book-recommendations

[steel viper]

its in something called twistor theory?

[narrow talon]

I know that topology does have applications to rigid bodies, especially manifold theory

But I am not especially well versed in physics so don't ask me

[steel viper]

from a non physics perspective it proves that pi_3(S^2) is non trivial

it generates pi_3(S^2) actually

[narrow talon]

Ehh, that’s definitely less interesting to me haha

[steel viper]

idk i just think the amount of structure and relative deepness of literally just maps from spheres to spheres is kinda crazy

i still dont know anything tho

F

[narrow talon]

Yeah for sure!

My mathematical tastes completely lean towards things where I can see the application though, even if I'm not actually planning to ever apply it. So just keep that in mind when I throw shade at algebra/topology

[steel viper]

to like physics?

[narrow talon]

I actually DO find them intrinsically interesting, just not something I'm really down to do

[narrow talon]

No actually, though it does tend to lean that way. I'm more interested in sociology/polysci actually

[steel viper]

oh ok

dont worry im sure you can scam some dumbass investor off a few million bucks by telling them TDA is a serious thing

[narrow talon]

But physics is slowly seducing me, so many results in probability are geared towards physics and interesting as heck

[narrow talon]

Oh god, freaking TDA

[steel viper]

simply wave the shiny math thing in front of the people with money until they throw it at you

[narrow talon]

Though I have used ideas from persistent homology before in practice actually

Usually for prototyping certain clustering results/tuning hyperparameters

[steel viper]

hes taken the pill

[narrow talon]

If done correctly it can get you a vague idea of what the optimal hyperparameters are without any metrics. But it's not super accurate

[steel viper]

theres actually neat theory behind persistent homology

[narrow talon]

Yeah I'm sure, applied homology theory in general is pretty cool. Anything graph theory is also pretty cool

[steel viper]

TDA is like objectively conceptually cool as fuck

[narrow talon]

Mathematical finance is somewhat seductive, but also don't want to become a leech

[steel viper]

like if i was going to go into data sci and i knew TDA was a serious thing id definitely do TDA

but i dont plan on that and i also dont know anything about TDA

[narrow talon]

I am hoping to get into a program which is half data science (other half math), don't know much about TDA though

And probably wouldn't do TDA even if I did know something about it

Just not the types of problems I really like thinking about

[steel viper]

the problems i like thinking about are playdo

xd

[narrow talon]

Instead I'll just spend 5 hours trying to prove basic ass results about the Brownian Bridge

[steel viper]

[gray gazelle]

topology

[steel viper]

tterra moment

[gray gazelle]

every moment is a tterra moment

[flint forge]

i need to talk to someone who is into like

neuro/cs

so i can be sure once and for all

that tda is a meme

[raven citrus]

TDA?

oh, topological data anslysis

yeah that's kind of BS

[karmic thorn]

[wooden sparrow]

A-thon?

[sudden granite]

Too many acronyms

[steel viper]

this is like the math equivalent of those brand advice seminars for social media influencers

utilize time-boxed tutorials to optimize engagement and maximize your platforms reach!

[silk quartz]

Why are you using the catking pfp? I was confused and thought you were mniip for a moment.

[steel viper]

its cute

i wanted to do it when i first saw it but mniip got it first

[static crest]

mniip and moth like swapped pfps

[karmic thorn]

[sterile cove]

[river rock]

What are some math books that follow a "discovery" approach to math? Asking questions and telling a story instead of "area of a triangle is ½bh bye"

A more elementary topic would be preferable so I can read with my younger brother but you can recommend any book which have that approach to math

School textbooks that I can see doesn't quite tell me the why of things imo that's why I'm asking

[buoyant spire]

On that note, are there any youtubers that introduce math in a digestible manner for children?

[quick hornet]

borcherds

[marble solar]

Spivak's Calculus

[golden cargo]

not sure if this is the right place to ask this, but is there some internal formating that arXiv does to Latex/pdf files in order to format them to their style standard? I've never published there but I would assume there's either a standard format or some internal program they use to make all their publications in the same style

[tranquil ocean]

No, but basically everyone submits a latex document so it ends up looking pretty similar

[timber mesa]

yeah, there's some guidelines but they aren't too restrictive formatting-wise: https://arxiv.org/help/submit_tex

arXiv also puts a watermark over all tex submissions so that might be partly why they seem to follow a fixed style

[golden cargo]

yeah, that's what I was wondering about

[winged palm]

any realistic fiction books that are highly recommended?

[sudden granite]

count of monte cristo

brothers of karamazov

proof of ramanujan sum😳

[novel iris]

it's not a book per se but UTAustin's Discovery Precalculus (on edx.org) was pretty great

also Visual Group Theory lets you explore things a bit too

[warm glen]

i havent tried it but "combinatorics through guided discovery" sounds exactly like the kind of thing u want and it's free online

also there's "algebraic geometry: a problem solving approach" but working through the entire thing requires some abstract algebra

[dapper root]

Lol, the problem solving approach to algebraic geometry is just trying to learn it through Hartshorne

[narrow talon]

Hey anyone know a complex analysis book which assumes grad reals but not a ton of topology?

I’m only aware of Narasimhan

Or Rudin i guess, is that actually a good presentation of complex? I thought it was pretty nonstandard

By topology I mean algebraic, point set stuff is fine

[gray gazelle]

Oh, I thought topology in complex analysis was more of a meme

[narrow talon]

Nah, there are a number of books which use (usually pretty light) AT

[gray gazelle]

I guess like a sort of "complex analysis done right" with no winding numbers, maybe we can get axler to write a book 🙂

[raven citrus]

11 22 63

[fossil island]

Anyone have lecture series recommendations for a rigorous first course in dynamical systems? Ideally the course uses Brin and Stuck.

[molten wave]

there's a bit of topology you could involve

with like covering spaces

and windings of course

[sage python]

@narrow talon anything wrong with Narasimhan? I heard it's pretty solid actually

[narrow talon]

I was under the impression that it was a bit too sophisticated or otherwise used a lot of AT

[sage python]

It introduces the algebraic topology it uses I'm pretty sure

But yeah looking around I don't see too many ones tbh

Hmm

Okay idk if these are good at all

But note they exist

https://www.springer.com/us/book/9780387973494

https://www.springer.com/us/book/9780387947549

Stumbled on these which seem like they are willing to rely on a lot of real analysis but less topology. So yeah see if you like these or Rudin I guess?

[marble solar]

I think Marshall's text doesn't have a lot of topology

[narrow talon]

I’ll check them out thanks!

[molten vine]

are there some good books that can help with high school maths

[molten vine]

algebra 2

and calc ig

oki thanks

[junior merlin]

anyone have any graph theory books (or lectures) you'd recommend? I'm interested in the proofs but I have basically no proofs background

[quick hornet]

harary

although admittedly idk how approachable it is with no proofs background

its also dated, i think it calls the four colour theorem a conjecture lmao (though this leaves it in the interesting position of teaching all of the "tools" used in the proof in the form of "x implies the four colour theorem"; that is, you can read the proof paper and immediately understand it just with what harary already gives)

but its good

its also very mathematics-focused rather than computational/algorithmic; like it doesnt cover djikstra's

[junior merlin]

cool ill look into it, yeah i'm more interested in the math then the algorithms (ironic since i'm a cs student :l)

[quick hornet]

again its a very dated presentation but its what i learned out of

if someone has a more modern text, feel free to recommend it

[river rock]

What are some good books that teach proofs? A level somewhere between high school calculus and real analysis, linear algebra, etc. I don't think I have a rigorous understanding of proofs. I can understand most of them by reading it though, I just need more experience by doing exercises and stuff.

[karmic thorn]

How to Prove It by Vellerman and Book of Proofs by Hammack seem pretty standard.

Other than that there's one called A Transition to Advanced Mathematics by Zhang?

But I don't really suggest diving too much into these books if you can prove basic set theory results. Learning to prove things in context is more efficient Ig.

[narrow talon]

Diestel is what graph theorists always recommend to me

[quick hornet]

oh yeah diestel

its a very good source but seems even less appraochable than harary lmao

[narrow talon]

There’s lots of good probabilistic graph theory books too, though that’s def more specialized lol

[quick hornet]

but yeah i totally forgot about diestel

its the "standard" modern text

i just recall it being very "slick"

at least when i reference results out of it

its no rudin but still, the proofs often seem really succinct and like they wouldnt be great for someone unfamiliar with them

[narrow talon]

I definitely got that vibe as well, at least for those minimal parts I've needed for tangentially related work

[hearty steppe]

Try Voloshin

Errr sorry Chartrand and Zhang have a more introductory book. But I’m assuming Voloshin is around there, being a bit easier than Diestel. I think I skimmed a bit of Voloshin

If Voloshin too hard, then Chartrand and Zhang definitely the way to go. It might be a bit too introductory though depending where you are in graph theory

[hearty steppe]

Wdym

[karmic thorn]

Learning to write proofs from a proper subject(linear algebra or advanced calculus/analysis are good starting points, imo)

[narrow talon]

I’m not actually the one requesting a graph theory book haha

[hearty steppe]

I think the relations chapters are pretty important too but I hear a decent amount of people pick that up in analysis

I didn’t quite pick it up intuitively in analysis texts as I hoped too. So I’m spending a little more time rn with relations

[karmic thorn]

Most analysis texts pre-suppose basic knowledge about sets and stuff, but some intro analysis texts do cover it.

[wooden sparrow]

Isn't it best to go from intro, like Tao, then after a few chapters, jump to Rudin?

[hearty steppe]

I mean Tao is not the closest when it comes to friendly Intro analysis books from what I hear

Most people that jump into a book like that, already have decent math maturity built up

[wooden sparrow]

is there like a friendlier intro to analysis book?

[hearty steppe]

Try Abbott

[wooden sparrow]

Tao seemed fine BTW

I read a little

Okay I'll check it out

[hearty steppe]

I avoided Tao based on what several people here had to say about it compared to other texts

[wooden sparrow]

Oh okayy

[hearty steppe]

But everyone likes certain flavors of textbooks

Abbott is probably the most hand holdy of the real analysis texts. There are some other texts like Ted mentioned that are more intro level covering proofs like Bartle, Marsden, Aubrey, or Alcock

Then there are books like Velleman or Chartrand and Zhang which basically are as intro as it gets for proof writing and pre analysis

Velleman has the hardest problems of all the more intro level books tho. The psets are way harder than in Chartrand and Zhang for example

But to be Frank, the actual learning experience per chapter/section is probably best illustrated in Velleman. Chartrand and Zhang doesn’t feel as clean

[narrow talon]

So this book is really weird so far. It assumes more than Rudin, but seems to keep things at a rather concrete level when it can

[hearty steppe]

Diestel is pretty nicely written I’ll be honest but still a little over my head

[narrow talon]

And covers similar, though slightly better selected, topics to Rudin

[hearty steppe]

Like it would be the perfect graph theory book for me if I had already taken a course in graph theory

Instead I kinda half baked learned it from discrete math second semester, and like two algorithms based courses lol

[narrow talon]

Also uses differential forms, which is a no-go from me

[sage python]

This could be a motivation to learn about differential forms!

@narrow talon

[narrow talon]

It could! But not today

[sage python]

I feel like if you're not into differential forms then just roll with Rudin probably

Or pick a book that doesn't assume measure theory

[narrow talon]

I’ll probably use S&S actually

Save Rudin for a second read

The actual course text is Brown and Churchill, so the disconnect between something like Rudin and B&C is just too large

[sage python]

I mean if you know real analysis then that's probably fine?

Like, the gap between the course and you is just too large in that case 😛

(I assume "real analysis" = measure theory, if you just had Baby Rudin then yeah use Stein (or Freitag which I like better tbh)

[narrow talon]

Lol, it is indeed a little painfully easy

Makes for an easy A but not necessarily a lot of learning

The only thing with Rudin is that I really don’t recall a ton of that general measure theory stuff, I’ve mostly remembered those results useful in probability. It’d be worthwhile to spend time on it, just not sure I have that time to spend atm

[sage python]

Gotcha

[warm glen]

do y'all have opinions about the complex analysis book by cartan

i bought it a couple weeks ago bc it was cheap and i heard it explained things pretty well, but i can't judge it for myself yet bc i dont have enough background

in a few months i'll prolly be ready to read it

where would y'all place it among the other commonly suggested CA texts

[timber mesa]

it's pretty fast-paced and only the first 3 chapters are single-variable complex analysis, the whole idea of the book is to see several complex variables, spaces of holomorphic functions and diff eqs in C

I'd read Ahlfors first or parallel with that one

The Math Sorcerer on YT has a review of Cartan's book: https://www.youtube.com/watch?v=5JJzHUKyxrE

and correspondingly one of Ahlfors': https://www.youtube.com/watch?v=LsYs-lIhwiY&t=12s

[warm glen]

thanks for the rundown

would u say it covers all or most of a grad level sequence on complex analysis?

i actually dont know what the usual topics are that everyones expected to know from such a class

[timber mesa]

probably more than what you'd expect to see in such a grad course -- several variables and DEs are not usual topics

but the first chapters might skip some topics; I haven't read the book. That's why your best bet would be to complement it with a standard reference like Ahlfors

[warm glen]

gotcha gotcha, thanks again

[marble solar]

am I the only simp for Marshall's book?

[zealous elbow]

Books on optimization geared towards machine learning/statistics?

Do I need functional analysis to understand optimization?

At the very least I want to understand optimization enough to be able to recognize it's use/setup in an applied context.

[willow pecan]

It depends on how well you want to understand optimization theory

[gray gazelle]

just learn what a lagrange multiplier is and you're set for the future

[willow pecan]

Things like Hahn-Banach hyperplane separation are essential for optimization theory

But you usually don't need the full functional analytic statement

[zealous elbow]

I don't need full abstract beauty.

For instance, understanding how optimization plays into this: https://en.wikipedia.org/wiki/Expectation–maximization_algorithm

would be nice.

Learning functional analysis would be hard enough on my own as is.

[sudden kindle]

I literally cant learn math on my own

[zealous elbow]

It's do-able

[dapper root]

Rohde is also a simp for Marshall's book

This is how I feel with Aluffi

[marble solar]

It's ok Chmonkey, I didn't get into UW, Davis, or Irvine

I just took my job offer out in the south

Gonna wait out the pandemic funding

[dapper root]

So many people I know got rejected from UW

It actually like... scares the shit out of me

[broken meadow]

oh no

[zealous elbow]

Anyone have recommendations?

[hollow peak]

uw is the harvard of washington

[willow pecan]

UW is the only university in Washington

[hasty turret]

Is it as expensive,tho?

[zealous elbow]

Who wrote UW?

I can't seem to find it.

[normal rain]

What is the best introductory textbook to game theory?

I have taken introductory classes in combinatorics, junior level probability, and junior level statistics.

Not sure what else is relevant that I should take first.

I was told Osborne's isn't really math intensive, not sure if I'd be better off with something else having a little math under my belt.

[gray gazelle]

Does anyone have book recommendations related to algebraic independence?

[sudden kindle]

Transcendence?

[willow pecan]

Isn't this usually covered by Galois theory?

[sudden kindle]

Idk why you need a book on it, it's just a definition

[noble pebble]

[valid moth]

@gray gazelle i gotchu fam https://www.amazon.com/Savage-War-Peace-1954-1962-Classics/dp/1590172183

book on algerian independence

[willow pecan]

[gray gazelle]

Blocked

[dapper root]

You can find that kind of stuff in a field theory book

there's a few that I've seen, but I don't know one off the top of my head

my impression of Lang is that it has more field theory than a lot of similar books, D&F, Artin, etc.

you might be able to find some stuff relevant to transcedental extensions in there

[sudden granite]

😍

[sudden kindle]

Books I wanna read:
• A Gentle Course in Local Class Field Theory by Pierre Guillot
• The Arithemtic of Elliptic Curves by Joseph Silverman
• Ergodic Theory with a View Towards Number Theory by Manfred Einsiedler Thomas Ward

[sage python]

I've got you hooked on this stuff 😛

[ionic wren]

how many victims?

[sudden kindle]

Well, I've heard it mentioned once before

And I was curios what it's about

[sage python]

Yeah so pretty much everything I told you about I learned in like

A few days

To write my NSF research statement

[ionic wren]

stop flexing

smh

[sage python]

I didn't go into much detail lol

Or okay there's this talk by Peter Humphries

https://www.youtube.com/watch?v=m9pSjgXtimQ

[ionic wren]

what

[sage python]

At some point in time I watched this and understood nothing

[ionic wren]

me rn

[sudden kindle]

Then this dude who does mathematical physics gave a talk in which he talked about eigenfunctions of laplacian on hyperbolic manifolds and how it's related to number theory. I'm like,why do you care about this, what's the physics. So it's cool to see it explained AND related to AQUE

[sage python]

And then I was like yo this could be something I could talk about in my research statement right Simon?

[ionic wren]

man

[sage python]

And he was like yeah coo

[ionic wren]

i found this paper

about mock modular forms and black holes

i just

??????

why

[sage python]

Oh yeah there's something called a non-abelian black hole

And at that point I'm like

[ionic wren]

yeah

????

[sage python]

Alright somebody's shitposting

[ionic wren]

like

what the fuck god

[sage python]

Honestly when I first heard of arithmetic quantum chaos I thought it was a meme

[ionic wren]

wat

[sage python]

I remember in my last year of undergrad

[ionic wren]

wait is that a real thing

[sudden kindle]

I feel that! I learned a lot about elliptic curves and arithmetic statistics in a short period to write my NSF proposal

[sage python]

I was going through some prof webpages at Madison with a friend

And I stumbled upon my current advisor's webpage

[ionic wren]

oh my god its a real thing

[sudden kindle]

Too bad my personal statement wasn't as polished as it could be

[sage python]

Originally I was like eh analytic NT

But then I realized it wasn't like

Additive BS

It was more topological

[sudden kindle]

I was mainly stumped with writing the research statement

[sage python]

And I'm like oo

And then I see this paper

[ionic wren]

why are physicists appropriating maths

physicists should be about things i can see

[sage python]

https://arxiv.org/abs/1006.3303

And I'm like

[ionic wren]

if i need glasses, the physics shouldnt work

[sage python]

Wow this guy has actually cracked the NSF

[ionic wren]

btw i made a shitty meme

https://i.imgur.com/mNlCYeY.jpg

[sudden kindle]

You posted this already

[ionic wren]

ik

im proud

i shouldnt be

[sudden kindle]

Yeah writing the NSF grant proposal was surprisingly helpful

I should do more mathematical writing

[sage python]

Yeah the NSF statement I wrote in undergrad was quite bad

I just mumbled about bounding ranks of elliptic curves

[ionic wren]

wtf i cant even read the abstract

[sudden kindle]

Hehe

I also talked about ranks x_x

[sage python]

And like yeah you know there's BSD but that's hard but maybe something about Tate-Shafarevich group

[ionic wren]

ok so ill be clever and talk about cranks

[sudden kindle]

Tbh I'm not even interested in elliptic curves that much, I wanna see how it's related to galois representations tho

[ionic wren]

https://tenor.com/view/george-lucas-its-like-poetry-it-rhymes-poetry-gif-19259245

[sage python]

Complex multiplication on elliptic curves is kinda cool

[ionic wren]

i honestly have no idea

how cm works

[sudden kindle]

So much to learn

It's like when the lattice has extra symmetries I think

[sage python]

So idk the details whatsoever here

Pretty much all my knowledge of elliptic curves is contained in this paper I wrote summer after third year of college

[sudden kindle]

Haha

[sage python]

http://math.uchicago.edu/~may/REU2018/REUPapers/Idelhaj.pdf

[sudden kindle]

But galois reps tho

Oh

This is not the NSF proposal

[ionic wren]

ok imma turn ur paper into a meme dami

[sage python]

No my NSF proposal was baaaaaaad

[sudden kindle]

I need to sleep

Gn

[ionic wren]

gn

[sage python]

Yeah the only open conjectures I talked about in my undergrad NSF were BSD and finiteness of Tate-Shafarevich group

And I didn't even hint at a plan of attack lol

"While BSD itself is a very difficult open problem, a rather tractable intermediate goal is finding bounds on the rank. There is always the potential for smaller steps to eventually lead to a full proof of BSD, and the bounds in themselves often allow for important information, such as special cases of its corollaries. For example, the Tate-Shafarevich group is already known to be finite for a certain class of elliptic curves with rank at most 1."

Like that's it lol

Jesus this is bad

[ionic wren]

Ah yes

The proof is made of proof

[sudden kindle]

I mean

I still think it's useful to write as NSF GRFP proposal

Because it forces you to think about what you may be interested in

For a lot of us, this is the first time we ever really think hard about what we want to research

And not just some enormously large and unspecific field like "number theory"

You actually have to propose a specific problem, we were not used to thinking about those

So it's very helpful to try to figure out what those are and write about it :)

[sage python]

Lmao so much for sleep

But yeah this was my more recent proposal

[gray gazelle]

As they say, sleep is for the weak

[sudden kindle]

I got a few hrs of sleep

"In addition, formulae such as that of Waldspurger and Ichino-Ikeda connect period integrals of arithmetic eigenfunctions to central values of L-functions."

How does this work?

Are the eigenfunctions of the laplacian for an arithmetic surface going to be rational functions?

@sage python

[sudden kindle]

Also what is Selberg trace formula?

[willow pecan]

[sudden granite]

[fossil island]

Thoughts on James Meiss: Differential Dynamical Systems?

[hearty steppe]

Never heard of it

[blazing wyvern]

I am looking for books that have a general overview of mathematics, as a reference to understand mathematical symbols. I can handle it being aimed at grad or above students. I am considering buying Handbook of Mathematics for Engineers and Scientists By Manzhirov because it seems very complete and detailed, however, if there are better options I would like to kow about them.

[obsidian valley]

understand mathematical symbols.
what does this mean

it's pretty hard to find good references for math as a whole but you can always get field-specific ones

I think stanford? has a big math reference though

sorry no

The Princeton Companion might be what you're looking for

[blazing wyvern]

noted, thanks

Mostly as a reference for self study, instead of having to look through the internett

having a clear concise explanation of a term or a refresher of a subject

[tranquil ocean]

maybe the infinite napkin by Evan Chen

[obsidian valley]

yeah if you're studying something like the napkin will be better

[quick hornet]

though napkin is very pure-biased

[blazing wyvern]

Currently studying fluid dynamics on my own, but I quickly realized I have to remember parts of multivariable calculus

[quick hornet]

whereas id expect a "handbook [...] for engineers and socialists" to be more applied-focused

[blazing wyvern]

that napkin book has an unusual name, but seems nice

[quick hornet]

("biased" makes it sound negative, but that's not my intention; it's just a different target audience)

honestly though whenever i forget a definition i just wikipedia it

[blazing wyvern]

that handbook is very nice yeah, I am gonna probably buy it, but I wanted to have more just in case, no one book can suffice for reference

wikipedia can get very dry or technical at times

[steel viper]

engineers and socialists

[hollow current]

[fluid bay]

engineers and socialists

[karmic thorn]

Need recommendations for an introductory topology text which has lots of geometric motivation. I'm currently reading chapter 2 from Pugh's analysis, and I would probably like to take a second look at the idea of homeomorphisms, continuity, etc.

[steel viper]

hatchers point set notes

unironically

[karmic thorn]

Oh

I kinda forgot about them

Thanks!

[hollow peak]

also munkres

and if you're a real fucking hotshot, I've been reading analysis now by pederson and he does a very comprehensive review of point set topology in like 40-ish pages, although it's extremely dense and most material is in exercises

(he even covers nets. goddamn nets.)

[karmic thorn]

Nice

[steel viper]

bredon moment

i still honestly dunno why people care about nets but i also dont know why people care about sequences so thats not surprising

[flint forge]

a lot of topological properties can be tested for with sequences in nice situations

in less nice situations nets suffice

(for a good example, you can see a convo in topology-geometry between me sham and some other guy talking about annoying function continuity stuff and it turned out that the problem was trivial if we stopped thinking about open sets and used sequences instead)

[bleak canopy]

is linear algebra done wrong gud book

or is it just meme

[zinc basalt]

Can anyone recommend a group theory book to me? Specifically, the course I am in is mostly about linear representation theory of SO(3) and SU(2) and others, and the Jordan-Wigner representation. I'm having trouble finding a book that covers that concepts and yet isn't far more advanced than I can read (this is only a third-year uni course). Yet I kinda need to, since the notes the professor provided are short, hard to understand and (I'm pretty sure) entirely wrong in places.

[hollow peak]

I haven't used it for any of the more advanced linear algebra I know but it's a very good pass for a lot of intro material

[bleak canopy]

👍

ok

[hollow peak]

it's very succinct and the exercises are good as well

[tranquil ocean]

@zinc basalt wait so are you looking for a introduction to group theory book? Or a representation theory book?

[zinc basalt]

Closer to representation theory, probably - the course is called group theory, and we started with a bit of classical stuff like examples of finite groups and conjugacy classes and stuff (and that I don't need materials for), but then went straight into linear representations and characters and how to find irreducible representations. I essentially want to have a second source on all of the latter.

[sage python]

If you're doing rep theory of finite groups, Serre

[tranquil ocean]

@zinc basalt You might be interested in Hall's Lie Groups, Lie Algebras, and Representations, since it seems the class is mostly focused on matrix groups

[zinc basalt]

Indeed, it's almost all rotation groups relevant to physics, so SO(3), SU(2), SU(3). Thanks!

[gray gazelle]

How many hours should you take by page on a book like, says, rudin principles of analysis?
Is 10 pages an hour realistic?

How many hours would it take for me to go through such a book? (i generally work 10 hours a day)

thanks

[marble solar]

It also depends on how many exercises or what level of understanding you're going for

If you're going for passing familiarity with some exercises solved, maybe around 6-8 weeks

For chapters 1-9?

If you're going for complete mastery of each chapter (which is nigh impossible) and almost every exercise, could take around 20-30 weeks

Math isn't really a subject you can sit down and just "put hours in"

You have to put hours in for sure, but putting more hours in one day won't necessarily get you through more material or understanding

It's some combination of time spent reading, time spent thinking, time spent solving problems, time spent discussing, and then time spent away from it

e.g. you might be more productive if you work on it for 3-4 weeks intensely

take a two-three week break, come back to it

And you'll probably be better

@gray gazelle

[karmic thorn]

Long breaks between studying are under-rated

[broken meadow]

god i could use a break

😔

[karmic thorn]

Revisiting stuff after several weeks or months always tremendously boosts my understanding

[broken meadow]

i am my own cause of suffering though

[karmic thorn]

Just start with random stuff now Metal

[broken meadow]

i should not complain

[karmic thorn]

Then revisit it in summers

[broken meadow]

yeah i am doing a lot of random stuff rn lol

and yea definitely i will be revisiting especially cus i have to

ill be getting a second look at linear algebra next fall and a proper course in algebra in fall as well

which should boost my understanding

[hasty turret]

Group theory again?

[broken meadow]

er

drake this semester is a 1 semester course using gallian

so it doesn't really count

next fall and spring constitutes a 2 semester course using d&f

so yeah

[hasty turret]

Do it in one semester

[broken meadow]

kek

o o

[hasty turret]

[broken meadow]

one whole semester for da whole book

o my

idk man i can't do that since i also have other classes 😭

i am trying Not to repeat what i did this semester

like

[karmic thorn]

Overloading classes?

[broken meadow]

it was permissible this semester because everything is relatively low level

yeah ted

[karmic thorn]

Aahhhh

[broken meadow]

all of my courses this semester are just first courses in stuff and they mostly have second and third courses which i do plan to take

so it shouldn't be Too bad

but i am in Pain

[karmic thorn]

I often overestimate how much I can take at once as well 😛

[broken meadow]

every day it's like

just so much

[hasty turret]

Same

[karmic thorn]

:(

[broken meadow]

it is the dream though

[karmic thorn]

But yeah

[broken meadow]

this is what i envisioned college might be like and i realize that this is my limit

[karmic thorn]

Even a half-baked understanding now could be reinforced later

[broken meadow]

yeah

still im just

amazed at how much ppl can do in 4 years

i must be ready to meditate

on the material i learn

[karmic thorn]

Hahahaha

Indeed

But I think mathematical maturity is the biggest factor

Like

[broken meadow]

yea

[karmic thorn]

When I looked at Thomas' back in HS it looked like a ginormous tome

[marble solar]

I think 4 years isn't enough time

[karmic thorn]

Now it just feels like a few days of speedrun

[broken meadow]

yeah i can totally see that moonbears

[marble solar]

I was fortunate enough to have it spread out over 5.5 years for undergrad

[sage python]

Wait is it?

Hmm

[broken meadow]

like i looked thru the coursework of my school

and im like

how does an undergrad do all of the important parts in 4 years

crazy

[sage python]

Overall goal is to prove that invariants are iso to coinvariants for completely reducible guys

[broken meadow]

but some ppl are able to do it

[sage python]

And if you know shit splits under direct sum you just cheese it

[karmic thorn]

I think LA, AA, RA, CA, some topology, and maybe some understanding of graph theory/combinatorics/basic set theory are sufficient for an undergrad?

Or is specialising in something the norm now?

[hasty turret]

Is that it?

[sage python]

Depends on what you're trying to do

[hasty turret]

That feels doable

[broken meadow]

yeah i can definitely have those done

hm

[sage python]

I think that's about the gcd of what I think a decent graduate applicant should know

[karmic thorn]

I think so, at least this is what I've always thought the theoretical minimum of mathematics is.

[sage python]

Now it seems the more time goes on and the higher up you're aiming

[broken meadow]

and then the rest is just standing out i suppose

learnin gmore stuff

reading courses in fun stuff

[sage python]

The more important it is to go beyond that somehow. But then there's less of a specific direction

[hasty turret]

Where do things like projective geometry fall under?

[sage python]

e.g. the analysis inclined folk will put measure theory and functional analysis on top

[karmic thorn]

Classic geometry

[hasty turret]

The point line duality and stuff

[sage python]

Perhaps algebraic/differential topology

More advanced algebra

etc

But there's no specific thing on that list that everyone needs to know

[karmic thorn]

Not a lot of unis seem to offer courses on classical geometries, big sad.

Sufficient to explore more advanced/specialised topics, Ig

Since ideas from these seem to be pervasive

So advanced analysis and algebra as well?

[sage python]

slim you could argue that eventually people should know it but I'm saying as of when you apply

If it were expected that all applicants new measure theory then they wouldn't have first year grad be measure theory

I'm assuming in the context that it's just, what undergrads are expected to know

[steel viper]

[karmic thorn]

Like, I consider these topics to be the Theoretical Minimum for maths, analogous to physics if you're familiar, but now I feel grad level understanding is indeed indispensable.

Yeah, I'm not saying there shouldn't be extras

But there should be atleast this much

[sage python]

Hmm? I think 2 semesters each of algebra and analysis lol

And a semester of complex

Oh 1.5 years meaning

If you're doubling up

I thought you meant the pure course count

Yeah I mean it's one of those things where, if someone misses that then it's fair to say their background is almost deficient tbh

[karmic thorn]

Is Aluffi good for a first look at AA?

[hearty steppe]

Pinter and Fraleigh

[karmic thorn]

Pinter is too baby

[hearty steppe]

Two Diff books

[karmic thorn]

Oh

[hearty steppe]

What? I love pinter lol

You want a first look I don’t think you can do better than Pinter

[karmic thorn]

I'm looking for something more comprehensive, I can slowly work through it

[karmic thorn]

I've worked through Gallian and it felt okay haha

I'm just wondering if I could keep working through something like Aluffi for a year to get a better and deeper understanding of algebra.

Lang is far too intimidating, Aluffi claims to be self-contained and accessible to advanced undergrads.

[hearty steppe]

Idk. I’ll let you know a year from now or so lol

I’m working my way there

[karmic thorn]

Ahahaha, alright.

Goodluck!

[hearty steppe]

Yea only reason I recommend some of these books is cuz I was able to get thru some of the introductory chapter stuff and I really liked what I was reading

Compared to other books people suggested

[karmic thorn]

I think I have worked through the first 2 chapters or sth in Pinter in the past

[hearty steppe]

And I am still working with a limited background to proofs exposure

[karmic thorn]

And yeah, it's excellent as an intro, but I think I have some more experience writing proofs now

So I can struggle through a more standard textbook

[hearty steppe]

Yea I think it was the intro and first two actual chapters I hit in Pinter but I didn’t do the psets yet

[karmic thorn]

Ah, I see.

[marble solar]

I feel pinter is solid

[karmic thorn]

[broken meadow]

painter

[karmic thorn]

🖌️

[tribal kernel]

I think so but there are several who disagree with me on that. I’m doing my first real algebra course with it and I feel like I get things

[karmic thorn]

I see. I think I'll keep going with it for now.

[brave kayak]

Hi, there is some Schaum book that everyone keeps suggesting. I dont know which books he has, but whats the title of the one that touches basic calculus (not including integrals) but with lots and lots of proofs and definitions, including series, functions and so on. I hope im making some sense

[static crest]

d&f

[hearty steppe]

Schaum is kinda half baked imo your not missing much @brave kayak

[brave kayak]

good to know, any good practice book on all these basic definitions? I mean the stuff I mentioned, and stuff like supremum, limsup and more...
I have a test in less than 2 weeks, looking for some good book to practice with

[gray gazelle]

Does anyone have a good recommendation for a topology book? I tried Munkres, but I didn’t jive with it

[tranquil ocean]

What didn't you like about Munkres?

[flint forge]

hatchers notes

[gray gazelle]

Thank you, these look very nice

[hearty steppe]

Try Mendelson

Sorta started reading that and I enjoy it so far

[gray gazelle]

Okay, thanks!

[karmic thorn]

Aluffi feels good so far

[gray gazelle]

i haven't read aluffi but i am also a fan of d&f. i'm not sure why people shit on it

[hasty turret]

I started with aluffi,changed to d&f

d&f felt much better

[sudden granite]

can we get a calc book review

[sage python]

Idk many calc books

So this isn't likely pinnable but

Stewart: standard, kind of a ripoff

Spivak: the correct proof-based calc book

Apostol: older, weirder Spivak

Courant: older, more applied-y Spivak

[sudden granite]

what about larson, lang, and thomas

😳

[sage python]

Idk those

[sudden granite]

🙁

courant seems like an interesting read

i will take a look

[gray gazelle]

I've heard strange things about Apostol. Doesn't he start with integral calculus?

[karmic thorn]

Yes.

[sudden kindle]

Yes and I like that approach

Integrals are better than derivatives

Upper Integral is inf of areas under step functions which upper bound the function

Lower integral is sup of areas under step functions which lower bound the function

Integral exists when upper integral and lower integral are equal, and equals that common value

[karmic thorn]

[old jasper]

is there a good book/workbook for functions (stuff like 1/f(x), sqrt(f(x)), f(|x|), |f(x)|, etc)

im a high school student in year 11

[karmic thorn]

Lang's Basic Mathematics

[sudden granite]

can we add langs basic maths to #books-old

i feel like that would be a good decision

we seem to be forgetting about the little guys

[old jasper]

it doesn't go over y=1/f(x)

y=sqrt(f(x)), y^2=f(x), y=f(|x|), etc

[karmic thorn]

[old jasper]

it just skims over what functions and polynomials are

not specific types of graphs

¯_(ツ)_/¯

[obsidian valley]

use desmos?

[karmic thorn]

[old jasper]

i have to learn how to graph them

[obsidian valley]

this is a very specific thing to want

look up "graphing functions" on the internet

[karmic thorn]

I haven't used it myself, just heard good things about it. ¯\_(ツ)_/¯

[frosty ermine]

Such a shame! I was really hoping it'd have an infinite number of graphs 😆

[old jasper]

:/

[wooden sparrow]

I used it

It's good, but some precalc stuff like inverse trig is missing in it

[frosty ermine]

tbh, It'd be interesting to learn the formula for inverse trig functions in pre-calc.

They have all the tools they need to get it

No one would use it, but it would be interesting

[karmic thorn]

But likely every calculus book skims these topics in a preliminary

So you don't lose much anyway

[frosty ermine]

Indeed, but if the student's algebra game is weak, they tend to struggle really hard in calc.

[karmic thorn]

Yeah, I think Lang does a fine job at drilling the algebra though

I definitely owe a lot of ease I had at doing calculus at school to a very thorough background in preliminary algebra

[wooden sparrow]

or just fill in that using khan academy

One thing I regret doing is sticking to one source for studying

no matter how many times ted told me to not do that

[karmic thorn]

Well you know that now

[wooden sparrow]

Yeahh... though I'm still sticking to apostol for calc now

[karmic thorn]

[old jasper]

[cobalt arch]

Friedberg or hoffman for LA?

I can't decide

[narrow talon]

Yeaaa boi lax ftw

[tiny goblet]

I have Hoffman-Kunze LA book and I am still sticked to him

[timber mesa]

don't know about friedberg, but myself I learnt from Hoffman-Kunze and liked it

[static crest]

it's really long, that's pretty much the biggest issue I've seen anyone have with it

people find it a drag to read, since d&f basically assumes the reader is borderline stupid

(which is a good assumption in my case)

[static crest]

the exercises still really let you learn a lot, I think d&f exercises are 11/10 outside 3 sections

4.5, 6.2, and 9.6

[sage python]

Yeah pretty much that was my only complaint with D&F, it's just boring to read lol

[fossil imp]

Hi everyone! I'm very new to the server so I hope I'm writing in the right channel. I recently became very interested in manifolds. I'm a graduate student in France (for those who are familiar with the French system, classes prépa MP + engineering school), and I think I've been taught the basics in maths, though I don't really have an idea of the portion of maths I explored so far to be honest (very little i'm sure though). I was looking at some books on manifolds to get started, and I heard multiple times about Munkres' book on topology, and Lee's books Topological Manifolds (ITM) and Smooth Manifolds (ISM). From what I understood, Lee's ITM is very specific on manifolds and rushes a bit the global topological concepts outside of this notion. But Munkres seems to partially repeat what I already know and doesn't really explore manifolds I guess. Apparently ISM is much more difficult to read and might need Munkres?
If any of you has some comment about this I'd be really happy to read it!
Thanks all!

[flint forge]

Read hatcher's notes

they are designed to prepare you for like

all the point set you need to study what topologists care about

without too much extra stuff

Importantly they are also short

@fossil imp

[cobalt arch]

Is there a book on the different properties sets can have or not have. So for example there exist dense sets, posets, powersets, etc. Is there a book that covers all of that? I know it is insane on the one hand since these are defined in different branches of math but on the other hand I am curious to know if such a book exists, that is a book with all the various characteristics sets can have.

[flint forge]

Strictly speaking such a book is probably impossible

[obsidian valley]

A set theory book

[flint forge]

That wouldn't cover what they want though jesse

[obsidian valley]

It's sort of unclear what Forsaken wants most of the time

[flint forge]

A set theory book would cover a lot of them

[cobalt arch]

That is unfortunate

Yeah

[karmic thorn]

@cobalt arch Please don't fall for the foundations first approach again. 😬

[cobalt arch]

Haha

No no I am aware of such pitfalls my dear friend

[karmic thorn]

You'll likely get all the required set theory for each subject in a book on that subject.

[obsidian valley]

Read a set theory book if you want to learn set theory

If you just want some compilation of "set characteristics" I think you're SOL

[cobalt arch]

What does SOL stand for?

[fossil imp]

ok nice, so hatchers then ITM then ISM and then I'm a topology master?

seems like a good plan

[karmic thorn]

...or Wikipedia

[obsidian valley]

"shit out of luck"

[cobalt arch]

You meant my soul

My Soul for the devil

[flint forge]

not quite haha

lmfao

manifolds are a subset of the spaces

topologists in general care about

[fossil imp]

yes well I'll accept being only a manifolds master

[flint forge]

there is still more to learn just about manifolds

they are disgusting

thats for sure

[gray gazelle]

give it a month and it'll be my complex analysis notes

[steel viper]

.pin

[sage python]

@gray gazelle I've been eventually meaning to read Forster

Or Donaldson

[marble solar]

Terry tao 246C, 2018

[ripe granite]

Donaldson is good

and Miranda

[marble solar]

Miranda is solid

||I also like Fulton||

But nobody likes that one

[ripe granite]

"On Riemann's Theory of Algebraic Functions and Their Integrals" had some interesting stuff

you don't have to read all of it

chapters 1-4 are on basic riemann surface stuff

[flint forge]

all based textbooks have dependency diagrams

[ripe granite]

5-6 is Riemann Roch iirc

[marble solar]

Terry has like two weeks worth of notes

[ripe granite]

7-8 is Abel's thm and applications

9 does Cech cohomology

[marble solar]

Honestly his whole 246ABC sequence is solid

I'm surprised you didn't even try 246 this past year bro

I think you'd like complex

[ripe granite]

I was doing 226

which was on complex geometry

[marble solar]

Just sneak into 246C

Skip AB

[ripe granite]

I don't think I can do another class lol

Im doing 135

[marble solar]

Does differential equations really count?

[ripe granite]

count for what?

the 33b req?

ye

[marble solar]

As a class for you

I mean like

[ripe granite]

idk

[marble solar]

What is that 2 hours/week

[ripe granite]

im also doing algebraic algebra

[marble solar]

On the homework

Lol

[ripe granite]

and the algebra seminar

[hollow peak]

algebraic algebra

[marble solar]

It's like topics in Algebra

Usually Balmer or the merk will teach that

[ripe granite]

merk

[marble solar]

Either way, one hell of a class

[ripe granite]

and I might do a gelfand and manin reading course

[hearty steppe]

Algebraic Algebra is a thing? That sounds like funny wording

[marble solar]

It's topics in Algebra

[hearty steppe]

Oh

[marble solar]

It's like 211?

[ripe granite]

um

216

I think

[marble solar]

216!

You can't get cleared for a 299 can you?

[hollow peak]

are 200+ grad level at ucla?

[marble solar]

Yes

All UCs

Are that way

[hollow peak]

that explains why the tao notes I've been reading are obscenely difficult

[ripe granite]

dunno

havent asked

[marble solar]

Some are harder than others. His 245ABC isn't that good, the 246ABC are better. His analytic number theory notes are great

[hollow peak]

I've been reading 247A

[ripe granite]

is that harmonic?

[hollow peak]

yeah real analytic harmonic

[marble solar]

Yeah, that one is hard

[hollow peak]

B is when he goes in torus stuff and rep theory

so I'll either do that next or go through some of stein

[marble solar]

You need all the 245ABC, 246ABC, and some Fourier/PDE background

I audited his 246B last year

[ripe granite]

I think the only prereq is 245A moonbears

[marble solar]

247B**

[marble solar]

There are formal pre reqs

And there are the real pre reqs

[ripe granite]

true

[hollow peak]

I haven't found it impossible without that level of background

I think the way he writes makes it clear what gaps you need to fill

[ripe granite]

noice

[marble solar]

Someone typed up Visan's notes

For harmonic

Those are very good

[ripe granite]

lmao Visan's harmonic class would be scary

[marble solar]

That's what John did, he said he loved it

[ripe granite]

ye I know a few people who did that class

[marble solar]

AA as well?

[ripe granite]

I think AA did it the year before?

not sure

mightve

[marble solar]

I took harmonic at Irvine

That was substantially easier

Than the UCLA version lol

[ripe granite]

have you ever been in Visan's class?

it's terrifying lmao

on the first day of 131bh

she was explaining some stuff

[marble solar]

I had totaro/garnett/gangbo for 131abc

The worst was gangbo

The best was garnett. Totaro was good, but too stressful

I've heard he's calmed down

[ripe granite]

and then suddenly says, "Hey new guy, what's [insert question]"

I blanked for a few seconds lmao

[marble solar]

Yeah that's what they do in Romania

I work for Russian School of Math, and we're constantly encouraged to do that to students

[hollow peak]

it's so unappealing that math is so oriented around suffering and trial by fire

and so much more so than like every other field

it just gets obnoxious after a point

[ripe granite]

her class was really good tho bacono

it's just that I wasnt ready for it

[flint forge]

okay i think that that type of teaching is cool and good as long as people don't suffer like

significant consequences

for fucking up

or having an off day

[ripe granite]

2 off days and the quarter is done lol

[flint forge]

wait what?

[marble solar]

At UCLA, one of my friends had a schizophrenic break down, hospitalized and everything. Another person had a rash from the stress/insomnia, dropped 40 pounds. Had to drop classes

[hollow peak]

I feel like I can't fuck up at least

[marble solar]

The pace at UCLA for Honors/grad courses is insane

[ripe granite]

nah I meant a quarter is pretty short

[flint forge]

i mean im at uchi

[ripe granite]

you dont have too much room to fuck up

[hollow peak]

and I'm sure a lot of math students feel the same

[flint forge]

im familiar

[ripe granite]

ye

[marble solar]

The competition is always there, and you can't really take too much off. The professors just keep pushing/piling on material and give very little wiggle room for mental health issues

[flint forge]

thats cancer

[marble solar]

I had night terrors for the first time in my life after my first year at UCLA, I woke up shrieking in my sleep

My now wife and mother in law were very concerned

[ripe granite]

I don't think it's as bad as the chicago honors analysis tho

[flint forge]

chicago HA is just a dumb class lol

[marble solar]

It varies a lot from instructor to instructor

[flint forge]

its a bad bar

no one even learns anything

[marble solar]

Like Totaro's course was just impossible

[flint forge]

Like of every person I've surveyed who took HA not one of them feels like they remember the majority of the material

or even main ideas

[hollow peak]

my friend in it atm says the same things

[flint forge]

Dami is the only person I know who is both sane (arguably) and seems to have a somewhat positive association w the class

[marble solar]

This is why I decided to go to CSULB for my Masters in Math, the profs were really good, and gave a lot of time for mental health/emergency

[ripe granite]

I thought 132H (complex analysis) was a lot harder than 131AHBH

[marble solar]

When my father unexpectedly passed away, I got a year to finish InCompletes, almost no questions asked

[marble solar]

I had Gieseker, so my 132H was just...not very coherent

The only people that seem to get a good end of the deal at LA for Math are the post-docs or applied math PhD/Post-Docs

The PhD students are mostly unhappy since they make nothing (with rent being too high) and courses/quals being exceptionally difficult

[ripe granite]

undergrads?

[marble solar]

Undergrads only get a good deal if they aren't paying for tuition

Cuz they could have gone to literally any other school, graduated near top of their class, completely debt free, got research elsewhere, and moved on with their lives

[ripe granite]

lol that's almost certainly not true

[marble solar]

e.g. schools like Irvine, SB, SD, etc.

[ripe granite]

maybe

[marble solar]

or even Fullerton/Long Beach

[flint forge]

i do think if ur paying sticker price at a top school

it almost certainly isnt economically worth it

i say that as someone paying sticker price at a top school

[marble solar]

I'm sorry Max, are you on student loans?

I hope not

[flint forge]

No uchicago is good w financial aid

[ripe granite]

chicago seems like a super cool place to be tho

[flint forge]

i just dont qualify for the obvious snd therefore not worth concern reason

chicago is a great city

with godawful weather

[ripe granite]

I meant uchicago

yes, the city is also good

[flint forge]

oh its mostly cool

i hate the core

[hollow peak]

I would hate my college if they forced me to take french as well

[willow pecan]

[hollow peak]

thank fucking god I don't have to take a foreign language

I am awful at them

[ripe granite]

you need to do a foreign language at LA as well

[willow pecan]

You need to for all the UCs

But you can fulfill it with hs stuff

[hollow peak]

I had 65 in german for three years straight

it singlehandedly tanked my gpa

luckily I somehow passed the state exam and they released me from my shackles

[willow pecan]

[ripe granite]

rip

[hollow peak]

meanwhile I have lost all of my german ability

ich nicht spreche deutsche

[ripe granite]

what is it in proper grammar

ich spreche keine deutsch?

idk

[hollow peak]

I think I said that in correct grammar

[ripe granite]

the verb is supposed to come second

[hollow peak]

yours translates to "I speak no german" whereas I said "I don't speak german."

[ripe granite]

I think

ich spreche deutsch nicht

maybe that works?

or perhaps ich spreche nicht deutsch

the verb definitely needs to come second in this case iirc

[hollow peak]

basic sentence structure is similar to english: subject (cancellation) verb object

at least that's how I remember it

[willow pecan]

book-discussion

[hollow peak]

[ripe granite]

es tut mir leid

[hollow peak]

sounds like something I definitely should have memorized by second year german but never memorized at all by the end of third year

[flint forge]

i have creatively managed to learn almost no french

and still get an A- so far

by purely memorizing sounds

and patterns

[quick hornet]

max this is how people learn languages as children

you realize

[flint forge]

yes

but like I memorize wholesale sentences

off google translate

[quick hornet]

my french pronunciation is dogshit

somehow i pronounce "il y a" wrong

i have no clue what i do wrong

[static crest]

it could just be how you stress the words

[flint forge]

ill e ah

is how i do it

[static crest]

if you actually pronounce it like the english word "ill", I'm pretty sure it'd sound kinda really off

[flint forge]

i do

[steel viper]

its more like eel

[valid moth]

i imagine it's the same as spanish

there's probably a name for it but im not an ipa nerd

@ fiona

[marble solar]

eel-e-ah

[paper finch]

ich spreche ein bisschen Deutsch

[timber mesa]

I think the French "a" is more nasal? I might be making things up tho

[pseudo forge]

Looking to learn proof based linear algebra

Any suggestions?

Axler?

[broken meadow]

friedberg

[pseudo forge]

Looks good!

[slate spire]

can vouchfor this

[warm glen]

does friedberg seem alright as a 2nd/proof based course in linear alg

like, easy enough to self study

[karmic thorn]

Yes

[warm glen]

ok bet

thanks

[karmic thorn]

[hearty steppe]

Peter lax? Haven’t heard of him

[karmic thorn]

[clear sail]

hoffman kunze

[buoyant flare]

nice blue balls dami

[warm glen]

would anyone b willing to skim thru the linear alg book by liesen and mehrmann and tell me how it compares to the standards (axler, h&k, friedberg)

i saw some reddit comment saying it was better than axler and it seems like an interesting book

cos it starts out w some basic facts ab what groups, rings, and fields are

then it introduces matrix groups and rings

THEN it does echelon form and stuff

[karmic thorn]

Does anyone happen to have a concise set of notes covering elementary number theory?

Something that covers this content

(Equivalent to first 10 chapters in Burton's book)

[hearty steppe]

just look at the table of contents

and best to compare that to university syllabi of various courses in the subject.

[warm glen]

ok i should have been clearer

[hearty steppe]

then finally, read and have your own opinion

[warm glen]

i wanted a comparison in terms of difficulty, readability, etc to the others

[hearty steppe]

I won't hesitate on recommending Elementary Linear Algebra by Friedberg et al

[warm glen]

i, in fact, am able to read a table of contents

[hearty steppe]

Everyone has diff preferences for books. Try what I recommended along with Linear Algebra by Janich, also check out Intro to Linear Algebra by Lang

I like those books a lot personally from reading them so far

[warm glen]

yea probably i asked for too much by saying i wanted full on comparison to other books

what id for sure like to know is what people think of the approach taken in the liesen book pedagogically speaking

like some ppl in this server would say that axler doesn't teach u in a very good way bc of the fact that he banishes determinants to the end and then doesn't give a great treatment of them

so what would the opinion be on a book that starts w algebraic structures, then goes into matrix groups, and only then starts going into usual linear algebra stuff

[gray gazelle]

you can just study those topics individually i guess

[karmic thorn]

I have an oral exam based on this stuff scheduled for day after tomorrow. Need to speed-learn this stuff, so a concise set of lecture notes would have been easier to work with.

[gray gazelle]

ah i see

[karmic thorn]

Would keep scrounging the web till I find something. Thanks anyway!

[lucid hazel]

have you heard of the guy who memorized all french words to win at scrabble without knowing the language?

[wooden sparrow]

Did he get some big money prize?

[quick hornet]

dont most like, top scrabble players memorize dictionaries regardless

i dont think it being in a different languaeg would change much

itd make it a bit harder of courses

but same "study" process id imagine

top scrabble strategies are weird, you intentionally make small words in order to try and set up your letters to make a scrabble (a word where you use your entire rack) because they get a ton of bonus points

so most scrabble pros can recognize "oh, i have two Ses, an E, and a T, if I get rid of this Q and W im pretty close to a scrabble"

i looked into this when i was way younger

weird metagame

[steel viper]

seek help

[quick hornet]

doesnt seem that fun at a high level TBH

[flint forge]

the only good meta is civ meta

honestly i really wonder what civ meta would look like if the scene were bigger

[steel viper]

the smash meta is fun

unfortunately the smash community is not

[gray gazelle]

hlo

[flint forge]

ive never had the like

input ability

to play fighting games

i just cant press button good

[gray gazelle]

hey there i want to know abt a good book

which i can buy for knowledge

[flint forge]

it depends largely on what knowledge you seek

[quick hornet]

thats a bit vague.

[gray gazelle]

i m indian i want to crack JEE

[quick hornet]

then either get good at pressing buttons

or play ganondorf

[gray gazelle]

mathematics in it is really hard

[karmic thorn]

You won't get the best recommendations here.

[steel viper]

im not good at it either

but its still fun

well i also play spacers for this reason

[flint forge]

maybe if i got into it i'd like it

[karmic thorn]

With JEE, it's mostly consistent practice of the same stuff. Any standard book series(Cengage/Arihant) would suffice @gray gazelle .

[quick hornet]

you see the secret is

[gray gazelle]

looks hard

[quick hornet]

play top tiers with lots of options so you look smart

the secret is

becauses theyre top tiers

[flint forge]

you could also get away with just buying the second book I listed above as they spend very little time on the JEE at havard business school

[quick hornet]

all their options are good

[steel viper]

but i dont want to play top tiers

i want to play samus

[quick hornet]

ew

[steel viper]

and ledgeguard with bombs and bair

[flint forge]

i just want to master isabelle

[karmic thorn]

It's a lot of work for sure.

[flint forge]

is that too much to ask

[steel viper]

isabelle is fun

i mained villager in 4

[flint forge]

fuck villager

[quick hornet]

wow i hate yall

[flint forge]

i only want to play isabelle

[steel viper]

copium

[flint forge]

oh i played a lot of duckhunt too

[steel viper]

duck hunt dog is hard

[gray gazelle]

@karmic thorn maybe I'll try in December for Jee till then i will read almost all suggested books

[steel viper]

he seems like hed be really fun though

[quick hornet]

duck hunt has some serious tech in ultimate

[gray gazelle]

or maybe Hc verma