book-recommendations

[marble solar]

and I attended two separate CCs

[sudden kindle]

wow

thats a lot of explaining

[marble solar]

so it took a while for my transcripts to get all ordered and done

[sudden kindle]

okay guys

i failed a course this semester, should i keep sending the transcript without fall grades or would that be bad idea

[marble solar]

send it without

Lol

Just explain what happened

[sudden kindle]

why would i explain if they dont see the F?

[marble solar]

I mean

When you send in your official

after you get accepted or something

[sudden kindle]

oh ok

sure

i thought you meant explain in my applicaiton

[marble solar]

nah no need to explain lol

I got a B in a very easy class in the spring

That should have been an A but

🤷

My life goes on with two arms, two legs, and a beautiful spouse in a beautiful house

[sudden kindle]

i literally got an F tho

not in a math class but in a minor class (CSE)

[ripe granite]

probably doesnt matter if it isnt in a math class

but again, I do not know much about how the process works

[gray gazelle]

Yeah, like eg what if you took a computability course from the cs dept? That's basically a math class

[sudden kindle]

its scripting languages, we did python, ruby, bash, and rails scripting

[ripe granite]

yeah idk

are you going to apply to more places?

or just those?

[sudden kindle]

im applying to eight more, earliest deadline is Dec 30, i plan to submit them all by then if not earlier

[ripe granite]

good luck

[summer moth]

Best books for trig/precalc? For preparation of college, would also be nice if it had some more advanced stuff in it too!

[summer moth]

Also is there a book that I can read on more abstract mathematics that alg 2 level can understand? It doesn't need to be in depth, just interesting.

[still umbra]

This is a very broad request but: I'm looking to read a book which has a lot of very good word problems. I'm currently entering my 2nd year of university study in mathematics and stats. I've found that symbol juggling is very boring and I really like problem solving.
I would be interested to learn some math with a large focus on solving worded/project type questions

[karmic thorn]

Try combinatorics/graph theory?

[summer moth]

Me or cursor?

[still umbra]

Probably me

[still umbra]

I'm reading Mark Newman's "Networks" at the moment and really liking it. I'll have to check out some combinatorics stuff

[obsidian valley]

Yeah try anything that CS uses

[still umbra]

I am actually formerly a CS major

[obsidian valley]

Me too 😎

[still umbra]

So I've come across a lot of graph theory stuff in competitive programming scenarios

• algorithms in general

[obsidian valley]

Given that you are math/stats the obvious thing is like

ML things

but Cs bad

so idk

[still umbra]

yee

ML things trend into engineering type stuff

"stack layers yolo"

/joke

[obsidian valley]

I mean if you want word problems any sort of uh

[subject] for engineers textbook

will do that

I think

[still umbra]

algebraic topology for engineers

category theory for engineers

[obsidian valley]

well cat theory

i could see that

[still umbra]

https://www.nasa.gov/sites/default/files/atoms/files/mssrc_uah_nasa_30-09-2018.pdf

bruh moment

[obsidian valley]

cuz func programming

[still umbra]

yes

[obsidian valley]

[still umbra]

but it's not really cat theory, more focus on type theory specifically

But I see what you mean

I just want to find a super dank textbook which has these crazy pure-math concepts but instead of having you prove random bs thigs it gives you a worded question

i.e. making pure math stuff applied x)

[obsidian valley]

Take up cryptography

B)

[still umbra]

ew number theory

[karmic thorn]

Try Miklos Bona's A Walk Through Combinatorics. The problems I've encountered so far are proof-based but combinatorics inherently requires thinking outside the box which I find fun.

[still umbra]

Skimming the questions right now, I'm actually quite liking it

[karmic thorn]

It is a nice book. Ideal for learning on your own since the solutions are contained within the book.

[fathom monolith]

I’m taking real analysis next semester. As anyone who has helped me can attest, I’m not ready for that. What’s a good book to pick up over the break?

[silver herald]

Rudin

[fathom monolith]

I guess I should say it’s a senior level undergrad course. Since I’ve seen some real analysis courses early on in curriculums

Yea I tried reading rudin. Sorry but if that’s the standard I’ll take my F now

[regal elk]

you can look into Tao's analysis books

they seem to be pretty good

[fathom monolith]

I haven’t heard much about his. I’ll look into them though

[cobalt arch]

Has anyone read aluffi's algebra: chapter 0?

[obsidian valley]

Do you have a specific question concerning it

[cobalt arch]

Yeah I want to learn cat theory

I want a gentle intro to it

[obsidian valley]

Weren't you asking me basic set algebra questions the other day

[cobalt arch]

Yeah

[obsidian valley]

UGCT

[cobalt arch]

Haha

[obsidian valley]

Why do you want to learn cat theory

[cobalt arch]

What is that?

[obsidian valley]

UGCT: Undergrad Category Theorist

HSCT: Highschool Category Theorist

etc.

[hasty turret]

Aluffi exercises are not very good

[cobalt arch]

Because I want a general overview of many different topics of mathematics treated at once in a formal way

[obsidian valley]

Thats...

Listen I don't know fuck all about category theory but you should probably learn some other fields of math first

[hasty turret]

And category theory was usually not very useful in aluffi

Just do it the normal way

[cobalt arch]

Haha lawvere seems promising

Have you read that drunkendrake?

[hasty turret]

Yes

I don't see why category theory is useful(in context of basic abstract algebra)

[cobalt arch]

I must mention I have not the best exposition to mathematical branches but I do want a formal way to learn it. Allufi gives a somewhat motivated approach from what I read about his book.

[obsidian valley]

Do you know any algebra at all?

[hasty turret]

Like I get that,you could draw the commutative diagrams but I didn't see the point

[obsidian valley]

Like Group/Field/Ring theory

[cobalt arch]

No that is why I want to read aluffi

At least try to

[hasty turret]

Just use a book like d and f

[cobalt arch]

Hm

[obsidian valley]

I guess he wants to learn algebra thru CT

[fathom monolith]

My math journey largely consist of buying a book above my brow and getting mad so i give this my stamp of approval

[hasty turret]

Or just check the recommendations

[obsidian valley]

Are you not literally taking intro linear algebra like

next semester?

Slow down dude

[hasty turret]

Probably try artin

[obsidian valley]

Try Axler

[wintry edge]

Anyone have any recommendations for books for an introduction to Kalman filters?

[cobalt arch]

No no you get the wrong end of the stick I want to learn category theory in a more friendly and motivated context and then try to get into it more seriously

[hasty turret]

Artin: The objectively correct entry point for most people. Does a good job at showing you algebra is cool, and doesn't assume any linear algebra background (like I'm pretty sure he defines a matrix lol).

[cobalt arch]

Hm interesting

[hasty turret]

Why everything

[obsidian valley]

I still don't understand why you are rushing into cat theory

[cobalt arch]

Because I want a formal treatment of many topics at once without overlapping knowledge

[obsidian valley]

is there some youtube video all the UGCT are watching that treats CT as some amazing treatment of mathematics

[hasty turret]

I mean there are some decent ugcts here

[obsidian valley]

of course

[hasty turret]

Like the cat guy

[fathom monolith]

my CS professors talk about it alot and make the motivation for it seem interesting, even if i dont really get it because i have no background.

[obsidian valley]

But he hasn't taken Calculus I apparently?

Like I don't wanna be judgy lol

[cobalt arch]

Well CT is one of many foundations so why choose say set theory/model theory or the like over cat theory

That is why I everything

[obsidian valley]

Learning foundations is not a way to magically learn the other areas of math

[hasty turret]

Are you a philosopher,by any chance?

[obsidian valley]

It might give you a cool lens to view things through, I guess

but that's it

[hasty turret]

Because I don't think people think foundations are well useful(in context of doing other math)

[obsidian valley]

Yeah

[hasty turret]

Yea,Just do normal algebra

[cobalt arch]

I want a formal treatment of different kinds of topics on math. I don't want to rush into anything but I don't understand why there needs be such an upheaval because I want to learn and become a UGCT as jesse put it.

[hasty turret]

That's literally normal algebra

[obsidian valley]

The formal treatment will come from doing textbooks relevant to the area of math you want to learn

The most formal treatment of algebra will be from an algebra textbook

You can do whatever you like, but the idea of learning CT before you've done calc 1 or whatever is pretty funny

[cobalt arch]

I agree

[obsidian valley]

Just go read Higher Algebra tbh

Break out a hardcopy of Higher Algebra during your calc 1 lectures and flex on your prof

[fathom monolith]

I have never met anyone ever that was at the precalc level capable of engaging with any form of formal treatment of anything. It's just not normal for an individual to be capable of something like this.

[obsidian valley]

Yes.

[static crest]

read dummit and foote for good algebra and then you can flex on your hs teachers

[obsidian valley]

idk if just feels like you're treating category theory as a "cheat" to learn other stuff or whatever

But it's really not that

Well, maybe it is, I don't know

but I doubt it

Lmao

Yeah I agree

[static crest]

I wasn't being ironic

abstract algebra is very learnable in high school

[cobalt arch]

So wait would it be good to learn abstract algebra before I learn cat theory? What are the prerequisites to cat theory. They seem to be many to fully understand and appreciate the field but I want to know if there is a shortcut of sorts . I didn't put it the best way I could, I just want a formal treatment of many different subjects at once because I want to learn the underlying structure of it all .

[static crest]

So wait would it be good to learn abstract algebra before I learn cat theory?

yes

1000%

[hasty turret]

You learn cat theory,When you need cat theory

[obsidian valley]

You literally will have no lens to view the "underlying structure" if you don't understand the structure to begin with.

[cobalt arch]

Right

Well isn't then aluffi's book a good intro to both ?

[fathom monolith]

its like investigating the soil without any idea what you plan to build ontop of it

[cobalt arch]

Or d&f will do it

[static crest]

there's a lot of good textbooks on it

I just threw d&f because I use it

some people hate it

[obsidian valley]

[static crest]

gallian is apparently decent for abstract algebra for a first intro

[cobalt arch]

Because apparently I am good for nothing . So fits the bill.

[fathom monolith]

I have Charles C pinter's abstract alg book. Its cheap and decently reviewed.

[obsidian valley]

You are good for learning things that aren't category theory in first year.

[static crest]

learning cat theory without abstract algebra first is like learning calculus without learning functions

[obsidian valley]

We're just saying this is best way to spend your time.

[cobalt arch]

I see okay

[obsidian valley]

Same as - model theory doesn't make much sense if you don't know algebra

Because all the examples are from algebra

[static crest]

undergrad math is a pretty big tree of subjects you have to learn

it's all interconnected somehow

[obsidian valley]

Set theory is probably the lowest pre-req required to learn "foundations"

[static crest]

hard to jump somewhere

[obsidian valley]

I guess

If you're just deadset on doing foundations

[cobalt arch]

Oh:)

Well in a sense I am sullying myself

[obsidian valley]

I think you should just read Enderton if you want to start learning foundations

[fathom monolith]

Theres no more powerful force in academia than interest. You are interested, and that will carry you. This isnt a bad thing, everyone just wants to point your interest in the right direction. So please dont be so down on yourself

[obsidian valley]

Read enderton while you learn algebra

That will be useful

[cobalt arch]

Okay so abs algebra + a logic textbook and then aluffi would be good?

[obsidian valley]

Make sure you learn calculus I first.

[hasty turret]

Just don't do aluffi then

[cobalt arch]

Okay I see thank you.

[obsidian valley]

The concern I'd have is that you literally just lack the mathematical maturity to understand some of the stuff in enderton

[hasty turret]

I don't get your obsession with aluffi

[obsidian valley]

These subjects that are "high-level math" but with low pre-reqs usually require a ton of mathematical maturity

[cobalt arch]

I guess I abide by what is recommended on math se so apparently I am more than I thought I was.

[obsidian valley]

But people see that you "can" learn CT in highschool/early undergrad and think it's viable I guess.

For example, you cannot do enderton without knowing really simple stuff that you would pick up in first year math, like induction proofs

I'm being a bit harsh but

Better than you banging your head against Aluffi and not getting a single proof.

[static crest]

should also throw in some lin alg somewhere

before going near cat theory

[obsidian valley]

Of course

[static crest]

or any advanced math really

[valid moth]

imagine not studying constant algebra

[obsidian valley]

I can only imagine that doing first year math before you do CT is a good idea.

[cobalt arch]

Well if the treatment of many a subject was different we could probably discuss this topic more in depth and with the seriousness it requires since cat theory in its own right is a useful branch of math whether or not I can appreciate it fully yet. It will be useful to me because I want to be able to have a bird's eye view of many topics and how they are interrelated. So in that sense I find cat theory a worthwhile pursuit. Thank you for the help I guess and I don't want to come off as condescending.

[valid moth]

i dont think you need to do AG before cat theo jesse

[obsidian valley]

You can't come off as condescending when you don't understand what you are talking about B)

But yes okay I see

Do your thing.

[cobalt arch]

Well who does know

[obsidian valley]

You know that

Tao blog post

about different levels of mathematics

let me find it

I think it does to an extent

I'm not saying its gigabrain

I'm saying it probably won't make sense without knowing like... other math?

¯_(ツ)_/¯

shrug, I don't know cat theory myself

[hasty turret]

You wouldn't see a point to care about cat theory

[obsidian valley]

~ connections ~

xd

[cobalt arch]

Well I don't have anything to say than that my spirit has been broken but probably for the better. I am very down to earth but I just wanted a heuristic to mathematics and I would prefer if we had such a bird's eyes view instead of the opposite.

That is my two cents

Haha well I am :(

[drifting elm]

yes this exists here https://www.amazon.com/Princeton-Companion-Mathematics-Timothy-Gowers/dp/0691118809

you can read the table of contents

but if you buy the book you get 1 or 2 page summary of every area of mathematics

[obsidian valley]

What is this

Oh it's not relevant

To what forsaken wants

[drifting elm]

a birds eye view of mathematics?

[cobalt arch]

Thanks for the recommendation though

[obsidian valley]

"birds eye view" as in the connections between different fields, he means

[static crest]

he wants to be an undergrad category theorist

[obsidian valley]

yes

I wish I was a UGCT.

[drifting elm]

oh I see

[static crest]

why

[obsidian valley]

Then I could talk in #category-theory

[cobalt arch]

Why you ask?

[static crest]

not you, why jesse wanted to be one

[obsidian valley]

Of course he would

Every time I send a message in #foundations I get worried

Ultra

[static crest]

me but in #groups-rings-fields

every time I want to help or correct, I'm worried I'm gonna look dumb

it has to do with my internship, I need to learn a good amount of abstract algebra before it

[obsidian valley]

I've been watcing Lex Friedman a bit

and he asks the most fucking stupid questions

and I want to be more like that

I'm working on getting over worrying about looking stupid

[static crest]

[obsidian valley]

cause it leads to better learning I think

ye

[drifting elm]

serious question though what kind of book has all this in one book

[obsidian valley]

that

[static crest]

wikipedia

[stray veldt]

hopefully none

[static crest]

if you want a quick refresher on something in math, then you go to wikipedia or like wolfram or something

maybe the appendices of some algebra tb has that as a table

[drifting elm]

how much of this is group theory how much is category theory?

[static crest]

I mean only the bottom two rows are group theory

ebut like they are all algebraic structures

so as like a fun appendix table in an algebra textbook, it might exist

[obsidian valley]

Unital magma

[drifting elm]

so this is abstract algebra?

[static crest]

kinda but not really

I doubt normal ug abstract algebra

would deal with that

[drifting elm]

or just advanced algebra?

[stray veldt]

its not advanced

you just almost never need this stuff

well, groups are everywhere

but the other stuff not really

[static crest]

monoids come up a lot in cat theory

no?

but ya, other than the groups and monoids, idk how much literature exists

on the rest

[drifting elm]

monoids and magmas right?

magmas are cat theory right?

[velvet briar]

You can even see "small category" near the top

Which is an algebraic interpretation of a category

[stray veldt]

a monoid is a category with a single object

i don't see how this is interesting for category theory at all

[velvet briar]

Much of this isn't abstract algebra but some of it is useful in other courses

[static crest]

"More generally, in category theory, the morphisms of an object to itself form a monoid, and, conversely, a monoid may be viewed as a category with a single object."
-wikipedia

for whatever it's worth

idk much about cat theory

I just hear monoids thrown around a lot

[stray veldt]

small categories aren't really interesting to category theorists

[drifting elm]

they like to make the hypergaphs?

so a monoid would be a graph of S2

[stray veldt]

what

[drifting elm]

binary operation

[stray veldt]

as for magmas, the only reason i ever heard that term is because of the computer algebra system magma

[drifting elm]

that maps to itself

[stray veldt]

you can think of a monoid as that i guess

a single objects with only loops

[drifting elm]

I thought category theory was about hypergraphs and automated proofs?

[stray veldt]

category theory is about categories

[drifting elm]

I get that

but you put things in categories for a reason

[stray veldt]

i dont see how hypergraphs come into play

the reason is natural transformations

[drifting elm]

I was listening to a lot of steven wolfram but maybe he is not the best to explain it

[stray veldt]

well, that was the original reason

other than that it provides a useful language

[hollow current]

||wow||

[still umbra]

guys im just finishing primary school and i have started reading Mac Lane's Categories for the Working Mathematican, its kind of tricky, can you give advice on some category theory books which arent so hard

[drifting elm]

has anyone finished the two knapp books? https://www.amazon.com/Advanced-Algebra-Anthony-W-Knapp/dp/0817645225

[still umbra]

virgin UGCT
vs
chad PSCT

[stray veldt]

read Riehl

[drifting elm]

https://en.wikipedia.org/wiki/Emily_Riehl#Books

?

free book she posted https://math.jhu.edu/~eriehl/elements.pdf

[stray veldt]

not that one

this https://math.jhu.edu/~eriehl/context.pdf

[drifting elm]

thank you very much

I will read it

[limpid gazelle]

Category theory in context

[marble solar]

Is that book any good?

[pearl imp]

has anyone experience with Stewart's Calc book?

[static crest]

kinda garbage

by kinda, I mean very

if you plan on never learning math past calculus and basic linear algebra, then I guess it's fine

[quick hornet]

one advantage of stewart is that half of the US has learned out of it at some point

and "half" might be an underestimate

so theres a lot of resources out there if youre struggling with anything

i dont think its a bad text as far as computational calculus goes

its probably one of the better ones, they actually invested in the pedagogy and whatnot

although it is a bit bloated

[timber mesa]

bloated as any computational calc book is

[pearl imp]

I'm self learning calc from the book (and a few others like Thomas and Larson)

I was wondering what a good strategy is for doing exercises

There are a lot, really a lot

like integrals and whatnot

I did the odds but I think it takes too much time

[quick hornet]

well you shouldnt (and probably physcially cant) do all the exercises

you should do exercises until you feel confident that the other exercises would be easy

[pearl imp]

I wanted to do only the red ones for some sections/chapters

[quick hornet]

this is admittedly a tough thing to judge

[fossil island]

i honestly dont think it matters too much tbh

there's a lot of resources wrt calc

[pearl imp]

like for integrals

there is always something new

almost always

[fossil island]

for me, i found youtube videos really helpful

[pearl imp]

at the beginning

the amount of exercises helped me to fill some gaps in algebra etc.

but now, they start to feel repetitive/boring

like grind

[fossil island]

yeah that's usually what happens

if you are forced to do them, then dont

choose ones that might not be obvious

[pearl imp]

yeah, you right

[dapper root]

tbh if you're just self studying

like closing your eyes, randomly picking 20% of them

you'll probably have very few gaps

[gray gazelle]

This is probably a stupid question but can you like read two books concurrently

[broken meadow]

...

How concurrently are we talking

[dapper root]

one eye for each book

same time

[broken meadow]

damn that's concurrent

[marble solar]

Not memorizing the book before you read it

Are you even trying

[silk quartz]

Interleave the words.

[dapper root]

MoonBears is applying the "how to succeed in hard math classes" strat to reading books

just know it all before you start lol

[gray gazelle]

idk how reading two books at the same time works, but people apparently do it

so like how do you read two books at the same time

[silk quartz]

More seriously, I think it can be beneficial to study two different texts on the same subject at once.

[marble solar]

See you read one book, go back in time and read the other one at the same time your other you was reading that book

Also, I agree with Samantha

[dapper root]

I disagree

or at least I would have

1 year ago

But now, yeah

[gray gazelle]

if it is not on the same subject?

[fossil island]

maybe if you have your corpus callosum severed you'll be able to read two things at the same time

[silk quartz]

Especially if the two texts approach the material differently.

[dapper root]

I think if you're struggling then that's helpful

but if you're just breezing by it isn't necessary

[silk quartz]

Oh, two different texts on two different subjects?

[gray gazelle]

yeah

[silk quartz]

That's... like all of school.

Unless you really mean 'at the same time'

[gray gazelle]

if you're self-studying

[dapper root]

what's the difference?

I'm sure you've gone to school before

and had to read more than 1 text at the same time

[silk quartz]

Interleaving study of different subjects may well be a good thing.

[dapper root]

It's clearly possible, and I'm sure you've done it

[silk quartz]

It gives your brain a break from the same topic.

[gray gazelle]

ofc I have done it in school but not while self-studying

[silk quartz]

I recall a finding from Memory research, that showed that returning to the same topic for a short duration over time led to better retention than doing a single long study session.

[gray gazelle]

I have a hard time grasping how it would work, like do you read one book and then the other book the next day?

[fossil island]

just create a schedule

do a few problems from one book and a few from the other

[silk quartz]

So I find it plausible that say, 2 hours of subject A, and then 2 hours of subject B each day would be better, in the long run, then 4 hours of subject A every day until done, and then 4 hours of subject B.

Provided subject B does not directly depend on understanding subject A.

[gray gazelle]

hmm that sounds good

[fossil island]

but importantly, if you're not understanding something from subject A, dont just decide to go to subject B

really take the time to understand whatever it was in subject A

you don't want to sort of use subject B as a way to push off understanding subject A

i say this because i've had trouble with this

[silk quartz]

At the same time, sometimes taking a break from subject A and returning to it the next day can be helpful.

[fossil island]

yeah that's why it's hard to say something concretely

[drifting elm]

https://www.youtube.com/watch?v=mjYZrVP312o

[quick hornet]

i should review stewart's calculus from the perspective of being used as a blunt weapon

it's probably more effective than most options.

[drifting elm]

is it ironic that the thumbnail is a picture of a disaster?

[dapper root]

Not the copy I bought from my community college bookstore. That was... LITERALLY LOOSE PAPER. I had to put it inside of my own binder, and there's so much it literally started to destroy my binder because of how much paper there was

[marble solar]

But if you don't, then students complain about buying 3 books

[hearty steppe]

Probably as catapult ammo

[pearl imp]

what calc book would you guys then recommend?

for someone who's at the start of the journey?

[hearty steppe]

Do exercises from Stewart and read Paul’s online notes

[marble solar]

Spivak is good

[static crest]

ya, but spivak isn't for someone who's at the start of the journey

[pearl imp]

I was thinking about starting to read spivak when I'm 2/3 through Stewart

as a bridge to analysis

or go directly to Tao's analysis book

IDK

[valid moth]

if you already did calc you can just do tao

[marble solar]

Spivak > Tao

[cobalt arch]

[marble solar]

At least in terms of writing, clearly Terry is a first rate mathematician

[wooden sparrow]

Wait

I read Tao a little

His writing seems fine:thonk:

[quick hornet]

theres that famous "second rate mathematician" stackexchange story

a well-respected professor writes to a reference letter recommending one of his undergraduate students

the admissions committee reads through and its an absolutely glowing letter

[wooden sparrow]

Okay?

[quick hornet]

talks of best student in the class, huge accomplishments, etc

that is, until they get to the end

where the letter concludes

[subtle siren]

At this point I'm an n-th rate mathematician and that is because we are assuming the set of all possible rates of mathematicians is countable.

[quick hornet]

"In conclusion, [x] would make a brilliant second-rate mathematician."

[subtle siren]

my we=I

[wooden sparrow]

What

[quick hornet]

the school, surprised by this sudden change of tone, sends a letter back to clarify the wording

and the professor replies

"i don't see what the problem is; you are, after all, a third-rate school."

[subtle siren]

This story really needs to change to writers and journals

[wooden sparrow]

Wait

Who decides the rating though?

[subtle siren]

Actually for books

Is there even a 'first rate' math publisher

[subtle siren]

Biased people

[quick hornet]

i dont think anyone cares who publishes your books no

like springer is the most well-known

but i dont think its any more prestigious

than any others

[flint forge]

I only read orang publications

[quick hornet]

i only read Publish-or-Perish Press books 😠

i have read baby rudin 500 times

[subtle siren]

Lots of Springer's books are 100% downloadable for so I guess that makes me biased a bit

[wooden sparrow]

Okayy... Soo.. Spivak is better than tao because?

[pearl imp]

is this a comparison between Spivac's calc book and Tao's Analysis I? And if so, does it mean the first is greater/better then the second? Also, are there even comparable? Or is it just the individuals you compare?

[marble solar]

I'm comparing Spivak's Calculus text to Terry's Analysis I and II

In terms of a text, I think Spivak's Calculus text is superior because of the better exposition, more problems, although it's not as advanced

That can easily be remedied by moving onto Spivak's Calculus on Manifolds for multivariable, where I think Terry drops the ball hard

[cobalt arch]

The classic is baby rudin right?

[marble solar]

That is one of the classics

Along with Apostol's text

[cobalt arch]

Well apostol's text is 50/50 in theory and applications

[marble solar]

I am of that opinion Yohan

"Applications"

Not really, but it is good for analysis

[cobalt arch]

Oh is it?

[marble solar]

I'm speaking of Apostol's mathematical analysis texts

[cobalt arch]

Oh

[marble solar]

Not his calculus one

[cobalt arch]

I see

[marble solar]

It's very similar to Rudin

[cobalt arch]

I didn't even know he had such texts

[marble solar]

Just more fleshed out

[cobalt arch]

Well I think that Rudin is golden

You will reap off the rewards if you read through the text.

[marble solar]

This is mostly true of baby rudin

Not true of papa rudin

[pearl imp]

For probability, what book would you recommend alongside Stewart/Thomas Calc? Like that level for self-studying?

[cobalt arch]

Hm how so moonbears?

[marble solar]

I'm at work

[cobalt arch]

[wooden sparrow]

@marble solar are analysis books supposed to have solutions?

Somewhere?

[pearl imp]

have you checked Slader?

don't know if they have that level but normal calc books yeah

[flint forge]

Almost all intro analysis books have their solutions online somewhere

[wooden sparrow]

Okayy

[storm sleet]

Abbott Understanding Analysis is tougher to find for the last few chapters in my experience

[pearl imp]

those you make it the last chapter are martyrs

won't find many

[storm sleet]

We have a 2-term advanced calculus series using Abbott

second term is second half (ish)

[cobalt arch]

Any books on proofs?

[storm sleet]

Book of proof is p good from what I've heard

also, see #books-old for other recommendations

[wooden sparrow]

Okay, I didn't think I'd have to ask for this even though the chances were high, but here we go

Anyone know a book on calculus which is not as rigorous as spivak? But gets through the portion well enough?

I don't dislike rigour. I don't have the time unfortunately

something that can get me through this engineering nightmare

[gray gazelle]

try engineering math books

Like, kreyzig?

[wooden sparrow]

single variable calculus?

there's no engineering oriented books for that I believe

[gray gazelle]

It has ODE

But

For single var

If you want a quick way out you can see jee calculus books. Else there's Stewart calculus

[wooden sparrow]

jee

[gray gazelle]

Or Thomas calculus maybe

[wooden sparrow]

okay I'll check them out

[static crest]

if you want to just get through engineering, and not pursue higher math really

stewart is fine

stewart is perfect for what it's meant to do (teach 1st years how to grind calculus computations, like eng students normally do)

[wooden sparrow]

I want to pursue higher maths. I just have to get through this now

I have 16 subjects and 4 labs in my backlog

[static crest]

if you can't really deal with spivak calc atm, I'd just suggest putting off more rigorous calculus until later, like a summer self study kinda thing

[wooden sparrow]

Thanks.. I'm kinda in a dilemma since a few days

[sterile pelican]

I wanted to reiterate why I still stuck to Spivak's Calculus is due to how he tries to tell you the story of numbers then eventually towards calculus, Tao does seem to have a similar conversational style, albeit a tad but slower and more comprehensive (then again it is an analysis book and I didn't read all of it), but I think it is far better to learn from Spivak as a first exposure to rigorous maths, let alone calculus. Lastly, I learnt a lot from not just his conversational style but from his exercises they are challenging and in some cases mindbogglingly hard but very fulfilling once everything clicked, his definition of a function is all so nice (and the exercise that tests you on that makes it all so clear) and his explanation of a limit is expressed so clearly (still requires a bit of effort on my part) that I think everyone should learn that part.

[wooden sparrow]

@sterile pelican If all goes well I was actually thinking about learning analysis from tao while doing exercises from spivak 😛

[sterile pelican]

I think an extra supplement would be good like apostol, if you could afford or go 2nd hand, or libgen. The other is to look at Larson's or Schaum's book and do all the exercises there. But honestly I think Spivak gives a lot of hard problems and initially understanding them would do wonders of remembering the concepts (for example his exercise about functions is one of them). I find the prologue really difficult at first and it demotivated me initially but I guess I got used to his style a bit.

[wooden sparrow]

Apostol calculus?

[sterile pelican]

Yes but it is quite costly unless 2nd hand

I did not find apostol enjoyable but it is the sort of book you would read at some point I guess but I only use it for the exercises as mines is pretty banged up

[static crest]

Apostol's content is just speedrunning calculus

[wooden sparrow]

Oh, okay..

[static crest]

unless you already know a lot of the content, or someone else is helping you learn (like a teacher)

it's not particularly good

for self learning

[sterile pelican]

Hence why I think Spivak is better

[static crest]

ya, I like Spivak

[wooden sparrow]

Spivak for exercises and tao for learning?

Or is tao that bad?

[sterile pelican]

Tao is not bad but I think it is too comprehensive for a calculus book

I think it could replace Rudin but I am not sure

I did not read Rudin yet (I merely skim) so don't quote me on that

[wooden sparrow]

I mean you can learn calculus and analysis both right?

[sterile pelican]

You can but it is painful for me

I'd rather develop my understanding before I go into the deep end of analysis

And Spivak just does that and he does it well

[static crest]

I don't think Tao replaces Rudin

[sterile pelican]

I mean Spivak does not have the analysis topics like metric spaces and all

[static crest]

it's just a smoother intro to Analysis

[sterile pelican]

Hmm then it is like Abbott?

[static crest]

no idea about Abbott

I would just suggest still doing Rudin post-Tao if you're serious about analysis

which is not always necessary

not everyone cares for grad level analysis

[sterile pelican]

I mean Rudin makes everything so clean and easy based on the initial pages

Until I read Dedekind cuts

I have no clue what he is talking about there :^)

[sterile pelican]

But one must complete the 3 stages of Rudin!

Baby Rudin, Papa Rudin, and Grandpa Rudin

[karmic thorn]

Is there any abstract algebra textbook which also deals with elementary number theory in sufficient depth(and probably some introduction to algebraic number theory)?

[static crest]

tbh, I don't really care much for papa rudin

I feel like there's better sources for complex analysis

[sterile pelican]

Conway, Ahlfors, or Needham?

[static crest]

Ahlfors is very nice for a first course in complex

[karmic thorn]

Stein/Shakarchi

[static crest]

I find the order of contents in Stein/Shakarchi

to be kinda weird

but idk, never read it properly

maybe it makes sense if you actually read it

[karmic thorn]

Jk, I just happened to purchase a copy in hopes of learning more about complex numbers in HS.

[static crest]

I think Ahlfors is pretty standard

for a first entry to complex

For Needham, it's certainly a very fun read

[sterile pelican]

I hear a lot of good things about Pinter but I don't know about the number theory part

[static crest]

I think there's better textbooks for a geometric approaches to complex

although, they're not as inviting

to a new person

[sterile pelican]

I was considering Needham as it is titled visual complex analysis

[static crest]

it's name doesn't lie

it does take a very visual and geometric approach

it makes things easier to digest for some, I personally just prefer Ahlfors

and then approaching the geometry aspect more rigorously

Like jones and singerman, complex functions an algebraic and geometric viewpoint

which also does stuff geometrically, but it's nowhere close to being good for a first look into complex (it's based on a fourth year ug course at some uk uni)

[karmic thorn]

Pinter's definitely great for a light introduction to AA, but I'm really looking for something with ENT.

[sterile pelican]

I guess Algebraic Theory of Numbers by Samuel but I did not read any of that :^)

[flint pagoda]

What do you guys think about the dover maths series

I know they have a book on pretty much any topic you could think of

and usually you can find them for pretty cheap

[sterile pelican]

Dover has some really nice gems there

Gelfand's Functions & Graphs, Method of Coordinates are great when I started out. Then Halmos' Naive Set Theory is one of those books

[flint pagoda]

hmm i see

so i guess they are pretty good bang for your buck then

[sterile pelican]

Yup

[flint pagoda]

yea i picked up "a course on group theory, regular polytopes, and lectures on differential and integral equations" cuz they were all like a few dollars each

[drifting elm]

I have this from dover https://www.amazon.com/Axiomatic-Theory-Dover-Books-Mathematics/dp/0486616304

[flint pagoda]

how is that one?

i should probably get a book on set theory some day

[drifting elm]

I will warn you if you are a beginner this is not the book to get

there are probably books that are way easier to understand

because this is axiomatic set theory, the book makes a lot of distinctions that should be obvious

lots of qualifying statements

but also more general statements they call axiom schema which is really really general. then you have to realize that there is a distinction between what is being asserted as an axiom schema, an axiom, or an example.

I also didn't think the wording and the notation are really best as an introduction to set theory

using the word dominance instead of precedence.

[storm sleet]

This may not be a "looking for a book" question, but does anyone have any tips for self studying from textbooks?

[flint pagoda]

@drifting elm what would you suggest instead then? I am familiar with all of the basic maths needed for a CS major, so calc I&II, linear algebra, discrete maths, I have also taken various courses in computational compelxity and a grad course in logic

[slender sphinx]

Do a lot of exercises in the chapter. At first, you wanna get feedback on your work to ensure you aren't messing up your foundations (ask in the appropriate channel here or ask someone irl to check it)

Besides that just be honest with yourself and your progress

Don't rush ahead if you don't get the current material

[storm sleet]

Is 50% a good baseline?

And if I don't get it, do more from the chapter?

[drifting elm]

well then this book could be fun

[flint pagoda]

aight cool

i guess ill find a pdf first and try to read ch1

[slender sphinx]

@storm sleet I wouldn't aim for a percentage

Also what topic is the book on?

[storm sleet]

I have a couple I want to work through, but currently axiomatic set theory

[slender sphinx]

I'd spend some extra time to solve more problems; it's hard to quantify how many you should do, but you should try to understand most of the results

[drifting elm]

@flint pagoda if you have taken real analysis then you already know about cantor which helps with axiomatic set theory

[flint pagoda]

nah never did real analysis

[drifting elm]

did you do cantor set in calc II?

[flint pagoda]

hmm i think we may have briefly talked about it

[sterile pelican]

what are your guys take on Concrete maths by Knuth?

[drifting elm]

knuth is the big pappa

you know you gonna learn something good when you read knuth

anything he puts out just read it

if you are CS you need some knuth

but it touches all areas of mathematics

probably the best reason to get that book is that you don't need to read the 6 volume set art of computer programming

if you just need the basis for computation then that would be a good book. not the only book on the subject either so I'm not total fanboy

[sterile pelican]

Hmm

I should read it at some point in my life in that case

[cobalt arch]

anyone that has read hubbard and hubbard's text on vector calculus?

Does it cover linear algebra thoroughly?

[cobalt arch]

is shifrin's book on linear algebra good?

[fossil island]

Thoughts on Introduction to Topology: Pure and Applied by Adams and Franzosa for a first course in topology? https://1lib.us/ireader/2032808. We'll be going over the circled sections

[stray veldt]

haven't read it, but seems like standard stuff for point-set

although not a lot of stuff is covered

and it's kinda funny that your professor(?) choose a book with applied in the title and then elects to skip everything applied

[fossil island]

yeah i thought that was funny too

but wdym not a lot of stuff is covered

[stray veldt]

eh, i haven't looked at it in detail

it just seems like not a lot is covered for a single class

5.4 is possibly interesting as well imo

and not sure if it does tychonoff

or urysohn stuff

[fossil island]

thanks for that, and would a reasonable future self study just involve doing some of the later chapters like homotopy, manifolds, etc.?

[stray veldt]

depends what you want to do

if your end goal is learning more math, you have to learn algebraic topology at some point

and manifold stuff

[pearl imp]

anyone know of a good book on probability that goes with Stewart/Thomas Calc, level-wise?

[fossil island]

I like Hogg et al Mathematical Statistics

https://fac.ksu.edu.sa/sites/default/files/hogg_craig_-_introduction_to_mathematical_statistics_4th_edition1.pdf

Not a very good copy of the book

The first like 5 chapters are about probability

which you will see with pretty much most statistics books

It's fairly consice

but a little dense

[pearl imp]

is this like the Apostol of statistics books?

[fossil island]

ehh not really

idk if there even is one

one thing with probability though is that you should be careful of understanding the "locations" and indexes of formulas

idk how to describe it

[pearl imp]

what does that mean?

[cobalt arch]

is shifrin's linear algebra and multivariate mathematics a good book for la and calc 3?

[pearl imp]

I'm very beginner math-wise but have some experience in self-teaching. Get 2 or 3 books on your subject and treat one as primary and the others as complementary reading material on a topic. They give different perspectives that help to fill the gap of a teacher. Also, this helps to avoid getting stuck/bored when encountering difficult stuff.

[grave egret]

What's the hardest book you guys have read?

[marble solar]

Finnegan's Wake

That or the Bible

[grave egret]

I mean math but oo.

[marble solar]

If you're speaking in terms of math

The hardest book I've read through in math was 3 Manifold Topology by schulten's

But a primer in mapping class groups seems substantially harder, but I'm on like page 20

[sudden kindle]

MoonBears-C gonna be a geometric topologist

[marble solar]

Maybe!

Depends where I get in for phd and go

I might pull a reverse Larry guth

[summer moth]

So. Anyone have a good book on Mathematical Logic? Something that basically gives you a more fundemental understanding of maths? Would discrete maths be the way to go? If so any book that would be fairly accessible? (From what I heard to have a basic understanding of discrete maths you don't actually need calc or algebra? Is that true?)

[flint forge]

hardest book ive read is the cat in the hat

[gray gazelle]

I will say that I have not read the cat in the hat, but I cannot imagine it to be a hard book

[summer moth]

I mean. That's true. That book is trippy af. Lol

[gray gazelle]

You are looking to learn about mathematical logic, or about how to write a proof?

[summer moth]

I mean. Both. But that question is mathematical logic. But any suggestion for proofs would also be nice! XD I kinda know proofs but also not.

[gray gazelle]

To learn mathematical logic, you should certainly know how to write a proof, and not that it is strictly necessary but you should know calc and algebra (both the hs kind and abstract algebra). As for books on how to write a proof, I don't know off the top of my head

[flint pagoda]

well there is the freely available "book of proof" that is fairly good if you have some mathematical maturity and want to get into proof writing

[summer moth]

Alright. Thanks!

And oooh. Sorry. In not used to having stuff in pins. XD Every time I check a pin hoping there is something there isn't. But good to know there is pins galore!

[timber mesa]

that pinned Topology book seems pretty cool by the way

[calm crane]

terrible intro to point set IMO

probably a ok bridge between point set and tom dieck

[stray veldt]

from what max said about that book it is exactly how i was taught topology

in one lecture the prof introduced all of category theory we needed

and in the next lecture he tried to introduce infinity categories

[ripe granite]

wait wut

was this an intro course?

[stray veldt]

yes

taught by a category theorist, who got carried away a bit

[ripe granite]

and they taught you about infinity cats in one lecture?

[stray veldt]

he mentioned them

i only know this because of my notes

because i didn't get much in that lecture

as we had only just defined what a category is in the previous lecture

so that was kinda too much

[ripe granite]

[fluid bay]

terrible intro to point set IMO
i don't think it is supposed to be an "intro to point set." Its supposed to be a second pass (or at least a first pass assuming knowledge of the topology seen in analysis). I'm reading it right now and i really enjoy it, and i like how it introduces category theory in a context i can mostly understand.

[pulsar dome]

hello friends

anyone ever read the number theory book by gauss?

any thoughts on that?

namely disquisitione aritmeticae

I have a digital version if you want it

[quick hornet]

i havent read it, but i have to imagine it falls into the same camp as most historical texts

ie "interesting for its historical position but absolutely terrible to learn out of, and probably not a great idea to use as a reference either (unless youre referencing historical facts)"

[timber mesa]

yeah I'm considering reading that before taking my grad department's alg top; had point set (chapters 2-5 of Munkres) this semester

[timber mesa]

that's exactly what I recall from glancing at Disquisitiones

[marble solar]

There was a recent paper by a mathematician (smale?) who went through Gauss' proof of the fundamental theorem of algebra

Recent relative to uhh

Gauss' time lol

[sterile pelican]

I gauss so

[pulsar dome]

lol

is there a text that covers binary and trenary quadratic forms as thoroughly as he does?

or the last section?

that's what interest me the most

the last section regarding roots of unity

like is there a text that covers comprenhensively those topics?

I read the first chapters and are basically like elementary number theory

then he goes to cuadratic congruences

and then to quadratic forms

and then to roots of unity

but the qudratic forms sections is like half the book

idk

anyone knows about books or text that cover those topics? I'm to lazy to investigate all my self atm and I g it would be faster to read the ideas

[drifting elm]

https://www.amazon.com/Logic-Boolean-Algebra-Dover-Mathematics/dp/0486483851

this says no previous knowledge necessary

this is $12 used https://www.amazon.com/Mathematical-Thinking-Writing-Transition-Mathematics/dp/0124649769/

more complete more for proof writing but logic is included here.

[obsidian valley]

Learn to write proof by learning proof theory

[drifting elm]

google has the first thirty pages of that dover book if you want to preview

[karmic thorn]

Libgen has all of them

[wooden sparrow]

https://tenor.com/view/johnny-depp-captain-jack-sparrow-pirates-of-the-caribbean-smiling-gif-8223934

[gray gazelle]

Inb4 „learn it in lean“

[hasty turret]

Learn proofs by doing the interpretative dance

[cobalt arch]

There is the book by goldrei that covers propositional and predicate logic.

https://www.amazon.com/Propositional-Predicate-Calculus-Model-Argument/dp/1852339217

[cobalt arch]

Anyone?

[feral lotus]

Anyone wanna read this book wimme? https://softwarefoundations.cis.upenn.edu/lf-current/toc.html

[obsidian valley]

I don't read, sorry.

[feral lotus]

That sucks 😔 I was hoping atleast you, yes you Jesse, you would say "Hell yeah pardner! Lesss goo, less read that shit!!". But alas, I stand here dejected and disappointed.

[obsidian valley]

Oh this looks sort of cool actually

My winter is already booked up or I would say yes

Bookmarked for later tho, ty

[drifting elm]

actually they don't

😢

black hole of books this one

take a look around logic and boolean algebra by arnold

https://www.amazon.com/Logic-Boolean-Algebra-Dover-Mathematics/dp/0486483851/

[sterile pelican]

what does one think about Shafarevich's Basic Algebraic Geometry 1 and 2?

[cobalt arch]

[sterile pelican]

No clue :^) Why not try Spivak's Calculus on manifolds :^)

[cobalt arch]

:(

[gray gazelle]

spivak CoM is a good book

also it's short

great exercises

[cobalt arch]

But I want some exposition to la as well at the same time

Not two different books but one that integrates both

[gray gazelle]

just intuit all of linear algebra

trivial

[sterile pelican]

Hoffman and Kunze's LA?

Or Axler

Not sure if Axler is enough though tbh

[cobalt arch]

I will try shifrin

[gray gazelle]

they want a book that does linear algebra and mvc

[sterile pelican]

Get Hoffman and Kunze then tape it with Calculus on Manifolds, then you will have one book

[static crest]

uh, that doesn't sound like a good idea

should just get 2 tbs

[hasty turret]

What about func anal?

[gray gazelle]

this is your brain on the american university math curriculum, doing LA not literally before anything

[static crest]

the only math lin alg can be done after is like calc 1/2

lin alg should just be done alongside them

[gray gazelle]

similarly, trivial. just extend linear algebra (trivial) to infinite dimensions

[static crest]

true?

[sterile pelican]

just tape two books to become one :^)

[cobalt arch]

:)

How didn't I think of this:)

[sterile pelican]

Spivak is pretty small anyway :^)

[cobalt arch]

Ig:)

[static crest]

any textbook that does do lin alg and mvc in the same book is bound to be garbage

[cobalt arch]

Why is that?

[sterile pelican]

No Stewart is ama-oh wait true :^)

[gray gazelle]

ive also heard of differential equations at the same time as linear algebra and that sounds even worse

[static crest]

because they're both vast subjects that need their own textbook to cover properly

also one almost directly depends on the other

so the textbook would end up being lin alg stapled to mvc

[gray gazelle]

mvc without linear algebra

[static crest]

at which point it would be better to just get lin alg and mvc separately

[sterile pelican]

hmm but apostol volume 2 is not that bad

[static crest]

nah, I dont like apostol

you don't learn from apostol

[gray gazelle]

the generalization of the derivative is literally a linear map, at which point it should be pretty clear what depends on what

[cobalt arch]

Okay so what would be a good book to study LA from in preparation for MVC

[static crest]

you learn from a teacher, and apostol is just a review on the side

[sterile pelican]

Hoffman and Kunze LA and Spivak's CoM

[static crest]

axler lin alg :^)

[cobalt arch]

I have one month until exams:)

[gray gazelle]

axler "linalg"

[sterile pelican]

really, is axler even enough?

[static crest]

I was just joking

[obsidian valley]

Just don't learn LA

Thats my opinion

[static crest]

axler gets recc'ed far too much

[cobalt arch]

Is that a good idea?

[sterile pelican]

Axler has a nice book but it is not enough

[obsidian valley]

Fraleigh LA is the best LA book cmv

[gray gazelle]

the third edition of axler is ugly tbh, second edition much better

[cobalt arch]

I mean what about matrices?

[obsidian valley]

What about em

[gray gazelle]

just encodings of linear transformations with respect to a choice of bases, trivial

[cobalt arch]

I will have a matrix of partial derivatives and I will just stare into it.

[static crest]

just learn tensors, and matrices are kinda just a special case?

[gray gazelle]

physics "tensors"

[cobalt arch]

Tensors

[static crest]

ya, I had a long argument with a physics friend

that tensors are in fact more than an n-dim array

[gray gazelle]

multilinear map that eats covectors and vectors and shits out an element of the base field

[cobalt arch]

So which mvc book should I read? Spivak?

[obsidian valley]

You can intuit most of mvc

[gray gazelle]

*most of math

[static crest]

what level of mcv are you looking for

[obsidian valley]

yeah this tterra

[static crest]

like do you want to persue further math after mvc

are you in engineering

[obsidian valley]

Just watch 3b1b videos to prepare for diff top tbh

[cobalt arch]

Actually the textbook we use is tromba

[obsidian valley]

It's all just visual

[gray gazelle]

trombone

trumpet

[cobalt arch]

So it is all trivial

[gray gazelle]

🎺

[cobalt arch]

I see

[sterile pelican]

though is herstein enough with these two books?

[fossil island]

so if linear algebra is just a special case of modules, was is abstract algebra a special case of?

category theory?

if so, then what is category theory a special case of

[static crest]

abstract algebra is no special case

[fossil island]

so learn abstract algebra and then linear algebra follows trivially

[stray veldt]

that's a bad way to think

[static crest]

ya

[fossil island]

yeah im just joking around

functional analysis also follows trivially

[stray veldt]

functional analysis is a simple corollary of commutative algebra

(scholze et al are currently trying to do that)

[fossil island]

so is basically algebraic geometry, from what i've heard

[gray gazelle]

ah, so one should read atiyah macdonald before learning functional analysis

[stray veldt]

algebraic geometry is a lot of commutative algebra, yes

[gray gazelle]

[stray veldt]

but it's

[fossil island]

so functional analysis = algebraic geometry $\qed$

[hasty eagle]

Trichloromethane

so functional analysis = algebraic geometry $\qed$

[stray veldt]

a lot of commutative algebra was developed to do algebraic geometry

[fossil island]

where does topology fit into this

[stray veldt]

it was a meme ttera

https://ncatlab.org/nlab/show/condensed+mathematics

Related aims are to turn functional analysis into a branch of commutative algebra, and various types of analytic geometry into algebraic geometry.

this is just further proof that algebraic geometers are stealing all of mathematics

[fossil island]

algebra is omnipresent

[stray veldt]

and making it their own

[fossil island]

should've paid more attention in middle school

damn

[stray veldt]

i don't know if this new approach will help functional analysts to do what they want to do

(i.e. solve PDEs)

[static crest]

we already know how to solve PDEs smh

I've used matlab quite a bit

[fossil island]

noooo you cant just simplify all of mathematics into arrows. category theory go brrrrrr

[static crest]

I can attest to it

[stray veldt]

personally i am waiting for a purely algebraic theory of analytic number theory

[fossil island]

thoughts on applied topology?

[stray veldt]

isn't it mostly a meme

[static crest]

applied ...

🛌

[fossil island]

i retract my statement

[drifting elm]

you can apply your knowledge to stack exchange for points that show people how smart you are

there are definitely applications for topology though. 3blue1brown has a video about applications.

[gray gazelle]

It‘s for making mugs to donuts and eating them

[fathom flower]

Y'all know any good book on Group theory?

[static crest]

what kind of thing are you looking for

easy introduction that doesn't delve too far, but does a decent amount
a very long but complete introductory text (emphasis on very long)
a complete text, but it's not really that good for someone who might be self-studying, or for someone who is newer to higher math

[fathom flower]

I am looking for both. Once I complete intro I will go for the other

[static crest]

a lot of people hate this, but d&f is good as an intro text, it's extremely easy to understand and covers just about everything you'd possibly want in an undergrad abstract algebra tb

gallian is yet easier, but it also covers less content, so you could try that instead, and then jump to a harder textbook later

[fathom flower]

Thank you

D&f?

[static crest]

dummit and foote

[fathom flower]

Thank you

[static crest]

it is hated by some people because of how extremely long it is

but it is thorough and easy to understand, and has good exercises

if you're just doing the groups part, it's only ~250 pages

however

[fathom flower]

Go on please

[static crest]

there's not much more to say, the entire textbook is just short of 1000 pages

but it also goes on to cover rings, modules/vector spaces, fields, galois stuff, and an intro to even higher level abstract algebra

so you can decide how far in you want to go

[fathom flower]

Thank you

[fathom monolith]

Im looking for a CS book that delves into the more mathy underpinnings of CS. I did Undergraduate research in Data structures and Algorithms (specifically compression), so im well aware of that branch of inquiry, but does anyone know of other subjects or books that have similar rigorous treatment?

[spice sparrow]

well CS is such a wide subject, you need to tell a specific topic whose mathematical treatment you want to find?

@fathom monolith

[fathom monolith]

Well ive heard that programming language construction and compilation can be presented through math, but my CS program at my uni skipped past these ideas because "You just need to know how it works"

But yea its a kinda wide open question, mostly because im really not that picky. I just feel that alot of CS books really take the perspective of "This is what you need to know, You can do it like this, moving on"

[spice sparrow]

You can first go for a good book on Graph Theory and Discrete Mathematics

[fathom monolith]

I actually took a graph theory class out of the math department at my uni

[spice sparrow]

If you already have that, I have heard that Concrete Mathematics - Donald Knuth is great in this aspect

[fathom monolith]

oh wait ive heard that name before

[spice sparrow]

Concrete Mathematics: A Foundation for Computer Science

[fathom monolith]

yeaaaah this guy made the Big O notation

okay cool ill check that book out thanks

[spice sparrow]

and he has a famous book too, Art of Computer Programming

[pulsar dome]

bruh

you guys burried my question

lmao

[spice sparrow]

well ask it again

or just paste it

[pulsar dome]

no context lmao

any ways

anyone has read this ? https://artofproblemsolving.com/articles/files/MildorfNT.pdf

"Olympiad number theory - An abstract perspective"

wanna read it with me?

[spice sparrow]

@fathom monolith to add on, that book is only for the mathematical stuff needed, for mathematical aspect of programming you will have to see another

[pulsar dome]

bruh what math do you even use at programming?

like

logic

and that's it right?

[fathom monolith]

Depends

[spice sparrow]

Go for the Art of Computer Programming by the same author , even Bill Gates praised it

@pulsar dome well , that's not true

[fathom monolith]

I know people have investigated deeper and written alot about stuff like monads and software construction but so much of the material out there is focused on getting readers "job ready ASAP"

[pulsar dome]

well like

combinatorics

[spice sparrow]

@pulsar dome this is not the 20 th century, you have computational complexity, computational number theory, cryptography ( now even elliptic integrals are used in it ) etc. there is no end

[fathom monolith]

Theres also levels to programming, programming at the kernal level is not quite the same as software construction, and malware design is not quite the same as synchronization, etc.

[pulsar dome]

yeah but like asymtothic complexity and number theory are like ez at the level needed for like the best payed programming job, also you don't use eliptic curves or integrals if you don't work at like a 3 letter agency or smth

computer science is really different to programming

maybe this is just a semantic misunderstandig

[fathom monolith]

not all programming is computer science, but computer science is chiefly concerned with programming.

[spice sparrow]

that's right

computer science , algorithms etc. form the basis of programming

and if you want to understanding programming in good detail you need to understand the stuff behind it well

[pulsar dome]

but computational complexity and cryptography are problems of theoretical computer science

imo

you only need to understand computation, turing machines and how modern computers work in order to understand programming

ofc some algorithms if you want

but like if you can code on assembly you can do anything

if you understand coding on assembly I mean

[fathom monolith]

well no actually

[pulsar dome]

lmao

[spice sparrow]

Ok ! I am off . Nice arguing with you Astrolopithecus43. 😫

[pulsar dome]

lmao

why

[fathom monolith]

software construction still presents a major problem for the solo programmer

[pulsar dome]

I wanna hear your opinion

[spice sparrow]

on what?

[pulsar dome]

on what the basis of programming is

[spice sparrow]

well I am tired , now. Sorry. I am going

[pulsar dome]

lol

good luck dude

bye

[hearty steppe]

So is that topology text in pinned a graduate level text?

[marble solar]

Munkres isn't

[hearty steppe]

The one with Terilla

Category theory approach to topology one

Seems eye catching to me

I’m thinking of checking out Visual Group Theory by Carter

[valid moth]

y

@flint forge do you think math3mas book is fine as a first intro