book-recommendations

[tender river]

nahh this ain't it

[gray jungle]

exactly , which is why we are saying people should avoid using it

[tulip hearth]

Ok bro. I'll keep that in mind, 'is there any I should use'?

[gray jungle]

[tender river]

also toma, if just some random person wrote the book then i don't know if it is going to be easy to find its pdf

[tawny copper]

ah wait, im beign autistic

[gray gazelle]

Books these days are crazy expensive on amazon

if only knowledge were free

[tulip hearth]

I lost interest to study looking at it price...
I mean... What do u think I wanna buy the book for? I could have just bought vid games if I had that kind of money.

[urban pecan]

What the textbooks used for this playlist
https://www.youtube.com/playlist?list=PL4C9296DF81B9EF13

" any book have exercises and practice what I learned "

for more info about my request and what I'm looking for
#1120239861924892763 message

[tulip hearth]

I totally didn't use it. That's why I couldn't find it.

Can u guys recommend any books that has short tips and tricks mentioned in it to solve questions faster?
Similar to some mentioning "heavy side coverup method" with integration by parts topic.

or maybe a bunch of books that would contain short tricks from different chapters—

[lime sapphire]

and make sure not to use anna’s archive either

[tulip hearth]

I'll keep that in mind.

[flat jackal]

Is there any books of laplace transforms

I’ve looked through a few complex analysis books and it’s not listed as a topic

Or any good resources for learning it? Because I’m only using madasmaths rn but I need more questions

[orchid mortar]

You can always freely use the PDFs of the authors who publicly publish it. For example, a lot of the ML publishers.

[tulip hearth]

But pple who include easier and faster methods are rare ._.

[orchid mortar]

It's better if you ask for a specific subject

[tulip hearth]

hmm there any book on short tricks for indefinite/definite integration?

[tawny copper]

Im also interested in that actually. But the best is to try to solve the integrals on your own first, that's how you learn. Of course, you wont be able to solve all, so then you look up some solution and learn a new "trick".

but I cannot give you recommendations. I also need to work on integration. But maybe you can look up Michael Penn's channel? He has many vids on cool integrals

[tulip hearth]

I'll try that thank you.

[sudden kindle]

Can someone recomend a resource that has a SIMPLE and INTUITIVE proof of the UNIFORMIZATION THEOREM

[wispy bison]

Never heard of it before, now I know where it is so I can avoid it

[mossy comet]

In university, I studied probability and statistics, but I found myself relying heavily on memorization rather than truly understanding the concepts. Now, as my interest lies in the field of AI, I'm seeking a comprehensive probability book that provides clear explanations to enhance my understanding. Also thank you for the suggestion!

alright tyy

[tender river]

i think megumi was trolling with that answer

[mossy comet]

just searched it up and its an actual book

so i have no clue

[lime sapphire]

its a book with quite a prerequisite

[quartz verge]

SAME!

except id buy both

good math books appeal to me sexually

cant live without them

[ocean mulch]

Lol, I told you I didn't know how accessible it was

No but srsly, it's not a book for UG. You should look for something else

[storm sage]

Hi I was offered principle of mathematics by bertrand russell (not by himself sadly) and wondered whether it is worth reading and if the book is beneficial to the modern mathematician

[quartz verge]

no its not

give it to me

you can take my manga collection instead

[storm sage]

I don’t like anime sorry

[quartz verge]

theres nothing to be sorry

[gray gazelle]

that's injustice why denounce people like that ?

[fast gull]

do people exist that read textbooks in entirety/front to back?

[lime vessel]

Depends on textbook

[quartz verge]

obv

[sudden granite]

should i read the idiot by dostoevsky first or anna karenina

[burnt geyser]

@sudden granite the idiot

[gray gazelle]

The Idiot

[scarlet steeple]

use archive.org

[tulip hearth]

Anyone knows somewhere I can find VKR sir's maths books for free?

[unreal token]

would you guys say that stewarts is the best book for someone self-studying engineering math

thats what my courses recommends but i thought maybe theres better ones out there

[thorn cloak]

i dont envision you need very rigorous books for engineering so stewarts should be solid. Its a good/standard book in general for calculus

[novel sluice]

Wait, who's that

[pseudo oyster]

Any reccomendations for a precalculus book to selfstudy or an online course?

[coral prawn]

Khan academy. Or do you prefer books?

[pseudo oyster]

probably want both im asking for a friend

[coral prawn]

Ok then

for books there's stewart's Precalculus

[pseudo oyster]

can you give an amazon link or something of the sort?

[coral prawn]

https://www.amazon.com/Precalculus-Mathematics-Calculus-Standalone-Book/dp/1305071751

[pseudo oyster]

thanks

[pure solstice]

Has this ever even happened?

[gray gazelle]

does anyone knows a good book on linear applications with proof for theorems and propositions

[thorn cloak]

like linear algebra?

[prisma cliff]

more like linear alGAYbra

[thorn cloak]

...

anyways Lin alg done right by axler i heard recommended a lot to the "advanced" student. linear algebra by strang is prob better for a first introduction

[quartz verge]

Axler is good as a first introduction too

[prisma cliff]

why are u doing lin manuel miranda algebra

[lofty agate]

Idk I read soviet books which are very interesting to read, I don't think there's an english translation tho

[gray gazelle]

yea

[thorn cloak]

i believe it. I personally havent used it so idk, though i wish my class did

[subtle mango]

please please please do not use LADR for a first course

he saves determinants for the end and imo it does more harm than good

theres a good list of lin alg textbooks in #books-old

#book-recommendations message

also see here

[quartz verge]

i like it from that perspective but yeah thats a good heads up

[prisma cliff]

Personally this is my favourite piece of literature. I found it to be very informative - would highly recommend! https://www.wattpad.com/story/230339182-baby-daddy-bakugo-x-reader

[quartz verge]

sus

[tender river]

@prisma cliff last warning, there's better servers to troll in

[quartz verge]

yeah troll in #chill

you need to act productive in #book-recommendations

[tender river]

no, #chill ins't the place to troll, it is the place to chill

[quartz verge]

its the same thing

[thorn cloak]

really? that is quite interesting to say the least

[quartz verge]

yeah he mentions why he went down that route and its very interesting

[thorn cloak]

im not a very advanced algebra student but like i found determinants to be pretty intutive. I dont really get why people dislike it so much

[thorn cloak]

oh, i guess its worth reading why then

[quartz verge]

absolutely

[subtle mango]

iirc his whole claim is “determinants are geometrically unintuitive” or something like that

[quartz verge]

yeah the gist of it is that

[subtle mango]

https://cdn.discordapp.com/attachments/268882317391429632/1119368623904006174/Down_With_Determinants.pdf

[quartz verge]

yep

[subtle mango]

heres his little paper

[quartz verge]

thanks was about to share that

[subtle mango]

imo determinants arent geometrically unintuitive — see 3B1B’s “Essence of Linear Algebra” series on youtube for visualization

[thorn cloak]

really? i feel like they are like one of the most intuitive things. aka the scale factor of area/volume of the paralepidid caused by a linear map

[quartz verge]

well it wasnt as intuitive for me when i started

[thorn cloak]

i suppose thats fair. i remember my prof just assigned that section to be read instead of motivating it in class

[subtle mango]

theyre not immediately intuitive based on definition alone

[quartz verge]

well i self studied most of it and found kinda weird to digest

[subtle mango]

but to neglect it to the end is quite odd

[thorn cloak]

hmm thats true. I could not tell you why that definition represents what it does

[subtle mango]

if you visualize a grid, the determinant of the matrix represents the area of the parallelogram created by the linear transformation

https://youtu.be/Ip3X9LOh2dk

[quartz verge]

good seried

seires

seires

series

[thorn cloak]

yeah that video is amazing. Guess now would be a good time to re watch it

[quartz verge]

will need a series on probability soon, been a while since he dropped something of bigger magnitudrle

magnitude

[thorn cloak]

if i were to do a little self-study for a second course on lin alg is there a certain book you would recommend instead of LADR?

[thorn cloak]

i hope soon. Taking prob next sem and really need him to save me again lmao

[subtle mango]

see the messages i linked above

[subtle mango]

^

[subtle mango]

^

[thorn cloak]

hmm i see. is roman's book immediately accessible? as im def not ready for a grad text

[tender river]

roman is nice

but i dunno what you mean by a second course on linalg

[thorn cloak]

i took a class using lay and lay. we went up to eigenstuff

not very proof based but also not ignored

[tender river]

was your first course strang level linalg or axler type proof based linalg, if it is the latter then roman is a good reference for quickly reviewing things i think

[thorn cloak]

yeah def more strang level

[quartz verge]

friedberg's linear algebra

[subtle mango]

im biased to hoffman kunze bc that’s what i used

[tender river]

you can still use roman to surplus the material from a more approachable textbook like hoffman-kunze, axler, ladw, etc nice to get a more advanced perspective on things

[subtle mango]

its tough but fun, tho i agree w dami wrt the multilinear algebra stuff

[thorn cloak]

i see. thanks everyone

[ocean mulch]

It is intuitive until you see various equivalent definitions of it, then it becomes less and less intuitive

Like, the classic "the only multilinear form such that bla bla" or the summation over all permutations of elements in canonical basis are in no way intuitive to me

I have never managed to work with any of these definitions of det, only the derived properties

[subtle mango]

yeah same tbh

cant remember last time i explicitly used laplace expansion or whatnot

[foggy relic]

Does anyone have a pdf of this paper https://www.semanticscholar.org/paper/L'anneau-spectral-et-l'anneau-filtré-d'homologie-et-Leray/64010462b6dd6054d498fe770e9c13a6d88046ff

[lavish pier]

if its this then yeah

The spectral ring and the homology filtered ring of a locally compact space and a continuous map

i gotta find it tho

idk if its exactly what you asked

but

https://tinyurl.com/y9mh5ezc

[foggy relic]

no the authors r different

[lavish pier]

yeah no i cant find the one written my J. Leray

[flint forge]

losing my mind at the fact that no native macOS app can open a djvu

[acoustic turret]

I am starting functions and vectors next year and want to get a head start in the summer. what books would be good for this? it is grade 11 mathematics

[flint forge]

khan academy is the standard recommendation for anything before calculus

[coral prawn]

So I've been looking for an intro to DEs book.
At first I started out with "Elementary DEs with Boundary Value Problems" by William F. Trench, but I had some issues with the "theorems" in the book- they weren't quite well phrased to me.
I looked a bit further and heard of Boyce's (which shares the same name ). It seems pretty common, so I was thinking of it.
Then I also heard of this ODE book by Marris and Pollard published by Dover, which at first sounded nice due to the some of the additional contents it covered, but unlike the other 2 it didn't have BVP nor PDEs. Furthermore the first few pages threw me off the moment I saw them treating dy-s and dx-es as fractions. "We multiply both sides of the equation by dt/x and integrate...." 💀

1. Is it an issue if the book doesn't cover BVP nor PDEs? I've been told that it's fine since they'll be covered in a PDE book like Taylor (...I think?)
2. I've always liked rigour, proofs and theorems, but after hearing and looking through a bunch of proofs for uniqueness/existence of solutions and... Boy, they are wild. I'm hoping that there's a book which approaches it from a "pure math" perspective- perhaps not as rigorous as the theorems, but doesn't neglect it either.... around those lines.
3. I'm quite against the use of the treatment of the differential forms as fractions and whatnots, so unless the book clarifies what the notation means.... I don't think the book would quite suite me.

Any reccs based on these? Perhaps I should just stick to Boyce?

[remote sparrow]

i don't think saving the determinant for the end is necessarily a bad idea. however, i can understand if you have a problem with how axler defines them.

like you can show the geometric interpretation of determinants for R^2 and R^3, but it's still not immediately clear how this connects to the determinant's property as an invertibility test

and it can't be much worse than defining the determinant by the permutation formula

[finite gale]

This is still useful sometimes though

But I guess it's a little unwieldy to prove stuff with that definition

At least you can do computations with it though

[remote sparrow]

as far as computations go, row reduction is more efficient for applications than determinants. most students taking linear algebra are probably going into some applied field. determinants are still important theoretically, but i'm not sure if it's really worth putting a lot of emphasis on computing numerical values of determinants.

[flint forge]

as far as computatins go you probably don't really need to compute any determinants at all by hand

maybe one or two to get the feel

[remote sparrow]

meckes is a first course in linear algebra that defers determinants towards the end and defines the determinant as an alternating multilinear function mapping the identity matrix to 1

[finite gale]

True, I don't think I actually had to compute any determinants in undergrad, or I just forgot, just like everything else I did in my first two years of undergrad

[flint forge]

i mean its easy to pick the algo back up

[ocean mulch]

Tf? How come that you didn't have to compute any det?

[flint forge]

but i can only do the 2x2 case without googling

I don't think I computed any determinants in undergrad

certainly none by hand bigger than 2x2

[ocean mulch]

Didn't yall have quadratic forms? Or diff geo?

[flint forge]

no

[ocean mulch]

Whaaaa 😄

[finite gale]

Oh wait I might have had to do some in ode class but I'm pretty sure I just chucked everything into wolfram alpha lol

[flint forge]

I think rep theory was the only place I could imagine I actually took a determinant

and even then I probably put it into wolfram

[ocean mulch]

Yeah, det in 2D dynamical systems is classic

[flint forge]

not a diff geo kinda guy

[ocean mulch]

I wonder what you did, cus you know insanely lot

[finite gale]

I don't recall taking a determinant in rep theory but I do remember using them

[flint forge]

i just know many things that aren't diff geo

too coordinatey for me

[orchid mortar]

Intro DE books more about solving them than proving things.

[ocean mulch]

Just a bunch of functions, can't be that bad

[remote sparrow]

the dy's and dx's are given a proper definition, not merely treated as fractions

[flint forge]

its not aesthetically pleasing

[remote sparrow]

the definition is unwieldy though

and i don't think you should really get too hung up on them

[ocean mulch]

at least it has some aesthetics, lol, unlike algebra

[remote sparrow]

Taylor's PDE book is a graduate text

and undergrad PDE books like Strauss are still mainly concerned with closed-form solution of PDEs

graduate PDE books have a completely different focus

they're thinking about existence, uniqueness, smoothness, etc. of solutions

there are also graduate texts for numerical solution of PDEs

[finite gale]

I'm also fairly sure pdes requires quite a bit more analysis background than ODEs

But I'm not sure how much since I never actually took a pdes class

[remote sparrow]

my undergrad pde class only requires some ODE background

[finite gale]

Oh

[coral prawn]

Well they are but its not like I'm anywhere near understanding what a "differential form" is

[coral prawn]

Yeah that's what pisses me off but w e l p they're needed before you can go on to proving existence/uniqueness etc....

[coral prawn]

Ic... welp long way to go ig

[remote sparrow]

no, tenenbaum and pollard actually defines dy's and dx's in an elementary fashion

just a definition you'll likely never see again

[coral prawn]

Wait they do?

Oh

[twilit oak]

I'm looking for a book ideally avaible in free pdf which covers logic and basic logic proofs. I want it to be as most rigorous as possible (ideally without truth tables) so it should use just rules of inference and maybe some "axioms".

[subtle mango]

#book-recommendations message

[twilit oak]

thx

[coral prawn]

Still though how'd you go through 2 textbooks covering the same material (one as reference/additional material) at once? Like, how are you juggle between the two and be sure that you aren't missing out on any content? It doesn't seem practical to attempt all the exercises in both books do you just judge by content page/if you feel that this concept hasn't rlly been explained well enough for you you look it up on the 2nd book?

[flint forge]

normally I would pick one book to be my primary source and go look at other books if i don't like a particular section. you can also cross reference tables of content to see whether or not theres an obvious omission in one of the books

[acoustic turret]

is there nothiing written? I was looking for something I would be able to read as opposed to a video

[flint forge]

khan academy has written versions of the notes, but tbh no one can really recommend a great textbook since the textbook industry for pre-calculus subjects is super cursed

you can probably just use any textbook

[coral prawn]

If you rlly want book then stewart's precalc would do.

[coral prawn]

Hm... what abt the exercises? How do you manage/select which ones to do?

[flint forge]

randomly

[remote sparrow]

just do what looks interesting

also don't worry if you can't solve everything

you don't need to be able to do every exercise to move on

sometimes certain exercises from a prior section are not really necessary to understand later material

[coral prawn]

Ig it's like after doing 1-2 of the same qns and you feel like "ok the rest is just the same computation" then just skip ahead

[mossy flume]

I pick one as my favorite (and that's where I'll do exercises) and only look at the other if I hate a proof in the favorite

[gray gazelle]

Advanced Engineering Mathematics, 10e by Erwin Kreyszig (2018, Wiley)

[coral prawn]

Right, right (or if content is missing from the favourite ig?)

[orchid mortar]

What's this about?

[mossy flume]

yea that too

vacuous hatred of a proof for when a proof doesn't exist

[coral prawn]

[gray gazelle]

about advanced math that you will use more often in a day as an engineer or searcher

[orchid mortar]

....

sounds like a block to me

[gray gazelle]

lol you are free to do what you want ^^

[tender river]

#book-recommendations message

[tulip hearth]

An author, Vinay Kumar sir.
My coching teacher recommend everyone that book cause the author is my teachers teacher, and my teacher knows a lot of short tricks which he said his teacher taught him. So I thought maybe I should try the book. But it's too expensive of a book 💀

[hasty turret]

So you won't be finding Indian coaching books on most websites

Because no one cares enough to pirate them

[fervent nova]

Can anyone recommend me some book on self learning differential equations and summation?

our school didnt teach them

[coral prawn]

You're talking abt 2 rather different things- one is about summation and the other is about DEs-

For summation, what are you referring to? Geometric, arithmetic etc? Or calculus-type infinite sums, convergence, divergence?

As for DEs- I asked the same question a few hours back, and decided to stick with Marris and Pollard's ODE book, and use Boyce's elementary DE book to complement stuff which it misses out, such as PDEs, boundary value problems.

[fervent nova]

i would like to learn those should be taught in high school

there are some ways to solve calculus questions by summation and i would like to know it

thx for your advices!

[coral prawn]

U could check out Paul's online notes for that part

[fervent nova]

oh thx you very much!

[remote sparrow]

it's morris btw

[coral prawn]

Spelling moment

[late plinth]

anyone got any recs for more advanced numerical optimization books, i already read Numerical Optimization by Jorge Nocedal Stephen J. Wright and i would like something a bit more advanced

[wraith nova]

What book for self study calculus im high school

[coral prawn]

Stewart if this is your first encounter with calc

[white summit]

Any book recomendation for Set Theory , Group Theory

[sudden granite]

spivak

[coral prawn]

personally I'm a fan of it but I feel that it's not a great recommendation for those who are first begin with calc. It's honestly too advanced for the beginner

[sudden granite]

i shouldnt be trolling in book recs

mb

but yeah i read like the delta epsilon definition for limits in spivak and then checked out

problem sets in like stewarts or whatever is better

[coral prawn]

you were trolling? I was thinking it was a good recc... But I realised that I didn't consider that others may not have a first hand encounter with calc already so I default to recommending others stewart if it's a first time encounter and spivak if they want a challenge + have some experience already

[sudden granite]

spivak is just a meme at this point

but yeah the book is good just takes a lot of time to understand if you go line by line trying to self study

each line is super valuable though

[coral prawn]

imo tho

what's more valuable of spivak

is the exercises

those are the really tough stuff

like he gets you to prove theorems and all

not just blind computation unlike most calc books

[sudden granite]

yeah

goatvak

the spivak vibes

[bright stirrup]

Looking for a good book on measure theory

[tender river]

#book-recommendations message

[shut flame]

Can anyone suggest some good calculus practice books to begin with

[coral prawn]

do u have familiarity with calc?

[shut flame]

high school level

[coral prawn]

so I'm assuming basic derivative rules all covered? What abt integration? IBP? U sub also covered?

[shut flame]

Yup all basic stuff done for derivatives and integrals and also differential equations

[coral prawn]

damn noice
In that case spivak calc would do just right it covers a bit of introductory analysis too

[shut flame]

Okay

[wraith nova]

Omg stewart book is just so good

[wraith nova]

Purcell or stewart? there is translated purcell for my native language but not for stewart

[rancid hollow]

always thought Purcell was just an E&M book

honestly I have no opinion since I learned Calc in classes and only ever had to open the textbook to read the homework exercises

[wraith nova]

Wow my teacher only attend the class once a month he just give homework

[orchid mortar]

I never read this myself, but this is the other book I know on Numerical Optimization.

[orchid mortar]

I think you'll easily find advanced math books if you are looking for numerical analysis instead though

[novel sluice]

agreed

[thorn cloak]

has anyone used Stochastic Processes by ross? it claims to be non-measure theoretic and was wondering if its worth reading before trying stochastic calculus down the line

[hot flame]

hey any book recommendations?

for a 14 year old

[chrome yacht]

Naomi Klein: The Shock Doctrine 😁

[mossy flume]

What sort of math have you done or seen

And what sort of math have you liked / disliked so far

[fast gull]

captain underpants

you are too young to read textbooks its probably better if you go through workbooks/khan academy or reading blogs.

textbooks are meant for focused interests so no reason to have one when you are this young and havent had too much math exposure

[tender river]

for maths? idk just start off with like one of those discrete math thingys, rosen or scheinermann should be simple enough for 14 year olds, sets you up nicely with a good intro to proofs ig

[minor knot]

Calculus for infants

[idle cairn]

i needed this

[ornate haven]

Why is Precalc by Stewart so overwhelming? There are too many questions and it makes me dread the act of problem solving itself sometimes. Simply coz I know this book will never get over 😦

[mossy flume]

ok a couple things

1: Precalc is a bunch of different topics and seems to jump around the place. It's just like an odds-and-ends thing which makes it feel more overwhelming unlike calculus which builds on itself in a semi-linear progression

so if you're overwhelmed it's fine, it happens, that's just how learning is

2: don't do every question. Not every question is worth doing

You're probably noticing alot of questions are similar, just different numbers essentially

so why repeat them over and over again.

the goal is to learn techniques and ideas, not number crunch

3: Why do you feel you dead solving problems?

[quartz verge]

why do you think that?

My first course on Calc was done through Spivak

Enjoyed every bit of it

Yes it was a struggle but i dont think theres any better feeling than to complete Spivak as a first encounter to Calculus

Its super intuitive

It wouldnt pack the same punch if you do it as a second course

[mystic blaze]

You might be able to read Proofs: A Long-Form Mathematics Textbook, check it out and see if it's any good for you

[quartz verge]

Itll be similar to like listening to an album that makes you feel like "only if every single listen to it could be my first"

[quartz verge]

uhh man this brought back some bad memories for me

I had a chapter named Formulae in middle school where they just shoved every types of polynomials you learn i school in exercises with instructions that said "solve for x" and i kept wondering almost my entire life the purpose of having such a useless chapter amongst all other things in that book until recently where i discovered they were meant to provoke a thought process that should somehow lead to make you think of the bifurcation of transcendental and algebraic numbers

and from that very moment, im unsure if anything is even useless anymore

[maiden halo]

everyone is different, that's why. not everyone will enjoy it as a first look at calculus

[quartz verge]

possibly

[ornate haven]

The way the book's organized is that every chapter has like 5 questions of each topic covered before the exercise. So it's kinda hard to figure out which questions to not solve. Like what if a question actually reaches me something new?

[ornate haven]

I wanna reach calc FAST 😭

[mossy flume]

sure but if you reach it too fast by skipping essential material then you're just going to have a bad time learning calc

then again not all of precalc is essential

[late plinth]

Gotcha any recs?

[fallow cypress]

Oh I've heard of this, did you like it?

[ornate haven]

Agreed

[ornate haven]

Any tips for this? @mossy flume

[quartz verge]

is this out of excitement or youre tryna speedrunning things?

speedrunning would make zero sense as thatd essentially mean you want to learn and dont want to learn at the same time

[devout shore]

Oh this is interesting

I took calculus several years ago and I kinda wanna tackle precalc and trig and geometry etc before running into calc

I'll have to check out that textbook

[vagrant mason]

For pre calc do you reccomend James Stewart or Sullivan ? Like which is better

[devout shore]

I was about to order a book by Simmons

[vagrant mason]

I can look into Simmons but most schools reccomend James Stewart

I like his book. But it’s always nice to see more options.

Currently looking at this book for basic geometry and it’s amazing when you get a brain fart and forget something. It’s easy to look back and the book can fit in a purse so you can have it anywhere

[remote sparrow]

axler has written textbooks for algebra, algebra and trig, and precalculus

[vagrant mason]

If I remember correctly, algebra and trig is relatively the same as pre calculus

[remote sparrow]

https://stitz-zeager.com/

[quartz verge]

has anyone read Strang's Calculus?

[remote sparrow]

there's also this free precalc book

[vagrant mason]

Hmm

Anyone read sullivan’s book and can tell me how it was?

[maiden halo]

the "in a nutshell" book? it's pretty short but not bad

[devout shore]

Yes! That one

A lotta good resources around here. I really like this server

[ornate haven]

Excitement. The thing is I've learnt some calc in high school and am heading to college this fall. Just that I wanted to make my fundamental in Precalc strong before going into (hopefully advanced) calc

[wanton spade]

I want to get better at combinatorics and probability. Does anyone have a book for this?

Im also very bad at it so im looking at something beginner friendly

[orchid mortar]

Nope, this is too far into math world for me

[thin hollow]

game theory math books

[hallow oriole]

winning ways for your mathematical plays

[coral prawn]

you were guided by a prof no?

it made things easier since you had a guide

but me and most people I've recommended stewart over spivak to so far are HS-ers who don't have such people to help irl

• it really is challenging, if you've read it I think you can agree. And if it's your first time reading calc you may not even understand why tf are you doing a good chunk of the content- especially when this book has some intro anal mixed into it. Not everyone wants that sadly.

[past blade]

Does anyone have any good book/paper recoms for

1. Fuzzy Logic
2. Evolutionary Algorithms? (I already found a few books on EA, but not for Fuzzy Logic since there are more books of different qualities)
   Any input is welcomed, and thank you!

[heady ember]

I think Spivak is doable with some persistence, and some level of challenge is certainly required in proof-based mathematics. At some point or another, one will most probably experience a challenge much greater in difficulty than they had previously

[coral prawn]

fair enough

[quartz verge]

no

[coral prawn]

wait then how was it a "first course"?

[quartz verge]

Because it was

I self studied it

[coral prawn]

a course without a professor?

oh.

[quartz verge]

yes

[coral prawn]

I thought you meant in uni

[quartz verge]

nope

im still in the process of understanding a decent chunk of after almost spending 3 years reading it

[coral prawn]

exactly

not all students wanna go for the rigour sadly

so they may not find spivak to their liking

[quartz verge]

i mean theyll immediately get the gist of what theyre gonna be subscribing to after going through the first few pages of the book and i think its better to take a call after doing that instead of just ignoring it altogether

[coral prawn]

true LOL

in the preface I remember smth aroudn the lines of

in the 2nd edition "this should have been named intro anal but eh it's too late"

around those lines

[quartz verge]

i still have the preface saved somewhere

#chill message

my favourite part of the preface to be precise

[coral prawn]

~~I have permastudying so I can't see it ~~

but yes

the preface got me hooked the moment I read it

based book

[quartz verge]

same

[quartz verge]

https://ibb.co/nD9ccWr

[coral prawn]

ahhhh

right that part

[quartz verge]

so eloquently put

[past blade]

Does anyone have any good book/paper recoms for

1. Fuzzy Logic
2. Evolutionary Algorithms? (I already found a few books on EA, but not for Fuzzy Logic since there are more books of different qualities)
   Any input is welcomed, and thank you!

[chrome yacht]

Thought it was pretty good, yeah. It is as good a critique of neoliberalism as any. Klein's writing evokes genuine emotions and anger, it is a great way to get started with the literature. Definitely recommend, you'd rather read Klein critically than do any of the garbage that comes out of Friedman and his ilk uncritically.

[heavy pelican]

I tried to read This Changes Everything and I got bored

It just seems like a ragetext which at this point changes nothing lol

[chrome yacht]

the shock doctrine does come off as a ragetext too, it's just that when i read it i didn't have as much knowledge regarding the history of the things mentioned in it, at the time it was a great read

[heavy pelican]

She writes well

I'd much rather read a comic book than the American left frothing at their mouth at how much the corporations need to be held accountable though

[gray gazelle]

Hello ppl

[hasty turret]

There's a canonical Christian discord?

Meet Martin Luther and Huldrych Zwingli. These two reformers shared much in common but their differences would lead to a legacy of Christian discord that continues into the present day

[uneven sundial]

Does anyone have recommendations for graduate level ODE? I just finished analysis 1 and 2 (single and multivariable functions). The prof lists GTM 182 as a possible reference for the class, but I was wondering if there are other ones I could take a look at during the summer.

[quartz verge]

Amen

[wanton spade]

Need a combinatorics book. Any recommendations for a beginner?

[hollow shore]

what's your background?

[wanton spade]

@hollow shore 2nd semester software developer

Ive gone through discrete math and I want more in that area

[tender river]

i have been following loehr bijective combinatorics and bona's intro to enumerative and analytic combinatorics (not the walk thru combinatorics book) lately and i like them

[wanton spade]

Is loehrs beginner friendly?

[tender river]

idk about that i don't consider myself a beginner and i only started with it recently, thought i did pretty well with it

bona i think is friendlier for beginners though

[wanton spade]

Ill check out bonas then. Ty!

[hollow shore]

I will second bona

[hasty turret]

Like you are doing a degree called software engineering?

[alpine rover]

best introductory books on functional analysis?

[heavy pelican]

Hall, “Quantum mechanics for mathematicians”

[sturdy shore]

einsiedler ward functional analysis

[sage python]

I'm more team the latter yea

Rudin functional, Einsiedler-Ward, Brezis for what it does

[gusty smelt]

Pederson analysis now, you should listen to me as I work in a subfield of functional analysis

[crimson leaf]

What are people's thoughts on Conway's book?

[prime pollen]

which one?

[hearty steppe]

Any good text recommendations on differential forms that provides a nice angle for dynamical systems, Fourier analysis, with a focused angle on translating physical models?

Rather than something too general and not very motivated in exposition outside pure mathematics

[crimson leaf]

functional analysis

[hearty steppe]

Hopefully there may be some information about langlands program in such a text as well

[sage python]

Those are very different things

The answer is probably no lol

[prime pollen]

oh sorry didnt realise it was related to above

[hearty steppe]

I have other interests too like exploring motivation of p-Adics to calculate measures in restricted spaces that translates well to physics

Maybe a nice general approach to differential forms that considers the depths of exploring many body interpolations/convolutions of manifolds in physical models is fine

I think I might juggle a couple books that may have some flavor of what I’m looking for that is very general in approach but a little heavy in terseness like Folland’s real analysis which I thought was a really nice general exposition approach to measure theory

Those last three chapters especially man, they are crazy abstract and trippy to think about

[sage python]

I don't think you understand what differential forms are about

Differential forms are just how you integrate on manifolds

So if you integrate the omega = (-ydx + xdy)/(x^2 + y^2) over a curve

That's a differential form

"General approach to differential forms that considers the depths of exploring many body interpolations/convolutions of manifolds in physics models" feels like you're just sticking words together that don't make sense

[hearty steppe]

Well so I am thinking in terms of how the manifold takes up and spreads over space

[sage python]

What does that sentence mean?

[hearty steppe]

So like thinking about how I have some object in some n-tuple mapping to space where we are working in R^n as well as C^n

[sage python]

Alright I think I'll just suggest a few books that you might find interesting

[hearty steppe]

Yea I may be asking for something a bit too rigid like you said

[sage python]

Not even too rigid I just don't think you have a clear idea lol

Like you're associating things that aren't associated

Anyway I'll give some general pointers

Because you mention physics and dynamics a bunch

Try "Mathematical Methods of Classical Mechanics" by Arnold

[hearty steppe]

When I say manifold I’m being very general about how I have a collection of points that take up the space with some fundamental topology but then that could mean something else like I get some pattern or some shape where I have a volume that takes up the spaces or spreads over it over time

[sage python]

Yeah don't do that lol

Manifold is a technical term with a technical definition

To learn about them, try Tu Introduction to Manifolds

It includes differential forms

[hearty steppe]

Yea it seems like I should think more fundamentally about how a manifold is derived. Jumping from generalizing a measure to the behavior of a manifold is a jump I guess

I am thinking more about onions and how they have layers to them and how I peel the onion as opposed to add another layer to the onion or if I have clay

[still umbra]

ogres are like manifolds

[turbid mural]

i used perderson's book

[alpine rover]

thanks!

[summer lagoon]

Hallo ! I'm looking for books with a lot of exercises while following Lee's book on smooth manifold, there are some exercises but I feel they aren't enough... !

Can be past courses with exercises, I just need a lot of exercises

[grand thistle]

the conversation above is so funny to me for some reason

[glacial crypt]

exercises
did you do the problems lol

lee has a webpage where he posts the problems he asks his students to do

[stoic nova]

<@&268886789983436800>

[primal summit]

Ty

[river kernel]

[frosty basin]

is there anyone who has used serge lang's undergraduate analysis as analysis textbook?

my school uses it but afaik most schools use pma as textbook

[shadow hedge]

Do I need to do every exercise in the book of proof by hammack or just the odd ones which have solutions in the back.

[frosty basin]

i recommend just doing like 1/5 of the problmes

no need to spend too much time of the book

[coral prawn]

it depends on

1. the individual
2. The quality of the questions
   1st point is obvious- it depends on your strengths and weaknesses.
   2nd point- Try to run the proof/solution in your head. If you can't do it naturally then work through the question and any other similar ones till you gain familiarity. After that there's no need to repeat those sort of computational qns.

[hazy elk]

Anyone here read Vassiliev's Introduction to topology? It seems to cover a startling amount of content in just 160 pages

Chapter 1 . Topological spaces and operations with them 1
§1.1. Topological spaces and homeomorphisms 1
§1.2. Topological operations on topological spaces 4
§1.3. Compactness. 7

Chapter 2. Homotopy groups and homotopy equivalence 9
§2.1. The fundamental group of a topological space 10
§2.2. Higher homotopy groups 12

Chapter 3. Coverings 21

Chapter 4. Cell spaces (CW-complexes) 25
§4.1. Definition and main properties of cell spaces 26
§4.2. Classification of coverings 31

Chapter 5. Relative homotopy groups and the exact sequence
of a pair 35

Chapter 6. Fiber bundles 41
Locally trivial bundles
The exact sequence of a fiber bundle

7. Smooth manifolds
   Smooth structures
   Orientations
   Tangent bundles over smooth manifolds
   Riemannian structures

8. The degree of a map
   Critical sets of smooth maps
   The degree of a map
   The classification of maps —> The index of a vector field

9. Homology: Basic definitions and examples
   Chain complexes and their homology
   Simplicial homology of simplicial polyhedra
   Maps of complexes
   Singular homology
   Main properties of singular homology groups and
   their computation
   Homology of the point
   The exact sequence of a pair
   The exact sequence of a triple
   Homology of suspensions
   The Mayer—Vietoris sequence
   Homology of wedges

§10.7. Functoriality of homology 92
§10.8. Summary 93

Chapter 1 1 . Homology of cell spaces 95
1 1 . Cellular complexes 95
§11.2. Example: homology of projective spaces 97
§11.3. Cell decomposition of Grassmann manifolds 98
Chapter 12. Morse theory 103
§12.1. Morse functions 103
§12.2. The cellular structure of a manifold endowed with a
Morse function 104
§12.3. Attaching handles 106
§12.4. Regular Morse functions 106
§12.5. The boundary operator in a Morse complex 110
§12.6. Morse inequalities 114
§ 12.7. Standard bifurcations of Morse functions 115
Chapter 13. Cohomology and Poincaré duality 119
§13.1. Cohomology 119
§13.2. Poincaré duality for manifolds without boundary 122
§13.3. Manifolds with boundary and noncompact manifolds 124
§13.4. Nonorientable manifolds 125
§13.5. Alexander duality 126
Chapter 14. Some applications of homology theory 129
§14.1. The Hopf invariant 129
§ 14.2. The degree of a map 131
§ 14.3. The total index of a vector field equals the Euler
characteristic 132
x Contents
Chapter 15. Multiplication in cohomology (and homology) 137
§ 15.1. Homology and cohomology groups of a Cartesian
product 137
§15.2. Multiplication in cohomology 140
§15.3. Examples of multiplication in cohomology
and its geometric meaning 142
§15.4. Main properties of multiplication
in cohomology 143
§15.5. Connection with the de Rham cohomology 144
§ 15.6. Pontryagin multiplication 144

Look at this bad boy

Just 144 pgs

Average redpilled Russian topologist

[spark hill]

Hi! I am looking for a book on complex analysis. Does anyone here know a good one?

[hazy elk]

I really enjoyed Ulrich's Complex made simple

Possibly one of my fav books of all time

[spark hill]

oh, cute title too. thank you.

[alpine rover]

i like Zill a lot

can do Bak, Newman for more rigor

there's always Ahlfors as the Rudin-like reference

[hazy elk]

Ahlfors is nothing like Rudin

Rudin is concise and elegant (and terse)

Ahlfors is confusing, chatty (and still terse)

[gray gazelle]

how do we explain the 4th Dimension

[hazy elk]

You can't directly, but you can sort of mimick the situation by using colors (see the first chapter of Pugh "Real mathematical analysis" )

[gray gazelle]

ok i will do that

[alpine rover]

isn't there some famous video of a high school kid explaining the fourth dimension

[summer lagoon]

Yeah i do them, not so hard at the moment. I will look on lee’s website then thanks 🙂

[glacial crypt]

https://sites.math.washington.edu/~lee/Courses/544-2019/hw.html

[slim bramble]

perfect advice. solving problems in you head even proving things really makes it much faster to go through the problems, it is a good indicator of your understanding and really makes sure you are not skipping anything.
especially with questions that are meant to be build muscles and are not expository.

[gray gazelle]

ok now i learned how to play chess a little bitt and the book didnt give me the asnwear im searching for but still thankyou

[gray gazelle]

ima go search for it

[swift cipher]

Anyone use the Hungerford text for undergraduate Abstract Algebra? I really liked it.

[rose bridge]

I'm looking for resources on SL(2,R), the special linear group of dimension 2. In particular, I want to learn about the classification of its elements. Since I am not familiar with Lie theory, I would like this to be approached assuming only a knowledge of linear algebra. Does anyone know a book/article/page that meets this criteria?

[hazy elk]

Are you looking for a classification based on the trace of elements or something?

[rose bridge]

Yes, that sort of thing

[hazy elk]

It seems like its just a linear algebra excercise, try looking at eigenvalues and JCFs ?

[rose bridge]

Yes, it is. But I want to develop a general familiarity with the specific properties of this group.

I am not looking to prove a specific result.

[hazy elk]

Would you mind settling for subgroups of $PSL(2,\mathbb{R})$?

[hasty eagle]

strugglinggeometer

[hazy elk]

Namely, the "discrete" subgroups of $PSL(2,\mathbb{R}$ (cus you can just pull back them to subgroups of $SL(2,\mathbb{R})$)

[hasty eagle]

strugglinggeometer

[rose bridge]

I don't really understand what you're talking about, so if this relationship between the groups is elucidated in the text, then sure

[hazy elk]

Okay so $PSL(2,\mathbb{R}$ is just the quotient group of $SL(2,\mathbb{R}$ after identifying +Id and -Id

[hasty eagle]

strugglinggeometer

[rose bridge]

I see, that seems useful

[hazy elk]

Anyways the book that I had in mind that studies discrete subgroups of $PSL(2,\mathbb{R})$ is "Fuchsian groups" Katok, but maybe you want to study $SL(2,\mathbb{R})$ as just a matrix group? I think Artin and Armstrong both have chapters on matrix groups

[hasty eagle]

strugglinggeometer

[rose bridge]

"Groups and Symmetry" by Armstrong
and "Geometric Algebra" by Artin?

[hazy elk]

The Armstrong book is correct. The Artin book is just called Algebra

[rose bridge]

Ah, yes I'm familiar with that one

Thank you @hazy elk. I will take a look at your recommendations

[quartz verge]

is Advanced Calculus by Patrick M Flitzpatrick a bridge between Calculus and Real Analysis or something entirely different?

[tender river]

looked like an analysis text to me, spivaky but more rigorous and also had some multivar if i recall correctly

[quartz verge]

alright!

is it equivalent to Baby Rudin or even more advanced?

[tender river]

i don't think so, just slightly more advanced than spivak, if anything more like bartle sherbert for the 1var stuff in terms of problems

Babyrudin does metric spaces from the get go, im pretty sure that's not how it's done in fitz

[quartz verge]

thanks!

[rose geyser]

wow looks nice

[magic marlin]

Hello, I am going to be a sophomore next year and I need a textbook to learn pre-calc over the summer to be prepared for Calculus. I don't need a textbook that goes over algebra 2 and all of the other pre requisites, but rather one that teaches the content of the actual course.

[remote sparrow]

pre-calc is usually just more algebra and trig content

towards the end of the semester, there may be some coverage of limits

but really it's not a super special class

[weary cape]

Any precalc textbook will do. If you want a pdf I can give you one

[frosty basin]

use stewart's

its the best one out there

[weary cape]

I didn't know stewarts had a precalc textbook. I'd also recommend Larson tho

This? https://www.amazon.com/Precalculus-Mathematics-Calculus-James-Stewart/dp/0840068077

This one is the one I used

http://prodimage.images-bn.com/pimages/9781133947202_p0_v1_s1200x630.jpg

[magic marlin]

ty

[weary cape]

iirc, the exercise problems were challenging so if you want to challenge yourself, theres that

[snow gate]

good shit

[gentle forge]

Can someone suggest some really good and reader-friendly books on beginner calculus, like someone who's ready to move on to calculus after pre calc by self learning

[coral prawn]

Stewart

[quartz verge]

Apostol

[gentle forge]

ok

Am reading Calculus for the Practical Man rn

[gentle forge]

is it a good book?

[gritty wedge]

calculus by m spivak

👽

[tender river]

babyrudin stewart's books is readable, try that

[quartz verge]

https://www.docfly.com/editor/b7b91ae0bf22a0c6f805/209zq2vrstkh-b45fea41

thanks to Namington

[gleaming geyser]

I want to start learning math in a systematic way

I could start with algebra. Is there a book that covers most of algebra

[formal bronze]

You certainly wouldn't find one book that covers 'most' of algebra.

[novel sluice]

^^

[formal bronze]

What sort of algebra are you talking about, linear algebra, abstract algebra, or something else?

[gleaming geyser]

Where do I start

[formal bronze]

Depends on what your goal is.

[novel sluice]

Are you in high school or early university?

[gleaming geyser]

High school

[novel sluice]

oh okay then the matter changes a bit

[formal bronze]

Their role says pre-university

[formal bronze]

Ah

[gleaming geyser]

My bad

[finite gale]

I'd say start with linear algebra if you haven't done that yet

Then you can see what you want from there

[novel sluice]

See, the algebra you see about polynomials in your curriculum - if you want to learn about them systematically - first you gotta learn about Linear Algebra, and then slowly creep in Abstract Algebra

[gleaming geyser]

Okay

I'll do that and keep you updated

[novel sluice]

which will take a long time obviously

start with 3b1b's essence of Linear Algebra before picking up a book, it'll help you develop a bit of intuition.

Then maybe uh.... some easy linear algbera book...

I'd have directly said Hoffman Kunze, but I don't know if you'd find that easy given you're just in high school and it might take you a fair amount of time to get used to the idea of writing proofs

[finite gale]

#book-recommendations message

[novel sluice]

actually that's a nice thread

yes, refer to that

I'd recommend Spence and Artin from this list

Artin will be a bit dense though

but it's a favourite of mine

[finite gale]

I like ladw

[novel sluice]

ladr is also nice

no pikachu please no 😭

[finite gale]

Just don't use ladr for determinants

[novel sluice]

for specifically linear algebra though I'd always recommend Hoffman

but lmao the section with Multilinear forms there

[hollow shore]

I like hoffman and kunze so far

just read a few sections

[novel sluice]

it's a pretty cute book

[gleaming geyser]

I'll keep you guys updated

[hollow shore]

wish they latexed it

[novel sluice]

yeah fr

some notations look ass otherwise

[hollow shore]

jee junkie

[gleaming geyser]

Corny ahh I know

[frosty basin]

what happens if you fail twice at jee

i've heard theres no third chance

[novel sluice]

el o el

[slim bramble]

what do you think of artin as a first time studying linear algebra with formal notation and basically proving everything
also considering that i took a computational linear algebra course which was basically solving systems up until Cramer's method and also watching 3blue1brown series

[novel sluice]

if you want to focus on specifically linear algebra maybe don't start with Artin

Hoffman is just nice on that regard

[frosty basin]

artin had linear algebra book?

[novel sluice]

but if you are just like "ohh algebra" artin is epic

[frosty basin]

i'm using lang's linear algebra and its pretty good imo

[novel sluice]

You can also do the easier (lol i mean introductory) version of Serge Lang's LA

Introduction to Linear Algebra

[frosty basin]

i mean you can directly skip to linear algebra without doing the introduction

but i guess its better to do intro first

[novel sluice]

Lang's general algebra book though 💀

[slim bramble]

to be honest i read in that recommendation thread that it would be efficient and since I'm a math major i started with artin but now I'm afraid that the abstract algebra material would take away from my la experience

[frosty basin]

i wont even dare touch that book

[novel sluice]

ah then I'd just say maybe Lang or just Hoffman

[frosty basin]

imho dummit foote is too much for me too

i'm sticking with gallian

[novel sluice]

my personal favourite is Hoffman

[novel sluice]

Dummit Foote killed me I passed my Group Theory just because I had Artin with me

[slim bramble]

abstract algebra but la is included there

[frosty basin]

some people start learning algebra directly with d&f

maybe i'm not as talented as them

[novel sluice]

our college 💀

[frosty basin]

really?

good luck to you

[novel sluice]

(if eric sees this i'm sorry again but really i can't read dnf everytime I do tha i come out more confused)

[frosty basin]

at least dnf has plenty of resources

[novel sluice]

it has shit ton of stuff

[frosty basin]

you must be in a really good college

[novel sluice]

but none of it goes through my head most of the time

lmao 💀

[frosty basin]

i don't think that dnf was intended for novices

[finite gale]

D&f is nice enough

[hollow shore]

were you self learning or did you take an algebra class?

[finite gale]

Can be a bit too wordy though

[novel sluice]

For Group Theory Gallian is just built different, but then again it takes on Sylow so late

[frosty basin]

i tried to self learn prior to taking uni classes

via dnf

[novel sluice]

i really believe it's an encyclopedia

then there's Herstein, cryptic ass book

[frosty basin]

of course it is a very good book

[mossy flume]

D&F is a reference text

IMO bad for learning

Artin better, heard good things about Hungerford

[hollow shore]

ig you can download ug psets assigned from d&f and focus on it

[frosty basin]

oh thats a way too

solving every problem in d&f is pretty idiotic thing in my opinion

okay not idiotic, but inefficient

[mossy flume]

Very few texts it's worth solving every problem

Usually you're better off moving a little faster and doing just the interesting problems

[frosty basin]

i don't hate d&f tho

i really like its explanations

[mossy flume]

I hate D&F as a first text, especially for self study

[frosty basin]

thats exactly what i tried to do

[mossy flume]

I think Artin is gentler

[novel sluice]

man i had to struggle with it entire last sem

i wanted to die

[frosty basin]

mind sending me link?

[hollow shore]

for me even artin was tough

[mossy flume]

Artin is tough still yes

[frosty basin]

it certainly will pay off

[novel sluice]

artin is tough but it's pretty good

[frosty basin]

tbh its better than using rudin as a first text tho

[mossy flume]

Learning algebra for the first time is tough

[novel sluice]

😭 I only got 60% in Group theory 😭

[hollow shore]

sure man, just give me some time

[frosty basin]

thank you so much

[frosty basin]

how about other students/

[novel sluice]

NO WAY DON'T REMIND ME OF RUDIN PLEASE 😭

[frosty basin]

i don't think that you are expected to get more than 80% of the problems correct in most math classes

[novel sluice]

our first year maths has intro analysis on 2nd sem

[frosty basin]

unless you are a genius

[novel sluice]

there was this prof who just

came in

with the brown rudin

this

and started copying lines on the board without properly explaining anything

so ofc self study time

[frosty basin]

self study with rudin lol

[novel sluice]

and I hate this book so much what are these proofs bro

😭

[frosty basin]

even serge langs undergraduate analysis textbook was gentler than rudins one

the profs can't shake off their old ways

[novel sluice]

I gave up and read Kenneth Ross

I hate Bartle and Sherbert btw

hate is a strong word

[frosty basin]

like rudin could be used if combined with good professor, lots of resources, and significant amount of effort

[novel sluice]

i don't like it

[hollow shore]

I have heard you have to read between the lines with rudin

[frosty basin]

especially chapter 2

people say that it is beautifully written

[novel sluice]

definitely miles better experience

[hollow shore]

SAME!!!!!!!!!!

[frosty basin]

but in first timer's pov it is just a complete mess

[novel sluice]

Point set topology? i'd say it's pretty decent in that book

[frosty basin]

like rudin just bombards you with some theorems with no explanations

expecting you to magically 'get' what is occuring behind the scenes

[novel sluice]

but tbh

[frosty basin]

really? I hated that part with my passion

but i guess people are different

[novel sluice]

if that's my first time introduction to topology i'd hate it for the rest of my life

[frosty basin]

it was for me lol

[novel sluice]

i didn't read it from there

[hollow shore]

I think abbott is the best for intro analysis

[novel sluice]

i read point set topology from Apostol, on R only though

[frosty basin]

this

[novel sluice]

Yeah I missed out on Abbott

I read Ross though

it's pretty cute

[frosty basin]

serge lang's textbook is pretty good too

but you have to get used to his style

[novel sluice]

(when i mean a book is cute I mean it helped me understand stuff)

[frosty basin]

my prof recommended me ross

but i ignored him and read abbott instead

[novel sluice]

SAME I bless my 2nd Year Analysis professor

funniest fact is

he's an AlgGeo guy

our college is nuts

[frosty basin]

isn't alg geo some kind of nightmarishly difficult subject

[novel sluice]

yeah most likely

i was reading a bit of commutative algebra as a part of my summerproject and I dabbled only slightly in it

💀

i died

though Zariski Topology on Prime Spectrum was pretty cool

I now know very basic topology :3

[mossy flume]

I think the common advice is that AG is something you get used to

also alot of people do AG, and then commutative algebra, and then go back to AG now with better context

[novel sluice]

yeah i feel like I need to do that as well

you can't escape one

[frosty basin]

it does seem like an interesting field to me too

[novel sluice]

if you do the other

[frosty basin]

tho i don't plan on learning it

[mossy flume]

it is interesting

if you want a more gentle introduction

[novel sluice]

i'd probably do it unless I die doing it

[mossy flume]

Ideals, Varieties, and Algorithms by Cox, Little, and O'Shea

great great book

that I will forever shill

[novel sluice]

i know about this oneee

[frosty basin]

the only book i know about alg geo is hartshorne's

[novel sluice]

but my luck

[mossy flume]

you don't need any more prior background to it than basic algebra

[frosty basin]

my professor warned students that the book is a 'nightmare'

[novel sluice]

my summer project instructor told me to read Atiyah McDonald 💀

why do I keep getting forced to read the most difficult textbooks for a first timer

[frosty basin]

are you grad studnet riku?

[novel sluice]

ye i'm 3rd year now

[frosty basin]

i've never heard of undergrad reading those books

[novel sluice]

just started 5th sem

i mean technically i'm still undergrad

[frosty basin]

interesting

which country are you from if you don't mind me asking

[novel sluice]

India

[frosty basin]

oh

the country known for its unforgiving education system

[novel sluice]

LMAO 💀

somebody understands

[hollow shore]

lots of jee heads

[frosty basin]

i see indians everywhere on interent

[tender river]

shocking

[novel sluice]

i'm not one, i'll cry if you say that please don't :(

though I did attempt JEE and hated every part of the maths section

[alpine rover]

any recommendations for algebraic number theory?

[novel sluice]

it's literally COMPUTATION

how do these people do these shit bro

[hollow shore]

I meant in general, not you lmao

[frosty basin]

i tried jee problems

and told those problems to go f themselves

[sudden kindle]

Whats ur background

[novel sluice]

BASED

i love you

(was a joke btw)

[alpine rover]

Two semesters of algebra, covered field extensions and Galois theory. Also finished Apostol’s Analytic Number Theory.

[hollow shore]

https://personal.math.ubc.ca/~lior/teaching/1516/322_F15/

[hollow shore]

@frosty basin

[formal bronze]

Isn't Atiyah McDonald the standard book for commutative algebra though?

[frosty basin]

thank you so much

[novel sluice]

Probably

But it's so. uh. non-detailed

[formal bronze]

Hmm

[novel sluice]

especially for someone who is just starting stuff

but it's cool tbh

[formal bronze]

Yeah I haven't seen it myself yet, but I've heard good things about it. And I was thinking of starting commutative algebra soon.

[indigo mesa]

Consider Gathmanns Comm Alg script

[novel sluice]

if you already know most things about Rings and Modules I don't think you'd have problems

[formal bronze]

thanks, I'll check it out

[indigo mesa]

https://agag-gathmann.math.rptu.de/class/commalg-2013/commalg-2013.pdf

[finite gale]

Rip blue color

[indigo mesa]

Liked that one a lot

[formal bronze]

I see. In any case, it has to wait, because I'm busy with representation theory right now. Also, please don't use words like 'most' in this context, fills me with fear haha

[indigo mesa]

replace "most" with "basic"

[formal bronze]

Yeah I figured that was the intended meaning.

[sudden kindle]

Marcus Number Fields

[gentle forge]

james stewart, right?

[gentle forge]

james stewart, right?

[alpine rover]

thanks

[coral prawn]

Yes

[gentle forge]

the 2nd ed is like more than a 1000 pages!

[nimble gazelle]

[turbid mural]

i used stein and shakarchi's book

[gray gazelle]

Freitag is nice as a year-long course, use other books if you want a nice semester though

[flint forge]

it gets controversial reviews but I like Conway's book

very complete

[coral prawn]

the current ed is more than 1.4k iirc

you don't have to read everything

just the sections taht are relevant to u

[novel sluice]

yes, my bad 😭 I meant to say basic

[eager herald]

Hello guys, any recommendations for a high school level math book with challenging geometry problems

[novel sluice]

Maybe do Excursion in Mathematics? or Challenges and Thrills for Pre-College Mathematics - look at the Geometry Sections here

should be challenging for high school level

[eager herald]

thanks

[frosty basin]

damn munkres isn't easy

[formal bronze]

Haha yeah, that was sort of understood.

[formal bronze]

Challenge and Thrill was a great book indeed. A fellow Indian, I'm guessing?

[hasty turret]

I have the book but never actually used it

[formal bronze]

Ah. I enjoyed the introductory parts, the combinatorics stuff, the additional problems at the end and a bit of the geometry section.

Never managed to make time for the rest.

[meager fossil]

partial differential equations?

[coral prawn]

are you asking for a book on PDEs?

[meager fossil]

yes

[lusty sparrow]

Is “Complex Variables with applications” by A. David wunsch a good book to learn complex analysis?

[blissful pulsar]

is basic mathematics by serge lang good book if I don't even have high school math or begin math from ground up?

[frosty basin]

unless you are extremely dedicated, my answer would be no

its more of a review book

[blissful pulsar]

so what would you suggest? @frosty basin

[frosty basin]

from usa perspective: prealgebra-algebra and geometry-precalculus would be the standard course

[frosty basin]

https://www.youtube.com/watch?v=pTnEG_WGd2Q&ab_channel=TheMathSorcerer

[lusty sparrow]

Pls

[hollow shore]

what math do you know so far?

[blissful pulsar]

learn math even begin from summing/extracting because I don't have previous knowledge of math.

[hollow shore]

what grade are you in?

ig you can try school books and see how the difficulty level is

if it's too easy then skip it

[blissful pulsar]

I left high school

I don't go school

I am just a normal man with having no math knowledge

[hollow shore]

I think khan academy should suffice

[blissful pulsar]

some people tell khan academy is bad is like w3schools..

[blissful pulsar]

Looking for any good book but yeah this video may also work

[hollow shore]

khan academy is very good

[blissful pulsar]

I noted some books that I would look after reading serge lang basic math

[hollow shore]

what it lacks is exercises. so you can use any book to supplement.

[rough dagger]

Book recommendations for self study?

I finished high school

So something for students

[rough dagger]

Geometry trigonometry

Everything

[gray gazelle]

Not ideal for people with no experience self studying

I recommend Artin since it is more motivating and covers Linear Algebra, which helps high schoolers (especially those who have seen calculus)

[old hare]

which one is it

[gray gazelle]

Michael Artin’s Algebra

[old hare]

ok thanks

[gray gazelle]

Skip the misc. exercises first time around

[old hare]

alr

[gray gazelle]

It is a good book, just too dry and the number of exercises might demotivate the average student

[hexed basin]

Books (I mean resources it shouldn't be only books) recommendations for self-study for beginners in number theory , combinatorics and algebra pls ?

[gray gazelle]

Niven Zuckerman and Montgomery are liked by a lot of people and Richard E. Borcherds has a lecture series on it (this is NT)

[gray gazelle]

This for Algwbra

As for combinatorics I don’t know much about

[grand ingot]

im looking for a source material for learning AI and ML

for self study

[chrome yacht]

helps in test

you help people during their test or help them prepare for their tests?

[gray gazelle]

Elements of Statudtical Leafning

[crimson leaf]

If elements is too hard try An Introduction to Statstical Learning

[grand ingot]

it was an old click bait joke that i forgot about (i already removed it)

[chrome yacht]

is that the one by Vapnik?

[crimson leaf]

Tibshirani, Hastie, and Friedman

Hastie and Tibshirani also worked on Introduction

[chrome yacht]

oh, looks nice i'll give that a try myself, thanks.

[versed magnet]

can you recommend book to statistics in data science for beginners?
I'd be great if it covered characteristic functions

[orchid mortar]

Very disagree.
@grand ingot I'd say standard would more be like Shalev-Shwartz Ben-David or the 2 ultra standard Vershynin/Wainwright. Or even just lecture notes that reference those. I would recommend hard not to go into Boucheron, etc. unless you already know probability.

Then if you want really 'just' ML you can try ML-ish books like Murphy, which is quite comprehensive

[gray gazelle]

Listen Watson they know a lot more than I do

[orchid mortar]

TBH ESL/ISLR are 'okay' but would not be sufficient

[orchid mortar]

Math stats just go with Shao

[loud cradle]

my only gripe with murphy is that there are an awful lot of results that he just states instead of giving some sort of derivation to show why they're true... but i guess if he did that, he would need even more volumes

[orchid mortar]

Ya ML books are just like that, it's just 'the thing' you use. It's not how it's derived or really any detail about how it comes about and a lot of the 'why'

[versed magnet]

https://www.amazon.com/Jun-Shao-Mathematical-Statistics-second/dp/B008UB56YQ this one?

[loud cradle]

the bishop book has a lot of the grungy details for the core material, it's a good supplement for that reason even though its coverage is nowhere near as comprehensive

[orchid mortar]

It's not really beginners, but yes. I don't recommend reading anything too beginner tbh since you're mentioning characteristic functions

[versed magnet]

i have an exam that includes them in next 2 months, but I cannot get through typical statistic book

my brain just turns off while reading it

[loud cradle]

characteristic functions are really more of a probability/analysis topic than statistics topic, you can find them in most probability books and some real analysis books.. in case you want to cast your net wider

[orchid mortar]

uhh I also took a data sci-ish course. I don't recommend it. It's starting from nowhere and has high expectations. It's actually a lot easier to do foundations and work from there

Characteristic functions are just proof-tools in prob/stats. The only thing we care about is that they correspond uniquely with RVs

[loud cradle]

yep

[versed magnet]

could you recommend 2 books then, one about usage of statistics in DS, and one that can prepare me to exam with characteristic functions (with questions like: find characteristic function of certain distribution) ?

[orchid mortar]

That sounds computational. Instead of books you're looking for exercises. Just do exercises if you want to compute.

DS is stats

[versed magnet]

I want see the actual usage of what i'm learning

[orchid mortar]

A lot of it has to come from mathematics

[weary cape]

Not a book but a good video if u want to self study pure math
https://youtu.be/byNaO_zn2fI

[frosty basin]

would herstein's topics in algebra be too difficult for a first time learner?

[loud cradle]

no, but beware that he often gives exercises which are quite hard to do based on only the material covered up to that point, and which become much easier after you read the next section

so it can be a bit frustrating and time consuming for that reason

[frosty basin]

thats the problem i'm currently facing actually

i like the explanations tho

[loud cradle]

yea, the exposition is good for the most part

are you self-studying?

[frosty basin]

yep

[loud cradle]

imo there are better books for that purpose (and in general haha)

[frosty basin]

i've had thoughts of switching to gallian actually

[loud cradle]

gallian is pretty decent from the bits i've seen but i've never read much of it

[frosty basin]

which book would you recommend?

i've heard that different books have different strong points, like some books have better coverage of group theory but lack on galois

[loud cradle]

a relatively recent book which i wish existed when i learned algebra for the first time: Shahriari, "Algebra in Action"

very nice book imo

[frosty basin]

seems like quite a new book

but with positive reviews

[loud cradle]

it's excellent for group theory, i haven't really looked at the rest but at least it looks like it covers more of rings and galois theory than herstein

dummit and foot covers more, but honestly it's just a chore to read

[frosty basin]

dummit foote is an excellent reference

[loud cradle]

if D&F had been my first exposure to algebra it probably would have been my last

[frosty basin]

but not a good textbook for my level

anyways thanks for the recommendations

[loud cradle]

yes, also a good source of exercises

[loud cradle]

btw, i forgot to mention, but one reason it's good for self study in particular is that it has hints and answers for many of the exercises

[hasty turret]

Well it also has a lot of explanation for well basically anything

Can't hurt

[fierce hedge]

@frosty basin There's a new algebra book written by Silverman (of the NT book fame) called Abstract Algebra_ An Integrated Approach and I think it's really well suited for complete beginners. I personally haven't tried it but @hollow shore liked it, you can ask him.
Here's the MAA review if you're interested - https://www.maa.org/press/maa-reviews/abstract-algebra-an-integrated-approach

The only possible downside is that it's slower than Algebra in Action book that Bungo recommended which can be good or bad news depending on how you like the pacing

[shut flame]

can anyone suggest a good linear algebra book for a CS undergrad

[remote sparrow]

#book-recommendations message

[gray gazelle]

Anyone have any resource suggestions for complex differential geometry?

Need something covering the basics, potentially some Hodge theory also

[woven thorn]

any book recommendation to understand raycasting algorithm

[gray gazelle]

I don't know much about it myself, but the standard references here are Demailly and Griffiths-Harris, for a more Algebraic POV, Voisin and Arapura are highly regarded

There was a good post on r/math about it, but the subreddit is currently down indefinitely.

[rancid hollow]

shoot I forgot there were good things about r/math

[frosty basin]

thanks for recommendations!

[gray gazelle]

Thank you!

[gray gazelle]

Silverman is generally a very good author and i think it would also do you good to check out his "A Friendly Introduction to Number Theory" who knows you might be converted

[old elk]

yo prefiero contemporary abstract Algebra Joseph

[dense mantle]

we used that for my course... I liked it more than I have liked poking around most undergrad math books

the exercises are chosen pretty well/ made me feel like there was a consistent theme, whereas others I feel are sometimes just trying to show off breadth for no real reason

[quartz verge]

on cue https://twitter.com/3blue1brown/status/1673713627038380032?s=20

[wanton spade]

any books for a Long airplane trip? I wanna solve some problems

Thinking probability maybe

[fierce hedge]

Interesting what was the course like? say the coverage, how much material was covered, supplements etc?

[quartz verge]

Calculus by Michael Spivak

[quartz verge]

no

not expository enough

[tender river]

I wanna solve some problems

[quartz verge]

bruh missed that

thats an odd thing to do in a plane

[wanton spade]

thanks :D

[wanton spade]

Long plane trip. Have to kill time with something

[quartz verge]

reading > solving problems to kill time imo

[wanton spade]

I read enough. I want to do some math I enjoy and not forced to do

[dense mantle]

no supplements (excluding like lecture notes obviously)... we had access to a draft since this was 2021 (👀)

We got up to chapter 9 -- ie, up to the galois theory chapter

yeah I think chapters 1-7. homework was like 6 required and usually 5-6 optional problems per week

[quartz verge]

gotcha

[dense mantle]

the undergrad algebra curriculum at my university is two courses... the first covers ^^^ as described and the second usually covers Galois theory up to abel-ruffini and then a topic for the second half of the semester, chosen by interest

e.g. the guy who taught the second semester this past spring taught a bit about modules

[fierce hedge]

pretty good for a first course. The book seems nice and chatty

[dense mantle]

yeah I think it's written very well for its intended audience

[thorn cloak]

perfect haha

[quartz verge]

we do be eating soon™

[gray gazelle]

if anyone here has read fundamental of mathematics by peter g hinman can he tell me his thought about it?

[hushed stream]

why 'his'

[vagrant sedge]

Hi. Not really about a book, but video lectures. Are there sets of video lectures (on an advanced undergrad, or graduate level) on numerical analysis for PDEs? I mean talking about FDM or FEM. I mean from a more theoretical numerical analysis point of view. I've looked for those, but wasn't really successful in finding anything.

[clever bough]

are there any books on measure theory with an emphasis on pictures/ illustrations?

[gray gazelle]

Axler can be considered such

It has a decent amount of pictures, but not of math

Anyway it is an elegant approach you can find it freely online

[rigid barn]

Schilling's Measures, Integrales and Martingales is pretty visual

[gray gazelle]

i'm thinking about reading it , there isn't any specific reason

[frosty basin]

https://www.amazon.com/Real-Analysis-Theory-Measure-Integration/dp/9814578541 has anyone ever used this book for measure theory?

[frosty basin]

is the book's coverage as broad as other books like RCA or folland?

[subtle mango]

based on the TOC, it looks like it’s a general text on measure theory with a bias towards probability theory

[rigid barn]

Yes, it's very broad and the bias @subtle mango talks about is insubstantial, probability almost doesn't enter into it.

[subtle mango]

jumped to conclusions when i saw “martingales” in the title, my bad

[frosty basin]

okay thanks

[sage python]

Wait what

I thought it literally phrases a lot of theorems in real analysis like Radon-Nikodym using martingales

[gray gazelle]

what are good analytic geometry books?

[mellow wren]

what do people think of the K-book as an intro to algebraic K-theory?

[wooden cedar]

Any linear algebra textbook/resources people recommend?

[tender river]

#book-recommendations message for a review of commonly recommended la texts

[nocturne marsh]

is there an algebra workbook that is full of word problems?

[gray gazelle]

Is Thomas Calculus book good for Multivariable? As introduction. I've done single variable from this book, and think about taking multi

[foggy swift]

SAT maths for the clueless is a great book

[visual oasis]

What would be some prerequisites to efficiently learning noncommutative geometry ? I'm guessing some operator theory is needed, but is there anything else ? (Conway's book seems to be the reference)

[gray gazelle]

Refer to https://www.uwo.ca/math/faculty/khalkhali/files/Beginner.pdf

Obviously you need some Noncommutative Algebra to do the Geometry, for that Majid is nice, Etingof seems to be a cool follow-up to really nail in Tensor Categories, but this is only word of mouth (it seems very difficult and fast-pased)

I don't know any operator algebras, but I think from a mathematical physics point of view (that I assume you are coming from) the above and the book titled 'Operator Algebras and Quantum Statistical Mechanics' will help (esp. if you are looking towards Statistical Mathematical Physics ofc, which NCG has a lot of applications to!)

Then, after the volumous prerequisites above, Connes book would be ideal, but there are easier references if you need a little more railway

(wait I'll make a list:
https://arxiv.org/pdf/math/0408416.pdf - A Friendly Semi- Introduction / Moreso Overview, should be accessible if you are asking such a question
Elements of Noncommutative Geometry by several people is considered the pre-Connes for people who aren't ready for such a prose yet

You might also just get farther by going deep into QFT and seeing the need for Noncommutative Geometry, but this is less direct than going straight for NCG (but NCG is of little interest in its own right, atleast relative to the tools it provides for other areas)

Then again, this is for the 'Connes' school of Noncommutative Geometry, there is also Kontsevich's approach, which I feel draws much more from Algebraic Geometry, and there is also this person (https://web.archive.org/web/20181221093452/http://win.ua.ac.be:80/~lebruyn/index.html)

The above references are more so if you're interested in Connes school. I assume for the Kontsevich, or Algebraic Geometry route, you would obviously need to atleast know stacks (and derived stacks), you would also need quite a bit of Homotopy Theory (more so rthan introductory level for sure!) as it is needed a lot in Kontsevich's work. Some people would recommend reading through HTT, HA, but that is the biggest waste of time I can imagine a mathematician can do, I would asy wait until Lurie rewrites this work via Kerodon, and focus on learning w.r.t the geometry you actually need for Kontsevich's use of NCG (which incorporates some of Lurie's work). You can find a good pathway through this stuff by Adeel Khan's response to 'how to reach research level math: derived algebraic geometry' from 2011 or so

Edit: Definitely atleast read DAG 5: Structured Spaces by Lurie. This is important for a lot of later constructions.

NCG is intened to deal with 'wild' quotient spaces, DAG to deal special situations (typically bad intersections, quotients by bad actions,. . . ),so you can see how combined the technology becomes powerful

Some fun readings for motivation:
https://arxiv.org/abs/1401.1044
https://arxiv.org/pdf/hep-th/0003006.pdf
https://www.birs.ca/workshops/2005/05w5035/report05w5035.pdf
etc... (there is too much to link, these should be the most helpful, you can find more)

Speaking of NCG, some undergrad in South America is doing interesting work trying to find the connections between C*-Algebras (and perhaps eventually NCG) and Condensed Mathematics, which is a potentially rich area (but the idea was sort of rejected by Scholze last year)

Read about their question here: https://mathoverflow.net/questions/443059/noncommutative-condensed-sets (they are still working on this, but a less strong assertation than as asked here)

[forest marsh]

Is this accessible after Precalc

[dapper root]

No

[forest marsh]

why?