book-recommendations

[gray gazelle]

1355 results

you have also been very active in the server

13,258 results

[hollow peak]

it's very easy to be distracted by this server, but to be fair where else would I go for math help

[gray gazelle]

math stackexchange?

[dense wren]

for the fun

[hollow peak]

banter with other graduate students

[gray gazelle]

[granite sluice]

I'm here for banter, as bacono says. Since IRL department lounges are not a thing for the forseeable future.

[hollow peak]

yeah, I'm kind of isolated from other math people from my college until putnam training starts up I guess

everyone else is taking calculus

at least in my cohort

[granite sluice]

back in ye olden times I'd get more satisfying social interaction, e.g. shared meals with friends, that would satisfy the same banter quota more efficiently.

[gray gazelle]

I don't even need math help. Why am I here?
I don't know if I need math help tho I've certainly not done anything except banter in this server

[granite sluice]

Yeah. It was nice to feel part of a (physically present) community.

[gray gazelle]

It's also weird that #chill and #discussion are the most active channels in a math server

[hollow peak]

At the bare minimum this has absolutely been the most productive I've ever been at studying math

I have nothing else to do so no excuses

[gray gazelle]

[timber mesa]

I should too

[hollow peak]

godspeed ultra

[timber mesa]

I miss colloquia a lot, weirdly.
organizing online colloquia is kind of fun, fills the banter quota if it's a student one

[granite sluice]

zoom talks are just not the same.

at least when it comes to bonding activities, but also learning.

[marble solar]

I agree crustle

[timber mesa]

I know.

[warped sluice]

Is the book Advnaced Linear Algebra by Steven Roman recommended for undergrad students ?

[quick hornet]

certainly not for a first course in linear algebra

as a second/third course if you've already seen some rigorous theory of vector spaces, maybe

but it's not an easy text without good background

(even with background it's not an easy text)

how much linear algebra do you know?

[warped sluice]

I'm actually taking a course on Quantum Mechanics and like I wanted a book to help me with the vectors and the linear algebra used in QM...

[velvet briar]

I've read and enjoyed a fair amount of it, coming from the point of view of someone who has learned proof based linear algebra

[quick hornet]

i'm unconvinced that roman will help with QM lin alg all that much

although idk how mathsy your QM course is

QM courses range from "very mathsy but computation heavy" to "very mathsy and fairly theory-heavy"

roman might help with the latter, but if youre struggling with the LA in the QM course, i doubt you're "prepared" for roman honestly

[warped sluice]

Well it's the second option

[quick hornet]

roman expects a lot of mathematical maturity

i mean, it's literally marketed at graduate mathematics students

[warped sluice]

Ohh them I don't think so I should read Roman right now

Maybe I'll start with Gilbert Strang

I mean yeah what you're saying is true trough... LA in a QM course is fairly easy and if I like cannot follow that I prolly shouldn't pick up a Grad text book

[velvet briar]

Most physics students will not care about mathematical treatment the way Roman does. But I admit I know little QM I don't know if you may be the exception

[warped sluice]

No no... I'm fluent enough with bras and kets

The thing I'm not fluent with is with the Hilbert Space stuff... I just cannot get myself to understand what it means

Yeah I know all the properties and stuff

[tribal kernel]

@warped sluice Kreyzig has a good book on functional analysis with a chapter of spectral theory applications to QM

[warped sluice]

But I cannot understand the core concepts

Yeah

[tribal kernel]

Very applicable to QM cause it’s infinite dimensional Hilbert spaces that make up the vectors

[marble solar]

Self-dual stuff is as easy as 1/2 + 1/2 = 1

duh

I go for the low hanging fruit

[warped sluice]

Okay so it's like the math in physics isn't that hard?

[marble solar]

Something something L^p and L^q are duals when 1/p + 1/q = 1

So for L^2 it's just 1/2 + 1/2 = 1. It was a bad joke

[tribal kernel]

Holder conjugates

I like

[quick hornet]

yeah dont go thinking that like

the math used in QM is easy or whatever

especially if your first real time playing around with it is the QM course

[tribal kernel]

Ba dum tis

[warped sluice]

Idk Holder Conjugates

[quick hornet]

its like trying to learn to drive while in the Formula One

[warped sluice]

All I know are Hermitian Conjugates

[tribal kernel]

Not quite the same but both are useful for QM

[warped sluice]

So the point is I won't need Steven Roman for QM is what I'm taking away from this dicussion

[tribal kernel]

For holder conjugates the duel of L^p as a vector space is L^q

Or normed vector space

But yeah

[warped sluice]

Ohh okay thanks!!

[tribal kernel]

But yeah some concepts from functional analysis might be what you want to look up of you want to learn some math theory for QM.

[granite sluice]

The important thing to know about Hilbert spaces is that all bras have corresponding kets and vice versa. This is called being self-dual.
@sweet lotus Kind of like they are soul-mates.

[warped sluice]

But yeah some concepts from functional analysis might be what you want to look up of you want to learn some math theory for QM.
You suggested Kreyzig right? I'll defo take a look into it.. @tribal kernel

[tribal kernel]

Kreyzig is good and it doesn’t suppose you’ve seen measure theory before or really make use of it. Measure theory is necessary for the construction of the Hilbert space you work with and for the more technical aspects for he theory, but if you want a more thorough big picture understanding, I think Kreyzig will do you well

[sage python]

Did someone say Hilbert space

[tribal kernel]

Uh oh

Yes?

[velvet briar]

Like, a mathematician would care about what properties are preserved and changed under a change of basis. A physicist would just pick a basis haha. It's not that the math is harder, but you can easily get bogged down in details that aren't important for your application

Kreyzig was good though, not that I've gotten through much of it, sadly D:

[warped sluice]

Ohh okay I'll take a look into Kreyzig...let's see if I can understand

[tribal kernel]

Yeah that’s why I wanted to suggest an functional textbook that didn’t assume measure theory. That’s important for the theory and justification for the mathematical steps one might take in a physics problem but not of too much concern to a working physicist

[warped sluice]

The thing is that I looked for an online course on LA for QM but I couldn't find one so I ended up taking the LA for ML on Coursera, and it wasnt that great though... It was just basics with some early Uni stuff..
So, then I kinda understood that no online course would help it'll be better if I switch to a good textbook...

[tribal kernel]

What’s ML?

[velvet briar]

Machine learning

Which, admittedly, doesn't need too much LA haha

[tribal kernel]

Ah okay. I imagine it’s useful but mostly in a finite dimensional context

Did a tiny bit of ML in a class and it was mostly SVD

[warped sluice]

Yeah ML does not need too much LA but I ended up watching the course and wasting my time 😅

[warped sluice]

Okay so Kreyzig is exactly the kind of book I was looking for...
Thank you so much!!!

[hearty steppe]

Hey man it’s never a bad idea to learn more LA

[gray gazelle]

learn NF

[hearty steppe]

NF?

[gray gazelle]

yes

most useful area of mathematics

[hasty turret]

Number fractals?

[gray gazelle]

no

[long bear]

new foundations

[gray gazelle]

^

[hearty steppe]

Why is that

[gray gazelle]

ull understand once u understand it

[granite sluice]

[long bear]

100% creamy's alt

no doubt about it

[gray gazelle]

i thought u said im meaty person

[long bear]

meaty = creamy

stop trying to play dumb kekw

[gray gazelle]

ew

idk how to convince u otherwise

just cuz i have a empty pic, and boring name

dont meen im an alt

[long bear]

your typing patterns are the same as well kekw

[gray gazelle]

sounds like selection bias or something

im just probably a person who memes in similar ways

help me with my geometry hw in #geometry-and-trigonometry

@long bear

[long bear]

https://tenor.com/view/robert-de-niro-watching-you-eyes-on-you-looking-at-you-gif-12301153

[gray gazelle]

one day, the real meaty whatevers gonna appear and be like "wtf"

i think this is a sign that u infact "love meaty creamy chonkers"

[hasty turret]

Well, That is the not meaty's alt's name

[warped sluice]

Hey man it’s never a bad idea to learn more LA
Yeah i totally agree to this

[tribal kernel]

Okay so Kreyzig is exactly the kind of book I was looking for...
Thank you so much!!
Glad to hear! No worries! 🤗

[hearty steppe]

What book @tribal kernel

[gray gazelle]

fun anal

[hearty steppe]

Is it a lot of fun?

[tribal kernel]

Lol it's Kreyzig's Functional Analysis

[smoky surge]

if there are video lectures to accompy a book do yall recommend the reading or watching the lecture first

Which, admittedly, doesn't need too much LA haha
@velvet briar really? If you do to the AI channel they will tell you the opposite

[silk quartz]

Skim the reading, watch the lecture, then study the reading.

Maybe?

[smoky surge]

nearly every active person on this channel has studied more math than me so its helpful to get tips

[dapper root]

tbh man, IDK

it kinda depends on how your prof lectures

some of them just regurgitate the book mostly in which case reading it can probably be left for after

but some of them reference specific examples, expand upon points, etc.

if you want to be safe skimming it then going to lecture then reading probably covers all bases, but isn't the most time efficient probably

[smoky surge]

eh I have more time than I know what to do with atm so

[dapper root]

Just read it twice then haha

once before once after

this is dependent on the difficulty

if it's a really difficult class for you or high level or whatever I think this is legitimately a good idea

e.g. me with Hartshorne

I've reread earlier sections a few times (mainly since I decided to go about learning it again)

and each time it's definitely far more elucidating but this is also a more longterm kind of thing

[smoky surge]

fair enough lmao thanks!

[dapper root]

[hearty steppe]

I always read a chapter at least twice

unless the material is like super trivial and its just some really easy gloss over stuff

[dim venture]

Hi everyone. I'm a sophomore student at UCSC but I'm learning PDEs from University of Illinois

Their recommended book is Intro to PDEs by Brown Professor Walter A. Strauss. I'm finding it extraordinarily hard to get through and understand. It feels like he'd glossing over some important and possibly trivial details that the reader is just expected to know but aren't really clicking with me

Does anyone know of say supplemental lecture notes or of another textbook that follows Strauss' book but is just more digestible

?

[gray gazelle]

i don't know much about pdes or that specific text, but i've heard good things about evans' book on PDEs

might be worth checking out

[dim venture]

Do you have link?

[gray gazelle]

libgen

[dim venture]

oh gotCHA

thanks

[gray gazelle]

ah wait i mgiht have a pdf

one sec

like i said, idk if this is what you're looking for, i've just heard good things about it

[dim venture]

Ok Thanks

[marble solar]

No @gray gazelle Evans is a significant jump above strauss

[dim venture]

Oh Hi @marble solar

[marble solar]

@dim venture What're you going over in PDEs?

[gray gazelle]

ah alright, i see moonbears

thanks for letting me know

[marble solar]

Strauss is the standard intro upper div PDE book

Evans is the standard intro grad PDE book

[gray gazelle]

i see

[dim venture]

@marble solar

Syllabus for my Class

Seems kinda standard stuff, but Strauss is just not making sense to me

[hearty steppe]

Usually the very first chapter or two can be read over once or skimmed if its an intro book

[marble solar]

where in the course are you on?

[dim venture]

The early stages

Its a self-paced

Enroll anytime college credit course

[marble solar]

so first/second bullet I'm assuming

[dim venture]

Yeah

I'm right there

Thanks for taking the time @marble solar

[marble solar]

I've heard this book P.J. Olver, Introduction to Partial Differential Equations, Springer, 2014.

Is decent

[dim venture]

ah cool

Thank you

Libgen here I come

Now I'm not sure how it might be familiar to or different from Strauss

[marble solar]

Yeah, neither am I

[dim venture]

Should I also try and look for some lecture notes or simplification of Strauss to help me along?

[marble solar]

I never did undergrad PDEs, so I'm trying to extrapolate from what others are saying

[dim venture]

Gotcha

[hollow peak]

terra is just my go to for illegally downloading textbook pdfs at this point

whenever one is posted i click download

[dim venture]

Haha

Thanks @hollow peak

[gray gazelle]

ill dump the entire spivak diffgeo set

so you dont have to go through the trouble

moonbears jumping in joy rn

[dim venture]

@marble solar By the way, nice PFP. For a moment, I thought you had Doomguy as your profile photo. Then I just realized that it wwas a frog

[gray gazelle]

you might say he's on the moon

[dim venture]

@gray gazelle Yes please

[hollow peak]

you've singlehandedly destroyed the publishing industry from the inside out

[marble solar]

I mean Spivak's publishing company is publish or perish

[gray gazelle]

i choose the latter

[marble solar]

I wish I got the chance to meet him

My CC prof. met him a few times for research

I thought that was so cool

[gray gazelle]

@dim venture i don't mind posting them after this algebra lecture

[dim venture]

@gray gazelle Oh are you in class right now?

[gray gazelle]

yes

it is slow so i'm tabbed out

[dim venture]

@gray gazelle Thanks for multitasking

[hollow peak]

does spivak cover modern diff geo stuff? like tu does it super algebraically and then does stuff with cohomology toward the end

I imagine book one is classical, but I have no idea what the other books cover

[gray gazelle]

i think book two covers the "classic" stuff

book 1 covers the same stuff as tu's introduction to manifolds, but with a bit more

[hollow peak]

interesting, I was under the impression that it was closer to do carmo but now I am intrigued

[gray gazelle]

frankly i don't have a great idea of what books 2-5 cover

i know one of them goes hard into classic diffgeo though

(where i say classic to mean do carmo curves and surfaces type stuff)

low dimensional riemannian geometry

[dim venture]

I've never heard of this Spivak and his textbooks. What's so amazing about him and his books?

[hollow peak]

yucky 2d and 3d regular surfaces

spivak is a really good writer and usually writes good exercises from my understanding

[dim venture]

Oh alright

[gray gazelle]

I agree with bacono here.

[dim venture]

Guess I gotta check him out too. Is he an undergrad or grad or both author?

[gray gazelle]

both ig

[hollow peak]

both

[dim venture]

Ok

[hollow peak]

spivak calculus is really fun from what I've seen, I've been helping my friend who's never seen proofs before through it and it's been a good refresher for analysis on R specifically

I myself never used it to learn though

[gray gazelle]

the line between undergrad and grad is kind of blurry, but i'd say that
calculus, calculus on manifolds - undergrad books
comprehensive intro to diffgeo - somewhere in between to purely grad
in my opinion

[dim venture]

Is his Calculus a "Calculus" book or is it an "Analysis" book

[marble solar]

Spivak does a few things quite well. Ordering of topics, good prose, just the right amount of detail, and funny one liners

[gray gazelle]

stokes' theorem is trivial

[dim venture]

AH he's that kinda guy

[marble solar]

Plus a plethora of difficult exercises

[gray gazelle]

im ignoring this lecture lol

we are reviewing signs of permutations for the uh

third time

[marble solar]

Comprehensive introduction to diff. geometry is definitely at the grad level for most schools

[hollow peak]

what class is this terra

I am ignoring my logic lecture at the moment

[gray gazelle]

algebra

[hollow peak]

universal instantiation kinda do be really fucking boring

truth trees will be the death of me

[gray gazelle]

comprehensive intro to diffgeo (book 1 at least) seemed suitable for my undergrad diffgeo course

i really don't know what the line between ugrad and grad is lol

coming from me, an undergrad

[marble solar]

Some of it is, but there are things/exercises in there that are definitely at the grad level

[dim venture]

Ah ok

[gray gazelle]

any examples in particular?

just curious to see what you consider grad level

to be fair i am kind of talking out of my ass

[marble solar]

Chapters 3, 9, 10 and 11

I'd put solidly at the grad level

That isn't to say they aren't accessible to most math majors

But what it is to say, is that the background required to do that stuff requires some basic analysis, topology, and algebra

Which is what ppl usually cover across their junior-senior year

[gray gazelle]

are those years 3,4?

[marble solar]

Yes

[gray gazelle]

we don't use those terms in canada lol

ty for clarifying

[marble solar]

Remember, for most math majors

Rudin is too difficult

for baby analysis

[dim venture]

Are you talking about Rudin "Principles of Mathematical Analysis"?

[marble solar]

Yes

[dim venture]

Fucker

[gray gazelle]

i can hear my prof's cats meowing

[dim venture]

I just bought that book

Thinking I could read it

[gray gazelle]

rudin is a good reference at least

i use it a lot, despite having never read it for a class

[marble solar]

Eh even at that it fails, since it doesn't have a whole lot of detail

I think it's at rough-lecture notes

[hollow peak]

sometimes I forget the vast majority of math majors are not crazy people and just do it for job experience or interest

this discord is just filled with crazy people

[marble solar]

Yes ~ keep this in mind. I mean really think hard on it

[gray gazelle]

highschoolers learning x topic

whatever you're learning, some highschooler here is learning it too

Is there a “rigorous” entry to group theory? I obviously developed a lot of facets of group theory as i majored in math and physics but I don’t think I ever got a proper, comprehensive affiliation with group theory

[marble solar]

Richard Elman Lectures on abstract algebra

[hollow peak]

whatever you're learning, some highschooler here is learning it too

"can you solve this problem for korean second graders?"

clearly a usamo, imo, etc. geometry problem

[gray gazelle]

962 pages?

I’ll probably just look at the group theory sections

just be me and not compare yourself with anyone

i'm not a korean second grader

assign the jacobian conjecture to a korean second grade math class and see if you get a solution

it's not the hardest statement to understand so clearly they can solve it

[marble solar]

Oh Elman got to 962? Man he's been working at it like crazy

When I took the course it was at like 600 or so

[gray gazelle]

Imagine making a 962 page “lecture notes” with exercises and not bothering to sell it

Good man

will people get mad if i dump spivak's 5 volume set here

i said i would but i dont want to spam

[hollow peak]

anarcho-syndicalism formed entirely of mathematicians

free flow of information

[marble solar]

I think eventually he's gonna send it out for publication

[steel viper]

jacobson is good

artin is also good

[marble solar]

Elman lectures on abstract algebra is the best I've read

I think it supersedes all the other standard ones

[steel viper]

jacobson is nice because it covers a lot of stuff while still being concise and also very readable

[gray gazelle]

Ive gone through Artin

[steel viper]

i mean

[gray gazelle]

Wouldn’t call that a rigorous entry into Group Theory though

[steel viper]

it is lol

[gray gazelle]

His algebra book?

[steel viper]

intro group theory stuff anyway

yes

what is unrigorous about it

[slender sphinx]

Artin is quite rigorous imo; any specific section feel loose to you?

[gray gazelle]

I can’t distinctly recall because I took the course 2 years ago but I remember going from group theory directly into a bunch of linear algebra stuff? Maybe it was the course instructor or curriculum though

[slender sphinx]

Artin starts with Linear Algebra into Group theory

[steel viper]

artin is purposefully structured to weave linear algebra and an intro abstract course together

that doesnt make it not rigorous tho

[gray gazelle]

I might have misspoken on needing a “rigorous intro” then

[steel viper]

idk if you mean "covers further material" or "does the same material but 'more rigorously'"

[gray gazelle]

Both

[hollow peak]

is it worthwhile to go through artin if I know LA already

[steel viper]

the latter is like... idk maybe aluffi treats things in the context of categories? i guess? lmfao

[dim venture]

@gray gazelle Please deliver the goods. Thank you

[steel viper]

the former is like idk it depends on what u wanna do in algebra

[gray gazelle]

These Elmer notes seem promising though

[steel viper]

rep theory is an option

[slender sphinx]

@hollow peak just skip the first few LA chapters which should just be review

On that note, I need a book rec for rep theory

[steel viper]

why does the university of alabama think i am going to apply

[gray gazelle]

is it ok if i dm them @dim venture? there are 5 books so i think it'd be spammy

[steel viper]

when im oos

[dim venture]

@gray gazelle Yes please

Thanks

@gray gazelle Anytime you're ready

[steel viper]

@marble solar these look like they overlap heavily with jacobsons vol 1 and 2

i think

maybe jacobson has a little more content in random things like lattices

[marble solar]

Yeah they do ofc, but the exercises/problems is where this really shines

And the section on modules is great

[steel viper]

jacobsons exercises are okay

his exposition is really solid though

hes very good at bridging from topic to topic and making the progression feel very nat ural

[hollow peak]

@gray gazelle if it's not a hassle I would appreciate the books as well, thank you

[steel viper]

are they not on libgen?

[hollow peak]

yeah but libgen is so slow

[steel viper]

is it

i feel like that depends on browser

its really slow for me on firefox and like

normal on chrome

also lol my prof isnt letting me into the class

[hearty steppe]

Yes Artin is pretty dense. A lot of people like throwing densely packed recommendations on here. Not that they're bad, but I mean I guess a lot of people here don't rely on books to learn

[sudden kindle]

What's a good book to learn rep theory?

[sage python]

I think the three kinda standard recs are Serre, Fulton-Harris, and Etingof + n other people

[granite sluice]

Sternberg's Group Theory and Physics, and 'Linearity, Symmetry, and Prediction in the Hydrogen Atom' are also interesting options.

Actually one of my favorite books for intro rep theory is 'Expander Families and Cayley Graphs' , you get to see some nice applications to graph theory and computer science.

[dapper root]

When people give recommendations for rep theory

is this all group rep theory?

or do the books cover over kinds of rep theory?

[granite sluice]

The ones I mentioned are only group theory.

(Well, maybe some Lie algebra stuff also.)

[sage python]

Etingof's got a mix

Fulton does Lie stuff

Along with a prelude on finite groups

Serre is very finite groups

[small haven]

Looking for the solution manual for “discrete mathematics with graph theory, third edition” by Edgar b Good. Already checked lib gen and it is no longer in print. Can someone help me out, or worst case scenario, recommend a newer book?

[gray gazelle]

Is the Rudin book in #books-old Baby Rudin or big Rudin?

[quick hornet]

people use "big rudin" as a term all the time

for rca

[dapper root]

Wat

[broken meadow]

humongous rudin

[dapper root]

Then what the heck is functional?

Really fucking big rudin?

[quick hornet]

in this naming scheme? not given a nickname

its a more niche text

relatively

[dapper root]

Smh

[gray gazelle]

Hahah got it

Humongous rudin?: 👀

Are they different titles? or the same title with different eds?

[dapper root]

Different

It’s a series

[marble solar]

@quick hornet Baby, Papa, Grandpa Rudin in that order

@dapper root

[gray gazelle]

i dont like this baby/papa/grandpa thing. grandpa rudin makes me think of some old wrinkly dude

[quick hornet]

why am i being pingd

oh chmonkey deleted their message so mine makes no sense

chmonkey was complaining about the term "big rudin" instead of "papa rudin"

[marble solar]

Oh sorry, I just read the msg above

RIP

[quick hornet]

despite them being synonyms

[dapper root]

Oh I deleted it since I made a false claim lol and figured “eh okay guess this shit’s not needed”

[noble kettle]

Hey Im trying to review for the GRE can someone give me a good recommendation for a book I should use something that is best for review for the math portion would be fantastic?

[lost fjord]

I though func rudin was grandpa rudin

[valid moth]

yeah

[gray gazelle]

what is great grandpa rudin?

[sleek python]

I thought real and complex was baby Rudin

What's baby Rudin then

And grandpa

[tribal kernel]

What’s functions on polydisks then? Ancient Rudin?

[hasty turret]

Ultra Rudin

[white pebble]

hi peeps

has anyone used applied linear statistical models

i have it for med stats

[crystal kraken]

What’s functions on polydisks then? Ancient Rudin?
Great Grandpa Rudin

[cobalt arch]

Can someone recommend me a book on set theory proofs only?

Is there such a book?

I mean set theory by itself has many books about itself but I want to know how to prove intersections, unions, symmetric differences etc.

[gray gazelle]

maybe this one

[cobalt arch]

It is promising but this is a text on set theory itself. I would like specifically to know how to do proofs using set theoretic tools. Maybe I need to study set theory itself..

But I would like to know how to do proofs for exercises like the ones below.

[pine igloo]

you should use logic laws and inference rules

like for example, $(\forall x, x \in A \cap A) \iff (\forall x, x \in A \land x \in A) \iff (\forall x, x \in A) \$ Thus, by the extensionality axiom, $A \cap A = A$

[hasty eagle]

Patrick Salhany:

[cobalt arch]

I did prove this the same way.

It seems that I have to focus on arbitrary elements of sets to prove these.

[pine igloo]

you should also know like at least the first six axioms of the Zermelo-Fraenkel set theory, for the sake of understanding the usual set operations

[cobalt arch]

Hm

Does that apply to naive set theory?

[pine igloo]

I would say f naive set theory

[cobalt arch]

Because axiomatic set theory differs

Ok hahaha

[hasty turret]

I would say f naive set theory
Y

[hollow peak]

you can do all of those proofs with venn diagrams

[pine igloo]

or if you want to study it, I know that it is a matter of taste, check out Paul Halmos' book

[cobalt arch]

I know but I want more of a logical approach like the one Patrick used above instead of a more intuitionistic approach like venn diagrams.

[hasty turret]

What is wrong with naive set theory?

I don't think it matters much in non logic math

[pine igloo]

Y
I guess when someone understands a bit of ZFC set theory the axiomatic way, stuff become clear, in my experience
like you can do those proofs in naive set theory, but actually they feel harder

[hollow peak]

I mean, if you know the axioms and definitions of set operations then usually those basic proofs follow immediately from definitions

[cobalt arch]

If it is the case that I learn how to prove these using the axioms and logic of zfc I would prefer it.

[pine igloo]

I know but I want more of a logical approach like the one Patrick used above instead of a more intuitionistic approach like venn diagrams.
read about the first six axioms, understand them and you'll be finewhen it comes to set operations and proving all of the properties in the pic you sent

[cobalt arch]

Hm

Okay Patrick

Ty

[pine igloo]

you can do on scratch some Venn diagrams too, great for intuition

[cobalt arch]

Yeah ig

Thank you all

[pine igloo]

lemme tell you the axioms you should read about
extensionality axiom
empty set axiom
pairing axiom
union axiom
subset axiom schema
power set axiom

read about the regularity axiom too, you can skip infinity axiom, replacement axiom schema and the axiom of choice (for now)

also, try to prove that the empty set is unique

[cobalt arch]

Hm is the infinity axiom about there being at least the set of natural numbers?

The empty set is unique because if you took {}1 and {}2 they both contain no elements therefore they are equal.

Is that right?

[pine igloo]

it allows the existence of inductive sets

[cobalt arch]

Oh okay

[pine igloo]

and then you can define a natural number as element of every inductive set

hence you have the collection of natural numbers

[cobalt arch]

Yeah

[pine igloo]

you prove that it is a set

and that it is the smallest (as inclusion) inductive set

[cobalt arch]

I see

[pine igloo]

The empty set is unique because if you took {}1 and {}2 they both contain no elements therefore they are equal.
intuitively yes, here you used indirectly an axiom of the ones I listed above
try to guess which one, and use some nice property in logic, and you completed then the proof

[cobalt arch]

Smallest as in cardinality? The odd and even numbers can be considered as the smallest sets as well since they have a 1 to 1 correspondence with the naturals therefore their cardinalities are the same which means that they are of equal size.

[pine igloo]

smallest as inclusion

[cobalt arch]

I don't know what inclusion is:D

[pine igloo]

the set of natural numbers is included in any other inductive sets

don't worry about cardinals now

I don't know what inclusion is:D
being subset of

[cobalt arch]

I am also a non-native English speaker.

So yeah..

[pine igloo]

I am also a non-native English speaker.
same here lol, english is my third language XD

[cobalt arch]

Haha nice:)

Which languages do you know?

Except for English of course

[pine igloo]

arabic is my native language
french is my second language
and english is my third

[cobalt arch]

Nice

I know Greek and some Finnish which is not an indo-european language:D.

[amber furnace]

Hello,
Any good book for differential equations advanced math?

[marble solar]

Evans PDEs is quite excellent

but that is advanced

[amber furnace]

Cool

And any suggestions on good B.sc and M.sc math books?

[marble solar]

Stein and Shakarchi Fourier Analysis for B.sc. Stein and Shakarchi Real Analysis and Functional Analysis for M.sc

[amber furnace]

Thanks a lot!

[marble solar]

For Complex Analysis I like Marshall or Ahlfors a lot

For topology, I believe munkres is the standard. If you want to go further in topology there's Hatcher's Algebraic, Milnor's differential. My personal likes are Knots Knotes by Roberts? The notes are free pdf online

If you like Knots Knotes you can try Schulten's 3-manifold Topology, but that's a hard book to read

[amber furnace]

Awesome, I've been struggling to select good books, thanks man!

How about Joseph Gallien for linear algebra?

[marble solar]

Oh, Charles Chapman Pugh Real Mathematical Analysis is a good alternative to Rudin

[amber furnace]

Oh, Charles Chapman Pugh Real Mathematical Analysis is a good alternative to Rudin
So which one feels easy to go with?

[karmic thorn]

Pugh all day long.

Are you talking about Gallian's Contemporary Abstract Algebra?

[amber furnace]

Yeah

[karmic thorn]

I have it too, it's good.

[amber furnace]

Great!

[gray gazelle]

Are there any short expositions (online or otherwise) on methods of proof (a whole book on this topic would be overdoing it imo)

[karmic thorn]

I'll grab a link.

https://www.d.umn.edu/~jgallian/Proofs.html

@gray gazelle

[broken meadow]

lol

a whole book on proof you say

Enter Hammack.

there are some more tho too

[karmic thorn]

Velleman is another I remember.

[broken meadow]

yea

[stray veldt]

just read my pdf

[broken meadow]

chartrand

[karmic thorn]

And another one by Lochverstarker

[gray gazelle]

velleman is an example of overdoing it

[broken meadow]

i am taking

[karmic thorn]

I finally got Loch's complete name right, obviously with the missing umlaut on a

[broken meadow]

a whole semester

on introductory proof

[stray veldt]

i should just rename to Loch at some point

[karmic thorn]

Your current username sounds like a battleship so it's cool.

[broken meadow]

Loch Lomond

[lost fjord]

The lochness monster

Loch n loaded

[karmic thorn]

Same thought struck my mind @lost fjord

[gray gazelle]

loch lomond was honestly what came to mind my mind when I heard 'loch'

[broken meadow]

i wish to play loch lomond by ticheli one more time

[karmic thorn]

Lochness monster is what came to my mind.

[stray veldt]

i mean, it's the same word

[hasty turret]

[gray gazelle]

yes

[stray veldt]

in german you can build new words pretty easily

and this is just Loch + Verstärker

where Verstärker is the noun created from the verb verstärken

which is again created from the adjective stark

[gray gazelle]

which means?

[stray veldt]

stark = strong, verstärken = strengthen, amplify, Verstärker = amplifier

Lochverstärker = hole amplifier

[lost fjord]

Wait loch I might be stupid but

?

[hasty turret]

Yes 0=0(1)

[stray veldt]

what is that question

oh

0 | 0

because 0*0 = 0

or 0*k = 0 for your favorite integer k

[lost fjord]

Ig I understand the reasoning, I just find it weird

[stray veldt]

that's fine, but it follows from the definition

[lost fjord]

yeah

ok

[dapper root]

Has anyone ever used Bott & Tu? Is it amenable to a first pass in AT or will you get epic owned

I'm not interested in learning AT right now since I'm busy but at some point I'd like to learn some, and I'm not a stranger to hard books e.g. a lot of you probably know I'm currently destroying myself with Hartshorne

Apparently Bott & Tu is more modern or something, so like between Hatcher and May's Concise Course, and uses like differential forms shit to bypass not-very-insightful calculations you'd normally do, and introduces spectral sequences early enough so you get good practice with them

but also if it's just unga hard then I'd wanna pass

[gray gazelle]

unga hard

[gray gazelle]

someone pin this

[silk quartz]

@stray veldt If you'd like to add a more descriptive post to the pdf link, I can pin that instead.

[stray veldt]

can't i just edit that message?

[silk quartz]

Oh, maybe!

Nice!

[stray veldt]

i just did

many thanks

[hearty steppe]

Thanks for the write up @stray veldt

[scenic briar]

Hi

Can anyone recommend a discrete math book?

I'm planning to use Rosen's book. Is there anything else you would recommend?

[hearty steppe]

Rosen is what I used

[marble solar]

@scenic briar schaum's outline

[pine igloo]

"Introductory Discrete Mathematics" by Balakrishnan

[limpid granite]

using Rosen atm it's very good

[crystal kraken]

can't i just edit that message?
@stray veldt is this an updated version of what you posted earlier?

[karmic thorn]

I think he fixed typos and formatting.

[stray veldt]

depends on which earlier you mean

i actually fixed some more stuff since that

but nothing major

the pinned version has a handful of typos, but the important bits (the math) is correct i think

[karmic thorn]

Book recommendations for an introduction to graph theory and combinatorics?

[stray veldt]

'Invitation to Discrete Mathematics' by Matousek and Nesetril

[karmic thorn]

Thanks!

[gray gazelle]

I found combinatorical optimisation by Korte, Vygen pretty good

[pine igloo]

"Introductory Discrete Mathematics" by Balakrishnan

[gray gazelle]

Thanks!
@karmic thorn I can vouch for this book too , mk suggested me too😀

[karmic thorn]

Yeah, this book is just what I was looking for haha.

[hearty steppe]

Which one

[karmic thorn]

A walk through combinatorics by Miklos Bona.

[true swift]

Hey

I am looking for practice book recommendation

my last exposure to math was AP calculus ab. but my math is rusty
Now that i need to take courses in probability and statistics + multivariable calculus.
I want to revise what i know.
So i am looking for practice books with the solutions for
AP calculus, Statistics and probability, and multivariable calculus

[marble solar]

Spivak Calculus + Solutions book

Good luck

Multivariable Calculus, I like Apostol volume 2

[random spear]

I've heard really good things from a good friend about Vector Calculus, Linear Algebra, and Differential Forms.

Enough that he'd says he'd be gay for the author lmfao.

[true swift]

Thanks

[random spear]

On a PC, what's your guys' favorite application to read? I'd really like to find something like Flexcil but for a Windows laptop.

[gray gazelle]

I use firefox for pdfs

[karmic thorn]

The update in Firefox made it so comfortable for reading PDFs that I've ditched Adobe Reader for it.

[random spear]

Wait does Firefox support stuff like annotations.

[karmic thorn]

It is as functional as any PDF reader.

[true swift]

adobe acrobat?

Spivak Calculus + Solutions book
I am not sure i can find solution manual for Spivak.

It would be super hard for me to study a book when i dont have the correct answers.

i would be self learning btw

[runic hatch]

you should be able to find a solutions manual online

[karmic thorn]

For a book as popular as Spivak, it's likely that solution/hints for any challenging problem from it is already available on Math Stackexchange.

[runic hatch]

and i believe Calculus has solutions to odd-numbered problems too

in the book itself

oh it's selected problems

close enough

[gray gazelle]

I am not sure i can find solution manual for Spivak.
@true swift here you go

[true swift]

Thanks @gray gazelle 😄

[wooden sparrow]

Are there any books which teach infinite series specifically?

[gray gazelle]

There's Knopp's book

[wooden sparrow]

nice, what's it called?

[gray gazelle]

Theory and application of infinite series

Tbh I left it mid way, cuz it was not what I was looking for

But it is good

[marble solar]

@true swift the solutions book is literally available online

Or at least it was when I took the course

Do you have to be an instructor to buy it?

[hearty steppe]

Learn real analysis @wooden sparrow lol

[gray gazelle]

Haha yes ig that's much better

[dense wren]

What’s a good book if you want to get a PhD in linear algebra

[quick hornet]

[cunning lark]

I dont think you can get a PhD in linear algebra.

[hasty turret]

Can you even do a phd in LA?

[quick hornet]

computational LA yes

but thats more computer science than math (as in, one is typically given a CS phd if they do that field)

[cunning lark]

But I dont get how the Anglo-Saxon PhD system works so ¯_(ツ)_/¯

[quick hornet]

mathematically speaking, the thing called "linear algebra" is very well-understood

though there are certainly related fields, see functional analysis

[marble solar]

Iceberg stop shitposting

[marble solar]

Probability the string is knotted?

Jeez that's computable?

[granite sluice]

How is that well defined? What is the probabilistic model? (Bernoilli iid crosses [over vs. under] is my best guess.)

Of course, the probability is either 1 or 0.

Ohhhh

No wait, I was going to say maybe only knotted or non knotted knots can have that shadow.

idk maybe that's true?

no its not true ( could be trefoil or unknot, I think. )

That would be a funny trick question though. Maybe another knot shadow has that property.

[marble solar]

That's correct. It could be the trefoil, or it could be the unknot

There is no knot of crossing number 2

[granite sluice]

I think you can draw the unknot so that the shadow has crossing number 2. (Not the knot though.)

So yeah that would be an example of a funny trick question I think.

Good point.

[marble solar]

You can try modelling each crossing point as "under" or "over"

[granite sluice]

What about the other way -- is there a shadow so that only knotted knots have that shadow?

[marble solar]

So there's 2 possibilities at each crossing

3 total crossings. If you assume equal chance then you can compute

[granite sluice]

Yeah that's what I meant with the bernoulli thing. Seems like one would just tabulate and calculate each one.

[marble solar]

Which situations will lead to a a knot, which ones will lead to the unknot

[granite sluice]

I think this question is more interesting: " is there a shadow so that only knotted knots have that shadow?"

I think the answer is No, but for a stupid reason -- you can just double the unknot over itself and wind it around the projecting knot so that it has the same shadow.

[marble solar]

yeah

[granite sluice]

But it seems true that there are 2 shadows that only the unknot can make?

Are there more?

[marble solar]

I don't know what you mean by shadow exactly

Do you mean knot diagram?

Knot projection?

[granite sluice]

Yeah -- the orthogonal projection onto some plane.

(So the doubling of the unknot happens in the perpendicular to the plane, its shadow is the image of a closed interval, and you wind it around the shadow of the knot, changing elevation so the shadow makes a closed loop, but it doesn't run into itself.)

computational LA yes
There are tons of cool algorithmic questions related to LA. But for an example of something pretty well understood, but which has great math in it ( function fields, symmetric polynomials, ...) algorithms for computing inverses, characteristic polynomials, and rank in polylog parallel time are interesting.

For instance, you can compute the nth term of a recurrence in polylog(n) parallel time. Which is kind of insane to me (because it means you don't have to compute the previous terms, in at least some sense.)

( I learned this topic from Dexter Kozen's book on algorithms.)

[marble solar]

iceberg was just shitposting

[gray gazelle]

Hi, I need a problem book that will get me from zero to hero in classic geometry

I barely know what is central and inscribed angle

Here is what the book(s) should cover: congruence (of triangles), similarity (of triangles), construction problems, inversion, isometric transformations of a plane, stereometry, and isometric transformations of space

It's a 2nd year uni course

[marble solar]

It's a co-author with Terry on uncountable ergodic Theory

I followed the first 35 minutes

But after it got to the uhh other stuff

[gray gazelle]

Best book on the history of the Roman Empire?

[marble solar]

The rise and fall of the roman empire?

[gray gazelle]

Is that the book name or a question?

Preferably towards the later days of the Roman Empire

I’m particularly interested in the reign of Hadrian

The Twelve Caesars by Suetonius was very good up until that point

[smoky surge]

honestly if you are cool with a podcast

the history of roman by mike duncan is great

[soft terrace]

What is the best book to read to learn about Aristotle's views on philosophy? Someone brought it up recently and I haven't read it in some years would like to review it.

[smoky surge]

that i cant help you with i want to read some stoic stuff tho

[soft terrace]

i think i liked his system the best out of what we studied in my ethics class

[marble solar]

I like Aristotle's Politics

[soft terrace]

is that the name?

im going to guess so since i just googled it and it came up 8)

[sage python]

There's that, there's also Nicomachean ethics

[soft terrace]

is that aristotle too or a different author?

[sage python]

Also Aristotle

[soft terrace]

awesome

[wind trail]

do you guys have any recommendations for any areas of math that might qualify them as the "spivak" type text of that area

[hasty turret]

Charles pinter for abstract algebra,ig

[quick hornet]

in what sense?

as in like, a particularly approachable introduction?

[wind trail]

yea, approachable, elegant, intuitive

honestly reading spivak rewired by brain

[steel viper]

are you considering the spivak the rigorous version of calc or the light version of analysis

[wind trail]

former

[steel viper]

uh i guess for most fields that ik of there isnt really one book thats like

[wind trail]

im studying honours mathematic right now (in my first year) and would like to keep a list of books that might be useful later

[steel viper]

specifically more rigorous than others

bc rigor is expected past that level but uh

checked the pinned msgs for an algebra text

[wind trail]

yep, I'm going to check out some from #books-old as well

did you guys like axler for LA?

[steel viper]

books is kind of outdated now

i should ask DM to update it with some alg top stuff soon

oh damn it max is gone for now

crap

[marble solar]

Hoffman and Kunze for linear algebra is great; as is LADR

[steel viper]

H&K is good

the exposition is really fucking dry though

it was my first pass

[marble solar]

I haven't looked at it in 4 years

[steel viper]

i think artin is good for lin alg

esp as a second pass

[marble solar]

If you want good analysis exposition, Pugh seems to reign supreme

[wind trail]

you guys liked hoffman kunze??

i found it so hard to read

but yea, LADR is nice

[marble solar]

Complex Analysis, I'd go with Ahlfors or Marshall

[sage python]

A lot of my linear algebra was my analysis professor throwing Hoffman-Kunze at us and being like "Get good"

Which honestly kinda works

[marble solar]

Y'know, I think there's a way to pull that off without increasing the size of the amygdala

[sage python]

I don't quite get the reference here

[marble solar]

There's no reference. The amygdala is the part of the brain that grows in response to stress

[sage python]

Actually idk I think my REU class on linear algebra prob did a lot

[wind trail]

https://tenor.com/view/writethatdown-spongebob-gif-5313946

[sage python]

It was fairly heavy but good

[marble solar]

And inhibits future learning, supressing memory recall from the hippocampus

[sage python]

Because it 2 and a half hours a day, 5 days a week

For 3 weeks

We didn't have a book

That's what gave me the general picture

Then doing 200 problems from HK really made the deets stick

[marble solar]

There's a lot of neuroscience to learning/teaching that I would like to be mow knowledgeable about

But from what I've seen if your stress levels in math remain too high for too long, the amygdala grows and never shrinks back down

Which eventually drives burn out

[sage python]

My joke response is that amygdala growth is yet another trial you must power through as part of your mathematical baptization

[marble solar]

I think ppl should be pushed to their limits

But not for too long

[sage python]

My actual response is, I think there's something of a distinction between workload and stress

And I think your perception of that analysis class is that it was very stressful when in reality it was more a high workload

[gray gazelle]

https://en.wikipedia.org/wiki/Abramowitz_and_Stegun

[marble solar]

Yeah, it's hard to say about the UChicago H analysis when I haven't taken it

[sage python]

Like, that class we sorta knew basically curved to a B+/A-

[marble solar]

I'd love to give the combined linear + analysis a try in teaching

[sage python]

Now the class size drops quite a bit after a while

[marble solar]

Like I said, I think I'd write exceptionally difficult exams

[sage python]

Because people decide yeah this workload isn't for me

And in a neighborhood of tests it's a bit scary

But generically it's about pacing yourself

[marble solar]

I think my main gripe was I got near perfects on most of my hw at LA, but couldn't perform on the exams

[sage python]

Like if you pace yourself and don't throw

You're getting a B- at least

One guy got a C second quarter but like he didn't attend lectures and stuff

So like lol he did that to himself

Unless he had something going on idk

[marble solar]

One of my friends now at SB is in 4 grad courses, trying to knock out all his core requirements in one year so he can focus the next 4 on research

[sage python]

I do think the class could use a very different set of improvements

Namely that first prof was not great

(And you know he hasn't been teaching that class last couple years anymore)

[marble solar]

You know I actually ran into my 131H Professor at a conference

[sage python]

The guy who teaches it first quarter accidentally uploaded a pset of his to the Canvas for my difftop class

(This was after I graduated lmao)

[marble solar]

The one where I messed up hard on the final/exams. He said he was worried that he drove me away from mathematics

[sage python]

Elman?

[marble solar]

Totaro

[sage python]

Ah

Totaro's a name I recall I think he was one of the people I had in mind as a possible advisor at UCLA :0

[marble solar]

Yeah, that guy finished princeton at like 16 UG

[sage python]

Goddamn

[marble solar]

Cal PhD at 21 or 22

[sage python]

Sucks to be a mere mortal

[marble solar]

We didn't know the lecture was over on the first day of class til he walked out the door

[sage python]

Amazing

[marble solar]

But he asked me what I was doing. At the time I was working in LDT and hadn't the research opportunity in Analysis

So I told him I was working in LDT, and really enjoy the field

He was very happy I didn't give up on math

[sage python]

"Lmao look at this nerd"

[marble solar]

So there's that closure 4 years later

[sage python]

Hmm he's very AG lmao

[marble solar]

Yup. He regularly teaches the H analysis sequence at LA

[sage python]

But yeah, did you end up preferring analysis or did you not get into LDT because of fewer opportunities?

[marble solar]

The style of LDT that I love is out of fashion, there's less opportunities

There's only a handful of schools that work in that kind of LDT, the main one being UC Davis

or University of Iowa

My tentative plan is to just go with the flow on Analysis, then after getting tenure I can start exploring other interests

Ricci Flow & Curvature is one thing I'd be interested in exploring ~ since that requires intense LDT + Analysis, PDEs, Riemannian Geometry

I thought about going to a local school like Irvine, Riverside and having my prof. from LB as a supplemental advisor to do LDT

But ehh it's not worth it and doesn't look good

If opportunity wasn't an issue, I'd most likely do LDT or even AG

But it seems most of my talent lies in Analysis for now

e.g. when I took Sobolev Spaces I would predict proof methods without seeing them before

[sage python]

Ah yeah that's good

For me I feel like the way the areas of math narrowed down was basically like

Topology I was always interested in but never took a hard enough plunge into

If I did it would be mostly algebraic topology or maybe certain parts of differential topology, maybe with less of the visual combinatorics wackiness

The guy here who'd prob be my third choice advisor does a mix of topology and AG

AG, idk for some reason I've been super slow on the uptake

Representation theory is my shit

Analysis I feel like I've rediscovered a talent for somewhat recently

Number theory is 😍

[marble solar]

Yeah, analytic NT is a very cool subject

[sage python]

So yeah that's basically how I ended up here

[marble solar]

I'm so happy Irvine just hired that woman

[sage python]

I wanna eventually transition to the more topology sides of the subject

[marble solar]

Since more than likely I'll end up going to one of: Irvine, SB, or Riverside

Topologocial NT?

I know there's like some AG stuff connecting it

[sage python]

The topological side of analytic number theory

Cohomology of arithmetic manifolds

[marble solar]

There's a book, the arithmetic of 3 manifolds

I've heard it's interesting

[sage python]

Ah I think I've heard of that

[marble solar]

It was a possible project for my knot theory class

[sage python]

http://www.math.wisc.edu/~marshall/research.html see the first few papers here

[marble solar]

But I ended up doing knot distortion

This stuff looks interesting

[sage python]

Eventually I'd like to learn about most of the basic aspects of my advisor's research for sure, my NSF statement was very asymptotics of eigenfunctions but I still honestly know fuckall

So yeah we'll see how things go

[gray gazelle]

@granite sluice @marble solar

[marble solar]

Woot

It was right!

[hasty eagle]

Your roles have been updated!

[granite sluice]

what is string anyway? surely there are some naturally occurring loops out there

woah: https://en.wikipedia.org/wiki/Molecular_knot

[gray gazelle]

https://kconrad.math.uconn.edu/blurbs/

I was suggested to post this here as well

It's nice for undergrads

nice

[hearty steppe]

ahh... Now i know why someone mentioned Keith Conrad a while ago

woah: https://en.wikipedia.org/wiki/Molecular_knot
@granite sluice this is awesome

[fast turtle]

Currently looking thru Knapp's Algebra and tbh it is the best algebra book I have seen so far, I do not understand why it is not mainstream yet.

[granite sluice]

Textbooks recs are weird like that. Usually good to cast a wide net and try and use a bunch of texts when learning a topic.

[sage python]

@fast turtle I did mention it in my massive pinned list as "Challenger Approaching" 😛

[random spear]

The problem is I can't imagine how many people read multiple textbooks of the same subject.

If it's good enough, they're not gonna read another.

[hearty steppe]

That’s not quite how it works

Depends on how into the subject you are and how much your trying to learn

And sometimes you need other books for more angles of reference

[marble solar]

what subject?

[random spear]

Oh yea definitely. @hearty steppe

But not for the average person I'd say.

I can't imagine someone reading multiple fundamentals of algebra/calculus books.

Like, Idk about everyone else but like I could not stand reading a textbook for basic algebra/arithmetic.

Maybe I might glance at a chapter if it peaks my interest.

[warped sluice]

Can someone suggest me a book that will go through the complete mathematics needed for Quantum Mechanics

I'm tired of referring to different books

[marble solar]

Roger Penrose the road to reality

[warped sluice]

Useful for QM and is it too advanced?

I just glanced through the index of that book and like 5 - 6 chapters are based on QM...

Roger Penrose the road to reality
This book to be honest is pretty Advanced

[gray gazelle]

at what level?

[warped sluice]

I need one at undergrad level

[random spear]

Can someone suggest me a book that will go through the complete mathematics needed for Quantum Mechanics
@warped sluice I've heard good things about Griffith's. That's intro.

[warped sluice]

Ohh okay I'll check that out
Thanks

[random spear]

Np!

Happy reading.

Btw you might try the physics Discord for more reccs @warped sluice

[warped sluice]

Any links to that Discord Server?

[gray gazelle]

#old-network

[warped sluice]

Thank you!

[dense wren]

Munkres analysis on manifolds? Good or bad?

[quick hornet]

it's well written and IMO an easier read than spivak's equivalent

not that spivak's text is bad, in fact it's incredibly concise

its like half the length of munkres with the same content i think

this conciseness just tends to make it... a pain to learn out of

if you dont have a lecturer to guide you through it

a nice perk of Spivak/Munkres is that they're the texts MIT's analysis 2 course uses (primarily Munkres)

so you can take supplementary material off OCW

https://ocw.mit.edu/courses/mathematics/18-101-analysis-ii-fall-2005/assignments/

[random spear]

Neat!

[dense wren]

That’s really great thanks for the link!

[cobalt arch]

Any introductory set theory books with plenty of exercises on sets? Like the ones below this message:

Anyone?

[thorn walrus]

depends what level of abstraction and modern math gibberish you want

but I find Rosen's Discrete maths and its applications very good for anything that has to do with introductory material

[cobalt arch]

Hm

I want rigor and plenty of set theoretic exercises involving sets:)

I hope such a book exists haha

[hasty turret]

Velleman?

[gray gazelle]

jech

[cobalt arch]

Does jech contain such exercises?

I want a lot so that I can get used to proving with sets.

[hasty turret]

I don't get why anyone would want to do a bunch of set theory exercises.

[thorn walrus]

if that's what you're looking for, pick the Rosen one

[cobalt arch]

Is this rosen's?

[thorn walrus]

yea

[cobalt arch]

Indeed I want that:D

Are there solutions as well:D?

[thorn walrus]

as usual you have the odd numbered exos answers at the end

and you have them all on slader.com

[cobalt arch]

Oh okay

What is slader?

[thorn walrus]

its a community website where verified people solve all the exercices in textbooks

[cobalt arch]

That is crazy

[thorn walrus]

yeah, but I think you can only check a limited number of solutions per month, or else you need to subscribe

but I use it from time to time

[cobalt arch]

Ah I see

Thank you babama

[thorn walrus]

https://tenor.com/view/boy-kid-computer-thumbs-up-face-gif-9548945

[cobalt arch]

All of you actually:)

Hahaha

@thorn walrus can you send me the pdf?

[thorn walrus]

will I get banned for this or smtg >

[gray gazelle]

you can get it on libgen

no

you can send it

[thorn walrus]

you can basically just google the title and its gonna come up

[gray gazelle]

this server is basically a libgen cult

[thorn walrus]

we advocate free circulation of knowledge that's all

for"

[cobalt arch]

Hahaha

I agree with Alexander

[thorn walrus]

https://b-ok.cc/s/rosen discrete

3rd and 4th ones are what youre looking for

[cobalt arch]

What is the title of the book?

[thorn walrus]

http://cslabcms.nju.edu.cn/problem_solving/images/3/3e/Discrete_Mathematics_and_Its_Applications_(7th_Edition).pdf

[cobalt arch]

Ty

[earnest glacier]

Big Fat Notebooks anyone know that book series? are they any good? for math in particular

[rigid carbon]

Give calculus book. Thx

Self-study.

[gray gazelle]

calculus by spivak

[marble solar]

Unironically, if you know some calculus already

Spivak is good

[thorn walrus]

is the spivak book calculus or analysis ?

[marble solar]

Yes

[thorn walrus]

I got bad vibes

[marble solar]

That's at the very end

Nobody reads those chapters

[steel viper]

i read them

when i was an innocent baby

[thorn walrus]

damn I dont know what to think about that

[gray gazelle]

my first year class started with those ones lol

[steel viper]

they dont use any material from earlier in the book

debatably they're easier

[thorn walrus]

a calculus textbook that doesn't have curve images all over the place and doesnt talk about "instant speed of a falling object" is not a good calculus textbook

[steel viper]

also ttera

do you like it at UoT

omfg tterra will i ever get ur name right on the first try

[gray gazelle]

yes i like uoft

[steel viper]

im considering applying

[gray gazelle]

im undergrad so i can't comment on the grad program

[steel viper]

idr how admissions to canadian unis though

[gray gazelle]

debatably they're easier
they are. fields chapter is pretty easy

[steel viper]

oh i mean yeah but id be applying for undergrad though

[gray gazelle]

wait are you another high schooler prodigy

||/s||

[steel viper]

i am a high schooler

def not a prodigy tho unfortunately

[gray gazelle]

how much math do you know hegel?

the classes here are ok but first two years in math can be kinda boring if you don't speedrun to the higher level stuff

based on what kinda stuff hegel's posted

[steel viper]

not much

[gray gazelle]

what all do you know?

i can't say too much about uoft undergrad rn since im in a lecture

[steel viper]

i dont know anything

i have transcended knowledge

[gray gazelle]

aight

hegel

if you have any questions about uoft undergrad i can try to answer

no guarantees

idk if i can say anything in general other than "i like it" lol

[hearty steppe]

I heard UofT is good

I know people that went there for Comp sci

Waterloo is probably a better school tho if you want to go for Comp Sci. They especially have the strongest hacker community in Canada of all Universities there

[marble solar]

The only canadian universities I know of are UBC, U of T, and Waterloo

[hearty steppe]

how do you not know of McGill? Its like the top uni of Canada

[dark hedge]

hi

[rigid carbon]

Jimmy McGill?

[quick hornet]

mcgill is not canada's top university

maybe in a few fields

but on the whole toronto is better, and waterloo is better at a few fields (cs/math/engineering)

it's certainly quite good though.

[marble solar]

Oh yeah McGill too

I know McGill

I thought about applying to UBC, but I don't wanna deal with international paper work

[quick hornet]

pretty sure UBC is super stingy on grad stipendds for internationals

[marble solar]

OH really? I was gonna apply cuz Dale Rolfsen is there

Get a signed copy of Knots and Links

[quick hornet]

mostly because they know they can get away with it, since vancouver has a massive population of chinese expats (in particular from hong kong) and also chinese investors who own property there

[marble solar]

Yeah, I've heard Vancouver has changed alot in the past 30 years

I watched a few documentaries about the chinese business' opening there

Very interesting stuff

[quick hornet]

there was a huge exodus from hong kong when the brits handed it over to the PRC

but many ties were maintained with china

so it results in vancouver having an increddibly high population of chinese people, and yeah a lot of investors and businesses based there

theres some crazy stat that i cant remember now

something like

more chinese people in vancouver than the rest of canada combined?

thats probably not the exact stat, maybe its specifically chinese-born expats or smthn

but yeah