book-recommendations

[gray gazelle]

metal don't think too hard

[broken meadow]

for finite intersection i dont want the ball to be too big though

what if it leaks out

how do i make it smaller

[gray gazelle]

u tell me

[manic fox]

what are you doing

[crystal lion]

what if the ball leaks out

[broken meadow]

can i cheese it and say that it's small enough to still be in each of the sets

[crystal lion]

only mathematicians face such problems

[gray gazelle]

be precise metal

[flint forge]

whats the exercise

[manic fox]

will the ball leak out or not

[gray gazelle]

intersection of finitely many opens in R^n is open

• other top space axioms

[crystal lion]

“cheese” is a part of most modern mathematicians’ vocabularies

[broken meadow]

i think the union one is easy

[flint forge]

what defn of open does metal have

[broken meadow]

i just said that for x in the union it's in at least one of the sets and so one of those sets is open so just choose the ball from that

oh uh

open in this book says

[gray gazelle]

[broken meadow]

U is open if for every x in U, we can find an open set \subset U which contains x

[gray gazelle]

you defined open set using the word open

[manic fox]

Wud u like a hint for the counterexample or no metal

[broken meadow]

oh

shit

[crystal lion]

ball*

[flint forge]

no hints

[broken meadow]

no hints

[manic fox]

oki

[broken meadow]

something bit my finger

wait ill review

[manic fox]

Must've been charlie

[gray gazelle]

i did

[flint forge]

anyway i believe in u metal

[manic fox]

Dil dil metal jan jan metal

[broken meadow]

pain i guess i needed to define open rectangle/ball

[flint forge]

jesus christ what

open rectangles

[gusty smelt]

open rectangles

[broken meadow]

spivak does everything in rectangles

[flint forge]

what broke ass textbook is this

[broken meadow]

idk why

balls is so much more natural

Doze balls, even

[dense pewter]

i mean... it's not the worst definition depending on how you build up R^n

[manic fox]

DB

[gray gazelle]

metal i suggest that you prove that this is the same as the open balls definition and then literally NEVER use an open rectangle ever again

[dense pewter]

in general the product topology on two spaces is defined as "basis of open rectangles"

[flint forge]

its bad and i hate it

[dense pewter]

so it makes sense from a product topology point of view

but like

[broken meadow]

uhh ok ill try tterra

[flint forge]

iguess.jpg

[dense pewter]

i agree that you shouldnt actually use open rectangles

you should do what tterra says

i just think it's fine for a definition

[manic fox]

open hexagon moment

[gray gazelle]

when i very first started to work on this book i tried using the open rectangles and it was fucking impossible

then i learned what an ope nball is

[broken meadow]

his rectangle thing seems less tech tho

[crystal lion]

it would be much easier to open a rectangle than a circle

[gray gazelle]

[broken meadow]

like i don't need to think of what a radius is

[gusty smelt]

just define it with open 10-gons obv

[broken meadow]

im confused what am i allowed to use for open ball

[gray gazelle]

would you rather think of "point + radius" or "point and n edge lengths"

[flint forge]

okay wait

[broken meadow]

i like point and radius more

[flint forge]

what is going on here im confused

[broken meadow]

but he never talked about using the norm for this

im confused too

[flint forge]

have you read rudin?

[broken meadow]

no

[flint forge]

oh

okay

go read rudins metric space stuff

and just use all of that material

and then prove the thing tterra said

bc this is garbage

[broken meadow]

oh

ok

yeah this is so

confusing

ok

will do

[manic fox]

rudin defines neighbourhood literally as an open ball

Hextillionare grindset

[flint forge]

its worth knowing why this is equivalent as buncho pointed out

but like

its an exercise and then you never think about it again

[cursive orbit]

Prove the equivalence of norms

[manic fox]

equivalence of norms

there was some exercise where i had to prove sth like this

every norm on a VS leads to the same induced topology or some shit

VS is fin dim

was not able to do it

[gray gazelle]

what's the first thing you do when the exercise says "finite-dimensional"

[manic fox]

basis 😎

[gray gazelle]

[manic fox]

mebe i shud do that yus

will think aout it

[crystal lion]

encouraging pattern recognition, unbased ttera

[misty wyvern]

what's the first thing you do when the exercise says "finite-dimensional"

Write down "the rest is trivial".

[karmic thorn]

Write down "It follows from finite dimensionality that (conclusion)."

[hasty turret]

"By choice for finite sets,That is trivially true"

[fervent aspen]

is there any books someone would recommend for someone with a high school understanding of math

[gray gazelle]

The art and craft of problem solving by Paul Zeitz

[fervent aspen]

whats it about?

[gray gazelle]

exactly what it sounds like

[fervent aspen]

thought so

thank you

[gray gazelle]

You are welcome

[gray gazelle]

I am looking to get started in Proof Writing and am looking for an introductory text on the same. If you guys have some good recommendations do let me know.

[marble gulch]

Are you talking about formal proofs or just doing proofs in plain language?

[whole rain]

how is that an exercise

it's a bit hard for an exercise

I mean maybe its doable without any hints but definitely not easy

[gray gazelle]

@gray gazelle @sage python

you guys know that stuff

[atomic hound]

Hello guys, which book you would recomend for a topology beginner?

[gray gazelle]

munkres

lee if you want to focus on topological manifolds

[atomic hound]

Munkres?

Could show the cover?

[glossy grove]

It's been added as a sticker already xD

[analog pollen]

Depends what you want to learn

[fervent aspen]

i dont really know probably just how to build a good foundation

@analog pollen

[analog pollen]

For what?

There are lots of topics in mathematics

[fervent aspen]

basic math and problem solving

[analog pollen]

Is this what you want?

to learn

[late sinew]

Hey! Does anybody have some good resources of where to learn the basics of elliptic geometry?

Plz ping 😄

[slim peak]

@late sinew depends on what you call elliptic geometry. If you talk about the "true" one, you will need to learn differential geometry first then (pseudo-)Riemannian geometry to have a good construction

[gray gazelle]

A Synopsis of Elementary Results in Pure and Applied Mathematics:

by g.s.carr

this book is really good in giving concise and necessary examples etc.

and its the same book that awakened ramanujan genius

so it might awaken yours

i highly recomend it

[jovial copper]

The book of proof

[past ice]

Just use the Zeitz book you mentioned. It's gonna be way better and teach you a lot more than an "intro to proofs" type of thing.

[manic fox]

idk bro 🧠 will probably have to mess around with it for a while

just not in the mood

[weak apex]

What is a good book to get into computational number theory? Please @ me for any recommendations

[near shard]

@weak apex Cohen's book on Computational Algebraic Number Theory is great both as a learning source and as a reference

[weak apex]

Ahh interesting, thank you!

[gray gazelle]

thanks

[livid ermine]

how much complex analysis do you need to read "introduction to analytic number theory" by apostol? are the first three chapters of ahlfors enough?

[torn fern]

I just studied the proof of this result ! If you are interested I can tell you the book and section where I found the discussion 🙂

[bitter raptor]

is it worth going through all of dummit and foote doing nearly all the exercises (skipping the few redundant or trivial ones)

[bitter raptor]

though i havent worked through apostol myself i believe it is pretty self contained: having any background in complex analysis should be more than enough

dont take my word for it though

[flint forge]

no

it is not reasonable to do so

[woven spade]

Does anyone have a book I can study

That helps problem solving?

For beginner

I was thinking "The Art of Problem Solving"

Any thoughts?

[flint forge]

thats a fine start

honestly just download it and try it out

[woven spade]

I feel really crappy downloading books. but I sure as hell am not going to pay for it

I will check it out

[flint forge]

lmao why

the authors would probably encourage you to

they dont make much if anything off the sales

[tame glade]

Is there any book about functions in semi-log place?

[bitter raptor]

@flint forge how would you recommend working through it

Im annoyed at myself for doing barely any exercises when going through rudin, and now that i actually feel motivated doing them through a book (doing the same with SS though im putting it on hold for now) idk what the right balance is

[flint forge]

i would pick out like 3-5 problems of various difficulties

and stick with them

and if you really cant do one

do two more

[bitter raptor]

For each exercise set?

[sage python]

If it's a known book maybe it's not a bad idea to find a class which posts the psets online

[bitter raptor]

The thing is of yet theyve never been too hard and they tend to introduce concepts not there in the theory

Fair enough

[sage python]

The difficult thing is you gotta choose the right one in that case. Since a prof may choose exercises based on what's easy for him to mark, maybe eg there's a problem that introduces an important idea but he covered it in lecture rather than assigned, or just has bad pedagogy

But if you find something good then yeah a prof has a better idea of what's informative/interesting than you do

[bitter raptor]

True

Ill look into it

And otherwise ill just keep going at doing most of them 🤷‍♂️

[marble solar]

This is the thing with piracy, I think there was an extensive EU study that showed that piracy had little to no change in how well a book sold

I am not advocating for piracy, I am merely calling into question the economic reasoning of large institutions on piracy

Moreover a lot of these professors fund these projects with federal grants or dollars - why should tax payers then have to turn around and pay to access something they already paid to be written? It's certainly not helping professors salaries

[manic fox]

Sure, thanks

[torn fern]

In Undergraduate analysis by Lang, Chapter VI section 4 there is stated and proved (Theorem 4.3) that in a finite dimensional vector space over the real numbers any two norms are equivalent. From this you can then deduce that any two norms there induce the same topology , as you wanted !

[manic fox]

lang moment

[manic fox]

oki thanks

[magic moth]

does anyone here own the apostol calculus books?

[misty wyvern]

Own or "own"?

[magic moth]

Own?

sorry english isnt my main language

[gray gazelle]

would suggest you read spivak's instead

[misty wyvern]

I suggest you read Rudin instead.

[sudden kindle]

I have calculus volume 1

[magic moth]

mmm

im getting both volumes for 30 bucks

is it worth it>

?

volumes 1 and 2 i mean

[misty wyvern]

No!

The only calculus book worth buying is some big general methods reference.

Take your pick but you'll get your money's worth. You can otherwise learn calculus purely off Paul Lamar's notes or Khan Academy, take your pick.

[willow pecan]

[sudden kindle]

Apostol's Calculus Volume 1 is really an intro analysis textbook

[sudden kindle]

Idk I just used Vol 1 for my intro analysis class

I dont buy textbooks anymore. Have too many and not enough space to store them

[magic moth]

intro to analysis

is what i want

well maybe some context is necessary im a software dev that wants to get a good math background to get into scientific computing

[willow pecan]

Hmmmm

If you want to get into scientific computing, I would reccomend Demmel's Numerical Linear Algebra and Iserles' Numerical methods for differential equations

I think you'll be able to pick up the required real analysis along the way, it won't be very much anyways

Of course, if you want to get to research level scientific computing, a good mathematical foundation will be needed

[magic moth]

maybe i should just go back to the math major i dropped out of

still if i want to do that i need to get the rust off and start doing some proofs

[willow pecan]

Both books I mentioned have a lot of proofs

[magic moth]

good

[uncut zealot]

What are some good books for com alg? I've heard good things about both Atiyah-MacDonald and Eisenbud, but the first is over $150 and the second is 800 pages long, and I've also heard that they can be quite dense and are better references than for a first time learning.

[sage python]

Atiyah-Macdonald is short, excellent writing, but very exercise-heavy, so even though it's not that many pages it's a bit of a slog

Eisenbud seems locally very easy to read

But it's intimidatingly long

My impression is that "Commutative Ring Theory" by Matsumura is a good intermediate. It's somewhat long but not thaaaat long, and there's more material in the exposition and fewer problems. I don't know how it compares content-wise to the other two, I'd wager AM is mostly a subset of Matsumura is mostly a subset of Eisenbud, but idk for sure

[misty wyvern]

why should i study com alg anyways

why not pick up a book in something sexy like alg geo

[marble solar]

Approaches in AG require commutative algebra

[misty wyvern]

why should i study ag anyways

why not pick up a book in something sexy like pdes

[ripe granite]

To flex on other people.

[sage python]

You don't need need commalg for AG if you're going the complex geometry route

But yeah I mean, part of why I've had a hard time getting into AG is that commalg and the commalg-heavy AG start off incredibly boring

[crude geyser]

Gathmann also has some notes on commutative algebra that are pretty nice

[wooden sparrow]

I heard axler's LA done right book assumes something called axiom of choice? Is that bad in any way?

[gray gazelle]

yes

[willow pecan]

No one cares

[gray gazelle]

axiom of choice leads to some absurd results such as cartesian product of 2 nonempty sets is nonempty

[gray gazelle]

for what axler's doing, not at all.

[wooden sparrow]

Means it's not relevant at this level?

[gray gazelle]

yes

it literally does not matter

[wooden sparrow]

Okayy thanks

[gray gazelle]

the only time it will ever come up in any meaningful way in a linear algebra class at the level of axler is in the result that every vector space - finite dimensional or not - admits a basis

[wooden sparrow]

[gray gazelle]

Also cardinality stuff.

[wooden sparrow]

Okayyy

[frosty girder]

[gray gazelle]

i'm doubtful that an axler-level linear algebra class has to worry about the technicalities of cardinalities

just ignore infinite dimensional spaces

roman's book deals with that stuff tho

[wooden sparrow]

The book said whenever discussing fields, it means R or C

[gray gazelle]

even in finite I guess

showing you cant have two bases of different cardinalities

[gray gazelle]

your brain on operator theory (axler's field)

[wooden sparrow]

[steel viper]

Wait how

[gray gazelle]

functional analysis is typically done over R and C since that's where norms and inner products make the most sense. axler is a functional analyst

[gray gazelle]

@wooden sparrow

[steel viper]

The only complex geometry ive seen in AG is the construction that integral affine curves are riemann surfaces

[wooden sparrow]

Okayy

[steel viper]

[gray gazelle]

see his article "down with determinants"

[steel viper]

Is that real tterra

[gray gazelle]

what is

[steel viper]

the article

[gray gazelle]

yes

[steel viper]

🦗

[gray gazelle]

i strongly disagree with the third sentence. why is his reaction to ignore them completely instead of to write a solid, clear exposition of them if he think's there isn't one?

[wooden sparrow]

getting mixed signals here

[gray gazelle]

axler is delusional

[wooden sparrow]

What did you read for LA?

[gray gazelle]

axler is coping because he does functional analysis and all of his spaces are infinite dimensional and det doesn't make sense

[broken meadow]

lol

[frosty girder]

lol

[gray gazelle]

it's really obvious just from the first page that axler just doesn't like determinants

or wants to write a determinant free exposition but needs a reason that isn't just "i wanted to"

instead he maxes out on arrogance and goes and calls the book "linear algebra done right"

what a chad

[wooden sparrow]

How do noobs like me filter out cranks from chads though

[frosty girder]

i would also like to know

[wooden sparrow]

ngl self studying feels much harder than just getting into a good college and listening to lectures

Wait, what book should I read though

For LA

[gray gazelle]

axler

[willow pecan]

Friedberg

[gray gazelle]

it's actually a decent book, just the author's reasoning for postponing determinants to the end is kind of weird

[wooden sparrow]

Ok

[gray gazelle]

friedberg 2nd

[wooden sparrow]

I got 4th edition

Ok

[gray gazelle]

i meant that im seconding the friedberg rec

[frosty girder]

[wooden sparrow]

Okayy

[gray gazelle]

I have heard good things about Gilbert Strang

[eager stump]

i mean asides from the arrogance the axler is not a bad book

[eager stump]

his lectures are solid

[cinder owl]

The LA book here has some nice features: https://mtaylor.web.unc.edu/notes/linear-algebra-notes/

[long anchor]

mom, should i click the link scammer sent me ?

[cursive orbit]

no clickable table of contents and no pdf outline

[crystal lion]

is there a standard category theory textbook

one you can't go too wrong with

[crystal lion]

@cattheoryenthusiasts

(half this server)

(i think)

[sage python]

My impression is that the old school default was "Categories for the Working Mathematician" by Saunders Maclane, nowadays "Category Theory in Context" by Emily Riehl is the better one.

[crystal lion]

thanks a lot

[simple lava]

Any recommendation of a book of logic ?

[buoyant eagle]

assert your dominance and start with Chang and Keisler

As for a serious answer, the book recs channel lists this as a logic intro: http://builds.openlogicproject.org/

[sweet scaffold]

The open logic project is a nice project but not a nice book, it's literally scarce to death. My personal recommendation is Propositional and Predicate Calculus by D. Goldrei. Elsewise, always look at the Mathematical Association of America's book reviews.

[lime sapphire]

hi

anyone know any books with good calculus problems?

[narrow talon]

Maybe a book on calculus?

[lime sapphire]

uhh

to be more specific

calculus problems that are a bit olympiad style?

[gusty smelt]

you mean like a bit tricky and such? try spivak

i saw a few problems and i think that fits what you want

[gray gazelle]

Is pathfinder maths appropriate for beginners??

beginners to what

Beginners to the topics given in the book

link the book , https://www.amazon.com/s?k=Pathfinder+maths&ref=nb_sb_noss? cannot find it

[hasty turret]

This?

https://www.amazon.in/Pathfinder-Olympiad-Mathematics-JEE-Physics/dp/B08DJDQ828

[gray gazelle]

Yes the maths one

[gray gazelle]

Any recommendation from a book on logic and proofs for beginners?

[glossy grove]

There's always "Book of Proof".

[gray gazelle]

"how to prove it" by velleman

[hushed flint]

i also like axler

[long anchor]

ic ur a man of culture as well

[eager stump]

book of proof does no wrong, it's free too

[olive laurel]

any good books about optimization?

[sage kelp]

Static or dynamic?

[olive laurel]

both

[solar matrix]

Hi friends do you have any recommendations for a statistics and/or probability book from the ground up and with proofs

[sage kelp]

I’ve heard that Sundaram (first course in optimization) and Leonard & Long (optimal control theory and static optimization) are good books

[gray gazelle]

I'd like to build a math library

I know there's some books that should be there like the calculus by Spivak or the analysis by Terry Tao

Or Sheldon Axler's Linear Algebra Done Right

[obsidian valley]

sounds expensive

[gray gazelle]

Don't worry about that

This is a project

I have room for that

And I don't have any problem if I have to find the books

I just want to get some opinions and I think this Discord will give me some advice

If you had to create a math library with the best books, which 10 books would you add to that library?

spivak's 5 volume DG set and then its translation into some given language

[gray gazelle]

Good

[obsidian valley]

the most influential mathematics book of all time, Euclids elements

and also Godel, Escher, Bach

of course

[willow pecan]

Sounds bad

[gray gazelle]

Well, trying these books would be difficult

[obsidian valley]

cope ange

[gray gazelle]

Because if I want to add those type of books, I don't want a modern version, I want an original copy

[willow pecan]

Just get the top 10 most popular Springer Graduate Texts in Mathematics

[gray gazelle]

Good

[obsidian valley]

yes of course get the original elements

[gray gazelle]

Let's see

[obsidian valley]

its probably in the smithsonian

or something

[gray gazelle]

But that means travelling

[obsidian valley]

i am joking. anyways. you can probably pick 10 "core" math subjects and get a very good book from each those

[prisma snow]

Unfortunately you're off to a bad start with Axler and Tao :(

Spivak is good tho (both of them), Baby Rudin, Rotman, Munkres, Ahlfors, some linear algebra book that isn't axler.

[obsidian valley]

like algebra, topology, logic, geometry, analysis, other fields...

[gray gazelle]

Oh, okay, then it's good

Yes, that's what I'm thinking

[obsidian valley]

more interesting than getting Axler or something lol

[gray gazelle]

It has to be a library that can make anyone a math autodidact

[obsidian valley]

ok get one book for each advanced channel on here

[prisma snow]

Idk, if you just wanted to get good math books, sounds good. But the more you talk, the more it sounds like you want a study guide for learning all of math

[crystal lion]

what would the #get-advanced-access book be

[gray gazelle]

I already know some maths, but this summer I'm just chilling, so instead of studying maths, I'm focusing on other things and as I have a lot of free time, I think it's the time for starting the library

[obsidian valley]

oh.

[gray gazelle]

Yes

[prisma snow]

Just learn math bit by bit and collect the books that you like

There is no such thing as completing math, so that was not a positive thing I was pointing out.

[gray gazelle]

That is easy

,iam advanced

[hasty eagle]

Gave you the Advanced selfrole.

[gray gazelle]

Oh, okay

[hollow drum]

Anybody know of a good free graduate complex analysis resource?

Like a set of free notes or a free book

[dense pewter]

most textbooks can be found for free if you look in the right places

[glossy grove]

free doesn't mean legal though

[prisma snow]

They didn't ask for legal

[gray gazelle]

Ahlfors

[eager stump]

you like this one?

i've been recommended it by a musician

fair disclaimer i did music before math

[quick hornet]

do you want to learn math, or do you want to hear about some dude's mediocre philosophy?

[scenic oasis]

To your knowledge, what is the best Algebra II math book around right now? I want a textbook, the school type books and then a book that isn't a textbook, so no 1000 practice problems to solve and etc., just explains the concepts incrementally.

[quick hornet]

serge lang's algebra

not a book recommendation, but the second "book" you're asking for sounds like Khan Academy

[scenic oasis]

I already plan on using Khan Academy, but I also want a book

[obsidian valley]

No

well I got thru about 100 pages before I decided it was bad and boring

but others who have read it share my opinion

[eager stump]

yea i've heard similar

on the webs

[woven spade]

@gray gazelle

[still jay]

Has anyone used paul halmos’ linear algebra problem book?

[marble solar]

I think Halmos has

[hasty eagle]

Removed the Advanced role from you.

[narrow talon]

Aight, y’all know it pains me, but what would be a good algebraic geometry reference? Specifically, are there any graduate level introductions with a computational focus (I’m aware of one, the book by Cox and Little, but it seems quite elementary). I’ve ran into tropical geometry wrt optimization and have some questions

[halcyon garden]

I did a few chapters while my linear algebra course was going on... it was fun and I liked the chapter on scalars because this wasnt in axler (the book we were following)

[vocal hatch]

does anyone happen to know of a good book or something like a tutorial for algorithmic information theory?

[sage kelp]

Maybe you can check Introduction to Algorithms by Cormen

[gray gazelle]

is pathfinder good for Putnam too?

[misty idol]

Does anyone know a textbook that can help me master high school geometry?

[marble solar]

Euclid's Elements

[quick hornet]

[storm sleet]

My copy of Visual Differential Geometry arrive 😎

Time to see how good it is. According to one of my profs who published one of the reviews, it’s very good

[quick hornet]

whys everything have to be visual, whys no one basing their intuitions off audio

actually i guess thats the premise of Can you hear the shape of a drum?

[storm sleet]

Needham clearly only has 1 sense he can use: vision

[quick hornet]

personally i conceptualize homeomorphisms by taste

coffee is bitter whereas donuts are sweet

[storm sleet]

Ooo this one tastes injective!

Jokes aside, VCA is a p solid book

At least for a first pass

[zealous jetty]

Pi_n: can you feel the shape of a space by its holes

[crystal lion]

“I do math with proprioception” - Terrence Tao

[tidal elm]

Are there any active reading groups in this Discord?

[marble solar]

Get outta here moonside

Not right now

||I don't think||

[tidal elm]

stfu

[sage kelp]

Why is Tao so famous?

[calm crane]

i think occasionally ppl pop in vc to continue reading a couple books, theres "one" for Markus number fields and some cft iirc?

[past ice]

oooohhh i've been meaning to buy that one for a while. how's it looking so far?

[storm sleet]

The intro is p reasonable, doesn't touch forms until chapter 5

I think the exposition at the beginning is nice, reminds me a lot of his last book

ymmv tho, not too far in

tbf, it literally released today I think

[marble solar]

Because he was a child prodigy at math, who continued in math and made groundbreaking results, and is in general kind of a goofy guy

He's fun to watch in interviews or lectures

[hearty steppe]

Tao is just a savant man. People are lucky when they are savants.

I wish I could sit down for hours and work like a machine at math or anything for the matter. Anyway sorry for going off tangent. You know how to make me do that MoonBears lol

I really liked that one essay Tao made about how math is not just about proofs.

[narrow talon]

No actually I was referring to the other, Ideals varieties and algorithms. I was unaware of this one

👍 Thanks!

[past ice]

This is way overkill, but Hartshorne has an excellent book called Geometry: Euclid and Beyond.

[uncut zealot]

Lately I've been rereading the textbook of my ODE class (which did up until Laplace transforms to solve second order constant-coefficient ODEs and systems of linear constant coefficient ODEs). Any recommendations for further reading on the topic of ODEs? I've heard good things about Sturm-Liouville Theory; is that generally what a second ODE course would cover?

[gray gazelle]

maybe check out ODEs Basics and Beyond, iirc they do cover sturm-liouville

great book in general

[gray gazelle]

best math book for an incoming freshman?

[glossy grove]

High school freshman?

[gray gazelle]

nah college

[glossy grove]

[gray gazelle]

i have an advising session in 15 minutes

[glossy grove]

It depends on what you've already done in HS, maybe some calc/analysis book.

[gray gazelle]

off tangent but what do u think i should ask my advisor

[glossy grove]

how would I know

[gray gazelle]

i dont either ahh

[glossy grove]

Just don't go

[gray gazelle]

ask them about their childhood memories

[gray gazelle]

already did that

they put a registration hold on my account

which they wont release until i attend this one

[glossy grove]

[gray gazelle]

lol

[glossy grove]

Just go there and say nothing.

Always works like a charm.

[gray gazelle]

that sounds mega awkward

what was your pre major advising session like?

[uncut zealot]

Before I declared my math major my advisor was super chill. I had read the course catalogue, chosen the courses I wanted and then went into the meeting saying "I want to take these four courses, and these eight are my backups". Then we talked about music for the next 14 minutes.

[gray gazelle]

Nice. I just came back from mine

I havent decided all my courses exactly. What was yours like?

[uncut zealot]

First semester I did calculus and some other courses that everyone needs to take. Second semester for math I did proofs and linear algebra.

[gray gazelle]

I might be able to take calc 3 first semester if I email the professor for the course and they waive its prerequisite

[uncut zealot]

Do linear algebra first

[gray gazelle]

i might have to take it with calc 3 since they're corequisites of each other

if they let me take calc 3 ie

im self studying "Book of Proofs" so i should take a proofs class too

[clear hornet]

Thinking about purchasing this book. Does anyone have recommendations of a similar flavor? I'm most interested in being able to make nice looking renders of surfaces and animations. Currently learning sagemath, but am curious what tools people here use. https://bookstore.ams.org/mbk-135/?_zs=BWWMP1&_zl=AmpM6

[analog pollen]

Can I learn differential equations from Schaum’s outlines? That would be good enough for physics?

Ode’s

[clear hornet]

can't comment on whether it would be sufficient for physics, but the Schaum outlines are a good starting place in every topic I've used them for. Once you're familiar with the math, you'd be able to get a lot more out of a text focusing exclusively on physics applications.

[west tartan]

I have differential equations this semester in my mathematics course. Which books would help?

[analog pollen]

I heard that the book ‘differential equations and boundary value problems’ from nagle saff and snider was pretty ok

[hearty steppe]

eh its a plug and chug book

your not really learning much

elementary approach to diff eq. You are not really learning what makes Diff Eq relevant, other than "oh so here are some formulas that give us some insight into applicable things but we aren't going to explain why these formulas actually make sense"

[sage python]

Well, if the course is also plug and chung then it's decent I imagine

[hearty steppe]

Naggle Saff Snider is kinda like Boyce DePrima, you are getting a Diff Eq version of Stewart's Calculus book of plug and chug problems that really only care about basic algebraic manipulation

its good to sharpen your algebra more and some intuition of your first three elementary calculus courses but its more so of a detour than actually learning much.

You just learn what the relevance of Diff Eq is on the very surface... That is to study how things change over time where it is necessary to involve equations that include derivatives.

and just some little tricks to manipulate those derivatives so you can compute something

A few people here said if you really want to learn Diff Eq, then start with a standard PDE book that is well recommended around here?

[lament sage]

so I have around two weeks where I won't be studying much aside from some physics, and I'd like to read up on some functional analysis

I know two weeks isn't much, but eh.

[hearty steppe]

I guess as long as it gets the point across as why Diff Eq is relevent. I still need to learn Diff Eq formally.

I used Naggle Saff Snider a bit and its just hard for me to recommend it after going thru some of the math texts recommended in this server. It doesn't really feel like a legit math book in that sense.

and I would say Boyce DePrima is more or less a lot like Naggle Saff Snider but with a lot less exercises (I've played around with both of them a little and in fact started with Boyce DePrima)

[sage python]

Yeah I get what you mean, there are def gonna be better books on ODEs for people who wanna really learn the stuff

It's just that you have to know your audience. Not all people who engage with math have the priorities you might

[willow pecan]

There are no good ODE books

[sage python]

Perko seems good

But yeah if someone just wants a supplement to a plug and chug ODEs class then yeah something like Perko or Arnold isn't suitable

They want a book with explanations that might click when their prof's explanations don't

And perhaps some extra guided examples

Will they learn it well? No, but they're scientists/engineers, they don't need to learn things that well

[proven orchid]

Is there a list of book suggestions for number theory?

^

[marble solar]

http://www.math.byu.edu/~nick/ucla/205a/

I like these lecture notes

[willow pecan]

[dusty grail]

is baby rudin good to learn analysis from for the first time. I’ve heard that it’s really hard but i also hear that it’s a must read for mathematicians. In your guys’ opinion does the difficulty serve as a healthy mental exercise, or would it be more of a hinderance on understanding

[marble solar]

It's definitely not a must-read for mathematicians

There are good alternatives that cover the same material

Give it a try, see if you like it

[willow pecan]

The writing itself is definitely more of a hindrance to understanding

Consider a book written for people to read, like Abbott

[marble solar]

The problems are generally good, but the book doesn't really develop your problem solving skills in a systematic fashion

It just kinda throws hard things at you

And its sink or swim

Some people love that, others don't

[sudden kindle]

Number fields - Daniel A Marcus for an introduction to algebraic number theory
Multiplicative Number Theory - Harold Davenport for analytic number theory

[marble solar]

Is Davenport that good?

[sudden kindle]

Apparently

[marble solar]

oh ok

[sudden kindle]

I tried it but didnt get too far into it

[marble solar]

Ppl say amazing things about it, but I really like that and terry tao's notes

For analytic number theory

the 205A I linked above

[sudden kindle]

People do say amazing things about it

Yesterday someone was telling me how much they loved it

[dusty grail]

@willow pecan sweet thx i’ll check that one out. @marble solar that’s interesting that you mention how it doesn’t develop your problem solving skills… I’ve never considered that when thinking of reading a math book. What properties does a book need for it to develop problem solving skills and how could i pick those books out for myself?

[marble solar]

Well it needs to show you solved problems

with examples and how they use the theorems

how they prove the theorems

and how they're related to other structures you know & love

[dusty grail]

sounds good thanks i’ll definitely keep an eye out for that stuff

[uncut zealot]

Anything more specific? Like, do you want an elementary undergrad 1st course in number theory? Do you want something more focussed on algebraic number theory, building up to class field theory (Marcus is good)? Something about elliptic curves (Silverman is meant to be good but I've only read the undergrad version)?

[proven orchid]

1st course yes

[uncut zealot]

• In that case, Topology of Numbers by Hatcher is free and pretty good, looking at number theory specifically through the lens of quadratic forms and visual intuition about them. http://pi.math.cornell.edu/~hatcher/TN/TNbook.pdf
• A Classical Introduction to Modern Number Theory, by Ireland and Rosen, while technically a graduate textbook, is pretty good as well. The first maybe 7 or 8 chapters would cover similar material to an undergrad number theory course but with a higher degree of rigour and some challenging exercises.
• It requires some algebra, but if you want something accessible on a specific topic in number theory, Rational Points on Elliptic Curves by Silverman and Tate is a great undergrad introduction to elliptic curves. It also does things like quadratic reciprocity, diophantine equations, etc.
• Honestly if you have an abstract algebra background you could probably read Number Fields by Marcus with no number theory prerequisites. I'm still only on chapter 2 though so maybe I'm wrong about that.
• If you want something computational, William Stein's Elementary Number Theory is free and designed to be used along with the sage computer algebra system. It's pretty applied, and rather short, but it's what the course I took used. https://wstein.org/books/ent/ent.pdf

[proven orchid]

thank you

[uncut zealot]

#book-recommendations message has some more recommendations

[proven orchid]

What about the Large Number Law, any recommendations?

[sage python]

Law of large numbers is probability rather than number theory

[proven orchid]

Yes

[uncut zealot]

I just googled "Large Number Law Number Theory" and got nothing; it's not a case of two theorems having the same name (like Euler's Theorem, or Gauss's Theorem)

[proven orchid]

cool

[uncut zealot]

#books-old message also has some recommendations for number theory

[hollow drum]

This is late but thanks

[gray gazelle]

does anyone know how knapp's lie groups book is?

choosing between doing that or reading through Stein/Shakarchi functional analysis book with prof

[gray gazelle]

any calculus beginner books
thank you!!

[split pond]

can anyone recommend me books for multi-variable calculus?

[gray gazelle]

spivak's "calculus on manifolds" and/or folland's "advanced calculus"

if you hate yourself yeah

[split pond]

alright thanks

[analog pollen]

Stewart calculus

Or spivak if you want rigour

[gray gazelle]

do you need calc for learning proofs? a lot of intro to proof books have calc as an "expected familiarity" (chartrand, maurice eggen). but the calculus used on these books don't seem all that important. would i be fine learning from these books if i only have knowledge of precalc?

[glossy grove]

No, you don't need calculus for learning proofs

[gray gazelle]

they do have calc sections though. are they self-contained? (sorry if this is a dumb question lol)

[glossy grove]

I've never read any of those books.

I've read gazed through Book of Proof though, which does not require any calculus.

[gray gazelle]

ok, thank you!

[glossy grove]

(It's actually free to download on the author's, Richard Hammack's, homepage)

[lime sapphire]

you got anything on fraleigh?

[tulip blade]

fraleigh is ok @lime sapphire

Its accessible.

[sharp latch]

What prereqs do I need to read Lee’s smooth manifolds

[karmic thorn]

@gray gazelle

Although I guess the preface must have listed them

I'd wager basic real analysis, group theory, linear algebra, and topology/manifolds stuff at the level of his Topological Manifolds book

And multivariable calc

[gray gazelle]

group theory isn't really necessary

you want point set topology as the main one

linear algebra as well

and ideally you've seen rigorous multivariable calculus (at the level of spivak)

some algebraic topology would help

[sharp latch]

alright cool thanks

how accessible is his top man book

[gray gazelle]

i haven't read it in depth but it should be accessible with few prerequisites

probably just generic mathematical maturity prerequisite

[sharp latch]

thank u

[gray gazelle]

the books have detailed appendices for you to check what you need to know

[jaunty fern]

hello everyone,
soo I wanna learn Math to a level beyond my grade and by myself and i want some good book recommendations to learn math and because i live in another country else than the USA my school teaching system may differ from them soo maybe list books that will teach math from the beginning till some advanced math level

and the order of studying them

[analog pollen]

What is your grade level

[hasty turret]

Over 9000

[analog pollen]

?

[past ice]

should note that the multivariable prereqs aren't too high. Most important is to know the implicit and inverse function theorems and be comfortable using the usual multivariable differentiation rules. So the first 2 chapters of Spivak should be good to get you started.

[gray gazelle]

lee actually covers the stuff in spivak from chapters 3-5 i think

so having that stuff beforehand might help

but it's not necessary

(he does it all on abstract manifolds ofc)

(also i dont think he actually proves the change of variables theorem for integration in R^n)

[jaunty fern]

sorry i was doing something
i am gonna be in the 9th grade next year

[analog pollen]

So what level of math are you looking for?

Idk what you know and what you don’t know

[spring anchor]

Hi all. I want to learn representations of finite groups (actually in particular symmetric and alternating groups) over finite fields. For now, I am particularly interested in the semisimple case. Can anybody recommend me a suitable text or any other kind of source (notes etc.) to start with?

[jaunty fern]

@analog pollen why don't you send me the books for like elementary school level and i will walk through it and see what i understand and what i don't

[analog pollen]

I’m sorry I only know university books

But I think for elementary school level Khan academy is fine

[jaunty fern]

how about from middle school books?

[analog pollen]

Idk

My books weren’t in English

[jaunty fern]

what language were they in?

[gray gazelle]

Hey guys, question. . . .What Calculus book should I study for self-teaching?

I was trying Calculus Early transcendentals 2nd edition (my schools txtbook.) this book is BAD.

Thing is these books all have different contexts and don't do everything so its a trade off.

Early Transcendentals seems to be a well rounded book, but this book is horrible for chunking.

Whoever reads this and has time, just @ me when you get the chance, thanks.

[glad prairie]

I think a lot of people really like Spivak's Calculus.

It's a bit harder.

Idk about any less hard recommendations. Stewart (the one you mention) is very common and mediocre.

[analog pollen]

Dutch

[uncut zealot]

I've been getting ads for this book lately, but I don't know much about it. It might be of some use. https://www.springer.com/us/book/978146140775

[analog pollen]

I heard that spivak wouldn’t be very good for self studying tho

But if you want a challenge i would say it’s good

[forest sleet]

from what I remember the art of problem solving calculus book was nice. It covers the standard calculus topics but has some rigorous proofs and definitions. but it's been many years since I've looked at it so I don't quite remember

but it should be easier to read than spivak

[sage python]

Fraleigh feels like it's somewhat easier than Artin but at some point... I feel like if Artin's not accessible for someone they're just not really ready for algebra you know?

[lime sapphire]

Ah fair enough i get what you mean

[gray gazelle]

Yeah Spivaks seems a little...I don't know...intense? Is he going to give me a very small and general explanation in the 3rd chapter and then expect me to solve arcsin(sin(pi/12)) or something?

Cuz that's what the early transcendentals did and I was PISSED.

[prisma snow]

I don't think expecting you to know what arcsin(sin(pi/12)) is is unfair, unless you have no idea what arcsin is

[gray gazelle]

whats a really good real analysis book
I already finished my course but we didnt dive deep enough into it

[eager stump]

depends? have you looked at tao?

[gray gazelle]

i heard of it but no

[eager stump]

are you at a uni?

[gray gazelle]

yes

[eager stump]

you can get it for free probably if you're in a uni

through your library

springer offers a bunch of free pdfs

[gray gazelle]

sweet
i also had rudin’s book in mind but been told not to go into it yet

[eager stump]

i mean the worst thing that happens is it just doesn't work

i think tao's is very readable

[gray gazelle]

alright ile check it out ty ty

[prisma snow]

I'd suggest Rudin instead or literally anything else 🙃

[gray gazelle]

how come

[prisma snow]

I think it's terrible, and not even for the reasons people normally think it's terrible

But a lot of people like it, so ig it comes down to taste

[gray gazelle]

eh ile go with my intuition and see if rudin lives to his name

[prisma snow]

[past ice]

For a rigorous intro to calculus that's more explicitly designed for self-study, try velleman's book.

[gray gazelle]

@past ice have u done it before?

i have his book

its quite good

are there any good books on recurrence relations?

[balmy kiln]

hey can anyone suggest me a classic trignometry book for high school like trig-II

[gray gazelle]

you can try Durell

[balmy kiln]

is it like explained elegantly and like includes till advanced trig

[misty wyvern]

What's the best book on addition and subtraction

[fluid skiff]

Is there a good book on sieve theory?

[past ice]

in a similar vein, serre's a course in arithmetic

[tawdry orbit]

Is linear algebra by Freidberg suitable for a beginner?

[sage python]

Yeah it's pretty smooth

[tawdry orbit]

Ok, so it will not be a problem for me, even if I have never experience proofs?

[gray gazelle]

I can't vouch for the book's appropriateness for your purpose since I haven't used it much. Skim through a few chapters to get the vibe.

[timid musk]

How does Baby Rudin compare to other commonly-used undergraduate analysis texts?

I was recently gifted the book, so I'll likely read it after finishing Spivak.

[gray gazelle]

best algebra book i have read

[marble gulch]

I learned from Rosenlicht's "Introduction to Analysis". I like it better than Rudin.

The only book of Rudin's that I like is "Fourier Analysis on Groups".

[pale scarab]

I like this book also but my favorite intro to analysis is understanding analysis by abbott. It is great for self study since it doesn't have a ton of problems and comes with a solutions manual.

[tawdry orbit]

You read all pages or skimmed it?also, how long did it take?

[tawdry orbit]

Have you done it? Lol, I’m trying to get people opinions on some books, so that I can find one and focus all my effort on it.

[flint forge]

i doubt any human being has read every page of a textbook like that haha

[final meteor]

"Principles of Mathematical Analysis by Walter Rudin"

Has anyone read this book?

[flint forge]

many people have read that book haha

[final meteor]

it's kinda hard to read this book without proper knowledge of calc right?

[flint forge]

It would certainly be extra challenging

the book is hard by itself

[marble solar]

Rudin has

[gray gazelle]

https://tenor.com/view/tom-and-jerry-strong-wake-up-beat-up-gif-5963960

This reply is just plain annoying

[marble solar]

Well, maybe the question is poorly posed. Instead of asking "Has anyone read this book"

Why not do some quick google search on what the book is like

[gray gazelle]

u know what they meant just admit ur trolling

[marble solar]

Then bring a conversation forth

[gray gazelle]

/s

(i'd say the exact same thing given the opportunity dw)

[marble solar]

If you're going to put zero effort into asking a question, why should anyone else put effort into answering the question and filling in details on things you didn't ask?

[sharp latch]

#book-recommendations lol

[marble solar]

Don't boo me, I'm right

[broken meadow]

[mellow wren]

Anybody got a good graduate level abstract algebra text to get ready for Hatcher
Since I haven't really found a book that covers free groups, abelianization and similar I've come here to ask :)

[narrow talon]

… Lang?

[marble solar]

I really liked Richard Elman's Lecture Notes on Algebra

[halcyon hornet]

Guys, is -
Learning math till and including pre-calculus from KhanAcademy and then taking AoPs Volume 1 and 2 great. Or. Using all the AoPs books?

I have been seriously thinking about this a lot, so your help is greatly appreciated.

[sharp latch]

What grade/level of math are you currently in?

[flint forge]

Khan academy is great up through calc

For calc you might want a real textbook

[halcyon hornet]

HS Geometry, Completed Algebra 1.

[timid musk]

are you going through HS geometry for the first time, or do you have previous experience in such already?

[halcyon hornet]

1st time.

[timid musk]

i see. either approach is fine, but while the AoPS subject textbooks are decent for first-time learning, I found it much easier to go through them once you already have previous experience from something like khan academy.

[frosty girder]

Can anyone recommend me some book or article for doing stuff like line integrals and all?
i have encountered them a few times in physics, and feel interested to learn a little more about them

[slim peak]

What you want to know about line integrals ?

How to compute them ?

How to defined them properly ?

[frosty girder]

yes, not just computing though, how do we define and work with them

[slim peak]

Hmmm

[flint forge]

You might like tao’s little thing in differential forms

On*

I forget what it’s called

[frosty girder]

https://www.math.ucla.edu/~tao/preprints/forms.pdf is this what you are talking about?

[slim peak]

I think it is

[frosty girder]

Ah, alright thanks

[storm sleet]

Recommendations on books abt ODEs from a theory standpoint? Our course only covers computations sadly. Background is 2 terms of undergrad analysis

[slim peak]

Viorel barbu's book

[analog pollen]

griffiths e&m gives an explanation

idk if its enough for what you are looking for

[crystal lion]

what is a more thorough treatment (and less concise) of baby rudin chapter 10 "integration on differential forms"

[misty wyvern]

Spivak COM?

[crystal lion]

that's also pretty concise

[gray gazelle]

lee has a lot on integration of forms in his smooth manifolds book, but that's a LOT more general than what rudin's doing

[misty wyvern]

ur pretty concise

[robust kite]

Where did you find those? When I took his class a couple years back he said most of his notes were still handwritten and they definitely weren't on the internet ...

[marble solar]

I took his class in 2017-2018

[robust kite]

oh ok so they are not open to the public right?

[marble solar]

they are

[robust kite]

:/

do you have a link?

[marble solar]

google.com UCLA richard elman

[robust kite]

oh lol thanks

[eager stump]

the grillet book has a bit on free groups, i haven't read it tho

[frosty girder]

ah, ok, i will check it out

[split pond]

if you are going to check out griffiths , then you should have prior knowledge over double and triple integrals ,cause they don't tell about them

[frosty girder]

i dont really know much about that

[split pond]

they cover about line, surface and volume integrals, but they make use of double and triple integrals while computing some of them

[frosty girder]

Looks like i would have to do a lot of multivariate calc

[split pond]

yeah that's why i'm doing it before going there lol

[frosty girder]

Now where to do multivariate from?

[split pond]

i asked this a while ago , and Ttera recommended folland's advanced calculus

or spivak's calculus on advanced manifolds

[frosty girder]

Ok lemme check them out

[quasi lintel]

A good book for fractions/ratios and percentage? Especially to solve word problems, I always have a hard time figuring out what operation I'm supposed to use

[halcyon hornet]

Can I send PDF?

@quasi lintel .

[past ice]

I bought the book after already having gone through a lot of Spivak so I didn't read it thoroughly from the beginning. But I've skimmed most of it and I can say that it's really, really good. Far superior to Stewart.

[past ice]

Have you checked out Zorich's analysis texts? They have very extensive coverage of multivariable calc with a view towards physics.

[frosty girder]

As a matter of fact i have not checked it out

but i will check them out now

[desert oyster]

hey, is there a simple good resource for context free grammar? I have not been able to attend lectures, and I've not found anything helpful on yt, how can I start from basics?

[gray gazelle]

Sipser Theory of Computation

[gray gazelle]

Anyone knows (for engineers digestible) intro resources on differential geometry? From the calculation/usage pov, not proof based.

[gray gazelle]

is there any book that approaches univariate analysis and bivariate statistics in a more simple and digestible way

[silk raft]

What are the best books to study number theory from? I'm not new to the subject, i just want to study it more deeply

[sudden kindle]

What do you want to learn in number theory

[silk raft]

I want to learn everything about diophantine equations

[ripe granite]

[willow pecan]

No one knows anything about diophantine equations, especially those of degree 4 and higher

[silk raft]

Sorry to hear that 😦

[ripe granite]

[crystal lion]

I thought that’s exactly what alg geo tries to complete

[ripe granite]

a "complete" understanding is probably impossible

[crystal lion]

replace “tries” with “attempts”

[ripe granite]

alg geo does many things

[willow pecan]

Arithmetic and diophantine geometry to be more precise

[gray gazelle]

Anyone have a book on introduction to mathematical proofs?

[willow pecan]

See #books-old

[gray gazelle]

thx!

[sage python]

Did someone say number theory?

[manic fox]

Anyone know of a good lecture series on logic

im tired of reading and i feel like i shud get off my break

[primal summit]

You don't speak hebrew by any chance

[manic fox]

no

[primal summit]

Then nvm

[manic fox]

[viral scroll]

hey people

Im trying to check all the properties of the extender real number system

I mean properties about sequences, supremum, infimun, whatever

any good reference for that ??

is because Im taking real analysis course and Im supposed to know all that stuff but I forgot a couple of them and also I want to check them more rigorously

[gray gazelle]

Does Baby Rudin cover extended reals?

yea

suggestion of books for numerical analysis? gonna have it next semester and the recommended books seem to be all aimed at applied math people

and im not into that

[willow pecan]

What sort of numerical analysis

[sudden kindle]

Why is it so expensive 😿

[viral scroll]

Watkins matrix computations
Or
Kincaid cheney numerical analysis

It depends on your level of knowledge, kincaid cheney is a basic level

I used watkins matrix computations for my second course on numerical analysis

Both books are rigorous, with theorems and proofs. And obviously with pseudo-algorithms for programming

[sudden kindle]

I would not reccomend anyone to read Szamuely's book

Not even my worst enemy

[misty wyvern]

that Neeman book looks really neat actually

[lime sapphire]

Hi, can anyone recommend some combinatorics books?

[gray gazelle]

If you could switch Willard for Munkres, would you?

[timber mesa]

I haven't read Willard much but Munkres is for the most part very pedagogical, though it does some awkward stuff like avoiding nets and ultrafilters altogether which makes for a very complicated proof of Tychonoff's theorem, for instance.

[sudden kindle]

Reading group?

[misty wyvern]

I'm actually looking for a more graddy version of that book, if it exists. Algebraic geometry from the analyst's standpoint.

Or to put it another way, I don't have the time to work through comm alg and I want to understand string theory now.

[gray gazelle]

Alright, thanks!

[hallow geode]

Hi everyone, can anyone recommend some books about ac circuit analysis?

[willow pecan]

Ask in the electrical engineering discord linked in #old-network

[karmic thorn]

Math 114L by Yiannis Maschovakis. You can find the recorded lectures and notes on his course webpage.

Otherwise there's Antonio Montelban's Mathematical Logic playlist on YouTube.

[willow pecan]

Montalban is wonderful

[merry glade]

@smoky surge

How does this work exactly?

[smoky surge]

What kind of math did u want to learn/what books

[merry glade]

Up to precalc

[smoky surge]

You wanted a book on that?

[merry glade]

Book or books, what would you suggest?

[smoky surge]

I’d probably just say Khan Academy for that Level

[hollow current]

prolly some problem sets

[gray gazelle]

Can someone tell me how can I revise most of the topics up to precalc rigorously, in like 30 hours or something, like some reference which got a lot of questions with a decent explanation.

[merry glade]

problem sets?

[gray gazelle]

I am thinking AoPS Alcumus?

[hollow current]

well there are books containing a bunch of problems on precalc

i dunno them in english tho

[merry glade]

Alright well, I'll just try out Khan and see how it goes.

[gray gazelle]

School books?

• YouTube

Or you can also look into books like ‘mathematics for business students’

Or some dedicated university preparation math books if that’s what u wanna do

[gray gazelle]

That sucks, why would munkres avoid filters they are so cool. anyone suggests a book for introduction of topology that doesn't avoid filters?

[slate topaz]

Can anyone recommend a good book for precalculus?

[gray gazelle]

khan academy is pretty good for anything before calculus

[slate topaz]

Yea but I'd like to follow along with a book.....

I was actually going for the aops but PayPal isn't working correctly where I'm living

[gray gazelle]

Well, if you are so inclined you can give Serge Lang's Basic Mathematics a shot

just skip over some redundant parts

[slate topaz]

Hmm

[slate topaz]

Thanks you very much

[slate topaz]

Thanks for the answer

[hollow current]

repeating myself

find problem sets

[gray gazelle]

anyone read Willard, General Topology?

[half mountain]

I read munkers

[gray gazelle]

yea everyone reads munkres but idk

[pale scarab]

Sheldon axler has a good precalculus book

[slate topaz]

thanks

[kind cave]

How does one make the process of reading/learning from pdfs less painful. Its been incredibly hard so far, could I be doing something different (like using some software).
If you do happen to read from digital textbooks often please share your tips

[eager stump]

i tend to take more notes from digital books, just to have something tangible to look at

the less i can look at the screen, the better

it's not always practical but that's what i try anyways

and to avoid that i just get books from library

[kind cave]

What if the information is too dense? or taking notes results in you staring at the screen longer(this always seems to happen to me)

[eager stump]

if i can, it's a bit hard w pandemic

[eager stump]

you could try reading it into audio file and then transcribing

[kind cave]

+1 to getting books from the library, nothing beats paper

[eager stump]

i don't think this is as much of a waste of time as it seems

because it forces channeling the material through different senses

i'll take audio notes on some things, retention tends to be pretty good

then i can also pretend like i'm some PI in one of those old fashioned movies

[kind cave]

hmm I've never really tried audio notes, if I'am being honest I rarely take notes. My note-taking game is weak

[eager stump]

it's interesting. i used to never take notes because i had good photographic memory

i personally started enjoying material more with notes

(math or non math doesn't matter)

also good memory is like good looks, eventually it goes away...

but everyone is different

[kind cave]

I just cant look at what I write lol. I wish I had a photographic memory, I just stuff/abuse my memory to tank in as much info as possible(its a very bad techinque, but its always worked)

[eager stump]

yea that's the other thing i hate grinding hahahah

so anything that helped me move away from that was is welcome in my book

[kind cave]

I personally feel like for me to benefit from my notes they need to be legible, with some sort of structure to it. I am almost never able to achieve both of these things

[eager stump]

well it looks that that's another subproblem! but that could help too

honestly with my written notes i need a better organization system

i think the thing is, habits take energy to add on, so even just adding a few wrinkles at a time does a lot

as long as the intent is there to keep honing

[kind cave]

yup, habits! all boils down to that. I dont necessarily hate grinding because once you get into that flow state it feels really good. But I get it that the hardest and the least likeable part of grinding is getting started and maintaining it till you reach that state

[eager stump]

i mean it's fine in moderation

i can't just live day to day grind (anymore haha)

month grind is ok, and necessary too to reach heights

[kind cave]

oh yeah that sucks. You need to have breaks spaced out

[eager stump]

i think that kind of also informs the non-grind periods

[gray gazelle]

In Adobe Acrobat you have the option to view two pages in the single screen. View pdfs using that view option.

[sudden kindle]

Hey I wanna learn the uniformization theorem in complex analysis. Any resource recomendations?

[storm sleet]

I've been corrupted, I think Aluffi is one of my fav algebra books now

[hasty turret]

Now,Look at the exercises

You will soon realise your mistake

[storm sleet]

Yep. I agree lol.

Expositionally, I really like it, but in terms of exercises, most of them are ok to bad

Could be worse tho, I spent like, 7+ hours on a single exercise from Lang for a class

Look, galois theory is not easy

[hasty turret]

True

[quartz scarab]

hey guys, im trying to learn number theory on my own. I am at the very beginning and would like to know some of the best books that you guys know of to learn it.

[broken meadow]

Niven's book might be good

requires no abstract algebra to begin with

eventually you will want to learn abstract algebra

[quartz scarab]

thanks, i will try this book out

[past ice]

What's wrong with the exercises? Sure, they're a bit on the easy side for a grad text, but I find that they're pretty carefully chosen to teach you a lot. Though I guess it's sort of a problem that Aluffi never really makes you "get your hands dirty" with computations.

The AoPS subject books will almost certainly be much better for understanding than Lang.

[buoyant juniper]

Currently working on Lang's Basic Mathmatics, not super applied so in 3 weeks I'm still on Section 1, but I can say so far I really like it. Quite a bit more than any other math text I've used which would include Steward and books published by Saxon.

[gray gazelle]

yeah i have read it and it covers almost every part in algebra

[lime sapphire]

hi

wanted to hear ppl's opinion on abbott's and tao's anal books

as introductory texts

[crystal lion]

you can search “tao analysis” on this server as it’s been mentioned a number of times

munkres analysis on manifolds is the book i have been searching for

it’s spivak com but at an approachable pace

[mortal warren]

have you all eversolved the black book?

[narrow talon]

I use PDFs constantly since I have no local library which carries books in a language I can understand.

An iPad was probably the best investment ever here. When reading in general I tend not to take notes anymore (egads!) since I personally find it too hard to distill the information into anything useful for reference on a first pass

Instead I prefer to have physical pen and paper and follow through/preempt any derivations/proofs on that, and write out and try to answer any questions I have. Having the physical part definitely alleviates some of the issues I’ve got with digital textbooks

[radiant bay]

I've been self-studying Calc for the first time through Spivak and explored some Analysis with Tao's book, really enjoying the proof-based aspect of math and almost finished with both of them.

I guess the next step would be to go to multivariable/vector calc? Is there a book that tackles it like Spivak Calculus? More rigorous and proof based but still appropriate for someone's first exposure to the subject?

[quick hornet]

if you've read spivak you might be able to handle baby rudin

its a hard text but you already know most of the first parts, you just have to change some mentions of ℝ to ℝ^n

it doesnt do too much "computational multivar" though

[radiant bay]

Yeah, I kinda explored rudin and still on Chapter 1 exercises, it's really challenging 😅

[quick hornet]

like green's theorem for example is basically omitted

and that gets a few lectures in a more computational course

you could go hard for some calculus-on-manifolds but i dont think i'd recommend that approach

unfortunately im not aware of great "in-between texts"

(Though tbh i'd recommend learning at least a little bit of linear algebra first)

(on which there are many many great proof-based resources)

(its not strictly necessary but will help with intuition + first learning what a determinant is when youre learning about jacobian determinants is kind of miserable pacing-wise)

[radiant bay]

Yeah, I saw somewhere that Linear Algebra is integrated into it and I'm doing Axler's and Jim Hefferon's Lin Alg book. Really enjoyable, however most of the resources I'm seeing on "rigorous" multivariable is about manifolds, differential geometry? I don't know a single thing about them so I'm really hoping for a more lighter book than those "differential geometry" books

[quick hornet]

yeah i mean thats kind of the problem

analysis on ℝ and on ℝ^n are like... almost the same thing

like okay there are obviously theorems in ℝ that don't hold, but its usually obvious when that's the case

you replace your epsilon-deltas with epsilon balls

and besides that the analytic facts are kind of... the same?

compactness goes from "union of closed intervals" to "closed and bounded" but same deal

so there arent many resources that really cover the in-between in a rigorous manner

there ARE a lot of resources that cover the computational component

since going to ℝ^n increases the computational difficulty quite a bit

[crystal lion]

munkres analysis on manifolds

[quick hornet]

did you even read what i said

anyway, back on track

this creates a weird situation where theres kind of a lack of great resources dedicated specifically to a proof-based approach to multivar for students who already have a proof-based familiarity with single variable calculus

theres stuff like tao and rudin which just develops analysis in ℝ^n from the start

and green's theorem and gauss' and whatnot are only given like

a page

[crystal lion]

oh in between computational and COM style

i thought you meant in between in terms of difficulty

which is kind of paralleled

[quick hornet]

so like, the question there i guess is

how much computational content from multivar do you actually need to know?

eventually if you DO do calculus on manifolds stuff, everything is just a special case of generalized stokes' theorem

so one could argue for omitting it if you dont really have a pressing need to learn stuff like green's theorem

but if you're taking, say, physics courses, or writing the mathematics GRE soon or whatever

you certainly want to learn that

sooner rather than later

and typically in its own treatment (since you need to be able to do it quickly)

[radiant bay]

I'm just learning it for fun so there's really no requirement for me to learn the computational content. I checked out the Chapter 9 of rudin and I guess it's somehow manageable, I'll try to venture on it more and see some of the books on manifolds stuffs. Thank youuu!

[gray gazelle]

Any recommendations for somebody who wants to learn about statistics and probability and has an extensive pure math background?

[gray gazelle]

I'll give it a look, thanks.

[gray gazelle]

Any inferential statistics book with a lot of examples?

[gray gazelle]

Hubbard and Hubbards Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach hits the spot

[gray gazelle]

I mean, I already studied it but my probs base is very bad, so it's very difficult for me and even though I tried I could never understand it

@gray gazelle I like your pfp

Thank you!

[hearty steppe]

From personal experience I haven’t really learned much intuition from a regular stats book not designed for mathematicians. I’ll be going thru Casella and Berger soon @gray gazelle

It seems mostly like a bunch of plug and chug problems and not really trying to understand what your working with if your not using a text like I mentioned

[gray gazelle]

Willard or munkres?

[gray gazelle]

That was the book I was reading and I didn't like it, for me it was too difficult

[hearty steppe]

You should read it after you have done a bit of real analysis

That is why

It’s a stats book designed for math majors

It’s not gona be easy

But yea I feel like I’m not gona understand stats intuitively until I can get thru that book and I still need to work thru real analysis first on my part

It’s one thing to waste your time with layman surface level definitions in a book designed for engineers and scientists to take the content for granted and refer to formulas for certain types of collected samples. Your not gona get much else out of most other books designed like that.

Like I still struggle with the intuition a bit after getting about close to halfway thru my layman prob stats text. You end up taking the content in the book for granted and it doesn’t really challenge what you learned

This same problem happens for some other subjects like a variety of Linear Algebra texts and especially Differential Equations. Lots of books designed to be watered down for people that don’t actually study math

[misty wyvern]

Is there a good, comprehensive reference for harmonic analysis? Assume I'm already partially woke on the subject.

But am looking for something to read through to become better at it.

[gray gazelle]

From what I’ve heard and read, the Munk is better

[marble gulch]

I like Folland

I would not call it comprehensive though

[gray gazelle]

I'm not in a math degree

[gray gazelle]

Linear algebra and DEs are easier than stats

[marble solar]

Stein's mammoth is very good

I'm unsure if it'll actually make you better at the subject

[misty wyvern]

Thanks for the recs.

[primal summit]

Recs for a book for a second course in group theory?

[forest sleet]

Griffiths is pretty standard

[lapis sundial]

^ seems most use Griffiths for electromagnetism and quantum the first time round

[hearty steppe]

I disagree that they’re easier. Depends on the content.

So you want a book for engineers basically. Walpole et al works but again, be warned that the content in books like these will not give you much intuition other than having a layman’s surface level reference for certain statistical methods to conduct on certain experiments

You won’t have much intuition on how to go about using these methods unless it’s obvious what methods to use. Most engineers and scientists work with statisticians which I believe are at the very least required to actually know math stats as a foundation

If you are struggling to learn the content it is probably a sign that you should develop the intuition for your own sake

Depends on how much you care about these subjects. I’m assuming you just want to pass a class, so maybe YouTube videos and exercise problems for what you need to push thru is better for you

[gray gazelle]

How much physics do you know

griffiths is tolerable, but if you know classical mechanics, absolutely skip it and use shankar or townsend