book-recommendations

[sleek python]

I'm not a maths major for nothing

[granite sluice]

i think for a lot of people, IQ is just a shorthand for saying "smart"

maybe its just a shibboleth. if u want to signal that you belong to a different tribe you say 'g' instead of IQ.

[sleek python]

So for competitions the best is to look for prep books if there exists any good, otherwise a book gathering lots of exercises would be good

I'd suggest a french book but it requires french 🙄

[tribal kernel]

This was probably already said, but competition math is a lot different than coursework or research math. Being good at competitions doesn’t necessarily mean you will be a good mathematician or have a high IQ. Math competitions are really difficult though and it’s definitely a good skill to be good at those types of questions

They’re mostly supposed to be fun questions and the proofs are a bit like puzzles. It’s worth investing in that skill, just doesn’t automatically imply or is implied by being a good mathematician

[granite sluice]

ive becoming kinda interested in becoming better at competition math now, as a late stage phd student lol

it just seems like a fun way to become better at problem solving

[tribal kernel]

Yeah! I think it definitely fits that bill

[granite sluice]

but when I was in HS I was terrible at math compettitions and it made me feel really stupid and bad

now I have accepted that im an idiot tho, so things are better

[tribal kernel]

Lool good luck then my man

[granite sluice]

I wonder if there are other grad level ppl who would enjoy fake math competitions

lol

of just hs math stuff

[tribal kernel]

Maybe if I wasn’t so busy with my course work I’d indulge

[granite sluice]

yeah I guess instead one can always do exercises for your area instead

but its not as much fun , because hs math comp is more meaningless kind of puzzle solving joy

[quick hornet]

i do think that doing well on competition math tends to correlate with doing well in mathematics (coursework, at least)

since i think 90% of doing well in mathematics is just dedication and hard work

and those who are dedicated to competitions tend to also have the motivation and work ethic to excel in "regular" coursework

however, i dont think the converse holds; ie i think its possible for competition math to not really "click", and that doesnt necessarily mean anything

[tribal kernel]

Fair enough that could very well be true

[timber mesa]

in fact not many working mathematicians are former olympiad kids

(wonder if there's some sort of statistic for that, like a % over some departments?)

[tribal kernel]

I knew a guy at my undergrad place who excelled at competitions but wasn’t doing so hot in an intro PDEs course. But I also know several great graduate mathematicians who counts the get a 2 on the Putnam

[broken meadow]

the converse better not be true

math competitions make my head spin

i don't even wanna know how well i'd do on the putnam

[timber mesa]

the converse better not be true
@broken meadow it's not, I'd conjecture there's little to no correlation

[broken meadow]

:)

[tribal kernel]

Yeah I’d agree with that

Most math comps make my head spin but I’d like to think I’m pretty good at math and I do well in my courses.

[timber mesa]

same, I think I just find olympiad problems uninteresting

courses aren't exactly the same as research math either but I can seem to understand at least the point of "research" questions in some areas at least

[hearty steppe]

@long bear start with Meyer’s Matrix Analysis and Applied LA book for problem sets btw

[forest bluff]

Putnam is that collegiate Math IQ test right? Just go through an analysis book I'd imagine. Why take shortcuts and use test prep books lol. Just power through the actual textbooks on the topics.
@hearty steppe

You didnt understand...i want to solve a tons of problems...that is why i need real analysis problem books....for theory i have other books and i know only one problem book Putnam And Beyond...i need more

Look i am currently reading real analysis from

1. Rudin
2. Mathematical Analysis -Aopstol
3. Apostol calculus vol 1

Now i have to do tons of problems. I can not compete in putnam. But i want to reach at the level of Hardest problem in Putnam solver. So i only know one source of problems which is Putnam and Beyond book. I need more sources. Please suggest me

[timber mesa]

putnam and beyond is pretty much the definitive source for putnam-like problems

but (and this is unrelated to the Putnam) check out the AMS "Problems in mathematical analysis" series

try to get a compilation of past year problems, there's books which have those along with solutions

[forest bluff]

Thanks

Is Berkley problems in mathematics good ?

[undone flame]

Is this only for math books? I assume yes, but I'm hoping no

[long bear]

@undone flame i don't think there are strict rules on the subject, but the more you deviate from math the less likely you are to find someone who knows it

[tidal mural]

Is SAT hard?

[tribal kernel]

Regular SAT?

[tidal mural]

Yeah

For college

[tribal kernel]

Well in math it’s not too bad. Make sure you’re comfortable with proportions and simple geometry

[tidal mural]

Is the geometry hard?

[tribal kernel]

There’s probably a ton of math practice tests online, I’d recommend doing that. That’s what I did in high school

[tidal mural]

Website?

Or book？

[tribal kernel]

Nah mostly area and circumference of circles, triangles, similar squares

[tidal mural]

Ok

[tribal kernel]

I looked through some old Princeton review stuff. They usually do really well with test prep

[tidal mural]

Ok

[vagrant sedge]

Hi... Does anyone here know an interesting book about the applications of algebra to analysis?

[marble solar]

like

abstract algebra?

@sage python this is all you bud

[sage python]

Prob would need to be a bit more specific. I feel a lot of places where one can genuinely say that the algebra is being applied to do analysis (rather than the other way around) are somewhat specialized?

Like with harmonic analysis there's definitely a lot of interaction

[tribal kernel]

A good book on Lie groups and Lie algebras has a good intersection of algebra and analysis

[sage python]

But I don't know whether it's just recasting what analysts like to do in algebraic terms or whether there are problems that the analysts care about which the algebraic recasting solves for you

(This isn't the skeptical "I don't know if blah" so much as I genuinely don't know enough harmonic analysis to say)

Oof

Nice, good luck fam. Keep me posted on how things go

But yeah so things that come to mind are, I've definitely heard of people doing PDE on manifolds and then stuff like Lie theory kicks in by virtue of caring about the geometry/topology

This is the type of thing where I'd more or less unambiguously call it an application of algebra to analysis, since you start off caring about raw analytical things and now analysis becomes relevant

[tribal kernel]

Functional analysis is considered the application of linear algebra to analysis

[sage python]

Well I mean

Analysis is the application of linear algebra to analysis lol

[tribal kernel]

But I don’t know if that’s a super satisfying application for what you’re searching for lol

[sage python]

Anyway I'll interpret the question as the broader spirit of interaction rather than the more restrictive "application of algebra to analysis"

Since again I feel like if I say that abstract harmonic analysis on groups is such an application some of my undergrad profs will be like "Nah people who work in that area are representation theorists using analysis they're not real analysts"

[marble solar]

I think that's splitting hairs

Was Rudin not an analyst?

I'd consider them analysts

[sage python]

Idk but you should some of my undergrad profs lol

[marble solar]

yA good ol' walt

[sage python]

I think those guys would basically be like

Yeah analysis is PDE

Everything else is just words

[marble solar]

Mario Bonk called Rudin the undisputed master of analytic exposition

[sage python]

Specifically Soug would prob say that lol

Anyway so back to the question

[marble solar]

Sorry I misquoted

https://www.math.ucla.edu/~mbonk/complana.pdf

The real quote is here

That guy is insane. His grading scheme for grad real was

[sage python]

Lie theory, harmonic analysis on groups, functional analysis to a degree (especially stuff like operator algebras)

[marble solar]

1 person gets A+, 30 students so only two more left for A's

[sage python]

Folland seems to be nice for the middle one

[marble solar]

Everyone else gets A- or lower

Because A/A+ means top 10% of class

Dodged that bullet

Algebra used in analysis

[sage python]

More generally interactions of the two that come to mind

Oh speaking of analysis

I just showed that the Laplacian on the hyperbolic disk is
$$(1-r^2)^2\left(f_{rr} + \frac{1}{r}f_r + \frac{1}{r^2}f_{\theta\theta}\right)$$

[marble solar]

Yeah there's a lot of symmetry stuff you have to use. I haven't had to that much algebra

[hasty eagle]

Daminark:

[sage python]

It was a time

Mostly because I wanna reason about the Poisson kernel

$\frac{1-r^2}{1-2r\cos(\theta - \phi) + r^2}$ where $\phi$ is some fixed angle

[hasty eagle]

Daminark:

[marble solar]

Is that what it is on the hyperbolic disk?

[sage python]

Not quite giving me the option to delete my original message and just leave the tex

Yup

In polar coordinates

[marble solar]

I know on the upper half plane it's like

$$ \frac{1}{\pi(x^2+y^2)}

[hasty eagle]

MoonBears-C-:
Compile Error! Click the reaction for details. (You may edit your message)

[marble solar]

Or something

[sage python]

In Euclidean coordinates it's just $(1-x^2-y^2)^2 (f_{xx} + f_{yy})$

[hasty eagle]

Daminark:

[marble solar]

They're might be a negative y on top

[trim narwhal]

I've just finished Spivak, what should I read next?

[sage python]

Linear algebra

Hoffman-Kunze is the best of the books I'm familiar with

[trim narwhal]

Ok thanks

[sage python]

People like Spivak Calc on Manifolds

The book I found recently and advocate for is this

https://www.springer.com/us/book/9783034806350

[trim narwhal]

Ok thanks

[marble solar]

Calc on manifolds

[sage python]

But if this is a bit overkill then go with Spivak Calc on Manifolds

[marble solar]

is still the standard

And has lower tech

[limpid gazelle]

Spivak's calculus on manifold ch4,5 are kinda

Hard

Especially chapter 4

It was hella hard for me

[marble solar]

I had a professor that had taught it for 20 years

So he had a lot of experience ironing shit like that out

So it made sense

Maybe I was just lucky

[sage python]

The thing I like about this book over Spivak is that it introduces Lebesgue stuff earlier. Also I heard Spivak is kinda typo city

[marble solar]

It's really not that bad

and you can get the idea

pretty easily

[tribal kernel]

I like the Spivak differential geometry books so far too

It’s about 2000 pages worth of geometry though

[wooden sparrow]

If Spivak is that famous, didn't a lot of people help with errata? @sage python

[sage python]

Wouldn't be too surprised

[runic hatch]

I havent found any typos in my copy of calc on manifolds yet

Granted I’m only about halfway through

[hearty steppe]

I think I may have a couple pdfs that may have been re-typed or something. Idk the format of some of the texts can be a little weird

[runic hatch]

are there any good resources on er 'geometric' number theory?

im not sure if that's the right phrase for it

basically looking into the relationship between number theory and geometry

[runic hatch]

aha

that seems to work

[gray gazelle]

Hi, can anyone recommend me a book for self studying complex analysis?

I just completed first year of studies, real analysis on single variable functions

I have complex as a course in my third year, but it seems interesting to me, so I'd like to try it earlier

[brittle latch]

no but i can recommend you this

https://www.maths.cam.ac.uk/undergrad/admissions/files/reading-list.pdf

https://marktomforde.com/academic/mathmajors/textbook-suggestions.html

some good ones there too

[gray gazelle]

This looks nice

[brittle latch]

those links might be worth a pin but idk if any mods would agree and im not gonna ping them lol

[slender sphinx]

@gray gazelle using gamelin for complex analysis rn

pretty good so far

[gray gazelle]

Do you use some problembook with it?

[slender sphinx]

nah, i just do the exercises

might also check out Stein and Shakarch's book; I've heard good things about that and will read some of the other books in that "series" after gamelin

[gray gazelle]

Shakarch will be used on my upcoming course if I'm correct

[fluid bay]

How’s conways book on complex analysis?

[marble solar]

Not as good as ahlfors. Shakarchi is ok, has a lot of great exercises for complex

but his treatment of some topics is kinda lackluster

[fluid bay]

Thanks

[marble solar]

I think the two best are Ahlfors and Marshall

Terry has his notes on his blog if you're curious, but those seem to be a combination of ahlfors and shakarchi

[hollow peak]

ahlfors is just so algebraic though

he tries so hard to not be so analysis-y but it's very obnoxiously symbolic

[marble solar]

I think he's more geometric than anything

Shakarchi does this crap with toy contours

[sage python]

The toy contours seem annoying in Stein-Shakarchi tbh

In general I feel like SS is scared of topology

[marble solar]

Yeah, undergrads at princeton r so scaed

[hollow peak]

is the princeton analysis series actually any good?

they seem pretty solid for a second or third time around with analysis

[marble solar]

Volumes 1, 3, and 4 are god tier

Fourier, Real, and Functional

I've done nearly all the exercises in volume 1, 2 and 3

At one point or another

[normal isle]

Can you recommend any books for statics, maths major

not the engineering books

[marble solar]

Volume 2 again has great exercises and some great topics

But some of the treatment/development of the theory is lackluster

Volume 3 is what my Real Qualifying Exam was on

[sleek python]

A maths server isn't the best place to find statics books 👀

[normal isle]

:(

[sleek python]

Ask in the physics server, they'll be more likely to know books

[normal isle]

kk thanks

[hearty steppe]

Err nvm about the channels I mentioned for stats server. They should really pin that server somewhere around here.

[trim narwhal]

A good book for starting Euclidean geometry?

[marble solar]

Euclid's Elements?

[hearty steppe]

Isn’t recommending Euclid’s “Elements” to learn Geometry basically exactly like recommending Newton’s “Principia” to learn Physics? Lol

[marble solar]

No newton's principia is almost indecipherable how it's related to physics

Euclid's elements is pretty readable

[tribal kernel]

I got to hold a third edition of Principia written in latin published in the 1700s

Tried reading a bit of it, but my latin is not good

[runic hatch]

there're also a lot of resources online to help you get through Euclid's elements

including sites that give a lot of nice pictures to help you understand what's going on

[quick hornet]

elements is very well-written considering the time it was published

its still readable today (translated obviously) although the occasional error makes it strongly recommended you read it alongside a guide/errata collection

i wouldnt read it to learn geometry though, yeah

no one does geometry in the same way euclid did

(in fact, it's probably fair to say that euclid's biggest contribution to mathematics (besides popularizing it) is the axiomatic method rather than his geometric contributions specifically)

[marble solar]

I know several people that learned it from elements

[quick hornet]

you certainly can

[marble solar]

I never learned euclidean geometry, they all told me it was the best way to go

They all seemed pretty good at math

So I just took their word for it

[quick hornet]

i mean my hot take is that

only a specific subset of people have any reason to care about euclidean geometry without coordinates

this subset contains:

• people in specific subfields of mathematics
• math historians
• high school teachers

group #2 should absolutely read elements, group #3 probably shouldnt

that leaves group #1

in which case i think it depends on what subfield you belong to

investigating formal logic in geometry? absolutely read euclid (which provides appropriate background to stuff like tarski's modernized axiomatizations)

why not both

well sure

but i'm taking it for granted that you have some reason to learn euclidean geometry

that reason may just be "interest"

in which case, euclid is great for the historical context and for the insane wealth of resources on it

but more practically speaking

¯_(ツ)_/¯

[hasty turret]

this subset contains:

• people in specific subfields of mathematics
• math historians
• high school teachers
  You forgot math competitions

[quick hornet]

well they certainly shouldnt learn out of elements

unless theyre fine being inefficient with their time

which people "serious about" competitions probably aren't

[granite sluice]

artin has a weird book about axiomatic geometry

weird/interesting: https://en.wikipedia.org/wiki/Geometric_Algebra

[hearty steppe]

that's the father of Artin that wrote Algebra btw

[sage python]

Lol, if anything the father is prob the more significant mathematical figure

[granite sluice]

that must have been an interesting family

[sage python]

Actually Michael Artin is based too

He had a hand in the Weil conjectures

[gray gazelle]

see #books-old

i personally like apostol, vol 2 for multivar

[dusky remnant]

Anyone got a recommendation for a book in differential equations? An introductory one.

[long bear]

nice name

[dusky remnant]

@long bear lol

[gray gazelle]

@trim narwhal folland's "advanced calculus" and spivak's "calculus on manifolds" are ones that i've read and can say for certain that they're good. munkres' "analysis on manifolds" is another common one in my experience but i don't think it's very good - bad exercises and its proofs are way too wordy. good if you want clarification on things spivak leaves out i guess

both require linear algebra

[trim narwhal]

A good book for starting Geometry?

[marble solar]

Euclid's Elements?

[broken meadow]

Deja Vu

[marble solar]

I think it's my go to now

[valid moth]

@trim narwhal hartshorne

[calm crane]

ega

[gray gazelle]

euclidean geometry in mathematical olympiads

[marble solar]

So met with my Math Ed. professor for this Fall; we couldn't find any "best practices" for math tutors (which is what I work in for now). Guess I'm going to be doing a small little project on it

[hasty turret]

What is your audience?

[marble solar]

Anyone have references for math tutoring? I know tutoring is a subset of teaching, but I think it's sufficiently different from teaching from a primary educator

I guess my audience are people that are working at college-level tutoring centers for now. May expand to cover k-12 private/public tutoring

[tribal kernel]

I think a good text on category theory and ZFC set theory should be sufficient. If you can explain the math to students in the most general terms they should theoretically be able to derive all results from there

Nah jk, I'm actually interested in this tutoring/teaching reference as well

[flint forge]

@marble solar have you reached out to TAs at other unis?

They might have proprietary resources they can share

[marble solar]

They didn't really have a whole lot

[flint forge]

Sad

Seems like a glaring hole

You could try to make an open project out of it

[tribal kernel]

I think providing lots of resources to tutors is an exception rather than a rule

When it comes to universities at least

[smoky surge]

@marble solar i think mathnasiums do a good job

they might publish info I worked at one and thought they had some good practices

[bold spindle]

What is this channel for

[gray gazelle]

book recommendation... specificlaly math books, or no?

someone could recommend eg dr seuss, it is a good book

[stray veldt]

this is a math discord

[long bear]

i am sam

[gray gazelle]

sam i am

[maiden stratus]

am i sam?

[normal sandal]

i do not like green eggs and ham

[gray gazelle]

Woa it jams

i say i do not, i do not like green eggs and ham

[sleek python]

Is this really a maths discord tho?

What if it's all a simulation and this is an engineering discord

We should meditate about that on #chill

[timber mesa]

What if it's all a simulation and this is an engineering discord
@sleek python judging by the amount of desperate lazy freshmen asking us to solve their questions, it might well be

they think this server is chegg or some sht

[nimble sable]

I need help proving the collatz conjecture can anyone help me with that?

[heavy barn]

[nimble sable]

I would like to discuss perko’s book on Differential Equations and Dynamical Systems

It annoys the crap out of me

[timber mesa]

why so

[nimble sable]

Bc it references other books for exercises hints. IMO that’s very annoying especially when I don’t own said text

And it includes the Banach Fixed Point theorem in the exercises as a hint. Why not actually include it in the section where the Picard-Lindlof theorem is discussed

[timber mesa]

those are good points

honestly I got nothing to say, though I still think it's the best book for it's topic at an adv undergraduate/beginning graduate level lmao

it probably assumes you've at least seen the Banach fixed point theorem at some point

Bc it references other books for exercises hints. IMO that’s very annoying especially when I don’t own said text
@nimble sable not sure I've seen this in my edition though, which exercise(s) in particular?

[nimble sable]

@timber mesa the section on Dependence on Initial Conditions and Parameters Exercise 8 it references a theorem in Rudin, which I don’t own so I was annoyed. Yeah but Terchels book on ODE does include it and I did enjoy including it the section rather than a footnote due to thoroughness

[timber mesa]

oh I see

[nimble sable]

It’s the principle

[timber mesa]

though it's probably referencing a well known result in this case (||continuous on a compact => bounded||)

(Gerald Teschl's?)

[nimble sable]

Gotcha. Which is fair but the principle irritated me. Yes lol I remembered incorrect

[timber mesa]

ah ok

[gray gazelle]

just libgen a copy of it

[karmic thorn]

Has anyone here read "Geometric Linear Algebra" by Lin? Is it good for a beginner to the subject?

[gray gazelle]

You can even prove that the supremum of the absolute value of the gradient is the infimum of all lipschitz constants of f on E

[gray gazelle]

why does it matter that E is convex? can't u just say that f is locally lipschitz, then it is globally lipschitz by E compact? (oh, nvm, im not sure how to show f is locally lipschitz)

[trim narwhal]

In average, how many minutes do you spend on a single page of a math book (a rigorous one)?

[gray gazelle]

depends how well i want to understand what the author has written

[karmic thorn]

5 seconds and I'll know this shit is beyond me

[gray gazelle]

[karmic thorn]

Jk, for pages which I find challenging, I often try writing stuff down verbatim somewhere else and see if I can make sense.

[hearty steppe]

I can spend a good 20+ minutes on a single page when it’s complicated enough. That’s not exclusive to math though.

I remember trying to get through baby rudin with no experience in analysis and boy it took me about that much time or more to get through a single page. I picked up less dense analysis books after getting halfway through the first chapter but even then sometimes I got to spend about 20 minutes or slightly more on some of the pages in Schroder or Apostol regarding analysis. Not too much trouble other than trying to read Hoffman Kunze Linear Algebra or Artin’s Algebra. Which is why I switched over to different algebra books as well. I’ll still have a go at them and rudin at some point

[karmic thorn]

For a first course in group theory, should I study from Pinter or Judson? I have a physical copy of Gallian but I don't seem to like it very much for unknown reasons.

[supple loom]

Lang looks nice to me, have you considered that?

[meager karma]

calais is really nice, in french though

[karmic thorn]

I've never looked at Lang, is it good for a beginner?

[meager karma]

lang undergrad algebra is nice

[karmic thorn]

I'm pretty sure I can't catch up with French 😅 Does that text have a translation?

[meager karma]

but there are more group theory specific books

[karmic thorn]

There are indeed so many that I can't make a call. I'll take a look at Lang though, thank you.

[meager karma]

am learning group theory now too

[karmic thorn]

Oh nice! Which text are you using?

[meager karma]

calais haha

gourdon, and lang

[karmic thorn]

//by the way Lang's Algebra is the text I should be looking for?

[meager karma]

mainly calais though

[gray gazelle]

lang's algebra is his grad algebra book

[meager karma]

lang's undergrad algebra

[karmic thorn]

Oww, just read in the preface it's undergrad algebra

Yep, I'll take a look at that one.

Lang seems to write a lot of books

[gray gazelle]

i really like lang's exposition of normal subgroups

idk if other books do the same thing, i know dummit&foote does

[meager karma]

i don't know if there are many french people here but calais is

[gray gazelle]

how does calais explain normal subgroup

[white pebble]

[trim narwhal]

Is Hoffman Kunze good for a first encounter with LA?

[hollow peak]

I was under the impression that hoffman kunze is extremely difficult but I may be wrong

nevermind thinking of the wrong book

[marble solar]

Hoffman and Kunze is a great book

Some of the exercises are incredibly challenging

[tribal kernel]

The book content is not too bad for a first encounter. It’s the exercises and later chapters that might be a challenge to those without a lot of proof or matrix experience

[marble solar]

Also chapter 1 is not that great

[civic carbon]

I'm definitely on Axler for linear algebra at the advanced undergrad level, and DF at the beginning graduate level. But there is widespread disagreement about this.

(To me, minimal polynomials are the one true LA invariant, and determinants and characteristic polynomials exist to calculate them efficiently. Determinants also have some cute mapping properties that are useful in very specific situations)

[quick hornet]

mehhh i feel like you downplay these "mapping properties" a bit

having an operator that very cleanly wraps multiplicative information about matrices into single numbers is very handy, not just from an applied/computational perspective

since now, when we study operations on matrices (b.e. linear operators), we can get a lot of information just by studying their effects on det

[sage python]

Yeah I'm of the take that really determinants should just be introduced through exterior algebra

[valid moth]

ok axler

[marble rock]

hoffman is good

should hit you hard enough for you to become better

[hearty steppe]

yea i mean that is the point of hoffman obviously. I'll get back to it after going thru a few other books

[white pebble]

recommend book on whack integration skills

[gray gazelle]

Inside interesting integrals

[limpid gazelle]

Thanks

The almost impossible integrals book had a lot of interesting integrals

[white pebble]

thanks

[granite sluice]

wow the story about Cornel in the foreward is pretty interesting

of impossible integrals

reminds me of that stackexchange person who would always answer completely insane integrals

and get into fights with people over whether or not doing integrals was 'real math'

[hasty turret]

Why not use a graphing calculator?

[granite sluice]

well some integrals you can't do that way because of oscillations

[obsidian valley]

is doing integrals real math

[granite sluice]

e.g. in fact there is a very simple class of trig integrals that are NP-hard to evaluate, or even to decide if the result is nonzero

[hasty turret]

Ask the analytic number theorists

[granite sluice]

and numerical attacks on them fail because of the high frequency oscillations

[velvet briar]

@obsidian valley
I think many pure mathematicians would say that "creating new knowledge" about structures is math. From this point of view, getting new integral theorems is math, but solving specific integrals using tricks is not math.

This is only one point of view of course and gets into some philosophy

[obsidian valley]

well they are both math i guess but one of them advances the field and one of them is more a fun game

though a formalist may argue that all of math is just a fun intellectual game

[velvet briar]

I have a pretty simple opinion. If it's cool and logical it's math. Why not? Haha

[obsidian valley]

I'd equate integrals with brain teasers or competition math I guess

if its in a channel in the math discord, it's math

[velvet briar]

Gottem

[granite sluice]

there are pretty profound integrals out there, e.g. im sure RH has some restatements of the form 'what is this integral' or 'derive a better bound on this integral etc.'

[obsidian valley]

reminds me of this https://mathoverflow.net/questions/53122/mathematical-urban-legends/60908#60908

[granite sluice]

one of the comments " Actually, that is not that bad of an idea! I have seen the face of my students when I tell them «you should go through your linear algebra notes to see how much of it carries over to the case of skew-fields» right before proceeding to pick a basis for an H-module, say.. "

hmmm

[quick hornet]

there are pretty profound integrals out there, e.g. im sure RH has some restatements of the form 'what is this integral' or 'derive a better bound on this integral etc.'
@granite sluice

if you can prove this youve proven RH

admittedly it feels kind of "cheaty" since theres a zeta in the integral

but if you count, say, the log integral

then there are a variety of identities based on that

now these generally arent considered suitable approaches to RH

but there are some integral-based results that people are seriously exploring to crack it

this is the subject of the polya-jenson program

indeed, this is based around a certain fourier analysis observation of the riemann Xi function

see https://www.pnas.org/content/116/23/11103

[gray gazelle]

Heh, pnas

[granite sluice]

@quick hornet oooh, cool. thanks 🙂

[quick hornet]

this is afaik one of ken ono's "big deal" results

and one of the reasons people care about him besides hosting a killer REU

[granite sluice]

as I was having a snack I was dreaming up writing up a fake 'calculus exam' consisting of RH equivalent calc problems

but yeah having zeta in there would sorta give it away lol

[quick hornet]

heh, they might be a bit too sophisticated to be believable on that front

but im sure theres a couple you could squeeze onto an analysis 1 pset/final

[granite sluice]

Presumably there are some explicit, rational values of zeta that are unknown?

[quick hornet]

for example, show that for all $n \geq 5041$, we have $\frac{\sigma(n)}{n\log \log n} < e^{\gamma}$

[hasty eagle]

Namington:

[quick hornet]

this could certainly fit on an analysis pset with some slight rephrasing and defining the gamma function

[granite sluice]

whats $\sigma(n)$?

[hasty eagle]

Crustle:

[granite sluice]

😮 didn't mean to yell

[quick hornet]

sum of divisors

[granite sluice]

oh ok

[quick hornet]

this is equivalent to RH

or at least implies it, idr exactly

the 5041 might make an analysis student suspicious but

im sure if you phrased it

[granite sluice]

ah ok, yeah that is a good candidate.

[quick hornet]

"find a lower bound on n that makes this true"

[granite sluice]

also sum of divisors would make students suspicious

[quick hornet]

it might be believable

and indeed if you DO find any lower bound, you've proved RH (since we can just computer verify every 5041 <= k <= that bound)

[granite sluice]

https://arxiv.org/abs/1505.01548 😮

coolest paper title of the day

[quick hornet]

what are you talking about

my approach-via-geometry-of-the-field-of-1-element approach

is totally sensible

and not at all contrived

[granite sluice]

woah : https://www.math.waikato.ac.nz/~kab/ERH/EquivRH.html

[granite sluice]

Oliver looks so happy wow 🙂

Or is that just a troll grin?

true

so what are the two elements?

[quick hornet]

{0, 1}

its just {0, 1} under *

if this sounds stupid

it kind of is

but its an appropriate fit for the types of geometry those people want to do

[granite sluice]

hm

ok...

I thought F_1 was like, vector spaces are sets, GL_n is S_n, etc

but idk just heard gossip at some point

huh

well what is the algebraic closure of F_1 ???

😮

[quick hornet]

heres the paper in question if you care

https://arxiv.org/pdf/1801.05337.pdf

its expository but i havent tried to seriously read it

so idk how approachable it is

idk

all i know about this is

heavily word of mouth

https://mathoverflow.net/questions/6508/what-is-the-algebraic-closure-of-the-field-with-one-element

[granite sluice]

sufficiently advanced shitposting is indistinguishable from math overflow apparently

lmao C is the field with one element, that is big brain

[quick hornet]

the more upvoted answer is probably the one youre looking for lmao

but that one is funnier

[flint forge]

Cohomology w coefficients in F_1

[craggy glade]

Can anyone help me understand a segment from godel escher bach?

what did hofstader mean exactly by placing G(n) below n for all n??

[dapper root]

Not the right place for this

[craggy glade]

well it said book discussion

so i thought

[dapper root]

no

[craggy glade]

alright

[dapper root]

help is for other channels, this is for book recs

[craggy glade]

i see

[dapper root]

like it says at the top of the channel lol

unless ur on mobile

[craggy glade]

didnt see sorry

[dapper root]

then You have to click the name I think

[gray gazelle]

Someone already read "30 secounds Math"?

[tribal kernel]

@craggy glade Yo I'm not super familiar with this stuff, but I'd imagine you may want to take this to #foundations. The people there should be able to help you out

[vagrant sedge]

Hi. Could anyone recommend me a book/resource with problems that mix math and computation? Something like projecteuler.

Thank you.

[obsidian valley]

@craggy glade how do you find GEB? I have a copy on my bookshelf I've been meaning to read for like a year. I got about 100 pages in and got super busy with school again

[flint forge]

the true take on GEB is that you read it until youre convinced pure math is cool

then you stop reading it and learn math

(optional: return to GEB down the line once you know more math)

i think sometimes the aesthetic is a good gateway drug

to actually doing math

[valid moth]

what's GEB

generalized Euclidean b...

[shadow nebula]

godel

euler i think

bach

[valid moth]

geometric enumerative b...

[shadow nebula]

who tf is escher

[valid moth]

😳

^ could this object be built

[shadow nebula]

[gray gazelle]

get rekt archsys

[obsidian valley]

i got far enough into the book to know escher made golden braids or loops or something idk

and so did godel and bach

err godels proof was the original golden braid loop

something like that

[dapper root]

Has anyone read Introduction to Lie Algebras and Representation Theory by Humphreys?

It’s the book for my Lie Algebra class, and I’m just wondering how ppl liked it / what was your intro Lie Algebras textbook if not that one

[tribal kernel]

Mine was a book written by my professor and published by my university in a spiral notebook

I’ve since looked at Lie Groups, Lie Algebras, and some of the Applications by Gilmore. It’s good but I think the author could definitely be more precise in his notation and math working. He’s more obsessed with showing the “beautiful symmetry” sometimes than the actual work.

[tribal kernel]

Maybe I should read this at some point

My intro Lie algebra book was almost all linear algebra

It's impressive that you can do most of the stuff from the linear perspective but you may loose some of the stuff working behind the scenes

[robust palm]

@obsidian valley I really liked GEB, he really doesn't tie the whole book together until he hits the stuff about the brain but the first half nicely builds up to a fairly easily digestible proof of godel's incompleteness theorem

so if you wanted to leave it off there, you could

I think the overall point of the book is that he sees similarities between formal systems strong enough to model arithmetic and the basic things that happen in a brain at a low level (like neuron level). The simple rules governing arithmetic are strong enough to refer to the system itself (the strange loops he doesn't stop talking about) even though the rules seem pretty mechanical

and he seems to use this as a framework for trying to understand how consciousness arises from processes in the brain, processes which he argues are just as mechanical as those governing the types of formal systems strong enough so that the incompleteness theorems apply to them

[hearty steppe]

The irony is I didn't even have to talk about GEB or incompleteness theorem this time around for someone else to bring it up. >.>

[robust palm]

I haven't been on here for too long, do you bring it up often?

[hearty steppe]

Don't get me wrong, I like GEB and I am a fan of Hofstadter. But I have been corrected a decent amount of times here that GEB does no justice for incompleteness theorem.

[robust palm]

I'm certainly not an expert so I wouldn't know how well he actually covers it

[hearty steppe]

primarily because it seems that the main point a lot of people on here make is that he fails to connect the rigorous logic behind Godel's incompleteness fully to everything else he brings up

[robust palm]

ah, so is the issue that he covers the incompleteness theorem pretty well but he doesn't do as good a job with the rest of it?

I know I felt pretty out of my depth in the chapters talking about the brain

@sweet lotus in what scenarios in particular?

well, I like the first half lol

[tight crag]

I really like the computability proofs of incompleteness and undefinability of truth

as opposed to the fixed point proofs

[robust palm]

I'm definitely not an expert but the parts on the brain felt like a stretch to me, but he was talking about something that I had so little knowledge in I felt like I couldn't appraise some of those chapters fairly

I'll check it out

I think calling it a book without substance is a bit harsh

I didn't really see it as a math book

[tight crag]

people who got into logic because of GEB seem weird to me

[robust palm]

It talks about it, yes

[tight crag]

I know exactly one such person

and he is very weird

(also he's not particularly good at logic)

[robust palm]

but it's very unique in the way he structures it, and quite entertaining if you're into it

he definitely discussed things that happen in the brain in the light of godel

but I don't think he said: the brain is a formal system in the sense of one satisfying the axioms that would leave it susceptible to the incompleteness theorems, so this explains consciousness

the way I read it, it was more like: the brain at a low level seems to behave like a formal system, and maybe the capacity of the brain to reason about itself (which is how he defines consciousness) has something to do with the "godelian" nature of formal systems

he argues that an analogy exists and that the ability of formal systems to talk about themselves in some sense is analogous to consciousness in the way he defines consciousness

but he does not say "this is definitely why it works"

it might depend on how you view a waste of time

perhaps the book was too bold in its aims in your opinion

I can certainly see that

Without stronger claims the book is a waste of time, with them it is wrong.
@sweet lotus also, to have any stronger claims about the topic, he would have to solve consciousness, and I don't think that's a reasonable expectation

"things are self referential dude" might be the most succinct summary of the book I've seen

it definitely meanders

but it wouldn't be geb if there were no digressions

is this the chaitin's constant guy

[craggy glade]

@obsidian valley uhh, someone metioned it to me, and im interested in godels proofs

[hearty steppe]

seems a lot of people including myself, become prematurely exposed to godel because of GEB. Again, I'll admit Hofstadter does an interesting job with GEB outside of trying to correlate Godel's incompleteness theorems. I kinda feel like demonstrating Godel's incompleteness outside of mathematics wasn't the point, but rather showing the recusiveness of the world around us through self-reference and self-replication patterns and how limitless it seems. Maybe some day a mathematician will tie that with incompleteness theorems, but it has yet to be done competently?

Like GEB makes you think incompleteness has a lot to do with the limitless feeling of recursive patterns in nature. On the other hand I think GEB just makes an interesting case talking about recursion.

[granite sluice]

I'm of the opinion that anyone reading GEB is probably better of reading a clear introductory textbook on mathematical logic or theory of computation or similar. I remember reading it a long time ago, and not knowing any math at all -- and the result was mostly just feeling really confused.

A different kind of confusion than what one would get by struggling to understand math, I mean.

Similar kind of experience with Penrose's Emperor's New Mind book.

[hearty steppe]

I think honestly GEB at this point has less to do with connecting incompleteness with the nature of recursion. Maybe there is a way to connect the two, but it has yet to be done rigorously? Like you have to connect mathematical logic with recursion in a very complex manner that has not properly been done.

Hofstadter tried but danced around a fire the whole time?

I still am a big fan of Hofstadter but I'm giving the guy credit for trying and providing good insight. He should probably stay away from incompleteness theorem, since most mathematicians disagree with him there?

[granite sluice]

But it has been done, that's one perspective on what computability theory is.

People would be better of reading Moore/Mertens.

[hearty steppe]

wdym

he tried to connect the nature of recursion as a whole to the extent of human consciousness

and tie that with incompleteness thereom

perhaps thats going a bit too far

[granite sluice]

Yeah I think that goes too far, into the realm of vagueness and stuff.

[hearty steppe]

yea sorry that was the point I was trying to bring up

what book by Moore/Mertens?

is it called computability theory?

[granite sluice]

"The nature of computation"

One of the best books ever imo

But, like, full of a TON of stuff.

Much that I have yet to really digest.

But it's where I would send someone if they want a view of what tcs is about.

They spend a chapter on models of computation, covering TMs, recursive functions, lambda calculus and stuff along those lines. GEB without the woo factor.

[worthy mesa]

Hey guys! So, what Springer books (both grad and undergrad series) would be good for me to have? I mainly like algebra

Asking this because I just learnt my uni pays for students to have access to springer books for free so I'm going a bit nuts and I want it all 😂

[karmic thorn]

By algebra do you mean linear algebra? Abstract algebra? Or algebra even beyond that(if there is one)?

[worthy mesa]

Ok sorry forgot there's people of all levels and backgrounds here 😂
I'm doing my master's degree, haven't yet decided for sure but I might write my thesis on representation theory of groups. I also like the idea of homological algebra but tbh I don't have nowhere near the background needed to actually study that yet

Master's in the european system, so 3 years undergrad, 2 years master's, and then PhD, and I do plan on doing a PhD when I'm done with my master's

[karmic thorn]

Stuff beyond my league, but I'm sure others will be able to recommend something.

[worthy mesa]

Yep let's see!

[tribal kernel]

Springers Graduate Texts in Mathematics are usually really well edited and good. Hungerford and Lang are good basic algebra books in that category. I know there’s also a good book about group representations in that series.

[flint forge]

I would suggest finding topics you think are cool

And then buying books

Rather than the other way around

[slender sphinx]

Buy books you will actually use

and find interesting

[flint forge]

Tbf i also collect math books so im a hypocrite

[slender sphinx]

~~I collect book pdfs via libgen ~~

[karmic thorn]

Guess I have like 30 physical textbooks and about a 100 PDFs.

[flint forge]

i should send a pic of my collection someday

[tribal kernel]

I have too many math books 😔

[flint forge]

but its combined w all my other books rn

[tribal kernel]

Nah you should do it

This is most of mine

[lost fjord]

Dang

[flint forge]

god damn

thats a good collection

[tribal kernel]

Lol thanks

[flint forge]

im torn though bc i only really want to buy books in subjects i find cool

[tribal kernel]

A lot of it is either free book piles or library surplus sales

[flint forge]

but most easy to get books arent my thing

or i have them

[tribal kernel]

Yeah I feel that sometimes

[karmic thorn]

Damn that's one library collection

[tribal kernel]

I like a lot of analysis and my old university had several older analysis professors who would purge some of their books every few months. That’s why I have so many analysis books

[slender sphinx]

[worthy mesa]

And then buying books
@flint forge point is that I'll have access to the ebooks for free xD

And I do have a few cool physical copies of books but I'm still a bit far away from a library 😂

[tight crag]

I recently learned I have access to springer link print on demand

just bought algorithmic randomness and complexity for $25

[sleek python]

I have exactly one maths book

[marble solar]

You can find lots of good used books at your local bookstores

[hearty ferry]

i like to buy pdf versions. i think it is more practical. maybe one learn more by using physical book because of spacial aspect of it.

[marble solar]

Yeah I like to 'buy' pdf versions too

[hearty ferry]

i buy pdf when it is necessary.

some of our profs will just send pdf versions to us via mail... that does not seem very legal...lol

i once contacted a author (not on my uni) and he just sent my the pdf 😄

i think there is a discrepency between the aurthours and the publishers

[marble solar]

I've contacted authors before

that told me they couldn't give me it

[tight crag]

Moonbears' life sounds like a collection of disappointments

[flint forge]

Afaik authors dont benefit (most of the time) from sales

Only book deals

So fuck it

Steal whatever

[quick hornet]

meh most authors make a commission

its just ridiculously small

usually royalties for sales are around 5-15%

often publishers offer royalties on a cost recovery basis

maybe you only get 1% royalties for the first 1000 books, and then 15% after that

or whatever

royalties for rentals are generally a lot lighter, if they exist at all

usually < a percent

and ofc profs dont make anything off used copies or w/e

but thats obvious

[worthy mesa]

The real heores are people like Hatcher, Thomas Judson and Sydney Morris

[marble solar]

It's hard to be in such a situation

where they'll let you just post PDF copies for free

[quick hornet]

yeah if i ever wrote a textbook (at least one meant for undergrads), i'd do my best to have my publisher allow me to distribute it freely online

at least to my students

but it isnt always possible sadly

[worthy mesa]

Yes, I believe it must be a rare case for publishers to allow that

[marble solar]

If you have access to a university library

Usually you get online stuff for free since the university pays large sums of money

[worthy mesa]

Yeah I said earlier I have access to any Springer book I want using my uni credentials

Hence me asking which ones I should download xD

Also the library is very cool, it has a lot of books I can borrow, even professors borrow books from there all the time

[hearty ferry]

Do you guys have access to any Springer in PDF ? if so, then cool

for mathematical litt PDF is the way to go

i once download all of Tom Apostels books in very high quality (vectorised, no different from a non scanned pdf) as djvu... but i deleted it. i regret. should have keep it.. not that i understood anything in the book. just wanted to make the content survive 😄

[marble solar]

yA. I like Apostol's books

I have his calculus books, his NT one, and the uhh analysis one

I'm a bibliophile so I collect books

[hearty ferry]

i collect pdf versions of books...lol

i was member of a torrent site for books which unfortunalty does not exsits anymore 😦

a lot great shit was lost

so that is why i'm not deleting anything if the queality is high

lol

[tribal kernel]

I’ve seen links to some questionable Google drives with thousands of books

[quartz pawn]

I have really nice versions of the Apostol's books

Oh you're not talking about Calculus

[hearty ferry]

TheDon, which ones?
edit: "TheCon" >> "TheDon"

I'm was talking about the old ones about calculus.

[gray gazelle]

TheDon is a trustworthy man, you shouldn't call him TheCon

[hearty ferry]

oh, ups 😅

[inner sentinel]

i collect pdf versions of books...lol
I have some PDF books but I prefer physical tbh, I get eye strain from too long on a computer. I mean, I get PDF books pretty easily since a prof has loads and just sends them out for free BC he’s nice

[gray gazelle]

Uhhhh, I think ur prof is doing something very illegal

that prof sounds based

[inner sentinel]

Facts

[flint forge]

Sounds like your prof is doing something super nice

Dont be a cop

[broken meadow]

i want a prof like that

[inner sentinel]

Yeah, what m said, when I said facts was responding to TTerra

[broken meadow]

as opposed to

[flint forge]

Imagine caring about piracy in 2020

[broken meadow]

mildly illegal

[flint forge]

We dont simp for corporations

[broken meadow]

https://youtu.be/HmZm8vNHBSU

[inner sentinel]

It’s not slightly illegal, it’s ‘’highly illegal”

[flint forge]

Im uploading a copy of any book i write to libgen myself

Smh

[inner sentinel]

M*x out here doing the good work

[flint forge]

The fact that journals

Dont pay you for articles

But make you pay to read them

Is the biggest scam

Of all time

[inner sentinel]

And make you pay to submit them

[flint forge]

Yeah

Fuck the publishint industry honestly

I only trust haymarket

And the V one

[inner sentinel]

The publishers just get all of the money from every possible source

Just upload it to arXive as well as the journal, not just on paywall journal

Since then, more ppl will see it so you can get more citations, there’s no downside to doing that

[tribal kernel]

I won’t encourage piracy but I also won’t really throw a fit if I see anyone doing it

To me it’s more like I would enjoy getting something for free rather than just hating the publishers.

A pdf of a book is not worth much in monetary value but a full text is. It’s why I’m not normally interested in purchasing PDFs but if someone offered the same pdf for free I wouldn’t mind

[hearty ferry]

Intellectual property
👍

[flint forge]

is not real property

jk property itself is the problem

[hearty ferry]

for me a pdf have much more value than a physical book.
regarding eyestrain; your night mode, find a good app, good screen... zoom abit

[gray gazelle]

how would it feel like if ur another prof and ur colleague is distributing ur copyrighted work to others for free

[hearty ferry]

this is how I read

[flint forge]

how would it feel like if ur another prof and ur colleague is distributing ur copyrighted work to others for free
@gray gazelle id be shocked that they did it faster than me

Besides profs dont make money on sales anyway so why would anyone care

[hearty ferry]

no eyestrain

SumatraPDF is good for Windows. I'm on macOS using PDF Viewer by (??? do notr emember)

[flint forge]

I feel serious eyestrain

+1 for sumatra

[hearty ferry]

reading glasses?

[flint forge]

No

White on black is less painful for me

Wait

[hearty ferry]

same

[flint forge]

Black on white

[hearty ferry]

oh, okay

i have an eye condition... and for me white on black is best

[flint forge]

Ah

[hearty ferry]

one eye is down to 30 % visual capacity (?? do not know the english word for it)

having bad eyesight makes learning much harder.

so get your eyes checked, boi 👀

[flint forge]

My vision is quite good

For now anyway

[tribal kernel]

I mean IP is important, but while I wouldn't specifically endorse doing this, if you're book PDF is easily available through google search, I'm not gonna feel bad about downloading it.

[hearty ferry]

what is IP in your context?

[tribal kernel]

Intelectual property

Or are you asking the deeper question of what even is IP?

Like philosophically?

[flint forge]

I mean IP is important, but while I wouldn't specifically endorse doing this, if you're book PDF is easily available through google search, I'm not gonna feel bad about downloading it.
@tribal kernel that first statement is controversial

but anyway long story short piracy good

[tribal kernel]

I don't think it is among most people

[flint forge]

in fact not pirating is immoral

[tribal kernel]

That sounds like a controversial statement

[flint forge]

woke

[tribal kernel]

I think it's pretty morally neutral

[flint forge]

wrong

[tribal kernel]

If you wrote/made/discovered something, you're not obligated to share

[flint forge]

imagine thinking that selfishness should be privileged over the intellectual achievement of the community

smh

[marble solar]

It's not necessarily selfish if you put lots of money or working hours into some research and want to be compensated

So you can eat or provide for yourself

i.e. in starting a journal

Journals cost money to run. There are open source ones

[tribal kernel]

Imagine if everyone had to pay to go to elementary school
This is not really what I'm suggesting, but we do in many ways. Public schools are supported by out tax dollars and someone needs to be paid to go into work and teach everyday

[flint forge]

well now ur getting deep into it

but hear me out

[marble solar]

Now if you want to make that argument, that public schools are funding by tax dollars so their research should be publicly available

[flint forge]

one shouldn't have to have significant achievements

in order to eat

[marble solar]

That's an argument I'll buy

Or even private ones getting things like NSF grants

[flint forge]

journals are vampiric moonbears

even if ur into austerity econ

[marble solar]

Some journals are pretty bad, some are pretty good

[flint forge]

its pretty clear journals provide very little service

[marble solar]

Yeah, they do seem like a relic of the past

[tribal kernel]

Yeah not a fan of how much research gets funded indiscriminately through government grants

But it also is true that journals aren't very necessary now

[marble solar]

Well, I don't know if that's true

[flint forge]

it totally is

[tribal kernel]

But one reason they continue to exist is because they get massive amounts of funding

[gray gazelle]

if i were rich and retired i would donate some money

[flint forge]

most pure math (and large swaths of academia) have no capitalistic value

but that doesnt make them valueless

it just shows that capitalism is not a sufficient framework

[marble solar]

I think it does have capitalistic value

[tribal kernel]

And it's really not true. Lots of companies near where I live have pure math research departments

[marble solar]

And I do think capitalism is a sufficient framework

[flint forge]

if you can give me even $1 worth of value to computing homotopy groups of spheres

ill give you that dollar

[tribal kernel]

Value to who?

[steel viper]

i dont think capitalism has an inherent conception of value attached

like there are capitalists that believed in the LTV

well

were lmao rip ricardo

[flint forge]

by value i mean 'in the absense of funding it simply to fund it, there is no productive use for it'

[quick hornet]

mathematics research creates value by incentivizing people to become professors

and thus fulfill the true goal of mathematics

being a service department

[flint forge]

msft does some 'pure' math

[quick hornet]

for eng/cs

[flint forge]

but not really

they are just gambling that things like TDA pay off at some point

[gray gazelle]

did TDA come out of microsoft research?

[flint forge]

no

but they currently fund some

there are also startups doing it and similar stuff

i think msft even funds some wacky mathphys stuff

which is hilarious to me

i guess if you have that much capital, fuck it

[marble solar]

Yeah, Mike Freedman gets a nice fat salary

To dick around with computers

Didn't he tell them to just fuck off with all their corporate/managerial BS and give him total control of his program?

[gray gazelle]

i feel like msft really has to watch out though, right now they capture a lot of the market with their windows, but if they dont watch out people are gonna start switching to mac/linux and msft will get fucked

[flint forge]

i mean honestly

do you think any execs at any company

have enough knowledge to supervise puremath

like might as well just let him fuck around

[marble solar]

Well, I think they were gonna give him quarterly deadlines, etc.

And yeah, there are some execs/ppl at companies that can supervise more than you'd think

[hearty ferry]

And it's really not true. Lots of companies near where I live have pure math research departments
@tribal kernel for what if i may ask?

[flint forge]

im not sure i buy that

since its kind of vague

[marble solar]

I mean, I know one who is in a PhD in physics right now. Runs his own companies

[flint forge]

im not sure phd in physics would allow you to understand contemporary tda

[quick hornet]

i read "locally private hypnosis session"

[tribal kernel]

Raytheon has hired several pure mathematicians from departments I've visited

[quick hornet]

and thought i was in the wrong field for a second

[marble solar]

The claim was do these companies have higher ups that can really supervise research

and the answer is surprisingly, yes

[flint forge]

hiring pure mathematicians =/= doing pure math

finance hires tons of puremath people

but theres no real puremath in finance

[hearty ferry]

i'm doing mathematical econ.

[flint forge]

mathematical econ is not even close to pure math lol

[gray gazelle]

most quant finance companies probably dont have an R&D division

but that's a total guess

[tribal kernel]

I'm saying they do pure math research and fund scholarships for undergrad and grad students in pure math

[hearty ferry]

mathematical econ is not even close to pure math lol
@flint forge wrong

[flint forge]

I'm saying they do pure math research and fund scholarships for undergrad and grad students in pure math
@tribal kernel give an example lol

@flint forge wrong
@hearty ferry give an example lol

i almost went into mathecon im fairly familiar

[tribal kernel]

I know someone who works there but the work is kinda can't take it home

[quick hornet]

my impression of research in mathematical econ is that

[tribal kernel]

Asked her and she says its pure math research

[quick hornet]

it like requires a good background in measure theory and shit

but the "feel" of research is very different

[tribal kernel]

It's a lot of optimization problems

So yeah like measure theory and functional stuff

[hearty ferry]

@flint forge so i'm a 2nd year. i have had 8 course. 6 was in pure math. 2 in mathematical econ. i'm not fra usa

[quick hornet]

do you think 2nd year undergrad reflects actual mathematics research

[marble solar]

I think max is talking more about what you do when you work in the field

[tribal kernel]

It's kinda like you can do pure math physics. Pure math theory motivated by physical questions

[flint forge]

yes my point is

[hearty ferry]

do you think 2nd year undergrad reflects actual mathematics research
@quick hornet no? 😄

[flint forge]

this does not exist in econ

there is no research area in econ

using actually advanced math

to my knowledge

[quick hornet]

idk about that

[flint forge]

im pretty confident

[quick hornet]

certainly very little uses algebra

[flint forge]

even the analysis involved is usually elementary

[quick hornet]

hm, maybe im under the wrong impression then

[flint forge]

its a lot of like

[quick hornet]

i thought there was at least some graduate-level analysis

[flint forge]

very hard computations

[marble solar]

What about mathematical economists? like nash

[quick hornet]

involved

[flint forge]

nash's biggest results

were just applying mathematical ideas to econ in a way never done before

i.e. noting you can apply kakutani to the set of possible game states

to get equillibria

[marble solar]

Sooo...isn't that using advanced research

To do economics?

[hearty ferry]

wow, someone kknows econ

[flint forge]

i dont even think it was advanced at the time

[quick hornet]

i mean i feel a lot of math research is of the format "realizing you can apply this to another field" too

so idk

[flint forge]

maybe i should phrase it this way

i'd be shocked to hear about an econ paper using math that isn't at the level of a grad student in math

like a grad class

i could be wrong

but ive never heard of something as wacky in econ as Urs's stuff in physics

[tribal kernel]

Entry level grad I'd buy

Mostly modeling and functional analysis

Got a few math econ books about optimization problems and hamiltonian systems

Which isn't typical undergrad stuff

[hearty ferry]

I do not think what I call mathematical econ is what some of your understand as mathmatical econs. It probably depends of were in the world u are

[gray gazelle]

there's probably al ot of stuff that math students don't study though, eg, would u consider topics in game theory to be considered "grad level material" of a math student?

[tribal kernel]

No

Not necessarily. Very accessible at an undergrad level but there are difficult problems that require graduate math techniques

[flint forge]

game theory is math

thats kind of a hot take

but calling it econ seems false to me

theres some pretty advanced game theory out there

[gray gazelle]

yes, but im sure many econonomists/econ students work on game theory

[flint forge]

yes

companies don't do game theory though

[tribal kernel]

Optimization is more limited to grad students because they will have needed at least a year in analysis to start doing anything beyond finding maxs and mins for f:R->R

[flint forge]

thats not true

multivariate legrangians are introduced in first year at UChicago

first year undergrad

[tribal kernel]

That sounds like a focused or accelerated program

[hearty ferry]

yes. we did ot in our first course

[steel viper]

are they max?

[flint forge]

only if you take honors calc and then take honors econ early

[steel viper]

in ibl/honors sequence? or the honors analysis sequence?

lmao

[tribal kernel]

Look don't be reductive

[gray gazelle]

but even if they took mv calc first year, an optimization course could be second year, rather than grad student

[flint forge]

im not being reductive

[steel viper]

did you do ibl + honors econ in ur first year max

[flint forge]

yes

[steel viper]

F

[flint forge]

i didnt do well in honors econ

must be the whole

not studying

or caring

part

[tribal kernel]

I'm just saying that it's normally taught in functional analysis, which is usually a grad class that require a year prerequisite in real analysis

[steel viper]

btw max i never got the full picture how awful were your honors alg courses

[flint forge]

what

[steel viper]

*how boring

[flint forge]

optimization in R^n is not functional analysis

uh

most of them were okay

ring theory was fun

galois theory sucked

[steel viper]

did you do all of them after the grad alg courses?

[flint forge]

group theory is just lame as a concept

no

grad alg at uchicago sucks

[slender sphinx]

what why

[steel viper]

lmao

[flint forge]

bc the prof gives bad grades

and i dont want that

[sage python]

Just the first one

[slender sphinx]

is group theory lame max

[flint forge]

its dry

[sage python]

Kato number theory is a free A

[flint forge]

groups are a tool to study other things

[tribal kernel]

But it's not just optimization of R^n, its linear operators that may have real inputs or functional inputs

[flint forge]

dami im so out of my depth in smooth dynamics

[steel viper]

it kinda is tbh i get existentially bored every time i think abt group theory on its own now

[sage python]

AG second quarter I think is not especially hard gradewise

[flint forge]

but i answered a question in class

and that makes me special

[sage python]

Who's teaching this year? Emerton or Nori? Or someone else?

[flint forge]

can i take alg2 without alg1

do i have to fight someone

[sage python]

Yeah I did

[flint forge]

oh sick

[steel viper]

lmao

[sage python]

Feff gave it to me real easy

If it's Nori you gotta be careful

[flint forge]

yeah feff was a real pushover now that im a 4th year

[steel viper]

at some point i want to see what a theoretical 4 years at uchi would look like for me

[sage python]

His undergrad complex was legitimately plebian tier

But his grad AG was in a way that hardest class I ever took in my life

[steel viper]

but im lazy and i dont wanna plan it out

[flint forge]

if i take his AG

do i have to learn what a variety is

or can i play w schemes

[sage python]

Depends on how he runs it

He changes his mind each time

[steel viper]

lmao

[sage python]

Tbh I think he was banned from teaching it though

[gray gazelle]

nice

[steel viper]

based

[sage python]

Or like not banned officially but before whichever prof was like yeah sure I'll teach it was the one who taught it

Now they have to be approved

And I don't think Amie will ever let Nori do it again

After my year

[gray gazelle]

alright yall im gonna go do productive shit. the last 3 days ive literally been on discord all day

[flint forge]

all high level math classes should be of the form

stupid hard psets

with very nice grading

[gray gazelle]

and no exam

[flint forge]

all math classes should have no exam

[sage python]

We had a take home in AG which is why I got an A

And honestly it was so easy

Like comically easy

I don't know any AG and I did it

And he stopped giving psets halfway through

But the fucking speed of that goddamn class

I thought Nori was slow after taking his undergrad complex analysis class

[flint forge]

amie respond to my email challenge 2020

[sage python]

But like in 10 weeks he got through everything

[flint forge]

academic advisor respond to my email challenge 2020

[steel viper]

kek

max the point set review in this alg top class is soul sucking

literally

[flint forge]

if i taught point set review

[sage python]

Like week 1-1.3 was Nullstellensatz and Noether normalization, then 2 weeks of localization and Spec

[flint forge]

id make the psets optional

[steel viper]

its been like 4 weeks

he did too thank fuck

[sage python]

Huh

Jesus

That's bad

[steel viper]

he hasnt even given psets

idk wtf is happening re: psets

[sage python]

But yeah after that we did products of varieties, then smoothness

[flint forge]

thats kinda sick tho dami

amie is moving real quick w this dynsys class

[sage python]

Then presheaves/sheaves/sheafification

[flint forge]

i cant tell if there are any other UGs

no one i recognize

[sage python]

And then schemes, projective varieteis, sheaf/Cech cohomology

Around then I stopped coming to class but I think he reached Serre duality, then Riemann-Roch for curves

[steel viper]

i feel like my undergrad ring theory class is going faster than my grad top class its kind of dumb

[sage python]

You should tell your prof to git gud

[steel viper]

and the ring theory class is not going fast

[tribal kernel]

Algebraic top?