book-recommendations

[cyan rapids]

rudin is cool but also old

[gray gazelle]

munkres

[cobalt arch]

What about jänich?

I found the book by dugundji to be good

Thank you for the recommendations nonetheless

[karmic thorn]

Have you started reading any of the books

[cobalt arch]

Oh no 🤣

Yeah I am currently reading the analysis book by amann and escher

[hollow peak]

janich I own mostly because I like to collect some math books, it's okay I guess

not really great

[pine igloo]

books about order theory?

[gray gazelle]

Like ordinals?

I guess I imagined the theory of literal orders to be somewhat uninteresting

[pine igloo]

no, not ordinals
order theory, like the general theory of orders, by order I mean a binary relation that is an order relation

but if you know books about ordinals (or cardinals), I would also be interested

[ocean flame]

please suggest a good starter textbook for differential equations 🙂

[hollow current]

kreyszig's one is not bad

Advanced Engineering Mathematics.

[narrow talon]

Lol, I wish I knew a good book on ODEs, every one I’ve tried is never as good as I’d want

I’ll read Hirsch Smale eventually, looks like what I’d want more of less, but I’ve been disappointed by everything so far

[timber mesa]

depends on whether you want an engineering recipebook kind of approach or a dynamical systems one. For the latter Hirsch-Smale's, Teschl's and Perko's are all good yet substantially different approaches

Gerald Teschl's is perhaps a good bridge between what's usually seen in an undergrad course and what you'd see in a dynsys course, a draft is freely available on his webpage: https://www.mat.univie.ac.at/~gerald/ftp/book-ode/ode.pdf

on another hand the engineering recipebook sort of books are all pretty much the same lmao

[cobalt arch]

https://www.amazon.com/Theory-Ordinary-Differential-Equations-Coddington/dp/0898747554

@narrow talon

This is an advanced textbook in theoretical ODEs

There is another book by coddington that is introductory but I don't know if it is as good as that or up to par with it. It is worth checking it out.

[gray gazelle]

whatever you do, stay far away from Boyce DiPrima

literally the worst math book I have ever come across and it was our textbook for ODEs

there's circular references and half the time it didn't bother to give any explanation for anything

"clearly by method of inspection"

today's book:

[marble solar]

I thought it was pretty good

What edition sucks

[gray gazelle]

looks like the one we used

idk if they fixed stuff in the later editions

[sudden kindle]

Math Bookwork

Why do you always share the more unaesthetic textbooks

GTM or GTFO

[warm glen]

has anyone given sagan's combinatorics: the art of counting a try

there's a class i wanna take next quarter that uses it but i havent taken abstract algebra and i have no idea how much it uses and whether a rly strong background is needed or i jus need to know some definitions and theorem statements

also i'd ask the prof teaching it but it's the weekend so .-.

[peak trout]

Can someone help me

find ICE-EM Year 9 Mathematics Third Edition Textbook

PDF online?

[gray gazelle]

I take it you tried libgen?

[pearl imp]

I've completed single var calc except for some advanced subject and I am starting multi var calculus. I wanted to read a linear algebra book to help me better understand multi var calc.
What are some most introductory linear algebra textbooks?

[buoyant spire]

https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/
I loved Gilbert Strang's video series (he also has a textbook on linear algebra)
https://linear.axler.net/ <-- I haven't read through this, but it seems like a good book on linear algebra
https://textbooks.math.gatech.edu/ila/ <-- an interactive linear algebra textbook. I found this pretty cool

[gray gazelle]

Do you need LA to understand MC though?

i think so

Hi, What's LA and MC?

how do you study calculus - a large part of which is the study of linear approximations - without knowing linear functions?

[gray gazelle]

LA = linear algebra
MC = multivariable calculus

granted, you don't need a deep knowledge of linear algebra to get by in multivariable calculus

but you'd be missing a lot if you weren't already comfortable with linear algebra

[pearl imp]

^ yeah, this is what I was told. Also, having read a little bit on vector calculus, it was clear to me that there is a deeper connection between the two.

[pearl imp]

Thanks, Zimon

[gray gazelle]

MC = minecraft

[pearl imp]

Mortal Combat

[gray gazelle]

Massive cunt

[pearl imp]

Misogynistic Cosine

[frigid flare]

I agree it’s no good but it is popular.

[frigid flare]

Lay’s Linear Algebra

[frigid flare]

If you have Stewart Calculus take a look in there first.

[pearl imp]

thanks, will have a look at it

[gray gazelle]

i've been researching a lot about introductory la textbooks, i haven't read any yet, so take this with a grain of salt: the most recommended ones were by shilov, axler, friedberg and lax. And also some people recommended me Cohn's Algebra vol. 1 and Godement Algebra. In the end i chose Lax, mostly because someone here on discord has so many convincing arguments for why it's the best possible choice. Unfortunately, after 3 weeks it still hasn't been delivered to me, I hope I get it soon. I would suggest you to consider these books also and then see what you think is the best option.

you know you can look at books online right

l*bgen

Lubgen

[pearl imp]

those are godsend

[buoyant spire]

Also, if you're a student/faculty member (i think?) of a university that has a deal with springer, you can download certain books (like Axler's LA) for free, through your (or at least, in my case) school's library portal

[narrow talon]

many books really, as well as journals and such run through springer. They're generally very high quality PDFs too (so do this if you're interested in anything Serge Lang wrote)

[narrow talon]

Oh no! I do hope it gets to you soon, shipping is a PITA during COVID

[frigid flare]

These are more rigorous books. Lay is closer to a calculus book.

[ripe granite]

https://mathoverflow.net/questions/50025/problems-where-we-can't-make-a-canonical-choice%2C-solved-by-looking-at-all-choices-at-once

[gray gazelle]

Opinions on this book?

[gray gazelle]

that guy has a youtube channel

Bartosz Milewski i think

[narrow talon]

Maybe not the place to ask, but anyone know a Polynesian history book ?

[hearty steppe]

@narrow talon https://www.google.com/amp/s/amp.reddit.com/r/history/comments/5wy5l9/the_rhistory_discord_server_is_now_live_talk/

[narrow talon]

👍

[livid ermine]

what are the prerequisites for ravi vakil rising sea

[stray veldt]

he tells you in the preface

[stray veldt]

essentially

why is this book named commutative though

it looks more intimidating that way

[hasty turret]

What if it's actually about commutative algebra?

[stray veldt]

i guess it technically is

but at this age it suffices to call it algebra

that's already a scary enough word

[valid moth]

no it's commutative algebra

[livid ermine]

do you think you could get by never having done any algebra, just googling terms as they came up?

[gray gazelle]

no

[livid ermine]

what is the connection between homotopy type theory and algebraic geometry

[molten wave]

b a d

I mean the guy is great, but the scope of the book is just terrible in my opinion

it doesn't actually teach you any math

[gray gazelle]

I don't think it's supposed to teach any math

It says in the preface that it lacks rigour to make it more palatable to programmers

[gray gazelle]

What do you suggest for learning category theory anyway?

[tribal kernel]

A(x)=Find(x)

[late harness]

Stumbled upon this when looking for a solution to a diagramming problem I was facing. Hadn't heard the term nomogram before: http://myreckonings.com/wordpress/wp-content/uploads/nomography.pdf?bcsi-ac-cde40c890bd19f3d=2719301D00000002d/CnwHsPs9KAf6mJOLWhCnd71pFwMgAAAgAAAM+PvQCEAwAA3QAAAH3kEQA=

[gray gazelle]

Hi, I need a calculus book where rather than problems,proofs of calculus theorems explained.

[livid ermine]

analysis 1 and 2 by terence tao

[gray gazelle]

Ok

I just checked first. Does a chapter need previous chapter as prerequisite?

[karmic thorn]

You can skip chapters 2 and 3 if you're acquainted with basic set theory. However, if you have little to no prior exposure to writing proofs, I would suggest following 2, skipping 3, and then study all the subsequent chapters.

[hearty steppe]

What book?

[karmic thorn]

Tao's Analysis 1

[gray gazelle]

Do you find it verbose?

[karmic thorn]

I consider it to be verbose in a good way(as a beginner to the subject).

[gray gazelle]

Spivak's Calculus

[karmic thorn]

Is Arnold's ODEs text feasible as a first read?

[steel viper]

its definitely an edit

[stray veldt]

turns out i'm not so smart

[winter acorn]

sup

ODE book recommendation for first read

[hearty steppe]

Nagal Saff Snider worked for me so far

I started with Boyce DePrima but like this book better

[gray gazelle]

hirsch smale devaney

scroll up in #dynamical-systems

https://thalis.math.upatras.gr/~bountis/files/def-eq.pdf

[karmic thorn]

Nice, thanks everyone!

[sudden kindle]

has anyone read Serre's A Course in Arithmetic

[tranquil ocean]

ive read most of it yea

[potent trellis]

I’ve used Milnes notes on ant

[gray gazelle]

I was doing basic mathematics - serge lang and I got into the last section of chapter 9 and feels like I didn't master/grasp all the concepts, and was thinking on re-doing all the book from the beginning, any recommendations?

chapter 9
redo the book
:hypersully:

[obsidian valley]

[gray gazelle]

Hahahaha

:sully:

[obsidian valley]

how do you get to chapter 9 before realizing you don't know what you're doing

nice 1 tterra

broke yoru emotes

what is chapter 9

[gray gazelle]

wtf my emotes are not working sadcat

[valid moth]

skip to this instead

[gray gazelle]

Operations on Points

[obsidian valley]

huh

[valid moth]

operations on fleek

[gray gazelle]

And before that was Intuitive Geometry

just go do some exercises from previous sections to see if you're rusty, don't waste your time redoing literally everything

[sudden kindle]

Is it good

[gray gazelle]

Okay, thx

[tranquil ocean]

yeah i mean

its good but

its pretty short and I feel like you can get most of the material from other places in a more fleshed out way

like there's just 30 some odd pages on modular forms and its pretty nice as an introduction i guess

but you would probably just be better off reading diamond shurman or something

[sudden kindle]

Ah ok

[sudden granite]

"An analytic approach"

[hearty steppe]

What’s that?

[sudden granite]

i have no idea 😆

[grave egret]

Any good books on complex anal?

Introd.

[south ferry]

i read Complex analysis by Eberhard Freitag and Rolf Busam

and it was nice

[gray gazelle]

ahlfors

[static crest]

ahlfors

can we get the bot to just reply "ahlfors" every time it detects that someone wrote "complex analysis" in this channel

[narrow talon]

Anyone know a book about complex analysis on the real line?

I believe it’s called real in complex analysis

Maybe I’m misreading that

[gray gazelle]

[static crest]

[broken meadow]

uh

[sudden granite]

😳

[fast portal]

All complex analysis textbooks deal with a real line and imaginary line

Literally just pick something

[tribal kernel]

Is this supposed to be like calculating real analysis problems using complex analysis? Like improper integrals using residue theory?

[odd oracle]

Maybe "Real and Complex Analysis" by Rudin?

[timber mesa]

if that were the case most standard textbooks talk about that a bit

and I think Conway has an appendix about line integrals of real domain, complex codomain functions

but anyhow we're left guessing what they meant lol

[narrow talon]

I was joking

[sage python]

I think complex analysis has a bunch of books that compete awkwardly lol

[lavish ice]

Hi everyone, I am a high school student and I am looking for suitable math books for my current knowledge level, any recommendations?

[lavish ice]

Trigonometry and pre calculus prefered

[raven citrus]

I mean, why not try learning Calc?

[gray gazelle]

just read rudin analysis xd

[lavish ice]

It is alright I would do it if I see a good book

[gray gazelle]

spivak is a good book but if you haven't seen proofs before then it'll be a bit difficult

[lavish ice]

Will do

[gray gazelle]

don't.

that's a meme

[raven citrus]

https://tutorial.math.lamar.edu/

[gray gazelle]

rudin is notoriously terse

[lavish ice]

Oops😅

[raven citrus]

I went through these back when I was in High School

I was in roughly the same position as you

[broken meadow]

me going into real analysis next semester with rudin as the text 🤡

[raven citrus]

You should be able to go into the calc 1 notes, and then go backwards to the algebra notes as necessary

[gray gazelle]

don't worry, once my course notes are done, no one will ever have to write a complex analysis book again

[broken meadow]

im gonna try to spend the summer reading like pugh

to ease the pain

[gray gazelle]

i want to share complex notes but it's a super-dox

[broken meadow]

is ur name on like evry page or sth lmfao

[gray gazelle]

lol

something like that

[broken meadow]

lmao

[lavish ice]

Thx, I am also looking for a book that provides proofs for sphere volum and SA also, explaining sin and cos and their relationship with the unit circle, I am also wondering if there is a formula to find the sin, cos of any angle

[raven citrus]

this book goes through that

[sage python]

TTerra uses his name instead of z as the general complex variable

[raven citrus]

since it goes through the power series expansion

[gray gazelle]

how did you find them wtf dami

[lavish ice]

Great

[raven citrus]

(a way to model sin and cos as polynomials)

[broken meadow]

lmfao

[sage python]

🙃

[gray gazelle]

[raven citrus]

also you do multi variable calculus

[gray gazelle]

🦥

[sage python]

t h e r e i s n o e s c a p e

[raven citrus]

so you can calculate volumes of spheres, cones, etc.

[lavish ice]

That is awesome thx for help

[lavish ice]

Thx for helping guys, any helpful book you liked, let me know 🙂

[raven citrus]

"visual complex analysis"

good after you finish calculus

I enjoyed that book in high school

[lavish ice]

Sounds good

[sage python]

Oh yeah people seem to like that book lol

[raven citrus]

I mean the intuition it gives you is pretty rich

it's more like "complex calculus" than "complex analysis", but the rigor can come later

[sage python]

Doesn't quite seem like it "cuts it" for complex analysis, you need to learn it for real still when you do it

[raven citrus]

that is true

[sage python]

But yeah idk people seem to enjoy it

[raven citrus]

I like the idea of doing calculus -> analysis

in two phases

build up some intuition, then by the time you come back to the material, you have the mathematical maturity to appreciate a detached technical presentation

in fact, having analysis be one of the first very technical courses you take can be even better if you do it after calculus, because you can see how technical arguments align with intuition

so it helps you bridge the intuitive mode of mathematics you've been familiar with to the technical mode you're starting to develop

[sage python]

I could see it. What I liked was doing Spivak

It's a good way to simultaneously learn calculus and proofs

And afterwards when you do analysis you'll obv speedrun the "raw calc" bits, focusing more on topology and then multivariable calculus

[hearty steppe]

I mean maybe reading Spivak is a good flex to get thru analysis quicker even tho I already learned Calc lol

I still haven’t actually looked at Spivak cuz I learned that level of calculus already on a loosely applied level

Essentially what university expects you to know from Calc 1 to multivar

[warm glen]

speaking of analysis are there any books that follow p much the same order as rudin

i want something i can read side by side that will clarify what rudin says whenever it's too confusing for me

but books like abbott seem to do things in slightly different order or he uses alternative definitions

[hearty steppe]

Ehhh all books are different flavors but if you want to learn about a whole semester of analysis, I think Abbott is enough and you can pair that with Schroder and or Apostol

[warm glen]

ah the thing is i AM currently learning a whole semester (actually 2 quarters) of analysis and the required text is rudin :/

since they require us to read it that's why i was looking for something similar in order to rudin

but i will check out schroder and apostol, ty for the recs

[raven citrus]

why not just use Rudin?

[warm glen]

i do use it

but im stupid so it's hard

i didn't pick this profile pic for nothing

actually looking at apostol's table of contents it seems to cover almost exactly what rudin covers and reviews say it's more accessible so i might use that as a supplement

@hearty steppe thanks again

[hearty steppe]

Rudin is just brutal for people with minimal math maturity

[gray gazelle]

I'm not so sure if it is about maturity, or just already knowing analysis

[hearty steppe]

Yea basically already knowing analysis

[raven citrus]

imo

read Rudin before you read Rudin

that way you're prepared

[dapper root]

True

[hearty steppe]

I feel like learning enough analysis is that hump to progress further in math

[hollow peak]

that currently feels like algebra to me at least

picking up a decent repository of analysis isn't too hard

it pretty much only depends on your understanding of linear algebra and other analysis

[hearty steppe]

I mean like if you want to get through a graduate level text, I think you need to have like a semester of real analysis understanding at least

[slate spire]

yeah i think its nice since its somewhat familiar if youve already taken calc but is still rigorous

[robust palm]

Lol that probably sounds like nonsense to someone who hasn’t read Rudin but it’s so accurate

[gray gazelle]

@ripe granite this book is very good

i recommend it

i am forcing it upon you

[buoyant flare]

if i were to give a book to someone to introduce them to calculus what would you guys recommend

genuine question, probably better texts out there then how i learnt

unless google would give me the same answer

[karmic thorn]

What is the scope of calculus you're considering-more applied, or more theoretical? What is your target audience-someone fresh in HS or someone with a bit of mathematical maturity?

[ripe granite]

this seems to be actual geometry

[buoyant flare]

I guess id say fresh out of HS

[ripe granite]

and not category meming

[gray gazelle]

not npov'd enough for you? sadcat

[karmic thorn]

Hmmmm, Spivak should be good.

[ripe granite]

I was planning on reading mcduff and salamon at some point

[buoyant flare]

ty for the input

spivak is the default

but i mean nothing particularly wrong with that

[karmic thorn]

Thomas' is the one I continue to use, but I would still recommend Spivak if it's not for self-learning.

[ripe granite]

unfortunately, my class stopped doing simp geo after 2 lectures

[buoyant flare]

it would be for self learning

[hasty turret]

Dad is proud of you,son

[karmic thorn]

Oh, weren't you going to teach?

[buoyant flare]

Not completely

Its more for a friend of mine, ill assist them i suppose but majority self learning

[karmic thorn]

In that case, you can simply live off of MIT OCWs single variable and multivariable calculus courses online.

They have good notes and lengthy PSets

And I think they're really good

[buoyant flare]

whats the text you use?

[karmic thorn]

Thomas' Calculus

It's like

Primarily intended for every uni student who's probably taking calculus for the first time

So maybe it's not such a popular choice amongst math majors

[buoyant flare]

They aren't math major

Is there an online pdf of the book i can have a look at

[karmic thorn]

Yeah, it's good otherwise

[buoyant flare]

Thanks, ill look into it

i appreciate the recommendation

[karmic thorn]

You can get it through completely legal means

tsk tsk

[buoyant flare]

😉

that textbook was easier to steal than average

ty ted

wait out of curiosity, if you use that text what field are you in?

[karmic thorn]

Maths

Although my curriculum deceptively looks like...not-math

I've been using Thomas' for speedrunning and skimming parts of Calculus I already know about

[buoyant flare]

i see

everything available for free on the internet to learn, but sometimes having a collective source for material is helpful

esp for someone self learning

[karmic thorn]

Agreed

[buoyant flare]

1205 pages

standard

[karmic thorn]

It's not dense like Spivak lol

[sudden granite]

speaking of spivak

someone told me to read it

😳

[buoyant flare]

im skimming over it now and it seems like itd fit well

[karmic thorn]

Most of the contents are easy, 1205 pages only amount for the comprehensiveness and truckload of descriptive exercises(largely repetitive)

[karmic thorn]

If you've done precal, go ahead!

[buoyant flare]

it really starts off the from very beginning

whats precalc for a non american?

i mean the name suggests before calc but whats that include

[karmic thorn]

Algebra, trig, some basic idea about analytic geometry(conics, straight lines)

[buoyant flare]

there is a chapter just on functions in this book

i feel like i learnt some of this stuff in grade 10

or before lol

[karmic thorn]

Yeah, do learn how to graph functions by hand haha

It's insightful

[sudden granite]

it definitely takes some getting used to

[buoyant flare]

its my state in aus we are made to learn most of it by hand

[sudden granite]

the book i mean

[karmic thorn]

It would

Spivak isn't easy for someone getting into calculus

[sudden granite]

yeah

i skipped the first four chapters 😳

[buoyant spire]

^^ If it's alright, I wanted to recommend Professor Leonard channel
I think he's great, and I hope you find him helpful: https://www.youtube.com/channel/UCoHhuummRZaIVX7bD4t2czg
He has some, imo, quite nice playlists regarding calculus

[buoyant flare]

i love the ability to pirate everything

[sudden granite]

we do not do that here...

🙄

[buoyant spire]

Arr, we be good law abiding folk, especially since pirating is against discord TOS

[buoyant flare]

i mean i said the ability

[sudden granite]

lmao

[buoyant flare]

i never said i did it personally

that would be illegal

i follow all laws

yessir

[gray gazelle]

a good law abiding citizen would be disgusted by the ability to do such a thing

[buoyant flare]

exactly 8da

[buoyant spire]

Exactly, matey

He was referring to real life pirating

Like with ships

[sudden granite]

both are bad

but

[karmic thorn]

Pirating bad, buy from Springer/Elsevier, fill the pockets of those multinationals-it's our basic obligation as a human to pay ridiculous sums of money to read a damn book. Love you Springer

[sudden granite]

lmaooo

pin that 😳

[buoyant spire]

Especially since the authors of those works get a tiny fraction of the cost of the textbooks, despite the proportionally larger amount of work they put into the books

[buoyant flare]

i also love to pay for all scientific papers and journals

[sudden granite]

i hate that textbooks are so overpriced

[tranquil ocean]

is springer even like a bad company, like i don't think its anywhere near elsevier bad

[sudden granite]

why can't we live in an ideal world

[buoyant flare]

as we all know it directly goes to the pockets of those who wrote the paper

[sudden granite]

where textbooks are like $30

[gray gazelle]

but they are, springer sells $30 textbooks

[sudden granite]

why do we have to wait 200 years before we can finally get a $30 textbook

😕

[karmic thorn]

Yeah, Elsevier is S-tier pathetic, but I don't really think Springer is being as reasonable either.

[buoyant flare]

honestly why does paper have to be nicer than digital

i wish i could be sated with just a pdf

[tranquil ocean]

I mean, when your demand is literally nothing, its hard to make hard cover books to sell for $30

[gray gazelle]

this is admittedly probably true

[karmic thorn]

Make them paperback, offer cheaper digital versions

[gray gazelle]

but springer does make paperback books, for $30

[sudden granite]

everyone is out there buying calc by spivak

[tranquil ocean]

Like, I've talked with the head of AMS publishing and they said they're not really trying to make money from their books

[buoyant flare]

while your reasoning is sometimes valid

[sudden granite]

and stewarts calc

[karmic thorn]

E-books are unreasonably costly

[buoyant flare]

often times there is no way to rationalise some exorbitant markups

such as e books

or scientific journals

[gray gazelle]

so are you saying that books cost as much as manufacturing costs?

[tranquil ocean]

He said something to the effect of that they don't print very many, and so the upfront cost is higher than for other, like normal publishers

[karmic thorn]

Publishers making ridiculous amounts of profits is a testament to how bad things are, although I think most of the dough comes from institutional subscriptions(which is even more concerning).

[hasty turret]

There's always the library that shall not be named

[buoyant spire]

The public library?

[hasty turret]

The library of genesis

[karmic thorn]

@hasty turret

[hasty turret]

Where you can find holy texts on the genesis

[buoyant spire]

Great, I love reading about the genesis

Are there any libraries dedicated to the new testement?

[hasty turret]

The genesis contains all

[gray gazelle]

haha, teste-ment

[obsidian valley]

yes

fuck springer

im still out $30 after 20+ emails to their garbage support team

[gray gazelle]

oh?

[buoyant flare]

library of babel contains alll

😉

[hasty turret]

Why is God such a douchebag?

[sudden granite]

why is paperback langs basic maths $70

[hasty turret]

There's no reason the tower of Babel had to exist

[buoyant flare]

library of babel different thing

or if you are just commenting on a seperate tangent then yeah i agree

God was a dick but damn it bade for some interesting stories

Biblical canon got some good tales

[gray gazelle]

blasphemy in da server

[buoyant flare]

blasphemy in da server - Azazel

Azazel

[gray gazelle]

irony moment

[steel viper]

its not manufacturing costs

per se

its probably an economy of scale problem

when ur making a teeny number of each product the initial costs of every step in the production chain (logistics, transportation, organization, getting the books written at all, etc) that ordinarily would be covered very easily are very significant

like 5000 dollars is nothing if ur selling 45k copies but if ur aiming for like... 500?

thats enormous

[sudden granite]

#book-recommendations message

someone pin this

[late harness]

If anyone is interested, I set up a temporary (free) transfer of my e-book entitled "My Little Big Math Book" for someone who wanted it, and I thought I'd make it available here if anyone else wants it? Here's the info on Amazon: https://www.amazon.com/My-Little-Big-Math-Book/dp/9198282603

There's also a recording (in English) of a presentation I gave at the Ministry of Finance in Sweden on this topic: https://www.youtube.com/watch?v=0Mqp1DNUVUw

[molten wave]

interesting, though I question whether members here could be the intended audience

[late harness]

Could be, even mathematicians may have forgotten how they learnt to count. Could also be the case that you work as an educator where being aware of the steps kids need to take in order to learn to count is beneficial.

[molten wave]

fair fair

I work in foundations so counting is a nontrivial construct to me

nuanced, that is

[late harness]

Cool, I did research in foundations a long time ago. Are you on the FoM mailing list?

And, anyway. Here is the download link to the ePub: https://www.dropbox.com/t/dEYGKZmGQMVRkyUS

[molten wave]

no, is there a mailing list

[late harness]

https://cs.nyu.edu/mailman/listinfo/fom

To be honest, I haven't looked at it in a long while, but there used to be some really interesting topics there.

[molten wave]

I mostly specialize in type theories, in particular HoTT, and its applications to foundations of math and software

computational trinitarianism is weirdly complemented by abstract homotopy theory, it's wild

[late harness]

Interesting, I have to look into it. I'm in information modeling now, and there may be some parallels with my concept of a posit and "propositions as types", from the quick glance I just gave HoTT.

A posit is a syntactical construct that looks like a statement, but has no truth value. Posits are instead ascertained in assertions, where they are given a certainty value in the range [-1,1] by some asserter. We're straying from the topic of the channel though.

[dire comet]

haskellor

[sudden kindle]

PA PA /TU TU /TU TU /TU WA WA.

[molten wave]

Yes

[warm glen]

i see jacobson recommended often for algebra here, which of his books are y'all referring to tho

lectures in AA vol 1 or basic algebra 1?

[narrow talon]

Probably BA1

[long anchor]

how good is this for learning diff eq ?

diff eq book suggestions anyone ?

[hollow current]

@long anchor kreyszig advanced engineering mathematics

[long anchor]

k ill check that out. thnx for the suggestion

[long anchor]

@hollow current this book is fking lit

[hollow current]

[uncut zealot]

Does anyone know any good books for learning ODEs? My class is using Elementary Differential Equations with Boundary Problems by William Trench, and it's not really working well for me.

[gray gazelle]

https://thalis.math.upatras.gr/~bountis/files/def-eq.pdf this book is good

[novel iris]

I thought it sucked personally

it's full of bs handwaving >:(

[long anchor]

@novel iris bruh cwab reced it

[novel iris]

well her opinion is wrong [jk don't murder me cowb]

[zinc lichen]

Hey! Does anyone know any book similar to Art of Problem Solving Pre Algebra? I found the website exercises quite fun and interesting. Since I'm not from the US the Textbooks are pricey.

[gray gazelle]

@long anchor yo soapfuck what kind of diffeq course you takin? calculus or theory

[long anchor]

godelfuck im taking the calc one

@gray gazelle

well self studying so it can be whatever i want

wait wdym by theory

[novel iris]

do theory \o/

it's nicer

the difference is like

one is just a recipe book for diff eqs

one is about proving shit

[gray gazelle]

@long anchor read ODEs basics and beyond

[long anchor]

kk ill check that one out too

gud suggestions godelfuck

this the one right ? @gray gazelle

[gray gazelle]

yes

[long anchor]

kk

[hearty steppe]

I feel like I need that book

[fast portal]

What is your recommendation then

[novel iris]

idk, I'm currently taking an analysisy ODE class that doesn't use a textbook

[sage python]

For ODEs I know two books that are supposed to be good. One by Teschl and one by Perko

Both I think are named something like "Differential Equations and Dynamical Systems"

[hearty steppe]

Dami in with the FLEX!!! Why did you not tell me about this sooner

Maybe you did mention it in your Dynamic Systems recs a while ago

[sage python]

I feel like I haven't seen too many ODE book requests aside from like

Intro stuff

These aren't gonna be suitable if someone wants the sorta "engineering-style" class so I haven't mentioned them much here, I def brought up Perko before

Thing is I don't know either of these well myself. Perko I know of because my analysis class had about 5-6 lectures on ODEs, and it was a bit of a dynamicsy take

One person found Perko and said that a certain part of it corresponded nicely to what we were doing in class. Teschl because I did this summer thing in analysis which did 4 topics, one of which was dynamics

The year after me my classmates were TAs, and they said they switched to more ODE style dynamics (rather than ergodic theory and Anosov business) and used Teschl

[fast portal]

Math is a never ending ocean and I am glad I never have to deal with its unfathomable depths

[sage python]

Teschl is free I think if that's relevant to you Cat Man

https://www.mat.univie.ac.at/~gerald/ftp/book-ode/

[hearty steppe]

just consider anything relevant to me Dami. I'm all in with math. I'm probably one of the only people focusing largely on a theoretical mathematical rigor perspective to biological systems.

[sage python]

I guess for ODE type stuff there's that, what else do you want recs for?

[hearty steppe]

I've yet to meet a serious mathematician that studies biology

Not sure yet

I'll let you know

[sage python]

Obv that's a bit outside my area so there's a good chance I won't have good recs

[hearty steppe]

I might consider Number Theory soon but not sure yet.

[sage python]

Do you care about stuff like

Idk Markov chains?

[hearty steppe]

yup

[sage python]

I feel like that's something biologists would care about

Stochastic business

etc

So the book my undergrad used for that was by Greg Lawler

Probably just titled "Intro to Stochastic Processes" or something like that

[hearty steppe]

ye there are a lot of things I'm considering. Millenial got me to openly care more about combinatorics so combinatorics recs are welcomed too

dude, this George Teschl guy is a fucking saint. We need more people like this in academia/mathematics

His page is amazing

[sage python]

Hmm, I haven't looked at his page lol, what's his deal?

Let's see

[hearty steppe]

you can download his book for free like on the spot and I'm like wow. This is awesome

[sage python]

Oh yeah that's def nice

One thing I appreciate Hatcher for lol

As for combinatorics, I didn't really learn it out of a book tbh

My combo prof from undergrad likes "Combinatorial Problems and Exercises" by Lovasz

That's more a list of puzzles that teaches you a ton than a "Let's systematically develop the combinatorics that a given demographic or other ought to know"

This was our recommended class reading list

@strange mulch spit it out!

[hearty steppe]

Rosen is cool

[strange mulch]

Uh what

Did it say i was typing? Must have been a bug

[gray gazelle]

Rosen book 700 pages

basic introduction

[hearty steppe]

Rosen not that bad to read. I found it pretty manageable when my math background was pretty shit compared to now

Knuth is more appealing

I mean a book is a book too mate. Gotta keep reading to keep learning xD

[calm crane]

sounds about right

more pages there are more basic it is

[gray gazelle]

actually Lovasz looks best out of the mentioned so I'll try to read it

although its just exercises with solutions

[steel viper]

@calm crane so true

lurie

[calm crane]

[hearty steppe]

its like a perpetual feedback loop. The more you learn, the more you need to learn cuz you know that much less.

[hearty steppe]

yo hit me up DM about that book.

Question, would it be too pre-emptive for me to dive into functional analysis right now with hardly any exposure to real analysis?

[static crest]

yes

[hearty steppe]

Cuz I want to better understand quantum mechanics and everyone who has studied quantum mechanics in depth has said that it is important to know functional analysis.

im not sure in what way I should understand functional analysis tho, like is there a minor short cut to learn it on the surface and get to the theory later?

[static crest]

like ya, you can understand the fourier and other transform shit

without much knowledge of any analysis, just calc

[hearty steppe]

but will it give me enough intuition?

I'm assuming yes because there are many people that study physics that don't take a functional analysis course in mathematics?

but ill pick up on the theory eventually, assuming I need to work a bit more on the maturity to get there

[static crest]

I mean ug physics level functional analysis is probably easy enough

probably hard to even call it analysis

if I'm being honest

[hearty steppe]

hmmm do you have a curriculum link to refer to on the topics in a ug course for functional analysis?

[static crest]

more like being a bit loose with what's alowed with calc

[hearty steppe]

or i should just search it

[mild narwhal]

Anyone knows a good problem book to practice Analysis. At the level of a first year grad student

[static crest]

I don't think there's really "undergrad functional analysis" really

it's just abusing calculus a bit

what they do in ug physics (and engineering)

[hearty steppe]

ahhh ok so basically screwing around with lagrange

[gray gazelle]

pugh's book has an absolute shitload of problems. it also has some preliminary exam problems that were given to 1st year grad students on exams, which is right up your alley

it's not a problem book but it certainly works as one

[mild narwhal]

Okay, I’ll have to check it out

[frigid flare]

Not a book but almost 30 years of prelims https://researchguides.library.syr.edu/c.php?g=258216&p=1725292

[mild narwhal]

This look like what i need, exposure to variety of problems in Analysis

[narrow talon]

Laughs in Charles Peskin

[hearty steppe]

Well I never met the guy so my point stands

[narrow talon]

Damn, so many people in my department are math bio

[hearty steppe]

Are you into it as well?

[narrow talon]

Not even a little

[hasty turret]

laughs in Hardy

[gray gazelle]

now he might object that hardy didn't do real bio, just population genetics

[deft sedge]

https://www.amazon.com/Euclids-Elements-Thirteen-Books-Euclid/dp/1420956477/ref=sr_1_1_sspa?dchild=1&keywords=euclid+elements+hardcover&qid=1614955967&sr=8-1-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUFYNE9ZNFVSSzQ0WDQmZW5jcnlwdGVkSWQ9QTA1MjM3MTUxMEU5N0Q1VlRFVFBVJmVuY3J5cHRlZEFkSWQ9QTA4NjAyNzVNVDZDQjFJVE9RVDImd2lkZ2V0TmFtZT1zcF9hdGYmYWN0aW9uPWNsaWNrUmVkaXJlY3QmZG9Ob3RMb2dDbGljaz10cnVl vs https://www.amazon.com/Euclids-Elements-AU-Euclid-dp-1888009187/dp/1888009187/ref=mt_other?_encoding=UTF8&me=&qid=1614955435

are those identical books just one hard cover one soft or is the second one a up todate revision

[buoyant spire]

You might be able to find the different editions available for that book on goodreads

[gray gazelle]

hardy didn't do real bio, just population genetics

[gray gazelle]

bl*cked fuck you!!!

ok

[warm glen]

eyo so i wanna ask for some book recs for core classes: real and complex analysis, linear and abstract algebra, topology

but not necessarily the best ones to learn from for the first time

i remember seeing advice somewhere that math students should read well written books and try to emulate the way the authors write proofs and stuff

what are some books for the above topics whose authors mathy bois should try to emulate?

[timber mesa]

Gregory T. Lee's "Abstract Algebra" is a bit dry but I liked how the proofs are written, very thorough and I don't think he skips important things

[timber mesa]

can't say recs. for the rest of these topics though

[warm glen]

oo it's pretty new too

thanks for the rec

[fast portal]

@molten wave I need textbook recommendations for compiler designs and compilers in general

[frigid flare]

Consider that Rudin’s POA is widely regarded as a great book but I don’t think you want to write proofs like him as a student since they take thought to understand. Reading those proofs is fairly significant academic endeavor. Your professors don’t usually want you to hand them something they have to go study.

[deft sedge]

i want the most recent whicih i thikn its this one bc it says 2017 and it has all 13 books in 1

[warm glen]

are there any particular real analysis books you'd recommend that a student can learn to write good proofs from then?

[hasty turret]

Pugh seems good for that

[warm glen]

ah yea ive heard lots of good things ab that one

[narrow talon]

In terms of "writing like the masters" and using things as reference texts, I'd say take a look at Jacobson's Basic Algebra, Stein is of course a grandmaster of analysis, and has a rather long sequence on analysis (4 books at the undergrad level introducing harmonic analysis, complex analysis, real analysis [not a first course], and functional analysis, as well as 3 very famous monographs on harmonic analysis. There are many books in analysis at a slightly higher level that are written by masters (Riesz, Yosida, Lax, Villani, Varadhan, etc.). As for topology, I am not sure of sort of "introductory" books by experts

[hasty turret]

Munkres?

[narrow talon]

Mind you, though Rudin is quite popular, Rudin is not necessarily a master of analysis! Surely not to the level of the others I have mentioned here. He is largely known due to his textbooks

[deft sedge]

why is euclid so beast mode

[narrow talon]

I am not sure, I just don't have any idea as to how much influence Munkres has had on topology. Thinking a bit harder, Milnor is a colossal figure in topology with great books, though they don't cover general topology I think

as for linear algebra, Peter Lax has an excellent book on the topic and he is certainly a master of the topic (or rather, functional analysis but same difference)

[deft sedge]

fav/best mathematican of all time... go ... euclid in the house boom boom boom i have a square room

[warm glen]

thanks for the recs! i didn't really consider that the books i choose should probably be written by mathematicians who had significant impact on the field they're writing about

do u think books with those types of authors are the best options for the specific goal i have in mind?

for example, would lax be better to emulate than roman, would stein be better than conway, etc

i know there's probably not a definite answer but im curious ab what ur opinion is

[narrow talon]

Ultimately it depends, both on the book and the level you're at within a given subject. Just because a text is written by a master doesn't necessarily mean that their exposition will help you understand the material, and often these books are best used as a second read because what's really interesting is the perspective.

I think a good example is perhaps Functional Analysis. There is sort of a canon of functional analysis (despite the subject being very far from standardized relative to other fields) heavily influenced by people like Conway and Rudin. However, if you pick up Riesz Nagy, Brezis, Yoshida, or Lax you'll find completely different perspectives on the material. Riesz Nagy emphasizes integral equations and some classical DiffEQ stuff, Brezis offers a more modern perspective on FA in PDEs, Yoshida is abstract and tries to include everything, and Lax is rather applied (but doesn't deal with Sobolev spaces nearly as much as Brezis).

What I'm getting at is that books written by these people often focus on what they think is most important, and getting a glimpse into what a massive figure in a field things is important about that field is definitely a great thing. But it doesn't help so much in understand the intuition behind why things work in any particular proof.

Sorry for the massive (and probably somewhat trivial) message

[sage python]

Did someone say functional analysis

[narrow talon]

Treves is still my goal text for FA, one day I'll read that book cover to cover

I left it in the US though because I wasn't planning on taking FA this year
oops :/

[warm glen]

thanks for the thorough reply

and yea i figured these kinds of texts would be better as second reads

[sage python]

My class vaguely worked out of Brezis? Though our prof referenced some other books since Brezis kinda treated functional analysis as a prelude to PDE, and he wanted to do stuff like spectral measures and applications to ergodic theory

[warm glen]

my idea was to pick a text that's good for first time exposure to learn from, and then a text written by a master to learn more and also learn how to write better

[sage python]

Sometimes masters write more intro books

[narrow talon]

That's what I'd do, though sometimes they overlap

[karmic thorn]

Tao 😌

[narrow talon]

[sage python]

My undergrad analysis class used "Elements of the Theory of Functions and Functional Analysis" by Kolmogorov and Fomin

[narrow talon]

Tao, Lax (LA and FA), Stein, and Brezis are all great introductions to subjects, as well as texts by masters

[narrow talon]

I've heard mixed things about it, that the translation sort of botched Kolmogorov's brilliance

[karmic thorn]

Nice.

[sage python]

There are two translations is the weird thing

[narrow talon]

That is weird

[sage python]

This caused us a lot of confusion

[narrow talon]

I could probably find a copy of it in Russian at a market nearby where I'm living

[sage python]

One was retitled "Introductory Real Analysis"

Translated by Silverman

And he reorganized things a lot

The other keeps the original title and I think is mostly true to the original. Problem is they translate an older edition which doesn't have as much content, and some of the terminology is odd

But it's clean for sure

[narrow talon]

Found a copy of Механика (L&L Mechanics) a while back

[narrow talon]

Yeah they're at like edition 4 right?

[karmic thorn]

Landau

[narrow talon]

I know Levy has an autobiography too which is dope... except it's all in French

[karmic thorn]

I tried reading Mechanics back in HS, had to give up after 3-4 pages but it felt like a very nice text

[sage python]

Something like that? Our prof was like yeah the newer ones are super thick and contain more about stuff like calculus on Banach spaces

[narrow talon]

Oh jeez

[sage python]

But yeah I'm not gonna say K&F is the correct intro to functional, just that it's very intro among the functional analysis books

Volume 1 doesn't require measure theory, volume 2 introduces it

[narrow talon]

I tried reading about Martingales in Banach spaces(from a book of the same name). It’s not too bad but I’m not sure what its use is

Lots of connections to harmonic analysis iirc

[sage python]

So yeah evidence that masters can write intro stuff

[narrow talon]

Brezis is intro, so is Stein

[sage python]

That's true, I guess I meant intro meaning like, you don't even need to finish baby Rudin intro

Compared to Brezis which is more, intro to functional analysis once you know measure theory

[narrow talon]

Oh yeah, then definitely

Riesz Nagy technically falls in the same category, but doesn’t have exercises

[sage python]

Idk that one lol

I just know the ones I used mostly

[narrow talon]

It’s nice, I haven’t read much of it but found the small amount I did read to be interesting if not particularly well motivated

[sage python]

K&F for undergrad analysis, Brezis for grad, plus occasionally referencing Buhler-Salamon's online notes

Our prof in grad also liked Lax

[narrow talon]

I’m reading Le Gall right now (master of probability) and the text is not good

[sage python]

And at the end he found one by Einsiedler and Ward which is what he would've used if he found it at the beginning of the class lol

Since it does literally everything

[narrow talon]

But the exercises my god

[narrow talon]

Wonderful

[narrow talon]

Lax and Brezis are pretty similar vibe

Lax is thicc tho

[sage python]

Makes sense. I'll venture a guess and say you're interested in a lot of the math connected with physics?

[narrow talon]

Yeah, but I don’t know any physics (like at all)

[sage python]

I'm mostly inferring that the gcd of mechanics, probability, and functional analysis in my mind is quantum-type stuff

[narrow talon]

From what I’ve gathered, you sort of pick it up as you go

[sage python]

Ah gotcha, so you're more math looking at physics than physics looking at math

[narrow talon]

Nah, mostly probability

[sage python]

Good stuff. You like representation theory at all?

Integrable probability? 🙂

(I've so been meaning to learn that)

[narrow talon]

Not even a little. Had an awful teacher for it and it left a bad taste in my mouth and I know nothing about it

[sage python]

😦

[narrow talon]

Err, what exactly do you mean by that?

[sage python]

I don't know much about it but there's a guy here who works on the stuff

http://www.math.wisc.edu/~vadicgor/research.html

[narrow talon]

Interesting, one of the people I applied to PhDs to work with is in the integrable probability group

Probability is tricky because there's a LOT of introductory stuff you have to know

[sage python]

Yeah for sure. I did this measure theoretic probability class last semester but I was wayyyy too checked out so I just winged it

[narrow talon]

Yeah, I'm at that point where books that I'm reading along for class are just as much about descriptive set theory as probability

And it's totally introductory

All the weak convergence stuff needed for stochastic analysis

Combinatorial probability has slightly less intense prerequisites, but it's not really where I'm aiming right now

[sage python]

I didn't expect probability used much more descriptive set theory other than maybe some super basic stuff about the Borel hierarchy

[narrow talon]

Yeah mostly borel hierarchy/analytic sets and some of the harmonic analysis associated with all that

[sage python]

Even that's more than I thought

But yeah eventually I wanna learn a lot more probability lol

[narrow talon]

You can avoid it for sure

There's sort of two canonical books on weak convergence, one uses borel heirarcy/analytic sets, the other avoids them a bit more

But since everything is done over Polish spaces in probability, it's sort of unavoidable

[sage python]

Ah

That kinda makes sense lol

[narrow talon]

But to be honest I definitely need to work on my measure theory still. Lots of very sticky results in basic measure theory when dealing with abstract spaces. Very easy to run into problems when things like separability aren't assumed

[gray gazelle]

This sounds sort of like "one man's trash is another man's treasure", shitty set theoretic details of analysis being something that set theorists are interested in

[narrow talon]

The classic example is Kolmogorov's theorem when we get the existence of a stochastic process with prescribed finite marginals but don't have continuity a.s. because the set of $\omega$ where $t \mapsto B_t(\omega)$ isn't necessarily measurable

[hasty eagle]

Probably_Jason

[narrow talon]

And then have to either create a continuous sequence which converges uniformly, or prove Kolmogorov's lemma which gives us a modification that's continuous a.s.

Err, I guess that's not really a statement about separability. Oh well

[narrow talon]

I did jack shit all of last semester, was super rough

[sage python]

Yeah mentally I'm just off idk

I feel I need a vacation

[soft terrace]

what are some typical graduate level statistics theory books?

[vague mason]

Mandelbrot set

[gray gazelle]

Some books I hear about are schervish, shao, maybe lehman. Not that I have read these, but I own schervish book, for what it's worth

[wooden sparrow]

So in Apostol's contents, there's no mention of riemann sums anywhere

[frigid flare]

He mentions them in chapter 7

[wooden sparrow]

Oh okay thanks

[gray gazelle]

is there a good book on the history of pi?

[warped cedar]

A History of Pi

is the only book I know

On it

[gray gazelle]

Any recommendations for a stats book that assumes (or covers) measure theory? Preferably a 'wordy' book (with examples and shit)

[compact snow]

lol if you want a lot of examples you're in the wrong field 🙂

You may have to write your own book.

[gray gazelle]

did you read every stats book

idk why your comment annoyed me but blocked

[compact snow]

fair.

[livid ermine]

Have anyone read any good books on the big picture of mathematics, philosophy of mathematics, interesting history of mathematics etc?

[warped cedar]

a book literally called proofs from THE BOOK

[tranquil ocean]

try reading the Weil conjectures by Olsson

[livid ermine]

thjat looks pretty cool

what are the prerequisites in it?

[sudden kindle]

whats this

[tranquil ocean]

kinda a historical biography of the weil siblings combined with an autobiography of Olsson's own journey through math

[gray gazelle]

yo any recs for functional analysis book? Heard of Conway's and Pedersen's book, not sure what I should stick with, maybe you know of something else you enjoyed.

[narrow talon]

Brezis

or Lax, they're both pretty great

[gray gazelle]

any of you read the ones I mentioned?

[narrow talon]

More applied (to PDEs/analysis that is)

[narrow talon]

I've heard of Conway through reputation (which is not a good reputation). Not familiar with Pedersen

[gray gazelle]

yeah conway didnt look good to me, brezis seems like not what im looking for tbh

[narrow talon]

What are you looking for?

[gray gazelle]

1.normed spaces, hahn-banach, mazurs theorem
2.banach spaces, comapct operators, riezs-schauder thm
3.hilbert spaces, orthogonal shit, radon theorem, dual spaces to L^p
4.Unitary and Self-adjoint operators, spectral theorem
5. Banach-steinhaus theorem
6.weak and *weak convergence in banach spaces
this is the syllabus

[narrow talon]

Is there no listed course text? Or is it the two books you mentioned?

[gray gazelle]

rudin and conway and some notes

[narrow talon]

Kreyszig seems to match all or almost all of that, and Lax, but probably best with multiple expositions

I'm in a FA course right now and my approach is to use a book from sort of three different levels of abstraction for different stuff. So one book from each of the sets {Kreyszig, Brezis, Lax}, {Rudin, Conway}, {Yoshida, Treves}. Brezis and Treves are overall some of my favorite math texts overall

[gray gazelle]

this pedersen book looks good actually

and lax

[narrow talon]

Lax will also cover all of that I believe, it's a long book though. Maybe look at it next if Pedersen ends up being off

lol

[gray gazelle]

ye although I have no clue if what I will read will be off since all this stuff is new to me lol

but Ill switch from one to toerh one

ye

I mean I will ahve notes of my course

which I guess hsould be ebnough

but idk

[narrow talon]

There's lots of good stuff in Functional Analysis, what other stuff you're interested in should pretty heavily dictate what book you'll end up enjoying and learning most from

[gray gazelle]

this course seems hard af after 1st class tbh

[narrow talon]

Bobrowski isn't in this list because it's not really a general FA book, but is very probability focused. Riesz-Nagy is pretty focused on integral equations (so is Brezis, but not until much later in the book)

[narrow talon]

My class took 5 weeks to get through chapter 1.1 and 1.2 of Brezis, I hate it

[gray gazelle]

i hope I wont see pdes in my course

[narrow talon]

Naaaaaah, PDEs are really nice motivation for FA, I don't know shit about them but it's still really helpful

[gray gazelle]

although this year an analyst is running the course, instead of probabilists that do usually

but not the converse

[narrow talon]

Oh no a PDE

Oh wait, it's just probability

[gray gazelle]

ok by analysis I mean pdes

and shit

I dont think probabilists deal with a lot of pdes but idk

[narrow talon]

Depends on thee area of probability

[gray gazelle]

ye

I came up with somethingg similiar one day

[narrow talon]

This is used to prove a result in convergence of stochastic gradient descent

And Markov processes are extremely closely tied to potential theory

[gray gazelle]

I once thought what if you have a diffeq and the IVP depends on the probability

and someone told me this is stochastic diffeq or sth I remember cause I like that word

[narrow talon]

I think SDEs are DEs with a Wiener measure/measure of infinite variation, but don't quote me on that

I'll get there later this semester

[dapper root]

WIENER HAHAHAHA

[sudden kindle]

[quick hornet]

"brownian" is an unfortunate adjective, given the context

[narrow talon]

Definition: we define a $\textbf{Brownian Motion}, B$ as the terminal byproduct of a class of destructive foods $\mathcal{F}$.

Theorem: Chipotle $\in \mathcal{F}$.

Corollary: $P(B | \text{Chipotle}) = 1$

[hasty eagle]

Probably_Jason

[sage python]

Lmao

Does Chipotle cause brownian motion? I have more frequently heard this associated with Taco Bell, though it's never happened to me lol

[broken meadow]

irritable bowel syndrome theorem

[hearty steppe]

irritable bowel theorem

[broken meadow]

intermediate bowel theorem

[buoyant flare]

if anyone has good physics or math podcasts lmk

[hearty steppe]

@buoyant flare try Dark Horse, I think that is Eric Weinstein’s podcast channel

[buoyant flare]

Ty for the suggestion

[sonic vessel]

which book is good for learning trigonometry and geometry

i know basics of them

[buoyant flare]

be more specific

[sonic vessel]

wdym

[gilded zodiac]

Whats a good book i can get for challenging linear algebra questions?
like for vectors and vector geometry

Questions like these

[buoyant flare]

@sonic vessel this is how U ask for book recommendations

Unfortunately Idk how to help you Mani

[gray gazelle]

Putnam problems

[timid vector]

victor blåsjos podcast is pretty epic

[buoyant flare]

Ty

[timid vector]

its mostly a history of math podcast

ive listened to a bit of my favorite theorem and its nice as well

[buoyant flare]

oh that sounds good

Ill check that out now

I'm about to head to sleep

Is it on Spotify?

[timid vector]

not sure

[buoyant flare]

damn doewjt seem to be

ill download and listen to another time

[hearty steppe]

Ikramov
Blyth

[gilded zodiac]

are these names of the authors???

[hearty steppe]

Of two different books yes

[fleet jacinth]

Could someone recommend me a good book for:

-Learning basic combinatorics

-Learning descriptive statistics

[hearty steppe]

Stats - Walpole et al

Still new to combo but start with a good discrete book like Knuth

[sudden kindle]

I want to learn complex analysis better

Any book recommendations?

[sage python]

Time for the complex analysis book review

Ahlfors: Old school and very chit chatty (in particular, bad as a reference since theorems can just happen in the middle of paragraphs). Decent, but mostly been surpassed by newer books.

Gamelin: Requires extremely little background (calc 3 but tbh you might be able to wing it as you go), covers a whole lot of material (uniformization for Riemann surfaces). Very geometric angle. Probably the correct entry point for beginners.

Stein and Shakarchi: Kind of the standard at this point, requires a bit more background going in than Gamelin (Baby Rudin - epsilon, though I feel it's a bit confused about exactly how much background it wants). Supposed to have good psets, its treatment biases number theory and Fourier analysis. Toy contour business is kinda stupid imo. Overall I don't like it.

Conway: The Dummit and Foote of complex analysis books. Extremely easy to read but slow enough that it gets boring.

Freitag and Busam: S&S with less Fourier and more number theory (including some modular forms). I probably recommend this if you've already had real analysis (which you prob should before starting complex). Has a followup volume (just by Freitag) which covers a fair bit.

Narasimhan: Faster and more sophisticated, takes a topological viewpoint from the start. You should prob know some measure theory and a bit of functional analysis going in, but if you do this is probably the best.

Schlag: Written for the third quarter of graduate analysis at Chicago, where students have to take a full year each of algebra, analysis, and topology/geometry. Thus, and due to the professor's own proclivities, it assumes a good bit of background and moves fast. The advantage is it does cover a lot of material, and emphasizes a geometric viewpoint.

[gray gazelle]

how the fu k you pin message

[sudden kindle]

.pin

[gray gazelle]

[sage python]

Yeah you have to use the bot, honorables don't have manage messages anymore

[sage python]

I'll just do it lol

[gray gazelle]

gamelin

[sage python]

It's not narcissistic since TTerra wanted it pinned anyway

[gray gazelle]

time to see what schlag is all about

[sage python]

I know that prof as a person and... yeah

He's intense

His book does non-trivial hyperbolic geometry on page 12 lol

[gray gazelle]

ah it's got the yellow/blue cover

that means it's good

the table of contents is exciting

[sage python]

Okay maybe a bit more than 12 but yeah

[tribal kernel]

Schlag has grown on me but it’s a dense book. Pretty small and yet goes through a TON of stuff.

Any thoughts on Churchill?

[gray gazelle]

oh cool schlag has proofs of some of my homework problems

[sudden kindle]

I read Ahlfors and I hated it

[sage python]

@tribal kernel idk it well but Churchill seems to be more of a calculation-based book for engineering students, doesn't quite compete for the same demographic as the other books

[gray gazelle]

yes but it's due tomorrow and the next one's already out

checking my work takes fucking forever

some of the questions are so long

prove that the infinite product converges uniformly and absolutely on compact subsets of C

[sudden kindle]

People told me complex analysis was gonna be elegant and beautiful. I read Ahlfors and just feel like complex analysis is black box magic.

[gray gazelle]

the best way to learn complex analysis is to come to uoft and take it with my prof

[tribal kernel]

Wouldn’t doubt it. Never done much but flip through but it’s the book my undergrad university apparently uses for their complex class.

[gray gazelle]

different class

real analysis is the shitty one

complex analysis is consistently top tier

😌

[static crest]

the complex analysis course is very high tier

the lectures at least

[gray gazelle]

real analysis is shitty because im bad at it

[static crest]

real analysis is bad because it's not as clean as complex analysis

imagine being differentiable but not analytic

cringe

[gray gazelle]

cringe

imagine being differentiable and bounded but not constant

[sage python]

Wait how's that

[static crest]

also cringe

[gray gazelle]

[sage python]

Think about that sentence real quick

[gray gazelle]

no

[sage python]

I'm not asking I'm telling

[gray gazelle]

ok i read it

and thinked it

my brain cells are leaking out

[gilded zodiac]

I got the two books, but most of the content in them, i havent learnt yet

[static crest]

you still have some left after algebra and real analysis?

[gray gazelle]

no

another algebra test tomorrow

[static crest]

rip

I have a test and lab due tmrw

should start working on that

[gray gazelle]

good luck

[hearty steppe]

You wanted challenging linear algebra problem books mate. Not sure what your looking for then. Why don’t you try Friedberg et al then? Start with problem sets that are manageable for you.

I’ve been working thru Friedberg as of recent. I’d suggest both their books. I’ve been flying through it so far and it gives a nice visual conceptualization of linear algebra.

[gilded zodiac]

@hearty steppe honestly speaking im not even like a quarter way throught linear algebra, i've only just started, so i was just looking to practice

Ill try the other book out as well

[pure gate]

hii does anyone know any books for SAS and R

or like any websites or places

I could look ?

[wet orbit]

Hi, does anyone still recommend reading Howard Anton's elementary linear algebra for an LA beginner? I've been trying to follow along with Strang Gilbert on MIT scholar but his lectures seems to build off of his Intro to LA textbook which I can't get hold of a copy atm.

Ah, I should've known this earlier. Thanks mate

[dapper root]

Required Aluffi plug

If you want harder go to Lang

whereabouts in D&F are you tho?

[tranquil ocean]

Lang > Aluffi

[dapper root]

Don't listen to Zoph

Like still the sections on groups?

have u hit like

uhhhh

Sylow and stuff

I feel like group theory is kinda boring until you build up enough machinery

The start is kind of like

definitions constantly

¯_(ツ)_/¯

😩

another soul saved

and sees the light

[tranquil ocean]

no pls do not read aluffi it is literally a waste of time

[dapper root]

Zoph mad

mald harder

who did Aluffi and is now mr. algebra man

that's right, chmonkey

[sage python]

Aluffi is a waste of time lol

Lang or Jacobson

[dapper root]

You people are haters

Fuck you all

Chmonkey is Aluffi gang till I R.I.P.

[static crest]

uh

don't link those

@ mods?

[gray gazelle]

oh, is dami memeing when he says aluffi is a waste of time?

[sage python]

Nah it's too slow and the exercises I as I recall aren't that good

D&F even is just better

[tribal kernel]

I’m with you. Aluffi is good for me

[static crest]

there were some links to pirated textbooks

I'm a good boy and would never support the use of pirated textbooks of course

[calm crane]

fake

just dont call out lah

if everyone shut up about it

it'll "secretly" be there

[indigo mural]

H G Wells is a lit author

I especially liked "the invisible man"

epic book

[gray gazelle]

lol that book

[compact snow]

Luminaire is a lit Disney character ...

[buoyant flare]

🔵

[raven citrus]

I like Aluffi

[hearty steppe]

I like Lang’s intro LA book

[gray gazelle]

i haven't read aluffi but lang's algebra is not really interesting to me

[narrow talon]

I have little feel for what algebra as a topic is even for

Even for AT since I don’t really see what AT is for either

Maybe math history would help there

[gray gazelle]

read the papers of the pioneering mathematician

[steel viper]

its for computing homotopy groups of circles

[narrow talon]

Sick

So I can know that one circle is not another circle

[molten wave]

petition to rename S^n into circles

[narrow talon]

But it won't tell me that one circle is another circle sooo

[steel viper]

memeing less the pi_k(S^n) tells you about the structure of maps from S^k into S^n in a way that does matter

and it can be identified with/connected to all sorts of stuff

[narrow talon]

Maybe if I touch complex geometry or something I'll start to care

[steel viper]

they are intrinsically interesting smh

this is what analysis does to ur kids

no appreciation for topological beauty

[karmic thorn]

Analysis g u d

[sudden kindle]

no

[steel viper]

yes

[sudden kindle]

the most meme talk title: Calculating homotopy groups of spheres in dimension 60 to 90

[narrow talon]

Topology: right but what if squish?

[steel viper]

cope and seethe

nothing u do will ever be as pretty as the hopf fibration

or as ugly as spectral sequence computations but

[narrow talon]

What even is the Hopf fibration? Big sphere is many little spheres?

[sudden kindle]

"Mahowald’s uncertainty principle states that no finite collection of methods can completely compute the stable homotopy groups of spheres." 🤔

[steel viper]

fiber bundle

fibration thingy

[narrow talon]

[steel viper]

from S^3 to CP^1

[narrow talon]

My mathematical beauty receptors are astounded

[steel viper]

which describes the 3-sphere in terms of S^1 and S^2

[narrow talon]

So big sphere is little spheres, no?

[gray gazelle]

[steel viper]

do u know what a fiber bundle is

tterra

top 10 images taken seconds before disaster

[narrow talon]

Analysis: one of the first results is that many functions we care about can be written in terms of sums of oscillating functions. Helps solve deterministically a problem which can be seen as a scaling limit of random walks in space.
Topology: big sphere is little spheres but these two spheres aren't the same sphere, sick. Takes a year of study to understand.

[steel viper]

cope

ok if you have a continuous surjective map p: E -> B we say that p is trivial over U subset B if p^{-1}(U) is homeomorphic to U x F

and it like commutes so basically u have a homeomorphism phi from p^{-1}(U) -> U x F and phi composed with the projection onto U is equal to p

fiber bundle just means its locally trivial i.e every point has an open set U w/ p trivial over U

(and all the F are homeomorphic and we call it the fiber)

so basically the statement is that we have a fibration p: S^3 -> S^2 with fiber S^1

more or less it tells you that S^3 is not globally homeomorphic to S^2 times S^1 but it is locally homeomorphic to S^2 x S^1

[sudden kindle]

why does discord work but chrome doesnt

[steel viper]

admit it

this is based

[narrow talon]

Yeah, I'll concede this one. That's pretty cool

But also I must maintain this memey-arrogant persona. Very conflicted

[steel viper]

fibration stuff is based

i need to learn more about fibrations and cofibrations

this chapter did covering theory basically entirely from that perspective and it was like but also

[narrow talon]

Neat, but also like, what do you do after you get this Hopf fibration?

[steel viper]

i think it has physics applications actually

and others but i assume the physics would be neat to u

rigid body and magnetic stuff somehow

[narrow talon]

Huh, that is interesting