book-recommendations

[halcyon terrace]

Mhm looking at the contents think im ganna go with Halls

has more of what I need

ty for the recommendations!

[marble solar]

no worries!

[tribal kernel]

I really like Hall’s writing style. His quantum book is also really good

[odd oracle]

Hall's books are dope!

He actually did a lot of work, finding pathways to proofs that before had been solved using more advanced methods. So in a sense a lot of his Lie grps book is "new"

One weird thing though, different definition of semisimple.

[hollow current]

recommendations on lambda calculus?

[drifting elm]

@hollow current I think it helps if you have a background in computer programming with those same structures

mathematica, lisp, haskell, python lambda functions

learning lambda calc from a book is the worst because you can't check your work and you usually don't have a lot of practice problems

they just dive into theorems

I don't think anything else in math prepares you for lambda calculus

mathematica is especially useful because you can have the computer check your work

something I learned after about a year was that there really is an equivalence between lambda style computation and classical computers aka turing machines

[warm sundial]

something I learned after about a year was that there really is an equivalence between lambda style computation and classical computers aka turing machines
@drifting elm The book Structure and Interpretation of Computer Programs (see e.g. https://sarabander.github.io/sicp) is great to explore computers in terms of lambda calculus (and also to learn CS in a mathy way)

It uses a lisp dialect called scheme which is essentially just lambda calculus with a little syntactic sugar

[cobalt arch]

Any books on a theorem that has actual math in it (for motivation)?

Like GEB but formalized

No one

[gray gazelle]

I thought these books are called textbooks

[cobalt arch]

Hahaha

I knew someone would say that but is there such a book? I want one with historical footnotes as well.

Or do I go raw into the abyss?

i.e. Frege sense and reference

I guess what I am looking for is a book on the philosophy of mathematics.

Or both

A book about a theorem and a book on the philosophy of math

No takers?

[quick hornet]

its hard to give an answer that isnt just a textbook

[cobalt arch]

I know:)

[quick hornet]

since as you can imagine, this is a pretty niche audience

[cobalt arch]

Yeah

[quick hornet]

and most people interested just dive into shapiro's thinking about mathematics or w/e

[cobalt arch]

Hm that seems like a pop-sci book just by the title:)

[quick hornet]

(which does cover frege)

it's a textbook

[cobalt arch]

Oh

Hm

Is it about the history/philosophy of math?

[quick hornet]

it's just written to be approachable

yes

[cobalt arch]

I see

[quick hornet]

cover text:

This unique text by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. The first describes questions and issues about mathematics that have motivated philosophers almost since the beginning of intellectual history.
Part II is an historical survey, discussing the role of mathematics in such thinkers as Plato, Aristotle, Kant, and Mill. The third section covers the three major positions, and battle lines, throughout the twentieth century: that mathematics is logic (logicism), that the essence of mathematics is
the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism). Finally, Part IV looks at contemporary positions and work which brings the reader up-to-date on the discipline.

Thinking about Mathematics is accessible to those with little background in either mathematics or philosophy. It is aimed at students and professionals in mathematics who have little contact with academic philosophy and at philosophy students and other philosophers who forgot much of their
mathematics.

[cobalt arch]

Okay I will check it out

Oh ty

[quick hornet]

i think its on libgen

save $50 or w/e

[cobalt arch]

Yeah haha

[obsidian valley]

sounds similar to Linnebo Philosophy of Mathematics, it's really new.

I'm about 3/4 of the way through, it's pretty good

[steel elm]

Calculus by Spivak vs Calculus by
Ron Larson, Bruce Edwards

?

[broken meadow]

uh spivak one has proofs right lol

wait are you asking

i am confused

for yourself?

i havent gone thru spivak but i know it's a step up from standard books like stewart/thomas/larson

type things

[gray gazelle]

Best calculus book is rudin hands down and don't listen to anybody else who wants to block your eyes from true art

[dapper root]

Maybe if ur really Chad

[dense wren]

Best calculus book is rudin hands down and don't listen to anybody else who wants to block your eyes from true art
@gray gazelle i assume you're referring to real and complex analysis, his principles of mathematical analysis book is a bit too simple imo

[hearty steppe]

Get out. That book is hard as hell to read

[gray gazelle]

all of rudin's books are trivial, you should have learned that stuff in middle school

[umbral hinge]

i found out about module arithmatic the other day and its opened up a huge door in the way i think about math... are there any good books that go into depth on modular arithmatic and stuff like that

i wasnt sure what type of math that was

[gray gazelle]

a number theory textbook?

[umbral hinge]

if thats what its under

i wasnt sure if it was abstract algebra or what

[velvet briar]

Abstract algebra is a good idea to check out

[drifting elm]

@umbral hinge https://www.amazon.com/Elementary-Introduction-Number-Theory-Calvin/dp/0881338362

I have a lot of number theory books but this one starts assuming you know nothing about number theory or notation.

all the other books on the subject assume that you have some background already. I also noticed that most number theory books have identical information. you probably only need one book unless you are full time analytic number theory professor or researcher.

this leveque book is more comprehensive but it is only usable if you can make your own proofs and learn from very short dense explanations. like a quick review of advanced stuff pretty useless at my level. https://www.amazon.com/Topics-Number-Theory-Volumes-Mathematics/dp/0486425398/

[umbral hinge]

Thanks!

Sorry for the low quality screenshot but does anyone know anything ab this book? It’s $5 so I’m debating also getting it lol

[hasty turret]

Libgen it?

[umbral hinge]

I know I could do that. Something within me really likes physical textbooks though

[hasty turret]

Check it out first then

[umbral hinge]

Ohh yea right

[obsidian basalt]

Any recommended book for generating functions?, if it is friendly with people who is new in math I would appreciate it.

[hearty steppe]

Generating functions? Like moment generating functions?

[obsidian basalt]

Like something like this:

http://discrete.openmathbooks.org/dmoi2/section-27.html#:~:text=There is an extremely powerful tool in discrete,But not a function which gives the n

Wilf.
This one?

https://www.amazon.com/-/es/Herbert-S-Wilf/dp/1568812795

[sudden kindle]

Yes

Theres A pdf online

[soft terrace]

anyone got a recommendation for stochastic differential equations books? The purpose is for review for someone that has, um, kind of forgotten a little bit of it

[marble solar]

I've heard evan's is ok

[soft terrace]

lawrence evans?

[marble solar]

mhmm

[soft terrace]

looks good nice and cheap

[marble solar]

https://www.amazon.com/Introduction-Stochastic-Differential-Equations/dp/1470410540

mhmm

[soft terrace]

i learned from a print out that i no longer have needed something new

found the pdf of it 😄

this is a nice book thx

[marble solar]

nw

[white pebble]

i mean rudin's books aren't explicitly hard

some ppl just think his approach is uncomfy

[sterile pelican]

It is not needed to learn spivak to learn rudin is it?

[marble solar]

No it's not needed, but it may ease the transition

I'm a fan of reading both at the same time

So it sticks

[sterile pelican]

Ah that is interesting, at the moment I am just finishing my transition book then to read halmos' naive set theory (or jech) and herstein's topics of algebra I felt like I wanted to learn abstract algebra first

so I wonder whether I really should read spivak or I could just jump straight to rudin

[marble solar]

So the way I say it is

Spivak's Calculus has most of the exercises Rudin does

And is more enjoyable to read

[sterile pelican]

alright!

[frigid comet]

I don't think that is true. It is probably a more pleasant and friendly read, but it definitely does not have most of the exercises Rudin has, as single variable calculus is only a small part of what Rudin covers.

[sterile pelican]

Rudin does have a multivariable section and covers metric space

and the lebesgue theory

the book does have a nice read too, I am just aiming to do abstract algebra first really

[frigid comet]

even not counting the multivariable and lebesgue stuff, because I don't think that part is so good, the best things rudin will teach you is just general basic analysis stuff, topological (metric, really) concepts in analysis, the role of concepts like completeness, etc.

good choice of herstein by the way kani, I think that book is beautiful for a first course in algebra.

[sterile pelican]

I love that book

[frigid comet]

dami is about to disagree

[sterile pelican]

I tried gallian and freligh but I think herstein does it well

[frigid comet]

based on a notational convention choice

[sage python]

Yeah I feel like Spivak might have the majority of exercises in Rudin chapter 1, 3, 5, kinda 6

Mayybe 7?!

Majority in the strict sense of \ge 1/2

4 idk

8 also idk

But both seem unlikely

[frigid comet]

have never really explicitly compared the exercise list but anyway the books serve pretty different purposes

[sage python]

Lol my thing with Herstein's choice is more like

I actually think his convention is strictly better than that of everyone else

But you can't really roll with it long term

And unlearning habits is a nightmare

My reservation is more that Herstein's kinda limited to group theory, after that it doesn't cover enough and you want other stuff

But group theory in Herstein is clean

[frigid comet]

yeah am mostly talking about group theory here

I think his writing is in general great though.

In the same way that I appreciate Spivaks writing

Rudin I love too but is different stylistically

[sterile pelican]

I got dummit and foote initially

but someone told me herstein is a far better first approach

[gray gazelle]

These days I just say fuck big books

Either I do a short book that's easy or a short book that's terse

[sterile pelican]

also not a fan of digital books they are convenient but for some reason my retention of learning has significantly decrease

[drifting elm]

I didn't really grok group theory till I watched the socratica videos

I saved something from stackexchange that I think is really concise

[gray gazelle]

Strange. Why would you add closure as an axiom? A binary function on a structure S is always SxS → S.

[prisma snow]

Emphasis

[drifting elm]

I am noob. this helped me a lot. saved it. read it all the time.

[hearty steppe]

Socratica videos? Like on YouTube?

[shell grail]

topology books, for first time learner?

[silver herald]

My Tops. Guy recommends Munkres

[stray veldt]

munkres is very long

why do you want to learn topology?

[calm crane]

munkres

[shell grail]

idk seems neat

[calm crane]

munkres isnt so long

like you only need up to say

uryssohn is stretching it

[stray veldt]

i recommend topology - an introduction by waldmann

[prisma snow]

How mathematically mature you are? There is a free online book called Topology Without Tears that is very thorough, but also very long with a lot of explanations and even explanations of proof techniques. If you're more mathematically mature, then a more standard book like the ones the others mentioned are better

[shell grail]

casual

i can prove things competently enough imo, explanations sound good tho

[prisma snow]

You may as well try it, it's free (legally)

If you think it's too slow, you can find another book

[shell grail]

yeah okay

ty

[obsidian valley]

is Topology without Tears by the same guy who wrote Godel without Tears

nevermind, it's godel without too many tears

[hearty steppe]

Loch why didn’t you recommend that to me

[prisma snow]

Books under 200 pages give me joy

[calm crane]

AM is under 200* pages

[prisma snow]

Books under 100 pages give me anxiety

[broken meadow]

free books...

[dapper root]

AM is 🤢🤢 tho

[steel viper]

noooooo

AM is nice

[gray gazelle]

am is expensive

[steel viper]

its free if john ships it to u

[gray gazelle]

i would just libgen and print it out tbh

is talking about piracy allowed here

[prisma snow]

Yes 🏴‍☠️

[heavy barn]

I've seen people encourage using libgen many times here, so probably

[obsidian valley]

It's fine as long as you dont link any pirate links, right?

cuz discord tos

[gray gazelle]

just libgen the book and upload it right here

Somehow discussion of illegal activity is allowed here

(as in, it's not against the rules)

People even post book PDFs here which I'm pretty sure is illegal lmao

(distribution of copyrighted work)

if any action was taken against posting book pdfs here i would be locked up

[broken meadow]

lmao

[slender dragon]

Everyday in this chat, Rudin is discussed

[gray gazelle]

it's just that good, huh

[slender dragon]

it's just that good, huh
@gray gazelle

Or that bad

Just kidding

[marble solar]

hey guys there's this cool free book for knots

http://math.ucsd.edu/~justin/Papers/knotes.pdf

[broken meadow]

'knotes'

that's clever

[feral pond]

For linear algebra for comp-sci. Which of the books in the #books-old Would you recommend
https://discordapp.com/channels/268882317391429632/556194300912861205/696811221013233705

[gray gazelle]

not roman

[hasty turret]

Why is kunze not there in the list?

[supple loom]

Strang

[marble solar]

LADR, H&K > Strang > Any other elementary linear algebra text

[sage python]

H&K > LADR easy

[steel viper]

hi dami

[sage python]

Yo

[marble solar]

(I agree Sloth)

[gray gazelle]

[wise vine]

Is Friedberg and Insel the modern substitute for H&K? I like H&Ks exercises and rigor tbh, but haven't read Insel yet.

[raw herald]

Its good

that's probably what counts

my uni uses it for the linear algebra course for math majors

[gray gazelle]

For CS strang's LA is good enough

[sterile pelican]

Out of curiosity are there any prerequisites for Hrbacek and Jech's Introduction to set theory? I am currently half way through hammack's book, currently reading on mathematical induction, and I want to know whether I need more background from the material

I had a little peak and chapter two is quite readable so far, albeit a bit of effort on the problems, but I am not sure how it translates towards the long term

[karmic thorn]

Mathematical maturity. Other than that Hammack's book would cover the basics.

[sterile pelican]

Hmm mathematical maturity feels a bit vague, is there any way to gauge it? Is Hammack considered a good bedrock to start developing one's maturity in maths?

[karmic thorn]

I don't think Hammack does much, it's more like a bridge text to understand basics of formal mathematical reasoning. I don't think mathematical maturity can be gauged either, but once you've done some undergrad math, Jech's text should be more understandable.

If you haven't already, you could learn some linear algebra, abstract algebra, and analysis before you move on to rigorous Set Theory.

Not that they are formally needed, but they lend much greater mathematical maturity.

[fast portal]

Rigorious set theory is a spook, learn differential geometry instead

[sterile pelican]

I do have herstein's topics in algebra and baby rudin

but I thought to read jech's introduction to set theory beforehand as my basis

[karmic thorn]

No, you don't need that kind of set theory for either.

I used to think one can learn maths in a linear order, starting from the foundations, then build up to more and more complex structures.

Took me a while to realise one doesn't(and probably shouldn't) learn maths that way.

[sterile pelican]

Hmm so i could jump straight to baby rudin or herstein after hammack?

[karmic thorn]

Sure. Rudin's a pretty terse text for a first read as I've heard. Have you done some proof-based calculus or linear algebra before?

[sterile pelican]

I only learnt books from Lang, like Calculus a short course

linear algebra was more computational based

[karmic thorn]

Did that include proof writing?

[sterile pelican]

No it wasn't really that rigorous

I do have Spivak's Calculus and Hoffman's LA though

[karmic thorn]

Well, Hammack's text is good at what it does, but I suggest you could probably work through proof based intro text first.

Spivak should be good.

You should start off with Spivak, and then slowly step into Rudin.

[gray gazelle]

no prerequisites for jech

[karmic thorn]

(when you're comfortable reading it)

[sterile pelican]

But do I need LA to know herstein's topics in algebra?

[karmic thorn]

@gray gazelle I acknowledge there are no formal prereqs, but mathematical maturity is definitely needed.

[gray gazelle]

welp

[karmic thorn]

I don't know about Herstein honestly. Gallian is the text I'm using for AA.

It's more suited to a beginner like myself. 😛

[sterile pelican]

So I am guessing like fraleigh then

[karmic thorn]

Well, start with any textbook and see if you're comfortable digesting its contents.

If not, look for a different reference, or just keep banging your head against things over and over till you get them.

Either approach works, but the latter is more time consuming.

[gray gazelle]

set theory charles C printer is good for beginners (if not jech)

[sterile pelican]

I do have halmos' naive set theory

[karmic thorn]

Pinter seems to write nice book for beginners, his AA book is also nice for a first read.

[gray gazelle]

too wordy

[karmic thorn]

Halmos is good, but again, some mathematical maturity would be beneficial.

Eh I like wordy books.

[gray gazelle]

eh

[karmic thorn]

Gives me more time to think lol

[gray gazelle]

i like terse books

[sterile pelican]

I think for now given I am still doing hammack I will move to spivak and hoffman then

Thanks Ted and CityHunter

[karmic thorn]

Sounds good!

Good luck!!

[sterile pelican]

Thanks dude

I was a statistics and data science graduate but I wanted to do pure maths now

[gray gazelle]

keep in mind jech is huge, so if you are not looking forward to learn any advanced set theory then jech is a nono

[karmic thorn]

I was a statistics and data science graduate but I wanted to do pure maths now
Interesting, I suppose you do have a working knowledge of a lot of undergrad maths?

[sterile pelican]

I studied a lot of applied maths without knowing why really

the only formal proofs class was discrete maths but even that wasn't too deep

After I graduated, and currently working as a programmer, I ended up at the rabbit hole of buying books and doing them whenever I have time

currently half way through hammack, though I did read chartrand's, polimeni's and zhang's book on mathematical proofs (just not cover to cover)

all and all I like the subjects thus far, it felt easier to understand the why compared to most of my statistics course

[karmic thorn]

You don't have to learn how to write proofs from proof/intro logic books, really. Pick up introductory undergrad texts, they'll usually guide you through proofs in the beginning so that you become comfortable with them.

For a very brief overview of basics of set theory and logic you need to get started with intro undergrad math, refer to the latest text pinned in this channel.

[sterile pelican]

is it called "intro to proofs"?

[karmic thorn]

Yes.

[sterile pelican]

Hmmm alright then

so this then off to spivak I go

[karmic thorn]

Sure.

[sterile pelican]

thanks Ted you are a big help

[karmic thorn]

No worries, and good luck!

[true swift]

Does calculus early transcendental does a good job on covering all 3 semesters of calculus?

[karmic thorn]

You should check what is being covered in those 3 semesters. Maybe your course has recommended readings?

[true swift]

i am self studying

I've studied calculus 1, and 2. But i want to refresh my knowledge before jumping into calculus 3

[karmic thorn]

Yeah, Stewart's book is good as far as I've heard.

[fast portal]

(for engineers)

[karmic thorn]

Welp, I think Calc 1-2-3 is how non-mathematicians see calculus.

Mathematicians would just be calculus and then intro analysis without sometimes even making any distinction, which is reasonable.

[true swift]

Yeah, Stewart's book is good as far as I've heard.
But early transcendental is not by stewert

it is by howard anton

[karmic thorn]

Oh, mb.

[true swift]

I am more confused now, Because there are 2 books with the same name and different authors

[karmic thorn]

The go-to advice when you're confused about multiple books when they do more or less the same job is to check out all of them. Grab their digital copies ||from Libgen||, see which one works for you, and get a physical copy then if you find it more convenient.

[broken meadow]

early transcendentals is a generic name

there are several of those

[quick hornet]

yes, people name their textbooks the same thing all the time

[broken meadow]

by different people

[quick hornet]

there are 12 billion books with the name "algebra"

thats why people generally refer to texts by author

rather than name

[broken meadow]

@true swift there is also a copy of thomas's calculus pinned in the #calculus channel - his book is also comparable with stewart calculus

[hollow current]

as poly would say: go and read rudin

[karmic thorn]

Thomas is the one I used and I like it.

[hollow current]

i do not like thomas much

[hasty turret]

go and read rudin

[true swift]

I've already ordered Howard Anton's book anyway

[hollow current]

it can be used for getting like basic notions and maybe some intuition but no more

[karmic thorn]

It's good at what it does, it should be an HS textbook or first course in calculus text imo.

[latent brook]

I was planning on starting to self-study some advanced statistics. I've started "An Introduction to Probability Theory and Its Application", and its pretty good, but it seems outdated. Is this a good book to continue, or are there better ones? I should add, I'm more interested in the pure math aspect than any applications.

[lilac jackal]

Hello.
Is it fine to recommend "Introductory Econometrics: A Modern Approach" for an entry-level student?
(big sorry if I used a wrong channel)
👉 😳 👈

[gray gazelle]

this is literally the book discussion channel, of course it's the right one

[buoyant spire]

Thank you for the recommendation, Introductory Econometrics looks very interesting! (you're fine)

[late bobcat]

What books would you guys recommend for real analysis?
It's my first proof based course so I am struggling a bit. For other modules I just buy a textbook and the solutions manual and work through problems and its worked fine for stuff so far.

I tried this approach with Analysis using Abbott's book and while the content is fantastic, I am only getting around half of the exercises 'right'. I read online that looking up solutions for analysis too quickly is more harmful than good so I do try to give it a fair attempt but lots of my solutions are different from the book and I can't tell if its a valid alternative or not due to online teaching giving us far less contact hours.

So my question is like a 2 in 1 pretty much, what books do you guys recommend and how do you recommend learning this subject?

To see if your solutions are correct, try to just read them and see if they are logically correct
@gray gazelle I try this, and its good and I show my teacher sometimes but quite a lot of the time I am missing out details which is a bit disheartening, but I am assuming this should get better in a month or two?

yeah, I'll try asking my teacher more often

Thats true

idk what it is about real analysis that just frustrates me more

yeah thats fair, thanks

Also, have you read Rudin?

and if so, would you recommend it?

Yeah, I'll give it a shot. Not as a main book, but just for an alternative perspective on things

ah yeah, that makes sense

doing a proof based course online feels kinda weird

like our midterm was just multiple choice pretty much

yeah, I will do cause as it stands now I don't even know what to expect on the final 😂

All he said was

"People who struggled on the midterm, please work harder. The finals will be much more difficult"

[cobalt arch]

Any set theory books with lots of exercises?

[obsidian valley]

I have not personally used it just yet but my course in set theory next term uses Hrbáček

I know Enderton has a Set Theory textbook as well, and his logic one is quite good, so I expect good things out of that.

[cobalt arch]

I see thank you

[sterile pelican]

I am not sure if I should mention it here but I am currently reading a book by Lara Alcock called, "How to study as a mathematics major" as it gives some pointers of trying to adopt abstract thinking. I think it serves as a supplement, alongside some introduction to proofs, to help transition that mentality towards mathematical maturity...she gives some great summaries and further reading, if you need, to see what is expected from an undergraduate student

and provides reasoning as to why, I am currently on the second chapter and it is a nice read

[hearty steppe]

Oh shit nice rec @sterile pelican I need to check that out

[sterile pelican]

hell yeah dude

[hearty steppe]

Btw there seems to be a couple other books she’s affiliated with that seem worth checking out. Check out her biblio

[sterile pelican]

hmm there are a lot of "How to think about..." books which are quite interesting

I will give my current book a finish, then give my overall view about it

[pulsar aurora]

lol alcock. All cock.

[still umbra]

is there a "best book"/goto book for category theory?

[molten wave]

mac lane

[still umbra]

Categories for the Working Mathematician

ty

will check it out

[modern silo]

Hi guys! My friend wrote a book for olympiad number theory, and I felt this is one nice place to share https://artofproblemsolving.com/community/q1h2344755p18942323
If you're aware of Evan Chen's EGMO, this is supposed to be a number theoretic analogue in the sense that it's very complete.

[late bobcat]

I love you and your friend @modern silo Thanks!

[modern sorrel]

It looks very well written

[modern silo]

thanks!

[gray gazelle]

can you recommend a book on optimization for a visual learner with no attention span? I think this book might not exist

(I really like the openstax textbooks for example, because they are very clear with lots of images and have short chapters)

[prisma snow]

Work on improving your attention span

[hasty turret]

Try a lecture series on youtube?

Books are usually not the ideal medium for visual learners

[gray gazelle]

even if I improve my attention span, I still need visuals. I will try lectures, thanks @hasty turret

[velvet briar]

Calculus is very visual yeah. YouTube will have lots there

[gray gazelle]

well the thing is calculus 1 had a lot of visuals but what I need help with is the envelope result and convex optimization - we’ll see what i find

anyways, thanks

[velvet briar]

Oh I see, not what I was expecting

[vapid scroll]

Article preferred, any small introductions on manifolds? I want one of those 20 page pdfs that have some exercises scattered throughout.

[gray gazelle]

you said "small" and i was gonna say spivak's calculus on manifolds

but then i saw 20 pages

[marble solar]

Spivak calculus on manifolds chapter 5 only

That'll be 20 pages

[velvet briar]

Books like Tu and Lee are considered introductions but their main content is a few hundred pages haha

[fast portal]

From 1 to 10 how good is serge lange's book on complex analysis

[vapid scroll]

Does anyone know what I am talking about when I am talking about those small introductory articles. These are a couple of examples:

http://pi.math.cornell.edu/~hatcher/Top/TopNotes.pdf
https://people.math.gatech.edu/~trotter/book.pdf
http://people.math.harvard.edu/~jjchen/docs/Group%20Theory%20and%20the%20Rubik%27s%20Cube.pdf

[gray gazelle]

Hey guys, does anyone know how I can get the solutions to even numbered excercises to a textbook I bought?

By solving them

[marble solar]

Sometimes it's in the back of the book

[gray gazelle]

In the back of the book, only the odd numbered excercises answers are given

[marble solar]

Hrmm

I think ya just gotta hunker down and solve

[gray gazelle]

I just want all of them to have more practice

[broken meadow]

is there like a slader for these kinds of textbooks or

[marble solar]

COURAGE SHUKI COURAGE

[gray gazelle]

How do all these websites even work?

[marble solar]

You can solve the even ones with only the odd solutions

I believe in thee

[gray gazelle]

What do you mean?

How would I know if I did the even ones right?

[marble solar]

You should be able to solve them with just the odd solutions as an example

You won't. You have to think

Real hard

[gray gazelle]

Ok. I wanted to double check, but ok

[marble solar]

Part of the reason textbooks do that is so that students develop a sense of solving problems

Independent of some authority telling them what the answer is

[gray gazelle]

I guess there is just no way to know the answer to the even ones

I guess you are right

[marble solar]

Other than solving them

[gray gazelle]

I am currently studying multivariable calculus

I am using Stewart Calculus for problems

[marble solar]

If you have questions go to an instructor or office hours

Are you self studying?

[gray gazelle]

Is there a better book?

[broken meadow]

thomas is similar

[marble solar]

Stewart should be fine

[broken meadow]

but i think stewart is fine

yea

[gray gazelle]

I am self-studying to get better at the class. I am majoring in math

[marble solar]

If you're real stuck

[broken meadow]

you want to focus on the Problems plus

[marble solar]

You can always wolfram alpha

There's a $5 app for phones that can do lots of integrals with steps

[gray gazelle]

I am currently taking calculus 3, but there is no textbook for me to use.

The class just doesn't use a textbook. Only lectures

[umbral hinge]

What kind of textbooks do u like

Or do u just like good textbooks lol

[gray gazelle]

I would like rigorous problems and good problems

spivak

But I guess good textbooks would all work

[marble solar]

Well if you want rigor

Apostol Volume 2

But that might be a bit much.

[gray gazelle]

What does Apostol Volume 2 have?

the answers to everything

except my homework problems

[marble solar]

It has a good theoretical development of Calc 3

The theorems and proofs in Stewart are mostly lack-luster. Which is fine for a first pass of calc 3

[broken meadow]

@gray gazelle since i know you from elsewhere you may want to check out the calc 3 honors textbook from the school u go to

[marble solar]

But if you want rigor

[broken meadow]

i don't want to name names since i don't want to dox

[gray gazelle]

@marble solar That is what I would like

@broken meadow Yeah man. You are in my other group

[broken meadow]

yus

[marble solar]

wow metal is in the same class

What a coinky-dinky

[broken meadow]

shhh

[marble solar]

Hey can I be in ur calc 3 club

$$ \int \del \times F = \int F \cdot n $$

[hasty eagle]

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

[umbral hinge]

I just bought a vector analysis book from 1911 the other day I’m hoping it’s good

[marble solar]

it's not del?

Is it \grad

[gray gazelle]

\nabla

[marble solar]

fudge

See how much I latex calc 3?

Not at all

You're in RG

So you do it alot

[gray gazelle]

hehe

[umbral hinge]

Do u guys ever watch the math sorcerer on YouTube

[gray gazelle]

$$ \int_M \nabla \times F , dV = \int_{\partial M} \langle F, n \rangle , dA $$

[umbral hinge]

He does math textbook reviews lol

[hasty eagle]

TTerra:

[gray gazelle]

or something like that

i don't use divergence thm a lot

[broken meadow]

is it not the divergence and not the curl

[gray gazelle]

oh

[broken meadow]

nabla dot

[gray gazelle]

divergence is nabla dot

yeah

mb

the curl one is the weird kelvin-stokes thing

something about a unit tangent to the boundary??

this is what happens when your "calc 3" class is spivak's calculus on manifolds and you do the last section in a single class

ah wait i think proving the divergence theorem was on my manifolds final

optional question

[broken meadow]

lol

[gray gazelle]

you can literally define the divergence of a vector field on a manifold to make the divergence theorem work

lol

like one way to do it is if $X$ is a vector field on a riemannian manifold $(M,g)$ with volume form $dV$ then you can define $\nabla \cdot X$ as the unique function satisfying $$ \nabla \cdot F , dV = d(i_X(dV)), $$ and then stokes' gives $$ \int_M \nabla \cdot F , dV = \int_{\partial M} i_X(dV) $$ and you can show that $i_X(dV) = \langle X, n \rangle , dA$, where $n$ is the outward (unit) normal on the boundary and $dA$ the volume form of the boundary

[hasty eagle]

TTerra:

[gray gazelle]

divergence literally defined so the divergence theorem is true lmao

[broken meadow]

lmfao what

that's hilarious

[gray gazelle]

i mean

stokes' is doing a shit ton of heavy lifting

ah i forgot to say oriented

but maybe you don't need that

[marble solar]

Kelvin-Stokes

Only in the English commonwealth

[broken meadow]

stonks theorem

i just learned it recently

and man

i gotta rewatch that lecture

[shadow nebula]

wtf weren't you irrotational like 2 years ago

[broken meadow]

yeah

but

dont worry about that

only now am i actually like

in a calc3 class

[normal rain]

What are some good contemporary books to read on Philosophy of Mathematics? Anything written before Gödel I imagine is useless.

[quick hornet]

the standard intro text is shapiro's thinking about mathematics

the name might strike you as juvenile but the content is good

(and his follow-up text, the Oxford handbook, builds significantly on the material)

the Maddy essays are mandatory reading at some point

i.e. "believing the axioms" (pts 1 and 2) and whatnot

[normal rain]

Thank you 🙂

[gray gazelle]

Does someone know of a reference with solved problems (or discussion) for quotient spaces of sequence spaces

In functional analysis

so for example it has problems of type: let l be bounded sequences and l_1 bounded sequences with their limits existing. find dimension of the quotient?

I've looked everywhere and I cannot find anything

[hearty steppe]

@quick hornet is the follow up book your referring to "Foundations without Foundationalism: A Case for Second-Order Logic"

[gray gazelle]

Second order logic - the poor man's set theory

[hearty steppe]

hey where can i get ahold of believing the axioms by maddy

nvm

found it

@sweet lotus which papers/books you referring to

[odd oracle]

@hearty steppe https://www.cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms1.pdf

just axiomatize googel

[errant swift]

What would you guys recommend for an intro self-study calculus book? Right now I'm using Morris Kline's Calc book. Not sure if that's the right way to go 🙂

[sudden kindle]

I bought that book in highschool and never opened it

[errant swift]

Oh did you have any issues with it :(?

[sudden kindle]

No i just dont naturally tend to read things

[warped cedar]

i recommend khan academy if your are doing single variable calculus

[sudden kindle]

I'm more inclined to watch things, I learned from MOOCULUS https://mooculus.osu.edu/

[hearty steppe]

thanks I already found Maddy's believe in the axioms Pt 1 and 2

[warped cedar]

i have the MIT calculus text pdf

if you are interested in that

[errant swift]

The one by Gilbert Strang?

[warped cedar]

yes

[errant swift]

I got that one too :). Thank you though :).

[warped cedar]

that ones good

[errant swift]

Can that book be self-study'd? I heard that it relies on the lectures

Also thanks for the lecture notes @sudden kindle

Lol maybe above my head @sweet lotus 😦

[warped cedar]

theres a pretty good amount of information

that will get you through to calc 3 in there

[sudden kindle]

https://www.youtube.com/watch?v=2MrH499MvHw

I forgot how great these videos were

[errant swift]

I gotcha. Thank you. I think my only problem with Morris Kline's book is I understand all the lectures well enough, but some of the later exercises I feel aren't solvable through the material already covered

[warped cedar]

thats what i love about calculus

figuring out how to apply your knowledge to new problems

[hasty turret]

Why is that specific to calculus?

[warped cedar]

idk i just like calc in particular

[errant swift]

Fair enough

If an object moves along a circle of radius 𝑅, its position can be described by specifying the angle 𝜃 through which it has rotated. The derivative of 𝜃 with respect to 𝑡 (time) is called the angular velocity and is usually denoted by 𝜔; that is, 𝜃′=𝜔. The derivative of the angular velocity with respect to 𝑡 is called the angular acceleration and is usually denoted by 𝛼; that is 𝜃″=𝜔′=𝛼. The linear distance covered by the object is 𝑠=𝑅𝜃 if 𝜃 is measured in radians. Answer the following questions concerning circular motion:

What is the linear velocity? Answer from key: since 𝑠=𝑅𝜃, 𝑠′=𝑅𝜃′

This was the problem in the book. It's the last exercise and I had no idea how to solve it. Because the book up until that point mentions nothing about implicit differentiation or chain rule, which I assumed were pre-reqs for solving it. So wanted to look at some other text material to figure it out

[warped cedar]

im getting a minor in engineering and I use a lot of calc xD

[errant swift]

I'm trying to get through Ian Goodfellows book which relies a lot on calc, de, probability, stats, and linear algebra. It's been a minute since i've taken those courses 😦

[warped cedar]

why the sudden reinterest ?

[errant swift]

Machine Learning

Trying to switch away from being a backend dev into a machine learning role

@warped cedar the question about. Would you happen to know how to solve that without implicit differentiation and chain rule? Like I can't think of how I'd be able to figure out the solution otherwise 😦

[warped cedar]

you are given almost all you need to solve it

you are given linear distance function 𝑠=𝑅𝜃

you might know velocity is the derivative of distance

derive both sides with respect to time

ds/dt = d(𝑅𝜃)/dt = R𝜃'

thus s' = 𝑅𝜃'

[errant swift]

Ah thanks, yeah that notation d(𝑅𝜃)/dt, I didn't think that was feasible. Up until now the book has treated it as a unit expression

[soft terrace]

this is going to be a hard one but is there any material on doing fractals in non euclidean planes?

[warped cedar]

you might be best to look at some publications on those

not sure what youd find in terms of traditional texts

[calm crane]

often the limit set of some discrete subgroup of PSL(2,C) has fractal like structure and we do take the complement of limit set as boundary of hyperbolic manifolds

but yh doing fractals is super vague

[vestal otter]

For a introductory account Indra Pearls is pretty tame and have extremely beautiful pictures!

[candid girder]

I agree

[soft terrace]

indra's pearls looks good thx guys

[gray gazelle]

I just had to take a screenshot of that dude in the function video

[karmic thorn]

#chill

[raw herald]

this is sexy: http://www-math.mit.edu/~rstan/ec/catadd.pdf

[odd oracle]

An enumaddendum

[blissful turtle]

In the field of combinatorics I personally liked this book (as a student of this subject) Principles and techniques in combinatorics

Really good explanations for each ideas

[raw herald]

ooouu

I kinda love combinatorics but im a young one still

gotta read read read

[vale garden]

has anyone read a good very intro to logic and set theory

[obsidian valley]

Enderton

[polar tulip]

@vale garden at what level?

[waxen elbow]

opinion on Roman's linear algebra ?

[calm crane]

if you really need more information on modules over a PID, go ahead

[stuck depot]

guys can you suggest an algebra book?

[sage python]

Check pinned messages

Has the ultimate guide to algebra books lol

[stuck depot]

thanks

[gray gazelle]

.

[soft terrace]

this one is lowercased though

[strong plank]

Does anyone have good books that I can ask for Christmas ?

[vivid brook]

yes

depends on what you are interested in

[gray gazelle]

oooh shiny!

[dapper root]

Pls ignore his recommendation

That’s a book for babies it wold be like buying 80 dollar nursery rhymes

[gray gazelle]

sure buddy

[marble rock]

why does every1

make memes on this textbook

higher topos theory

whats funny

[stray veldt]

have you tried reading it?

[marble rock]

no

it seems to be higher than me

rn

( and prob forever )

why does it contain memes

[calm crane]

stay innocent

[marble rock]

omg i dont get it omg

[strong plank]

i m interested in number theorie and linear algebra

[stray veldt]

both "an introduction to the theory of numbers" and "a classical introduction to modern number theory" are nice number theory books

[strong plank]

and for linear algebra ?

[stray veldt]

i don't have strong opinions, maybe linear algebra done wrong or linear algebra done right

the former is probably better for a first reading

but also not sure if physical copies exist

[strong plank]

ok

[steel viper]

if you havent seen linear b4

a classical intro to modern NT is a bad choice

it assumes an algebra background

its not elementary

[stray veldt]

the first chapters are

but yes

[steel viper]

idts

iirc even chapter 1 references ideals

[stray veldt]

it does

but it states that you can ignore it

[steel viper]

mhm i guess

[strong plank]

ok

[stray veldt]

it just rephrases statements in the language of ideals

[steel viper]

i think youd still get more out of it if you had a background though

[stray veldt]

probably

[unkempt grove]

I recently found these books on the archive and they're pretty interesting but the age shows. Are there any more modern books with more or less the same content? first volume's table of contents is attached
https://archive.org/details/in.ernet.dli.2015.502134
https://archive.org/details/in.ernet.dli.2015.502136
https://archive.org/details/in.ernet.dli.2015.502137

[strong plank]

@unkempt grove thx, I m going to check that

and do you have some good linear algebra books ?

[valid moth]

@unkempt grove basic mathematics by lang maybe

[unkempt grove]

ill check it out, thanks

[valid moth]

not exactly modern either but probably less old

[unkempt grove]

bet

[calm crane]

is h&k recommended as a intro to lin alg these days?

[unkempt grove]

these are books from 1932 lol

[stray veldt]

maybe for the math major

[marble solar]

H&K is great

[stray veldt]

it is, but i wouldnt use it for an intro class

[valid moth]

y

[calm crane]

ye but it seems like it traumatises people as intro xd

[marble solar]

Hrmm I think it's doable as an intro course

[steel viper]

its doable

the exposition is just really fucking dry lol

[marble solar]

You can pair it with a computation focused text

[calm crane]

as a math intro course ye

[marble solar]

maybe like schaum's outline to linear algebra

[stray veldt]

mostly because i would want something more modern

dunno, just the feel of it

[steel viper]

it could be traumatizing on its own ari

[calm crane]

idt physicists care about anything outside of R&C

[marble solar]

The modern books are ass

[steel viper]

it kinda was to me

[stray veldt]

i would just write my own notes

[valid moth]

do axler and a separate source for determinants, the exposition is better

[steel viper]

if u had a class

itd prolly be good

[stray veldt]

yeah, axler seems good with a teacher

that introduces determinants on the side

[marble solar]

I dunno, I don't like these more modern texts

[calm crane]

idk whats up with him and determinants

[marble solar]

I like the ones like Ahlfors

[calm crane]

dets are such powerful tools

[stray veldt]

but like, my point is, there isn't the ideal linalg text at least not for me

[valid moth]

how about narasimhan

[stray veldt]

(at least not in english)

why sully me 😦

you may not believe it, but there are non-english math books and they are sometimes better

[valid moth]

what book 🤔

[calm crane]

i need to start looking for those

idk how to math in chinese at all kinda sad

[steel viper]

what do germans use to learn AT loch

[stray veldt]

there is one by Jänich on linalg

not sure its translated

[valid moth]

@calm crane don't you have some chinese physics books

[stray veldt]

i like that

i used lecture notes for AT

[calm crane]

i mean math

chinese physics is pretty like self explanatory

[valid moth]

https://kupdf.net/download/klaus-janich-linear-algebra_58ab2d4c6454a7a236b1ea31_pdf

this?

[calm crane]

at least basics

[valid moth]

yeah but i imagine they include some math terms 🤔

[calm crane]

i mean like math math

how do i communicate noetherian module

[stray veldt]

seems so

is this a bootleg translation

[vivid brook]

I know about 1 semester of number theory I saw above someone recommended "a classical introduction to modern number theory" what should I know before I read this?

[steel viper]

basic ring theory

[calm crane]

^^^^^^^^^^^^^^^^^^

[stray veldt]

basic algebra

later in the book you will also need galois theory

[steel viper]

yea

u can get thru a lot of it w/out any

[stray veldt]

and some calculus for the analytic stuff

[unkempt grove]

what would this be called? its not modern day "advanced algebra" and not high school algebra either. and yes i got serge langs book delivered over the internet and its ToC doesnt quite have the same stuff

[fast portal]

hey has anyone used theodore shifrin's differential geometry notes/book
i'm wondering how it compares to do carmo's

Posting for my directionally challenged friend

[marble solar]

Ok, so I've looked at ted's book; my prof was office mates with him when they were in grad school

It's ok at best

[gray gazelle]

[marble solar]

There's some nice applications that's done there

[fast portal]

@cloud bobcat

[cloud bobcat]

yea playa

[gray gazelle]

yohan how do you keep finding the money for nitro

[marble solar]

However, I think spivak's calculus on manifolds when combined with something like schaum's outline to differential geometry is much better

[fast portal]

I just have a lot of simps

[gray gazelle]

are people buying you nitro

[fast portal]

yes

[cloud bobcat]

lol nice

happened to me once

[gray gazelle]

yohan's popular

[marble solar]

The schaum's outline to diff. geom. is great because there's lots of explicitly computed examples of torsion, curvature, fundamental forms, paramterizations

It's very analytic. Also spivak's calculus on manifolds is one of the best math books ever written

[cloud bobcat]

moonbears have u seen ted shifrin

o

i s

ee

my eyeballs now work

[marble solar]

I haven't met him, no but my prof is good friends with him

[gray gazelle]

moonbears is objectively right when he says that btw

[cloud bobcat]

hmm ok. my prof was a student of his

[marble solar]

Told us stories of him and Ted fucking around

At Berkeley

[cloud bobcat]

im going to be like

"yo prof, my friend says he worked with the author and his book sucks"

and suggest schaum instead

wait

[marble solar]

Spivak calculus on manifolds

[cloud bobcat]

i only have the time to go through 1 consolidated source of material this semester

[marble solar]

• Schaum's outline to differential geometry

[cloud bobcat]

i'm not sure i can suggest 2 sources to work off of

[marble solar]

My professor wrote a supplement to spivak calculus on manifolds

but that's hard to get a hold of

[cloud bobcat]

i am doing it as a guided reading course

[marble solar]

Oh, suggest spivak calculus on manifolds

(You read spivak cover to cover)

[cloud bobcat]

i will be honest i thought spiivak com was like

a follow up to baby rudin or smth

in the vein of munkres' aom

im learning them

slowly but surely

i'm self-reading Tu's intro to manifolds rn

[marble solar]

Teddy has good youtube videos online too

for his course

[cloud bobcat]

i might study under him at uga if he is still teaching next year

[marble solar]

Didn't ted retire and move to LA?

[cloud bobcat]

@gray gazelle if i can argue well for it, then we'd use 2

[marble solar]

https://www.math.uga.edu/directory/people/theodore-shifrin

[cloud bobcat]

but the premise is that the instructor assigns reading per week or so

[marble solar]

Teddy is retired

[cloud bobcat]

i'll use multiple sources no matter what

awwww

that's unfortunate

i'm just wondering what's best to guide a class on

so the idea here is that i cover the material in shifrin's book, or in do carmo's book

my goal in the end is to study riemannian geometry later which i realize wont much be helped by this but it is nevertheless a prerequisite

[marble solar]

Shifrin is interesting. I still think the best bet is spivak calculus on manifolds and put it together with schaum's outline to diff. geometry

[cloud bobcat]

no, do carmo has a non-riemannian book

[marble solar]

That's my 2 cents

anyway gtg

[cloud bobcat]

ok thanks moonbears

yes

lemme grab the info from uga's catalog, sec

diff geo of curves and surfaces

[marble solar]

are you at UGA?

[cloud bobcat]

i already have good texts for the other 2 subjects

[marble solar]

waiting for my student to show up for tutoring

[gray gazelle]

toponogov... triangles...

[cloud bobcat]

@marble solar i am trying to get in on recommendation from my algebra professor

i go to ung currently, we do not have diff geo courses

i'm doing independent study under a mathphysicist

okay

thank you

[gray gazelle]

same toponogov as in toponogov's comparison theorem?

i guess ill check it out

neat

[steel viper]

hello evil gristle

[cloud bobcat]

hi mothy

[steel viper]

[gray gazelle]

tiny

[cloud bobcat]

moth do you know diffy geo

[steel viper]

no sorry : |

[gray gazelle]

i like small books

[steel viper]

idk any analysis

[cloud bobcat]

ok

[gray gazelle]

[cloud bobcat]

gonna be a geometer

[gray gazelle]

wtf

yeah stuff like that wouldn't be a problem

i gotta learn the classic curves and surfaces theory at some point

so id prefer a shorter book

[cloud bobcat]

why do ppl say a curve is a mapping : I -> R3

its not

[gray gazelle]

probably referring to its image/

?

it gets abused a bit

[cloud bobcat]

well u dont map an interval to a point in R^3

[quick hornet]

uh

do you not know how function definitions work

[cloud bobcat]

u map points in R to R3 continuously

[quick hornet]

...but you dont map points in R to R^3

im so confused

[gray gazelle]

nash embedding sounds like a cool theorem

[quick hornet]

unless youre interpreting R as the extended reals with silly addition, ie a structure isomorphic to [0, 1]

[marble solar]

Oh yeah

[gray gazelle]

sure, i'll check it out

[marble solar]

that's a good idea

[cloud bobcat]

well the preimage of a parametrized curve is a real number

and the image is... a point in R3

[quick hornet]

...yes...

[marble solar]

https://www.math.ucla.edu/~petersen/DGnotes.pdf

Here's something from peter peter

[quick hornet]

you realize that the interval is a subset of R

right?

[cloud bobcat]

and so it's R -> R3

yes

but you don't map subsets to R3

you map subsets of R to subsets of R3

[marble solar]

Whomever was interested in DG of curves and surfaces, that online notes I just sent is pretty good too!

[quick hornet]

so then its a map from I to R^3

[marble solar]

Written by a master of differential geometry

[quick hornet]

where I is a subset of R

its not a map from P(R) to R^3

i dont think anyone is claiming it was

[cloud bobcat]

peacock, why is it not I to something like I but 3dimensional

[steel viper]

oops wrong channel

[quick hornet]

a function needs to be defined on all its domain

it does not need to map to everything in its codomain

[cloud bobcat]

ah ok

[quick hornet]

if it does we call it a "surjection"

[cloud bobcat]

i see now

makes sense yep

u just unretarded me

thx

yea

i cannot explain what i was thinking

without a paragraph

but believe me it was bad

moonbears i will take a look at petersen

[obsidian valley]

Why does it need to be called a surjection while the other one is called an injection

That didn't make sense to me for so long until I realized it was just french

[cloud bobcat]

hmm

i'm really curious now; just what does spivak cover?

is it the same material?

here's the content

this is what i'm meant to be learning

hmm?

indeed

the first pic i posted was calc on manifolds

ye

indeed ok

i see. i'll cross-compare the three of do carmo, petersen, and shifrin and make a decision by january

no, i know it's not from what i've been reading in tu

petersen looks really, really good

[marble solar]

Yes. Petersen is an excellent teacher

He's very careful when he writes

Also exceedingly clear

[sudden kindle]

jORDAN peterson

[marble solar]

Read properly

Petersen

Peter petersen

If I had to pick one to teach out of, I'd probably do peter peter's text

[cloud bobcat]

thank you so much moonbears

^_^

[marble solar]

No worries! I've ta'd a curves and surface class a few times

and calc on manifolds thrice

[gray gazelle]

three times

[marble solar]

I took the course in 2016 - I Ta'd 2017, 2018, and 2019

[cold juniper]

I've just started reading Munkres's Topology(2nd Edition), and while going through the review of sets, I've noticed some over-complications, such as the definition for the rule of assignment. Is that definition necessary in topology? I was wondering if there are any better options for learning Topology or is Munkres the way to go?

[marble solar]

Just skip chapter 1

start in chapter 2

[gray gazelle]

people actually read the intro logic/set theory chapters of books?

[cold juniper]

Well I did because I thought it would say something I didn't know that was topology-specific. Is there not anything like that?

[steel viper]

there is not

[gray gazelle]

nothing in munkres ch1 is about topology

you can skip it

and just come back to it when you need

it is useful for things later in the book

[cold juniper]

Ah ok, tyvm.

[gray gazelle]

as long as you're familiar with like, 60% of the stuff in ch1, you should be fine to start ch2

i pull that number out of my ass as i stare at the toc

[molten wave]

@cold juniper which "rule of assignment"?

[vale garden]

opinion on "naive set theory"?

[obsidian valley]

I need to know the definition of the naturals TTerra

[gray gazelle]

uh oh

1,2,3,4,5,6,...

am i in the clear

or is it over for me

[polar tulip]

@vale garden good book. a novice could easily read it but it covers all the advanced set theory you'd need to know for regular mathematics (choice, zorn's lemma, well ordering, ordinals, cardinals)

the first half is a breeze, the second half will take more time if the content is new to you

[hollow current]

hi @gray gazelle

whats up

[gray gazelle]

alg midterm tomorrow

[obsidian valley]

hi @gray gazelle

[gray gazelle]

hi did i get the naturals right jesse

[hollow current]

so it is time to go and not to learn, ye?

[gray gazelle]

soon

i have to do a few things

idk as long as like

i know sylow

should be good to go

[hollow current]

"Proof we leave as an exercise to professor"

[gray gazelle]

plus a few facts about group actions

wtf even is there

[obsidian valley]

no tterra

0,1,2,3,4..

[hollow current]

no jesse

-1, 0, 1, 2, ...

[gray gazelle]

orbit-stabilizer...

[hasty eagle]

jesse:

[gray gazelle]

ok i have t ogo

[obsidian valley]

[hasty eagle]

Commander Vimes:

[obsidian valley]

good luck with sylow tterra

[gray gazelle]

thanks

[obsidian valley]

idk what sylow is but good luck

[hollow current]

good luck with group sex ttera

[gray gazelle]

[hollow current]

[obsidian valley]

wtf

i thought group theory was supposed to be cool

[hollow current]

i thought my life was supposed to be cool

[obsidian valley]

[hollow current]

[gray gazelle]

i don't like questions that are just like

compute this random thing about this random group

bro i dont fucking care about like

[obsidian valley]

ok back to mathematical logic lectures good luck in your future endeavors every 1 B)

[hollow current]

ok ttera another question

[gray gazelle]

quick

[hollow current]

Prove Riemann hypothesis

[gray gazelle]

before i really have to go

no

[velvet briar]

Yeah Sylow is kinda lame

[hollow current]

ok ttera prove Collatz

then do your test

[velvet briar]

For me the good stuff is "you have this relation, find the group"

Which is like a puzzle

[fluid bay]

Sylow is kinda lame
I’ll fight u

[dapper root]

Those questions are the best

Sylow baby too big

[gray gazelle]

i just did "prove that no group of order 6545 is simple"

idk what compelled me to

how is this fun

[dense pewter]

sylow is dumb

[dapper root]

Cuz lots of elements

Smh I’m gonna leave this server

What is this anti-Sylow propaganda

[gray gazelle]

it was simple (hah) since the number of sylow subgroups of a given prime was either 1 or something else

so like if G is simple

you just add some things

and get a thing bigger than 6545

[dense pewter]

it's not that sylow is dumb, it's that sylow shouldn't really occupy such a big place in intro group theroy classes

[dapper root]

Yeah TTerra that’s fun

You get to go

TOO BIG

[gray gazelle]

im expecting at least one problem like this tomorrow

maybe not with such an astronomical number

but hey this prof writes some pretty fucking awful tests so i wouldn't be surprised

[dapper root]

Prove groups of order 1,004,913 are NOT simple

This is very hard with Sylow and a multi-step process

[dense pewter]

prove that every simple group can be generated by 2 elements

[dapper root]

...

Wut

[gray gazelle]

[dapper root]

Wait

I messed up the statement

LOL

[sage python]

Yeah Sylow was my favorite part of early group theory for sure but I do admit that undergrad algebra should focus a bit less on it since, if you're not into algebra it's not likely useful to you at all, even if you are it's sorta limited

[cloud bobcat]

p!=np otherwise we would have found a counterexample by now

[gray gazelle]

my class barely focused on it

just

[dapper root]

It’s not really even useful if you’re into algebra

Tbh

It’s just fun

[dense pewter]

for the record the only known proof of my statement uses classification of finite simple groups

[gray gazelle]

i literally have a midterm tomorrow so i need to be covered

[sage python]

I think people like it because it kinda shows.. I don't wanna say the power of group theory but like

[dapper root]

Because group theory is fun (objective fact btw)

[dense pewter]

but it's known that if we could give another proof of that statement which didn't use classification, then the proof of classification would be much much easier

[sage python]

Idk it's one of the fewish theorems of substance

[dapper root]

Wait Buncho

Is what you said actually true

[dense pewter]

yes

[dapper root]

What the fuck

[dense pewter]

yep

[gray gazelle]

[dapper root]

Nah the classification is wrong

[dense pewter]

I have lots of fun finite simple group facts for you if you want them

[dapper root]

Bruh what the

[dense pewter]

well

actually no I take that back

[sage python]

What else in a group theory class has real substance? I guess the p\mid |G| implies element of order p but that can be deduced from Sylow anyway

[dapper root]

If you pick two random elements they generate it with probability going to 1 as the size increases

[dense pewter]

yes that is also true

that was actually the one fact I had

[sage python]

As currently done, I think intro group theory should cover more representation theory

[dense pewter]

so "lots of" was maybe an overstatement haha

[sage python]

"More than the average person"

[dense pewter]

I do have some fun facts about solvable and nonsolvable groups (which are built up from noncyclic simple groups)

dami have we had that conversation? I also think that sylow should be replaced with baby rep theroy

[sage python]

I've actually been thinking maybe even Galois theory

Like thing is

I love Galois theory

But its use is a bit more specialized to algebraists