book-recommendations

[quick hornet]

it might not be phrased quite like that

but that result will be included somewhere

it might be phrased like ``$ab \in P$ if and only if one of the following is true:

$\cdot a \in P$ and $b \in P$ \
$\cdot -a \in P$ and $-b \in P$"

[hasty eagle]

Namington:

[quick hornet]

or it might be spread out over a couple statements

or the statement might actually be from another problem in the problem set!

but in any case, you should have a result of this form

so you know, to figure out when (x+1)(x-2) > 0

i.e. when (x+1)(x-2) in P

you have to determine:

(1) when are both (x+1) and (x-2) in P?

(2) when are both -(x+1) and -(x-2) in P?

determining this is fairly rote from there

the point is: you need to identify what the problem is asking for, look for relevant properties, and see what they tell you about the problem

in this case, the problem comes down to

"how does multiplication interact with positiveness"

so you look for theorems/statements/remarks/whatever about multiplication and positiveness

and see how you can apply them.

[gray gazelle]

Fair

[quick hornet]

anyway, this isnt an easy process

[pulsar aurora]

maybe try to graph it on a number line might help too. Visual representation helps a lot for me

[quick hornet]

youre meant to spend some time on these problems

[quick hornet]

you dont have to work exclusievly from definitions

[gray gazelle]

This is what he says about it

[quick hornet]

by which i mean

your proofs should come from definitions ultimately

but if using more "intuitive" approaches helps you "figure out a path to the proofs"

do it

in this case, yeah, drawing out a number line is often helpful

anyway, yeah, youre not supposed to be able to like

rapid fire through the problems with 0 thought

you're meant to spend some time thinking about how to approach them

it's not out of the ordinary to spend dozens of minutes on a problem (although these ones are "short" enough that they shouldnt take that long)

its a very different "style" of mathematics

like if it helps demonstrate the difference:

i've TAed a fair few subjects in my time

one of the classes was a computation-heavy calculus 2 class

we gave students a 15-question problem set every week

meanwhile, a more proof-based introduction to abstract algebra I TAed gave students

7-8 problems every 3 weeks

we got wayyyy more complaints about pset workload in the second class than the first

and eventually cut it down to 5 problems + a "bonus"

(which students were happy with)

[gray gazelle]

damn

I think I should attempt some more then you gave pretty good rational stuff

What is your advice besides this great speech you just gave to my current sit

Drop the book and go for something easier like Lang/Apostol?

Or continue and see

where I get

[quick hornet]

er, does lang have a calculus textbook?

[gray gazelle]

yeah

[quick hornet]

honestly i dont have great calculus textbook recommendations sadly

[gray gazelle]

pretty good reviews too

[quick hornet]

so i wont be able to help you much there

[gray gazelle]

don't worry about that

[quick hornet]

it might be worth a shot to see if it "clicks" with you better

[gray gazelle]

I'm not looking for a book

[quick hornet]

depends on what your end motivations are

[gray gazelle]

I'm asking if I should stay or switch

[quick hornet]

if you feel burnt out by spivak, then yeah, its totally fair to try something a bit more computational

for context a lot of students only learn the content of spivak as

a second/third course in calculus

so its nothing out of the ordinary

[gray gazelle]

@sacred wagon im not gonna touch stewart

3 books for calculus, why? they cover same toppics

[gusty smelt]

dont waste time reading calc from 3 books tbh

pick one and stick to it

i think you arent far enough in spivak yet imo, give it a chance

[pulsar aurora]

@gray gazelle the benefit of apostol is he likes to give geometric proofs/representations.

[gusty smelt]

the steep difficulty curve might end up helpful when you do more mathmetical things later

[gray gazelle]

that's my only philosophy for wanting to stick with it @gusty smelt

@pulsar aurora interesting

it also has similar amount of pages as spivak

both are ~600

[gusty smelt]

i think if you are new to proofs and such spivak will be incredibly difficult atfirst

from what i have seen atleast

but you'll get used to it

[gray gazelle]

Stewart is 1400 pages and heavy computation no thank you

@gusty smelt I want to die doing it

I have done 10 problems in 2 days

on prologue chapter

[gusty smelt]

dw higher math books have long problems

[gray gazelle]

it's not even the real book yet

[gusty smelt]

even in prologue lol

the problems are meant to make you think hard and long

[pulsar aurora]

Really depends what you want though. I found Apostol agreeable, and I like having geometry to play with. I studied both books and found apostol more engaging then stuck to apostol

[gusty smelt]

(for example it took me a week+ to do ch 1 problems from atiyah macdonald)

its normal to spend a lot of time on problems in these books

(unlike hs where problems take 2 seconds)

dont be discouraged if you spend a lot of time on them

[pulsar aurora]

Yeah. It okay to push along too. I found it will click a bit later as they use it for other proofs or concepts

[gray gazelle]

@pulsar aurora how about i switch between apostol and spivak

like if i dont understand something

i can go see how apostol explains

[pulsar aurora]

Sure. Cross referencing is okay to me

[gusty smelt]

(also i find it helpful to find some kind of lecture supplements or such to books you are finding difficult, if you can)

[gray gazelle]

I wouldn't mind a 10 hour lecture on inequalities

actually 12 even

[pulsar aurora]

I originally used spivak initial stuff to help me with algebra and used apostol for calc 1. :p

[gray gazelle]

lol

[pulsar aurora]

That said, I see my casual studies as exploration. I dont expect myself to understand everything the first time. If I dont get it, I don't get it and move on until I need to know it.

Otherwise math gets boring and discouraging

[valid moth]

@gray gazelle you can try asking for help here

specifically namington, there's a good chance you might provoke him to go on an informative rant about whatever topic you are having problems with

[gray gazelle]

no I feel like when I ask for help people just facepalm and stop trying to help

[valid moth]

there are people who wouldn't do that

[stiff knot]

just talk shit about some topic that someone on here likes

[valid moth]

lots of them on this server

[stiff knot]

you will learn a lot about that topic

[slender sphinx]

Yeah

Fuck k-theory

wheres namingotn's elia5

[pulsar aurora]

I mean, I'm studying nearly the same information, so I'm always available to ponder a question with you, but I wouldn't put the expectation I know anything. 😛

[stiff knot]

fuck differential topology

fuck number theory

[slender sphinx]

ah, wait this is #book-recommendations

We shouldn't get too off-topic

[sage python]

Fuck RedAurora

[pulsar aurora]

Yeah, if you're going to shit on math topics, you have to bring a book into the equation

[stiff knot]

Rudin sucks

[gray gazelle]

fuck algebra

[shadow nebula]

Spivak sucks

[lone flower]

fuck number theory
@stiff knot
I would if I could, but it's an unrequited love.

[gray gazelle]

NT feels like it's a for a cult

[valid moth]

@gray gazelle what's an example of something you had trouble with recently

in spivak

a problem or a section perhaps

[slender sphinx]

that username...

[gray gazelle]

from iv to xi

[slender sphinx]

Also, rare occasion of archsys helping someone

owo whats this

[gray gazelle]

i to iii was trivial cause you just had to add and stuff

[valid moth]

can you tell me what (x-1)(x-3) looks like

[gray gazelle]

but then i lost it

[valid moth]

the graph of it

[gray gazelle]

ab>0

uhm

[valid moth]

it's a parabola yes

[gray gazelle]

yes

[valid moth]

and which way is it tilted— does it tend towards infty or -infty

[gray gazelle]

I think towards infinity

havent explored graphs of ineqaulties that hard

mostly quadratic equations

and functions

[valid moth]

im not talking about an inequality

just (x-1)(x-3) itself
also let's go to #help-1

[slender sphinx]

why do you need solutions

work for what

Just ask around here in #discrete-math

Someone will gladly check for you if you are patient enough

[gusty smelt]

well its better to do these on your own usually except for a few problems here and there

(and usually if you have a proof there isnt much to check, as your proof might be different than some guides for example)

[slender sphinx]

As long as you put in some work, people will help

Also, somewhat wrong channel #book-recommendations

Yeah many don't

[gusty smelt]

they dont have solutions to exercise period usually

its good practice/habit to not rely on solution manuals so you might wanna try devoloping that

[tranquil ocean]

I mean, if you're looking for a hint, trying to read the first line of the solution could be dangerous

[slender sphinx]

we can give hints too

[restive raptor]

an upside of asking people is that the book only shows you one solution. However, if your intuition goes one way, people can help you develop that into a valid solution from the one presented in the book

if you're checking a numerical answer, wolfram alpha can usually do that

[limpid gazelle]

I don't think this is the channel to ask for clarification about the actual text

But rather about book recommendations

[fiery sail]

Oh oof

[limpid gazelle]

Idk probably ask in #groups-rings-fields

[wooden sparrow]

Guys, whom is Lang's basic mathematics good for?

[wooden sparrow]

Umm anyone free?

[civic carbon]

This Fall, I'm teaching a course about unsolved problems in math aimed at non-majors. So the focus is more on the history, philosophy, biography, experience, etc etc than on any hardcore math. Does anyone have any books they recommend that would be suitable for such an audience? I'm already going to use Fermat's Enigma and Fearless Symmetry, but I'd love any more recommendations!

[lone flower]

There's this playlist of videos by David Metzler on Youtube that I remember liking years ago: https://www.youtube.com/playlist?list=PL613A31A706529585

Not a book, but could be a decent resource for an example of how to discuss the topics.

[civic carbon]

perfect, thanks! I am definitely going to make extensive use of YouTube

I've been incorporating more and more YouTube into my teaching even before I started making my own stuff.

[wooden sparrow]

Hey anyone here?

[civic carbon]

To the extent possible. The students will be doing a lot of their own research and the ones who are more inclined can pursue that side of htings

[pulsar aurora]

3blue1brown has a live-lockdown video regarding problem solving that might be worth looking into. It's the last video of the series

[civic carbon]

I do love his stuff

[civic carbon]

I have

[marble rock]

oh fuck

nerds help

i sent nudes in the wp teachers group by accident

thinking its the normal schools wp group

XDD what do id o

[valid moth]

just say it's for your sex ed assignment

[marble rock]

there is no sex ed assignment

idk

help now xd

[gusty smelt]

wtf

why in this channel

[marble rock]

lmfao

similar to what i did

i thought this was chill

oh my god

XD

[valid moth]

just follow it up with some other stuff

to distract them

[marble rock]

yea i did that

okay guys what do you think of polya

how to solve it

[broken meadow]

accept your fate with dignity

[marble rock]

XD

[nocturne dust]

can someone recommend any Arnold-style undergrad textbooks?

if such exist

[sudden kindle]

?

[nocturne dust]

https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html

Arnold was a Soviet mathematician

the book above consists of his lectures to high school students on abels theorem

in short, he hated abstract theoretical math for math's sake and always advocated for a more applied approach

[smoky surge]

When it comes to reading a book how long is too long to spend on a chapter

I’m going through linear algebra done right and it takes me like 10 days to get through like a section so 3.A

Is that too long?

[pulsar aurora]

In my opinion, duration only matters if you have a deadline to hit, otherwise if you're making progress, then progress is progress.

For example, I spent about nearly two months on the first chapter of Concrete Mathematics.

However, despite that duration, I learned a lot in that one chapter

[smoky surge]

Thanks yea cause It’s really my first introduction into proofs and it’s hard lmao

I didn’t take a lot of proofs in college all computational

[pulsar aurora]

@sacred wagon Uhh... when I dived into it, I haven't even touched algebra in nearly a decade, then the fact I never had calculus.

etc

So, it was extremely hard, and full of new ideas. That said, if you have calculus, it might be more of an exercise of turning problems into a general discrete formula.

However, that's for the first few chapters. Other chapters does more, I just never got that far.

I put it down in favor of actually learning Calculus.

Depends on the book. Knuth and friends really lay the foundations for what they're going into, but I think having some notion of calculus would allow you to tackle the material much better.

Some things they did just baffled me. but when studying calculus, I go "oh, okay, that makes sense now" although, there are still some things that baffle me

That said, Concrete Mathematics is really for CS students who want a firm math background for it. I'm unsure how useful it is for someone who is in general interested in Mathematics

Sometimes, it's good to shift gears and find a more suitable material. So, if proofs are hurting you, find a book designed to introduce people to proofs.

I sometimes see mathematics as a muscle. You don't jump right into 300 pounds, you gotta work from where it's hard, but doable

I mean, depends... I'm studying Apostol's Calculus. Roughly an hour a day. I've studied one chapter for a month or so now.

I agree with that. After a certain point, you should look to find something easier

or get help

I never studied that text specifically. The linear algebra book I have is proof-lite where they will hand-wave anything that involves a lot of work.

Except for Determinates. I hated that chapter

[smoky surge]

I mostly mean the problems are taking me a while

Like I get through the chapters fast and feel like I understand the material but when it comes to actually writing the proofs I struggle

[pulsar aurora]

Struggle in what way?

[smoky surge]

Just no idea where to start

Like if I find an answer on online I understand it

And I do feel like I grasp the ideas like if the book was computational I’d be cruising through it

[pulsar aurora]

Yeah, proofs are a new muscle. I am not the best with it, but you have to try to get anywhere with it. For me, I usually accept geometric proofs from myself.

[smoky surge]

Just about done with that Hahahah really enjoyed it

Idk I guess I just need practice with proofs

I also think I’m trying to do too much on my own atm

Did the proofs

Ch 2 I did the odds

Didn’t find it bad at all

Honestly I’m not sure how to explain it... I guess I’m not approaching it super systemically

Like it felt like it was 100p clear or it wasn’t I’d ask here on a few if I got stuck

Hahahahah probably the best

I do think I get frustrated with myself too easily too

I expect to just get everything

[pulsar aurora]

Yeah, lower expectations. They help me get through self-studying

[smoky surge]

Yea cause I get so frustrated with myself I just walk away and move onto things I’m more comfortable with

[pulsar aurora]

Of course, my thoughts are to be taken with a grain of salt. I have no expectation of being good with mathematics, but it's all about the exploration.

After all, it's mostly casual for me than whatever I may face in school

[smoky surge]

Really? Do you have any recommendations on which/how many

I appreciate that

[pulsar aurora]

Really depends. Beginning of a problem list usually are easy to exercise what is established. Mid-list can establish new ideas based on the solved problems for the last few challenging ones.

[smoky surge]

I appreciate all the help

[pulsar aurora]

At least, that's what I've seen in the more difficult math texts

[smoky surge]

Yea that’s how it feels here too

[pulsar aurora]

I'm not advocating to do it all though. Usually I do the first few to make sure I understand the text for the most part, then I'll do the challenging ones. It really depends on my motivation.

[smoky surge]

Hahahahah that’s fair

[pulsar aurora]

Like this section on trig integrals... While I know I should do the problems, but I really don't want to because I am really sucking at trig in this case.

So, part of me considered just skipping it all. 👀

[smoky surge]

I honestly have done that on calc

Def not the best but hey 👀

That’s actually... super clever

Super simple too

Thanks will do!!

[warped wave]

What would someone recommend before diving into Baby Rudin's Analysis

[velvet briar]

You really can go right into Rudin, it's got no prereqs

I would suggest at least knowing the basics of calculus first, haha. You don't have to, but it would mean less to learn, and you get some of the motivation

[midnight skiff]

@warped wave just use some complementary text of your choice if you get ”stuck”. I remember using it together with Pughs analysis for self study while in high school

Pugh had some good exercises I recall and gave some more intuition

[warped wave]

Thanks guys.

[marble rock]

i am almost done with basic linear algebra

and i got extremely bored from df

im supposedly at the end of rings

i was looking at basic algebra by jacobson and i liked it

should i learn ring theory from jacobson from start

?

maybe skim through GT just to see notation?

can i even do that

and is there going to be any difference between df and jacobson

[calm crane]

jacobson is nicer to read

[marble rock]

is it more advanced than df

[somber mica]

i never understood why people like baby rudin so much

is it because it covers everything that you would need in undergrad analysis? or is it just because the problems are really nice?

[gray gazelle]

the problems are great

exposition is a bit meh

[calm crane]

Jacobson covers more than basically all intro algebra books

[wooden sparrow]

intro to college algebra?

[main flax]

abstract algebra

[mossy flume]

@warped wave just use some complementary text of your choice if you get ”stuck”. I remember using it together with Pughs analysis for self study while in high school
@midnight skiff

I remember seeing somewhere someone made some good complementary notes for Baby Rudin

I don't think it was published as a book? Just hand written or maybe a PDF

[warped wave]

ooh, please do share!

https://bomongiaitich.files.wordpress.com/2008/10/silvia-em-companion-to-rudins-principles-of-analysis-web-draft-1999434s_mcet_.pdf

is this it

[mossy flume]

I can't remember what it's called ;-;

Maybe?

Regardless that looks good

[vestal basalt]

@mossy flume what Rudin book?

[mossy flume]

Principles of Analysis

Colloquially called baby rudin

[vestal basalt]

Thank you for mentioning a companion book with it my issues have been I’m not sure what material to look for when it comes to solving these problems

[indigo stone]

Michael Spivak

[warped wave]

[neat basin]

WTF

Wow, Spivak seems so flexible

If i do that, my columns will snap

[neat hornet]

when does song of ice and fire plot separates from game of thrones tv show plot?

[neat basin]

i read the first 2 books, i think it's almost the same until then

But i don't really remember, it's been a long time since i read them

[neat hornet]

oof

[pulsar aurora]

I never read the books, but how people discuss it, the separation is more or less the consequences of removing characters from the book.

As there are a lot more potentially critical characters that doesnt make an appearance in the show

[gray gazelle]

anyone know any good multivariable calc books

[radiant crown]

Henri Cartan's pretty good

[frigid comet]

spivak calc on manifolds

[warped wave]

Anyone have spivak's calculus PDF?

I dowloaded online but it's thin so it's pretty hard to read

[dim relic]

im supposedly at the end of rings
you cld start on field theory

[flint forge]

Do modules

[gleaming folio]

If anyone has done Commutative Algebra from A term of commutative algebra, how does the book stack up against atiyah-macdonald?

I found the later exercises in each chapter of Atiyah-MacDonald to be too difficult and I was looking for an alternative book

[tranquil ocean]

atiyah macdonald is the standard for a reason

The exercises are definitely hard, but they're both insightful and educative

[gleaming folio]

Alright, I'll try and give them another try tomorrow

[tranquil ocean]

They definitely took me a really long time when I did them, but even now I continue to use the facts from those exercises

[gleaming folio]

Yeah I think that I'm a bit used to doing most problems within an hour max

And the exercises in Atiyah-MacDonald will probably take a lot more time than that

[sage python]

Altman Kleiman is billed as a more modern Atiyah-Macdonald basically

[gleaming folio]

Have you used it?

[valid moth]

what about eisenbud

[sage python]

Eisenbud is much larger and more geometric. And no I haven't used the stuff myself (what little I glanced at Altman-Kleiman rubbed me off the wrong way for some reason though)

[valid moth]

eisenbud seems like a really chill and likeable boomer

[tight crag]

Eisenbud seems pretty great

[gentle smelt]

I used atiyahs book back then but I skimmed through bosch’s algebraic geometry and commutative algebra and it seemed really good and like a fresh approach.

If you’re interested in AG

[marble rock]

do you have to relearn commutative algebraa

if u already had learnt it from a normal algebra text

[tight crag]

Yes

[sage python]

Unless you first learned it from Lang or something

I've heard that Lang pretty much contains Atiyah-Macdonald as a subset. Prob better to read the latter anyway but still lol

[somber mica]

the open logic project was recommended in one of the tabs here, can anybody else second that recommendation?

[pearl kelp]

Anyone with an opinion on how good Sheldon Ross Probability and Statistics books are?

Also, what are good books for DE? Is George F Simmons good?

[maiden slate]

hey what are some good books for a high schooler to get into higher maths?

im in 12th grade and am pretty comfortable with differential calculus

[slender sphinx]

I would just continue learning calculus

[primal patrol]

The book of higher math

[slender sphinx]

Do you know integration yet

[maiden slate]

not beyond the basic concept,

[primal patrol]

then you might as well continue with the thingy

Have a good grasp of single variable calc first

[maiden slate]

well what books should i use to learn it

[slender sphinx]

Really doesn't matter for calculus right now

I would say just focus on time and effort

If you want what I used, it was 2 separate books - one by spivak and another by apostol (2 volumes)

[somber mica]

i've heard both good and bad things about stewart's calculus textbooks

[slender sphinx]

Just work your way up to multivariable/calc 3

[primal patrol]

^

[somber mica]

but on the whole stewart seems to be a good textbook to use

[maiden slate]

alright

[somber mica]

are you talking about open logic project or stewart?

i assume you meant stewart

[pulsar aurora]

'It's cheap" as I see prices up to 200 dollars

Compared to Apostol where I got for 50 bucks. 😛

[quick hornet]

or just get your favourite textbook for free

off of gib len or something

:^)

[pulsar aurora]

That is an alternative sure. 😛 Although, I do like having printed text to study on as staring at a PDF on a computer or even phone hurts my eyes after a while

[somber mica]

all of my books have been pdf's for...reasons

the only hard copy i have is a copy of rudin's analysis textbook that i got a few years ago

[pulsar aurora]

I typically harvest books at used book stores. They're of various qualities for the most part. So, I have more random texts book than the 'big names'

[flint forge]

Try going near a local university if you havent

The bookstores there have better selection

Even the used ones

[pulsar aurora]

... So, a used book store, the books may be at most 20 dollars, sometimes a bit more than that. I can get texts books for less than 10 dollars usually. If I went to a university or my local college, i'm looking to put down over a 100 dollars even if used.

Now, that said, I could always go to the campus's library and simply read any better quality books, surely

[sudden kindle]

Dummit & Foote is Dummy fat

[flint forge]

Thats just not true haha

Ive been to our used book stores

They are not $10 but they are def cheaper

And not quite

You cant read any books at most university libraries

Without ID

[pulsar aurora]

My local college campus policy allows people to go to the library, last I checked, just unable to check them out

I guess this is where it comes down to... inconsistency of prices and location's policies

Plus, even if there weren't a policy, I doubt the librarians would care unless you look incredibly out of place. Hell, they have rules stating nobody can eat in the library, yet professors themselves will eat the crunchiest, smelliest shit in the study cubicals

[flint forge]

They dont even let me in

without ID

in my library

and i know some of them have seen me countless times haha

[pulsar aurora]

Yeah, probably depends on the campus. I'm unsure the strictness of the university here. The community college is very, well... community. 😛 There is even a track park for anybody to walk. It's highly accessible.

[hasty eagle]

work:

[flint forge]

oh thats funny

[pulsar aurora]

From reading, the university here allows non-students or staff to access the library freely too. So, it's an option if local university allows it

[valid moth]

@sudden kindle how long is DF

[gusty smelt]

like

968 iirc

968 pages of shit

[sudden kindle]

^

[wooden sparrow]

From reading, the university here allows non-students or staff to access the library freely too. So, it's an option if local university allows it
@pulsar aurora
That's really good

[pearl kelp]

Can someone please tell me how good Differential equations book by GF Simmons is?

[somber mica]

do you mean "differential equations with applications and historical notes"?

@pearl kelp if that's the one you're talking about, then we used that book when i took an ODE class a little while ago

the book did a decent job of explaining stuff and the exercises were ok too, but i think you're better off doing a google search

i just checked and it doesn't appear on anybody's "recommended" list, but i can't say more than that

[pearl kelp]

Oh ok

Thanks

[gray gazelle]

Hmph bad title

[young surge]

anyone have any reccs for measure theory books?

[blazing dagger]

Terence tao, or Stein and Shakarchi 3

[young surge]

Thanks I'll look into those+

[wooden sparrow]

What is AOPS volume 1: the basics for? algebra? or precalc?

ohh

wow so it's for contest math

[restive raptor]

Yes and no. it teaches problem solving strategies useful for contest math, but it also just teaches helpful problem solving strategies

[wooden sparrow]

got it, thanks 🙂

[sage python]

@young surge for something that's good but more efficient, try Bass

[young surge]

oh ok thanks

[sage python]

The other two kinda do Lebesgue first and then repeat themselves

[fluid bay]

do any of you have an opinion of carothers real analysis?

[gray gazelle]

What do you guys think about The road to reality by Sir Roger Penrose

I'm only at chapter 2 and I'm already getting skull fucked by basic hyperbolic geometry

Still fun though

I think it maybe the case that my math knife has been dulled as I havent been using it lately(quarintine made me graduate HS early)

[sage python]

@fluid bay it seems pretty nice at a glance actually

[fluid bay]

nice, i thought so too. I think its the book my school uses, so im becoming acquainted with it lol

[outer carbon]

Any recommendations for books on mathematical history?

[radiant crown]

what kind of history book do you want ?

[outer carbon]

Wdym

[radiant crown]

maths books can have different flavours, they can be textbooks, they can be exercises compilations, they can be vulgarisation, they can be targeting people sitting a particular exam

same for history books

[wooden sparrow]

What's vulgarisation?

[radiant crown]

are you looking for an essay on applied maths and the race to armaments ? are you looking for an brief overview of the past 3000 years of maths ? are looking for a compilation of history of some specific areas in maths ?

[outer carbon]

Like just a general intro to the subject ig

Like i want to learn more about the motivations and history which led to the development of math

[radiant crown]

maybe popularisation is the word you're used to @wooden sparrow

[wooden sparrow]

Ohh

Okayy

Lol so popular= vulgar?

[radiant crown]

lmao no look up the latin roots

[outer carbon]

@radiant crown any suggestions?

[radiant crown]

maybe Bourbaki's Elements of the History of Mathematics

[gray gazelle]

Are you looking for a book on some specific topic in math history?

[stray veldt]

the great german historian of mathematics Hans Wussing wrote a 2 volume book titled "Mathematics 6000 years – a cultural and historical journey through time", that covers pretty much everything, unfortunately there does not seem to be an english translation 😢

[gray gazelle]

fermats last theorem by simon singh

thats a nice historical book

[stray veldt]

however if you happen to care a lot about group theory, he also wrote about the history of the modern abstract group in a book titled "The Genesis of the Abstract Group Concept: A Contribution to the History of the Origin of Abstract Group Theory", which was translated and is a great read as well

other than that i liked "Men of Mathematics" which takes a look at famous mathematicians and how they lived, rather than examining the mathematics they did

[outer carbon]

Ooh that sounds interesting

Gonna look at those

[radiant crown]

and if you want something a little spicy, you can have a look at the postface of Roger Godement's Analysis II

which is freely accessible here http://rogergodement.com/gallery/(2005) postface à analysis ii.pdf

[gray gazelle]

Spicy?

@radiant crown

[radiant crown]

yes, spicy

actually the whole website is a goldmine but that Analysis II postface seems to be the only english document http://rogergodement.com/Documents/

[wise vine]

What do you guys think about Amann-Escher's analysis series?

[stray veldt]

it's the standard "hard" analysis book in germany

it's good and has everything in it you might want

although i wouldn't use it for self-study at least not solely

[wise vine]

@stray veldt I find the definitions quite hard to follow(or maybe because the translation is not that good) but I like its exercises and the contents

And I just read that this covers the 1st year of a typical german math undergrad? Woah, our system here is like in America lmao. We don't even cover Analysis up until 3rd year

[stray veldt]

the first 2 books are covered in the first year

although ofc the books are very complete and it's in the nature of the lecture that a lot of stuff has to be omitted in actual classes

but ye, it is notoriously hard and most students use some other book to supplement it

(somewhat like Rudin i guess)

[wise vine]

Holy hell, German math undergrad is quite hardcore kek. So you guys consider Rudin as easier?

The recommended books here are honestly not that challenging

[stray veldt]

Rudin is still considered a good book, but solely used as a reference (papa rudin then)

i mean analysis is usually taught in german in germany (surprising i know), so we use german books

[remote seal]

what kind of cocksucking book has 2 long pages of questions after each chapter

and doesnt even provide the answers to the questions

after i did them all

cant even find them online, motherfuckers.

[boreal juniper]

why should the author put in the answers if he knows them already

which book?

[stray veldt]

typing out detailed answers is a lot of (unnecessary) work

you should be able to tell yourself if your answers are sound

[civic carbon]

In some contexts, I think solutions can add a lot of value. But they are of course very time consuming to produce

[restive raptor]

sometimes they can also be counterproductive. It's easy to convince yourself you "would've gotten it right" if you look at a solution manual and it makes sense to you. Example solutions in the text are sufficient for showing you the method, and if solutions aren't provided, it forces you to write up a solution and get someone to check it, where there's a lot less "oh I would've gotten this right for sure"

[civic carbon]

yeah, I think the way Project Euler does it is perfect. You do the problem, prove you did it, and then yo uget to see all the solutions that are better than yours 😛

but I think it is super helpful, after a student does an exercise, to see a paragraph or two saying "This was the key idea here, this is why this exercise was included, to show you X"

because it is very easy to do an exercise and spend so much time looking in so many different directions that you don't actually get that at the end

[restive raptor]

according to my profs, when you read books, you should try the examples before you look at the solution

you can get that from those examples (which are common in a lot of texts)

[main flax]

i think hints are more than enough

[civic carbon]

I wish more books had a lot of examples haha. Hints can be very helpful too, but serve a very different purpose, imo.

I think especially for grad studetns, hard questions with lots of hints that make them easy are good, because they give them practice writing more complicated solutions.

[gray gazelle]

@restive raptor I want to agree with you as it makes sense .
But i spent 4hours on a example with no answer with it so em.... solutions please.(btw it was something easy aswell)

[vestal basalt]

Quick question has a lot of you read books on problem solving? I’ve seen recommendations I’m just not sure whether I should add that to my study.

[civic carbon]

do you want to get better at problem solving competitions?

[vestal basalt]

You mean on here ? Or in general?

[civic carbon]

in general. If the question is "will problem solving books make me a better mathematician" I think the answer is no. But if you want to get better at competition techniques, if you just want to have some fun, if you want to engage with math in that way, by all means.

[vestal basalt]

Gotcha. Im not really interested in math competitions. In your opinion what will make you a better mathematician?

Or people in general?

[civic carbon]

I don't know your level, but I think learning new things and doing exercises that reinforce that learning is always valuable.

[main flax]

hey zetamath, nice first video, when is the second one coming

[vestal basalt]

Awesome. Well it was just a general question but it can definitely be applied to me

[civic carbon]

Audio is recorded, my editor (aka husband haha) is working on animations and stuff

[vestal basalt]

I’m trying to retake some classes to brush up and go further I love math so much

[civic carbon]

and I have scripts (or drafts) written for a large number of them after taht.

[main flax]

noice, what is it about?

[civic carbon]

The next two are about Euler's proof that zeta(2) is pi^2/6. So the first one (that should be out soon) is about Euler-Maclauren approximation and how, without a calculator, he found the value of the sum to 17 decimal placs

And then the second part is about his proof, and analogies between that proof and Riemann's proof that there is a formula relating the zeroes of the zeta function to the distribution of the primes

[main flax]

noice

i really enjoy number theory stuff

[civic carbon]

well the first "Season" is all number theory

(or stuff like complex/fourier analysis with the goal of applying ot to number theory)

[main flax]

that's hot.

do you have more seasons planned out already?

[civic carbon]

I have rough ideas, but I will see how this one goes, who my audience is and such before going in detail.

but it is possible I will want to talk about Birch and Swinnerton-Dyer in the way that this season is all about the Riemann Hypothesis

[main flax]

looking forwards to that!

[civic carbon]

the big thing I'm getting a feel for is what background I should assume people have vs not. I'm currently aiming at "If I do it in my calc 2 class, its' fair game to assume"

[main flax]

true

maybe you can do a survey from time to time via the youtube voting thing

[civic carbon]

Yeah, I'm sure as I post more I'll get more of a sense of who is engaging

[main flax]

[sudden kindle]

What's project Euler

[limpid gazelle]

A website that has a lot of programming problems, and all the problems are more mathematical

[civic carbon]

it's beautiful, most of hte problems require both a mathematical insight and an algorithmic insight

[slender sphinx]

Very cool site

I don't like programming, but thinking of the optimal solution is fun

[civic carbon]

it's super fun to team up with someone who programs and collaborate

[gray gazelle]

Has anyone used an especially commendable resource for understanding trig identities? (Using OpenStax but looking for others too. Umn has a nice open trig book but I'm looking for a more concise resource).

[gray gazelle]

Cheers I'll have a look! This looks like a better pace.

[gray gazelle]

What are some good free online books about chess

[gray gazelle]

My copy of Basic Mathematics arrived today 😁

[wooden sparrow]

@gray gazelle nicee

[open orbit]

http://math.ucr.edu/home/baez/books.html#math

great site

[sullen field]

@civic carbon you have a youtube channel?

[gray gazelle]

@sacred wagon - props for the recommendation. This is just at the right level, thanks!

[vestal basalt]

@gray gazelle who is the author

[civic carbon]

@sullen field https://www.youtube.com/watch?v=oVaSA_b938U&t=1272s

[gray gazelle]

am I the only one who shouts out the letter/number instead of saying factorial?

[civic carbon]

haha that seems like a good technique!

[vestal basalt]

@sacred wagon thank you

[main flax]

how do you say n!! tho? as n!! < n!

[gray gazelle]

Do you guys recommend James Stewart early transcendentals for calc BC?

[pulsar aurora]

I've seen people recommend him for calc, yes

[civic carbon]

I think Stewart's BC content is well organized

and Stewart has the best problems of any of the calc books I've taught out of.

[white cradle]

@main flax n-double-factorial

[main flax]

you ruined my bad joke

[dull moon]

Here is a reading list from Cambridge university.

[vestal basalt]

Is it wrong to say this is my favorite section of this server

I love helping people solve problems don’t get me wrong but I love books

[cold lagoon]

tell it woog

they'll be happy

[shadow nebula]

shout it even louder

[cloud trench]

what is a good book on probability and statistics for undergrad level?

[pearl kelp]

I recently had a discussion in #probability-statistics regarding this. Sheldon Ross books seem to be good. But he has books at all levels

[valid moth]

bazinga

[pearl kelp]

Currently we have beem recommended "First course in Probability" and "Probability and Statistics for scientists and engineers" @cloud trench

I'd also been recommended a few other books a couple of months ago

Don't remember what book though

[cloud trench]

Is "A First course in Probability" good?

[valid moth]

probably

[gray gazelle]

What's the probability of it being probably good?

[cloud trench]

hahaha

close to 0 since there are so many terrible not well written books in the wild

[gray gazelle]

Try this
An Introduction to Probability Theory and Its Applications - William Feller
(Needs analysis)

@cloud trench

[cloud trench]

okay, and any good book on statistics?

[quick hornet]

i only wrote an algebra qual, which i prepped for mainly with atiyah-macdonald and hartshorne

this of course lacks AT and group theory stuff, but I got by those mostly off of lecture notes

[warped wave]

i ordered gilbert strang's linear algebra

let's play a game called how long until my motivation fades

😩

[vestal basalt]

@warped wave get started with a pdf then when the book comes you have already started

[warped wave]

yeah I think I'm gonna start 2moro

just hoping the book will not fuck me in the arse

[cold lagoon]

books shouldn't do that

at least not without outside aid

[warped wave]

[vestal basalt]

Lolll

@warped wave I think you will do well when I took linear algebra that the the book we used but I will say it is not the math that will get you it is the theories. When I took it the teacher moved extremely fast causing people to drop I thought the teacher did really well.

Since this is self paced im sure you will do awesome

[warped wave]

thanks for the support dude

[sage python]

@gray gazelle so, I didn't take the first year classes but:

Analysis first semester uses Folland, second you choose either functional (more Folland + Rudin) or complex (Gamelin)

Topology first semester uses Hatcher, second you choose either more Hatcher or Lee smooth manifolds

Algebra uses D&F + A&M (though some years Lang)

[hearty steppe]

doing a lot of head scratching right now with Rudin. I still am interested in reading Rudin but I think just using Rudin especially for what is covered in this first chapter will be a problem for me. Definitely think I should read another more broken down analysis book with this one. I have a few in mind but I would like to know what your thoughts are.

[marble rock]

yea if you are new

try reading easier analysis texts

like understanding analysis by abbot

or tao analysis 1

imo

but at the end of the day rudin is just the best

[hearty steppe]

A colleague of mine recommended Wheeden, but I'm considering Abott or Schroder. A number of people told me to avoid Tao cause the notation is way different compared to Rudin

[marble rock]

cool

have fun

[sage python]

If the Wheeden is the one I'm thinking of then that's not really comparable to baby Rudin

[hearty steppe]

is Ross good too?

[sage python]

Wheeden Zygmund is closer to (an easier version of?) big Rudin

[hearty steppe]

ahh ok

thank you for clarifcation dami

Abhijeets recommended Schroder so I am gona try Abott and Schroder first as a supplement for getting thru Rudin

[cold sky]

what do folks think of the book "Probability and Statistics for Engineering and the Sciences" by Jay L. Devore

[hearty steppe]

Abott is MUCH easier to read.

wdym @gray gazelle

I didn't read Ross yet

I am gona stick to Abott and I'll also take a look at Schroder a little here and there as I'm getting thru Rudin for now

ahh ok

thats kind of what I was starting to feel as I was reading it

Abott seems like it helps break down some of what I was reading in Rudin so far

[uncut knoll]

Go with Apostol.

It is decompressed Rudin with more graphics.

[pearl kelp]

Go with Apostol.
@uncut knoll for what topic?

[marble rock]

apostol is a calculus text

it is not https://en.wikipedia.org/wiki/Tom_M._Apostol

[sage python]

There's Apostol analysis as well

Which is what Millennial was prob describing

[marble rock]

uh oh sry

[pearl kelp]

Apostol Calculus Vol 1 isn't to great. Had it in my 1st sem. Didn't really like it

Though Vol 2 with Linear algebra and Multivariable calc is decent

[marble solar]

For analysis I prefer Pughs Real Mathematical Analysis, it's got everything Rudin does and so much more

Plus hundreds of exercises

[marble rock]

is it easier/harder?

i think im goign to have learn analysis p soon

and i just was bombarded by rudin in chap 2 soo

¯_(ツ)_/¯

[hollow current]

chap 2 is sequences?

[marble rock]

topology

in rudin that is

dk purhg

prugh*

[sage python]

I'm not fond of Pugh's topology, Rudin's to me is somehow easier to follow, but Pugh almost surely has a way better treatment of multivariable calculus

[limpid gazelle]

So far I really like Spivak’s Calculus on Manifold

For multivariable calculus

[marble rock]

why is there everytime topology

in analysis texts

what if someone is interested in nalysis and not topology

:d

[pulsar aurora]

How else can they recruit topologists?

[blazing dagger]

Topology helps contextualise many concepts in analysis

Also sometimes provides more streamlined and natural proofs

Eg IVT

[marble solar]

Pugh has an excellent approach to Topology from an analytic standpoint, but a terrible one from a topologists standing

[hearty steppe]

I mean it sounds like I should avoid Pugh in that respect.

Some people told me to avoid Tao because the notation can be confusing compared to Rudin?

I am enjoying Abott and I am going to also take a look at Schroder. I want to take a look at Tao at some point as well but I will wait until I get a little further in Abott and then can translate that properly to Rudin to get to Topology chapter.

Actually. I think after I get to Topology chapter, that may be a good time to take a glance at Tao to see what the fuss is about.

I feel like sometimes I learn better from multiple angles of reference.

This seems to be similar difficulty to learning operating systems when I was in undergrad so its not all that bad to digest. It's the strategy behind interpretation I feel is important here when dealing with densely packed subjects like Analysis.

[hollow current]

In principles of mathematical analysis?

well, it is good in the sense that it provides most of necessary information for real analysis

but it is not comprehensive

[hearty steppe]

i think I have a good strategy to learn analysis now. Thanks guys

[gray gazelle]

i want to read some math books casually

what should i read

[long anchor]

@hearty steppe wait whats the strat

tldr pls summarize

[gray gazelle]

stare at a proof for 12 hours straight and then give up. repeat.

[blazing dagger]

Sanatg what’s ur background

[gray gazelle]

its my dog

oh

you mean my math background?

[blazing dagger]

Yea haha

[gray gazelle]

well, i just read a book on linear algebra and i have an ok understanding of multivariate calculus although i probably should do more of that

[blazing dagger]

Hmm

Casual read huh

Do u know analysis

[gray gazelle]

a little bit

[blazing dagger]

Maybe try dynamcial systems

Brin and stuck is a nice read

[long anchor]

@gray gazelle we literally have the same math background

[gray gazelle]

lol nice

im mostly self learning

[long anchor]

me 2

[gray gazelle]

so its hard to say what my "background" is

[blazing dagger]

Well just like what books have u covered etc

[long anchor]

im reading bretscher and axler

for lin alg

[gray gazelle]

I read lays linear algebra, naive set theory, i watched the gilbert strang lectures

[hearty steppe]

uh Soap you can DM me lol

[gray gazelle]

i tried reading spivak

[long anchor]

ew spivak

[gray gazelle]

im kinda having difficulties

thats an understatement

im having a lot of difficulties

[long anchor]

for analysis right ?

[gray gazelle]

yeah

[long anchor]

read abbott man

its super good

[gray gazelle]

well, i was reading calculus on manifolds

[blazing dagger]

Yea Abbott is good

You need good mastery of lin alg and multivariable Analysis for that one

Also maybe a bi of topology

[gray gazelle]

yeah i realized

painfully

[long anchor]

[gray gazelle]

i should probably read prerequisites to that instead

someone suggested reading an electricity and magnetism book

axler 💔

[long anchor]

gtfo godel before i get violent

[gray gazelle]

bruh whatchu gonna do, sneeze on me?

[north spire]

? Read analysis before calculus on manifolds

[gray gazelle]

u cant u have a mask on kid

[north spire]

Calculus on manifolds is used for the analysis II course at my uni

[gray gazelle]

analysis is calculus on manifolds

[north spire]

Well, it’s recommended

[gray gazelle]

yeah idk why i was suggested that book

[long anchor]

manifolds book by that james munkres dude ?

[gray gazelle]

sanath im reading calc on manifolds by spicak right now

its really niec imo

[north spire]

My uni uses a sequence of 3 books for analysis

But calculus on manifolds is recommended as an extra reference

[gray gazelle]

no, i actually like the book or at least the first sections until it just became too confusing

well im right now on section 3 so idk lol

but Im mostly for the 4 and 5

im at inverse function derivatives

or im trying to read that

and i think i get it

[long anchor]

im on compact and topology shit

[gray gazelle]

yeah I just skimmed thorugh it, its hella confusing the firstt time you read it though

oof compact is a bit hard to understand but it makes sense now

the wording for the definition is so wack

what definition?

the finite subcover?

yeah

[restive raptor]

The convergent subsequence definition is so much easier

[gray gazelle]

yeah its kinda weird especially if u study R^n only

[blazing dagger]

Open cover definition is much more useful a lot of the time tho

[restive raptor]

yeah, for sure, and I'm more comfortable with it now. When I first learned about compactness though, I'm glad I learned the subsequence property

[flint forge]

finite subcover is the only defn that matters

everything else is a coincidence

[long anchor]

[gray gazelle]

soap your moms so fat there is no finite subcover for her

[blazing dagger]

Heine borel property is no coincidence.. it is very special

[flint forge]

its a coincidence

its just the nature of that topology

[long anchor]

@gray gazelle that just means shes not compact in R^n dumkbfuck

[civic carbon]

I really dislike when people sneak Hausdorff into the definition of compact

[gray gazelle]

why

but anyway, did you say something about dynamical systems?

[flint forge]

do people do that zeta?

[blazing dagger]

Yeah it’s good topic

[flint forge]

i just sneak hausdorf into my definition of topology

[blazing dagger]

Brin and stuck good intro book

[gray gazelle]

idk what it is though

[blazing dagger]

It’s a book

[gray gazelle]

every space is hausdorff proof by induction on spaces

[flint forge]

every space should be hausdorff (or at least sober) is so morally true to me

that im willing to say bye to the zariski people

[blazing dagger]

Isn’t the zariski topology like not even t2

[flint forge]

and make them use a new word

[blazing dagger]

wait t2 I Hausdorff

I mean t1

[flint forge]

dont use those numbers lol

no one remembers which is which

they all have better names

[blazing dagger]

I don’t rmb what the name for t1 is

[gray gazelle]

t3.45

[blazing dagger]

It’s used so rarely

[flint forge]

whats the statement

[blazing dagger]

It’s like for points x y there’s an open set containing x not containing y and vice versa

I think

[frigid comet]

yea

[gray gazelle]

yeah dynamical systems seems out of my reach lol

[stone dragon]

uh what r some good books for hs elementary geometry?

[valid moth]

http://farside.ph.utexas.edu/Books/Euclid/Elements.pdf @stone dragon

( )

[broken meadow]

lmao

[gray gazelle]

lol

[zealous elbow]

Opinions on Visual Complex Analysis (Tristan Needham)

[civic carbon]

Not my favorite

But it is a good companion text

[valid moth]

I prefer Olfactory Complex Analysis by S. Melly

[hollow current]

in complex analysis for a moment i like Ian Stewarts haha

[hollow current]

any good books treating DE?

[marble solar]

Boyce and DiPrima is a good entry level DE book

[sudden kindle]

@civic carbon what's your fav complex analysis text

[civic carbon]

Gamelin

[sudden kindle]

opinion on Ahlfors?

[marble solar]

Ahlfors is the greatest complex analysis text ever written

[sage python]

Ahlfors feels a bit old school but pretty good. Gamelin seems promising

[marble solar]

It starts off with a lot of geometry at the beginning. If you're impatient you can jump to the derivatives

[sage python]

I wanna look at Narasimhan

[marble solar]

And keep coming back to the geometry

If you're looking for something more modern "Marshall Complex Analysis" probably fits that better

It's a new book, and the latter chapters are really well-done

[sudden kindle]

i took a course with Ahlfors and it was pretty bad.

[marble solar]

(Marshall actually wrote part of Gamelin's text)

[dapper root]

Hey lmao I used that book

Marshall is a prof at my uni

I hated it

[marble solar]

UW?

[dapper root]

Yeah

I took the complex series this year

[marble solar]

I had his advisor

Garnett

[dapper root]

I don't like power series first

[marble solar]

I'm moving up to the seattle area this august

[dapper root]

I had taken a course following the standard development before it, and it was hard to adjust

[marble solar]

Trying to get impromptu research at UW

[tranquil ocean]

@dapper root what year are you at UW?

[dapper root]

Rising junior

[tranquil ocean]

Know a guy named kasper?

[dapper root]

Yeah I do

[tranquil ocean]

He's a good friend of mine

[dapper root]

He was in my analysis class last year

He like

Didn't say much

[tranquil ocean]

I'm surprised he went to any classes

[dapper root]

and always talked like he was a mega idiot and didn't know what was going on, but he did well in all his classes lol

[marble solar]

Are Rohde and Bobby Wilson approachable?

[dapper root]

Like he beasted the final for our set theory class and did it all last minute then got a 4.0 in the class lol

I don't know Wilson

[tranquil ocean]

He's a pretty big memer/has insomnia/works like full time so

[dapper root]

Rodhe is a little gruff

[marble solar]

How about Toro?

[dapper root]

Maybe from being like more oldschool german and such

I don't think I know Toro either

I don't really know the analysts

[marble solar]

Tatiana Toro, geometric measure theorist

[dapper root]

I stick to the algebraic side

Ohhhhh Tatiana

I can't speak about approchability, but I know she's mega legit. I think she's probably really busy

[tranquil ocean]

How's Viray?

[dapper root]

Sorry, if you want to know about the algebraists I'd be a lot more help, but i really don't stick to that side at all

[sage python]

Oh I've heard of Toro

[dapper root]

Bianca is cool

[marble solar]

Analysis is in my blood and bones

[sage python]

Who's Marshall?

[marble solar]

Complex Analyst, student of John Garnett

[dapper root]

Marshall is a guy at UW

complex analyst

Wrote a book recently which develops complex analysis with power series first

[marble solar]

It's an interesting one

[sage python]

Oh Lang style

Let's check it out!

[marble solar]

I've only used it for the riemann surfaces, dirichlet problem etc.

I thought it was excellent

[dapper root]

I think the main like, draw of the book is there's a "constructive" proof of the riemann mapping theorem using the geodesic zipper algorithm, some thing he and Rohde developed together

I put "constructive"

in the quotations since I haven't bothered to see if it actually is, since I don't give a shit about constructive proofs

It might be, it might not be, I can't make a say on it

[sage python]

I put "constructive"
@dapper root brother

[dapper root]

I don't know if that's good, or bad

[marble solar]

Analysts love constructive stuff

[dapper root]

Yeah, and I am super not an analyst haha. Zorn's lemma in something? Let's go

[marble solar]

I can dig algebraic curves a la Fulton

Something nice, concrete

[sage python]

I'm half an analyst

I should go through some Fulton tbh

[marble solar]

I had a course on it, and it was great

We spent a lot of time computing explicit examples

I'm mulling over what I should read this summer

[dapper root]

Hartshorne

[marble solar]

Oh God

[dapper root]

:^)

[sage python]

Lmao

I'm doing Ravi's online course so hopefully I'll finally learn AG for real this time

[marble solar]

I'm debating between Stein's Harmonic Analysis, Harmonic Measure by Garnett and Marshall, or Terry's Random Matrix Theory

[dapper root]

You mean the one that's been pushed back 3 weeks in a row 🥴

[sage python]

Lmao yeah that one

Moon: Do Federer 🙃

[dapper root]

I kid, he said this would happen haha

[marble solar]

Federer?

[sage python]

Geometric Measure Theory

Especially theorem 4.5.9

[marble solar]

I don't know much about GMT

The other stuff I've taken courses on at some level

[dapper root]

Learn ergodic theory, that's something I hear get thrown around as some buzz word a lot

lol

[marble solar]

My topics in real analysis final presentation was on ergodic theory

50 minute lecture

Lots of fun

But sadly it hasn't been related to the research I've been in recently

[dapper root]

are you a postgrad?

[marble solar]

I just finished my MS

and submitted my first paper to a journal for review with some guy at UCI

[dapper root]

Are you trying to do a PhD?

[marble solar]

Yeah, trying is a good word for it

I'm applying this fall for next years admissions

[dapper root]

Ah, gotcha

[marble solar]

My SO is starting at amazon so it's like UW or bust

[sage python]

Good luck

At least you guys will be able to afford Seattle :P

I remember their stipend was something like $26k?

[dapper root]

Eh, PhD students can survive at UW

they usually room with another grad studnet tho

[marble solar]

Amazon is well in 6 figure range

We'll be good

[dapper root]

It isn't luxurious, but people at Berkeley are way more fucked

[sage python]

Nice

[marble solar]

we'll**

[dapper root]

And yeah I think it's about that much

Once you pass your prelims it goes up a bit and then again after the general

[marble solar]

LA is around 22?

[sage python]

Jesus fuck

[dapper root]

So just pass all the prelims when you come in 🥴

[marble solar]

Do you think they'll let me take prelims before being admitted mathemagician?

[sage python]

@dapper root is it based on your status as a grad student or just, it going up each year?

[dapper root]

Uhhhhh

Idk

Status

How far along you are

So moon

[sage python]

Oh wow that surprises me

[marble solar]

I can pass the analysis one

[dapper root]

I emailed them to ask if as an undergrad I can take them

They're gonna get back to me on it

[marble solar]

I've worked through 3 of them already haha

[dapper root]

you can take them right as you get in tho

So you can take it right as you come in and you don't have to take that sequence or whatever

So I don't know if you can take them in the fall, but it won't hurt to email and ask

[marble solar]

Ok

ty for the info

You guys used Marshall for grad complex?

[dapper root]

This year, yes

[sage python]

Also let's migrate to #math-discussion

[marble solar]

Thanks sloth

[valid moth]

[dense pewter]

he's back

[foggy fiber]

Anyone worked through Abstract Algebra by Greg Lee (from Springer)? I'm looking for a rigorous intro to abstract algebra, but the other books I've looked at are either too "intro-y" or for graduate level.

[main flax]

check pined message

[foggy fiber]

oh, sorry, new to discord

[main flax]

no worry

[sudden kindle]

Very good recommendation

[valid moth]

sully

[sudden kindle]

Archsys#2547 I will beat you up

[civic carbon]

Great choice

[valid moth]

https://cdn.discordapp.com/emojis/393085077866938368.png?v=1

[ionic wren]

archsys i could beat yamin in a fight i reckon

[main flax]

what is that book about?

[valid moth]

how high can you kick

[ionic wren]

pretty high ig

[valid moth]

in cm

[main flax]

[ionic wren]

atleast to my head height

or chin

[valid moth]

so, not very high

[ionic wren]

lmao

why tho

[valid moth]

because yamin is 6.9m tall

[main flax]

lmao

[ionic wren]

ohno

ohno

ok

i think i lose

[sudden kindle]

How do you know that

[ionic wren]

who

[sudden kindle]

Idek how many meters I am

[ionic wren]

6.9420

[storm sleet]

Anyone have any recommendations on good books for calculus of variations?

Upper undergrad level preferably

[marble solar]

My prof used bruce van brunt

Idk if it's any good, but he liked it

[wet badger]

Can anyone recommend me a book to self-study Number Theory?

[tranquil ocean]

What math do you know?

And why are you trying to learn number theory

[wet badger]

Well, it's in my curriculum for the next semester lol

I'm a 3rd year undergrad student and just finished taking Group Theory

[tranquil ocean]

If you know some basic ring theory things, Ireland Rosen is your best choice

[wet badger]

I'm kinda confused why you asked what math did I know, is there any preeliminaries for NT?

[dapper root]

There are differing ways to approach it

[tranquil ocean]

You can study NT using group/ring theory, which makes things a lot nicer

[dapper root]

You could go super basic, or do algebraic number theory

If you know a ton of algebra already

[tranquil ocean]

Fermat's Little theorem and Euler's theorem are just corollaries of Lagrange's theorem for example

[velvet briar]

Basic NT << Abstract algebra

You pretty much know it all already lol

[tranquil ocean]

So if you know algebra, you should read a book that uses algebra things

[wet badger]

Alright, I think since I already learnt a bit about Group Theory, might as well check Algebraic Number Theory too, thanks all!

[tranquil ocean]

Algebraic number theory requires galois theory

Algebraic number theory doesn't mean "algebra applied to number theory", its a bit more specific

[wet badger]

Ohh

Might skip that then, I haven't touched anything about Galois Theory lol

[tranquil ocean]

And you'd usually learn algebraic number theory after a course in elementary number theory

Using something like Ireland and Rosen's book

[wet badger]

Alright, going to check that out, thanks!

[tranquil ocean]

It's a great book

[dapper root]

Yeah algebraic number theory is super advanced

It requires a shit ton

[tranquil ocean]

Eh, you can learn basic algebraic number theory with some basic understanding of galois theory

And you can probably avoid schemes for a while too if you really wanted to

[dapper root]

Oh sure, but I mean it takes a good bit more than a first pass in groups and rings

Class field theory builds on Galois theory a ton and you deal with topological groups and stuff from what I’ve heard

[marble rock]

can you read ireland rosen

without reading basic NT

[civic carbon]

Yes.

It is "basic number theory"