book-recommendations

[quick hornet]

have you seen raito play?

[steel viper]

namington what do u have against samus btw

[flint forge]

no

[quick hornet]

insane

https://vods.co/ultimate/player/Raito

[karmic thorn]

It's insufficient. Again, a standard series would be better.

[quick hornet]

watch some of their vods

raitos sick

[gray gazelle]

@karmic thorn thnx for advice

[karmic thorn]

That might be a bit too ambitious, especially if you're still at school.

[gray gazelle]

i m in 12th

[karmic thorn]

It's hard to juggle with school and studying on your own.

[steel viper]

i wonder if i can finish this hw by 11:40

eh

i guess we'll find out

[quick hornet]

eg https://www.youtube.com/watch?v=e4_Xs8ySoWY&t=1s

[karmic thorn]

So, you're finishing this May?

[gray gazelle]

my board is easy tho, i can easily get 90%+

[gray gazelle]

yep

[sudden kindle]

I mained peach in 4

[karmic thorn]

All boards but ICSE are easy

[gray gazelle]

ye

Cbse's math is easy too

[fast portal]

Bois what book should I get for symplectic Geo

[gray gazelle]

[karmic thorn]

So yeah, you could possibly cover a bit of stuff. Although doing well in JEE is a lot about handling the time-constrained exam environment.

So try to simulate tests regularly

[karmic thorn]

@ terra

[ripe granite]

mcduff and salamon

[fast portal]

Mcduffin and salmon, got it

[gray gazelle]

ye gonna try it

[karmic thorn]

(As a strong aside, do not go all in for JEE. Do ask yourself what you would like to do in the longer haul)

[gray gazelle]

i may go abroad or iit Delhi

[karmic thorn]

That's...quite ambitious but good luck haha.

If you plan to apply abroad, keep an eye out for the prerequisites expected of international students.

[gray gazelle]

that's why i joined this server

[karmic thorn]

This server will math-pill you and make you give up on the idea of pursuing engineering.

[gray gazelle]

Yes

[gray gazelle]

that's good even mobile and friend's are doing the same thing

[karmic thorn]

Well, I do think your choice of a career should be a balance between what you enjoy doing and something that aligns with your long term aspirations.

[gray gazelle]

[hasty turret]

Do you even know what you want to do?

Apart from "go abroad or join IIT D"

[karmic thorn]

Shhhh Drake, let them become woke on their own.

[hasty turret]

If you are not doing CS,I am pretty sure the syllabus is stupidly outdated and irrelevant in an IIT

[gray gazelle]

i should have just joined iit d and become a quantitative trader or something

[flint forge]

no

[gray gazelle]

why

[flint forge]

quant trading bad

[gray gazelle]

but..it's just other rich people's money

[flint forge]

a lot of quant trading involves ripping off normal people too

its not as bad as like military contracting

but its still bad

[gray gazelle]

lol

okay

[quick hornet]

imagine having morals

classic mistake

[hasty turret]

Indeed

[gray gazelle]

what other profession has such a huge earning potential

while also being moral

[hasty turret]

Whitehat jr

[gray gazelle]

ahahahahahaha

[flint forge]

I would say it is difficult to acquire large amounts of capital ethically

[quick hornet]

buying lottery tickets

[flint forge]

actually yeah that works

[gray gazelle]

lol

let me rephrase

[quick hornet]

i wouldnt exactly consider it a good career path

but it does have high potential.

[gray gazelle]

what other profession has a huge expected value of lifetime earnings

[quick hornet]

medicine might be your best bet

maybe law

[hasty turret]

Politician?

[quick hornet]

if you do like

[gray gazelle]

lmao

[quick hornet]

immigration law

or family law or w/e

though i think those guys make less than, like, patent law

[gray gazelle]

law kinda sucks though, like the stereotype of lawyers being rich isn't really true anymore

[quick hornet]

which is more morally dubious

[flint forge]

i think the focus on accumulating wealth is a bad one

[gray gazelle]

you'd earn more as a 25 year old quant than as a debt-ridden associate at a big firm

[flint forge]

if your question was what professions are ethical and have a high probaility to earning enough money to be happy

there are a lot more examples

[gray gazelle]

well i'm just saying

[hasty turret]

Wallstreetbets?

[flint forge]

theres more to life than being a millionaire

[gray gazelle]

i'm not rich enough to not worry about money

[karmic thorn]

How much money do tenured profs generally make?

[flint forge]

theres a lot of ground between quants and not worrying much about money

[hasty turret]

I guess do software dev jobs

[karmic thorn]

Scam rich people

[narrow talon]

How do quants rip off the little guy?

[hasty turret]

So,Coaching institutes?

That works too

[karmic thorn]

One of the possible ways

But ew

[narrow talon]

I’m just curious as to why it would be considered ethically dubious

[flint forge]

HFT, Dark pools, etc

[gray gazelle]

in the low six figures i think

[narrow talon]

Pretty worthless sure, but otherwise

[karmic thorn]

INR or USD?

[flint forge]

usd

[narrow talon]

And how do those rip people off? HFT maybe but why dark pools?

[karmic thorn]

[gray gazelle]

wait how is hft ripping off the little guy

[karmic thorn]

6 figures USD is legit good

[flint forge]

Dark pools often involve preferential deals that help the owners of the dark pools at the expense of the consumer

[narrow talon]

Volatility slides can happen with hdt iirc

[gray gazelle]

ah right

[flint forge]

no

thats not it

a lot of HFT involved fast middle-manning trades

[narrow talon]

But like, how is it at the expense of the consumer?

[flint forge]

causing loss for everyone trading

You should read about it, it gets complicated

[gray gazelle]

thank you, i shall

[hasty turret]

Is this what economists do?

[flint forge]

no

[gray gazelle]

and then i will become a quant

[flint forge]

well i cant stop you

but i can tell you ive never met a happy banker

lol

[narrow talon]

Yeah, I should

[flint forge]

Basically theres some hard-to-catch illegal stuff

and some just like, pseudo-legal stuff

For example dark pools can sell and record your trade patterns

to rip you off on future trades and stuff

[narrow talon]

To me the big drawback has always been that quant just seems like sort of a bullshit job

[flint forge]

it is

[narrow talon]

Like, you don't really produce value just exploit a system for profit

[flint forge]

but its not net-neutral

of the jobs i judge

it is the least harmful probably

[narrow talon]

Why do this though?

[gray gazelle]

isn't most of finance like that

[flint forge]

yes

[narrow talon]

Nvm I thought about it for 2 seconds

[flint forge]

finance is a bullshit sector of the economy in general

[hasty turret]

Like?

[narrow talon]

Wasn't saying it wasn't

[gray gazelle]

i wasn't saying that you were saying it wasn't

[narrow talon]

I mean, there's managing financials within a company

[gray gazelle]

i was just saying

[flint forge]

doctors, (some) lawyers, most engineers, accountants, many corporate jobs

[narrow talon]

Which I guess helps that company so if you believe in what they're doing you could produce value there

[flint forge]

a lot of software dev is harmless but not all of it

[narrow talon]

data science

... sometimes

[flint forge]

depends on the data

lol

[karmic thorn]

Why doctors?

[flint forge]

these are good jobs

not bad jobs

[karmic thorn]

Oh

Okay

[flint forge]

or neutral jobs

[karmic thorn]

Because I was ready to buy the remaining ones as bad jobs lmao

[flint forge]

well some lawyers are bad

i mean any job has bad examples

but there are a lot of ways to make a living without directly harming anyone else is more my point

[karmic thorn]

Fair enough.

[narrow talon]

I think there are quant jobs which are not ethically negative

[flint forge]

probably a few

[narrow talon]

Lots of data-sciency ones lean more on gleaning insight from non-market data

[flint forge]

you could also always do the earn-to-give strat

[narrow talon]

Yeah, but then you're getting super utilitarian

[gray gazelle]

lol

peter singer

[flint forge]

i dont have anything against util

[narrow talon]

The number of market actors which are individual investors is relatively small, so consider the amount lost to individuals (consider a loss to a corporation as net 0 ethics points) and then consider the amount gained via skillfully choosing where to spend that money. Sounds pretty fucking sketchy tho

[flint forge]

i would buy that a single quant probably does a limited amount of overall damage

that could be offset by donating large amounts to charity

and that someone would replace that quant if they quit

and probably not donate much to charity

[subtle fossil]

any good books that have exercise with solution for precalculus?

or a site or anything really i just want it with solutions

[karmic thorn]

Khan Academy, Paul's Online Maths Notes

There's also an OpenStax book on precalculus

And you should be able to find several many precalculus books on well known online libraries for acquiring books legally.

[subtle fossil]

ok thank you

[analog spruce]

What about professions for math majors that fit that bill?

[flint forge]

almost any profession one can do without a math major one can do with a math major

including all the ones ive listed

[analog spruce]

Really? Even doctors?

[flint forge]

Yeah you can get into med school with a math major for sure

might not be the easiest path but its certainly doable

[analog spruce]

I mean you need to earn a second degree or another set of skills after taking math

Might as well study the skills for the field you are moving into right?

I sort of want to know what all can you do with just a math degree?

[tranquil ocean]

I mean you also need a second degree in math to do math research too so

[analog spruce]

XD

[gray gazelle]

Probably jack shit

[tranquil ocean]

plenty of people go into government work or finance after just a math bachelors

or go into some sort of CS job

[analog spruce]

So that's about it then e.e?

[tranquil ocean]

That's a pretty wide range of jobs?

There's also like actuarial things, or tax consulting things that friends of mine have gone into

[flint forge]

I think the important takeaway is that like outside of jobs requiring graduate education

any vaguely stemmy degree can get you any vaguely stemmy job

maybe minus software engineering jobs

but you can still get SE jobs as a math major

i don't think major makes a big difference in the grand scheme of things

[warm glen]

^ i think it's actually very common for people to go into careers that don't have much to do with their degree

like more common that it is to get jobs directly related to ur degree

[flint forge]

esp bc at the end of the day (with again possible SE exception) you aren't that advanced in your major subject by the end of college

thats why grad school exists and isn't just straight 2 thesis

[analog spruce]

Ahh

Makes sense

Thanks

[junior merlin]

anyone have any multivariable calculus book recommendations?

[sudden kindle]

i assume you mean calc 3 stuff?

[junior merlin]

yeah

[sudden kindle]

https://openstax.org/details/books/calculus-volume-3

Written by Gilbert Strang

[junior merlin]

oh cool

[sudden kindle]

based free online textbook

i love that OpenStax exists

[junior merlin]

yeah ive never heard of it until now but ill check it out

[frosty ermine]

Does anyone know a decent abstract algebra book that can help me understand the foundation of rings within the week?

I plan on learning more after, but I definitely need that ground work

[static crest]

d&f

[frosty ermine]

That face makes me think you are joking

[sudden kindle]

No

[frosty ermine]

Why ping me for that?

[sudden kindle]

To reply

[gray gazelle]

ptyamin is on light mode so they probably couldn't see the "do not ping original author" button

[frosty ermine]

Ah okay. Well, does anyone know a good abstract algebra book to start learning from?

[gray gazelle]

unironically d&f

[frosty ermine]

What is d&f?

[gray gazelle]

dummit and foote

[frosty ermine]

I'm gonna see if my library has it

Is that the author?

[gray gazelle]

the authors

[frosty ermine]

Yea, the library catalog has no idea what that is

[gray gazelle]

david dummit, richard foote

the book is literally just titled

"abstract algebra"

[dense pewter]

you mean it's not first name "david richard" last name "dummit and foote"?

[frosty ermine]

There are three written by david dummit

[gray gazelle]

https://www.amazon.ca/Abstract-Algebra-David-S-Dummit/dp/0471433349

[frosty ermine]

Looked at the link. That's the one

[sudden kindle]

Oh I see it now

[gray gazelle]

you're email is visible in this

you're

[frosty ermine]

Whoops

It's a school e-mail, so it's a little less worrisome. But still, thank you for pointing it out

So.... I have this book already 😆

[gray gazelle]

Wow, that cover looks creepy

[frosty ermine]

Maybe that's why I bought it

The moment I saw the table of contents on the e-book, I realized it looked very familiar. Turns out, it was.

[shell grail]

hmmm

[gray gazelle]

NEW

[shell grail]

that's disgusting

[frosty ermine]

Well, it was at some point

[shell grail]

this is the only good version

[frosty ermine]

I am good with my own thank you

[shell grail]

i'm sorry but to learn AA you must print that picture out and paste it over the front

[frosty ermine]

No

Anyways, I remember dealing with the first two sections quite well, and I was able to grasp some of the 3rd, but I remember it just felt really confusing at that point.

I tried, but they go balls deep on the notation and it was really tough to process

[gray gazelle]

this looks like it's going to curse me if i spend too long reading it

[static crest]

it's only partly a joke

it's mostly serious, but it's also a meme tb for reasons

[gray gazelle]

tensor product of modules section

they try to account for noncommutative rings in that part and it makes everything so much more complicated

smh

all rings are commutative!!!!!!!

[static crest]

that's the next section for me

10.3 is pretty poggers

you should do exercises 9, 10 (maybe 11 too) for sure

in 10.3

[gray gazelle]

the main ideas are

1. tensor product allows you to extend the ring of scalars for a module in some way (if you've seen complexification of a real vector space, it's just tensoring with C considered as an R-vector space)
2. tensor product (by the universal property) turns multilinear maps on M x N into linear maps (homomorphisms) M \otimes N

the entire section is just proving properties

nothing is really too complicated

[static crest]

I see

[gray gazelle]

it's just long as fuck

[static crest]

I just saw it's a thick section

ya

[gray gazelle]

turning bilinear maps into homomorphisms is useful

the book spends a lot of time dancing around "bilinear"

because some rings/modules are garbage

[static crest]

rings without 1

[gray gazelle]

$M\otimes_R N = F_R(M \times N)/S$, where $F_R(M \times N)$ is the free $R$-module on $M \times N$, and $S$ is the submodule of $F_R(M \times N)$ generated by elements of the form
\begin{align}
&(m+m',n) - (m,n) - (m',n), \
&(m,n+n') - (m,n) - (m,n'), \
&(rm, n) - (m, rn).
\end{align}

[hasty eagle]

(T*Terra, dqⁱ ∧ dpᵢ)

[gray gazelle]

bilinear maps on M x N induce homomorphisms because the induced homomorphism on the free R module (exists and is unique by that thing's universal property) contains S in its kernel

by definition basically

q e d

[hearty steppe]

what does that x circle mean

[gray gazelle]

tensor product

this is the definition

[hearty steppe]

oh

[gray gazelle]

i'm trying to think of the word that describes this well

[sudden kindle]

Meme

[gray gazelle]

it feels like it's basically defined to get the universal property of bilinear maps factoring to homomorphisms

[sudden kindle]

Direct construction

[gray gazelle]

yes

[sudden kindle]

Instead of appealing to universal property

[gray gazelle]

you're a universal property

[sudden kindle]

Thanks

[frosty ermine]

In regards to the book, I feel like the set $\mathbb{Z}\setminus n\mathbb{Z}$ is particularly confusing to me.

[hasty eagle]

dackid

[frosty ermine]

Is that basically $\mathbb{Z} (\mod n)$

[hasty eagle]

dackid

[frosty ermine]

Ah okay. I guess I am just not used to that representation

coset being?

[gray gazelle]

It's like a closet

[frosty ermine]

I've heard the term, don't quite know what it means

Well, the goal is for me to learn ring theory.

That is where my focus is at the moment

Can you provide a concrete example by chance?

so you are shifting all the rationals by \sqrt{2}

and then the reason why this is a coset is because our group is closed under addition

which is the operation we care about

Is it necessarily true that a subgroup intersected with it's coset is empty?

Okay, that was just true for this specific example

I thought you said we were adding, not multiplying

So when we say cosets, do we mean all of the cosets of that particular subgroup?

dum that down for me please :p

[gray gazelle]

pretend many thing is one thing

[frosty ermine]

Given that I have a foundational understanding of groups, would you say it is a big jump to start learning about rings?

So what you are saying is I am going to have to get back to you on that. :p

yes, but I don't understand what you said.

Learning the definition of Cosets and working with cosets are two very different things

with respect to euclidean space yeah

I do not think that is the same thing though

oh, not at all

so basically it is commutativity but for a specific subgroup

[gray gazelle]

[frosty ermine]

I follow

I can get behind that

okay sure. Also, can we do this in #math-discussion

[sudden kindle]

Bob ross studies rings

[frosty ermine]

we definitely deviated from book talking :p

[gray gazelle]

hey everyone anyone know a good book to start learning statistics? I had taken it before I know how to use the z, t, tables just forgot and a bit rusty on it any commendations would be appreciate it.

[gray gazelle]

when it says for engineer is that only applications towards engineering?

man if james stewart did a stats book....

[static crest]

"for engineers and scientists" usually means the math content is made a bit stupid

and less rigorous

[narrow talon]

Just got a hardcover textbook for under $20 from Springer

[hollow peak]

WHERE

[narrow talon]

They sent me a $20 voucher

Otherwise it would've been like 35-40

[karmic thorn]

Nice

(Mandatory I got Tao's Analysis 1 hardcover for $3 brag)

[hollow peak]

i wonder if I can email springer and gaslight them into giving me discounts

[karmic thorn]

Set up a libgen mirror

Report it to Springer

[hollow peak]

3. profit?

[karmic thorn]

Ask for a gift in exchange

[hollow peak]

I've gotten some nutso deals

[narrow talon]

Niiice

[hollow peak]

I bought like 10 dover paperbacks for 10 bucks

[karmic thorn]

That's one banger deal

[narrow talon]

I got Rudin's R&C hardcover for $20 a while back, as well as a hardcover copy of Treves for like $10, and that's been out of print for a while

[hollow peak]

now that's actually insane

R&C is so expensive

I think the one lauded math book that you simply cannot get in good quality anymore for a reasonable price would be ahlfors

as far as I can tell only the shitty international paperback still is in print

[karmic thorn]

The paperback for Rudin's RCA costs $8.15 here

[hollow peak]

if it's an international edition then it's much lower quality unfortunately

[narrow talon]

Oh boy

I got THAT for $15 at the exact same book store as the other 2

[karmic thorn]

But yes, that's a possibly shitty Indian edition

[narrow talon]

Bookstore in downtown Jacksonville which has very few mathematicians in the area, so the textbooks just trickled in over time

[hollow peak]

you hit the motherlode

[narrow talon]

Hardcover

And Doob's/Halmos' measure theory

Alltogether like $50

I was visiting family at the time and they had no idea why I was so hyped

[hollow peak]

that is by far the most insane haul I've ever heard of

[gray gazelle]

BOOKA

[karmic thorn]

Why do some paperbacks cost more than hardcover editions of the same book?

Currently looking at Lee's ITM

[hollow peak]

I haven't seen that too often

sometimes it's just that softcovers end up out of print

[karmic thorn]

The paperback is a tad more expensive than hardcover

[gray gazelle]

supply demand homie

[karmic thorn]

Yeah, but I'd usually expect more demand for hardcover

Unless the supply is very erratic for books

[narrow talon]

Apparently I got Herstein, Lang (Basic mathematics, just to have it), Ahlfors, Royden, and Rudin all top shape for $50, then Treves, Doob, and Halmos from the same bookstore later for around $15 each

[gray gazelle]

@gray gazelle Recently I've been studying a bit of statistics, do you have any opinions on this book?

[narrow talon]

Place was a gold mind

[gray gazelle]

lol

Especially interested in Coping chapter

yeah you would be

[gray gazelle]

Hmmm alright I didnt interpret it that way. I will take a look ty.

[proven hound]

Would anyone today recommend Polya's "How to solve it"?

[tranquil ocean]

I've read it, and I feel like it's much more a book about how to teach mathematics rather than how to do mathematics

[sudden kindle]

Oh interesting

I read some of that book very early when I was starting with math in highschool

I found it helpful

[gray gazelle]

I wish I read that book earlier

It is helpful if youre new to pure math Id say

[proven hound]

I know the book is really helpful, but what I wondered is. Is it still one of the best books on its subject?

[hearty steppe]

Felt the same exact way from taking a peek at Polya

[pale scarab]

Its good he has a longer book on the same thing which is better if your into pedagogy. Best is a subjective thing though. As far as actually becoming better at 'problem solving' there is really nothing better then just doing lots of problems and learning new techniques with experience

[dapper root]

Any recommendation for a field theory text? Particularly, having some details on seperability, normality, infinite Galois extensions

[sudden kindle]

DUMMIT AND FOOTE

Why hasn't anyone made dummit and foote fanart

Oh for infinite galois theory you can look at Keith Conrad's notes

[steel viper]

please seek help

therapy mayhaps

[broken meadow]

oog

[dapper root]

Bruh I know the stuff in Dummit and Foote

I want moar

[sudden kindle]

What do you want to know that's not in D&F

[dapper root]

Everything

[sudden kindle]

D&F contains everything

[steel viper]

lang

[dapper root]

I like textbooks that are specialized cuz they’re cooler

I don’t want to use Dummit and Foote, that’s for babies

[sudden kindle]

Do you want to learn big boy galois theory

Or big girl

[dapper root]

I was using Dummit and Foote when I was 0 years old now I’m 2

[sudden kindle]

Oof

[dapper root]

Big boy Galois theory 👦

[steel viper]

i like that chmonkey was born in his soph year of undergrad

[sudden kindle]

Big person galois theory is what moth is doing

[steel viper]

[dapper root]

I used D&F my freshman year

AT?

[steel viper]

galois moment

[dapper root]

Is this mf saying Galois theory is just covering theory

[steel viper]

Yes

[dapper root]

No stop

[sudden kindle]

Galois group = fundamental group

[dapper root]

I don’t care about this

[steel viper]

cope and seethe

[dapper root]

Stop it

[steel viper]

oh chmonkey are u doing dold kan with shamrock

[sudden kindle]

Blame grothendeick

[dapper root]

we already did it

[steel viper]

his explanation was kind of big brain and also made me realize that the transport stuff is not dissimilar from sheaves

[dapper root]

Idk what his explanation was

Lol

I mean he might’ve only told u certain aspects

Or maybe he told u the statement, idk

Also idk what transport is

[steel viper]

it was basically just the statement

[dapper root]

This mf said sattemenet🤣🤣🤣

[steel viper]

for certain conditions under a topological space covers are equivalent to functors from the fundamental groupoid to SET

[dapper root]

[steel viper]

and the fundamental group is the opposite group of the automorphism group of any point in the fund. groupoid

[dapper root]

Topology moment

[steel viper]

Yes.

take the AT pill

[dapper root]

Don’t care xDDDDDDDDDDDD

[steel viper]

read tom dieck

[dapper root]

No

[steel viper]

or hatcher cuz ur a nerd

[dapper root]

Shut up

I will just do concise course to flex on u

[steel viper]

[dapper root]

I will pwn champ you

[steel viper]

i will just force you to explain concise to me then

i win either way

[dapper root]

No

I will refuse

[steel viper]

u wont

u will cope and do it anyway

[dapper root]

Yeah I will

When will I learn AT lol

Maybe the summer of 2022

Lol

[steel viper]

idk but its based af

[dapper root]

Replace T with G

😎

That’s what I do, even tho I didn’t do much this quarter tbh

Poser

[steel viper]

AG arc in T minus

idk

several months

possibly longer

[dapper root]

You should use Kempf and learn it from sheaf-brain perspective

but as varieties

[steel viper]

[dapper root]

So u don’t become sad like Chmonkey when you don’t understand what this abstraction means

[steel viper]

learning AG will by my 2022 post college application new years resolution

[molten wave]

when's your 2022 start

[steel viper]

oh right different calendars

uh like

9 months

lol

wait i have more of 2021 than i thought

[sudden kindle]

Anyway

Galois theory goes very far

[dapper root]

Galois

[sudden kindle]

Grothendieck galois theory phrases galois theory as an anti equivalence of categories

[molten wave]

I was just shitposting about you putting "my" before "2022"

[steel viper]

oh

lol

wait that made sense cuz its my 2022 resolution

[molten wave]

that's a very long bracket

[sudden kindle]

And then theres something called motivic galois theory which I know nothing about but nGroupoid#5061 can pill you on that

[warm glen]

@dapper root i screenshotted a reddit comment that i think answers ur request for resources ab more advanced galois theory

[ripe granite]

isnt advanced galois theory just algebraic number theory

[karmic thorn]

Tao, Prime Gaps?

[warped cedar]

Lurie is a interesting guy fr

[karmic thorn]

He is

[ripe granite]

actually Hopkins has some very nice talks for a general audience

[karmic thorn]

But I don't get any of the stuff he talks about

[warped cedar]

Lurie is definitely super autistic tho

Which is ok

That's the vibes I get as a sperg myself

[obsidian valley]

[narrow talon]

Wtf my application was sent to be evaluated with a different group of students because apparently the committee couldn’t come to a decision regarding my app

[marble solar]

That's a good book Jason

[warped cedar]

[ripe granite]

lookup bernoulli numbers, homotopy groups and milnor by mike hopkins

pretty good talk

[obsidian valley]

maybe tahts a good thing jason

[warped cedar]

Watch Leonard Susskind lectures

[karmic thorn]

He's good

[narrow talon]

Sorry, didn’t realize I was in book-discussion!

[karmic thorn]

But the Theoretical Minimum lectures are very long drawn

I even have all 3 volumes of his course lmao

[marble solar]

Wait until you see a grad book on physics

[karmic thorn]

[marble solar]

Those are even longer!

[karmic thorn]

I did try reading Landau V1 once

[warped cedar]

Hopefully I can get past all the physics but I doubt it if I wanted to study fluid dynamics

[karmic thorn]

And I plan to do it some day when I'm smart enough to move past page 3

[ripe granite]

lie algebras and homotopy theory by Lurie is also good

[karmic thorn]

Lanczos' Variational Principles of Mechanics is another apparently good book I have

But I have no idea about calc of variations

Or PDEs

[warped cedar]

Categorification of Fourier Series

[obsidian valley]

i like the lurie lecture where he's gesticulating wildly the entire time

yes that one

I thought he was 13 for the longest time Ultra

[karmic thorn]

Hahahahaha

I'm like

[ripe granite]

geordie williamson rep theory and geometry

[karmic thorn]

Scratching the surface

Everywhere

And I've been doing so for years

[hasty turret]

Indeed

[warped cedar]

banned

[karmic thorn]

In HS I was obsessed with theoretical physics

[obsidian valley]

i thought you were 19 ted?

[karmic thorn]

Yes

I am 19

[obsidian valley]

oh wait nvm that makes sense

[karmic thorn]

I should've started as an undergrad at 18 but covid happened

[obsidian valley]

yeh

[ripe granite]

actually a lot of the ICM plenary lectures should be pretty understandable and good

[karmic thorn]

I think so too, but I think I should start making some meaningful progress in some direction too haha. I'm still toying about with ideas about how/what I should focus on studying.

Study what is the question lmao

[ripe granite]

algebraic geometry

[hasty turret]

Any recommendations for projective geometry?

[karmic thorn]

Shaferavich

[obsidian valley]

what does it mean to learn logic in full

[karmic thorn]

Actually, I have been toying with the idea of studying like a normal student at uni, and self-studying logic, set theory and theoretical CS by myself for the coming years. So I can dispense with the need to study linear algebra, analysis and the likes and just wait to get to them at uni.

[hasty turret]

I guess it means you understand choice

[karmic thorn]

Choice is obviously true.

[obsidian valley]

choice is just picking balls from bags

cmon

[hasty turret]

[karmic thorn]

Yeah, but at the same time logic and set theory are tough as hell

[warped cedar]

[karmic thorn]

So I might have to start with something down to Earth first

Like Automata Theory

[obsidian valley]

choice is pretty understandable as "the cartesian product of non-empty sets is non-empty"

the only reason choice is confusing is that it's equivalent to a zillion things

I should learn more automata theory

[gray gazelle]

here is another false principle

[karmic thorn]

False in ZF+not(C)

[gray gazelle]

"subsets of finite sets are finite"

[karmic thorn]

Oh, isn't there a notion of some infinite sets which don't have any countable subsets?

I could be wrong

[obsidian valley]

huh

[karmic thorn]

But I vaguely remember something of the sort

[obsidian valley]

Couldn't you just pick exactly one element from the set

[karmic thorn]

It had to do with some inaccessible cardinal stuff

[gray gazelle]

logicians are snakes

[obsidian valley]

🐍

where is that from floppa

[karmic thorn]

Can one canonically establish if a certain statement can only be proved through contradiction?

[gray gazelle]

the five stages of accepting mathematics by andrej bauer

[karmic thorn]

Aahhh

[sudden kindle]

Maybe theres some hidden infinite subsets of finte sets

[broken meadow]

the five stages of grief

[gray gazelle]

the empty set is countable

qed

[gray gazelle]

chad yes.

[obsidian valley]

I'd like to know more about this if there is some setting where this is true lol

[broken meadow]

lmfao

that's funny oxide

[karmic thorn]

My memory has been declining hard, let me try to dig it up if I can

[broken meadow]

18 pages

this seems like something i should read this weekend why not

[obsidian valley]

what is the statement of countable choice?

[broken meadow]

never really thought about constructive mathematics

should take a crack at dis

[obsidian valley]

N being minimal

I'm getting flashbacks

[karmic thorn]

What version of AC do we usually work with(when referencing to ZFC)?

[obsidian valley]

Hm

Ohhh

[karmic thorn]

How do we say a set is bigger than N, then?

Isn't the idea to show an injection from N to that set

Ohhhh

[obsidian valley]

Okay so if we reject countable choice we can have a surjection f: S -> N which doesn't imply that there is a injection g: S -> N g: N -> S?

[karmic thorn]

That makes sense

[obsidian valley]

this is because there is no choice function on S?

oh yes sorry

Why just not on the set of preimages of pts?

sorry that makes no sense

I mean "why just on the set of the preimages of points"

On N, I think

You're saying there's no choice fn on the preimage of g, right?

g: N -> S

[karmic thorn]

I think I'm partly following this discussion and also not following it a bit. So a surjection f:S->N can be reduced to an injection g:N->S by weeding out extra elements from sets of pre-images of every element in S, but this needs countable choice?

Aah, I see

Nice

[obsidian valley]

sorry I had to write a quiz

ah

Okay that makes sense

[dapper root]

Yo, thanks

[tranquil ocean]

@dapper root read lang's galois theory section no cap

[wooden sparrow]

Algebra?

How far are you in it?

[static crest]

read d&f

then

[tranquil ocean]

Older books tend to have some bad notation

[static crest]

d&f is pretty boring, true

but the content is good enough

[tranquil ocean]

Yea that's the good part

Just think of it as more exercises

[static crest]

also the exercises are really good in d&f

for the most part

[sudden kindle]

i liked reading D&F

i was intimidated by it because of its reputation so i read other books before D&F

[warped cedar]

My copy of D&F came with the binding broken

So I hot-glued it back on

[static crest]

I was also scared of d&f bc of its reputation

but it's a very approachable tb

[gray gazelle]

I thought d and f has a good reputation?

[static crest]

idk, there were people in this server giving anti-recomendations for d&f because it's apparently so bad

it seems like a polarizing book

some people really hate it

[warped cedar]

Most people I have seen said its too verbose

I don't think they hate it though

[static crest]

there's some real haters for it

but ya, it does kinda go too in depth at times

in basically everything

on one hand it's very comprehensive, but on the other hand, not everyone wants a 900 page algebra tb

[warped cedar]

fair

[dapper root]

Does D&F have a reputation?

[warped cedar]

I think it has a reputation for being a great alg book

[sudden kindle]

I had the impression that D&F was very dense and not an good introductory text

[shell grail]

nah

it has a good amount of explanation of things

and then lots of examples and practice in the exercises

[sudden kindle]

yeah

[static crest]

idk, I think it's like the opposite of dense

it goes into excruciating detail

it's great as an introductory text

literally spells things out for you

[sudden kindle]

that's true, once i actually started reading it was surprised by how much detail therewas

[static crest]

ya, it's very thorough

you don't need like any other algebra resource

while using d&f

it also goes into very niche concepts

in the exercises

[sudden kindle]

A thing I've been doing to improve my (mathematical) writing is to look at how people write their textbooks and model my own writing it after them

Like I noticed D&F introduce definition of a group and immediately give 5 examples, so maybe I'll do something like that

[static crest]

ya, it's a good practice to give examples after presenting abstract concepts

usually d&f gives a bunch of examples, with the first couple ones that are obvious

and then going into some nontrivial examples

[steel viper]

i think it kind of depends

its a trade off of space/time investment vs intuition

[static crest]

I don't think d&f cared at all about space/time investment

[tribal kernel]

Most people I hear who say D&F isn't a great intro text will qualify by saying it's invaluable as a reference text or an encyclopedia of basic algebra topics

[gray gazelle]

there are people who think it isn't a good intro text?

[sudden kindle]

yes

[gray gazelle]

I guess to me reference text is more like lang, that book is unreadable

Not that d and f cannot be used as a reference

[dapper root]

Am I the only person who doesn’t really care for examples? Like, when people introduce a new thing, I don’t care to just see “x with y operation is a ___” or something, rather I like to see uses. An example of how you can use this new concept to take a hard problem and make it easy helps me 100x more

[gray gazelle]

Yeah, I agree with that, but I wouldn't say examples are totally worthless. I guess more so I am interested in motivation

[dapper root]

I guess if you’re just introducing the first sort of algebraic structure you should probably give a few

One thing with D&F I remember is like

Having 1.5 pages of examples

With like 7 or 8 examples

And my eyes glossed over

[static crest]

I mean depends

I like that the examples are there

sometimes I just gloss over

sometimes I really like that they're there

but the fact that there are examples is always nice to know

[dapper root]

Idk I always feel like I can figure out examples myself. Maybe like a super-textbook example is nice, eg group algebras for a Hopf algebra, but I never felt great when they spend like 10 minutes working through examples when I’d rather you just use the object to prove something cool

[willow pecan]

I mean you would introduce examples for definitions and cool uses for theorems and the like right?

[dapper root]

Eh. I feel like you can use cool uses even for objects

[static crest]

I just like examples at times because it kinda solidifies the abstractions

sometimes you can get lost in the sauce

[gray gazelle]

that moment when you develop the theory of continuous functions with holder constant 2 and give no examples

[marble solar]

I used to think this way, but as I got more into research, the more I like very concrete things

I almost became an undergrad cat theorist

But I had some sense knocked into me

You should add something about Marshall and Conway

[dapper root]

Well the type of stuff ugcts learn wouldn’t motivate me because I’m interested in how it applies to other math to make it nicer

[sage python]

Oh true yeah, idk Marshall tbh

But I'll mention Conway

[dapper root]

I mean my point is moreso I don’t care as much about examples of the objects itself

Because we don’t know why we care about these objects

I much prefer examples of why these objects are useful

[marble solar]

At this point, we should get a PDF file going for text recommendations

And just pin that somewhere

[sage python]

Alright I think I have a good description of Conway in there

[marble solar]

"Don't use conway"

I can agree with that

Also Rudin?

[sage python]

I actually don't know much about its treatment of complex analysis

What's your impression?

I heard it's awkward somehow

[marble solar]

It relies a lot on real variable knowledge from the first few chapters; it does things in a very slick manner that often obscure more standard arguments. Exercises tend to be trivial to difficult. Not enough time spent exploring the intricacies of complex analysis through examples. Great for theory, a second look, or a reference

Difficult to learn from. Pairs well with literally any other complex book

[steel viper]

they are good for developing intuition of the thing

also sometimes theyre just intrinsically interesting

[dapper root]

😪

[sage python]

I feel sometimes examples are cool, they can be useful but I don't have a big "examples for the sake of examples" style

[quasi delta]

Just out of curiosity, did your introductory set theory book present a proof for |R|=2^aleph0? My professor discussed the proof but the book left it as an exercise, which seemed pretty wild to me

[quick hornet]

i never had an "introductory set theory book" but my analysis class did have "demonstrate a bijection between ℝ and the power set of ℕ" as a homework question IIRC

or at least prove that a bijection exists

(which is cantor-schroder-bernstein)

idk if you had less machinery than we did

but it was a perfectly reaosnable question with cantor-schroder-bernstein

[pale scarab]

I went through pinters algebra book to start and liked it a lot. I am now going through aluffis algebra book which is much more enjoyable then d&f in my opinion.

[static crest]

I find aluffi's order of contents strange

jumps back and forth too much

[dapper root]

Based

[static crest]

does groups, then halfway through starts rings and modules, goes back to groups, then goes back to rings

and then it goes to like linear algebra or some shit?

[hollow current]

yes

well

otherwise he won't be able to delete msgs e.g

why this in #book-recommendations tho

[willow pecan]

You also asked this in the texit support server

[wooden sparrow]

Was kinda in a hurry

@hollow current sorry

[mild narwhal]

Dummit and Foote is easier than Pauli

[hasty turret]

And is better written

[mild narwhal]

Pauli go over category theory, homological algebra

[static crest]

d&f also goes into homological algebra memes

in part 5

[gray gazelle]

homosexual algebra

[static crest]

[warped cedar]

Now we're talkin

[gray gazelle]

[prisma snow]

If D&F really did homosexual algebra, I would have to stop hating on it and read it again!

[fast portal]

Luna moment

[mild narwhal]

D&F doesn’t really go into homological algebra like Pauli tho

As for homosexual algebra I can’t speak on that lmaoo

[gritty apex]

is there any good book for learning calculus? Please ping

[pure iris]

howard anton, james stewart

for calculus 1,2,3 for beginners

[gray gazelle]

Good book for intro ODE?

[karmic thorn]

ODEs: Basics and Beyond by Cain seems to be good.

[karmic thorn]

I have

More than 5 pages

[marble solar]

Boyce and DiPrima

[fossil island]

You guys read books?

[hollow current]

no we eat them

[willow pecan]

[timber mesa]

that's the best way to absorb knowledge

[gray gazelle]

you mind if I have some of your tasty beverage to wash this down?

[grizzled prairie]

whats a good book for learning category theory

[inland otter]

bok hmm??

never heard of it

[tranquil ocean]

Riehl's category theory

[devout bobcat]

Anyone knows a solution manual for werner gruebs linear algebra?

[prisma snow]

All the solutions are in your head, you just have to transcribe them!

[devout bobcat]

already have solutions that i wrote to the exercises, i just need double checking

[prisma snow]

Oh, nice

You can just try to go through and think about if it makes sense to you. And you can send the questions and solutions here to have people check it for you.

Idk about a solutions manual

[devout bobcat]

aight thats cool

thanks

[grave egret]

Best books on game theory?

[quick hornet]

osborne-rubinstein

assuming you mean the "mathsy-econ" sort

e.g. using kakutani's fixed point theorem to justify the existence of nash equilibriums

if you mean more modern combinatorial game theory, i dont think theres a great recommendation

maybe conway?

(Winning Ways)

but it doesnt really feel like a... traditional textbook thatll teach you the subject through a systematic method

if that makes sense

its moreso a collection of examples

a compendium i guess

a mathoverflow search brings up Maschler-Solan-Zamir which is apparently quite rigorous

but i havent heard of it

[thorn zinc]

hi

recommended books on type theory/course notes

[gritty apex]

best books for learning algebra?

best books for learning trignometry?

[silk quartz]

Please don't spam in this channel, folks.

[sand vortex]

Oh....

[willow pecan]

Dummit and Foote is good for algebra

Aluffi has a "unique" perspective

[prisma snow]

Also, everything other than Dummit and Foote is good for algebra

[willow pecan]

I've heard bad things about Lang

[hasty turret]

Add Aluffi to that list

[karmic thorn]

Lol

Are we overlooking the fact that OP wants algebra and trigonometry recs

Go for Lang's Basic Mathematics

Then Artin's Algebra

[willow pecan]

For basic middle/high school algebra, perhaps Khan Academy

[timber mesa]

yeah I was thinking precalc level too. I think Gelfand has some books for basic algebra and trig, and the typical large textbooks aren't bad either.

[karmic thorn]

Yeah, I've heard Gelfand is good!

[tribal kernel]

Man all this hate for Aluffi makes me sad

For really basic algebra, you'd probably want something that's more example focused rather than trying to teach the way any "real" math text goes. The recommendation of khan academy, or really any good youtube channel, is pretty excellent imo

https://tutorial.math.lamar.edu/Classes/Alg/Alg.aspx

Or something like this. This professor also has a lot of tutorial stuff on basic calculus and differential equations that I think could be very helpful

[static crest]

bad take

[marble solar]

D&F is excellent, just beefy

Did you finish every exercise poros

[static crest]

every exercise up to section 10.4

[karmic thorn]

[ripe granite]

noice

[willow pecan]

If you do every D&F exercise you will be an algebra god

[warped cedar]

write a full solution manual

slader has one and its got 1944 problems solved

idk if thats all of them but it sure is a lot

[static crest]

I'm probably gonna not go past the end of galois

I do plan on doing every exercise up to (and including) chapter 14

nothing past that though, I don't care for commutative algebra, AG, or homological algebra memes

[sudden kindle]

If you do every D&F exercise you wasted your time

[steel viper]

too verbose

just do lang

[sage python]

Lol haven't I already solved the problem of algebra books?

[steel viper]

i actually do think D&Fs approach is like Too Much to be helpful on a first pass and Too Wordy to be very readable on a second

jacobson first then lang

this is correct

i think

[sage python]

I mean D&F is a fine first book

You'll need to be resilient and skim a lot

But yeah the flowchart is:
Artin first if you don't know linear algebra
Jacobson first if you do
D&F if Jacobson is too hard
Lang if Jacobson is too easy
Aluffi if you like category theory and flowery chit chat

[warped cedar]

pin that

[marble solar]

it already has been

[sage python]

Yeah a more elaborate outline is pined

[warped cedar]

oh shit my b

[dapper root]

Why

That’s surely hundreds of exercises already

Are the majority of D&F exercises just like 3 minutes

[willow pecan]

Probably not

[gray gazelle]

poros owns a hyperbolic time chamber

[dapper root]

This is believable

[willow pecan]

[ripe granite]

D&F

[gray gazelle]

Imagine saying you like algebra but you haven't even done all the exercises in D and F

[ripe granite]

idk if the rep theory and homalg sections are good tho

[static crest]

yes

[ripe granite]

petthecat

[willow pecan]

[static crest]

I think the group theory exercises alone were like 600 in count

[dapper root]

Why

There’s no way doing all of those is maximizing your time

I mean if your answer is literally just

[sage python]

Yeah it's quite a bit. Probably a lot can be autopiloted though?

[dapper root]

“I want to be able to say I did”

I can respect that

[sage python]

Like instead of writing it down you're like

Yeah this makes sense

[dapper root]

I mean that’s the thing but like

[static crest]

it's not maximizing my time at all

[dapper root]

There’s probably tons of “show a group of order xxxx cannot be simple”

[static crest]

it's mostly a waste of time

there are

those were painful

to do

[dapper root]

Oh okay so you aren’t under any pretense of it being useful

You just want to

[pliant patio]

at least you'll kill your quals if you have any

[static crest]

ya lol, there's no way it's useful

I'm just doing it for funsies

[dapper root]

That’s fair lol

I can respect that

I haven’t skipped some really painful Matsumura exercises

Since I want to be able to say “yeah I did em all lol”

At least those exercises are mostly all useful haha

[ripe granite]

The module theory and Galois theory problems aren’t bad

You can work through all of them pretty quickly if it isn’t your first time doing algebra

[gray gazelle]

How to kill all the "show this group of order blah is simple" exercises: write a logical deduction system program involving remainders of the number of sylow subgroups or whatever shit, and run it on all the orders given

[dapper root]

Yeah but this guy showed 1,004,913 can’t be the order of a simple group without rep theory

That’s painful

[ripe granite]

Yeah some of the group theory problems suck

[dapper root]

And also not particularly useful haha, idk maybe a technique you invented to attack that shows up on a qual

[ripe granite]

I hope 4n +2 shows up on whatever qual I’m doing haha

[dapper root]

What’s that?

Can you show any group of that order isn’t simple?

[ripe granite]

Yes

[dapper root]

Wtf haha

Is this where you take the sign map?

[ripe granite]

Yes

[dapper root]

That’s pretty cool

[static crest]

I just calculated it, it's 974 exercises done so far

in d&f

[dapper root]

...

Jesus

[static crest]

401 pages of latex

[gray gazelle]

Oh, you are texting them all up?

[static crest]

ya

[dapper root]

This guy is project crazy project or whatever

What if you finish it

[gray gazelle]

Publish a solutions manual

[static crest]

idk, once I reach my goal of doing everything up to galois theory

we'll see

[dapper root]

Hahaha

[static crest]

maybe I'll just make it available publicly

it's on my private github repo rn

[dapper root]

some guy did that

And got to like chapter 12

The blog is private now tho

[ripe granite]

Probably not a good idea

[static crest]

probably not

[dapper root]

Also yeah, I feel like these things are dicey

[static crest]

that's why I haven't done it yet

[dapper root]

1: legally

2: it’s morally questionable even

I think

[gray gazelle]

Oh, it's illegal?

[dapper root]

It’s nice to have solutions but also if it exists like...

[static crest]

I mean it might not be

[dapper root]

I mean potentially

[static crest]

covered under fair use probably

[pliant patio]

if you put the problem statement then maybe

[dapper root]

For one

[static crest]

but who wants to get into that kinda issue

[dapper root]

Countless courses pull exercises from there

So suddenly you’re an accessory to cheating which tbf like

[static crest]

my bigger issue is that I'm kinda morally opposed to full problem solutions

[dapper root]

You aren’t at fault

But you did publish them

And aside from cheating you could argue it’s too tempting

I also think having solutions to shit can be beneficial so

¯_(ツ)_/¯

I was thinking on publishing my Hartshorne solutions but have changed my mind

[static crest]

I honestly doubt d&f are gonna come after my ass if I make a pdf of solutions available on github, I just know many of my peers straight copy solutions if they see them

[dapper root]

^^^^

I figure I might just like

Let people email me when I make a website or whatever for my math crap

And I’ll send a solution here or there or a hint

At least if I’m not famous

And getting tons of emails all the time lol

[ripe granite]

lmao

[static crest]

I was thinking of an alternative thing where I just make an attenuated solution thing, where I only put answers for like a select few exercises I found interesting in each section

[gray gazelle]

There is an alternate perspective: those who want to gain something from your solutions can do so, who cares what the copiers do

[dapper root]

That’s potentially okay

[static crest]

true

[dapper root]

I mean that exists but

It’s not really rational imo

Even for people who have good intentions

It could be hurting them

If someone of weak will just looks up all the problems they’re self studying with

Again, that’s on them, but...

[ripe granite]

yeah I dont think it's a good idea

just use your solution manual to flex on others

should be good enough motivation

[dapper root]

Lmao

[ripe granite]

I'll do that when I finish writing up hartshorne 2 and 3

I'll print it out

and carry it around

and flex

[static crest]

lmao

I'll walk into my ug field theory class with my (then) 600 page d&f solution manual printed off

[ripe granite]

ye

do that

[sage python]

"Get on my level"

[dapper root]

Lmfao