book-recommendations

[bitter raptor]

What’s a book with good complex analysis exercises?

Exercises in things like the basics on integration and analytic/holomorphic functions, residue theorem, prime number theorem, Riemann mapping theorem and elliptic functions?

[solemn rover]

yeah i'll edit it and reuplad it later

[sand crescent]

latex

[remote sparrow]

that's pretty normal. i learned AP calculus without ever being taught the formal definition of a limit.

[remote sparrow]

https://www.amazon.com/Collection-Problems-Complex-Analysis-Mathematics/dp/0486669130

https://www.amazon.com/Complex-Analysis-Problem-Book/dp/3319421794

maybe these?

[mossy flume]

we had to know the definition of limits and some basic properties but never formally proved them

and tbh they never came up in the AP exam

[remote sparrow]

https://www.amazon.com/Schaums-Outline-Complex-Variables-Outlines/dp/0071615695

[mossy flume]

I think that was my teacher just adding stuff cause it was good to know

[remote sparrow]

btw the books i recommended are just problem books, not quite textbooks per se. you can check pins for that

[clever mica]

Any thoughts on Concrete Math? Is it helpful for CS self-taught?

[blazing parcel]

Hi, What do you think about The Joy of X by Steven Strogatz ?

Also do you have any recommondations for studying calculus ?

[remote sparrow]

you can do spivak or apostol if you want a rigorous intro to calculus. alternatively, you can look at my recs for nonrigorous calculus: #book-recommendations message. 3blue1brown's videos on the essence of calculus are helpful supplements.

[remote sparrow]

https://www.youtube.com/watch?v=8bM9gDJataM

[clever mica]

Thanks!

[split basin]

im looking for books on stochastic calculus, brownian motion as well as markov / levy processes which also gets into stuff like connections to PDE and doesnt focus too much on finance stuff

[tender shell]

Would you say Tom apostle is good for first time studying of calculus or should I do other calc books and come back to it?

[slim rose]

Ok thanks! I found both of these books on Evan chens website so I’m assuming the etc are the other books listed there

[remote sparrow]

if you do other calc books first, apostol would be redundant.

[sage python]

I think Spivak is probably better than Apostol anyway

[remote sparrow]

#book-recommendations message

[jade spear]

general-interest type question -- does it happen much that physicists, who are of course no slouches at math, consult mathematicians for help and advice when things get tough out there in the quantum mechanics trenches?

[remote sparrow]

bar analysis and multivariable calc, you can do any of the other topics that i linked

it's not necessary to do calculus asap

[granite viper]

no? it's a good idea to do some shitty text like Stewart, then use Apostol or Spivak

It's like proto-anal

[remote sparrow]

you can just move on to real analysis by then

[granite viper]

you need to have covered proofs and set theory before using spivak/apostol

[sage python]

Not really

[granite viper]

if you just want a good understanding of calculus without properly going into analysis. but i guess there's nothing stopping you from picking up papa rudin

[remote sparrow]

?

there are many easy analysis books

like abbott

[granite viper]

basic proofs yes, set theory definitely

[sage python]

My school teaches out of that book with students who know none of that

[remote sparrow]

proofs in calculus would be tricky to newbies without a mentor though

hard if you're studying by yourself

[sage python]

So students are learning proofs for the first time using that

That = Spivak

[granite viper]

oh it does have some set theory in the introduction, right?

[sage python]

It doesn't really bother much with the set theory formalism

Just sets of numbers

[granite viper]

well, you need to be familiar to make proper use of the text

[sage python]

Which I agree is suboptimal from a "logical" pov but it does the job

[granite viper]

otherwise just use stewart

[sage python]

Most people had some calculus going in but not necessarily much

[granite viper]

pure mathematics?

[sage python]

People had not decided their major yet

[narrow fiber]

Spivak is definitely tractable for people who haven't encountered much calculus before I think

[sage python]

Some were future math, some physics, some econ, CS, chem a little, maybe a mix, etc

[calm pagoda]

Is there an abstract algebra book thats more readable than dummit and foote and more concise than gallian?

Introductory*

[remote sparrow]

maybe pinter or judson?

make sure you do a lot of the exercises in pinter, though, as some critical material is developed there

you can google syllabi that use it as a main text for suggested problems to work

[sturdy shore]

do you mean more introductory than gallian or DF?

afaik gallian is as introductory as it gets

[remote sparrow]

presumably by introductory he means undergraduate

and not something like lang

[sturdy shore]

no shit

[gray gazelle]

what is “future math”?

[calm pagoda]

I meant an introductory abstract algebra that compares to those two books in those ways

[sturdy shore]

I see

[calm pagoda]

I forgot to say introductory

[calm pagoda]

Okay ill check them out thank you

[sturdy shore]

I'd recommend aluffi - notes from the underground for an introductory algebra text

[calm pagoda]

i like books where the exercises are important

[remote sparrow]

it's rings first fyi

not a huge deal but just something you should know

[sturdy shore]

yes, aluffi is rings first

[calm pagoda]

Nice, i finished the first quarter of classes which was groups and this qaurter starts with rings so maybe its a good option

Ijust felt overwhelmed by dummit and foote, maybe i wasnt putting in enough efforr

[sturdy shore]

DF can definitely be intimidating for a first text for a couple of reasons

[remote sparrow]

one of my professors used Audrey Terras' Abstract Algebra with Applications

[calm pagoda]

applications

Thx for the recommendations

[tender shell]

I know proofs and I know some rudementary set theory

[remote sparrow]

you can do them

[tender shell]

Nice I’m still trying to decide apostle or spivak

When I get time Ill look through both of them, currently leaning toward apostle since I heard it covers more and it also has volume 2 which I actually have at home

[sage python]

As in future math majors

[calm pagoda]

I never read spivak but everyone seems to like it

[narrow fiber]

check out Artin maybe if it catches your eye

[remote sparrow]

spivak has an official solutions manual

hubbard and hubbard (rigorous multivariable calculus around the same level as apostol's volume 2) has a student solutions manual for sale

[narrow fiber]

the hubbard^2 book is fun I like it a lot

[onyx wren]

is there a hartshrone complaint list

i genuinely think a lot of people dislike the book

[remote sparrow]

many do

though i don't know of someone that lists all their complaints with hartshorne

probably a review out there

[onyx wren]

yeah im feeling a bit spiteful rn so i wanna read it

[molten mason]

I'm still a few semesters away, but I enjoy reading the chat and getting a grasp on book knowledge for future use. Seeing abstract algebra recently discussed, what do you guys think about A First Course in Abstract Algebra - John Fraleigh?

[fallow cypress]

it's p good if you know absolutely nothing about abstract algebra

if you do, then it's probably too easy

[molten mason]

Perfect lol

[fallow cypress]

I did skip the stuff on solvable groups and ascending central series though, so can't speak to that

[molten mason]

Yeah it's not a required class for me but it's something I have no knowledge on and want to eventually learn more about, probably later next year or so.

[mossy flume]

any good resources for this?

because I did not understand any of that stuff when taking algebra

and reviewing my notes isn't making it clearer

[fallow cypress]

I don't know anything about it so no idea lol

[mossy flume]

rip

welp if anyone has resources that explain solvable / nilpotent groups and other stuff group series type things, please let me know

[broken meadow]

i only remember learning it from dummit and foote lol

theres a couple sections on it

ehhh its probably not going to help you too much

so i not sure

it is cool though that solvable groups are aptly named

[narrow fiber]

i think i also only learned it from the short bits in d&f

[broken meadow]

relating to solvability by radicals

[narrow fiber]

i do not remember very much of the hardcore details im ngl

[narrow fiber]

this is def neat though

[dapper root]

Frankly

Unless you’re gonna be tested on it

You don’t need to know that stuff unless at some point further down in the line you do

But then just review it then

[topaz zinc]

why there is no specific textbook for plane, solid, and analytic geometry???

[dapper root]

Nilpotency and solvability are important in some places, but not in most places

[loud cradle]

if you are interested in the finite case, then isaacs' "finite group theory" is a nice book

[mossy flume]

yea I basically only knew it when I needed to be tested lol

but ok

[oblique dove]

anyone want to study calculus w me

more specifically AoPS calculus book

[crimson leaf]

Does anyone have resources for Schroeder's analysis?

[sage python]

Nilpotency is connected to Lie theory, solvability also to Galois theory. There may be more connections but that's what I know

Rotman's Intro to the Theory of Groups is pretty good

[narrow fiber]

Galois theory is the only place I've encountered solvable groups I think

Other than just seeing how the idea of like, central series of solvable/nilpotent Lie algebras mimic solvable/nilpotent groups' commutator series respectively

[vagrant oak]

what would be a good undergrad discrete math book that would build a strong foundation? I have seen Discrete math Susanna Ep and Kenneth rosen which seem standard. Are they good? or is there some better stuff?

and someone recommended me this
Lovasz Pelikan Discrete mathematics
though it seems very heavy

[heady ember]

Rosen was very boring in my experience with its first 30 pages or so tbh

[vagrant oak]

yeah i was afraid that would be the case and its 1000 pages long

susanna ep seems to be the same thing

[heady ember]

I wouldn't want to do discrete math even if I'm starting out. Though I would perhaps do an intro to proofs or go learn lin alg / real anal from Schroder (very friendly book apparently)

[crimson leaf]

Concrete mathematics is good

[heady ember]

(Personally I am doing Enderton's Elements of Set Theory as my first real math book. But you shouldn't unless you legitmately wanna learn about axiomatic set theory / cardinals / ordinals / etc)

[vagrant oak]

Yeah I heard abt it with the comment that it isn't for starters

[crimson leaf]

I think it's fine if you want something easier book of proof has a section on combinatorics and introduces some graph theory near the end of the book

[vagrant oak]

Well Im going through Howard Anton's elementary linear algebra rn and it's kinda very basic

[heady ember]

Try friedberg then

Or look in pinned

[vagrant oak]

And I was thinking of doing how to prove it before jumping for a discrete math book or maybe apostol's/spivak

[heady ember]

If you wanna learn proofs you can either jump straight into doing Schroder or you can look at something like loch's summary of proofs in #proofs-and-logic I guess

[vagrant oak]

I'll check it out

Ight ty!

[heady ember]

[vagrant oak]

And ty ig I'll try going through a chapter and deciding from there

[vagrant oak]

Btw would you recommend doing apostol calc volume 1 to proceed in calculus?
I did A level math and further math which cover calc 1 - Calc 2 and they cover first and second order ordinary differentials (after maybe going through a proof book that is)

[heady ember]

Idk about Apostol tbh

But if you wanna be more efficient you can just jump into Schroder's real anal book. Its quite friendly from what I heard from Dami and from my peak at the book

[gray gazelle]

Is this book famous in your country?

[gray gazelle]

cool

[scarlet pumice]

any book recommendations before entering my first semester in mechanical engineering?

[granite viper]

Yeah, the linear algebra is covered well in apostol

[spare ridge]

Jet Propulsion: A Simple Guide to the Aerodynamic and Thermodynamic Design and Performance of Jet Engines

[spare ridge]

ol

• walter rudin

[karmic thorn]

Principles of Aerodynamics is for masochists, please read Understanding Aerodynamics instead 🙂

[crimson leaf]

For some reason I don't think we're talking about aerodynamics anymore 🤔

[spare ridge]

thank you, i shall read this book

lol

[slate quarry]

Hi guys. I would like to self-study linear algebra, but I don´t know witch book I should use. Since it will be my first time studying the subject I'm not looking for a highly theoretical/proof-based approach, but also not necessarily a highly applied one: something in between would be great. I was thinking in using Serge Lang's book because I really liked his geometry book, or maybe using Strang's. Idk.

[gray gazelle]

"PRACTICAL LINEAR ALGEBRA: A GEOMETRY TOOLBOX".

by Dianne Hansford and Gerald E. Farin

(Possibly 4th edition)

I use this FOR MY LEARNING

[karmic thorn]

Applied Linear Algebra, Olver

[inner nymph]

Hey, I am doing this. Half way through the first course, but I am liking it. I am looking for things to supplement and the book suggestions seem good

https://www.coursera.org/specializations/algebra-elementary-to-advanced

[gray gazelle]

Linear Algebra Done Right by Sheldon Axler, Sheldon Axler also has a video series on his book and it's a pretty basic level book

[icy knot]

Any publisher promotions going on, like the Springer books one last month?

[slate quarry]

Thanks, it seems like a cool book.

[slate quarry]

I've check the preface, and although the book seems great, I guess it is not a good option for me now, since I don't know calculus yet (I shall be self-studying calc and LA at the same time)

[slate quarry]

Thanks, I shall check it out.

[gray gazelle]

https://youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmSinFV0wEir2Vw
Here ^°^

[karmic thorn]

If you're learning it side-by-side, going through this book should not be a big hurdle, imo.

Calculus itself is not necessary to develop most (if not all) ideas in linear algebra, so you can also skip around

[crimson leaf]

Elementary Linear Algebra with Applications by Hill

[sturdy shore]

how is axler basic?

he literally wrote the book for an audience that has already taken a linear algebra course

it is doable without that background but you would absolutely need some mathematical maturity

[gray gazelle]

It's very much doable and informative tho, it is certainly a bit advance if u didn't take Lin alg before but it is still doable
Compared to other books for beginners which can be too easy or books for people who have done it, they can be too hard
Axler manages a balances between doable yet hard and if u r only gonna read one book for linear algebra and not a lot and still want most out of it
It seems very much good

[sturdy shore]

how much of it have you read?

well, the book is out of the picture for @slate quarry anyway, because it uses calculus constantly and unreservingly for examples

[sage python]

The thing about it that's not really introductory is that it only does the coordinate free stuff, so you miss shit like RREF

It isn't needed for the presentation so it's not exactly "required background"

[sturdy shore]

yeah previous linear algebra background is not needed, but comfortability with proofs certainly is

[sage python]

But it's something Axler doesn't bother covering because he assumes you probably took a matrix-focused linear algebra class already

Is it? I feel like the writing is giga gentle. The calculus in the exercises is a barrier, and you should see the matrix business together with the coordinate free arguments if you're gonna do it all at once

[foggy relic]

axler can definitely be done for a first course

[sage python]

Also he's a dumbass about determinants lol

[foggy relic]

for row reduction just assign 30 mins of bedtime reading

this is why you need Shilov :)

gigachad for determinants chapter 1

[sage python]

Shilov feels like a meme

Ngl

[foggy relic]

u r a meme

[sage python]

A good one but a meme nonetheless

Determinants should be viewed in terms of exterior algebra

[sturdy shore]

I do think LADR is extremely gentle for its intended audience but there is still a difference between LADR and a book that assumes literally nothing out of the reader

H&K > Shilov for determinant section comparison alone

shilov determinants really are a meme

[foggy relic]

h&k is good

[sage python]

I like Hoffman-Kunze, that's where I... "Learned linear algebra"

[fossil nest]

what’s a nice textbook that introduces continued fractions?

[sage python]

By which I mean I had a class on it taught by a combo guy which didn't have any associated book

[foggy relic]

https://ocw.mit.edu/courses/18-781-theory-of-numbers-spring-2012/81634d22f185742647f70f1d8969feee_MIT18_781S12_lec18.pdf
https://ocw.mit.edu/courses/18-781-theory-of-numbers-spring-2012/188dd907b2b5567d40be6f18591d10a4_MIT18_781S12_lec19.pdf

not a book but u might find it useful

[sage python]

And then I took analysis and we had supplemental linear algebra psets from H&K and had to read the book by ourselves

[foggy relic]

these 2 notes

[fossil nest]

thank

[sturdy shore]

not sure whether I would have loved or hated that

I guess depends on my workload

[sage python]

It was... Rough

[foggy relic]

fun

[sage python]

My_trauma.jpeg

[sturdy shore]

??? no way

jfc

[sage python]

"attached notes" = Hoffman-Kunze chapter 3
"attachment" = Rudin chapter 4
Sally chapter 5 was multivariable differentiation

I did learn a lot of linear algebra that way though

[foggy relic]

Sally?

[sage python]

"Fundamentals of Mathematical Analysis" by Paul Sally

[foggy relic]

sounds doable

[sage python]

It's... quirky in a coolish way but not the greatest tbh

[foggy relic]

unless u were taking like 7 classes like this

[sage python]

Nah I was just in 4 classes, I didn't do super well that quarter since I choked on the final

[foggy relic]

ripp

4 math or 4 overall?

[sage python]

It was to this day the hardest exam I've done

4 overall, it was my only math. The problem is I didn't really understand the multivariable calc well because it wasn't coordinated with the linear algebra

[foggy relic]

oh rip

[sage python]

Our book and the prof were taking gradient f at x dot h

But HK hasn't introduced inner products or Riesz rep yet

[foggy relic]

tbh i just learned partial derivatives and only learned the rest when i actually needed it for a specific line

[sage python]

So we were just incredibly confused

Like why are we taking dot products of linear maps and vectors

And that prof often was super super disorganized

Also his choice of material to cover was often questionable. At the end instead of doing multivariable integration he told us to just learn it on our own

In 2 days

And then instead jumped to curves and surfaces from the most garbage calculus book on the planet

Everyone here's a strong anti-recommendation

NEVER use "Advanced Calculus" by Buck

[foggy relic]

that sounds based but for most people it would be a nightmare

[crimson leaf]

So how bad is Rudin second half

[sage python]

Let me say this much, the second quarter of the class was well taught

[foggy relic]

but tbf if you have solid background in calc 1/2 you can learn multi integration in an hour

[sage python]

And the psets were reasonable

[foggy relic]

baby?

[crimson leaf]

Yeah

[sage python]

Still very hard, but 6-12 hard problems rather than 50-60 book problems

You learn a lot more because you no longer are in this state where it's like, oh if a problem takes too long you have to immediately start looking up solutions since there's not enough time

[narrow fiber]

I also learned from Hoffman-Kunze

[foggy relic]

about the same iirc

[sage python]

Kenshin - chapter 9 is fine but I don't think the whole "barely teach enough linear algebra to make it work" formula makes sense, chapter 10 is incredibly stupid, chapter 11 is prob fine but doesn't make sense here

[narrow fiber]

I haven't read beyond like, chapter 8 in baby Rudin

I don't think anyone really needs to

[sage python]

You're better off switching gears at that point

[crimson leaf]

Hm I was just curious a professor at my school is planning to teach from Rudin for Analysis 2 so it's gonna be chapters 7-11

[foggy relic]

i like browder, just do it all in 1 go :)

[sage python]

Yeah that's what I like

For someone who does Rudin 1-8, I would then switch to Calc on Manifolds for 9-10, and hold measure theory to grad analysis

[foggy relic]

btw whats a good book for grad analysis?

[narrow fiber]

folland is my suggestion

[sage python]

Browder is that path but better

[foggy relic]

ive briefly looked at big rudin, folland, and royden

[sage python]

Folland or Bass for you Invictus

[narrow fiber]

oh I haven't read much royden but it looks good as well

[foggy relic]

Bass?

[crimson leaf]

How's Stein Real Analysis

[sage python]

Real Analysis for Graduate Students

By Richard Bass

[narrow fiber]

do you mean the one in the Stein/Shakarchi series

[crimson leaf]

Yes

[sage python]

That's my personal favorite

[narrow fiber]

I like all of them

[sturdy shore]

Bass is definitely slick for its size but also way less detalied than Folland judging from the parts I've read of both

[narrow fiber]

Granted I haven't read through the last one in functional analysis all that thoroughly

But I adore the first three

[sage python]

There are two types of measure theory books basically

[sturdy shore]

Bass is the book you want if you need measure theory for something like pdes asap

[narrow fiber]

I think Bass does probability in his own research iirc

[sage python]

You have those like Royden and Stein-Shakarchi that do a bunch of stuff on Lebesgue measure and then at the very end do some more abstract stuff

[narrow fiber]

Only reason I know this is because he's at UConn and I live in CT lol

[sage python]

And then stuff like Rudin and Folland that start right away with general measure theory

Now, Royden actually covers everything in Baby Rudin that isn't in Spivak Calculus

So in a weird way I kinda like the Spivak -> Royden route

That said, I think it generically makes more sense to do general measures from the start

So you know that, okay this fact is just a set theory thing

This fact crucially involves Borel-ness or Radon-ness

Etc

Big Rudin wraps up caratheodory within Riesz rep

Which imo is stupid

And why I didn't really stay with it for very long lol

I don't have much comment on it otherwise

[molten mason]

Are you able to share your linear algebra homework pdf?

[narrow fiber]

Yeah that proof took like 12 pages too

[crimson leaf]

That homework just looks like the professor has it out for students

[sage python]

My solutions or the "attached file"?

Keep in mind in my solutions I don't rewrite the problem statement

[crimson leaf]

I like the idea of having a bunch of recommended problems but only certain ones are required gives people who have the time and desire stuff to practice while also keeping a low mandatory workload

[sage python]

(re Corwin)

[molten mason]

Oh those are your solutions lol, I was interested in the problems

[sage python]

Well no those are the problems, the attached file is just second half of Hoffman-Kunze chapter 3

He pulls them from there

[sage python]

So this class in particular is advertised as having a high workload, 25+ hours/week

But the problem with this approach is that you can't really afford to spend that much time thinking about a single problem before just looking it up

Tbh you do learn something that way but it's nicer to, say have a set of problems that are more straightforward (if you're hesitating at all, review the lecture), some intermediate (requires some idea but you should eventually get it after sufficient thought), and some that are rather on the hard end (spend at least a couple hours thinking about these but after that it's fine to look it up and learn how it works if you couldn't figure it out in time)

[crimson leaf]

Yeah a 25+ hour/week class seems pretty insane for an undergrad simply because you have several other courses to juggle probably about 4 other ones on average

[quick gyro]

When I do classes I make sure I have time to spare so I can exhaust the material. I love looking up tangentially related material, applications, and related problems. It really sets the material in and gives it texture.

I also put a ridiculous amount of time into the basics. Building on a strong foundation is easier.

Interesting too is the fact that the basics seem to be some of the harder concepts if you really get down to analysing them.

Like, why is the gradient of a multivariable function automatically the highest rate of change? It could be any of an infinite number of directional derivatives, but it is the steepest.

If I remember right it has to do with the dot product and cosines.

[slate quarry]

I really appreciate your observation. It seems that, at least for now, Axler's is not an option for me. Other people have mention books that maybe will suite me better. Do you have any suggestion?

[sturdy shore]

I personally don't know much about LA books for beginners

I see Anton, Lay and Strang get brought up fairly often so you could look at any of these if you haven't

[remote sparrow]

#book-recommendations message

[calm pagoda]

i dont remember it having a lot of calculus

[remote sparrow]

#book-recommendations message

[calm pagoda]

in fact i remember it being incredibly readable

all i can think of is the derivative as a transformation over the polynomials as a vector space

[sturdy shore]

which book?

[calm pagoda]

axler

[sturdy shore]

I remember quite a few calculus examples

[calm pagoda]

oh does this person not know any calculus at all

[sturdy shore]

in one of the sections he develops a better polynomial approximation for sine than a taylor series approach (given some degree requirement)

that example alone should dissuade anyone that doesn't know calc from reading the text

[calm pagoda]

imo you could skip over anything like that

but to each their own

[sturdy shore]

sure you "could" but by then is it really worth it over another book?

[slate quarry]

Not yet. My plan is to self-study calc and LA side-by-side

[calm pagoda]

yes imo because its such a good book

[sturdy shore]

well, I disagree

[slate quarry]

Thanks. It looks like there are plenty of options!

[calm pagoda]

Also axlers books are free online on his website so you can always check it out

[remote sparrow]

note that meckes', hefferon, and beezer assume you are a student that has taken calculus, but the examples and problems involving calculus can be safely skipped

cohen assumes and uses no calculus examples

[remote sparrow]

ladr is not free, but his measure theory book is free i think.

[calm pagoda]

Its on his website

[remote sparrow]

well, ladr will be free online with the 4th edition

[calm pagoda]

isnt it

Ohhh

you can find the pdf for free with a google search even thi

[slate quarry]

Now I remember that a while ago a teacher I took a course with in college suggested me to study from hoffman and kunze. What's your opinion about that book?

[sturdy shore]

way too hard for you right now

but it is one of the most popular LA books here from what I can tell

[remote sparrow]

it was used for a standard(?) undergraduate course in UCI but even now i don't think they use it anymore

many books are possible with a sufficiently dedicated and skilled teacher and a reasonably motivated student

but self-study is generally very different

[molten mason]

Curious, why not devote all your time into getting a foundation of calculus under your belt first and then do both, instead of splitting it between Calc and LA from the beginning?

[remote sparrow]

you can do linear algebra before learning calculus even

well, you can learn a good deal of math besides linalg and calc if you want

[slate quarry]

Well, from the responses and suggestion I've read, it looks like studying some clac before LA is a good idea. I thought studying both at the same time since I shall take a calc 1 course and (probably) an LA course in a couple of months, so since I'm into math and I've just finished Axler's precalc book a few days ago, studying both subjects was a good idea in my mind. As you have said, some calc before LA sound right.

[icy knot]

Is Schroeder’s Analysis book considered intermediate or beginner? Looking for an intermediate text that’s not Rudin or Graduate like Folland or Royden. I used Fitzpatrick for undergrad “Advanced Calculus.” I was recommended Kolgomorov’s book by Dover.

[sturdy shore]

so you are looking for a book that's not rudin, but similar in level?

[grizzled harness]

Hey folks, I'm looking for an intro to fluid dynamics (or fluid dynamics, not sure if there's a difference!). I'm especially interested in conformal mappings, which I understand are useful in that field

[remote sparrow]

maybe carothers?

carothers' Real Analysis advertises itself as something after something baby rudin level, but below the level of folland

[forest sleet]

Yeah it's around the same level as baby rudin but not as terse and it does some measure theory

It starts with metric spaces

Doesn't do a lot of the specific details for just R

[copper radish]

Hello, first post. I'm looking for a recommendation on a tensor calc book. I have an interest in linear algebra & optimization problems.

[glad prairie]

The standard text that people love is Batchelor. It's pretty big and comprehensive though. Might be a little much. Idk how much it goes into conformal mapping

[honest flame]

Whats the difference between intro to linear algebra by strang and linear algebra and its applications by him?

[remote sparrow]

https://math.stackexchange.com/questions/217836/difference-between-gilbert-strangs-introduction-to-linear-algebra-and-his-li

[slim gate]

are there any books that explain the why instead of what of algebra

so i can understand why things are the way they are

and why do we use them

[molten mason]

I did Calc 1 and 2, now I'm studying Calc 3 and LA together. I got the LA textbook by Friedberg

[molten mason]

Of course when I say "now" I mean just starting this week

[remote sparrow]

what algebra are you talking about first of all

algebra of the solving equations variety or abstract algebra?

[remote sparrow]

sounds like the perfect opportunity to use hubbard and hubbard or shifrin's multivariable calculus books

they develop LA along with calc 3 in a rigorous manner

[molten mason]

Oh interesting, I'll check them out

[tawny copper]

What are resources on combinatorics?

[remote sparrow]

what level resource do you want

[tawny copper]

like intermediate

2-3 rd year undergrad maybe

I'll be focusing on problem solving and I have some resources alreaday for that, but I would like to get a glimpse of what more sophisticated combinatorics looks like

[crimson leaf]

Walkthrough combinatorics or Stanley sounds good if you want the enumerative variety

[tawny copper]

I have already gone through some parts of Bona

[crimson leaf]

If you like generating functions then analytic combinatorics by flajolet and sedgewick is good (and free) but it doesn't have problems because it's not a textbook

[tawny copper]

I'll check that out, thanks

[slim gate]

high school algebra

[narrow fiber]

Stanley is my favorite for enumerative combinatorics

It's also one of my favorite books ever bc my teacher got me into parts of it early on and Stanley was her PhD advisor lol

[remote sparrow]

Introduction to Enumerative and Analytic Combinatorics by Miklos Bona is an intermediate text at a lower level than Stanley, but higher level than Bona's introductory book

[near forum]

is Axler+Rudin+Munkres enough for ""Kobayashi Nomizu Foundations of Differential Geometry VOLUME 1""

[sturdy shore]

which one is the introductory book then?

[remote sparrow]

A Walk Through Combinatorics

[slim gate]

so books like this don't exist?

[sturdy shore]

isn't that the same book as Introduction to Enumeration and Graph Theory?

[remote sparrow]

no

[sturdy shore]

https://www.amazon.com/Walk-Through-Combinatorics-Introduction-Enumeration-dp-9813148845/dp/9813148845/ref=dp_ob_title_bk

[remote sparrow]

https://www.routledge.com/Introduction-to-Enumerative-and-Analytic-Combinatorics/Bona/p/book/9781482249095

i meant this

[sturdy shore]

alright

[remote sparrow]

edited

[sturdy shore]

which part of high school algebra are you having trouble finding the "why"?

[slim gate]

everything

i mean

i wanna know everything

[tawny copper]

thanks

[sturdy shore]

serge lang - basic mathematics might interest you, but I am still not very sure what it is that you are looking for

you need to be a bit more specific about what you are confused about

[tawny copper]

highschool algebra is not usually really deep. If you want to learn algebra, its fine, there are many books for it. But you shouldnt be looking for thick books that "explain" the "why" of the facts of high-school algebra

[sturdy shore]

just one concrete example

[remote sparrow]

maybe they feel symbol manipulation is unmotivated

[tawny copper]

if you are skeptical of any of the things you have seen in algebra, try proving them or disproving them

[crimson leaf]

I think linear algebra and groups made something's more clear to me for like basic algebra

[calm pagoda]

Holy shit

They assigned almost all the exercises from rudin ch 4

[molten mason]

Crazy that a 34 year old book with a dead author still costs $70

[sturdy shore]

sadly an extremely common occurrence

[loud cradle]

and that $70 buys you a shitty springer print-on-demand copy, no doubt

[crimson leaf]

Stein&Shakarchi Fourier Analysis is almost 20 and it's $100

Book prices are kind of insane

[dapper root]

20 years old is new

In my eyes

Lol

If it came out while I was alive it’s modern

[loud cradle]

just checked my amazon history, S&S Fourier was only $43.40 when I bought it (July 2005), that's some nasty inflation

[dapper root]

Bruh

You bought that book 17 years ago?

[loud cradle]

indeed

tbf, $43 was pretty cheap for a hardcover math book even then

[crimson leaf]

Maybe a weird question but who is Shakarchi?

[crimson leaf]

Apparently you can get it new not from Princeton hardcover for ~$70 with shipping

[loud cradle]

ah, that's not totally out of line

esp. as it's a really good book

[loud cradle]

iirc, he was one of stein's graduate students at the time the original course was taught (on which the books are based)

he left to work on wall street before vol 4 was published, which is why it took so long

(cool that it was published at all given the circumstances)

[crimson leaf]

Ah okay that makes sense cause when I googled him I didn't find much

[loud cradle]

ah my mistake, he was fefferman's student, not stein's

according to https://www.genealogy.math.ndsu.nodak.edu/id.php?id=69514

[crimson leaf]

Still interesting that he co-authored the series

[loud cradle]

yea

probably did most of the actual writing i'd guess

[crimson leaf]

That would make sense, yeah he writes it based off of Stein's lecture notes Stein makes changes or approves it

[loud cradle]

writing of the books that is, i assume stein wrote the original lecture notes

[calm pagoda]

I LOVE SHELDON AXLER

[sudden kindle]

Bruh 2005 was 17 years ago?

[quick hornet]

depends on time zone actually

[crimson leaf]

Almost 18 years ago

[sudden kindle]

Bruh if you were born in 2005 you would be 17 years old

What the fuck

[calm pagoda]

jesus

[crimson leaf]

If you were born Jan 1st you might be 18

[sudden kindle]

Thats crazy

[calm pagoda]

I feel old af

[sudden kindle]

Yeah

Bro I was like5 years old

[narrow fiber]

you bought this before I was born

what on earth

[dapper root]

someone born after 2005 shouldn't have read Hartshorne

[narrow fiber]

The other day I came across this video series of this 14 year-old explaining derived functors and I put him under do not recommend because no one born closer to 2010 than 2000 should have that kind of capacity

Ultimate moment

[dapper root]

YOU ARE ALSO BORN CLOSER TO 2010 THAN 2000

[loud cradle]

omg people are not all the same age!

fun fact, my parents bought some books before i was born as well

[narrow fiber]

I didn't mean it like that more as in just

Sometimes I don't even realize how comparatively "old" some books are

[loud cradle]

compared with many math books that have become canonical to some degree, the stein/shakarchi books are relatively young

rudin PMA was first published in the 1940s for example

spivak calculus in the 1960s

[narrow fiber]

When was Gelfand's linear algebra published I know it was fairly early as well

Oh wow 1948

[loud cradle]

amazon says 1961, but i'm guessing that was the English translation

yea russian version 1948

check hardy's "a course of pure mathematics" - 1908!

[dapper root]

RUDIN WAS PUBLISH IN THE 40S???!!?!

That shit has to be replaced as the canonical textbook come on

[narrow fiber]

I also thought it was later like. the 60s-70s at Least 😭

[quick hornet]

why do u think it introduces topological spaces as if they're a remarkable simplification tool

[dapper root]

I didn’t read it

[loud cradle]

oops, i was off slightly - 1953 apparently

[dapper root]

That’s still absurd

[narrow fiber]

Yeah I was gonna say lol that's still way earlier than I thought

[loud cradle]

the first edition was old enough to have horrible typesetting, like using $\varepsilon$ instead of $\in$

[narrow fiber]

Also the fact that hardy & wright was first published in 1938 is kinda wacky to me

[hasty eagle]

Bungo

[narrow fiber]

varepsilon my behated

[dapper root]

Okay but that’s also in Matsumura commutative algebra

Which was published like…

1960?

[narrow fiber]

is there a substantial difference between "commutative algebra" and "commutative ring theory" as far as Matsumura's books go

[dapper root]

1970!!!

Not really

But there are some

I’m gonna call them old and new

[narrow fiber]

I haven't read anything from either one I've just heard they're both brutally difficult lol

[dapper root]

So old has some scheme theoretic language barely, and the real difference is the appendix to the 2nd edition

[calm pagoda]

Yall not rocking with varepsiln?

[dapper root]

This covers stuff not in new like excellence and Japaneseness

Also included are stuff about like, uhhh

I don’t remember the name but I do remember the result lol

Typesetting is bad

[calm pagoda]

Lmao

[dapper root]

New has exercises

Old has barely any

[calm pagoda]

Its still pretty good i think

[dapper root]

But the content minus the appendices of old are like 95% the same

[dapper root]

Is it?

I read new in like 2 months

Summer after jr year

Like, I didn’t think it was that hard

But also I’d been toiling in the Hartshorne mines for like 1.5 years by then

[narrow fiber]

I should add that I read this on stackexchange and iirc specifically in comparison to like, Atiyah-Macdonald

[dapper root]

Oh sure

Anyway, Johan prefers old

But I like new more

You just

Have to go back to old afterwards and read the appendices

Also I’ve on many occasions used the exercises of new Matsumura

many occasions

that means like 10 times

[narrow fiber]

LOL does new have a lot of problems in general or

[dapper root]

Like > 200 I think

I did them all

[narrow fiber]

does it just not have many overall

[dapper root]

I texed like 1/2 of them

[narrow fiber]

Oh damn wow

[dapper root]

And wrote down the rest

I should go and Tex them

There’s a few that are stupid hard tho

I just found the original papers for like

3 of them

[narrow fiber]

I'm downloading new rn just for the sake of Looking

Wait the one you call new is commutative algebra right

not commutative ring theory?

[dapper root]

No

Commutative ring theory is new

[narrow fiber]

Oh oops

[dapper root]

Commutative algebra is old

But you want 2nd edition

1st doesn’t have the appendices

Oh but for old

https://aareyanmanzoor.github.io/assets/matsumura-CA.pdf

You should use this

[narrow fiber]

This is gorgeous I have their copy of milnor/stasheff downloaded

Alright just downloaded both old and new

Someday I'll try studying through it lmao

[dapper root]

It’s good stuff

I’m a known commutative algebra enjoyer

THEY CALL ME CHMISTER COMMUTATIVE ALGEBRA

[delicate hemlock]

chommutative algebra

[dapper root]

Walter is my disciple

I have many disciples

[delicate hemlock]

word

[narrow fiber]

Big fan of commutative chmalgebra as well

[dapper root]

If u end up at Columbia for whatever reason and wanna learn Comm alg u can do a DRP with me :^)

Honestly this semester was kinda and I felt dumb a lot

But commutative algebra had my back

[narrow fiber]

This would be so awesome

[dapper root]

At my darkest moments, I could still ask my friends to see their CA HW sets

And be like “oh I’ve already literally done / immediately know how to solve 75% of them”

And that made me feel not so pain-peko

[narrow fiber]

Okay wait do you happen to have like

The full chmonkey image I'm making something

[dry ravine]

Hello everyone
I'm looking to learn the subjects that are usually required at a math olympiad (number theory, probability & combinatorics, etc.) from square one! I pretty much know nothing in most of these subjects (almost, I do know algebra, trig, and precalc of course). So please recommend to me any resources that suits newbies like me, it doesn't have to be a book. Thanks everyone!

[torn anchor]

Khan academy!!!

[karmic thorn]

AoPS

Pretty much the go-to resource for competition math at school level

[indigo mesa]

https://cdn.discordapp.com/attachments/805444998534922305/1025799055709839460/unknown.png

found it on google to make this emote

so i had it lying around on some server

[dapper root]

I dmed them

Kekw

[indigo mesa]

Wait this is book recommendations and from 4 hours ago

[swift dome]

good resources for graduate maths ?

[visual oasis]

looking at some uni's syllabus and looking at the bibliography

[heady ember]

By graduate you mean like masters/PhD stuff?

Or like highschool graduate

[swift dome]

masters

[swift dome]

HAHA

syllabus is indeed very big

[visual oasis]

??

well graduate math is

[narrow fiber]

do you have any topics in mind

[torn arrow]

Since no one answered my forum, I'll ask here.
Any HS level all-in-one math books y'all recommend?
Ones that are free and have a PDF copy are preferable. Thank you.

[swift dome]

Statistics

[slim gate]

i just want to know how can i use those principles in real life

why do they exist

who came up with them

i mean don't you math people ever ask questions?

[autumn narwhal]

what

[gray gazelle]

So, applications ?

There are a lot of books to study applications of mathematics and algebra as well

[crimson leaf]

https://www.csub.edu/~lwildman/comappalge1std.htm

[remote sparrow]

consider reading some books on math history

[remote sparrow]

sounds boring

no one wants to do taxes or calculate their budget

real life is very dull

why would you want something applicable to real life?

[heady ember]

Reject life, accept only math

[gray gazelle]

given ax²+bx+c = 0 file your taxes

[slim gate]

so can you suggest some?

[slim gate]

cuz am living in it

[gray gazelle]

Do u want to read in depth about them or do u just want to know them ? If u just wanna know without deeply understanding how they work you can look up some videos too, u wouldn't need books for that
But if u want extremely specific details for all applications then u would have to read multiple books

[slim gate]

is there any book that goes deep into graphing

and a book about functions

[gray gazelle]

Graph as in graph theory ? Or just graphing algebraic equations ?

[slim gate]

the latter

[gray gazelle]

There aren't many books on it to go in depth, cus there isn't much depth to it
It's pretty trivial stuff I think, so idk any books on it for school level things

Perhaps someone else may know

[remote sparrow]

do you have any hobbies? play videogames? what is "real" life exactly? is it stuff that will let you suck up to faceless corporations about how "useful" you are so you can get a shit job? do any of those hobbies help with that? i'd assume not. but you do them because they're fun, right? or if not fun, fulfilling. math is like that to some people. i'm aware that some people espouse the view that school should teach only "practical" things, but believe me, those are boring. and you can learn them on your own anyhow.

[manic cairn]

Pick up books on numerical analysis

[slim gate]

dang you could've just told me to fuck off and be done with it

[tawny copper]

This is very

[gray jungle]

you need to know the fundamentals of pure abstract boring math to be able to appreciate how its applied to the real world

[gray gazelle]

Here in this server, we don't say fuck off normally, we explain ourselves deeply and passive aggresively

[narrow fiber]

I think these are all terrible responses to a valid inquiry

[tawny copper]

Applications need not be boring at all, and can be "fullfilling" for many people

[narrow fiber]

Some people just want concrete applications yeah

Also like. what's the point of recommending numerical analysis books to someone who wants to learn about graphing algebraic equations

Anyway let me think of good resources

[remote sparrow]

(sergelangfan)

[crimson leaf]

I will send this again https://www.csub.edu/~lwildman/comappalge1std.htm

[tawny copper]

Personally, I dont know much about applications, so I cant tell you a lot. There is Steven Strogratz which has some nice lectures and books for a wide audience and talks a lot about applications. Maybe you can look that up @slim gate

[crimson leaf]

Here is a ton of applications for basic algebra topics

[tawny copper]

(But Strogratz talks mainly about calculus, still is probably interesting to you)

[manic cairn]

Because I thought computational algebraic geometry has too much baggage attached /s

[narrow fiber]

This person is clearly not looking for algebraic geometry

[gray gazelle]

That's the problem I faced while recommending any book too, there are a lot of applications of graphing and functions which he asked if there are any books on it
And while there are a lot of applications, there aren't many highschool level book specific on that topic so I couldn't recommend him anything
Do u know any for that purpose ?

I do have a lot of videos on it for highschool level tho

[manic cairn]

like, does he mean just like parabolas and stuff?

Or arbitrary polynomials

[gray gazelle]

Yep

Highschool

[manic cairn]

oh

[narrow fiber]

Eris have you looked into khanacademy much

[manic cairn]

I recommend Serge Lang’s basic mathematics

[crimson leaf]

If you think space is cool this might be worth your time

https://www.nasa.gov/stem-ed-resources/algebra-2.html

[narrow fiber]

Depending on what sort of applications you're looking for I can also like, write a few problems / ideas to think about in terms of graphing

[gray gazelle]

https://www.cuemath.com/learn/mathematics/algebra-in-real-life/
https://youtu.be/s-k9zIGu43A
I found these two, a video and an article that u may consider looking into because it is good for ur level and it's also very interesting @slim gate

[remote sparrow]

recommending applications is all well and good, but we should address the implicit premise that we should not be curious about anything unless it applies to the "real" world, and we should be worried about how limiting this view can get considering how the "real-life skills" advocates end up framing anything that doesn't teach you the barest life skills necessary for soul-crushing work as "impractical," even applied math.

[manic cairn]

I think whether or not this is fulfilling is more a personality thing

[gray gazelle]

@remote sparrow u don't like applied maths do u ?

[narrow fiber]

who cares lol

[manic cairn]

I hypothesize that trait openness determines whether a given math major will like pure or applied math

[crimson leaf]

It's also the tone taken which could come off as condescending/rude to what is most likely a high schooler or younger

[narrow fiber]

Yeah this comes off incredibly prescriptive

[strange crater]

Just tell him anything related to the fields of physics, chemistry, economics, computer science or statistics requires at the very least the kind of math he's seeing

[tawny copper]

Its crazy tho how this conversation is still going haha

[crimson leaf]

Many people ask the same thing Eris did while they're in school which isn't surprising seeing as many people probably never use algebra in their day to day

[manic cairn]

“I fear the man of one book”

[remote sparrow]

that was not my argument. people that like applied math are curious, too. they want to solve a problem that interests them. basic or foundational research in science could be applied math in some parts. these things aren't always profitable.

[slim gate]

imma just ask a question

who invented algebra

[strange crater]

I be solving optimization problems in my head to make cakes

[slim gate]

and why

[tawny copper]

Uhmm

This is like asking "who invented mathematics". I dont think no one really invented it

Its more like an evolutionary process if you want

[gray gazelle]

"Muhammad ibn Musa al-Khwarizmi" is often credited with creation of algebra

[remote sparrow]

i know algebra is derived from Al-Jabr, the word

dunno who is credited with it

[slim gate]

but why did he create it

what was the point

[gray gazelle]

That's the book

"Kitab (Arabic for book) Al Jabr"

[slim gate]

a man doesn't make stuff up so years later people in school study them

[tawny copper]

Well

The greeks didnt have algebra

[gray gazelle]

"a word derived from the title of his book, Kitab al-Jabr. His pioneering work offered practical answers for land distribution, rules on inheritance and distributing salaries."

Got that from Google

[slim gate]

ye so that's the point

i don't just wanna learn something so i apply it to my life

[tawny copper]

Numbers were like distances of segments or something like that. And thats a complete pain really

[slim gate]

i just wanna know what something is why it is needed and i want to get good at it

no i am arguing people don't learn in school useless stuff that some guy invented thousands of years ago

[tawny copper]

With algebra, you know you have some quantities and some relations among them, then you can simply apply purely formal easy manipulations to obtain another quantity you are interested in, forgetting about everything else

[slim gate]

we learn in school useful stuff that peopel created

so for us to learn algebra now it has some use

[strange crater]

Just take it as general knowledge

[gray gazelle]

If u ever wanna know something from a given set of data, u rely on Algebra
There are sooooooo many applications of it from basic to some extemely advance nobody considered writing book on it cus if u were to do that, that would be a very big book
But u can read on few applications of them easily tho dw ^°^

Also there are numerous branches to Algebra as well

[manic cairn]

multiple big books exist on algebra

[strange crater]

Then people are like "why do they teach farmers to read if they're gonna do manual work" smh

[gray gazelle]

Find one on the applications of high school algebra
I could tell him books on applications of linear algebra too but he won't get that cus he in highschool

There are also numerous books on applications of abstract algebra

Also, applications that are understandable to him

[heady ember]

Dummy and Thicc for example

[manic cairn]

Just look at any physical science book for freshman college students

[slim gate]

my man you clearly didn't understand what i said

[manic cairn]

Or, my personal favorite

[gray gazelle]

There's much more calculus in it as well
I don't think he has done calculus

[slim gate]

we learn algebra because it is useful to us

that's what i meant to say

if it wasn't useful then we wouldn't learn it at school

[manic cairn]

Not physics, but literally any physical science book

[slim gate]

so the creator of algebra created it for a reason

[manic cairn]

Or like basic paramedic procedure for dosages

[slim gate]

he didn't just make up stuff

[gray gazelle]

He wants to know applications of algebra but he in school so we are trying to recommend him things that aren't calculus or too much for him

[crimson leaf]

Well one person didn't create algebra or really any math what we have today is the results a lot of mathematicians work

[slim gate]

listen i just wanna be good at math and leart to think myself and not be a robot

[crimson leaf]

They may not have had any real world applications for it but now those applications exist

[manic cairn]

It can be made with no application in mind, and still have application

[manic cairn]

Like, many mathematicians today don’t think at all about their applications to reality

[strange crater]

Most of what you learn isn't useful, but it is still important

[gray gazelle]

..... Yes, we know that, but he in school, please be kinda normal to him and teach him normally ;-;

[manic cairn]

He could very well have just came up with stuff

[manic cairn]

He’s trying to say that he couldn’t have just made it up without application

[gray gazelle]

No, a lot of it is indeed useful

[tawny copper]

Algebra definitely had an immediate application at managing quantities more easily

[gray gazelle]

Yeah, cus he doesn't know much, he in school, u sound very aggresive to him

[manic cairn]

really?

[gray gazelle]

Yep

[remote sparrow]

it's not your fault these ideas were put in your head. but surely you like some things just because you like them, and not because you see some future use out of it. it doesn't have to be math. it could be art, programming, wood carving, writing, etc. to be quite honest, it IS true few people really use algebra in their day to day life. there is absolutely nothing wrong with that. but you should really abandon the notion that school is only a stepping stone to prepare you for the "real" world, something to be conquered and forgotten.

[gray gazelle]

Shouldn't that technically be the purpose of school tho ?

[strange crater]

The usefulness of high school math is to make you generally smart (all of you overlook the importance of teaching children to think logically)

[crimson leaf]

Theres also soft skills you learn from things

Like wr said

[slim gate]

exactly

thats what i want to do

think logically

so far i have only learned rules and concepts and where to apply them

but i still don't understand what these concepts do

so whenever i try to learn them i get bored

and quit

[narrow fiber]

totally fair. is there any specific area you're curious about applications in

[gray gazelle]

If you have 3x² apples and bob has 7x apples and Johny has 4 apples, and all of them add upto 0, find x

Best application of algebra

[remote sparrow]

No offense, but that sounds like the type of artificial, contrived word problem that would make Eris hate math.

[narrow fiber]

he's trying 😭

remarkably hostile chat in the past couple hours

[gray gazelle]

That's the joke, that's the whole concept of that joke
People hating word problems because they are worded like this in school books is the whole concept that the joke revolves around ;-;

[fallen knoll]

3x²+7x +4=0? x=-4/3 x=-1

[gray gazelle]

U must be very fun at parties

[karmic thorn]

Probably best to move this chat from here

[remote sparrow]

People do overrate how much math can impart the ability to think logically, frankly. Or rather, what they mean is critical thinking skills. Speaking of using math in critical thinking, it's been a while, so maybe my opinion on this book might have changed, but something of interest is how NOT knowing math leaves you vulnerable to people trying to take advantage of you. Innumeracy: Mathematical Illiteracy and Its Consequences by John Allen Paulos could interest you.

[gray jungle]

Honestly it wouldn't be too bad if someone wrote a book aimed at HS students to showcase why the math we learn is so important (Whatever you want important to mean).

[remote sparrow]

A fun, pop math intro to game theory is Prisoner's Dilemma by William Poundstone. I'm pretty sure only basic algebra is used at most.

[gray gazelle]

Sure!!! It would be kinda fun ig

It sounds like an interesting idea tbh

[gray jungle]

[remote sparrow]

I forget about that one book with the ex-tobacco lobbyist, but he talked about how to lie with statistics. That could be interesting.

[gray gazelle]

that's, don't tell that to kids, imagine kids growing up with those things and wanting to lie with statistics
It would be very harmful for society

I got scared rn after just hearing this message

[crimson leaf]

You got scared?

People lie with statistics all the time it's very common it's better if people are actually taught stats and can decipher some level of truth

[gray gazelle]

Well, terrified would be a better word, but this idea of mass psychology and mob manipulation and lying with statistics is indeed very harmful to society

[remote sparrow]

i saw it

[gray gazelle]

This makes me lose hope in humanity

I don't like people

[remote sparrow]

and it's very applicable considering how we are bombarded with ads every day

[gray gazelle]

Yes, but the fact that there are people who actually use these and lie such way is also terrifying to think about
I think it brings me to a question much more about psychology and human nature
Are humans inherently evil ?

Yes, also psychological I wanna do psychology & neuroscience stuff later on in life but I do ponder on this question time to time the more I get to know about these things
This shouldn't be a discussion in this server indeed, but it's just an idea I wanted to share ig

[tawny copper]

I think Strogratz works for that. I havent read any of his books tho, just heard his podcast on 3b1b and one or two lectures of his

[remote sparrow]

you may enjoy math-based puzzles or math-based games. i'm not really thinking of chess, although it could fit into both categories. i'm more thinking of something like martin gardner's math puzzle books, or stuff on mathisfun.

[icy knot]

Thanks. I will look at that. I was looking for something to look at after Abbott, but not quite super advanced. I realize PMA is supposed to be for undergraduates, but it has a love/hate relationship with its audience. I’ve already graduated so maybe I have the maturity to work through a more challenging text.

[icy knot]

Thanks for the suggestion as well.

[swift dome]

Any decent books with thorough explanations for graduate calculus?

[brittle breach]

lee smooth manifolds

[dapper root]

Lmfao

[blazing canopy]

what is your definition of graduate calculus?

[gray jungle]

Calculus on banach spaces maybe?

[swift dome]

Cal 3

Differential cal

[blazing canopy]

for some intuitive introduction, "Div grad curl and all that", for a rigorous treatment, Apostol's Calculus Volume 2

[karmic thorn]

I strongly recommend Don Shimamoto's Multivariable Calculus (available online for free, legally)

Cuts a good middle ground between something like the average American calc III course and a rigorous treatment like Spivak's CoM

[grave thorn]

What makes calc 3 graduate lol

[karmic thorn]

High school graduate

[calm pagoda]

WHATS calc 3

Is it vector calc?

calc 1 = limits, derivatives, calc 2 = integrals, calc 3 = vector ??

[dapper root]

In most places yeah

[broken meadow]

yes

[fallow cypress]

But not all places 😢

[pseudo forge]

Looking for a text on Differential Equations (mostly ordinary but some brief coverage of partial wouldn't hurt). Reader is currently in uG EE with a high likelihood of attending graduate school.

[solemn jolt]

Hello everyone, I'm a programmer and I would like to refresh my maths, especially trig and calculus. Any recommendations?

I am very rusty as I've not studied maths in a long time. I would also like to study linear and abstract algebra, but I guess that will come later.

[stray veldt]

start with khanacademy probably

[fallow cypress]

^^

Also for linear algebra, MIT OCW is a good resource, I also like the textbook Linear Algebra Done Wrong by Treil

[inland hatch]

For abstract algebra undergraduate algebra by serge Lang and a course in algebra by eg vinberg are pretty good

[buoyant vessel]

anyone read a book called a garden of integral? is it recommeneded

also where can i purchase the e copy

[remote sparrow]

Morris, Tenenbaum, and Pollard's Ordinary Differential Equations could work. It does not cover boundary-value problems. It does prove existence and uniqueness of solutions with Picard's theorem in the last chapter, however. Boyce and DiPrima's Elementary Differential Equations with Boundary Value Problems has boundary-value problems. The 10th edition copy I have (recommended by my professors) does not prove existence and uniqueness of solutions.

[pseudo forge]

hmm

[pseudo forge]

I need one with boundary problems so perhaps the latter will be more suitable

[mystic orbit]

if you wanna study linear and abstract algebra "algebra" by artin is an excellent resource

it only requires some proof writing knowledge

[solemn jolt]

Right, I need to learn proofs before going there

Is Khan Academy really good enough to get a foundation for higher mathematics?

[stray veldt]

probably

in theory you dont need anything, so yeah

[solemn jolt]

What do you mean "you don't need anything"?

I mean, I thought I needed to know trig and calculus at least

Unless the latter already falls into that cathegory

[stray veldt]

if you want to refresh your trig and calculus, you obviously need to look at that; khan academy is probably a good source for this

linear and abstract algebra dont use that at all though

some examples might use calculus, but it can be avoided

an intro linear algebra book will start with no assumptions (other than say arithmetic)

but things like knowing how to symbolically deal with fractions or more generally do "highschool algebra" will be useful

[solemn jolt]

I do want to refresh calculus 1 and 2, then do calc 3 which I never studied

[split bluff]

How good would it be starting learning math using "elements" by euclid right after learning arithmetic, just asking because that's what people did back in the day

[stray veldt]

calculus will be useful if you want to learn other things, say analysis; but even an intro analysis book will not assume any prior knowledge

calc 3 will require some linear algebra beforehand

[stray veldt]

not a good idea, it doesnt have much to do with modern mathematics

[solemn jolt]

Basically I'm heavily investing in Functional Programming, which is based on lambda calculus

Basically I thought it could he a good idea to first refresh my general knowledge of maths, which I stopped studying after high school, and then go into more complicated stuff

[stray veldt]

yeah, thats probably true

but more so to get used to thinking mathematically again

you can try to skip that and read some intro proofs and then try a linear or abstract algebra book

or possibly even skip an intro proofs text

i have written a short intro that is pinned in #proofs-and-logic, feel free to look at it

it introduces basic language required to read an intro linear algebra book, maybe the one by artin

you can try that, there isnt any hard prereq other than arithmetic

[solemn jolt]

Yes, I really need to get used to thinking mathematicslly again. I also forgot most of what I did back then

I can scarcely remember how to do derivatives tbf

[stray veldt]

that wont play a role in algebra, other than maybe in some examples

[solemn jolt]

Anyway, a general refresher wouldn't hurt, I guess

Maybe just remember how it all works, then to straight into what I care about for my job

[split bluff]

I'm kind of in the same situation as you gasc, right now i'm studying a book about proofs, it's named 'how to prove it' by daniel velleman, it has taught me a lot about understanding with great precision math related statements, definitions and the like

I don't know if my path is the best one but it has been entertaining and i have learned a thing or two

[stray veldt]

its a decent book

in my opinion its too long and pedagogically not the best towards the end

but ofc if you enjoy it, all is good

[solemn jolt]

My problem is that I don't really have a plan that's not retracing my high school steps

[stray veldt]

i just gave you a few options

[solemn jolt]

Yes, that's what I was getting to

[stray veldt]

you can also just try start and read a book on functional programming if thats all you care about

though i cant comment on how feasible that is

[solemn jolt]

I meant to say that those options you gave me are a lot better than what I was thinking

[split bluff]

I've been studying it for about a year now, i've read like 60% of it, currently working with cartesian products, partial and total orders to be more precise

[stray veldt]

i think that doing abstract algebra will be useful with functional programming mindset, but im not an expert here

[split bluff]

I think i could have finished it if i wasnt solving every exercise and trying to solve examples in the book before the author explains the solutions to it

I know nothing about abstract algebra but have read people talk about it a lot

What i had in mind after finishing the book was to read some discrete math books

[solemn jolt]

For that I would also need to review sets at least

Summation, etc

[stray veldt]

i mean yeah, but thats not a ton of work

you get used to it by doing it

[solemn jolt]

That probably true

[gray gazelle]

can anyone recommend a complex analysis book that can be done without having done real analysis?

an introductory text

[sage python]

Gamelin but tbh I don't recommend that route

[gray gazelle]

why not?

[sage python]

Real analysis is pretty foundational so the earlier you see it the better, and complex analysis is one of those subjects where, while in principle you can go in and learn basic stuff without much background elsewhere, it really shines when you have the background to think of things the right way

[narrow fiber]

^ This and you'll also appreciate complex analysis more after having covered real analysis

[sage python]

What? Who says that?

I can't quite fathom what he meant by that but I will say as much as that

If you've had complex analysis and look back on real analysis, maybe the contrast stands out to you in some way and that's enlightening

That said, the whole "complex not making sense until after real" isn't even just appreciating complex analysis because you see that real analysis isn't as nice in some ways, which is how many think about it

Complex analysis really relies on topology. Cauchy integral theorem is a homotopy thing

Argument principle as well, it's about winding number

So much boils down to trying to define branches of the log

etc etc

And if you speedrun to complex analysis too fast I think that aspect is lost

[dapper root]

Chmonkey

[mystic orbit]

Chmonkey

[narrow fiber]

Chmonkey

[narrow fiber]

Oh I meant this separately from it making sense in one order or another and more from just an appreciation standpoint

That definitely isn't the best pedagogical reason why learning real analysis makes complex stuff easier

[sage python]

Oh I wasn't talking about you with that

Just that everyone's heard the "Oh you look at complex analysis by contrast with real analysis because guess what shit's infinitely differentiable now hooray" spiel

[narrow fiber]

Ah LMAO

[sage python]

And I'm like not only that, but to understand what the theorems are "actually saying" you kinda want to have seen some differential forms/topology

[warm glen]

ive never heard this ab complex analysis but i've heard ppl say real analysis made more sense after point set topology

[sturdy shore]

shouldn't it be the opposite?

[calm pagoda]

it can be both

[sturdy shore]

I guess people learn in different ways

[lethal vault]

actually i am studying complex analysis right now and i cant see it, differentiation is different, integration is different, like everything is different

main impact in understanding real analysis for me was from studying measure theory

[sage python]

Which one? Complex and real or topology and real?

[sturdy shore]

topology and real

I guess if your topology resource starts with metric spaces, I can see how it would help with real analysis

[sage python]

Hmm, in a way I feel like point-set topology beyond metric space stuff often breaks enough of your intuition with metric spaces that it's hardly something to latch onto

I guess metric spaces sorta form that zone where you can see how the definitions you might be accustomed to turn into point set definitions

[heady ember]

I am aiming to eventually read Lee's series of 3 books on manifolds / diff geo

So, I want to check with you guys how much prerequisite material I need or should know.

The below are the stated knowledge readers should know, from the appendices:

First, Intro to Topological Manifolds:

Set Theory

Metric spaces
Euclidean spaces
Metrics
Continuity and Convergence

Group Theory
=Basic definitions - Groups, trivial group, subgroup, abelian group, order of a group, direct sum, homomorphism, isomorphic, endomorphism, automorphism, kernel, conjugation
=Cosets and Quotient Groups
=Cyclic Groups

Intro to Smooth Manifolds:

Topology

Linear Algebra
=Vector spaces - linear independence/dependence, basis, dimension, coset, quotient set
=Linear maps - determinants, permutation, modules and submodules
=Inner product and norms
=Direct products and direct sums

Calculus/Analysis
=Total and partial derivatives
=Multiple integrals - Closed/Open rectangle, volume, lower sum, upper sum, lower integral, upper integral, (Riemann) integrable, measure zero, Lebesgue integrability criteria, domain of integration, change of variables, Fubini's Theorem, Lipschitz Estimate for C^1 functions, sequence and series of functions, uniform convergence, converges pointwise, Weierstrass M Test.
=The Inverse and Implicit Function Theorems

Differential Equations
=Existence, uniqueness and smoothness
=Simple solution techniques - Separable equations, 2x2 constant-coefficient linear systems, partial uncoupled systems

Now, let me elaborate on how much I think need to read/learn to know the above.

Set Theory
I think I know enough already from doing Enderton, so this shouldn't be a problem. I plan to complete Enderton or at least do a bit more of it for fun. By then, I probably would have more set theory knowledge than needed so this prereq should be fine.

Metric Spaces
Calculus and Analysis
I am planning to do Schroder's analysis book, so I think up till chapter 17 - differentiation of normed spaces, which covers up to the Implicit Function Theorem, should suffice?

Group Theory
Up to Jacobson (Basic Algebra I) section 1.10, covering homomorphisms, isomorphism, endo, auto. Cyclic groups are also covered in a prior section in chapter 1.

Topology
Yeah I'm gonna read Lee's Intro to Topological Manifolds, so this should be alright when I reach his Intro to Smooth Manifolds book.

Linear Algebra
I think I need to read Friedberg up till section 6.6 which covers orthogonal projections and the spectral theorem. But one thing I am concerned about is the part on modules and submodules. It isn't touched on in FIS, so do I need to read Jacobson till chapter 3 which covers modules? Also, although there are quite a few questions provided for direct sums, direct products aren't covered in FIS. So would I need another resource to learn that from?

Differential Equations
=Existence, Uniqueness, and Smoothness
=Simple solution techniques- Separable Equations, Partially Uncoupled Systems
This I'm not so sure.

Do you think this covers all the necessary prereqs one should have before reading Lee's books? I would appreciate some feedback . Also, I have heard that ODEs, which are cookbook style, are not very fun. How true is that lol.

*I am not procrastinating. I am not procrastinating. I am not procrastinating. *

[remote sparrow]

Morris, Tenenbaum, and Pollard could be good for ODE. It's still sort of a cookbooky book, but at least it does have proofs of existence and uniqueness in the last chapter. The problems are pretty cool, and the applications discussed are nice. Blanchard, Devaney, and Hall's book emphasizes a qualitative and graphical approach to ODEs, deemphasizing analytic, cookbooky solutions. Bill Kinney has lectures to follow that book. Coddington's Introduction to Ordinary Differential Equations is a good, elementary reference that proves all the results of basic ODE.

[dapper root]

I’m pretty sure there’s appendices with all of this stuff in there in the books lmao

[heady ember]

Yeah I basically stated the prereqs mentioned in the appendices in my first message

[heady ember]

Mmm I see, thanks

[narrow fiber]

Lee has a good 75% of this in appendices yeah

[heady ember]

I orginally typed out most of the topics covered in the appendices in my first message so you guys won't be troubled to take your copy of Lee out, because I wanted to see if doing those books I stated (e.g. Schroder) up to those points would suffice. (Looks enough to me but just wanted to check I guess)

[narrow fiber]

ohhh that makes sense mb then

[heady ember]

Its alright, no probs

[onyx wren]

same

what book are you using

I am reading book by shakarachi and stein

[astral lake]

Hi, if I'm a beginner in Differential Equations, which of the following books would be best for me to use: Fundamentals of Differential Equations, A First Course in
Differential Equations with Modeling Applications, or Ordinary Differential Equations by Tenenbaum and Pollard. Also, would I need more books in order to master Differential Equations?

[leaden cliff]

Hi can anyone recommend textbooks on binary operations, group, relations?

[mystic orbit]

Any algebra book would cover those

But smth tells me you don't want a very rigorous book on algebra

Are you a math major?

[still umbra]

best complex analysis text is spivak calculus on manifolds exercise 4-33

[turbid mural]

recommended differential geometry textbooks ?

[acoustic ridge]

Any good book on 3D vectors?

[karmic thorn]

What is your background, and which topics do you want to look into?

[karmic thorn]

What exactly do you mean by 3D vectors?

[acoustic ridge]

Everything on vector that is needed to learn physics

Specially mechanics

[karmic thorn]

Physics does subsume a tremendous amount of mathematical background eventually. Are you looking for something that covers the math for introductory physics classes (mechanics, electrodynamics)?

[acoustic ridge]

Yeah

[karmic thorn]

A vector calculus book would be useful in that case, as Yohan suggested.

[acoustic ridge]

I am currently reading a calculus book right now which is calculus by james stewart

[karmic thorn]

I recommend: https://open.umn.edu/opentextbooks/textbooks/780

[karmic thorn]

Stewart must be covering more than enough math for introductory physics, imo

Have you looked into the later half of the book?

[acoustic ridge]

Why?

[acoustic ridge]

I read almost 500 pages

[karmic thorn]

Well single variable calculus is certainly necessary, but have you covered anything around multivariable calculus yet?

I don't remember Stewart very well

[acoustic ridge]

Nope

[karmic thorn]

You should look into the part on multivariable calculus in that case

Another good resource is Paul's Online Math Notes

https://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx

[acoustic ridge]

These are the topics discussed there

Is these enough to learn advanced physics?

[karmic thorn]

What does the term "advanced" mean to you?

If advanced means a first course in mechanics/electrodynamics, then sure

Otherwise, no

[acoustic ridge]

I mean tough physics questions it may include mechanics, kinematics etc.

[acoustic ridge]

Ok

[karmic thorn]

At least you wouldn't have anything left in the way of mathematical prerequisites for these classes

That wouldn't automatically guarantee that you'd be able to solve the problems in physics, fwiw, but certainly helpful to at least know the math

[acoustic ridge]

Yeah It's better to start with math first

Most of the physics problems are 3D so you need calculus everywhere

[karmic thorn]

Learning calculus is fine, just don't get too absorbed in this if your end goal is to get better in physics

You can also look into texts that are primarily geared for mathematics in physical sciences

See Mathematical Methods in the Physical Sciences by Boas or Mathematical Methods for Physicists by Afrken/Weber/Harris for instance

[acoustic ridge]

I have six months before my final exam and I am stuck learning calculus

[karmic thorn]

Final exam for physics, or calculus?

[acoustic ridge]

It's the year final exam

12th grade

[karmic thorn]

I'm not sure what that entails, it varies place to place

[acoustic ridge]

Yeah myb... We call it HSC here

[karmic thorn]

But if calculus is not what you'd be tested on, I'd be wary of spending so much time on finessing calculus skills

You don't need to be a master of integrating by parts to solve most physics problems you'd be tested on

[acoustic ridge]

Our syllabus is very limited than what the calculus book of james stewart is based on

[karmic thorn]

It must be

High school calculus doesn't cover as much

Which is also why it's not a fantastic idea to spend too much time on it if you have other things to address first

[acoustic ridge]

Sometimes solving the simplest physics question may need the help of multi-variable calculus. Like the volume of spheres etc.

[karmic thorn]

You need to know the formula, not be able to derive it from first principles on a physics test

Physics courses generally take standard mathematical results for granted

The emphasis is on being able to use those results to solve physical problems

[acoustic ridge]

Very true but I have doubts on my ability so I don't wanna keep a hole in my learning...

[karmic thorn]

You don't have to master a subject, especially when you're pressed for time

[acoustic ridge]

That's true

[karmic thorn]

As time goes by and you learn new ideas, the old ones make more sense and automatically assimilated

So don't worry too much about it

Just ensure that you can learn and understand enough for now

The gaps can be filled with time

[acoustic ridge]

I am trying to understand all the core of topics so that I don't face trouble in near future when I will be solving test questions. To my experience it works very well

[karmic thorn]

[acoustic ridge]

Thanks for the suggestions

[karmic thorn]

Goodluck!

[near wagon]

You should study enough to pass your test. But striving for perfect learning can be a trap. You’ll likely forget the bulk of what you learn now, unless you continuously apply it after the course. I think it’s nice to be top down. Learn as deep as you need for a big task. Acknowledge other areas exist, but resist the urge to dive into tertiary topics until you absolutely need those skills. @acoustic ridge

[civic python]

Maybe I’ve fallen into the trap. I try to learn stuff at such a deep level as possible so that I’m less inclined to forget.

[near wagon]

You’ll still forget if you stop using it. Maybe it takes longer to forget if you go deeper, but you’ll forget. I like top down because it guides your learning and requires you to be efficient. You could learn everything about a hammer or learn about a hammer when you need it.

[tawny copper]

what are some analysis texts that will focus on sums and series, and in real analytic functions?

if you know of a book with simply a nice chapter on the topic, you can also recommend it. The thing is, most standard analysis texts just cover the very basics, but I want something a little more in depth

Thanks

[sage python]

@tawny copper probably one of the classic ones, either Titchmarsh "Theory of Functions" or Whittaker-Watson "A Course in Modern Analysis"

@marble solar particularly enjoys the latter

[marble solar]

Whittaker and Watson is a great choice in this case, it recently got updated for type-setting

But it has a lot on special functions, which has fallen out of flavor in the math community

Yet when I went to go do research, I needed to know about hyper geometric functions

[narrow fiber]

Same here funnily enough lol

[marble solar]

Which modern books tend to stay away from. There's a lot of knowledge in those books that get slid right over in contemporary treatments

[sudden kindle]

Hypergeometric functions are pretty ubiquitous

[loud cradle]

another book with a lot of cool concrete classical material, especially in the exercises, is Stromberg's "Introduction to Classical Real Analysis"

a newer book that assumes you already learned basic analysis (like at the level of baby Rudin) and want some stuff to apply it to is Duren's "Invitation to Classical Analysis"

[tawny copper]

Thanks for the recommendations, I'll check that out

[heady ember]

Ah nice new books to "totally legally" obtain

[raven prawn]

hello!

i’m currently in 10th grade, any book recommendations to learn concepts beyond the syllabus?

[narrow fiber]

do you have any concepts in mind? what sort of syllabus are you learning from

[acoustic ridge]

I appreciate your suggestions. I would like to follow both

[proper shale]

Anyone here completed the book Schaums outlines: Advanced Calculus

[strange crater]

https://theportal.wiki/wiki/Read

[dapper root]

Eric Weinstein lol

[narrow fiber]

"two to three years" jesus christ

http://sheafification.com/the-fast-track/ dude

Recommending Serre for Lie theory and May for AT is sadistic