book-recommendations

[gray gazelle]

Or would I be better of just repeating the exercises in my book?

[trim narwhal]

A good book for euclidean and non-euclidean geometry?

[gray gazelle]

What exactly are you looking for in euclidean geometry?

[plain flame]

What kind of Geometry do you want to learn?

[trim narwhal]

Geometric figures on plane and on space and non euclidian geometry in general

[plain flame]

Saying you want to learn about non Euclidean Geometry is like saying you want to learn about plants that aren't asparagus. Not very specific.

[trim narwhal]

I know nothing about non euclidean geometry

[plain flame]

99% of Geometry is not Euclidean geometry.

[trim narwhal]

i just want to start with non euclidean

[plain flame]

Well, usually people learning Geometry start with Topology. Can't do much Geometry without Topology. So you might look into learning Topology.

But are brussels sprouts the same as asparagus?

[flint forge]

noneuclidean geometry is cursed

its like pretending that rings arent always commutative

you'd be wrong

[trim narwhal]

@gray gazelle I'll take a look at it, thanks

[quartz pawn]

We taught Euclidean geometry at my school.

@trim narwhal Here are a few books. We used this book https://www.amazon.com/Euclidean-Non-Euclidean-Geometries-Development-History/dp/0716799480/ref=sr_1_5?dchild=1&keywords=euclidean+geometry&qid=1600015977&sr=8-5

But I didn't like that book all that much so I supplemented it with this book: https://www.amazon.com/Foundations-Geometry-2nd-Gerard-Venema/dp/0136020585/ref=sr_1_1?crid=11AIXJMWIPAEF&dchild=1&keywords=foundations+of+geometry&qid=1600016022&sprefix=foudnations+of+geometry%2Caps%2C200&sr=8-1

And then I considered using this one https://www.amazon.com/Axiomatic-Geometry-Applied-Undergraduate-Texts/dp/0821884786/ref=sr_1_1?dchild=1&keywords=axiomatic+geometry&qid=1600016046&sr=8-1 but I haven't really looked all that much into it, but it is what you described.

That last one is written by the same guy who wrote "Introduction to Topological Manifolds"

So that's a book that's well known and people say good things about it.

[karmic thorn]

Is Coxeter's book a good first reading?

[quartz pawn]

No clue, never used.

[limpid gazelle]

I read a bit of Coxeter's "Geometry revisited," and it seemed pretty good

The exercises were boring tho, but I find all euclidean geometry stuff a bit boring

so

[valid moth]

try elements

[limpid gazelle]

Oh yeah Coxeter's Geometry does assume basic geometry stuff

But nothing too advanced (relatively) like the law of sin

Only like

Area of various shapes, and angle stuff

and also I believe nobody should read elements now

[gray gazelle]

is whoever into euclidean geo now

[limpid gazelle]

I got two geometry books from usamts

[gray gazelle]

sad

[limpid gazelle]

One is Coxeter's Geometry revisited, one is EGMO

[sage python]

@flint forge wait if anything I feel like as a topologist you should like hyperbolic geometry lol

[flint forge]

Why tho

None of the stuff people in rigid geo care aboyt is homeo invar

[sage python]

Well you see

Mostow rigidity is a thing

If M and N are complete finite volume hyperbolic manifolds in dimension 3+, then any isomorphism between their fundamental groups is induced by a unique isometry M->N

[marble rock]

what does hyperbolic manifold mean

[sage python]

But yeah I guess I was gonna say low dimensional stuff much as this isn't your thing lol

[tribal kernel]

Hyperbolic manifolds are homeomorphic to hyperbolic space, which has at least four isometric representations

[marble solar]

The cool LDT stuff is getting less and less popular

[sage python]

Aren't 4 manifolds still a thing?

@tribal kernel uh, I think you might want some adjectives

Simply connected?

[tribal kernel]

Locally homeomorphic then

It has constant negative curvature

Spherical space has constant positive curvature and Euclidean space has zero curvature

[marble solar]

It is, but they're using a lot of crazy algebraic type stuff now

I like cut, paste, and glue topology which is what topologists advertise it as, but very few work in

As seen in Schulten's 3-manifold book

[limpid gazelle]

Wouldn’t it be cool if humans were 6 dimensional beings

[wooden sparrow]

I don't know about that, but if 2 dimensional beings lived in a far right society, they'd need to keep on rotating

[valid moth]

why 6 specifically, seems like kind of a bad number

[broken meadow]

at least choose 7

so we can still do cross product

[marble solar]

You can do cross product in other dimensions

See Spivak Calculus on Manifolds

[gray gazelle]

the relevant part

[plain flame]

More generally, if you have a field k, n dimensional vector space V, fix an isomorphism k=det(V)=(upsidedown V)^nV, then you can define cross product.

[broken meadow]

/\

[plain flame]

My music friend laughed at me for calling # capital three.

[limpid gazelle]

[marble solar]

Thank you Tterra, I'm surprised a lot of ppl are unaware of this. It's not exactly a cross product, but it's good enough for me

[valid moth]

that font

🤮

[marble solar]

It's an old book

He doesn't have the rights to re-write it

[pliant jacinth]

Any good texts for alternative ways to visualize different mathematical methods?

[robust palm]

what do you mean by mathematical methods

that's very general

[gray gazelle]

calculus on manifolds doesn't need rewriting

even if it does have quite a few errors

[marble solar]

The errors are the real test

I love that theorem in chapter 3, which isn't correct and there's an errata correcting it in the back

(The proof isn't correct)

I tried convincing my professor (I TA Calc. on Manifolds sometimes) to give an outline of it on the exam, and have the students fill it in

But he said no

[gray gazelle]

the proof of integrable iff a.e. continuous, right?

my prof (taught out of the book) gave a correct version, and offhandedly mentioned that the book one has an error

good old times

i have the corrected proof in my notebook somewhere

[shut grail]

By outline do you mean like core concept questions that could lead to the proof completion, or like fill in the blank?

[marble solar]

Yeah, it's integrable if and only if continuous a.e.

There's an error in the proof "since M_s(f) - m_s(f) >= 1/n is guaranteed only if the interior of S intersects B_{1/n}"

The correction really isn't that difficult

[shut grail]

Ahhhh I seee

[marble solar]

You just cover the boundaries of the partitioning subrectangles by something with volume < epsilon

So you can just say "Fill in the details of this"

Explain the error, give them the idea of what is to be done, but have them write it up correctly in technical mathematics

And have them explain why it works

My friend had the Addenda 3. On his final exam for Third Quarter Real Analysis

[molten wave]

@plain flame it's not even capital three

it's capital C

[marble rock]

im done with algebra and im going to learn analysis

what do you guys think of mathematical analysis by S.C malik

[hearty steppe]

Never heard of that one.

[tribal kernel]

I actually haven’t either

[hearty steppe]

There’s going to probably be a million and one diff analysis books compared to anything else in math lol

[brittle latch]

anyone heard of history of mathematics by david burton

my high school mathematics teacher recommended it and im curious

[marble solar]

No; but I've read several accounts of history of mathematics

If your teacher recommends it, it's probably good

History of math is really interesting

[karmic thorn]

"Mathematics and its History" by John Stillwell is an excellent text for undergrads. What's different about this text is that it has a few exercises with each chapter, and actually covers the historical development of almost all undergrad topics(group theory, topology, analysis, etc.)

By the way, any suggestions for a textbook on single variable calculus for competitions?

[quartz pawn]

StillWell is comprehensive af

He's coming out with a new edition of the book that is supposed to be smaller

I want to use it as a math history book

[karmic thorn]

I read in through the first chapter I guess and found it to be brilliant in its approach(I actually made a small Python code to verify the values of Pythagorean triplets which appeared in that Plimpton clay tablet).

[marble solar]

I took a math history class with Stillwell's text

There was some geometry stuff that got really annoying without coordinates

and the TA was like "Just use coordinates"

[quartz pawn]

Analytic Geometry really makes Geometry that much easier

when you get coordinates it literally changes the whole game

I remember we did this in my euclidean geometry class for a while and we got to a point where we could finally use analytic geometric techniques for a certain part and I almost cried tears of joy

[marble solar]

was that in HS?

[quartz pawn]

No it was in college.

[marble solar]

Ahh I was gonna say

[quartz pawn]

It was a class on Euclidean and Non-Euclidean Geometries.

[long bear]

Synthetic geometry be like

[quartz pawn]

From the axiomatric i.e. synthetic approach

but htere was a certain part where we got to use Cartesian Coordiantes

[karmic thorn]

By the way, any suggestions for a textbook on single variable calculus for competitions?
In desperate need. Please ping me if you have any recommendations.

[hasty turret]

I don't think calculus is required for olympiads

Or are you considered some other type of comp?

[karmic thorn]

Not looking for olympiads, actually, a uni entrance which poses some beyond school level calculus problems.

Try AOPS's calculus book
Thanks, I'll check it out, although libgen seems to be giving me a hard time on this one.

[long bear]

@karmic thorn there are libgen equivalents

i recall ari telling me of one

@calm crane

[calm crane]

look up libgen mirrors

[gusty smelt]

libgen minors

[karmic thorn]

For this particular title none of the mirrors is working.

I'll accept dark web links too

[long bear]

lol

[gray gazelle]

John A Rice Mathematical statistics and data analysis 3th edition

Anyeone has te solution manual

[calm crane]

oh as in you need a book?

libgen mirrors are all basically the same thing

if theres a doi link can try scihub

but for random semiobscureish? books idt there will be

obscureish includes books for high school cuz no one uploads them on libgen

[karmic thorn]

I guess AoPS books fall into that category :(

Any other suggestions for a good single variable calculus text, perhaps aimed at undergrads for competitive exams?

[gray gazelle]

hahaha

@calm crane ... what?!

[calm crane]

i find for math olympiads generally you dont need lots of knowledge on calculus tho idk good books either :p

[trim narwhal]

Is Coxeter good for beginners?

[radiant basalt]

Well it can be. Mostly EGMO is good enough, I started from scratch out of it and went all the way up to IMOSL and National Problems. For Geometry I'd recommend also having a try over Chinese problems they're cool.

[flint forge]

@karmic thorn do you mean competitions

Or just uni stuff

[karmic thorn]

Competitions, specifically.

[flint forge]

If the later Spivak is the gold standard

Oh

No clue

Spivak is the gold standard for calc though

[karmic thorn]

Can I show you a sample question? Maybe uni stuff could work, I'm not sure at all.

[flint forge]

Uh sure

I know nothing about comp math

[hasty eagle]

TedNotKaczynski:

[karmic thorn]

My current background is high-school calculus, and I've never covered these sequences and stuff. I'm not sure if analysis textbooks are a good choice for me at the moment because their core emphasis is on theorems and their proofs as opposed to computational problems. Which books should I look out for?

[gray gazelle]

without thinking my first instinct is to apply mvt as much as possible to this

[karmic thorn]

Haha, thanks Terra, but atm I'm more concerned about a book which covers problems like these.

I have Thomas' Calculus, but it isn't as rigorous(somehow more applied). I also have Tao's Analysis, but it doesn't have a lot of problems. Does Spivak cover problems like these?

If anyone has any recommendations, please ping me.

[gray gazelle]

i'm not sure if spivak specifically does things like this problem, but it does have quite a few problems, ranging from easier computations to actual tricky stuff

[hasty eagle]

DrunkenDrake:

[karmic thorn]

I guess there's a TeX breakdown; regardless I don't know anything about the solution.

[gray gazelle]

tex broke lol

[karmic thorn]

i'm not sure if spivak specifically does things like this problem, but it does have quite a few problems, ranging from easier computations to actual tricky stuff
Okay, I'll take a look at Spivak. Guess I'll grind for a couple of weeks to dig into it.

It'll certainly have some positive outcome.

[gray gazelle]

also \leq @hasty turret

[hasty turret]

Is this a correct proof:
$|f'(x)| \leq 1/2 \implies |f(x)| \leq |x|/2$ therefore$ |f(x)/x)| < 1$

[hasty eagle]

DrunkenDrake:

[flint forge]

No. Let f(x)=1. Then f(0) is not less than 0/2

[limpid gazelle]

But $|f(x)-f(y)|\leq|x-y|/2$

[hasty eagle]

Whoever:

[gray gazelle]

now apply this a million times

qed

[limpid gazelle]

exactly

[hollow peak]

isn't f a contraction mapping?

so shouldn't the problem be trivial?

d(a(n), a(n+1)) is a monotonically decreasing and bounded from below sequence so it converges

since real numbers are complete then since a_n is cauchy it converges as well

then a_n is bounded by definition

[gray gazelle]

ah trivial

[karmic thorn]

Are these topics covered in Spivak's calculus?

[gray gazelle]

yes

[karmic thorn]

I should definitely look into it then.

[gray gazelle]

spivak might not use the term "contraction mapping" but he absolutely discusses everything else

[hollow peak]

that wasn't really trivial, I'm joking, but that is a neat problem

[gray gazelle]

just use pugh

[karmic thorn]

These type of problems appear in a uni entrance exam I'm aiming for, and although I don't have much time left(barely 3 days to go), I guess knowing some basics might still be helpful to get partial credit.

[gray gazelle]

this entire problem is basically reliant on MVT

well one way is

[hollow peak]

you can definitely do that entirely with MVT, contraction mappings and wacky analysis stuff makes it way easier

[gray gazelle]

i like bacono's solution the most, but there is a nice MVT argument you can do by looking at |f(a_n) - f(a_{n-1})|

they might be the same solution tho, idk

[karmic thorn]

Is there a more graphical way to understand this argument?

[wooden sparrow]

someone tell me what to do, most horrible thing with AOPS books is having to get a solutions manual for the textbook

[broken meadow]

"Write your own solution manual"

[wooden sparrow]

brrrrruuuuuuuh

[broken meadow]

😔

[wooden sparrow]

it's like, I'm wasting a lot of time not being able to figure out what to do, if the answers posted here are what this author's expecting me to think by or not

bruh why do I punish myself with this shit

it's way hard for me to watch videos

[valid moth]

is waiting for something that starts in like a minute
starts to play a map to pass the brief time
starts to play it very well...

might be able to FC but it's past the time

[wooden sparrow]

[raw herald]

@karmic thorn monotonically decreasing means it is always decreasing, bounded from below means it won't go beyond a finite spot which is below the values of the sequence. so you know that the sequence keeps on getting smaller but approaches a horizontal line on a graph. is that what you meant by graphical way to understand it?

[karmic thorn]

Yes, that's what I meant. Thanks for explaining!

[long bear]

I'd like to get a taste of number theory, what's a good book to start off with?

[valid moth]

try ireland-rosen

[long bear]

cheers

[flint pagoda]

What are people's thoughts on "Beginning Logic" by Lemmon... I skimed through it and it seems alright. Has anyone ever used it in an intro logic course?

[hearty steppe]

I haven’t heard of that one. Have you considered trying an intro to proofs book?

[tight crag]

@flint pagoda read enderton

[flint pagoda]

thanks for the tips. ill check out enderton too i guess

[trim narwhal]

What do you think about Introduction to Geometry by Coxeter? Is it beginner friendly?

[shut grail]

Hey guys need some help. I’m trying to self study fractals. What would be a good gentle introduction type book that could really help me conceptualize and internalize the notion of minkowski dimension.

[tribal kernel]

Not super familiar with those topics, but for a more general introduction into dimension theory, you might want to pursue a good measure theory text. Not sure if that’s what you’re going for though

[marble solar]

Stein And Shakarchi Real Analysis

Read chapters 1, 2, 6, and 7

It's a little tough tho

[shut grail]

Damn :/ yah the topics I’m exploring is basically the notion of 0 ≤ dim F ≤ 1

Non integer value dimensions

[gray gazelle]

Anyone has used this book?

Basically goes from 1+1 to solving integrals

[prisma snow]

And no one needs anything you learn after integrals :(

[gray gazelle]

that is not all of what i need in math

For example this exercises

Its a exercise book mostly

Ranging from basic to a bit more indepth on a topic just to get that foundation on math for college / university

[random spear]

Would you recommend reading texts that you're already experienced in? Even if you didn't have a necessarily rigorous education?

For background, I grew up in the middle of nowhere midwest, where learning math was shamed if anything.
I'm on a gap year now and I'd like to learn a lot more before uni kicks me to the curve.
I've "unrigorously" taught myself a lot of calc and such and had a Calc AB course. And Ig I feel pretty confident in it? But simultaneously I'm worried that the Calc AB course didn't cover much and that for what I have taught myself, it wasn't thorough.

What I plan on reading is Calculus I & Calculus II by Apostol, and Vector Calculus, Linear Algebra, & Differential Forms by John Hubbard

My uni gave us a pretty thorough glance at linalg, diff eqs, and a bunch of other stuff, but I'm not even sure if that was just shortened.

We do the entirety of Calc, Lin Alg, and some other stuff in one term or a year, forgot which one.

[shut grail]

@random spear where u from bro

[random spear]

@shut grail misery.

But most people spell it Missouri :P

Really hoping that COVID-19 will finally disipate next year so I can finally get out of here and head to California...

---

Also one more question, does anyone have tips for focusing on a book?

[tribal kernel]

Reading the preface can give you a good idea on the author’s intention with the book and the relative difficulty of the content and exercises. Definitely read through that and make sure you fit what the author describes. Sometimes the author might also give a way to denote which exercises in the boom are necessary for fully understanding the theory. Doing those exercises, and just doing exercises in general, helps me stay committed to a book.

I’ve personally never read these books, but I’m sure they are good for what you want. Additionally, taking good notes from a book helps me stay really invested.

[shut grail]

@random spear ah I see. I’m from California. Cuz I was about to say, I know uni’s out here in CA implemented linear algebra and diff eq into one course for a term

[random spear]

Hmm never bothered with notes, but Ig it does* make sense that I'd pay more attention to what I'm reading and focus.

Yea haha Caltech does that.

[shut grail]

Cuz my old uni and my current uni in CA I notice the undergrad programs do it for sure

[random spear]

Oh weird. A lot of my east coast friends told me that they don't, so I wonder why that might've happened.

[shut grail]

Maybe west coast thing 🤷🏽‍♂️

Idk

[long bear]

(Preemptively saying I'm very much aware of the physics servers existance, just want extra input) Hey guys, got any general physics book recommendations

[shut grail]

Like as an intro physics book?

[random spear]

@long bear we were actually talking about books over there earlier. If you're looking for some, tag @novel iris

And f

We love autotag.

[long bear]

aight

[random spear]

Well I guess he'll come here eventually anyways lol.

[long bear]

I'll shoot them a pm

[gray gazelle]

anyone have a good link to the rules/laws of arithmetic algebra ?

[wide meteor]

Is calculus by spivak a good book for analysis?

[quartz pawn]

It's an intro analysis book.

For a first course in analysis you can try it.

[wide meteor]

Ok cool

What would u recommend after it?

[plain flame]

So ambitious! Good to be ambitious.

[flint forge]

Its not an intro analysis book

Its a calculus book

It is great for a second course in calculus or an ambitious first one

[wide meteor]

um

[quartz pawn]

Yea it's a calc book but it's definitely more analysis-y than your standard calc textbook.

[plain flame]

I have never had more ambition than making it through one page. Let alone thinking a few books ahead.

[wide meteor]

What would u recommend as an into analysis book then

I have never had more ambition than making it through one page. Let alone thinking a few books ahead.
@plain flame xD

[quartz pawn]

It wasn't made for that but I'm using it the more colloquial sense in that it's definitely got more analysis flavor to it than say something like Stewart...

You can try Terrance Tao's book if you want to try a book that's made as an intro to analysis.

I've seen the problems though in Spivak and I'd argue that they are harder though.

You can try rudin to it's technically an "intro to analysis" textbook.

[wide meteor]

Rudin is hard

Whats terrance taos book called

[quartz pawn]

Analysis I and II

[wide meteor]

I cant seem to find it

Ohk

Have u used it?

[quartz pawn]

No.

But I've seen some of the problems though

Of course some are more challenging than others but they aren't that bad compared to something like Rudin that just kind of has problems that are difficult right out the gate.

No problems to sort of easy your way into the difficult problems in the case of Rudin.

Tao's got those problems that make it easier for you to get adjusted and then the problems in the section get more difficult.

[wide meteor]

Ah thats nice

[marble solar]

I'm not a fan of Terry's book

At some points he's overly technical on things that don't matter that much at an intro level

Spivak, Pugh, Apostol, Rudin all seem to do a better job

[flint forge]

The ideal analysis book

Is just a latex’d rudin

[quick hornet]

stop max youre making me aroused

[broken meadow]

does it exist

has some mad lad

done it

sounds like thousands of pages

good god man

[flint forge]

I feel surprised no one has

Is it a copyright thing

I feel like I could start a github

[broken meadow]

like

[flint forge]

And people would get it done over time

[broken meadow]

if a huge group of ppl do it

and then have some editors check it

it should be possible right

[flint forge]

Yeah

I dont see why theres no open source project for it

If every math major at a top 10 contributed 1 page

It woukd be like instantly done

Probably slower

[valid moth]

@sweet lotus @flint forge https://web.archive.org/web/20090318143423/http://www.vivaria.net/experiments/notes/publication/NOTES_EN.pdf

[flint forge]

Seems like you could build a community for it

[valid moth]

In 2002[12], lecturers and students from the University of Plymouth MediaLab Arts course used a £2,000 grant from the Arts Council to study the literary output of real monkeys. They left a computer keyboard in the enclosure of six Celebes crested macaques in Paignton Zoo in Devon, England for a month, with a radio link to broadcast the results on a website.[13]

[stray veldt]

nice, if everyone does a page, i dont have to do any

[flint forge]

I guess

Idk

Id bet there are 500 people who want this

Enough to do one page

Might as well just pay like 10 ppl

At that point

[valid moth]

I mean

you could just pay like 50,000 5 year olds

[stray veldt]

the thing is

you need relatively high skill to latex a math document

and you dont want to pay that much

[flint forge]

Does it

It take a first year uni student

[stray veldt]

i wonder if a symbolic fee would incentivise people who want it done anyway to do it

[flint forge]

You can buy an hour of their time w a slice of pizza

[stray veldt]

sounds like child labor

[flint forge]

They are literally not children

[stray veldt]

thats why it only sounds like it

[flint forge]

You underestimate the infinite energy inherent in a broke freshman imo

Freshman me did extra work for fun

Sad

[tight crag]

Nice

I wish I had some results to write up

I should be writing the slides for my talk actually

[gray gazelle]

coffee>energy drinks

then again, im too stupid to get any actual work done so

[weak fossil]

Hey guys, I assume there's not much difference, but can you think of a HS statistics book that is pretty cool?

[sage python]

@flint forge Lol I thought you didn't like Rudin

Also there's another book that I think officially replaces it as the correct answer

I was looking the other day at Igor Kriz's website

And turns out

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

[marble solar]

I still can't get the PDF

Would you teach analysis out of this book?

If you could choose any book?

[quartz pawn]

@marble solar it's on libgen

[marble solar]

O'really

[quartz pawn]

YEE

[marble solar]

I did look at libgen but didn't see it the other day

[quartz pawn]

It's been on there for a while

[marble solar]

Well moonbears is technologically illiterate

I only learned latex because my grad professors made me

In undergrad I didn't like using staples, so I would fit the entirey of my problemsets and solutions on 1 page hand written

[sage python]

You can use scihub for getting springerlink books

But yeah this book is probably what I'd use? I mean if there are curricular choices wherever I'm teaching which wouldn't fit well (e.g. this book mostly does Lebesgue integration)

[flint forge]

I dont like rudin because of the typesetting

[sage python]

Then no. But otherwise as far as content is concerned this seems best, it fully subsumes Rudin and Spivak Calc on Manifolds

[marble solar]

I don't like Rudin because it's notes for a lecturer to fill in the details and the lecturers don't fill in the details

So if you're confused it just doesn't help

[sage python]

I mean subsumes Rudin is tricky to say, it spends like 30 pages on single variable calculus

[marble solar]

If I taught undergrad Real I'd say pick your choice of Rudin, Apostol, Pugh, Tao, and Spivak's two books are great references

[sage python]

Actually yeah the way things are split up it's actually still reasonably complete

[marble solar]

I'll look at Igor

I think one thing should be emphasized is that rarely one reference is enough

[tribal kernel]

Marsden and Hoffman is my go to for undergrad analysis

I think it’s really clearly written and very thorough

[marble solar]

His <a,b> for interval is annoying

[tribal kernel]

Yeah that is really annoying

[marble solar]

Props for convex/concave functions in the first section

They really need to be treated early

[tribal kernel]

Also Kreyzig is a clear intro to functional analysis which is accessible to undergrads

[marble solar]

As far as I can tell this is a first rate text Sloth King

[sage python]

Yeah I don't like that notation since I use angle brackets for inner products

And [a,b] isn't used anywhere else that I know of

[marble solar]

I really like the extra time on Implicit and Inverse Function

[tribal kernel]

Also that analysis text looks crazy

500 pages, real & complex functions, functional analysis, and Riemannian geometry???

[marble solar]

It's just the basics of each

You can't go in-depth on any one of those in one book

[sage python]

Well honestly the complex analysis part isn't bad

Like it covers more than my dedicated complex analysis class

[tribal kernel]

Yeah but what a selection of topics

[marble solar]

Are you taking grad complex Sloth?

[sage python]

No I meant my undergrad one

Honestly my complex analysis is kinda lacking in general

[marble solar]

I did 4 quarters of Complex Analysis and it's still lacking

[sage python]

On my end it's weird

I kinda did it 4 times but really more like once?

In my first year my physics TA did some random Sunday sessions for some of us in complex analysis

But I really wasn't there yet

And he was fucking fast

I remember our, I think second session, we did 20 theorems in 90 minutes

[marble solar]

I think my issue was that it was my first graduate sequence and I wasn't entirely prepared for the difficulty - I did fine in the coursework and on the exams, but when I left LA I found not much of it stuck w/ me

[sage python]

So like that happened and I sorta knew a lot of nice theorems were true but that's about it. In the summer analysis bootcamp, I was sorta annoyed by our book's treatment of the subject, the lecturers weren't great (students were lecturing on the topics), and the psets were painful

So I sorta did it but not. Then I finally took the undergrad class and it was slow, also (and I loved this but it might contribute to my overall oofness on the subject) we didn't have many computational problems at all, never really had a contour integral at all

[marble solar]

People say papa Rudin is a good reference. I'm a huge fan of Ahlfors, and I liked the parts of Marshall that I read

Terry is teaching intro to grad complex right now - so his notes are on his blog

[sage python]

He did more like winding number problems

[marble solar]

If you want to go through it whenever you have a qual sloth

[sage python]

And then I took grad with no psets

Oh I'm done with my quals, I only had to do 2 lol

So I knocked both out last year

[marble solar]

Oh nice!

[sage python]

(Algebra and algebraic topology)

(No I don't know algebraic topology I just winged the shit out of it)

[marble solar]

Were they difficult at Madison?

[sage python]

Algebra qual was a joke

[marble solar]

Did you do the H sequence at Chicago + grad?

[sage python]

I did honors algebra at Chicago, this was enough for that qual

I didn't do first quarter grad algebra because the prof was notorious for giving undergrads Cs

So our undergrad director was not too happy with the idea of my taking that along with another grad class

[marble solar]

Sounds about right. I did the H at LA, and I got out of first semester algebra in my MS because of it. My undergrad alg. and my algebraic curves prof. had the same advisor so he kinda just let me in algebraic curves

[sage python]

(This was first quarter 4th year, when I would've been applying to grad school)

In hindsight I kinda wish I took it, I feel like I could've maybe pulled it off? And the material of that is really really cool

Noncommutative algebra, rep/Lie theory, etc

[marble solar]

It's a good call to not tank your GPA going in as someone who thoroughly tanked his undergrad GPA

[sage python]

Second quarter is commalg/AG from which I learned nothing lol

And third is algebraic number theory and I was so checked out that quarter that I only went to the first 2-3 lectures

But the psets were self-contained and honestly I got a decent bit out of them

So yeah technically I did 2/3 of grad algebra at Chicago but... did I really? Idk

[marble solar]

Third quarter at LA was Galois theory. Peterson was teaching Riemannian Geometry at the same time, and I was talking to Peterson. I told him I wasn't really liking algebra too much and he told me to take Riemannian. So I never finished the sequence in Algebra

[sage python]

Honestly I wish I was as tuned in to my classes 4th year as I was third year

[marble solar]

I think H classes just drain your motivation/energy/will power

It can really be overkill

[sage python]

Like, I would've more properly learned algebraic topology, geometry, and number theory. Prob would've started off much faster here lmao

[marble solar]

I think profs. should think harder when they assign their hw and exams. Really burns a lot of bright students out

My undergrad H analysis prof. thought he burned me out and turned me away from Math

https://www.math.ucla.edu/~rse/algebra_book.pdf

This is the book used for H algebra at LA

[sage python]

Nice

We used Dummit and Foote lol

[marble solar]

I think Elman's text is better than D&F

But D&F is a classic reference

[tribal kernel]

My grad algebra is using Aluffi with Dummit and Foote as a secondary text

[sage python]

I don't have a great impression of Aluffi tbh

Feels slow and has meh exercises

[tribal kernel]

I like the exercises but they feel necessary for the full understanding

Not an enhancement but a requirement

[sage python]

I see

[trim narwhal]

Has anyone read Linear Algebra: step by step by Singh? Is it better than Axler?

[timber mesa]

Axler is awful imho, passed my course with Hoffman & Kunze but that one's definitely aimed at math majors

[trim narwhal]

So do you know a good book for a beginner?

[timber mesa]

you might want to check out Jim Hefferon's, it's available for free on his webpage https://hefferon.net/linearalgebra/

[trim narwhal]

Ok thanks :)

[gray gazelle]

Which should be good for beginning with complex analysis ?

[tribal kernel]

A lot of people I know vouch for Churchill’s Complex Variables. I’m reading Complex Analysis and Riemann Surfaces by Schlag rn and it’s okay

[gray gazelle]

I'll check them out thanks !

[tribal kernel]

No problem!

[tight crag]

I think Ahlfors is a classic choice

[tribal kernel]

Hope it helps I haven’t read too much complex though

[tight crag]

But probably Churchill and brown is better for beginners

[tribal kernel]

I’ve heard that’s good for beginners. Schlag probably isn’t unless you’re strong with real analysis techniques

[worthy wigeon]

Hello , what do you think is a good resource on complex analysis ?

[tribal kernel]

Ah we were just talking about that. Churchill, Ahlfors, and Schlag were the three we ended up discussing.

[worthy wigeon]

Oh, cool, i am looking for an introduction on complex analysis

Which do you think is better at that ?

[prisma snow]

Out of those 3, probably Churchill

[worthy wigeon]

Thank you, i will check it out

[tribal kernel]

Yeah I’d agree with that. Churchill is probably best for a first introduction

[sage python]

@tribal kernel lmao Schlag

He was my prof

And he was quite something

[trim narwhal]

A good book on linear algebra?

[tribal kernel]

You read his book? What do you think about it?

Good linear algebra books for me have been Hoffman and Kunze, Halmos, and Mostow and Sampson

Hoffman and Kunze is the one I use for my graduate linear algebra course but it has plenty of material which is accessible from and undergrad perspective. Definitely treats it from an abstract perspective. For a numerical leanest algebra book I really like Ipsen. Very short and clear

[timber mesa]

H&K is good for a math major (maybe a honors-level course in some unis) if you skip some stuff like the entire chapter on the Jordan form. When I took linalg we followed that book verbatim but skipped Jordan and only learned how to compute that

Jim Hefferon's book is pretty good at a more introductory level https://hefferon.net/linearalgebra/

[valid moth]

axler

LADR

[sage python]

Axler is bad

Hoffman-Kunze is good

Linear Algebra Done Wrong is supposed to be good but idk it

[heavy barn]

Why would someone want to do linear algebra wrong

[timber mesa]

Linear Algebra Done Wrong is supposed to be good but idk it
@sage python I've heard this as well, I think the title is a play on how most linalg courses are structured (iirc LADW does determinants almost immediately after the first chapter on linear systems while Axler's LADR does them at the very end for some reason)

it's freely available as well so if you have any doubts just skim over it and see if you like it http://www.math.brown.edu/~treil/papers/LADW/LADW.html

[broken meadow]

Linear Algebra Done Rong

[hearty steppe]

The proofs are a bit strange but I am enjoying Intro to LA by Lang

The examples are pretty good

[sage python]

Yeah so basically Linear Algebra Done Wrong was written because Treil agrees with me that Axler's treatment of determinants is fucking stupid

Hmm

It's a bit matrixy for sure lol

To be fair so is Hoffman-Kunze

[civic carbon]

I've never seen a treatment of determinants I find satisfying that does not involve either hypervolumes or exterior algebras

[sage python]

I mean tbh I think the answer is just introduce exterior stuff from the get go

(I'm assuming here a math major linear algebra class ofc, if it's engineering than tbh you don't need it to be satisfying so just teach them the computational definition and roll with it)

I like chapter 6 of this book at a glance

[civic carbon]

"It's the unique thing with this giant list of properties. You don't really want me to tell you the list of properties. But if you don't believe me, read this. Then you will believe me."

[sage python]

This doesn't talk about the minimal polynomial which makes me 😠

[civic carbon]

my experience is definitely that the hypervolume notion is the one that is most useful in understanding the hard places the determinant comes up, like ANT.

[sage python]

Yeah this book seems alright but idk

I guess it sorta delegates certain topics to algebra?

Which I don't necessarily think should be

Mainly treatment of fields other than R/C, and anything at all about polynomials

Aside from char poly

[quartz pawn]

I've like LADW and I got the ame feeling that it really likes to restrict stuff to matrices and doesn't really want to abstract things like at all.

[sage python]

For what it does I think it's organized somewhat better than Hoffman-Kunze

[quartz pawn]

Hefferton seems pretty good and I almost used it.

But I chose Friedberg cause I thought it did a decent mix of trying to be LA - i.e. dealling with matrices - but also not straying away from the idea of abstraction so much.

[sage python]

I don't know Friedberg lol

[quartz pawn]

I think it's pretty good.

It has a level of abstraction similar to Axler but it deals with determinants.

I'd say Axler might be a little more theory and abstraction but Friedbergs pretty good too I'd say and it has good applied exercises some really cool applictions i.e. such as those relating to relativity.

I think it's a pretty good book imo.

[serene crater]

any germans here, who read Stefan Hildebrandt's 'Analysis 1'?

[hearty steppe]

Heard about that book a few times already.

the sooner i finish Velleman, Ill def spend more time with my analysis texts. I just want to get thru Velleman so I can actually spend time doing the proofs exercises properly at the end of the analysis chapters

but the analysis texts I been focused on for now are Schroder, Abbott, and Apostol.

[limpid gazelle]

Ayye

Nice

Now you can occupy #advanced-analysis like I did when I read stephe abbott

[marble solar]

yA best channel

[nocturne crane]

any recommendations for books on the application of linear algebra?

looking for something that talks about how linear algebra is used in fields of science and in tech

so like physics, chem, biology, computer science, engineering, etc

a book that gives an overview of how linear algebra is used in these fields would be great

[gray gazelle]

Maybe a book discussing linalg in multivariable calculus

Since like, isn't det used literally everywhere

Flux requires det in the integral

Jacobian is literally a det

So wait isn't basically usub Det

im14andthisisdeep

(not actually 14)

literally just take a good mvc course

[timber mesa]

any recommendations for books on the application of linear algebra?
@nocturne crane I read Carl Meyer's "Matrix Analysis and Applied Linear Algebra" for the "matrix analysis" part (Perron-Frobenius stuff mostly) but it's structured in such a way that it includes an overview of all the linalg you need to know (even though it's meant as a book for a second course in linalg) and every chapter has some applications of the topic at hand. It's a great book

it's not really a book about applications of linear algebra but certainly something that any aspiring applied mathematician should read

[gray gazelle]

Any abstract algebra text which a high schooler can understand?

[marble solar]

Pinter

A book of abs. alg.

[tribal kernel]

Artin is a good book and probably the best place to start for a beginner

[quick hornet]

artin is good but it does expect a bit of mathematical maturity going in

ie either prior familiarity with proofs or the ability to pick them up with minimal aid

i dont think it gives an explicit introduction to induction for example

it just starts using it (and some students, of course, will be able to learn from example + consulting other resources)

[hearty steppe]

I also would go with Pinter, as I’m using that rn

[tribal kernel]

True. Abstract algebra is probably best the perspective of someone with some amount of experience in proofs and abstract math

[nocturne crane]

@timber mesa I'll take a look thanks

[trim narwhal]

Is Pinter better than Artin?

[hearty steppe]

Yes

Imo

I like Fraleigh too

[sage python]

Definitely not lol, Pinter is like... Borderline deficient tbh

It is a bit more accessible than Artin but honestly I don't think algebra should be your intro to proofs anyway

[valid moth]

i agree, hartshorne should be

[hearty steppe]

It seems a lot of people’s intro to proofs are linear algebra.

Or some comp math experience in grade school

[lost fjord]

False unfortunately

I'd say most people's intro to "proofs" is their geo class

[hearty steppe]

Didn’t happen for me lol

[lost fjord]

Well for kids my gen anyway

[timber mesa]

yeah for some reason people conflate "proofs" with their HS geo class, proofs in quotes b/c those are awful

https://www.maa.org/sites/default/files/pdf/devlin/LockhartsLament.pdf

[hearty steppe]

I never learned shit in grade school unfortunately

[timber mesa]

as for proofs in "college"/"higher" maths it depends on the major. For math people it's usually their first calc/analysis class and for like engis and stuff it's their discrete maths class

[hearty steppe]

Except how to read and write lol

Discrete maths for me just went over induction

Very Briefly

[lost fjord]

I only know the bare basics of proving stuff sadly (induction, contra, direct) and wouldn't consider myself proficient

I have managed to prove a couple of problems before and a couple of theorems

The nice thing about proofs imo is that you don't have to memorize them if you understand their core or getting it started

Since after that it is just fitting pieces together

at least how I feel

[timber mesa]

yeah I feel like learning proofs is essentially that; you learn both the language and intuition behind mathematics

[tribal kernel]

My first class after my intro to proofs was real analysis. Most people went to either algebra or linear algebra after intro proofs though

[timber mesa]

my department doesn't have an "intro to proofs" class but it was a part of first semester analysis

boy did it help

[tribal kernel]

I feel like I learned a lot more about proofs in intro analysis honestly

[timber mesa]

I don't think "proofs" should be taught in isolation really, it's all about why would we want to prove stuff and how do we go about it

even Hammack's Book of Proof (which I followed back in the day to learn proofs) essentially introduces divisibility and modulo arithmetic for the sake of creating interesting problems: http://www.people.vcu.edu/~rhammack/BookOfProof/

[tribal kernel]

Having a motivation definitely helps

My intro proofs books were mostly basic number theory and some intro analysis and algebra

Like it introduced sequences and modular arithmetic a little

[timber mesa]

I feel like that's exactly the moment to introduce proofs, in an intro analysis or elementary number theory class

if I were in charge of designing the curriculum for a math major I'd put exactly those two in first semester with a focus on learning proofs well

[tribal kernel]

At my uni analysis was considered the toughest undergrad proof class

So a lot of juniors took it

By that point you would likely have lot of experience with proofs

That was the idea anyways. We spent a lecture going over proof techniques and there were lots of in class examples from my professor, so I felt like a learned a lot more about proofs in that class than my actual proofs class

[quartz pawn]

Most intro to proofs class isn't really all proofs.

It's showing you proof methods but also introducing you to basic results that you can prove in a variety of different areas of math; at least that's how it should be.

There's no real reason to have a whole class dedicated to necessarily the proof techniques.

[tribal kernel]

Yeah that sounds good

[quartz pawn]

Cause those can be covered really in like 2 or 3 weeks.

[tribal kernel]

A lot of these classes are called “Intro to advanced math” or something like that

[quartz pawn]

My class we proved some basic result in a variety of different areas.

[timber mesa]

Cause those can be covered really in like 2 or 3 weeks.
@quartz pawn that's exactly how it goes in my department lol

[tribal kernel]

Supposed to be a kind of sampler of techniques and topics

[quartz pawn]

Yea

[tribal kernel]

Like how a lot of physics departments have “modern physics”

Introduction to a lot of techniques and topics, but not in depth on anything

[timber mesa]

in our calc 1 (probably more similar to analysis 1 in some euro unis) we skim over set theory, logic and then proof techniques directly stem from the fact that e.g. $$P\implies Q \equiv \sim Q \implies \sim P$$

[hasty eagle]

bastian.uwu:

[quartz pawn]

At my school, we didn't do that and I don't think it's standard in most schools in America.

I have friends who went to clemson and USC and they didn't do that.

At least they didn't mention it.

I just asked what they learned there and it was standard calc sequence stuff like at my school.

[timber mesa]

yep, in American unis I think it's more usual for the calc series to be mostly computational and then junior analysis is "rigorous calculus" and maybe an intro to metric spaces

[valid moth]

pretty sure real anal is done in soph year

or 1st for people with calc creds

[timber mesa]

oh well can't speak for sure

[marble solar]

No, it's not. Most of the time it's junior or senior year level

It's only freshman/sophomore for people that are coming in prepared/motivated for math

[valid moth]

are you talking about math majors

[marble solar]

Real Analysis has a 50% fail rate across the nation, among math majors

[quartz pawn]

That's pretty crazy

[marble solar]

Err..approximately that

Yes I am talking about math majors Archsys

Most math majors aren't ahead of the schedule

[broken meadow]

i come with calc credits and i don't even get close to real analysis

like

my sophomore year will have this thing called "advanced calculus" which should be like

baby real analysis

i have to take two semesters of this "advanced calculus" before i get to take Real Analysis

[lost fjord]

principles of real anal?

[broken meadow]

so the earliest i get to do it is junior year

and that's with hella credits

[valid moth]

@broken meadow https://www.youtube.com/watch?v=FSnuF1FPSIU

[broken meadow]

coming in

[marble solar]

The Real analysis course via Rudin used to be a graduate course. You'd take advanced Calculus your junior year - and then senior you take like fourier, pdes, and complex variables. Then in grad school you take Rudin

[sage python]

Wait like Baby Rudin?

Graduate?

[valid moth]

lol what

[marble solar]

You can see this in the preface to Rudin where he said this is for graduate courses

[lost fjord]

my irl friend sent me that vid too @valid moth

[marble solar]

Yes

[valid moth]

that makes no sense

[marble solar]

Baby Rudin used to be the standard first year grad real analysis

[gray gazelle]

[valid moth]

@lost fjord cool stuff

are they on discord

[marble solar]

The curriculum changed in the late 70's and early 80's where schools phased out the advanced calculus course

[lost fjord]

yes

they used to be on this server actually

[valid moth]

invite them to this server so we can listen to music

[lost fjord]

but they left for some reason

[marble solar]

Go open up rudin read the preface "This is an introductory graduate course in Real Analysis, or for advanced underclassmen"

something along those lines. If you have an old copy of Royden, it's the same

[marble solar]

Yeah, advanced undergraduates or first year students

That's no longer the case, since the standards changed

[sage python]

20th century undergrads were plebs

Jkjk

[valid moth]

true

[marble solar]

Some schools still have advanced calculus courses instead of real analysis

[sage python]

But yeah wait isn't Royden a step up from Rudin kinda? With its measure theory?

[marble solar]

Well Royden was a professor at Stanford from what I can recall

[lost fjord]

those are like magnet schools though

[marble solar]

So not exactly your standard first year program

[lost fjord]

sorry high schools

[marble solar]

Rudin was for standard first year grad AT MADISON

Sloth King

[sage python]

Yeah I'm not saying the particular schools were plebs

I just mean like

[valid moth]

hah pleb

[sage python]

The 20th century in general lmao

[lost fjord]

mfw there are hs teaching kids complex anal in 11th grade

[marble solar]

It's interesting, even abstract algebra has changed greatly since like the 60's

For undergrad curriculum

[sage python]

But yeah it's insane how fast that has changed

[marble solar]

Vector Calculus used to be junior/senior year course

[valid moth]

https://www.youtube.com/watch?v=o7zEwssiSVE they have pancakes

but pancakes is not listed on the menu

@lost fjord

[lost fjord]

I'll send this to them as well

[marble solar]

There are books that detail the change in undergraduate mathematics education throughout the 20th century

They're really interesting to read

[valid moth]

send them this @lost fjord https://www.youtube.com/watch?v=DTIZikaOTDE

[sage python]

I kinda feel like nowadays, it's pretty much required for undergrads to have Baby Rudin level real analysis, associated level of complex analysis, some interaction with topology, and intro to algebra, like group theory and linear algebra at minimum

[timber mesa]

There are books that detail the change in undergraduate mathematics education throughout the 20th century
@marble solar I find that topic very interesting, any recs?

[sage python]

To the end of going to graduate school, missing any of those feels like it's bad news

[marble solar]

Hrmm..none that I recall. I read these a few years ago now

Most ppl don't cover that @sage python

[sage python]

And then really to be competitive you have to have at least one of intro to grad algebra, analysis, or topology

[tribal kernel]

I feel like Royden is an easier text than Rudin, but it probably goes more in-depth with measure and Radon Nykodym stuff

[marble solar]

Most people coming out with a Math B.S. are coming out of liberal arts or large public state schools that don't offer that many advanced courses

Very few Math Majors in terms of percentage wise have that experience Sloth King

[sage python]

I mean I'm talking among people who wanna go to grad school in math, and at a "reasonably good" place

[marble solar]

But then again very few math majors get into top grad programs and produce research

Like what do you do if you're coming out of Reed?

[valid moth]

what's reed

[sage python]

Reed I think is uniquely good at producing grad students actually

Like they're the exception among liberal arts colleges

[serene crater]

in your opinion what are reasonable good places

[lost fjord]

what is being a math grad like?

what do you learn?

[valid moth]

i'd say don't aim below MIT

[sage python]

But yeah like, I only got Wisconsin/Washington/Notre Dame, out of 15 schools, and at the time of application I had already completed and received As in a bunch of math courses

Especially in analysis

[quartz pawn]

Daminark are you from America?

Or you just went to school in America

[sage python]

By that point I had taken undergrad honors analysis, undergrad complex, grad functional, grad complex, and a seminar in geometric measure theory

[quartz pawn]

Is that too much to ask?

[valid moth]

imagine not doing geometric music theory instead

this is why you didn't get into princeton

[quartz pawn]

I don't want to seem weird. I assumed you were from Denmark.

[sage python]

I am from America

[quartz pawn]

lol

[valid moth]

denmark

lmao

uh

[sage python]

It sounds vaguely like Daminark

[valid moth]

lol

ok niel kranimad

[sage python]

Archsys: that is possible

But yeah I didn't have as many courses in algebra and topology at that point, basically just the undergrad honors algebra class

But I did a reading course in algebraic topology and my REU paper on elliptic curves/number theory so idk

I felt like I hit all the main points reasonably well, and analysis hard

[serene crater]

If eu students want to apply, do they have to do it te year before getting their bachelors

[sage python]

Obviously Wisconsin is fucking excellent

[broken meadow]

man

[sage python]

And my GRE was 77th percentile which is still in the zone where it starts to hurt for top 6 schools

[broken meadow]

i have no idea what im doing

[valid moth]

who's excellent 😳

[sage python]

Don't ask

The less you know the better

[valid moth]

wait, dami is excellent

[sage python]

But yeah point is like, 3/15 is a low success rate

(Well I had pulled back apps from 3 places, let's say with high probability I was gonna get into Rutgers, with less probability Penn and Minnesota)

Anyway idk I feel like it's fair to say that hitting the main points in undergrad analysis/algebra/complex analysis/topology, and having at least one at grad level, is probably necessary for going to a top 25 school. And I'd almost wager it's hard to go to a top 50 if you're missing, maybe more than one of the "main points" courses

Probably

[marble solar]

If you see that all Calculus books say "With analytic geometry"

That's because the calculus sequence used to be 4-5 semesters

with one semester dedicated to analytic geometry

It was Thomas at MIT who came up with a way of shrinking it down to the three semesters in the 50's/60's

If you get an early edition of Thomas' calculus it says this in the preface

Yeah, but the thing is if you're at Reed or Mudd, or something you don't have the whole list of grad courses to take like ppl at Cal, Harvard etc. have

So you have to have a way of evaluating well-prepared students coming from these very good, but smaller schools

But @sage python UCI, UCSB, U of A, and Boulder are top 50 and students regularly get in without too much advanced coursework. They usually offset it with Good GRE scores + REUs

But I agree that modern day you really do need to finish ur algebra, analysis, complex, top to have a decent shot at it

@timber mesa http://www.ams.sunysb.edu/~tucker/MathHistory.pdf I read this and a few other things

[sage python]

UofA lol, it's an interesting place. I feel like a lot of schools in that zone have one thing they're disproportionately good at

[marble solar]

It is a very interesting school - they're really good at a few things, and not so great at many things

[sage python]

UofA is number theory, Utah is algebraic geometry, Stony Brook and Notre Dame are geometry/topology

[marble solar]

UofA has some really good analysts there too

like Sunhi Choi

Which is why I'm applying

[sage python]

Interesting, yeah idk analysis was off my radar for the most part when applying. Like I mostly looked for having a couple interesting analysts, and mostly as a bonus

e.g. I was originally hype af for UCLA, less because of Tao and more for the functional analysts there

I remember there were 2 in particular that made me swoon

[marble solar]

Liggett?

He's old now

[sage python]

Sorin Popa

[marble solar]

ahh I see

I never met them

[sage python]

Dimitri Shlyakhtenko

[marble solar]

like the only 2

permanent faculty LOL

[flint forge]

imagine liking multiple kinda of mat

[sage python]

Normally I used to say I liked most math except logic and differential geometry

[timber mesa]

@timber mesa http://www.ams.sunysb.edu/~tucker/MathHistory.pdf I read this and a few other things
@marble solar thanks!

[marble solar]

Math Ed. and the history of math education/curriculum is a super interesting topic

Too bad they both get bad reps

[sage python]

Except I think I have inadvertently let myself get roped into geometric analysis

So tbh everything except logic

And who knows maybe if I ever think about operator algebras too much I'll get roped into continuous logic or smth

No math is safe from me

[marble solar]

Yeah! Math history rocks

[raw herald]

I need to get better at making definitions for problems im working on

[vagrant sedge]

Hi. In the advanced channels section, there is a "topology-and-geometry" channel -- tbh I never thought of topology as something related to geometry. Is there a good book which makes the connection?

[marble solar]

It depends on what you mean by geometry

But Topology is a really powerful way of thinking about geometric things

In fact, you'd be hard pressed to do any geometry today without somehow using topology

[vagrant sedge]

I've never studied advanced geometry, really. I had an introductory to differential geometry course. I've used topology only in a measure theory and a functional analysis course.

The connection between topology and geometry wasn't clear to me from those things.

[marble solar]

How do you define a manifold?

etc.

The modern foundations of geometry are in topology

In some sense

[vagrant sedge]

Hmm... Is that the reason why the two are connected?

[marble solar]

The concepts are sort of entangled together - Topology gives you a very precise set of tools, and linguistic description to otherwise near unimaginable and indescribable events

[vagrant sedge]

Ok.

Any book on sort of teaching the two in a more integrated way?

[marble solar]

Alright we're going off the de\ep end. Yeah there are introductions to topology with pictures

I think Hatcher has an introduction that people seem to like

Be warned - what Topologists describe as what they study in youtube videos can seem very far removed from the basic definitions of what a topology is

It's kind of a slow train moving and you finally get to your destination

[vagrant sedge]

That is something I've noticed already based on the topology I had to study for functional analysis and measure theory.

[marble solar]

All that stuff is basically just the setup that you need to describe wacky things like alexander's horned sphere

[vagrant sedge]

Ok.

[valid moth]

horny sphere

[sage python]

o boi

[shadow nebula]

uwu

[versed sail]

which course or book will you people suggest for an overall understanding of linear algebra? I am learning this for machine learning and deep learning
currently in the 4rth lecture of 18.06 but I find the concepts a bit scattered. Might be my problem though, I am a complete newbie.

[timber mesa]

Jim Hefferon's book is pretty good at a more introductory level https://hefferon.net/linearalgebra/
@timber mesa I suggested this one a while ago

[sage python]

What book does 18.06 use?

[marble solar]

Strang?

[versed sail]

seems like the book focuses on linear algebra problems more than the abstract part of it
Prof Strang does a brilliant job at that
I guess a more concept oriented book will be better for me atm

[sage python]

Oh uh

That's a tough one to answer then

[versed sail]

What book does 18.06 use?
@sage python http://math.mit.edu/~gs/linearalgebra/

[sage python]

Most of the more conceptual books I know are a bit over the top for someone whose main goal is machine learning

Like it's damn good stuff but the treatment might be inefficient toward that end

[versed sail]

I get it
yes, being a complete newbie, I found linear algebra to be so interesting to dive into just for the sake of the abstract part of it
but yea, my main goal will be machine learning and deep learning in the near future

thanks for the suggestion though
I appreciate it

[sage python]

Hmm

If you want to learn some of the abstract part

Here's one people seem to like that's geared as intro to proofs

http://www.math.brown.edu/~treil/papers/LADW/LADW_2017-09-04.pdf

(I was wondering if you wanted this, which is the treatment math majors would have, vs something that's still "conceptual" but not necessarily "proofsy")

But having a bit of both would def be healthy

And if at some point proof-based linear algebra becomes too much of a detour you can buckle down on 18.06

[versed sail]

thank you

[hot prism]

does anyone have a pdf on basic number theory?

all the ones on the internet are complicated

I need one for like an Olympiad problem

nvm i got one, but pls send me any you know!

(I beg you 😭)

[pine igloo]

Number Theory: An Introduction to Mathematics by W.A. Coppel

@hot prism

[karmic thorn]

Burton's Elementary Number Theory is pretty neat as well.

Apart from that if you need something geared for olympiads, you can find many recommendations on the internet.

Lemme see which one's I have

[hot prism]

I am a student rn and i can't really afford any books, do you have any pdfs?

(i know i sound needy but i have an exam in a few months so im really tensed)

[stray veldt]

try libgen

[karmic thorn]

You can download PDFs from Libgen

http://gen.lib.rus.ec/

[hot prism]

what do i search exactly?

[hasty turret]

Name of your book

[hot prism]

o

but i need a book

to search

[pine igloo]

you can download books for free in pdf, djvu or epub form from library genesis and bookfi

[hasty turret]

Burton's Elementary Number Theory is pretty neat as well.

[hot prism]

you can download books for free in pdf, djvu or epub form from library genesis and bookfi
@pine igloo yea but i don't know any good books

[karmic thorn]

You just got two recommendations

Number Theory: An Introduction to Mathematics by W.A. Coppel

[hot prism]

they dont come up tho

[karmic thorn]

I'm pretty sure Burton's there

[pine igloo]

the book I gave you its name is kinda advanced, although it starts from elementary stuff

I'm pretty sure Burton's there
so search for this

[karmic thorn]

And I'm pretty sure the other suggested title must be there too.

[hot prism]

no wait i got it

[lost fjord]

[hot prism]

yea yea i got it

[karmic thorn]

http://gen.lib.rus.ec/book/index.php?md5=092C85139F980F063A2EF1063277768C

[hot prism]

thx guys!

[karmic thorn]

No problem.

[hot prism]

what button do i press?

[pine igloo]

yeah you press on elementary number theory above

in blue

then press on get

[velvet briar]

"Mirrors"

[hot prism]

h e l p

[pine igloo]

it happens

try again

[velvet briar]

After choosing your mirror, you'll get a download

[hot prism]

mirror?

o found it

[velvet briar]

On the page before, it said the file extension of what you're going to get

[hot prism]

which one?

On the page before, it said the file extension of what you're going to get
@velvet briar where?

oh

yea

[velvet briar]

I meant these haha

[hot prism]

yea found that, pressing random buttons hope it works

[hasty turret]

Welcome to the internet

[hot prism]

lmao

let's hope this download won't send me to the shadow realm

[hasty turret]

It is actually not easy to get to the shadow realm

[hot prism]

(wait the shadow realm is actually a thing? I meant it as a joke)

[hasty turret]

(Dark web)

[hot prism]

(oh that okay)

i did something and something happened

[hasty turret]

You got the book?

[hot prism]

yea

it looks like a book

it is a book

b o o k

[tall sky]

(responding to @quick hornet from Sep 11) HyperRogue could be played on an Euclidean hex grid, yes, but it would not be a good game. You could not escape from a group of enemies in the Euclidean hex grid, but you can in hyperbolic geometry. And the map would be very boring if you could not fit an infinite tree into it (there is an Euclidean mode to test this)

[wintry hazel]

Renteln's book is the best intro book for differential geometry don't @ me :-

[quick hornet]

@tall sky yeah, in hindsight thats a good point

[smoky surge]

what are yalls thoughts on George Casella and Roger Berger: Statistical Inference . I tried Ross probability models but i felt like it lacked motivation and the chapters dragged on

[hearty steppe]

Personally I feel like your general intro to stats and probability book is very dry. The problems also aren’t very challenging.

If it is a prerequisite your trying to get through and you don’t have too much trouble, seems like your doing ok. I use Walpole’s probability and statistics for scientists and engineers but even looking at other books, seems like it’s really just pick your poison.

[hearty steppe]

Personally I am a bit concerned when I am ready, that I have the right book to use for Stochastic Processes, which is basically where I hear the fun begins from all the time you spend learning all that dry material from probability and statistics, and additionally numerical methods.

[sleek python]

There's the classic Probability with Martingales from D. Williams, tho I'll admit I haven't looked at it much (and first part of the book seems to be about reviewing proba, second is martingales). I've seen it recommended in almost all my classes, as well as numerous times online.

Karztzas seems to be a classic as well, more about Brownian motion tho. Don't know either if it's good but I'll check it out soon probably.

An other book, that I haven't looked at but suspect it may be good since the author writes quality lectures is Brownian Motion and Stochastic Calculus from Jean-François Le Gall. I'll also check this one out very soon so I'll be able to give a genuine answer as to whether it's good.

Durrett's Probability:theory and examples seems to be an other classic, more general this time, that I also haven't checked out.

Lots of books that I haven't read but will since I looked into it only recently. Three of them are apparently "classics" so they may be suited to your needs

[limpid gazelle]

Anyone has a book recommendation for functional analysis?

[sage python]

Since you're learning some measure theory

[granite sluice]

Personally I am a bit concerned when I am ready, that I have the right book to use for Stochastic Processes, which is basically where I hear the fun begins from all the time you spend learning all that dry material from probability and statistics, and additionally numerical methods.
@hearty steppe IMO the fun begins when you study algorithms and get to learn all of these cool probabilistic algs

[sage python]

Try this one: https://www.springer.com/us/book/9783319585390

I didn't use it myself but my class used a mix of things, and at the end of the class my prof was like

Damn I should've used this one

My main book was Brezis which is p good

[granite sluice]

last chapter is on prime number theorem 😮 surprising for a FA book

[limpid gazelle]

Dami, how does me learning some measure theory relate to that book?

Does it assume measure theory?

[sage python]

I think? Feels a bit like it does

Definitely for Brezis you want measure theory

[limpid gazelle]

ok

[marble solar]

I like Stein's functional

if you can call that functional

I mean the book is titled functional analysis, so is it functional analysis?

[long bear]

What is a solid introduction to probability book?

[sage python]

Measure theoretic? My class is using Durrett

[marble solar]

Stein and shakarchi volume 4

chapter 5

See it's got everything

Those are pretty high level

Never learned probability without measure so idk

[hearty steppe]

I think Ross is fine for intro. Any intro prob stat book is going to be very dry and you'll find yourself getting bored of the meticulous level of difficulty of the problem sets. If you want to really do interesting stuff with prob stat, learn enough to do stochastic processes

you can probably get away with using the book im using, which is Walpole

[wise vine]

Is it okay to study Probability with measure theory without experience in non measure-theoretic probability? If so, is shiryaev's probability a good book for this? I'm asking because I am almost done with Tao's Analysis I (I'm actually doing the 2nd part too at the same time). I can't bear to read nonrigorous books anymore lmao.

[granite sluice]

thats what I did so yeah I think its fine. but at some point it pays to go and learn about all the pdfs and classical distributions and stuff, which you don't usually get from a measure theoretic probability book.

[gray gazelle]

Hello I have started to read the book How to prove it. It is well explained but there is not any answer to exercises. Then I go on internet here: https://www.inchmeal.io/htpi/. Then I have two questions: 1 do you think the solutions online are correct? 2 Is there a book like this but with solution included? Thanks.

Can I ask again in proof and logic?

[hasty turret]

Sure

[gray gazelle]

@hasty turret sure I can ask?

[hasty turret]

That server exists for doubts on proofs

[long bear]

@gray gazelle those solutions are correct as far as I've gone

They are quite old as well I believe

but the mod keeps viewing comments

makes uh revisions when necessary

[gray gazelle]

sol 2, b :
F = I’ll have fish.
C = I’ll have fish.

instead of F = fish C = chicken

@long bear his github has no blog https://github.com/0vais

I can not correct him

[long bear]

what

https://www.inchmeal.io/htpi/

[gray gazelle]

@long bear do you know what is github?

[long bear]

You're able to comment at the bottom of every solutions page

And yes I know what github is

Although I have no reason to use it.

Which problem are you having trouble with?

Looks fine to me.

[gray gazelle]

yes but C = chicken

just a typo

[long bear]

oh kekw

Yeah just scroll down

and write it

🤦‍♂️ me irl lol

lmao i'm an idiot

but yeah theres a comment section

at the bottom of every page

[gray gazelle]

I hav ehis email. I will send him an email

I found his email with a git command

[long bear]

Mk

https://tenor.com/view/power-sun-hands-gif-18534188

[limpid widget]

Good day. Working on Triangulation algorithm for low poly shapes. Is that book fine for this ? 🙂 https://www.amazon.com/Voronoi-Diagrams-Delaunay-Triangulations-Aurenhammer-ebook-dp-B00GNTCKIM/dp/B00GNTCKIM/ref=mt_other?_encoding=UTF8&me=&qid=

[long bear]

I'm also in need of a book

I don't like Lang's introduction to linear algebra

Any alternatives

[gray gazelle]

I mean I can get answer online. But I want a step by step book for solutions

[vocal hawk]

Is there a good book/resource for recurrence and generating function type probability questions?

My probability course has a ton of these questions and recommends Sheldon Ross for reference but I can't find any questions of that variety in it

[hasty turret]

You might like generatingfunctionology

[vocal hawk]

A bit above what I need but it looks interesting, thanks!

[hasty turret]

Pretty sure generating functions are a pretty big deal

[brittle latch]

anyone know where i can find a pdf of spivaks calculus

cant find it on zlib :(

[hasty turret]

Just google it

[brittle latch]

huh

that was easy

lol

[sullen horizon]

cant find it on zlib :(
@brittle latch It is there

just search "spivak"

[pulsar aurora]

Also on Libgen

[sleek python]

never heard of zlib before :o

[hearty steppe]

With Intro to LA by Lang I didn’t waste my time reading most of the proofs. The examples are spot on

His proof writing is strange but he gives some great examples compared to other LA books I’ve read

[versed pawn]

Can you suggest me some real analysis problem books for putnam

I know Putnam and beyond...but i need more

Both hard and moderate problems on real analysis

[marble solar]

Pugh real analysis has a bunch of problems

can't say about its relation to Putnam

[hearty steppe]

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.

[marble solar]

It's a really intense math test

Most ppl get 0 points

[quick hornet]

I'm not sure I'd call it a "math IQ test" lmao

its a competition

there's a correlation between competition performance and performance in mathematical coursework (or research), but its not one-to-one

[flint forge]

wealth

[quick hornet]

every time a quora link pops up in a google search, i start hating myself for stooping so low as to search up a question that someone on quora would ask

nah i only score 70 on iq tests

[sleek python]

What is Putnam

I thought it was a book (or rather an author) when guy above mentioned it

[flint forge]

a math competition

[sleek python]

Oh so he's looking for prep boojs to it

[quick hornet]

excellent deduction chief