book-recommendations

[gusty jasper]

Cheers, i'll check it out

[timid plinth]

Book recs for calc 2 ?

[fervent lava]

Paul online math notes.

[timid plinth]

Do they also have previous subjects to reinforce my foundations?

[fervent lava]

Yeah the calculus 1 course of his website. Then again the algebra part of his website.

[timid plinth]

Thanks, Ill definitely check the site out

[mental flare]

Hello guys, i'm only 15 years old and i don't have a strong mathematics background and i want to learn linear algebra and calculus, so i'd thank if you recomend books about that stuff.

[smoky zephyr]

i used pauls online notes for calculus, not a book but a website

[mental flare]

Can you send the link please?

[mental flare]

And for linear algebra?

Thank you.

[mental flare]

Is khan academy good for this?

[quick hornet]

wdym by "dont have a strong mathematics background"

both linear algebra and calculus will require fluency with high school mathematics first

at the very least basic algebra and trig

[gray gazelle]

Higher Algebra by Barnard and Child

Some topics are left in undergrad books, I feel. The student is surrounded by an amount of material which he can find no source to cover from

[mental flare]

i live in a third world country

the education here it's not like the great thing, it's very very very basic

[quick hornet]

my point is that, if you dont know how to simplify $\frac{\frac{1}{x} + x^2}{2x}$, you'll be totally lost in calculus

[hasty eagle]

Namington

[quick hornet]

that's just an example of course

[gray gazelle]

There are some good books at introductory level, but I cannot assure that you would be able cover them

[mental flare]

i've never done calculus before

[sudden kindle]

Knowing highschool algebra well is very important for calculus

[gray gazelle]

Have you done the basics of set theory, algebra, and functions?

[quick hornet]

what i just wrote isn't calculus

[mental flare]

yep

[mental flare]

but can you answer my question please?

[compact swift]

khan academy is great, I love it, but usually the curriculum is a tint easier than what’s taught in schools imo

altho if you can’t simplify the expression namington wrote you should probably restudy algebra

since as others said before, not having a great foundation of high school math will be difficult for you in the future x.x

[mental flare]

I was good at algebra at school, but i forgot a lot of stuff

[brittle breach]

Then it should all come back to you when you need it

[quick hornet]

khan academy is fine for calc

idk about LA, my impression is that its treatment is probably pretty flaccid

[brittle breach]

#books-old has a link to a basic calculus book

https://youtube.com/c/MichaelPennMath

Any algebra you might forget should be here

[mental flare]

Thank you a lot

I will keep trying to continue my dream of becoming a deep learning research scientist

[real trail]

One of my favorite math channels

[brittle breach]

You might want to read a book on proof while doing calculus,

Being able to write a proof would help you converse more easily on the server when you start asking questions about problems or ideas

https://youtube.com/playlist?list=PL22w63XsKjqy8AClFS2nPjCeemTMcF0K0

You only need the short vids in this play list

[mental flare]

Thank you a lot

I need to have discipline

[brittle breach]

He has a play list on
proof writing,
problems solving

Watch all the proof writing playlist

[brittle breach]

Np, and ask questions in the def channels

[brittle breach]

https://youtube.com/playlist?list=PL22w63XsKjqykuLOimt7N59e6wn_aE0wd

[gray gazelle]

Would it be fine to study the chapter of Serge Lang on Matrices and Determinants before the rest of the book?

[sudden kayak]

Any book recos for Calc 2? Class starts in a few weeks. I'm nervous

[gray gazelle]

any vol 2 of a standard text like Courant

[trail wasp]

what book on complex analysis would you recommend?

[marble solar]

Marshall's

[trail wasp]

cool, thanks!

[sage python]

@marble solar inb4 you are Marshall himself

[marble solar]

It's ok, I put down marshall

I got my copy of Euclid's Elements

I've never actually learned any euclidean geometry

[hollow shore]

All I remember is ex equalli

[marble solar]

I like how he just assumes that you can move shit around

It's like no Euclid, this is not one of your postulates

[hollow shore]

I am looking for an introductory number theory textbook which does what a first course would do nicely

[restive falcon]

can't you use circles to rotate a line segment where you want

[halcyon hornet]

Any book recommendations for Cryptography?

[gray gazelle]

how rigorous?

[halcyon hornet]

Beginner level.

Rigorous uhhh....not too rigorous but not super simple either.

[gray gazelle]

check Paar, Understanding Cryptography

it's typically used by CS majors

[halcyon hornet]

Oh.

Thank You.

Any other ones are appreciated.

[gray gazelle]

Silverman

[halcyon hornet]

Name of the book?

[gray gazelle]

Intro to mathematical cryptography

[halcyon hornet]

Thank You!

[iron granite]

Can anyone link me resources regarding countability of sets?

[marble grotto]

rudin chapter 2

[gray gazelle]

Is concrete Mathematics by knuth really that good?

[frosty girder]

apostol chapter 2 has some nice exercises for this

apostols analysis

[tulip blade]

Yea

[gray gazelle]

.

[hollow shore]

Lang's Basic Mathematics?

[brittle latch]

has anyone used this before by any chance?

[gray gazelle]

Algebra (graduate texts in mathematics)

[hollow shore]

sorry I have little to no experience with Abstract Algebra

[sage python]

If you don't know linear algebra cold you will get eaten alive by Lang algebra lol

[gray gazelle]

what if you know linear algebra hot

[gray gazelle]

Linear algebra is not entirely new but I want to see Lang’s part before proceeding because it is needed elsewhere.

And I need better understanding, which I am not able to get without standard, non-spoon fed texts

[marble solar]

I'm talking like book 1 proposition 3 buddy

[fierce crater]

Does anyone have a pdf copy of Discrete Mathematics: An Introduction to Mathematical Reasoning, Brief Edition by Susanna S. Epp

[brittle breach]

Halmos finite dimensional vector spaces

[gray gazelle]

Thanks

[jolly summit]

How has a pdf that explains mathematical induction well Pls

**who

[gray gazelle]

I suggest you watch a video instead

and actually see someone perform a math induction, but unfortunately I don't have any books dedicated solely to induction

on another note, does anyone have an idea on which book I can use to learn set theory? (beginner here)

[jolly summit]

😩

[jolly summit]

Wait beginner asin beginner or asin a beginner in the deep part

[restive falcon]

when sin^-1

[gray gazelle]

Beginner in set theory

Im in hs

[quick hornet]

i think the question is "do you want to learn detailed fancy-schmancy logician's set theory, or just set theory as in basic definitions and functions and cardinality stuff" - both of these have a "beginner" level

for the former, probably halmos

for the latter, most intro pure math texts will have a chapter or appendix on it, but if you want more detail, see an intro proofs book

[gray gazelle]

I'm terribly sorry, what do you mean by logician's set theory? Thing is, I'm taking the international baccalaureate and I want to (also, have to) write a research-like paper on Math on some topic, and set theory has caught my attention. I'l definitely check out both books though (maybe serge lang for the latter if there is some content on ST), thanks for the recommendations.

I think I've found your book, here

[quick hornet]

okay, so when people say "intro set theory" they could mean 2 things

set theory as a service course: the language of pure mathematics is based around sets and functions. this topic (it doesn't really constitute a full course, there isn't enough material) is just getting students used to definitions - unions, intersections, relations, quotients, complements, cardinality/countability, functions, injectivity/surjectivity/bijectivity/invertibility, etc. - and basic results on them

set theory as its own thing: the study of set theory at a low level as a subfield of logic. here, the goal isn't to develop the necessary set theory to do other math (students are typically assumed to already know that), but rather to introduce some basic axioms and develop the theory of sets from there.

the former is learned at some point by every mathematics major (and most CS and physics majors)

the latter is considered a more niche topic, but you need to know it to do logic

as mentioned, any intro textbook has a treatment of the former (a lot of people learn out of Munkres' for example), whereas Halmos is the usual recommendation for the latter

the former is also, if you'll excuse my bluntness, really boring

the lecture on diagonalization is kind of interesting

but besides that, its all rote definitional stuff

probably not a good topic for a paper

[gray gazelle]

i understand yeah

thanks for the detailed explanation

I'll check out halmos and see what I can think of from there, once again thanks

[gray gazelle]

any book recs for abstract algebra?

[warm glen]

check pinned msgs on this channel, scroll to the bottom one

most ppl recommend algebra by artin

[gray gazelle]

that book is soooooooooooooooooooooooo bad

[warm glen]

what makes u say that

[gray gazelle]

its sooo bad

[warm glen]

yea but why

[gray gazelle]

examples are bad

everything is propositions

he doesnt even give the names of the law

[warm glen]

if the examples were an issue maybe u would like gallian? i havent read it

but it has a lot of examples apparently

more than other books

there's also a book of abstract algebra by pinter which i think is the easiest abstract algebra book out there

[gray gazelle]

im using this one

[warm glen]

yea that's the gallian one, might be a fine choice

again i haven't read it but i think the math sorcerer has a review of it on youtube

he's also reviewed many other abstract algebra books so if u haven't seen his channel check it out

[gray gazelle]

gotcha

[rich fossil]

hi, any book recommendation for introductory number theory course?

I know one, ELEMENTARY
NUMBER THEORY by DAVID M. BURTON

bt this does not cover anything in deep, it jst explain the basics of any topic

[paper plover]

thats wat introductory means...

[rich fossil]

yeah ik, bt a bit more depth on the topic is really helpful

[paper plover]

if u want to go deeper try Niven and Zuckermann

rly good bk

[rich fossil]

kk thx. I'll check it out

[cloud condor]

solving recurence relations like a(n) = a(n-1) + b(n-1), b(n) = 2*a(n-1) + b(n-1)

how does one do this

with a(0) = 1, b(0) = 0

you get stuff like
a(n) -> 1, 1, 3, 7, 17, 41, 99...
b(n) -> 0, 2, 4, 10, 24, 58, 140...

and her it turns out both can be redefined as a(n) = 2*a(n-1) + a(n-2), and b(n) = 2*b(n-1) + b(n-2), respectively

but how can you do that without calculating a bunch of terms

[restive falcon]

#❓how-to-get-help

also why did you post this in book recommendations???

[cloud condor]

oh shit i dont know

a sleep deprived misclick

probably

[frank oriole]

Does anyone have any good recs for introductory books on math pedagogy and/or the theory of math education (for 3rd/4th year undergrads or perhaps at an elementary graduate level if possible)? Thanks in advance 🙂

[prime oak]

is calculus on manifolds not considered a good text?

[gray gazelle]

It is a good text

[slate gyro]

it is good it's just a bit difficult well at least it is for me

[jaunty acorn]

i need some suggestions for multi-variable calculus books for Undergrad

[gray gazelle]

calculus on manifolds

[prime oak]

lol

[vocal gull]

Hey, anyone has a good book recommendation on Numerical Linear Algebra? I would like an alternative to the one I'm using: Matrix Computation by Golub and Van Loan. Thanks!

[jaunty acorn]

umm...ok

[gray gazelle]

Good books

For 3d coordinate geometry

And conic sections

And related topics

And what prerequisites do i need

To master them

Like I saw the 3b1b video

On why slicing a cone

Creates an ellipse

I loved the proof

Using tangent spheres to cones and slicing planes

How do i do that

How do i learn proofs like that

Myself

I want that type of intuition

That type of approach

To be originally able to prove

Theorems like that in conic sections, 3d geo etc etc

What books will you suggest me

And what prerequisites do i need

Also

I want a rigorous real analysis

For multivariable calc

What books

And prereuisites

And respective books

Do i need

[hollow peak]

Do you ever type in a single complete sentence?

[gray gazelle]

I try

But most

Of the times i am in hurry so i cannot

[stray veldt]

conic sections are kind of out of fashion so it will be hard finding a modern book on it

some books on linear algebra might talk about them as a side note, or you can look for books with "analytical geometry" in the title

maybe a book on projective geometry, since this is the correct setting for studying conics

[gray gazelle]

Any name in particular

[stray veldt]

alternatively there are probably books on classical algebraic geometry that will discuss conics (or more generally quadrics) more generally, but that is probably overkill

[gray gazelle]

I have sheldon axler and titu andreescu linear algebra books

[stray veldt]

the wikipedia article is also a good starting point

[gray gazelle]

I will study them soon

[gray gazelle]

Thank you

[stray veldt]

i mean you have to check the toc for the word "conic" of "quadric"

[gray gazelle]

I will have lot of free time after 8 months so i will do an overkill

[stray veldt]

i am not aware of any english linear algebra book talking about them

[gray gazelle]

Wait i have a projective book

I will check it out

Thank you friend

[stray veldt]

so the prereq is probably linear algebra (in any kind of modern treatment) and maybe projective geometry if you want to study them "correctly" (this also needs some background in linear algebra)

[gray gazelle]

Any prerequisites for projective geometry

[stray veldt]

linear algebra, mathematical maturity

[gray gazelle]

Anyways thank you, it is late here so i am going to sleep, goodnight

[gray gazelle]

Ok , thank you. Will learn linear algebra

[gray gazelle]

How many books can you guys juggle at the same time?

[dapper root]

Idk, I can only juggle three balls, but I feel like juggling books is harder so maybe 2?

[gray gazelle]

[vocal gull]

Hey everyone, tell me your favourite books on Numerical Linear Algebra!

[dapper root]

Just tried to juggle two books, I can't do it

I can only juggle one book at a time :(

[sudden kindle]

Chmonkey toss the first book and then pass the other to your throwing hand, then catch the 1st book you threw and repeat

@dapper root

[gray gazelle]

by induction you can juggle with any n books

[dapper root]

I can do it!

[hearty steppe]

I am really enjoying Casella and Berger’s Statistical Inference atm

[dapper root]

Nice job @sudden kindle

[hearty steppe]

@dapper root Yoo what up

[dapper root]

I can juggle 2 books

[sudden kindle]

Juggling 3 books is way harder

Idk how to juggle 3

Idk the technique

[hearty steppe]

I am starting to book juggle again right now

May add munkres into fold shortly

The linear algebra book I’m working thru is pretty much easy street atm so I think I can handle another book

[frail orbit]

Hello guys, Im going to IT university in 6 month, but there's one problem. I even don't know algebra... University not prestigious, but anyway I need to learn algebra, etc. Can you recommend me a book that give me knowledge and have good explanation?

[winged tinsel]

shoot, I wish I could handle two books. I can only currently handle quaternions and elliptic boundary value problems.

[surreal plover]

where can i find solutions to textbook exercise problems?

for this book Differential Equations, Dynamical Systems, and an Introduction to Chaos

can't find it anywhere except chegg

[sage kelp]

Have the exact same feeling lol

[frank oriole]

bump

[gray gazelle]

Can someone link me to a pdf of this book? I cant find it on b-ok.as

https://www.google.co.in/books/edition/Calculus_for_Engineering_Students

I really like the part available here

but am almost done with it

[lime sapphire]

hi, wondering whether to buy hoffman and kunze or friedberg for lin alg
opinions?

[marble grotto]

to quote lightning

[clear merlin]

Problems on Mathematical Analysis by GN Berman

Challenge and Thrill of Pre college mathematics

[clear merlin]

Hall and Knight is good for higher alg

[finite saffron]

wait a sec i just realized this is book recommendations, not chill :\

[limber hollow]

That caught my eye when I saw my last name.

Not very common, haha.

[lime sapphire]

NO

that book is scary

[lime sapphire]

bump

[hollow shore]

Is there a textbook out there which goes over an assortment of logic puzzles starting with an approachable difficulty and then gets more terse in the later half?

[gray gazelle]

terse?

[hollow shore]

Increased difficulty ig

[gray gazelle]

Do you know how to code?

[hollow shore]

No I don't

[gray gazelle]

Maybe art of problem solving

@hollow shore

[hollow shore]

I don't need heuristics

[gray gazelle]

What do you mean

[hollow shore]

I need a collection of problems (something like Cheryl's Birthday problem) which are logic puzzles

[karmic thorn]

Gardner has several books around logical puzzles

[hollow shore]

I will have a look. Thanks.

[marble grotto]

You got no more answers because I already gave you the objectively best one

[fossil imp]

Hi all! I'm following a differential geometry class that recommends reading Do Carmo's Riemannian geometry book. Last year, I read good comments on Lee's Smooth manifolds. I'm trying to decide which one to buy (or both). Does someone have any advice on this?

[astral laurel]

In our univ we used William Ford, Numerical Linear Algebra with Applications. I think it's decent, especially it having quite an extensive coverage on programming exercises (though all examples are in MATLAB)

idk, I have CS background and I don't really like matlab. Our professor tried to allow students to work on python instead (he said something along the line : due to rise of deep learning, python should be prioritized to learn) but all the example codes in textbook were in matlab and students just found it easier to learn some matlab.

[narrow talon]

They are entirely different books as far as I know? I'm pretty sure Lee is a reference text/textbook on differentiable manifolds, whereas Do Carmo is specifically on Riemannian manifolds and doesn't treat the smooth case so much

[vocal gull]

thanks! I will check it out. I am way more familiarized with MATLAB than python anyways so no problem

[hearty steppe]

Matlab is great for matlab things

Probably would be better if nobody had to pay to use it

[subtle siren]

But since it's paid, better to rely on GNU/C++

[hearty steppe]

You can use Octave or R

Instead

[sinful glade]

Tru imagine doing scientific calcs on c 💀

[subtle siren]

I didn't find Octave usable

[sinful glade]

R julia or python fr free

But pythons too slow

[indigo relic]

@rocky locust please i need a book in combinatorics? (since the probability book that you recommended was the best i've ever read)

[gray gazelle]

Hi Tammy

[hearty steppe]

What problems you have with it @subtle siren

[subtle siren]

Not running my .m properly

[sinful glade]

Hello oh wait r u frm phods?

[gray gazelle]

Yes

[sinful glade]

Cool

[gray gazelle]

I left it though

[hearty steppe]

@subtle siren is that a file for editing user preferences and macros?

Or wait

[sinful glade]

Ah i saw that u said that u were gonna leave fr a while

[hearty steppe]

https://stackoverflow.com/questions/23308280/how-to-execute-m-files-in-octave

@subtle siren

I never used Octave before but that seems like it’s not too bad

[subtle siren]

It's not a full port

There are some (many?) functions which are not in octave

Anyway I do have MatLab access in all my unis thus far

But GNU/C++/whatever I don't need to bother with 11GB of software and/license = good

Which is why Julia/R is pretty amazing

[hearty steppe]

Ahh yes that is also an issue

[brittle latch]

has anyone used/know of this textbook

it's what my class will be following but i dont wanna drop 80 bucks on a book before ive heard something about it from others

[gray gazelle]

🏴‍☠️

[brittle latch]

what does that mean

[smoky zephyr]

pirating

[gray jungle]

you know.......

[smoky zephyr]

is what it means

[brittle latch]

oh i cant do pdf's lol

if im gonna spend time studying this i like having the physical thing

[gray jungle]

you can check the legally bought pdf to assess the book before investing in it is the point 👀

but in your case i guess you have to either way

[normal sandal]

perhaps second-hand?

[vestal sphinx]

Does anyone know of good real analysis problem sources with solutions?

[gray gazelle]

Kaczor-Nowak book

[vestal sphinx]

Thank you!

[abstract walrus]

is A Walk Through Combinatorics good? I've just been doing Pablo Soberon's book instead I wanna know if anyone can tell the difference

[tulip blade]

Soberon’s book is geared towards olympiad problems. A walk through combinatorics is just a combinatorics textbook.

[abstract walrus]

ah gotcha thanks

[timid plinth]

book recs for calc 2 and higher?

[rapid token]

Which book is better, Baby Rudin or Understanding Analysis?

[sage python]

I think Baby Rudin is basically the correct answer for intro analysis books (there are some things I'd change but overall...) but Understanding Analysis I feel only "kinda" competes in the same category

Namely if Baby Rudin is appropriate for you, Understanding Analysis is probably unbearably slow

If you're not bored by the latter, the former is prob gonna be rather tough

[gray gazelle]

whats a good book for getting into abstract algebra?

[sudden kindle]

Abstract Algebra: A first course

By Dan Saracino

[gray gazelle]

thanks!

[marble solar]

Ok boomer

[golden bear]

I mean, Tao's Analysis beats these two anyways.

[sage python]

Eh not really

[marble solar]

Not at all

[sage kelp]

Tao? No way

[golden bear]

The way is written is probably what I should have said

[marble solar]

I disagree

[golden bear]

I tried reading rudin, but I felt discouraged

[marble solar]

I mean that's fine, but Tao's Analysis isn't done well either

and I don't think it's well written

[frosty girder]

i thought the first chapter was nice
But the 3rd chapter was such a mindfuck i couldnt go on

[gray gazelle]

Calculus 2 is covered in 2nd volumes of standard texts like Apostol and Courant, I believe. I would say Courant because I like it.

[hollow shore]

Hubbard and Hubbard is also a pretty popular choice for multivariable calculus

[wheat cargo]

apostol is my rec in there

or, spivak

spivak is more rigorous, but apostol is great too

[wheat cargo]

also, apostol's volume 2 doesnt contain calc 2 iirc, usually its content that is considered higher

volume 1 covers integration before differentiation

and sequences and series at the end i think?

[sage python]

Apostol volume 1+2 probably covers a typical Calc 1-3 + LA + ODE class with proofs I think

Or maybe does a bit less

Idk the deets of how much LA it does

[gray gazelle]

I found Apostol pathetic. In fact, I found all calculus texts except Courant to be very bad. It is my bad taste

[wheat cargo]

i dont think it really covers LA well enough

to say that it covers a "proof-based LA class"

not sure though, since i havent seen too much of vol. 2

[gray gazelle]

True

[wheat cargo]

ODE probably, calc 1-3 definitely

it also has introduction to probability sprinkled in it

spivak was fine imo

very challenging though

[gray gazelle]

I think Courant vol 1+2 is enough for all calculus spare a very few topics (Courant Introduction to calculus and analysis, not the older one). It also is coherent with analysis and is kind of a mixture of calculus and analysis, very finely done.

[wheat cargo]

hm maybe i should take a look, it sounds interesting

a mix of calculus and analysis?

how does that work?

ill find out by reading :)

[sage python]

Yeah LA is the one I'm less sure about

OVerall

I get the vibe that Apostol is kinda whatever in a way

If you want proof-based calculus, Spivak is the choice for "lower level" (meaning you can prob approach it both as an intro to proofs and as an intro to calculus simultaneously), sliding scale depending on maturity up to Rudin for which you prob want to have some kinda proof experience as well as knowing the def of the derivative going in

[gray gazelle]

Daminark, you said about being eaten alive by Serge Lang.
If I do linear Algebra from Werner Greub, would it be enough for starting Lang algebra?

@sage python sorry for ping

[marble solar]

It's not a whole lot, it's like an intro

[sage python]

Devansh: I mean you can always try Lang but I get the vibe that it's more a second course on algebra than a first?

Not sure if there's some specific algebra it assumes as background but overall it's considered the king

I don't know Greub linear algebra also

[gray gazelle]

Ok, thanks.
What I wanted to ask that day was that whether I could study linear algebra part of Lang before the rest of the book as I needed to study Linear Algebra early. Determinants and Matrices are not new to me, but linear algebraic maps are not studied till now.

[sage python]

If you wanna do linear algebra and algebra at the same time read Artin probably

[gray gazelle]

Ok thanks

[modern stone]

Do I need books to learn calc?

[stray veldt]

probably not, khanacademy might suffice

[modern stone]

Nice

If I supplement with Paul’s Online Notes and/or Prof Leonard would it be enough?

[stray veldt]

enough for what?
but i heard that this is a good strategy

[modern stone]

For learning calculus

[abstract walrus]

Is small the goto for functional equations

[hollow shore]

Seems like it

[jaunty acorn]

I am looking for linear algebra and abstract algebra book recommendation

plus any lecturer which i should follow for this course

Thanks in advance!!

[modern stone]

For AA I’ve heard that Pinter is a good elementary introduction

[empty mortar]

i liked a combination of axler + treil for linear algebra (done right + done wrong)

[timid plinth]

Appreciate it I will look into both when I have the chance

[jaunty acorn]

any lectures i should watch online

[jaunty acorn]

thanks man 👍

[modern stone]

https://youtube.com/playlist?list=PLelIK3uylPMGzHBuR3hLMHrYfMqWWsmx5

[jaunty acorn]

thanks ♥️♥️♥️

[sharp willow]

Does anyone here have a good book on formal logic more specifically mathematical logic?

[stray veldt]

i liked Ebbinghaus

[sharp willow]

I've only read Peter Smith's intro and watched some lectures. Most things ik of knowledge of formal logic is confined in the spaces of interpretations by philosophers like that of Stirner, Hegel and Frege

[safe relic]

Hey guys! I want to read: "discrete mathematics with applications" by Susanna Epp. Should I read the whole book in order, or is there a recommended sequence of chapters that I should read? I want to learn discrete mathematics mainly for programming(Induction/Recursion, Trees and graphs, etc).

Btw, I see that this book:"A Programmer’s Introduction to Mathematics (Jeremy Kun)" is recommended in this channel, however, what are the prerequisites for it? Could someone who sucks at math jump in right away? Or is it for people who are familiar with math, and just need to a book to teach them how to mix both math and programming together?

[hollow shore]

I suppose you can follow the course structure of an uni. The aims and objective part of the course should give you a fair idea of what the course's objectives are and if they align with your objectives, it should be good.

[safe relic]

That sounds good. Thank you!

[hearty steppe]

I’m gona check this out

[stray veldt]

this book is literally written by euler?
i suggest finding a modern treatment of whatever you want

[dapper root]

Lmfao

[stray veldt]

euler was not a great author and even if he was, you should not read his texts to gain mathematical insight
pedagogy evolved a lot

[sage python]

@knotty wagon so, not a lot in Rudin will be new. It'll recast what you did in metric spaces

But at that point I'd say read something like "Real Analysis" by Royden

(I don't agree with its organization and can't vouch for the writing but the topic list is good, it does metric spaces, functional analysis, and measure theory, so it's situated pretty much where you are at now)

[marble solar]

You should go w/ Rudin out of the two

Just don't do multivariable out of rudin, or measure theory. So like chapters 1-8 of Rudin is Golden

[brittle breach]

I think 9 is alright aswell

[jaunty hill]

Any books that are that aren't straight up course books but like, maybe looking at practical stuff or nature or something for trig / calc / proofs? A book that's "interesting" and not just a plain course book if that makes sense.

[fervent lava]

Probably spivak calculus, I have been using it as a supplement for my analysis book and I like it.

[dusty grail]

any recommendations for math pedagogy? have no background in the topic but recently have become interested. After a few youtube videos explaining the main theories i find that i specifically want to learn more about cognitivism

[jaunty hill]

I'll look into that one.

[odd spade]

Euler would be a really bad source for math

Well, for basic, basic algebra probably isnt invalid but a pretty bad book choice for practical purposes

[foggy relic]

I'm not sure what you mean by "practical" stuff but other than that point, SPivak seems to fit your needs.

[jaunty hill]

Something thats not just a collection of problems to solve for a course, more abstract? Idk how to phrase it

[foggy relic]

Yeah, Spiv is good then

I thought you meant heavy on applications but wasnt sure

[marble solar]

Spivak Calculus on Manifolds

[misty wyvern]

I would pick up Rudin instead of Tao. Once you've mastered basic analysis you will still like to flip through Rudin; Tao however will become a chore.

[misty wyvern]

I can't believe Rudin would write that then do Dedekind cuts.

I feel like Rudin just wanted to own students

with facts and logic

[sage python]

It does it in an appendix for exactly that reason

It's here for completeness but skippable

[grand thistle]

ive just started apostol's calculus volume 1 and its exercises are so hard

its all prove this and that

i have very little experience with proofs other than like the first half of the proofs chapter of 'how to prove it' by velleman

is it fine to just skip those proving questions

and look at hte solutions to see how they got to that

or should i try and prove each and every single of them

[gray gazelle]

Isn't the point of using a text like Apostol to practice writing proofs for calculus?

I just bought Spivak for that purpose.

[gray gazelle]

I'm also in the same boat with adjusting to proofs. I'd say definitely try before looking up solutions but set yourself a time limit.

Whether that's an hour, a day or a week.

[grand thistle]

yeah

its so hard though

i think ill read through how to prove it's first few chapters again

really make sure i know the basic logic and set theory

[gray gazelle]

There's that approach, or stab at it until you make progress.

FWIW we do a full semester of calculus where we're asked to prove things (it's not entirely proof based although rhe lectures are, the problems are a mix or prove/show and solve) before discrete math where basic logic and proof strategies are introduced

I infer there is a pedagogical reason for this

The guy who said you're exercises are trivial gave you a silly response. Of course, the entire freshman curriculum is pretty trivial but it's hard when you're learning it the first time.

[grand thistle]

ah i see

how do you prove things then?

do you just use your intuition to show things by direct proof?

[gray gazelle]

Fumbling. I think the point of it was to make us think hard about a novel task, fail, and then discuss the relatively elegant solution in the tutorials. And many of the proofs were 'trivial'.

I mean, nobody's proofs were very good

[grand thistle]

right

i think proofs are the hardest thing for me

my first introduction to calculus was very smooth except for epsilon delta proofs

[gray gazelle]

Yes, me too. We spend a lot of time being shown proofs and less time practicing them. They are also time consuming. We're expected to develop computational fluency by practicing problems and finding examplea in our own time, so it is difficult to spend time on proofs as well.

[south salmon]

I have gripes with a few of those books, but if you can read them and get something out of them, then probably

The ones I don’t like are personal gripes with spivak, and I just don’t like ahlfors or baby rudin all that much

not that they’re not good

bc people do swear by them

[dapper root]

These books r all classics but that usually comes with some problems

[south salmon]

yeah

[dapper root]

Like maybe they’re pedagogically outclassed, or a bit too hard for most to tackle on their own since normally it’s used in a class

But nonetheless they persist as being the classics because they’re already the classics

[south salmon]

the only way to outclass the classics is to gatekeep 😎

[dapper root]

Fwiw the list there is comprised mostly of well respected books

It certainly isn’t a bad list

[south salmon]

yes

[dapper root]

I say “mostly” just because I don’t recognize some of them hahaha

Not because some of them are bad

[south salmon]

It’s a good list, I’d just be wary of books like rudin to learn intro real analysis

bc they might be a little too dense or weird to read

[hollow shore]

Does the blue Rudin have typos?

[south salmon]

yeah probably

[hollow shore]

Lmao

I know

Thanks I will rectify it

[abstract walrus]

is the historical introduction in small just supposed to give an idea of what's to come? cuz I'm reading it and I'm kinda just like

[grand thistle]

for algebra 1 and 2?

just use khan academy

honestly algebra 1 and 2 textbooks are probably not very different to each other

there is only with so much variation you can teach factoring things like that

why use money on that when khan academy or some other online resources exist

imo i would probably only use textbooks starting from precalculus and up

[normal sandal]

Any recs for expository books about the history of mathematics over the years?

[manic cape]

Any recommendations for lie algebras? im looking for general stuff like classifications, relationships with lie groups, representations, root systems, isomorphisms theorems, etc

[prime cedar]

I was looking out for new books. I DEFINITELY AGREE with you

[prime cedar]

The ones made privately in china and korea helped me

[karmic thorn]

Mathematics and its History, Stillwell

[prime cedar]

But the common ones are a big waste of time really

[normal sandal]

Thank you

[sage python]

"Lie Groups and Lie Algebras" by Kirillov is good

[gray gazelle]

It seems they are used as an entertainment. Even handouts are better than books

[crisp radish]

Which book do u recommend for self learning calculus? Also which topics do u need to perfect to start?

[gray gazelle]

Courant Introduction to calculus and analysis. The first chapter on prerequisites and functions.

[marble solar]

Are you a fan of Stillwell's Naive Lie Theory?

I know it's kind basic, but I was a big fan

[prime cedar]

Yes. The books are so tiny to the point its impossible to make memos. The questions aren't organized or assembled. The reading tires you out even before the math part. No proper solution steps are given

[marble solar]

I like Spivak's Calculus if you're serious about math, if you're more interested in like Physics, Chem, Engineering Thomas' University Calculus would be great

[slender dragon]

I'm looking for a book or an online resource where they prove the method of solving second order (linear) difference equation

[grand thistle]

i wouldn't start with spivak, although that might just be me since proofs and rigor are difficult for me

[gray gazelle]

best book for galois theory in da modern times?

[hollow peak]

some people like the coverage in algebra by lang

if you're looking for a soft intro, rotman has one

I like Cox

[gray gazelle]

ive got lang, havent cracked it open awhile so okidokee

[sage python]

Don't know it

Yeah looking at it now it seems like the Guillemin Pollack of Lie theory haha

Assuming it's well written and all

[livid ermine]

I think bhattacharya has a good section on galois theory

[gray gazelle]

thanks!

[shy compass]

[marble solar]

It is pretty bare bones, but it is well written

Not super advanced, but I think it's good

[desert grail]

Hi guys, you guys have some books recommendations for algebra 1 and 2 / basic geometry just to revise? I have tryed Khan academy (it's pretty good) but it does't work for me because i think it's not my learn style... i learn more reading books... so can someone help me? even with some tips on how to proceed from here.

[fervent lava]

Hmm maybe serge lang basic mathematics since you mentioned the basic geometry part.

Covers algebra 1, 2, trig, geometry in 500 pages or so. I like it, someone at my part time job was looking to get started at math after my daily rants and I bought the book and gave it to him.

Since you said revise, it perfect for you. It can also be an introduction to reading/writing proofs.

[desert grail]

Wow, I don't know how to thank you, I'll definitely check it out seems really good.

[jaunty acorn]

i am looking for a text book like spivak for multi variable calculus but not cal on manifolds that is not for me

[solemn violet]

i'm also looking for a textbook for multi variable calculus and advanced math. any recommendations?

[grand thistle]

maybe try apostol’s calculus volume 2? i have his volume 1 and it’s really good and he teaches rigorously like spivak

but it also doubles as a linear algebra book

you can skip the chapters with linear algebra ig

[modern stone]

Is Geometry I by Marcel Berger a good book to learn Euclidean Geometry from?

[sage python]

@jaunty acorn and @solemn violet "Multivariable Mathematics" by Shifrin I've heard is pretty good

[jaunty acorn]

@sage python @solemn violet thanks i will look onto it 👍❤️

[ionic wren]

Hey moonbears

Stillwell is a patient of my dad’s (he’s a dentist), I have a bunch of his books that he’s signed

Not really relavent but I’m still really chuffed

[gusty smelt]

Lol thats funny

V nice

[ionic wren]

Btw I don’t mean the books he’s written I mean literally maths books he owned

It feels like a celebrity’s autograph but obviously it isn’t

[karmic thorn]

[gusty smelt]

Oh u read bumps Lie group?

Based

[ionic wren]

No lmao

He gave me a bunch of books

[gusty smelt]

Smh

[ionic wren]

I’ll read it eventually

[gray gazelle]

i havent read it yet but it looks pretty good

[vestal ibex]

any recs for quantum information theory books?

[quartz verge]

Need book reccs for Number Theory and Abstract Algebra

[gray gazelle]

it's actually a pretty good book but it's huge tho like 950 pages or something

[quartz verge]

noted

Thanks! 😄

[marble solar]

That's pretty neato

[hollow drum]

Can anybody recommend a textbook that masquerades as a college algebra textbook but is really a red pill into math?

I know someone who is taking a course and I'd like to give them a book that would be relevant to them but might inspire an interest in math

[manic cape]

huh lol

[hollow drum]

Sorry, I'm really just asking for a college algebra text recommendations and/or books that are good for supplemental reading

[remote ginkgo]

Serge Lang - Basic Mathematics

[hollow drum]

Thank you!

[marble solar]

A course in Arithmetic by Serre

[hollow drum]

This is just funny because it would leave them confused but you think it would be relevant because the title. This must be a common meme amongst number theorists

[marble solar]

The reviews are golden

[hollow shore]

Sheldon Axler's Precalculus

[gray gazelle]

hello all

can anyone please suggest me book for basic to advance trigonometry

[lime sapphire]

tbh when it comes to subjects you're learning at a high school level

i just recommend openstax books

"algebra and trigonometry 2e" on openstax should have you covered

[modern stone]

What would you recommend for learning Euclidean Geometry?

[rancid junco]

Hiya! What would ya'll recommend for an "open-source" graduate-level mathematical statistics textbook?

I'm thinking of something like Casella and Berger or Hogg, McKean, and Craig but "open-source" in a similar sense to the books here:

https://aimath.org/textbooks/

[marble solar]

Euclid's Geometry. Green Lion publisher has a beautiful copy

If you like historical comments, Heath's dover is good

But there are a lot of historical comments

[restive falcon]

any good DE textbooks

[marble solar]

At what level?

[empty mortar]

same ^ looking for a diff eq text book assuming knowledge of basic real/complex analysis

[smoky zephyr]

woah neko

[gray gazelle]

odes or pdes?

[empty mortar]

odes

[gray gazelle]

then I recommend ODEs Basics and Beyond by Cain/Schaeffer

[empty mortar]

I haven't taken a course in differential equations yet if that makes a difference

alright

[gray gazelle]

Assumes just lin alg, analysis and point set topo

[empty mortar]

yea that's fine

[marble solar]

I'm a fan of Boyce & DiPrima at the intro level

[restive falcon]

yeah sorry

should have mentioned like minimal prereqs

[marble solar]

Boyce & DiPrima is intro

[restive falcon]

thx

[gray gazelle]

I want to read Edmund Landau's Foundations of Analysis, and I have gotten a PDF from uhh questionable sources as I was unable to find a paperback version in my region, but the text seems very poorly formatted, for example, in the attached image, it is slanted.
This also makes it hard to read, and I haven't made much progress due to this?

Is there a newer version that is better formatted and easier to read? Or perhaps is the PDF I found just poorly formatted, and the paperback version isn't?

I genuinely am unable to find the paperback version anywhere for a reasonable price, else I would have already bought it, but if someone confirms that the paperback version is better formatted and doesn't have such warped text, I will try to get it imported.

[primal summit]

This looks like someone scanned a physical copu.of the book

The warping is an artifact of that

[gray gazelle]

That's what I was thinking too, but since the book is so old, I was wondering whether the physical copy also has this defect, due to the original being scanned the same way for subsequent copies.

All of the PDFs I found seemed to have the same defect, which is why I decided to ask

[marble solar]

It'll be hard to find new editions of Landau. What you will be able to find is a new edition of Whitaker and Watson Analysis

Which is a bit more comprehensive

[gray gazelle]

Oh okay, does it cover most of the same topics?

And what are the names of the books?

Is it https://en.wikipedia.org/wiki/A_Course_of_Modern_Analysis ?

[stray veldt]

i don't think the physical copy has this warping issue, the printing is not created from a scan

its simply that the book was scanned

(note there is no reason to read this book other than historical, if you want to actually learn analysis, there are many better books)

(this is also why i doubt there is a better scan, not many people will be interested)

[gray gazelle]

Oh, can you recommend some books to me then?
For context: I am a highschool student that has not paid much attention to math, mainly due to the amount of abstraction in conventional highschool textbooks, and have instead focused on other areas of studies.
I would like to understand the proof of many of the basic mathematical operators, and what numbers truly are.
I only found Edmund Landau's book due to a question about it being asked on Stackexchange, so I assumed that it was suitable for this purpose.

I would preferably like a book that does not depend on many mathematical concepts other than axioms, as I would like as little ambiguity as possible.

[marble solar]

I think Spivak's Calculus is your best bet

Actually

[gray gazelle]

Will look at it, thanks for the suggestion!

[foggy relic]

Do you need to know analysis to read Ireland Rosen

[gray gazelle]

standard calculus text courant. Higher algebra by Barnard and Child or Higher Algebra by hall and knight

[stray veldt]

not in the beginning (maybe rudimentary calculus), later on you will need some complex analysis

[iron granite]

Is Rudins Ch 2 supposed to be warp my mind or is that my fault?

[frosty girder]

What is it about?

[iron granite]

'Basic' Topology

[frosty girder]

Aah topology

That can be very weird yeah

[iron granite]

I think Rudin is to blame.

I'll try reading my other analysis book.

[frosty girder]

What in that chaoter is confusing u?

[karmic thorn]

Any recommendations for an introduction to measure-theoretic probability theory? I know some real analysis, nothing much about measure theory than some basic terms, and little about probability distributions, etc. that one might see in a first course.

So I'd like a comprehensive text that takes the pain to cover the basics and can do some handholding on technical results

[glad prairie]

Rudins chapter 2 is good but super hard and abstract. Working with another book is a good idea. Once you really solifidy your understanding of metric spaces pretty much everything in Rudin ch 2 becomes easier to understand besides the compactness and connectedness stuff, which stay confusing for a little while longer.

[karmic thorn]

Re: looks like Bremaud's Probability Theory and Stochastic Processes hits home, at least going by the preface and ToC.

[empty mortar]

still don't get the point of connectedness

[gray gazelle]

play connect 4 it helped me

[quasi oxide]

hello guys i have a general book related question

have you guys tried printing a book scan?

when I do, my printer prints the whole background as well

I'm trying to get it to print only the text

[gray gazelle]

some books to get started with calculus and linear algebra?

[main frost]

is there a good book online that has 11th grade lessons ? like barycenter and functions ?

[foggy relic]

around which chapter is analysis assumed

[stray veldt]

you need some in chapter 11 and definitely in chapter 16

[storm cipher]

Hello any one knows a book to study topology and euclidian spaces (I need to learn these to take general relativity courses as well as quantum physic)

[foggy relic]

oh, so for the first 10 chaps ill be fine?

[stray veldt]

you won't really need analysis at least

[modern stone]

From what I’ve read on this chat it seems there are a lot of good calculus books. Could someone tell me concisely what are the advantages/disadvantages/general characteristics of the four best ones as I had a hard time deciding which one to choose?

[gray gazelle]

kind of random but anyone know of any books that combines biology and math?

[short compass]

hello, does someone know a website or a book that list the name of the "chapters" that exist in mathematics?

[stray veldt]

chapters?

[short compass]

yeah... i didn't found a better word to describe what i am searching for even thought its not exactly that, what i meant is the name of the notions (for example, i consider "derivation" as a "chapter")

[slim peak]

Subfields of Mathematics I guess

https://zbmath.org/static/msc2020.pdf

[short compass]

thank you

[marble solar]

Durett is good

[karmic thorn]

I'll look into it, thanks!

[gray gazelle]

Does anyone know a good book for getting into mathematical logic?

[odd spade]

like, introductory from the beginning?

[gray gazelle]

yeye

[supple lynx]

any great free resources for Linear Algebra textbooks ??(websites)

Im looking for this book particularlyTitle: Elementary Linear Algebra, Applications Version
Author: Anton, Howard & Torres

[gray gazelle]

Its in cl1lib

[supple lynx]

thank @gray gazelle

[gray gazelle]

np

[brittle breach]

https://www.math.ubc.ca/~carrell/NB.pdf

I uses that and liked it

It has a nice application section as well

[drifting nymph]

https://youtu.be/7fZ-R7npXqw
Does anyone have recommendations for a book with problems like this one?
The entire channel is a gold mine and id like to have something like it in a book

German and English would both work

this one was rather easy tho so more difficult stuff would be appreciated aswell

[jaunty hill]

Any book or books that covers Congruence, Sets, Number sequences and Induction, combinatorics and differential equations?

[sage kelp]

Check out A Probability Path by Resnick. I haven't read it, just the preface, but it looks good. I actually want to read it some time this year. Also there is Measures, Integrals, and Martingales by Schilling

[drifting nymph]

thx guys

[gray gazelle]

Hi I'm a total noob in maths, I graduated from high school so that's the level of maths I know but I unlearned most of it already. Is there a good book that really teaches all the relevant math up to the level of everything taught in high school?

[quick hornet]

ALL the relevant math is a bit of a tough ask — after a certain point, a book has too much content to be really pedagogically sound

you could look at basically any high school math textbook series

theyre kind of all the same

there are some standout books like the AoPS series (harder problems, more problem-solving oriented in general, an eye towards competition math though certainly not competition prep) or Lang's Basic Mathematics (all of pre-uni math but with a lot more detail and rigour)

lang's basic mathematics is probably the most literal answer to your question but I don't think it's a good one

it's a hard book to learn out of if you're not used to the style

[gray gazelle]

Ok thank you I will check those out.

[soft drift]

anyone know of something like a mathematics fundamentals/foundations/philosophy history-themed book?

[hearty steppe]

did some people on here comment on the algebraic topology section in Munkres not being very good?

i guess thats a heads up for me then

[hollow shore]

I would also suggest you to look at Axler's Precalculus. Problems section is actually good. I did both Lang and Axler and from my experience of doing both textbooks I would say Axler is a better choice in terms of variety of problems and exposition.
Although the initial chapters of Lang is somewhat illuminating and I would suggest you to read them.

[marble solar]

I disagree, I think it's pretty good

It's much more rigorous than something like hatcher who just wants you to see it and sweeps detail under "geometric intuition"

[gray gazelle]

it's good when you consider the competition

[marble solar]

But it develops things very slowly as a consequence

For Alg. Top?

||Cries in Spanier||

[karmic thorn]

Thanks, will look into it!

[rancid isle]

yo, i need to git gud at group theory in like a week, anyone knows what book should i get? xd

[wooden cedar]

Joseph Gallian's Contemporary Abstract Algebra is a pretty nice intro into group theory and is relatively grounded. Lots of editions too so you can pick up an old copy for pretty cheap

[rose comet]

Any good book for discrete mathematics? Don't say Rosen

[fluid bay]

Chapter 1 of serge lang would be a quick introduction to group theory.

[rancid isle]

serge lang?

[fluid bay]

“Algebra” by serge lang

“Basic Algebra 1” by Jacobson is also pretty good I think.

[rancid isle]

i'll try that quicker route with serge lang, thx 🙂

[fluid bay]

Np. If lang isn’t making any sense, then try jacobson

[gray gazelle]

Thank you!

[zinc lichen]

i want to start int calc but not sure how to check my understanding of differentiation

any good web/book recommendations?

[analog pollen]

exercises

[gray gazelle]

any good books/resources to learn complex analysis (complex variables)? Not looking for something too rigorous and proof-heavy, but rather some sort of reference that's particularly good at giving intuition and explaining and talking about common mistakes and stuff

[analog pollen]

needham

visual complex analysis

[hollow drum]

Does anybody know of a resource to learn about subspace arrangements?

[hollow shore]

https://cdn.discordapp.com/attachments/837730725855756319/873426298041688084/CALCULUS_pdf.pdf

[hearty steppe]

ill check it out but I also plan on checking out hatcher

still at beginning tho

[marble solar]

In my MS program, they spend the first 5 weeks on Munkres

then switch to hatcher

I think too many grad programs jump into Hatcher or Spanier when students aren't ready or don't have a complete grasp

[hearty steppe]

haven't heard of Spanier

[hearty steppe]

if you want I can add you to the new study group I made where we are working thru Munkres and Casella and Berger

[marble solar]

I'd like to learn alg. top. properly one day

[hearty steppe]

how does one learn it properly? xD

i feel like im improvising but thats me

[marble solar]

Well just black boxing a lot of homotopy/isotopy results and then going in full speed with knot theory

Isn't learning alg. top. properly, it's just kinda citing the tools that you use

[hearty steppe]

i feel like these areas of mathematics morph around perspective a lot

wdym just kinda citing the tools you use? Then you would suggest an analytic text?

[marble solar]

Oh I mean when I did my venture into LDT

We literally just black boxed most of anything we needed from hatcher

[hearty steppe]

i mean at some point you gotta have a black box

this level of math seems like it gets pretty abstract quickly

[marble solar]

Yeah, I agree with that

But I'd like to look inside for basic alg. topology

It's very useful to think geometrically in pdes

[hearty steppe]

so i need to read an analytical geometry book at some point

[marble solar]

I dunno

[hearty steppe]

what are your thoughts on that area

[marble solar]

you mean like the analytical geometry you use to do calculus?

I'm not sure what you mean by analytical geometry

[hearty steppe]

nevermind

overthinking it probably

[marble solar]

I kinda wanna do analysis/PDEs that's largely geometrically motivated

So I'd like to learn how topologists and geometers think to see if that help provides insight into PDE type things

[main void]

do you guys consider lee's introduction to smooth manifolds a good introduction book to smooth manifolds?

it seems to be the one which is recommended a lot but there are some nice opinions on here...

[hearty steppe]

It’s very easy to spend a lot of time doing analysis stuff. I hope I’ll be allowed more of that time in the future lol

I’m just prioritizing what standard texts will be most useful for me right now that I know I can sort of work through with everything else on my plate

@marble solar

[brittle breach]

Loring Tu introduction to manifolds is good

i find it easier

[main void]

ok ill check it out, thanks!

[fathom elk]

For books, is Propositional Calculus -> Axiomatic Set Theory -> Group Theory -> Metric and Topological Spaces -> Complex Analysis a good course?

I ended up starting at prop calc because Axiomatic Set Theory assumed I understood proofs.

Axiomatic Set Theory, Group Theory, and Metric and Topological Spaces are to prepare me for Complex Analysis

[solemn rover]

i love spanier

i worked like a year and a half through this, it was love hate

advice is to skip over a lot of the stuff in chapters 4, 5, 6, like find a teacher or knowledgeable student who will go through the chapters with you and help you figure out what you can skip

a lot of it is only of technical interest, like good for a reference manual but not for a first intro

[cursive orbit]

Why would you need axiomatic set theory for complex analysis

[sudden kindle]

Opinion on this book?

@sage python

[fathom elk]

Set theory is a prereq according to the book

[cursive orbit]

Yes, but you don't really need to learn set theory independently

[sage python]

PTY: I heard it's pretty good

[cursive orbit]

Most introductory topology or algebra or real anal books should have a section on it that's enough

[fathom elk]

Either way, being able to follow a graduate level set theory book sounds like fun to me

[cursive orbit]

Fun...

[fathom elk]

In a way. Some of the exercises are monotonous, but some results really move me.

The problem I have is that the author takes huge steps in his proofs and I can't really follow all of it.

[cursive orbit]

To be expected if you're reading a graduate level book

[fathom elk]

The one that really bothers me is that he takes the definition of equality as the proof for the symbols defined to be equality.

[cursive orbit]

:dan:

What is that even supposed to mean

[fathom elk]

like a=b is defined to mean some stuff and to prove a=a, he uses the definition of equality, but replaces all occurrences of b with a, which is fine by me, but the axioms and stuff he introduces earlier do not say anything about being able to substitute stuff like that.

[cursive orbit]

:dan:

[fathom elk]

and for a=b->b=a, he just plugs in the stuff into the definition and says that is proof

My guess is the sentence "We will assume, without proof, those results from logic that we need." So I am hoping that Propositional and Predicate Calculus will clear up some of the stuff in the book.

[cursive orbit]

If you want to do foundations-first, go for it. Probably not the best use of your time if your end goal is to learn complex analysis though

[fathom elk]

And chapter 2 of Propositional and Predicate Calculus is so tedious, but I can do induction pretty good by now. The good stuff isn't till chapter 3. My goal is to solve a millennium problem. Complex analysis is a step along the way.

I like math a lot too, so that helps. I did 4 chapters of chaos theory, and really liked it. I am thinking of going to school for math.

[gray gazelle]

Honestly is there a field of math that doesnt require set theory as a prerequisite

[cursive orbit]

Set theory

[fathom elk]

I know set theory can't cover a lot of problems

[cursive orbit]

The thing is, you don't need to learn graduate level set theory to learn complex analysis

[gray gazelle]

What do you need graduate level set theory for

[fathom elk]

I know, it literally says in the prereq chapter the results from set theory that are needed.

Probably nothing

[cursive orbit]

And it definitely doesn't do you any good to jump to a graduate level text

[gray gazelle]

Is there a huge web of math topics with prereqs that i can find

[fathom elk]

I've done junior level college math before

I've covered set theory in school

I think the graduate level text will be ok

[fathom elk]

This would be cool

[gray gazelle]

ive always wanted to make a project that would show you literally every math topic with decent textbooks that show the prereqs for each topic

[fathom elk]

I saw some stuff on SE before

[gray gazelle]

SE?

[fathom elk]

https://math.stackexchange.com/

[gray gazelle]

Oh

https://www.cantorsparadise.com/the-web-of-mathematics-a-data-visualisation-baa5d478d908#ca0f

I found this

But its not enough for me

[cursive orbit]

More of a novelty than anything else

[marble solar]

spivak

[slim peak]

A very nice future book was released today on Arxiv.

It's about Applied Functional Analysis for PDEs, hence, PDE's from the Functional Analysis PoV. Many techniques introduced here can be generalized to more general functions spaces than L²-based Sobolev spaces. I just take a quick look on it but it seems to be pretty solid.

https://arxiv.org/pdf/2112.11166.pdf

[spare sluice]

does anyone have a good book for operator calculus?

[slim peak]

There is different Fucntional Calculus for operators depending on various context, this book prove that they all agree when they meet all those context. The Hilbertian Calculus of Operator, involving spectral measure is not deeply explored.

[slim peak]

The Hilbertian Functional Calculus through spectral measure can be found in

Chapter 7 - 8.

[spare sluice]

Oooh, thanks much!

I'll check them both out

[near spindle]

guys, i'm starting my journey in calculus but i don't know which one of these authors to choose

James Stewart
Michael Spivak
Tom Apostol```

who's the best for beginners?

some one reply quick pls

[slim peak]

You should check the book of Cheverry and Raymond first, since Haase's require to be comfortable with general Operator Theory

[near spindle]

uh

[slim peak]

I cannot answer to you Azorfus, since I don't know any of those well known books.

[spare sluice]

I think stewart is easiest

[near spindle]

well then do you know any other good beginner books?

[near spindle]

i see

is there something better than stewart?

[spare sluice]

I don't know, i started with spivak straight before reading the other two

But that's because my course was a bit advanced

[near spindle]

i'm in high school

[spare sluice]

Got it!

[hollow shore]

I am doing Apostol rn. It's okay for a first course.

[near spindle]

no calculus in my current grade

so very beginner

[spare sluice]

I suggest spivak then

[near spindle]

i see

[spare sluice]

wait no

NO

[near spindle]

?

[spare sluice]

I meant stewart

[near spindle]

lol ok

[spare sluice]

It's huge but it's easiest

[near spindle]

the early transcendental one?

[hollow shore]

Find a course page which follows Stewart. Doing all problems is inefficient.

[near spindle]

i just need the book for theory

[hollow shore]

You need to do problems too

[near spindle]

yeah i have other books but

should i just buy what is recommended for my course

IA Maron

[spare sluice]

I've never read Maron's book so

[near spindle]

i see

they recommend it for JEE

so ig i'll get that

[hollow shore]

That's a outdated and old book

[spare sluice]

I read spivak first, and then stewart for some reason

[near spindle]

since i'm from India

[hollow shore]

And Maron is sort of intro analysis

[near spindle]

and writing JEE

ppl are recommending some Indian author books

maybe i shouldn't start calculus

such confusion

https://tenor.com/view/burn-in-hell-elmo-fire-flame-gif-8764555

what about the book by silvanus p thompson

i'll just get a copy of stewart then

its so big

[spare sluice]

It's huge, but it covers you all the way to multivariable calculus

[near spindle]

i see

so if i get one

i can just have it with me till uni

i have to print it out, here it costs 100$ idk why

ok thanks

[lime sapphire]

just saying but stewart is nowhere near as hard as JEE questions get

[near spindle]

I know

But it's good for the theory right

[lime sapphire]

its very computational

[near spindle]

Not good for JEE?

[lime sapphire]

if you're looking for theory then apostol or spivak

[near spindle]

Oh no

I got it

[lime sapphire]

got what

[near spindle]

The book

[lime sapphire]

stewart?

[near spindle]

Yes

I was reading other others too but

It was the easiest to read

[spare sluice]

tbh spivak's questions tend to not be the same type as the JEE

[near spindle]

Am I doomed

[spare sluice]

it's great as a theory book though, i'll agree

[lime sapphire]

if you're looking to learn calculus for JEE, i'd just get books specially made for the JEE

[near spindle]

I'm learning to learn calculus

I'm starting JEE specific preparation next year

From 11th grade

[lime sapphire]

are you going to get coaching?

[near spindle]

Ofcourse

I'll just buy cengage then

G tewani

[lime sapphire]

if you are then you should be fine with stewart since you've already bought it

[near spindle]

I didn't

I'm gonna cancel

[lime sapphire]

yea cengage i hear is recommended a lot for JEE

[near spindle]

Nice

Nice nice

[grand thistle]

ive used stewart in the past

using apostol right now

for just learning calculus for JEE or some other test, just go with stewart

has so many questions and you can find the answers online

i have a solution manual, dm me if you need it

from what i've heard, JEE requires quick computations and thinking on the spot and completely mastering solving problems

apostol is proof based, basically like in between an introductory analysis book and a normal calculus book

the book's exercises require you to prove things, which im pretty sure is not necessary for the JEE

[hollow shore]

But it doesn't hurt to know

[grand thistle]

also apostol takes a different approach to calculus

you start with integrals, then move to limits and derivatives

[hollow shore]

And honestly I don't think proof based courses are necessary impenetrable

If you have a certain amount of math maturity you can certainly tackle it

[grand thistle]

they're not, i started apostol about a few weeks ago, a first was completely lost, then I read "How to prove it" by velleman

it helped a lot

for context, im was debating teh same thing as azorfus like 2 months ago, i had gone through a bit of stewart's calculus, but it was really boring for me since i didn't like how dry and computationally based it was

switching to apostol was like one of the biggest bursts of improvement in mathematical maturity ive had

like now a lot of the problems in stewart seem kinda shallow and easy, but i still think its a really good resource for a first exposure to calculus

also, stewart contains calculus 1-3 and apostol contains calculus 1-2 and an introduction to linear algebra

although it has like some preview of calc 3

like it has one chapter on partial derivatives

if i were you, i would probably start with stewart then maybe move onto spivak or apostol after learning the general ideas and formulas

[near spindle]

uhh, the JEE questions are much harder

so i just went with a book that has JEE level stuff

meant for JEE

covers almost everything

i like apostol, i may get it in the future

i just generally like his books

like his mathematical analysis one

[karmic thorn]

Sure, hit me up in DM.

[finite saffron]

im planning to retake calculus. which textbooks should i use? (all calc 1-3)

[empty mortar]

Stewart if you wanna relearn the calculations and stuff

[sudden kayak]

Hello, has anyone got a pdf copy of TC7?

[gray gazelle]

I have been switching between Apostol's Volume 2/Axler's LADR... I'm thinking of trying Hoffman and Kunze to see which of the three I like better for me.. any opinions on that book and how it compares to the previously mentioned two books?

[fervent lava]

I started with axler chapter 1, then switch to LADW(I am enjoying it) after receiving comments about how axler treats certain topics in the book. Before axler when I was looking for LA book, I stumbled across Hoffman and Kunze book, read a little bit of it but did not like it too much. Don't know much about Apostol's book.

[gray gazelle]

Okay thanks

[fervent lava]

LADW(linear algebra done wrong), Hoffman and Kunze book, and Friedberg's book are ones that people here usually recommended.

[gray gazelle]

What didn't you like about H&K if you recall?

[fervent lava]

It probably just me, but I dislike the way it looks.

But that was a while ago tho, so my opinion about it probably changed

[teal crater]

Could anyone recommend some good books on interpolation? Ideally it should cover different bases (e.g. monomial, Bernstein, Lagrange), their advantages, constructions, possibly numerics and relationship to quadrature rules. Also different generalizations of those to higher dimensions, e.g. thin plate splines, radial basis functions, etc.

[dawn widget]

Hello!

I need a book

On ODEs

The part I'd like to master

Are systems of ODEs

I want to understand Wronskians and everything related to them and systems

[gray gazelle]

my calc professor has a youtube playlist for ODE's if that'll help you

https://youtube.com/playlist?list=PLDfbHQkTEyeBXmqiSIFC9HBBXx5zHfBXz

https://youtube.com/playlist?list=PLDfbHQkTEyeAh7Lgs9T1ZLZg5r5tSV2kj

[empty mortar]

youtube playlists for math

textbooks superior

[gray gazelle]

i definitely have a bias towards him because he's the sole reason why i minored in math

diary pf a wimpy kid is cool ig

[marble solar]

They aren't contradictory

A youtube playlist can help you clarify points in a way that a textbook can't

[cursive orbit]

Audio book for math

[marble solar]

might be good for longer drives

[gray gazelle]

The Promised Neverland is a good book Ngl

[cursive orbit]

until "this is left as an exercise to the reader" with a 30 minute pause

[grand thistle]

what level would you say is LADW?

as in like is it good for a first time exposure to LA

[marble solar]

not really

[sage python]

It is don't listen to Moonbears on this point

(LADW not LADR, though LADR also would be fine for a first exposure if not for its treatment of determinants and char poly)

[marble solar]

It's too abstract for most beginning math students

Needs more computational examples

[sage python]

Talking about R or W?

[marble solar]

Both

[sage python]

Also I think we can stand to expect more out of beginning math students tbh

[marble solar]

If they're like me or you, sure

I'd say it's a good honors introduction

If you're dedicated

[sage python]

And if they're not the ability to pull it off will be beaten into them

[marble solar]

But if you're going to be meh about it, I'm a big fan of schaum's outline to linear algebra

Because of the examples

[sage python]

I think LADW is good on examples tbh, like chapter 2 is very computational in nature

[marble solar]

I think there needs to be a lot throughout the entire book

I think LADW is a great text

but I'd at least supplement it with something else that gives you a better feel for computational linear algebra

[sage python]

I guess I don't put a ton ton of weight into like

Doing a thousand hand computations

Get the picture learn to code it move on

[marble solar]

For most math majors it's a difficult jump

From computational to abstraction and having some support structure there can help most students

[sage python]

I mean it's difficult but not impossible. I guess yeah I'm just willing to be like

Yeah now time rise up to the occasion. They'll have to eventually

[marble solar]

I get that, I just modify my recommendations on what's best for most students

I'd be totally ok with someone reading LADR or LADW, as a first text as long as they really get enough examples to be comfortable with row reduction, matrix multiplication, etc.

[grand thistle]

hmm i see

i’ll probably use LADW once i finish apostol

it gives an introduction to LA

so that should be good

and it’s also a kinda rigorous calc book like spivak, so i think transitioning into proofs won’t be the worst thing ever

[eager sandal]

hey frends
if I covered something already but a while ago, but I want to just watch some lectures which covers the topic again, where should I find them?
I'm thinking of like 10 hours long total for going through stuff

[finite saffron]

does it cover, like, calc 2 and 3? (sry for late reply)

[foggy relic]

Thoughts on Chapter 0?

[fervent lava]

Yes.

[foggy relic]

I just ordered it on amazon; It's on sale for only $17.

[dapper root]

Algebra chapter 0?

By Aluffi?

[brittle breach]

hate it, takes too long to say anything , make things seem more difficult than it is

[foggy relic]

Yes