, 2021, 4:56 AM

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"But you wanna get some background first and aops is ideal for that."
Yeah exactly.

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That is what I want.

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But again AoPs is very costly.

karmic thorn Jun 23, 2021, 4:59 AM

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Try the Mathematical Olympiads book series by World Scientific?

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There are methods to acquire their digital copies for a trial stare Buy only if they seem nice.

halcyon hornet Jun 23, 2021, 5:00 AM

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karmic thorn Try the Mathematical Olympiads book series by World Scientific?

Let me see if I can pirate.

karmic thorn Jun 23, 2021, 5:01 AM

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cros

halcyon hornet Jun 23, 2021, 5:01 AM

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karmic thorn Try the Mathematical Olympiads book series by World Scientific?

Which ones?

halcyon hornet Jun 23, 2021, 5:02 AM

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halcyon hornet Let me see if I can pirate.

You found?

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Wait.

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But for those I need some good math background first. A good math background for mathematical olympiads.

karmic thorn Jun 23, 2021, 5:15 AM

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https://www.worldscientific.com/series/mos

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This is the one I had in mind

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16 volumes wew

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@gray gazelle You asked about a book which talked about problems concerning sequences/series before, right? Volume 16 of the above series seems to address that.

worldly basalt Jun 23, 2021, 5:17 AM

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stare

gray gazelle Jun 23, 2021, 5:32 AM

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https://www.isibang.ac.in/~statmath/olympiad/oldfiles/books.html

halcyon hornet Jun 23, 2021, 9:02 AM

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gray gazelle https://www.isibang.ac.in/~statmath/olympiad/oldfiles/books.html

Thanks.

sonic vessel Jun 23, 2021, 11:35 AM

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hello, Can I get a math book recommendation for introduction combinatorics?

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gray gazelle Jun 23, 2021, 12:11 PM

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Math book recommendation for introduction combinatorics!

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Check out Khan Academy! ^.^

sonic vessel Jun 23, 2021, 12:13 PM

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Khan Academy is not a book

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it is life style

gray gazelle Jun 23, 2021, 12:13 PM

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I printed out khan academy

sonic vessel Jun 23, 2021, 12:13 PM

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You can't print an academy

glossy grove Jun 23, 2021, 2:21 PM

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he can

coral narwhal Jun 23, 2021, 2:42 PM

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in spain they call him el god

gray gazelle Jun 23, 2021, 2:44 PM

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in france they call me le cat

sour briar Jun 23, 2021, 2:50 PM

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How feasible is it to jump into Dummit and Foote when learning abstract algebra for the first time? Should I read something like Pinter instead?

gray gazelle Jun 23, 2021, 2:50 PM

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its very beginner friendly

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d&f is a first algebra book

gusty smelt Jun 23, 2021, 2:50 PM

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dummit and foote is the worst algebra book

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do not read it

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read like artin

gray gazelle Jun 23, 2021, 2:51 PM

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stfu pls

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it spells everything out in extremely painful detail

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which may be good or bad depending on you

gusty smelt Jun 23, 2021, 2:51 PM

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D&F is super dry and unfocused

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seriously use like artin or jacobson for 1st yr algebra

gray gazelle Jun 23, 2021, 2:51 PM

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stfu plsss

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d&f bae

gusty smelt Jun 23, 2021, 2:52 PM

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ppl who like dnf have something wrong with them catThink

gray gazelle Jun 23, 2021, 2:52 PM

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Wow that was rude.

gusty smelt Jun 23, 2021, 2:53 PM

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anyhow in all seriousness

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#book-recommendations message

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pretty good explanation of the 1st year books

sour briar Jun 23, 2021, 2:58 PM

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ah

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oh, so artin is beginner-friendly too

gusty smelt Jun 23, 2021, 3:00 PM

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mhm and it explores a lot of applications

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probably the main complain is that their matrix stuff is a bit disgusting

timber mesa Jun 23, 2021, 3:01 PM

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then again you don't exactly read a book on AA for the matrix stuff

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most of the time you'll already have done a course in LA

tulip blade Jun 23, 2021, 3:19 PM

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hearty steppe How many math books have you read? There is a lot of value in having a main boo...

why are you asking how many math books I've read? Also, yea reading multiple books on a subject and getting a different perspective can be beneficial but what Im saying is if you need multiple supplementary books to make a book readable then it probably isnt good.

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Plenty of people think Rudin is overly terse it isnt a new thing. Also nothing is wrong with wanting books to be self contained and not needing multiple sources just to get through it.

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I've consulted multiple sources when reading a book it isnt bad but I prefer to just stick to one book and maybe some lecture notes unless another book covers something that the current book doesnt.

gray gazelle Jun 23, 2021, 3:31 PM

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Hello guys, what math books would you recommend to a CS major on his first year?

obsidian valley Jun 23, 2021, 3:37 PM

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cracking the coding interview

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dont bother with math

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its lame

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:)

hearty steppe Jun 23, 2021, 3:39 PM

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tulip blade why are you asking how many math books I've read? Also, yea reading multiple boo...

There are things in Rudin explained in ways you will hardly find in other books. Let alone the explanations that are as densely packed as they seem are supposed to motivate the critical thinking about the abstraction of the theorems and examples provided. It is very hard to find a book this consistent. Yes it’s hard to understand but I haven’t been struggling with it to the point it’s unreadable. The struggle with getting through it is consistent with your level of maturity in understanding math rigor mostly.

But perhaps some people have other preferences over analysis books. But Rudin also provides the standard of order in which you learn the content too.

You could try Apostol if you really don’t like Rudin that much. I like Apostol too

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There are also some really good companion notes online for Rudin so that does add some leverage as well as many academic and online peers that are consistently going thru it. Not to mention there are more academic peers that spent years trying to break down Rudin for their students and uploading notes online

gray gazelle Jun 23, 2021, 3:51 PM

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@obsidian valley I like the math part of it

obsidian valley Jun 23, 2021, 3:51 PM

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lol lame

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read the uh

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CLRS

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maybe

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thats a nice DSA book

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you can also do some theory of comp stuff but I don't know a good book thats approachable for a first year

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i mean you can also just do some of the math you're going to need to do in first year

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linear algebra first probably

gray gazelle Jun 23, 2021, 3:53 PM

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Yeah I thought about that

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Is axler's book good on that subject

obsidian valley Jun 23, 2021, 3:53 PM

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I think most people think Axler is good

gray gazelle Jun 23, 2021, 4:01 PM

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What about elementary number theory?

obsidian valley Jun 23, 2021, 4:02 PM

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any discrete math book is sufficient for first year cs

hearty steppe Jun 23, 2021, 4:02 PM

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It’s probably better to study CS in grad school tbh

obsidian valley Jun 23, 2021, 4:03 PM

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yes

hearty steppe Jun 23, 2021, 4:03 PM

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If you are interested in actual CS that is. I find undergrad programs disappointing for it

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Cuz it really depends on what you want to do. Do you want to study the intricacies of computer systems or do you want to study computability. You won’t learn much intuition for computability in an undergrad program.

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Most of your courses are geared toward understanding the motivation behind how computer systems work. Not necessarily the cool aspects of computation with algorithms

tulip blade Jun 23, 2021, 5:18 PM

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hearty steppe There are things in Rudin explained in ways you will hardly find in other books....

im a senior math major basically taking only graduate classes lol, I dont need to read apostol ive done undergrad analysis. Only reason I even mentioned that bc you asked how many math books have I read kind of challenging me and then saying I can read apostol like why are you assuming I dont know basic analysis? Bc I said I dont like rudin lol.

tulip blade Jun 23, 2021, 5:18 PM

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obsidian valley CLRS

I like algorithms by jeff erickson

hearty steppe Jun 23, 2021, 5:26 PM

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tulip blade im a senior math major basically taking only graduate classes lol, I dont need t...

Sorry I gave that impression

marble solar Jun 23, 2021, 5:33 PM

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tulip blade im a senior math major basically taking only graduate classes lol, I dont need t...

NERD

sudden kindle Jun 23, 2021, 5:37 PM

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gusty smelt ppl who like dnf have something wrong with them <:catThink:526983414226747393>

Fuck off

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You have something wrong with you

obsidian valley Jun 23, 2021, 5:43 PM

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tulip blade im a senior math major basically taking only graduate classes lol, I dont need t...

Mathematics 🤓 headass

glossy grove Jun 23, 2021, 5:46 PM

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tulip blade im a senior math major basically taking only graduate classes lol, I dont need t...

flonshed

worldly cove Jun 23, 2021, 6:10 PM

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hehe Im taking it right now the first day was yesterday and ive already learned so much

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mostly from the asking questions about the Alcumulus and homework

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the class itself wasnt too hard

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for some reason they make the homework 15x harder than the problems we do in class

rough hawk Jun 23, 2021, 6:47 PM

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LOL same

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Right now I'm taking intermediate number theory and the homework is so hard

iron lake Jun 23, 2021, 9:02 PM

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gray gazelle Hello guys, what math books would you recommend to a CS major on his first year?

from js, ive never needed anything more than some simple equations dont really think you need math for programming you just cant be dum

quick hornet Jun 23, 2021, 9:16 PM

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You might not need math for programming, but you certainly need it for CS.

iron lake Jun 23, 2021, 10:48 PM

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facepalm i misread it as CSS

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my b

willow pecan Jun 23, 2021, 11:09 PM

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brush

broken meadow Jun 23, 2021, 11:09 PM

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:brush:

sudden kindle Jun 23, 2021, 11:27 PM

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good meme

sinful pewter Jun 24, 2021, 2:06 AM

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quick hornet You might not need math for programming, but you certainly need it for CS.

super based take actually

pale scarab Jun 24, 2021, 2:37 AM

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Do I need to learn functional analysis before learning fractional calculus? I have done basic undergrad analysis/topology but have not learned functional analysis. Any recommendations at my level or what I need to learn before getting into it?

slim peak Jun 24, 2021, 2:43 AM

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pale scarab Do I need to learn functional analysis before learning fractional calculus? I ha...

Fractional Calculus may have many and very deep meaning (depending on functional space you want to study it), you need REALLY advanced functional Analysis to have suitable definition...

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You need to take a look on Spectral, and Operator Theory on Banach spaces first

#

Then looking more specifically on sectorial operators and their fractional powers

#

using deep results of Functional Calculus and vector valued Complex Analysis (which is almost the same as usual Complex Analysis)

#

If you really want a path to learn about it :

A Guide to Spectral Theory, C.Cheverry & N.Raymond
Semigroup of Linear operators, A.Pazy
Interpolation Theory, A.Lunardi

sage python Jun 24, 2021, 2:49 AM

#

Did someone say spectral theory

slim peak Jun 24, 2021, 2:51 AM

#

the two last books contains both chapters about fractional powers

#

but with different point of view, almost complementary

slim peak Jun 24, 2021, 2:52 AM

#

sage python Did someone say spectral theory

Spectral Theory ❤️

sage python Jun 24, 2021, 3:00 AM

#

THis reminds me I need to finish up revising my proof of the Weyl law

past ice Jun 24, 2021, 4:13 AM

#

So recently I got myself roped into an undergrad summer research thingy with a professor at my school and we're going to be working thru Alon and Spencer's book on the probabilistic method. I've completed a year-long graduate measure theory/real analysis sequence but know zero probability theory. I've expressed my concerns to prof but he says I should be fine picking stuff up as I go along. That said, does anyone know of a good probability text? I'm looking at the one by Cinlar but I'd like to hear more recommendations first.

past ice Jun 24, 2021, 4:57 AM

#

All 3 of those resources you listed look amazing for my purposes. thank you!

sage python Jun 24, 2021, 6:19 AM

#

When you say probabilistic method

#

In my mind that says combinatorics

#

Is that what you mean?

#

Stuff like e.g. proving existence of a graph with a property by showing P(random graph has that property) ≠ 0, etc

past ice Jun 24, 2021, 6:21 AM

#

yeah that's basically the sales pitch I have in mind going in

sage python Jun 24, 2021, 6:22 AM

#

Yeah in that case you might not need heavy probability. A full book is excessive for sure. Lawler's notes is prob the best of the 3

#

In my undergrad wombo combo class we mostly just used linearity of expectation lol

past ice Jun 24, 2021, 6:28 AM

#

oh yeah going by what my advisor said I don't expect to need to read a whole prob book cover to cover. but i think having a comprehensive text is still nice for psychological purposes, and I kind of want to use the project as an excuse to kickstart further studies in probability and analysis (i mostly pigeonholed myself as an algebra person way too early). but in any case, thanks for the remark on Lawler. Probably going to make that my main read for the next week or so.

however, i expect that no amount of consoling or preparation is going to make the exercises in alon/spencer any less intimidating lol. i've heard some stories...

sage python Jun 24, 2021, 6:32 AM

#

I'm intrigued

past ice Jun 24, 2021, 6:43 AM

#

basically the book is known for its lack of approachable exercises. The authors, who are two of the most recognizable names in the field, seem to not have time to contrive exercises of reasonable difficulty so they end up throwing in results that they themselves proved not too long ago. It's kind of terrifying

gusty smelt Jun 24, 2021, 6:46 AM

#

alon and spencer exercises are insane

#

i had a class around the book

#

and literally every single pset was optional

past ice Jun 24, 2021, 6:49 AM

#

prof was like "if we work thoroughly on some exercise we might get a paper by the end of summer" lolol

gusty smelt Jun 24, 2021, 6:50 AM

#

one of these days im just gonna like

#

take 2 months out

#

and do all the problems

past ice Jun 24, 2021, 6:51 AM

#

if you manage that in 2 months i will basically revere you as a god

gusty smelt Jun 24, 2021, 6:51 AM

#

yeah might be impossible lol

#

basically like just do alon and spencer all day catThink

past ice Jun 24, 2021, 6:52 AM

#

well, you're free to join me this summer 🙂

gusty smelt Jun 24, 2021, 6:52 AM

#

oh yeah sure

#

i think i never got beyond erm

#

ch 1 ex 3

#

spent like a week on it

#

👀

past ice Jun 24, 2021, 6:53 AM

#

I think I'm gonna start reading the book next week. this week i shore up on some prob/graph theory

gusty smelt Jun 24, 2021, 6:53 AM

#

nice

past ice Jun 24, 2021, 6:57 AM

#

https://discord.gg/9eM9PqgA
so i set up the discord if anyone wants to join. no pressure, feel free to drop at any time

scenic geyser Jun 24, 2021, 9:11 AM

#

no

gray gazelle Jun 24, 2021, 11:55 AM

#

hmmCat

slow matrix Jun 24, 2021, 12:46 PM

#

actually I'm starting to like Rudin (PMA), am I weird?

willow pecan Jun 24, 2021, 1:19 PM

#

yes

slow matrix Jun 24, 2021, 1:54 PM

#

I thought it's cool thing to like Rudin.

spring cedar Jun 24, 2021, 2:20 PM

#

Uh hello

#

Purcell's calculus is pog

#

Oh

#

Walpole's statistics too

hearty steppe Jun 24, 2021, 2:59 PM

#

slow matrix actually I'm starting to like Rudin (PMA), am I weird?

Welcome to the club. Did you just start reading it? I have a study group put together for it. We are at the appendix of chapter 1

slow matrix Jun 24, 2021, 4:25 PM

#

hearty steppe Welcome to the club. Did you just start reading it? I have a study group put tog...

I'm actually trying to follow MIT 18.100b
https://ocw.mit.edu/courses/mathematics/18-100b-analysis-i-fall-2010/index.htm
though lately I'm more focused on reading the main text than following it. I'm at chapter 6, when it comes to pure reading. Maybe after finishing with chapter 8, I would reread it, and this time doing the exercise too. maybe

#

I have a local study group that I sometimes use for my presentation to teach myself.

#

I haven't finished reading it, and I already could decently do entry test for math grad school in my place. So I guess it's not too bad I guess.

slow matrix Jun 24, 2021, 4:28 PM

#

hearty steppe Welcome to the club. Did you just start reading it? I have a study group put tog...

I would be interested with dedicated study group, but I have phobia with commitment. I'm scared of making commitment with slightest possibility I can't fulfill.

obsidian valley Jun 24, 2021, 9:08 PM

#

stare

narrow echo Jun 24, 2021, 9:08 PM

#

oops

obsidian valley Jun 24, 2021, 9:09 PM

#

this is ur fault

tulip blade Jun 24, 2021, 9:20 PM

#

past ice basically the book is known for its lack of approachable exercises. The authors,...

Glad Im not just dumb lol. I've read a few chapters mostly intro, linearity of expectation, second moment method and the excises were absurdly hard.

quick hornet Jun 25, 2021, 1:36 AM

#

uhhh

#

this isnt the place to advertise your stuff

gray gazelle Jun 25, 2021, 2:36 AM

#

quick hornet this isnt the place to advertise your stuff

Someone recomended me to put it here. My light novel was technically a book so I placed it here. Sorry

slate topaz Jun 25, 2021, 2:52 AM

#

Hello, I wanna teach myself trignometry. Can someone recommend me a book that's available free online

hearty steppe Jun 25, 2021, 3:28 AM

#

Paul’s online notes

winter veldt Jun 25, 2021, 5:16 AM

#

slate topaz Hello, I wanna teach myself trignometry. Can someone recommend me a book that's ...

khan acadamy

#

also didnt u ask this in multiple channels

uncut zealot Jun 25, 2021, 6:03 AM

#

slate topaz Hello, I wanna teach myself trignometry. Can someone recommend me a book that's ...

openstax.org has some books too

wicked nymph Jun 25, 2021, 10:21 AM

#

pure swallow just curious, r u indian?

yep

#

replied too soon right

sudden kindle Jun 25, 2021, 11:17 AM

#

I like KA

languid orchid Jun 25, 2021, 1:25 PM

#

slate topaz Hello, I wanna teach myself trignometry. Can someone recommend me a book that's ...

Triginometry - By S.L. Loney

gray gazelle Jun 25, 2021, 1:32 PM

#

Can anyone suggest book for discrete mathematics?

gray gazelle Jun 25, 2021, 1:48 PM

#

check out concrete math

#

by knuth

gray gazelle Jun 25, 2021, 2:18 PM

#

gray gazelle Can anyone suggest book for discrete mathematics?

Rosen's text is pretty good. I used it for my sem 1.

#

Okay

brittle latch Jun 25, 2021, 3:39 PM

#

pirate bay B)

gray gazelle Jun 25, 2021, 4:38 PM

#

.

signal bone Jun 25, 2021, 4:38 PM

#

heya

#

http://joshua.smcvt.edu/linearalgebra/book.pdf

#

im hovering on this book

#

the start look very good

#

i recommend you to check it up

gray gazelle Jun 25, 2021, 4:39 PM

#

ok, but what's the point of doing linear algebra now

signal bone Jun 25, 2021, 4:40 PM

#

why not

gray gazelle Jun 25, 2021, 4:41 PM

#

not covered in highschool

signal bone Jun 25, 2021, 4:41 PM

#

the book you gave not covered in highschool either

gray gazelle Jun 25, 2021, 4:41 PM

#

afaik, not rly

#

it's just honors' treatment

signal bone Jun 25, 2021, 4:41 PM

#

honors treatment?

gray gazelle Jun 25, 2021, 4:42 PM

#

gray gazelle not covered in highschool

he has two titles under his name. one is intro to algebra and another is algebra for schools and colleges. what is the difference between them?

hasty turret Jun 25, 2021, 4:42 PM

#

LA is just generally useful

signal bone Jun 25, 2021, 4:42 PM

#

gray gazelle he has two titles under his name. one is intro to algebra and another is algebra...

who is he?

gray gazelle Jun 25, 2021, 4:42 PM

#

gray gazelle he has two titles under his name. one is intro to algebra and another is algebra...

one is supposedly the prerequisite

gray gazelle Jun 25, 2021, 4:43 PM

#

signal bone who is he?

chrystal

signal bone Jun 25, 2021, 4:43 PM

#

listen

#

there is not a single reason, to a student that really want to learn, to read a book from 150 years ago

#

that doesnt make sense

gray gazelle Jun 25, 2021, 4:43 PM

#

hasty turret LA is just generally useful

which is why i will learn it in due time

signal bone Jun 25, 2021, 4:43 PM

#

if you are a researcher and you want to study the time - ok i guess

#

but this book looks extremly outdated

gray gazelle Jun 25, 2021, 4:43 PM

#

i asked you to find me an alternative

signal bone Jun 25, 2021, 4:44 PM

#

@gray gazelle can you look at the book?

#

http://djm.cc/library/Algebra_Elementary_Text-Book_Part_I_Chrystal_edited.pdf

#

this one right?

gray gazelle Jun 25, 2021, 4:44 PM

#

Algebra: An Elementary Text-Book - For the Higher classes of Secondary Schools and Colleges Volumes 1 & 2 by Chrystal
Higher Algebra: a Sequel to Elementary Algebra for Schools by Hall and Knight
College Algebra (AMS Chelsea Publishing) by Henry Burchard Fine
2nd has shitty formatting
3rd can only be found in djvu, online converters have a tendency to fuck up djvus converted to pdfs

#

and djvu is a shitty format generally

#

not going to read this shit

#

Well I know some modern books on this

#

I did Hornsby, Lial and Rockswold

#

https://www.amazon.com/Graphical-Approach-College-Algebra-7th/dp/0134696522 ?

A Graphical Approach to College Algebra: Hornsby, John, Lial, Marga...

Buy A Graphical Approach to College Algebra on Amazon.com ✓ FREE SHIPPING on qualified orders

#

The book is called "A Graphical approach to algebra and trigonometry"

gray gazelle Jun 25, 2021, 4:46 PM

#

gray gazelle https://www.amazon.com/Graphical-Approach-College-Algebra-7th/dp/0134696522 ?

yeah + the trig one

gray gazelle Jun 25, 2021, 4:48 PM

#

signal bone <@456226577798135808> can you look at the book?

idk I sorta like it 😂

signal bone Jun 25, 2021, 4:48 PM

#

gray gazelle idk I sorta like it 😂

srsly??

gray gazelle Jun 25, 2021, 4:48 PM

#

I have a fetish for old texts

gray gazelle Jun 25, 2021, 4:48 PM

#

gray gazelle yeah + the trig one

this looks like a shitty version of axler

signal bone Jun 25, 2021, 4:49 PM

#

i have an headache just reading the font

signal bone Jun 25, 2021, 4:49 PM

#

gray gazelle I have a fetish for old texts

it reminds me, when i was at 4th grade, my parents gave me a book who looked like it to "learn higher math". after 2 degrees, still had no idea what this book tried to teach me

gray gazelle Jun 25, 2021, 4:49 PM

#

gray gazelle this looks like a shitty version of axler

yeah I didn't like it either. lots of mundane and mechanical exercises.

gray gazelle Jun 25, 2021, 4:50 PM

#

signal bone i have an headache just reading the font

i get an epileptic episode from all these rainbows and shreks in modern textbooks, so i don't see how you could prefer them to scans

signal bone Jun 25, 2021, 4:51 PM

#

what shreks?

#

and rainbows lmao

gray gazelle Jun 25, 2021, 4:51 PM

#

gray gazelle this looks like a shitty version of axler

Is it Sheldon Axler's Linear Algebra text? How is it related to this?

#

rainbows because of all the colors
shreks because I heard Stewart's Calculus has a Shrek in it

signal bone Jun 25, 2021, 4:51 PM

#

i prefer a cleaner font and not a font that was meant to be printed by some inked machine in the laste 17th century

gray gazelle Jun 25, 2021, 4:51 PM

#

gray gazelle Is it Sheldon Axler's Linear Algebra text? How is it related to this?

Pre-calculus

#

oh I see

#

I don't find these sorts of books good tbh

#

i've read through most of it, but i skipped some stuff at the end because i got pissed off by how he presented a new concept in 1.5p while wasting previous 20p reiterating the same boring bullshit

gray gazelle Jun 25, 2021, 4:54 PM

#

gray gazelle I don't find these sorts of books good tbh

these sort of books? it covers the same material as yours does

#

I mean, you have to filter a lot of stuff

#

There is just lots of unnecessary and mundane things in it

#

if you mean the exercises, isn't it normal to just skip some

#

for example Axler's Precalculus had 'Exercises' and 'Problems', and every 2nd exercise was solved, so what I did was to check out every question, see if I have an idea how to answer it but not actually write it, and check out the solution

#

if I didn't know how to, I would attempt to solve it on paper

#

Is Axler's text good?

#

i found it to be very good till the end of trig

gray gazelle Jun 25, 2021, 4:58 PM

#

gray gazelle i've read through most of it, but i skipped some stuff at the end because i got ...

then

#

I plan to come back to it once I finish Chrystal's text or some alternative

#

I must say, I find Chrystal's text very intriguing by glancing at it

gray gazelle Jun 25, 2021, 5:06 PM

#

gray gazelle I must say, I find Chrystal's text very intriguing by glancing at it

again, it's apparently one of the best textbooks on Algebra ever written

#

some famous mathematicians have recommended it

#

so it's somewhat famous

#

where did you get to know about it?

gray gazelle Jun 25, 2021, 5:07 PM

#

gray gazelle where did you get to know about it?

google

signal bone Jun 25, 2021, 5:08 PM

#

gray gazelle I must say, I find Chrystal's text very intriguing by glancing at it

that what i was saying

quick hornet Jun 25, 2021, 5:14 PM

#

is there really a meaningful difference between texts at the high school level

#

like obviously some will be better and some will be worse but i feel like

#

a motivated student will pass and an unmotivated one wont

#

and the textbook wont really affect that

gray gazelle Jun 25, 2021, 5:20 PM

#

quick hornet is there really a meaningful difference between texts at the high school level

not each textbook covers the same concepts, is the main issue being addressed

quick hornet Jun 25, 2021, 5:20 PM

#

sure but i feel like the main purpose of high school courses is to develop basic fluency rather than to teach content

#

if that makes sense

#

like a high school treatment of complex numbers, polar form, etc. often takes multiple weeks

#

a mathematically mature uni student learns it in half an hour

#

so im unconvinced that jamming in as much content at a high school level is the right thing to do

#

feel like its better to focus on reinforcing foundational skills so that its easier for them to pick that content up quickly when they actually need it

#

that said, im not a pedagogy expert so im probably talking out my ass here

#

well, drop the "probably"

gray gazelle Jun 25, 2021, 5:23 PM

#

quick hornet feel like its better to focus on reinforcing foundational skills so that its eas...

each textbook reinforces different skills by covering different material

#

i think he argued against me using Chrystal's Algebra despite it's comprehensiveness and it's universal acclaim, due to the notation being dated

#

to which I retorted by saying that I may learn the modern notation later, and what matters is the clear explanation of the concepts and their relation

whole rain Jun 25, 2021, 6:19 PM

#

I agree with Namington here

#

hmmCat

sudden kindle Jun 25, 2021, 6:46 PM

#

I agree with Shika here

deep prism Jun 25, 2021, 6:46 PM

#

I agree with putin sushi here

crimson slate Jun 25, 2021, 7:41 PM

#

Hey y'all I was looking for a book on the basics of Discrete Mathematics, any recommendations are appreciated.
P.s. I'm looking to gain some insight as a CS student, so a very rigorous book might be an overkill, or I'm just confused atm.

velvet briar Jun 25, 2021, 9:08 PM

#

Google for Oscar Levin Discrete pdf. It's a very easy book and will get you understanding logical statements, sets, ect. @crimson slate

crimson slate Jun 25, 2021, 9:17 PM

#

Thanks @velvet briar it seem to be a nice start

oak umbra Jun 26, 2021, 9:03 AM

#

Hey guys, so I'm starting my masters in applied mathematics and plan to be doing it on mathematical epidemiology, specifically using random forests coupled with Markov chains (as that is what my supervisor is interested in). I myself have never touched Markov chains, i was trained more in time series and statistical inference. So I was wondering if there are any texts you guys could recommend for someone at the graduate level with a relatively gentle introduction to Markov chains and their applications. There are so many books its hard to know what best fits my purpose. Thanks

golden veldt Jun 26, 2021, 5:53 PM

#

Looking for books to prepare for a graduate analysis class. Previous books for the course were Lang, Folland, Bass, and Billingsey. I finished going through Spivak and want to prepare over the next year.

hearty steppe Jun 26, 2021, 6:41 PM

#

I would advise even if you did undergrad analysis just go through baby rudin so your that much better at math

gray gazelle Jun 26, 2021, 6:43 PM

#

how do yall read baby rudin? i never read it all, i always tried to prove theorems by my own before reading proof but i was too dumb to do all book

hearty steppe Jun 26, 2021, 6:45 PM

#

There’s a certain way to take notes from math books that I’m starting to understand and it seems to benefit most with standard books I think. Or books that make you really think about the rigor

#

Some books seem hand holdy and don’t really prompt you to take note of anything or think more about what’s going on

gray gazelle Jun 26, 2021, 6:47 PM

#

@hearty steppe can you describe how?

hearty steppe Jun 26, 2021, 7:05 PM

#

Like I think comparing Rudin to Abbott is a great example. Abbott is a good book but it feels like it doesn’t really probe you to think as much about the abstraction of the rigor involved in how Rudin goes about it

#

Or comparing Janich’s Linear Algebra to Friedberg’s elementary linear algebra and it’s applications

gray gazelle Jun 26, 2021, 7:08 PM

#

Begone bot

#

@sage python can you deal with this please

#

what a fucking --------

hasty turret Jun 26, 2021, 7:11 PM

#

No,He just skips everything

#

"ok this claim is obviously true. I leave it to the reader to prove it"

#

The claim turns out to be very nontrivial

#

And you try to look for the solution on the internet and don't find anything

hearty steppe Jun 26, 2021, 7:17 PM

#

I find it to be? I like it tho

sage python Jun 26, 2021, 7:18 PM

#

Oh you're saying catman is a bot?

#

Lmfao

#

Oh

#

I thought you were saying catman was a bot that talks about Rudin and Abbott whenever either comes up

storm sleet Jun 26, 2021, 7:18 PM

#

Is there any reason for the Aluffi hate here? Like, if someone already has a reasonable grasp of algebra, is it still a bad book to learn basic cat thoery

hearty steppe Jun 26, 2021, 7:18 PM

#

Bloop bloop beep

But idk I like Rudin. It just feels like it begs me to interact with it a lot to understand it and stuff

sage python Jun 26, 2021, 7:19 PM

#

deathcode the problem people have with Aluffi is more like

#

The exercises are quite bad

#

It's wayyyyyyyyy too slow

#

And I've heard from some who used it that it doesn't do a great job at making it clear which parts are categorical/just words and which parts are actual algebraic content

#

Yeah you need to ask people with the correct perspectives

storm sleet Jun 26, 2021, 7:21 PM

#

Is there a better alternative for like, motivated category theory? I was looking at Topology a categorical approach, but I just need something to get me into cat theory, under the assumption that I have a reasonable grasp of like, 1st year graduate algebra (second exposure to group theory, some commutative algebra, galois theory)

sage python Jun 26, 2021, 7:21 PM

#

Algebraic topology

storm sleet Jun 26, 2021, 7:21 PM

#

I do know point set, but our course only went up to topological groups in Armstrong. He said Munkres was "too advanced" for the course

sage python Jun 26, 2021, 7:22 PM

#

The thing about algebraic topology is that that's where you start jumping back and forth between different things

gray gazelle Jun 26, 2021, 7:22 PM

#

sus king daminark

storm sleet Jun 26, 2021, 7:22 PM

#

Oh christ I don't want to ever deal with lenses again @sweet lotus. I am a programmer and have done a fair bit with Haskell, theorem proving and PL theory in general

sage python Jun 26, 2021, 7:22 PM

#

Like if you're strictly within algebra then the functoriality of the functors you're dealing with doesn't feel like it's a big thing

#

At least at the beginning

#

But in algebraic topology the fact that homotopy and (co)homology are functors is, while not hard to prove, a substantial "statement"

#

Like alright these are good ways of jumping around between different settings

storm sleet Jun 26, 2021, 7:24 PM

#

I want to learn bc I feel like I'm getting to the point where not having cat theory knowledge will actively hinder me. I'm starting to get into AG and wanting to learn some AT, but I'm less confident in my topology than I am my algebra

sage python Jun 26, 2021, 7:25 PM

#

Yeah a number of AT/AG books introduce what they need as they go

#

You don't need a dedicated intro

storm sleet Jun 26, 2021, 7:25 PM

#

As an aside on the AG, we're using the Hulek book, so idk if it goes into much

sage python Jun 26, 2021, 7:25 PM

#

I do not know Hulek

storm sleet Jun 26, 2021, 7:26 PM

#

My main struggle is proofs and diagram chasing, at least as far as I can tell

#

Any time I've tried a book (god forbid the time I tried Mac Lane) the diagram chasing just wasn't followable

#

Thinking with arrows instead of sets is hard 😦

sage python Jun 26, 2021, 7:27 PM

#

Was it the simple diagrams that messed you up? Like did you stumble when you saw a square?

storm sleet Jun 26, 2021, 7:28 PM

#

Triangles and squares were fine, some limits were fine too, like basic ones like product/coproduct, equalizers and coequalizers

#

pullbacks and pushouts were not fun

#

And then there was that time Bartosz tried to introduce Yoneda embedding, and thats were I gave up

#

Haven't heard of it tbh

gray gazelle Jun 26, 2021, 7:31 PM

#

catThink

#

bilinearcating

storm sleet Jun 26, 2021, 7:31 PM

#

our grad tolopogy sequence touches it at the end, but our undergrad topology goes fairly slow

#

😦

#

I gotta finish my CS degree too :/

#

No time

hasty turret Jun 26, 2021, 7:35 PM

#

Is this a dual degree

storm sleet Jun 26, 2021, 7:35 PM

#

Nope, I'm just double majoring

#

I powered through an entire math degree in only 1.5 years tho

#

From freshman vector calc to graduate diff geo and intro to AG

#

We have a dedicated AG sequence too, which uses Hatcher, but even that goes p slow afaik

#

*AT yes

#

The keys are right next to each other lol

sage python Jun 26, 2021, 7:37 PM

#

Cohomology is but a prelude to sheaf cohomology

storm sleet Jun 26, 2021, 7:38 PM

#

Undergrad topology covers metric spaces, some general topological spaces, up to compactness, connectedness (some path), topological groups (sometimes) and if you're lucky fundamental group. Grad sequence does all that, fundamental group, and I think some stuff with covering spaces and some other stuff, not 100% sure, and our AT sequence is hatcher

#

We also run on quarters not semesters here

#

yep yep

gray gazelle Jun 26, 2021, 7:40 PM

#

stare

storm sleet Jun 26, 2021, 7:41 PM

#

Yeah... Just a matter of finding time

#

Self study is the only way I have time for

#

AT outline for our uni btw

sage python Jun 26, 2021, 8:15 PM

#

Well if he's hoping for category stuff then maybe not. If you want an easy book read Rotman. Hard one read May

steel viper Jun 26, 2021, 9:02 PM

#

van kampen is cute

hard lion Jun 26, 2021, 9:17 PM

#

Looking for a book to review odes. This one good? https://www.amazon.ca/Ordinary-Differential-Equations-Morris-Tenenbaum/dp/0486649407

gray gazelle Jun 26, 2021, 9:43 PM

#

Will Willard prepare for AT

steel viper Jun 26, 2021, 9:44 PM

#

What is willard

gray gazelle Jun 26, 2021, 9:48 PM

#

steel viper Jun 26, 2021, 9:50 PM

#

you dont need much point set at all for AT

#

in what way?

gray gazelle Jun 26, 2021, 10:33 PM

#

Is it fine enough to learn point set

gray gazelle Jun 27, 2021, 2:01 AM

#

atomic habits >>>

broken meadow Jun 27, 2021, 2:10 AM

#

i simply help others instead

gray gazelle Jun 27, 2021, 2:13 AM

#

you've got me pegged pensivebread

steel viper Jun 27, 2021, 2:35 AM

#

sully

spring cedar Jun 27, 2021, 2:38 AM

#

isleep

gray gazelle Jun 27, 2021, 10:13 AM

#

What would be some good books to start learning complex analysis?

prisma snow Jun 27, 2021, 10:27 AM

#

Gomez, stop trolling, you definitely know CA.

whole rain Jun 27, 2021, 10:27 AM

#

I thought the exact same thing

#

opencry

prisma snow Jun 27, 2021, 10:27 AM

#

😂

whole rain Jun 27, 2021, 10:27 AM

#

gray gazelle What would be some good books to start learning complex analysis?

Also check the pins

prisma snow Jun 27, 2021, 10:27 AM

#

^

gray gazelle Jun 27, 2021, 10:31 AM

#

ooh thanks

#

Found some good books, thanks thumsup

quick hornet Jun 27, 2021, 10:43 AM

#

what would be some good books to start learning calc 2?

gray gazelle Jun 27, 2021, 10:52 AM

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Second part of baby rudin

prisma snow Jun 27, 2021, 10:57 AM

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quick hornet what would be some good books to start learning calc 2?

I think you're advanced enough to try spivak

karmic thorn Jun 27, 2021, 11:05 AM

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Nami should fill in the pre-reqs first. Start with the bare basics.

shadow tusk Jun 27, 2021, 11:37 AM

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has anyone read Alex's Adventures In Numberland here?

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if so how beginner friendly do you think it is?

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a bit of a backstory I know like 0 calculus

atomic hound Jun 27, 2021, 12:51 PM

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HELLO Gays, so i am about to go to college ans a i wanna study the "DISCRETE MATH".what book could you recomended for a beginner?

quick hornet Jun 27, 2021, 12:53 PM

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"HELLO Gays" is somehow accidentally an accurate way to refer to this server's typical membership.

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anyway, why are you learning discrete math? for programming/CS or for mathematics? or out of interest?

atomic hound Jun 27, 2021, 12:56 PM

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Or my god sorry man

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Was misspelled the word

atomic hound Jun 27, 2021, 12:56 PM

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quick hornet anyway, why are you learning discrete math? for programming/CS or for mathematic...

I wanna for the two.

quick hornet Jun 27, 2021, 12:57 PM

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atomic hound Or my god sorry man

dont worry about it haha

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anyway, it might be worth reading the replies here https://math.stackexchange.com/questions/1533/what-is-the-best-book-for-studying-discrete-mathematics

Mathematics Stack Exchange

What is the best book for studying discrete mathematics?

As a programmer, mathematics is important basic knowledge to study some topics, especially Algorithms. Many websites, and my fellows suggest me to study Discrete Mathematics before going to Algorit...

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a lot of them seem more CS-oriented

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but admittedly mathematics majors usually dont take a course called "discrete math" unless its their first intro to proofs

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or required by their degree

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they tend to cover the material in more depth in dedicated courses - "elementary number theory", "graph theory", "games", etc

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discrete math is kind of a contrivance created for CS students.

atomic hound Jun 27, 2021, 1:04 PM

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quick hornet anyway, it might be worth reading the replies here https://math.stackexchange.co...

Right, i'll take a look.Thanks.

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More one thing, what about probrability for a beginner?

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I like this stuff too

formal solstice Jun 27, 2021, 2:24 PM

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What might be a good resource for elementary number theory?

karmic thorn Jun 27, 2021, 2:26 PM

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The latest pinned message has several recommendations.

formal solstice Jun 27, 2021, 2:28 PM

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What's the difference between discrete mathematics and number theory?

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or is a text in discrete mathematics a good intro before diving into elementary number theory

karmic thorn Jun 27, 2021, 2:31 PM

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Discrete mathematics is a loose umbrella term for topics like graph theory, some enumerative combinatorics, introduction to proofs, some elementary number theory, propositional logic(one or more of these things could be removed, or added, depending on course). This is basically supposed to be an entry point for CS students to learn some math that might come in handy for them. Number theory, on the other hand, is concerned exclusively with a dedicated study of "numbers", starting off in the familiar context of natural numbers/integers, gradually progressing into more general and abstract settings.

karmic thorn Jun 27, 2021, 2:32 PM

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formal solstice or is a text in discrete mathematics a good intro before diving into elementary ...

Several texts in elementary number theory are specifically written with a first proofs course audience in mind. Either works tbh, but some familiarity with basic proofs would be very handy for number theory.

formal solstice Jun 27, 2021, 2:34 PM

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I think eventually I'd love to dive into elementary number theory as a subject. I am a bit rusty on proofs at the moment, however.

karmic thorn Jun 27, 2021, 2:37 PM

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You could review some stuff from here. This is a very concise set of notes for that purpose.

formal solstice Jun 27, 2021, 2:39 PM

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@karmic thorn thanks. this PDF looks nice

karmic thorn Jun 27, 2021, 2:39 PM

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catthumbsup

atomic hound Jun 27, 2021, 2:43 PM

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Which some good euclides geometry books?

hasty turret Jun 27, 2021, 2:44 PM

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Why do you want to do Euclidean Geometry

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It's completely useless for any real life purpose

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Except for olympiads

atomic hound Jun 27, 2021, 3:11 PM

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I dont care, i like and that it

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and is useful for me

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Ans my projects

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i dont give a f**k if it is useful for other people or life in general.I just wanna be happy with this type of knowledge.

prisma snow Jun 27, 2021, 3:13 PM

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atomic hound HELLO Gays, so i am about to go to college ans a i wanna study the "DISCRETE MAT...

https://tenor.com/view/you-rang-gif-20538562

Tenor

hasty turret Jun 27, 2021, 3:14 PM

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atomic hound Ans my projects

Can't you just Intuit the Euclidean Geometry you need

atomic hound Jun 27, 2021, 3:15 PM

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Lol it was mispelled error of my part

atomic hound Jun 27, 2021, 3:16 PM

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hasty turret Can't you just Intuit the Euclidean Geometry you need

Spacial one.

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And 2d geometry as well too.

gray gazelle Jun 27, 2021, 3:42 PM

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atomic hound HELLO Gays, so i am about to go to college ans a i wanna study the "DISCRETE MAT...

hi

gray gazelle Jun 27, 2021, 4:22 PM

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Is discrète maths really that important

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I was gonna go vellman then axler's liniar algebra

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Is there a better choice for a CS major?

karmic thorn Jun 27, 2021, 4:25 PM

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gray gazelle Is discrète maths really that important

Depends on your needs.

karmic thorn Jun 27, 2021, 4:25 PM

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gray gazelle I was gonna go vellman then axler's liniar algebra

That sounds solid enough. Go for it.

gray gazelle Jun 27, 2021, 4:26 PM

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Alright thanks

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My needs are to have little background before starting college

karmic thorn Jun 27, 2021, 4:26 PM

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Sounds good!

gray gazelle Jun 27, 2021, 4:30 PM

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Thank you!

hasty turret Jun 27, 2021, 4:30 PM

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gray gazelle Is discrète maths really that important

Probably not

gray gazelle Jun 27, 2021, 4:33 PM

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@hasty turret can you elaborate

hasty turret Jun 27, 2021, 4:40 PM

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Can you solve basic logic problems

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Try solving
"Suppose you have to climb up a stair with n steps. You could either take 1 step at a time or 2 steps at a time. Find the total number of possible paths you could take"

gray gazelle Jun 27, 2021, 4:42 PM

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I'm fresh out of hs

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Oh

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I can

hasty turret Jun 27, 2021, 4:42 PM

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Ok,it might be relevant

gray gazelle Jun 27, 2021, 4:43 PM

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That sounds like probability to me

hasty turret Jun 27, 2021, 4:43 PM

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Suppose n=3 your paths are
0->1->2->3
0->1->3
0->2->3

gray gazelle Jun 27, 2021, 4:43 PM

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If that makes sense

hasty turret Jun 27, 2021, 4:43 PM

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This is combinatorics

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Combined with some recurrences

gray gazelle Jun 27, 2021, 4:45 PM

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And this falls under which branch of maths?

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As in what book do I need to read to be able to do this?

hasty turret Jun 27, 2021, 4:45 PM

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Well, Combinatorics

mossy flume Jun 27, 2021, 4:50 PM

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Discrete can be important for a couple reasons

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1 is if it's a CS oriented class, it can be a good introduction to the theory behind structures like trees and graphs

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2 it can be an intro to proofs class for non-math majors (engineering and CS types mostly)

tame sluice Jun 27, 2021, 4:52 PM

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will anyone Recommend me some books or papers of Hyperbolic, Hilbert, Hausdroff spaces(for beginners)?

sudden kindle Jun 27, 2021, 4:52 PM

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kot

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Why these topics

willow pecan Jun 27, 2021, 4:53 PM

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They are completely unrelated...

sudden kindle Jun 27, 2021, 4:53 PM

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On the surface, they seem to have nothing to do with each other

gray gazelle Jun 27, 2021, 4:53 PM

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LOL

sudden kindle Jun 27, 2021, 4:54 PM

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Is there a reason you want to learn these thing besides the fact that they are terms for spaces which start with an H?

glossy grove Jun 27, 2021, 4:54 PM

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He wants to study spaces xD

tame sluice Jun 27, 2021, 4:54 PM

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yes, I want to study Space times, for in Black holes & near Singularities

glossy grove Jun 27, 2021, 4:55 PM

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hmmCat

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A Hausdorff space is a topological space in which each two (different) points have disjoint neighbourhoods.

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introduction finished

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i don't know what the others are, so I can't help with those xD

gray gazelle Jun 27, 2021, 4:56 PM

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hillbert spaces are complete inner product spaces

tame sluice Jun 27, 2021, 4:57 PM

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I know that, I just want a Beginning start(papers?)

glossy grove Jun 27, 2021, 4:57 PM

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If you want to study Hausdorff spaces, read a book on general topology.

tame sluice Jun 27, 2021, 4:59 PM

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anything in Hyperbolic & Negative Curvatures?

gray gazelle Jun 27, 2021, 5:04 PM

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maybe read a book on elementary differential geometry

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idk

gray gazelle Jun 27, 2021, 6:54 PM

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glossy grove i don't know what the others are, so I can't help with those xD

Hyperbolic space is a non-Euclidean space with constant negative curvature + a couple other technical requirements (simply connected, etc.)
A Hilbert space is a generalization of Euclidean space; it’s a vector space with an inner product + completeness

sage python Jun 27, 2021, 7:11 PM

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Did someone say Hilbert space

narrow echo Jun 27, 2021, 8:14 PM

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gray gazelle Is discrète maths really that important

yea discrete math is all that matters

gray gazelle Jun 27, 2021, 8:18 PM

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What should I read then after axler's? @narrow echo

tulip blade Jun 27, 2021, 8:19 PM

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Whatever youre interested in

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@gray gazelle

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You should read things online and try to find something interesting.

gray gazelle Jun 27, 2021, 8:19 PM

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Well I'm doing CS major what do I need to know

tulip blade Jun 27, 2021, 8:20 PM

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You dont need axler for a cs major

gray gazelle Jun 27, 2021, 8:20 PM

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Isn't there a lot of linear algebra in CS

willow pecan Jun 27, 2021, 8:20 PM

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Depends on the type

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But linear algebra is widely applicable

tulip blade Jun 27, 2021, 8:21 PM

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Axler will be most abstract then you would likely need. But I think its still worth it to learn

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Bc you could very well need it if you wanted to do cs research.

willow pecan Jun 27, 2021, 8:21 PM

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However, the linear algebra you'll see in CS is less abstract vector space linear algebra and more computational matrix algorithm linear algebra

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For this, I recommend Demmel

narrow echo Jun 27, 2021, 8:22 PM

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"Linear Algebra Done Right for Math Majors"

tulip blade Jun 27, 2021, 8:23 PM

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gray gazelle Well I'm doing CS major what do I need to know

Well arent you doing the CS major to learn this stuff?

gray gazelle Jun 27, 2021, 8:23 PM

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@tulip blade yeah it's summer and I get bored and did math in my free time

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Now I have 3 months of free time

tulip blade Jun 27, 2021, 8:23 PM

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Then try to learn stuff youre interested in imo

gray gazelle Jun 27, 2021, 8:24 PM

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Might as well be ahead

tulip blade Jun 27, 2021, 8:24 PM

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It will still help when you take your classes. You have time to learn this stuff when youre in the class.

gray gazelle Jun 27, 2021, 8:25 PM

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But isn't undergradad math hand wavey for CS majors?

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I wanna know Why something is the way it is

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Or am I wrong

tulip blade Jun 27, 2021, 8:28 PM

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Depends it can be I guess.

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I just said learn something youre interested in. If its linear algebra then learn it. It will be useful.

gray gazelle Jun 27, 2021, 8:30 PM

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I'm interested in number theory tbh

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But I need some linear algebra for that

static crest Jun 27, 2021, 8:57 PM

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undergrad math is handwavey for all undergrad majors other than math

sage python Jun 27, 2021, 9:05 PM

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Linear algebra isn't really a subject that I would say is hand waved

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That's more what I think of physicists and analysis lol

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It's more black boxed

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Since it's not like they give you a wishy washy intuition. Maybe Cayley-Hamilton has a fake proof lol. But otherwise they either tell you why it's true or just say it's true. Which is more honest

broken meadow Jun 27, 2021, 9:24 PM

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the fake proof for cayley hamilton is to just substitute it in

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the one i saw was to form a cyclic subspace and form the char poly from there

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which then follows nice

gusty smelt Jun 27, 2021, 9:25 PM

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I like the "diagonalizables are dense in R^(nxn)" proof

slim peak Jun 27, 2021, 10:18 PM

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sage python Since it's not like they give you a wishy washy intuition. Maybe Cayley-Hamilton...

Complex Analysis proof of Cayley Hamilton for everyone, it's the best proof

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quite handy for Physicists and Analysts

broken meadow Jun 27, 2021, 10:21 PM

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ooh how does that start

slim peak Jun 27, 2021, 10:23 PM

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Look at this : https://math.stackexchange.com/questions/20677/cauchys-integral-formula-for-cayley-hamilton-theorem

Mathematics Stack Exchange

Cauchy's integral formula for Cayley-Hamilton Theorem

I'm just working through Conway's book on complex analysis and I stumbled across this lovely exercise:
Use Cauchy's Integral Formula to prove the Cayley-Hamilton Theorem: If $A$ is an $n \times n$

broken meadow Jun 27, 2021, 10:23 PM

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cool ill try it out

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i still need to get around to doing dami's question from earlier but aaah things have been rough

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need to get ahold of myself

slim peak Jun 27, 2021, 10:26 PM

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note that one can use such kind of formulas to give a good (and very deep) meaning to f(A), f being a suitable function, holomorphic, A a densely defined closed operator on a Banach space (but this may need additional assumptions : like spectral ones, the Banach space to be a Hilbert, etc... )

sage python Jun 27, 2021, 10:27 PM

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Oh yeah I meant the bs bs proof lol

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If p_A(t) = det(tI-A), then p_A(A) = det(AI-A) = det(0) = 0

gray gazelle Jun 27, 2021, 11:23 PM

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~~whats wrong with this proof?~~

willow pecan Jun 27, 2021, 11:25 PM

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Nothing it's a correct proof

ripe granite Jun 27, 2021, 11:36 PM

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Yup, it's correct.

broken meadow Jun 27, 2021, 11:36 PM

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yes.

sage python Jun 28, 2021, 12:45 AM

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thonk

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Okay I think everyone's in on the joke but I feel like there's a non-trivial possibility someone's actually bamboozled

gray gazelle Jun 28, 2021, 12:46 AM

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sully

willow pecan Jun 28, 2021, 12:49 AM

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TTerra do you know lie groups

gray gazelle Jun 28, 2021, 12:52 AM

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going by what you posted in #groups-rings-fields

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no

willow pecan Jun 28, 2021, 12:53 AM

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sad

slim peak Jun 28, 2021, 1:03 AM

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@gray gazelle to answer to your request in #groups-rings-fields , you should check this one, that you can expect to find on usual websites catThink

gray gazelle Jun 28, 2021, 1:04 AM

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the usual websites

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hmmCat

willow pecan Jun 28, 2021, 1:04 AM

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Anatole do you know lie groups

slim peak Jun 28, 2021, 1:05 AM

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Just the basics and nothing about Iwasawa decomposition, just already heard of it at most

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sorry bruh

gray gazelle Jun 28, 2021, 1:05 AM

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ask daminark

sudden kindle Jun 28, 2021, 1:09 AM

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Okay bro

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I just spend a couple hours

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trying to explain the proof that

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a polynomial is solvable by radicals iff the galois group of its splitting field is solvabel

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i have a pretty good contextualization of where Kummer extensions fit into Galois theory now

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uwucat

slim peak Jun 28, 2021, 1:11 AM

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that's not the channel to discuss about it right ?

sudden kindle Jun 28, 2021, 1:11 AM

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oh fk i thought this was #math-discussion

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my bad

slim peak Jun 28, 2021, 1:11 AM

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No problem haha

gray gazelle Jun 28, 2021, 1:14 AM

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coomer extensions

sudden kindle Jun 28, 2021, 1:15 AM

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haha funny joke

gray gazelle Jun 28, 2021, 1:49 AM

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slim peak <@456226577798135808> to answer to your request in <#496784958430380033> , you s...

Thanks

whole rain Jun 28, 2021, 6:21 AM

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sage python Okay I think everyone's in on the joke but I feel like there's a non-trivial pos...

(first time I've seen this proof, I got completely bamboozled and realized only a few hours later that there was a problem with it KEK )

sage python Jun 28, 2021, 6:50 AM

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Hah the story of me with it is funny

narrow crystal Jun 28, 2021, 8:11 AM

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Is Stewarts calculus good for someone who isn't too familiar with trig? I have tried reading the calculus book Quick Calculus but I couldn't understand it.

storm harness Jun 28, 2021, 8:31 AM

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whole rain (first time I've seen this proof, I got completely bamboozled and realized only ...

It is still correct once you embed the commutative ring into the ring of matrices over it right? The homomorphism should preserve the determinant

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I think one issue might be that the determinant would have different values for computations done by expansion along different rows since the matrix ring is non commutative but once you choose one of them as the definition it should work out

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Since the determinant for over the matrix ring is only being used in the intermediate steps

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Ah the det(AI-A) = det(0) step won't be justified then

tame sluice Jun 28, 2021, 8:52 AM

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sage python Did someone say Hilbert space

yes

analog pollen Jun 28, 2021, 1:08 PM

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narrow crystal Is Stewarts calculus good for someone who isn't too familiar with trig? I have t...

Yes it’s good

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It has a full appendix on trig

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Also it introduces trig quite a bit in chapter 1 as well as the chapter where derivatives are handled

barren raptor Jun 28, 2021, 3:35 PM

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Hey any recommendations for good book that takes from beginner to advance on algebra

flint forge Jun 28, 2021, 3:35 PM

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When someone says higher and algebra in #books-old 👀

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@barren raptor we normally just suggest khan academy

barren raptor Jun 28, 2021, 3:37 PM

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I was looking for a good to start

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Khan academy is okay but still .

hearty steppe Jun 28, 2021, 3:52 PM

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Khan academy is good for learning up to elementary level calculus and linear algebra. That’s really about it

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It’s not going to get you through an entire undergrad math program

flint forge Jun 28, 2021, 3:59 PM

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I dont think theres any reason to believe they wanted undergrad material

marble solar Jun 28, 2021, 4:08 PM

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well, They don't have a linear algebra module

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They only have lecture videos

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But they do have a calc 3 module

storm sleet Jun 28, 2021, 5:13 PM

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hearty steppe It’s not going to get you through an entire undergrad math program

Wait Khan Acadamy can't teach me real analysis and differential geometry?

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Though there are people who are just as good that are great post-khan academy math channels

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Michael Penn, Brighter Side of Mathematics, Richard Borcherds, and a few others come to mind

#

(just be sure to exercise caution when/if you discover Insights into Mathematics)

#

Fun fact: if you google NJ Wildberger, one of the top results is "NJ Wildberger crank"

gray gazelle Jun 28, 2021, 7:03 PM

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Khan academy is bad

#

Gn Berman is awesome for calculus
Russian book

analog pollen Jun 28, 2021, 7:24 PM

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gray gazelle Khan academy is bad

It’s mostly based on preference

slim peak Jun 28, 2021, 7:27 PM

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gray gazelle Khan academy is bad

the few I looked at was not bad, even good, but maybe it is quite overrated

gray gazelle Jun 28, 2021, 7:28 PM

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slim peak the few I looked at was not bad, even good, but maybe it is quite overrated

I never got to learn why things are like that. Just able to solve them.

analog pollen Jun 28, 2021, 7:29 PM

#

slim peak the few I looked at was not bad, even good, but maybe it is quite overrated

I think it’s good for like a quick review of a topic

#

Not for learning a subject

#

As far for calculus then

#

Algebra idk how good it is

analog pollen Jun 28, 2021, 7:29 PM

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gray gazelle I never got to learn why things are like that. Just able to solve them.

That’s why it’s not so good for learning a subject like calc

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But that doesn’t mean it’s bad

gray gazelle Jun 28, 2021, 7:30 PM

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Yes, solving wise it is good.

analog pollen Jun 28, 2021, 7:31 PM

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So it’s probably good good for elementary algebra

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Cuz there isn’t a lot of theory

gray gazelle Jun 28, 2021, 7:31 PM

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But it came too back when youtube didnt have much maths tutoring videod

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Now I think it's average comparing others.

narrow crystal Jun 28, 2021, 7:32 PM

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analog pollen Also it introduces trig quite a bit in chapter 1 as well as the chapter where de...

I see, how long does Stewarts take to finish?

analog pollen Jun 28, 2021, 7:33 PM

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narrow crystal I see, how long does Stewarts take to finish?

Very long

#

I haven’t finished it yet

#

It has calc 1 to 3

#

1400 pages

narrow crystal Jun 28, 2021, 7:33 PM

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Oh, how much is necessary for physics

narrow crystal Jun 28, 2021, 7:33 PM

#

analog pollen 1400 pages

Tf

analog pollen Jun 28, 2021, 7:33 PM

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narrow crystal Oh, how much is necessary for physics

Everything I would say

narrow crystal Jun 28, 2021, 7:34 PM

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Oof, I want to pass the F=ma exam for phys oly and I need to learn calc for it.

analog pollen Jun 28, 2021, 7:34 PM

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It’s just a basic calc textbook

#

Are you planning on buying the book?

narrow crystal Jun 28, 2021, 7:35 PM

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Yea

analog pollen Jun 28, 2021, 7:35 PM

#

Don’t then

#

If you are only gonna buy it for a exam

#

If you are planning on studying calc I would say buy it

#

Otherwise don’t

narrow crystal Jun 28, 2021, 7:36 PM

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I mean I haven't taken calc yet and it might help me in my calc class when I take it so idk

analog pollen Jun 28, 2021, 7:36 PM

#

For a physics exam there are plenty of other recourses out there then buying a 300 $ book

narrow crystal Jun 28, 2021, 7:36 PM

#

Is Khan academy fine for f=ma?

analog pollen Jun 28, 2021, 7:36 PM

#

I think so

#

Maybe you want to ask this in a physics discord or ssomthing

narrow crystal Jun 28, 2021, 7:37 PM

#

Im learning limits on Khan academy and so far it doesn't seem too hard.

narrow crystal Jun 28, 2021, 7:37 PM

#

analog pollen Maybe you want to ask this in a physics discord or ssomthing

Yea

analog pollen Jun 28, 2021, 7:37 PM

#

But if you are looking for a calc textbook without a lot of prerequisites then I would say Stewart’s is one of the best

#

As it’s easy to read and covers enough

narrow crystal Jun 28, 2021, 7:38 PM

#

I see, I think for the phys only I will just use Khan academy and in the future for a moreh in depth understanding of calc I will get Stewarts.

analog pollen Jun 28, 2021, 7:43 PM

#

For physics I would say you want a more in depth understanding of calc

#

Imo

gray gazelle Jun 28, 2021, 9:14 PM

#

whats the best textbook for practice questions for calc I and II?

#

that i can buy on amazon

slender spruce Jun 28, 2021, 9:15 PM

#

Schaum's Outlines "Calculus" has a bunch of problems with answers.

#

@gray gazelle Looks like there's also Schaum's Outlines "3,000 Solved Problems in Calculus"

gray gazelle Jun 28, 2021, 9:25 PM

#

thanks @slender spruce

slender spruce Jun 28, 2021, 9:26 PM

#

Apparently, you shouldn't buy the Kindle version of the last.

#

They made the mistake of not including any inequality signs.

crystal lion Jun 28, 2021, 9:48 PM

#

maybe don’t make the mistake of buying the kindle version of any math textbook lol

#

actually it doesn’t seem so bad

#

but still I’d prefer my computer if I don’t have the paper copy

cursive orbit Jun 29, 2021, 1:23 AM

#

Would bott-tu be a good book for me to learn algebraic topology if I have completed tu's intro to manifolds book and have rudimentary knowledge of point-set topology but no previous algebraic topology knowledge?

marble solar Jun 29, 2021, 1:26 AM

#

cursive orbit Would bott-tu be a good book for me to learn algebraic topology if I have comple...

no

cursive orbit Jun 29, 2021, 1:26 AM

#

sadge any recommendations then?

marble solar Jun 29, 2021, 1:27 AM

#

Hatcher algebraic topology

cursive orbit Jun 29, 2021, 1:28 AM

#

Thank you

warm glen Jun 29, 2021, 1:28 AM

#

what is bott-tu good for then

marble solar Jun 29, 2021, 1:31 AM

#

Making you read hatcher

sage python Jun 29, 2021, 2:48 AM

#

thonk

#

Okay so

#

Bott-Tu kinda does different things from Hatcher

#

Hatcher's a more standard intro to algebraic topology. pi_1, covering spaces, homology, cohomology, pi_n

#

Bott-Tu focuses on stuff like De Rham theory, spectral sequences, char classes, etc

gray gazelle Jun 29, 2021, 3:32 AM

#

AWOOKEN

#

another book i can say ill read but never do so

gray gazelle Jun 29, 2021, 4:15 AM

#

Can someone suggest a good and difficult book for single variable calculus I am learning it for the first time....I have heard a lot about spivak's calculus

cursive orbit Jun 29, 2021, 4:16 AM

#

sage python Bott-Tu focuses on stuff like De Rham theory, spectral sequences, char classes, ...

Thus, would they complement each other or would I read bott-tu after hatcher or something?

#

Or is there no point reading both

analog pollen Jun 29, 2021, 9:25 AM

#

gray gazelle Can someone suggest a good and difficult book for single variable calculus I am ...

If you are learning calc for the first time I don’t recommend spivak ( I heard it is best for a 2nd look into calc, and when you are planning on doing analysis)

#

For the first time I would recommend Stewart’s calculus

#

Or any book with the same kind of format

wraith ravine Jun 29, 2021, 1:30 PM

#

narrow crystal I see, I think for the phys only I will just use Khan academy and in the future ...

go to #old-network there you will find a link to a similar kind of physics and chemistry server join them, you will get more clarity

devout raptor Jun 29, 2021, 2:06 PM

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Does anyone have some Sat suggestions

quick hornet Jun 29, 2021, 2:06 PM

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khan academy.

devout raptor Jun 29, 2021, 2:07 PM

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Description?

quick hornet Jun 29, 2021, 2:08 PM

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its a free website so just check it out yourself

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has a bunch of videos and basic problems on every high school math topic

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not really a book but still probably the best free resource for high school

devout raptor Jun 29, 2021, 2:09 PM

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Thank you 😊

quick hornet Jun 29, 2021, 2:09 PM

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you could also check out the openstax free textbooks on algebra + trig but idk how closely they follow the sat curriculum

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i think they cover some stuff that isnt on the sat

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and go deeper into certain stuff than the sat does

devout raptor Jun 29, 2021, 2:33 PM

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Again thanks

past ice Jun 29, 2021, 5:49 PM

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analog pollen If you are learning calc for the first time I don’t recommend spivak ( I heard i...

Not sure why this advice is so commonly repeated.

Spivak is intended as a mathematically rigorous first course in calculus, and it absolutely serves that purpose well. Nothing about the book is written with a prior calculus background in mind. No, it does not need additional notivation or intuition from a book like Stewart, which is mostly a bizarre product of American educational culture.

hearty steppe Jun 29, 2021, 5:50 PM

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American educational culture is its own plague

north valley Jun 29, 2021, 6:14 PM

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Sometimes I wonder if I would have been more engaged in theoretical math if my first few semesters had been spent on Spivaj rather than Stewart 😩

sage python Jun 29, 2021, 6:20 PM

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Yeah Spivak is tougher than Stewart but it's an alternative rather than a "second take"

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If you've already done Stewart better thing is to use linear algebra as an intro to proofs and then go to Rudin or smth

gray gazelle Jun 29, 2021, 6:22 PM

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Spivaj

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Spivka

sage python Jun 29, 2021, 6:23 PM

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Uh TTerra, why are you misspelling Spivak?

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Is this a pun I'm not picking up on?

gray gazelle Jun 29, 2021, 6:26 PM

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stare

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(edited)

obsidian valley Jun 29, 2021, 6:27 PM

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gray gazelle Spivaj

isnt this the lgbt ikea shark?

broken meadow Jun 29, 2021, 6:27 PM

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what

gray gazelle Jun 29, 2021, 6:28 PM

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what

broken meadow Jun 29, 2021, 6:28 PM

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theres an lgbt shark

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at ikea

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i had to read that twice to make sure i read that right

gray gazelle Jun 29, 2021, 6:28 PM

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yeah some dude named spivaj who is gay and has a shark fursona is at ikea

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stare

broken meadow Jun 29, 2021, 6:28 PM

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it's you

gray gazelle Jun 29, 2021, 6:29 PM

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i would never be a shark

broken meadow Jun 29, 2021, 6:29 PM

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ah i see

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very good

obsidian valley Jun 29, 2021, 6:29 PM

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you guys dont know the trans shark thing

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sec

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gray gazelle Jun 29, 2021, 6:30 PM

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Yes

broken meadow Jun 29, 2021, 6:31 PM

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yes

stuck onyx Jun 29, 2021, 6:38 PM

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Which edition of How to Prove It by Daniel J. Velleman is best?

gray gazelle Jun 29, 2021, 6:40 PM

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presumably the newest one

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stare

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Yo

glossy grove Jun 29, 2021, 6:41 PM

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oy

gray gazelle Jun 29, 2021, 6:41 PM

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What math do you need for the eulers project

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I got the coding down

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But I'm afraid it will hit me with something I don't know

stuck onyx Jun 29, 2021, 6:42 PM

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gray gazelle What math do you need for the eulers project

Euler method in numeral analysis?

glossy grove Jun 29, 2021, 6:42 PM

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I don't think you need that much maths.

gray gazelle Jun 29, 2021, 6:42 PM

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No

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The website

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@stuck onyx latest version probablly

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@stuck onyx also his prénom was évariste

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His name was galois

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The French are weird like that

glossy grove Jun 29, 2021, 6:44 PM

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As I said, you need mostly coding, not maths.

sage python Jun 29, 2021, 6:45 PM

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Well I think you kinda want some math?

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My impression about project euler problems is that you can in principle code them a stupid way

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But the point is that the code runs in just a minute

glossy grove Jun 29, 2021, 6:46 PM

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gray gazelle What math do you need for the eulers project

you'll probably need some basic number theory, I guess.

sage python Jun 29, 2021, 6:47 PM

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And chances are knowing math or at least being able to figure out math is important to find the right simplifications

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It won't be technical math but in general being able to feel your way around discrete math is probably what helps

gray gazelle Jun 29, 2021, 6:48 PM

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Aight I'll add knutths book on discrete math to my to read list

sage kelp Jun 29, 2021, 6:54 PM

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stuck onyx Which edition of How to Prove It by Daniel J. Velleman is best?

If you will get a hard copy, then probably the 3rd edition is okay. If you will somehow get an electronic copy, I prefer the 2nd

warm socket Jun 29, 2021, 7:19 PM

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you shouldn't really judge the prerequisites from the first problems, also there are some problems where you really really need some maths theorems

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but they are the minority

crystal lion Jun 29, 2021, 9:32 PM

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glossy grove As I said, you need mostly coding, not maths.

most of the problems are math problems and once you find the solution it’s pretty straightforward to implement

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they’re not very algorithmic

quick hornet Jun 29, 2021, 10:21 PM

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using problem 1 to demonstrate the point is very weird

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id liken project euler more to competition math than anything

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the technical knowledge required isnt immense but solutions still require a fair bit of mathematical cleverness

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problem 1 is unnaturally easy, because its problem 1

cursive orbit Jun 29, 2021, 10:44 PM

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Can someone give a comparison between Folland and Big Rudin for self-studying real analysis?

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My analysis background is roughly on the level of first 7 chapters of baby rudin + analysis on R^n + basic measure theory

primal island Jun 30, 2021, 1:02 PM

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any differential equation textbook recommendations? (for self studying)

willow pecan Jun 30, 2021, 1:48 PM

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ODEs or PDEs

karmic thorn Jun 30, 2021, 1:58 PM

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anticipated 'all ODE books are bad' remark

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I think Ross' Differential Equations is a good mix of light theory and the techniques. Has lots of problems and some examples to highlight them.

willow pecan Jun 30, 2021, 2:37 PM

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All ODE books are bad

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ODEs is kind of a bad subject, especially at the undergraduate level

broken meadow Jun 30, 2021, 2:38 PM

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Never again.

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i don't want to do it

willow pecan Jun 30, 2021, 2:38 PM

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If you get more advanced there are some more things you can do with them

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But they generally aren't called ODEs

slim peak Jun 30, 2021, 2:39 PM

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True af, the only good ones I know are to almost graduate people

cursive orbit Jun 30, 2021, 2:39 PM

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Are the undergrad level courses prerequisites to the grad level ones?

willow pecan Jun 30, 2021, 2:39 PM

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Theoretically

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Practically, probably not

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All of undergrad ODE is solved by mathematica~~

slim peak Jun 30, 2021, 2:40 PM

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For computational techniques, and some basic theoritic results (for those who have theoritic results in their notes catThin4K )

cursive orbit Jun 30, 2021, 2:40 PM

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I see

slim peak Jun 30, 2021, 2:42 PM

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quite "difficult" for undergraduate but appropriate

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very theoritical

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is what I mean by "difficult"

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but it contains examples

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links with differential equations from casual Physics

broken meadow Jun 30, 2021, 2:44 PM

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o

cursive orbit Jun 30, 2021, 2:44 PM

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thonkid I see

opaque needle Jun 30, 2021, 3:19 PM

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good books in linear algebra? Looking to really understand the matrices I use in opengl

broken meadow Jun 30, 2021, 3:23 PM

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friedberg insel spence

opaque needle Jun 30, 2021, 3:44 PM

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appreciate it

stark creek Jun 30, 2021, 4:23 PM

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anyone selling algebra by artin in europe

obsidian valley Jun 30, 2021, 4:27 PM

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you can get it on Springer

stark creek Jun 30, 2021, 4:27 PM

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yeah but no hardcover

languid oyster Jun 30, 2021, 8:45 PM

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I know it's not a recent book, and I know this isn't really a "recommendation", but has anyone else noticed a mistake in "The Manga Guide to Linear Algebra", on page 56, when explaining combinations?

gray gazelle Jun 30, 2021, 8:46 PM

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i don't think many people here have read the book, and that's an awfully specific thing about it, so if you want good feedback you should include an image

hearty steppe Jun 30, 2021, 8:47 PM

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oh the manga guides are not necessarily designed for people who are serious about mathematics

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its really really surface level computations generally

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that are applied level

languid oyster Jun 30, 2021, 8:47 PM

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I couldn't find anyone talking about it, so I thought it might have been me misinterpreting...

languid oyster Jun 30, 2021, 8:47 PM

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hearty steppe oh the manga guides are not necessarily designed for people who are serious abou...

Lol, they still need to be accurate and informative.

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They still can't make mistakes just because it's not a super serious read.

hearty steppe Jun 30, 2021, 8:48 PM

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they are but like... its not something you would read if you wanted to do theoretical math stuff or you want to do grad level stuff in mathematics

languid oyster Jun 30, 2021, 8:49 PM

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Sure, I only rely on them for conceptual understanding.

hearty steppe Jun 30, 2021, 8:49 PM

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most of the manga guides are designed for like general STEM students that like anime and manga

languid oyster Jun 30, 2021, 8:49 PM

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I never read any manga in my life outside of them and still found them good.

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But yes.

gray gazelle Jun 30, 2021, 8:50 PM

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stare

hearty steppe Jun 30, 2021, 8:50 PM

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i mean it will get you through like very intro level calculus and stats/probability classes for sure and stuff like that

languid oyster Jun 30, 2021, 8:50 PM

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They give a conceptual understanding, but for actual calculations they are not ideal.

quick hornet Jun 30, 2021, 8:50 PM

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what's the mistake?

hearty steppe Jun 30, 2021, 8:50 PM

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idk how far in math you want to go lol

gray gazelle Jun 30, 2021, 8:50 PM

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i'm not sure how this conversation went from "there's an error in page 69 of this book" to "this book isn't suitable for learning mathematics deeply"

quick hornet Jun 30, 2021, 8:50 PM

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i feel like this hasnt been answered yet

languid oyster Jun 30, 2021, 8:51 PM

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gray gazelle i'm not sure how this conversation went from "there's an error in page 69 of thi...

page 56

gray gazelle Jun 30, 2021, 8:51 PM

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i know

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i wanted to write the sex number

quick hornet Jun 30, 2021, 8:51 PM

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haha tterra owned

languid oyster Jun 30, 2021, 8:51 PM

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Fine, I'll post a picture

gray gazelle Jun 30, 2021, 8:51 PM

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frogN

languid oyster Jun 30, 2021, 8:51 PM

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Hope I don't get sued.

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For copyright XD

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Capture_decran_2021-06-30_a_22.51.27.png

karmic thorn Jun 30, 2021, 8:52 PM

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uhhhh

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You actually read them all

languid oyster Jun 30, 2021, 8:52 PM

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32 and 33

gray gazelle Jun 30, 2021, 8:52 PM

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why would you do this

karmic thorn Jun 30, 2021, 8:52 PM

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I would skip this page without blinking

languid oyster Jun 30, 2021, 8:53 PM

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The pages afterwards still based themselves off having 35 patterns.

gray gazelle Jun 30, 2021, 8:53 PM

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ok, then it's definitely an error (the fact that they are the same, that is)

quick hornet Jun 30, 2021, 8:53 PM

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35 is the correct count, its 7 choose 3

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idk where they messed up

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probably missed a combination somewhere

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alongside the double counting

languid oyster Jun 30, 2021, 8:54 PM

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Yeah, that's what I was thinking

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But I can't spot it

gray gazelle Jun 30, 2021, 8:54 PM

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why would you

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stare

languid oyster Jun 30, 2021, 8:54 PM

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OK, what matters is there's 35 patterns

gusty smelt Jun 30, 2021, 8:55 PM

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repeat this exercise but for 100 instead of 7

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list em all out

languid oyster Jun 30, 2021, 8:55 PM

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The subgroups should decrease uniformly though.

quick hornet Jun 30, 2021, 8:55 PM

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DEF

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lmao

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they wrote DEG instead of DEF

languid oyster Jun 30, 2021, 8:55 PM

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languid oyster The subgroups should decrease uniformly though.

That would be one way of spotting the error.

quick hornet Jun 30, 2021, 8:55 PM

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idk what you mean by subgroups

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but all the counts are correct except for DEG instead of DEF.

languid oyster Jun 30, 2021, 8:55 PM

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quick hornet they wrote DEG instead of DEF

Yes!!

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Gosh, I read the F further down, and I was reminded order doesn't matter

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That's why I was confused.

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They should have had DEF for pattern 33

quick hornet Jun 30, 2021, 8:57 PM

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yes.

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not that the numbering really matters, but regardless

languid oyster Jun 30, 2021, 8:57 PM

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Unless you want to know which line you are talking about XD

molten agate Jul 1, 2021, 12:57 AM

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I'll make it quick. for calculus: stewart, larson, thomas or salas/hille? and why?

broken meadow Jul 1, 2021, 1:06 AM

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idk about larson or salas/hille but

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stewart and thomas seem to be well written, but out of the two i have more experience with stewart and it does an okay job. The best part of stewart has to be the challenge problems at the end of every chapter, i recommend to do as many of them as possible

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they are called Problems Plus in the stewart books but perhaps the thomas books have a similar problem sets

lofty sluice Jul 1, 2021, 1:10 AM

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Is there any book that treats euclidean geometry in modern axiomatic way

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As far as I know, Euclids Element isnt "complete" or "fullproof" axiomatically speaking

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Is there amy modern axiomatic systems that takes linear algebra and group theory to develop the euclidean geometry axiomatically?

willow pecan Jul 1, 2021, 1:12 AM

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Hilbert, Tarski, and Birkhoff have each proposed different sets of axioms to develop Euclidean geometry axiomatically

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You can probably find a translation of Hilbert's Grundlagen der Geometrie online

lofty sluice Jul 1, 2021, 1:14 AM

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And wht abt the others?

willow pecan Jul 1, 2021, 1:15 AM

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Tarski's axioms appear to have been exposited at a symposium so finding those proceedings might be a bit difficult

lofty sluice Jul 1, 2021, 1:16 AM

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I see..Thanks for the heads up

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BTW,are they all synthetically developed or analytically?

willow pecan Jul 1, 2021, 1:18 AM

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https://www.jstor.org/stable/1968336

George D. Birkhoff, A Set of Postulates for Plane Geometry, Based on Scale and Protractor, Annals of Mathematics, Second Series, Vol. 33, No. 2 (Apr., 1932), pp. 329-345

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This is Birkhoff's thing

lofty sluice Jul 1, 2021, 1:19 AM

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Thanks mate

quick hornet Jul 1, 2021, 1:49 AM

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theyre synthetic

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analytic geometry encodes arithmetic so is incomplete

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but tarski axioms are complete + consistent

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& i think the others are as well

past ice Jul 1, 2021, 2:00 AM

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cursive orbit Can someone give a comparison between Folland and Big Rudin for self-studying re...

Neither. Use Stein/Shakarchi for a first intro. But if you have to choose between those two, Folland is much better. Rudin uses this strange hyper-general approach and just does everything out of order.

pale scarab Jul 1, 2021, 2:09 AM

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What's a good history of math book? I read a journey through genius by dunham over the weekend and really enjoyed it but want something a little more in depth.

cursive orbit Jul 1, 2021, 3:07 AM

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past ice Neither. Use Stein/Shakarchi for a first intro. But if you have to choose betwee...

Does Stein/Shakarchi assume that I've read the other books in the series?