book-recommendations

[restive falcon]

so maybe you were on the older spec

[lapis heart]

I am talking based on my experiences almost 10 years ago

so my memory may not be accurate, also.

[restive falcon]

you may be remembering a level

[balmy flume]

anyone know of complete solutions to spivak?

the solutions manual on libgen only contains solutions to only some problems

[rancid fjord]

Do I need linear algebra for real analysis? I shouldn't, right?

[gray jungle]

no, linear algebra is not a prerequisite for real analysis.

[rancid fjord]

Good, thanks

[marble solar]

Look at the back of the regular text

The solutions + back of spivak should have just about what you need

[balmy flume]

ah thanks a ton, didn't know there were solutions at the back

[marble solar]

yUh

[neat sonnet]

Any book recommendations for basic algebra? Talked with some math guys on here about how I barely have education in math, I need to revisit exponents, fractions, prime factors, all that. they recommended basic algebra over pre algebra because they both revisit those?

[slate quarry]

Maybe Algebra for College Students by Kaufmann & Schwitters

[sage python]

Not a book but people seem to like Khan Academy

[shell geyser]

I'd recommend having a look at OpenStax. They have free online textbooks for everything from pre-algebra to calculus. I haven't used all of them, but from browsing through, they look pretty good. If you're looking for exponents, fractions and prime factors, you probably need to go to pre-algebra, as I think most algebra books assume prior knowledge.

[undone harbor]

anyone read Edward Frenkel's book Love and Math?

The book intrigues me and i'm curious if it's a worthwhile read

[serene falcon]

im going to be taking an intro to proofs class during my senior year of hs at a state university, it’s notoriously difficult despite being a 300 level course so i want to find the best book to help me thru it

[smoky zephyr]

i used “book of proof” by richard hammack

it wasn’t super hard

[serene falcon]

the professor recommends a transition to advanced math

[smoky zephyr]

it’s legally available for free online

[serene falcon]

but some friends recommended how to prove it

[smoky zephyr]

i’ve heard of that one, i didn’t like it that much personally

i don’t think people consider it bad though

[inner token]

@rugged flower oi Mano desculpe mas si vc não se importa posso perguntar vc alguma coisa?

[warm glen]

speaking of proof writing books

id be interested in knowing if anyones read solow's how to read and do proofs

[shell geyser]

I'd also second the recommendation for Hammack's Book of Proof. Besides being legally obtainable for free, the first 10 chapters (the actual proofs part) are very accessible. Last 4 chapters are a bit harder, but they're not needed if you're just learning proving techniques.

[smoky zephyr]

chapters 11 and 12 aren’t really hard, and functions are used very often in more advanced math, so it would at least not be a bad idea to do this

i didn’t do chapters 13 or 14 though

since they looked really hard

i couldn’t even really understand chapter 14

[shell geyser]

Yeah, 14 seems pretty hard.

[dapper root]

Cardinality is something you must eventually learn, but I don’t think it plays an important role early on

Really all you need to know is what it means to be countable

[shell geyser]

I opted to skip 11 to 14 as I intend to do functions and relations when I go through my discrete math book, but I can vouch for the first 10 chapters. They're well explained and exercises are of a reasonable difficulty.

[fickle granite]

Thoughts on Spivak vs Apostol for a first time student looking into an introduction to analysis?

[frosty girder]

Spivak has an analysis book?

i can say apostol is very good

i was using it myself (i have done like 4 chapters, but i have an idea about the book by now)

[shell geyser]

I think his Calculus book is considered an introduction to analysis.

[frosty girder]

it assumes u are a little mature with math

but i would say apostols great, he also gives a few examples after each def (starting in the topology chapter iirc) and also gives tons of problems

just really nice overall

[frosty girder]

ahh

icic

[fervent lava]

Apostol calculus is what Z7 is talking about.

[frosty girder]

Ohh

i havent used that

but it seems really rigorous

too much for a calc book really

[shell geyser]

I think that's why they are using it for an introduction to analysis. I don't think Spivak/Apostle are almost ever used for introductory calculus.

[restive siren]

Question: did anyone try out Demidovich books? I see they are very cool for analysis but do not really see them internationally.

[frosty girder]

Demidovich?

never heard that name before

[frosty girder]

@grand thistle was using apostol for intro calc

but yeah idt people use them for calc either

i didnt use either of them myself for calc, i jumped straight to Mathematical analysis by apostol

[broken meadow]

demidovich problems in analysis?

i looked at it

it has a fuckton of integrals

well

just a lot of exercises in general

idk if the content is any good but it doesnt go too deep into the theory

[frosty girder]

[broken meadow]

it strikes me more as the russian version of calc 1-3 + early ode

its good that it has a lot of exercises and i trust the russian tradition in mathematics

so its probably a good book

its just not like a real analysis text or anything

[gusty gorge]

What's the difference between the undergraduate Mathematical Logic by Ebbinghaus, Flum and Thomas and the graduate book?

[granite canopy]

about $14

oddly, the graduate text is cheaper

i think you're paying extra for the goofy cover art on the UTM edition

[grand thistle]

yeah im halfway through it about

slow progress bc of school tho

doing integration by parts and substitution now

[frosty girder]

[marble solar]

Spivak is a good book. I prefer it to Apostol for the lively discussion and more exercises

[granite canopy]

spivak is funny

[shell geyser]

I haven't done Spivak, but I did like the proof that pi is irrational. I think it's Chapter 16?

[granite canopy]

spivak's calculus has proofs that e and pi are irrational and i think one that e is transcendental, although i'm not sure about the latter

there's also a derivation of cos and sin from exp, along with a proof that the functions so derived perform their desired trigonometric roles

[gray gazelle]

https://www.booksetc.co.uk/books/view/-9781108441025 | https://www.booksetc.co.uk/books/view/-9780198845355 are helpful if anyone's interested

Will these 3 books give me a solid fundation to self study pure math?

[gray gazelle]

if you need Spivak's pdf pm me I somehow found a really high quality one like realllllllllly high quality 300 ppi or smth

[gray gazelle]

how much do you know?

if you know K-12 Math then you can skip Serge Lang's book

and what do you want to do after learning math?

[gray gazelle]

kind of but not in a rigorous manner, also I need a refresher

you could do this but I need to know your goals before I suggest you something

Basically, if you aspire to study more math after this, you should do Serge Lang's book, if your sole purpose is to use math as a tool in something like Engineering or Computer Science (In CS you're better off just using a Discrete Math text) then you could just use discrete math books and take up a calculus course instead of geometry

but your list is weird in the sense you sprinkle in some geometry too, I dont see why you would need it unless you are aiming for the Olympiads

[gray gazelle]

I want to at least be on parity with a bachelors degree on math, then I want to study statistics and computer science theory, also I want to know whatever math is needed for solving stuffs like a 4th dimensional rubik's cube

[gray gazelle]

I swear I knew this but I forgot what is used in this thing

but for the former part

you're better of using a discrete math book, and before that solving some problems in K-12 Math by using AOPS's sets, they are not very hard but not easy either, it will give you a solid grounding

@gray gazelle hey

I've seen gelfand's books get praised

For hs algebra knowledge

i dont think you need a book for HS Math if you know some of it

Make no mistake

you just need to solve problems

Gelfand's algebra is difficult

[runic hatch]

You could start with Spivak’s Calculus or Apostol’s Calculus series for a more rigorous approach to calculus

[gray gazelle]

grinding on hs algebra problems for BS Math knowledge seems sub optimal

[gray gazelle]

I'd suggest:

1. First read about the topic from AoPS, and then solve problems using AoPS Alcumus, keep solving till you get to 90% to 95% accuracy (~85% will do too)
2. Pick up a discrete mathematics book or course, and solve it while simultaneously doing Calculus from some book like Adam's Calculus (if you liked discrete maths, using some book like Spivak will be good too, but the problems are very hard)

after which stuff like Number Theory and Combinatorics comes in

Oh yeah LA too

[runic hatch]

You could use Artin’s Algebra too for an undergrad math approach to algebra, once you feel confident enough

[gray gazelle]

For cs

[frosty girder]

a bachelors in maths isnt really a well defined term, since around the world there are many different ways to major in math, many of which are wildly different from the others

[runic hatch]

And yeah what a bachelors in math may learn varies wildly

[gray gazelle]

he wants a grouding in Mathematics for theoretical computer science stuff as I make out from it

[frosty girder]

still too vague

[stray veldt]

i have a pretty good idea of what a bachelor in mathematics should know

[frosty girder]

[gray gazelle]

[frosty girder]

what should one know?

i wanna know

lol

[gray gazelle]

NT, Combi, Analysis

Calculus

DEs

Topology or smth

functional analysis

[stray veldt]

real analysis up to intro measure theory (maybe some functional analysis), linear algebra, abstract algebra(groups, rings, intro galois theory), complex analysis, basic point-set topology

[gray gazelle]

Optimization, Game Theory

[frosty girder]

u dont need to know that for a bachelors

for example, i will totally avoid this

and combi

[gray gazelle]

This, I want a really solid math background to understand CS theory well

[stray veldt]

eh, you learn combinatorics anyway

[gray gazelle]

see

[frosty girder]

that feels a little less

[gray gazelle]

this

[stray veldt]

yes, this is just the basics

you will learn more

[frosty girder]

nice

[gray gazelle]

@gray gazelle discrete math
And linear algebra are needed for cs

[stray veldt]

but you should have some room for decisions

[runic hatch]

The core essentials would probably be some form of analysis and basic abstract algebra

[frosty girder]

i will homological algebra and diff geo in first sem then

[frosty girder]

yeah i suppose

[stray veldt]

diff geo in undergrad is nice

[gray gazelle]

for this, do what i said earlier, then the thing changes very quickly as you shift domains

[frosty girder]

i was hoping to do basics of anal and alg and topo so that i can move to wider things

[stray veldt]

either diff geo or projective geometry

[frosty girder]

I will do both

[gray gazelle]

but a another very basic requirement will be linear algebra and statistics

[frosty girder]

[stray veldt]

geometry is such a wide field and essential to mathematics (both now and historically)

but its hard to do it in undergrad

since there are so many prereqs

[runic hatch]

Tbh I kinda lump lin alg into algebra

[frosty girder]

[runic hatch]

But yeah you def need it too

[frosty girder]

which kinda geo?

[gray gazelle]

differential geometry he means

[stray veldt]

diff or algebraic

[frosty girder]

hmmmm

[stray veldt]

projective geometry you can do as "algebraic geometry light"

or you can do it synthetic, which is niche and i wouldnt recommend unless strong interest

[frosty girder]

I suppose i can do both maybe, just maybe

[stray veldt]

maybe a class on "algebraic curves" is nice

[frosty girder]

synthetic as in?

[stray veldt]

if you get the chance

synthetic geometry is uhh

[sick wigeon]

I am curious about what would rigorous (basic) Euclidean geometry offer

[stray veldt]

you define lines, points as primitive objects

[frosty girder]

pain and pain

[sick wigeon]

Does hilbert's book do that

[stray veldt]

and make definitions on how they relate

[frosty girder]

interesting

[gray gazelle]

So Basically I'd suggest:

1. First read about the topic from AoPS, and then solve problems using AoPS Alcumus, keep solving till you get to 90% to 95% accuracy (~85% will do too)
2. Pick up a discrete mathematics book or course, and solve it while simultaneously doing Calculus from some book like Adam's Calculus (if you liked discrete maths, using some book like Spivak will be good too, but the problems are very hard)
3. Then once done with Calculus, switch to Linear Algebra (for this use MIT OCW courses, they are better in my opinion than just a book, but for a book, use the instructor's book that is Gilbert Strang's book) and do some statistics and probability (the book recommendations vary widely depending on what type of Theoretical CS you are aiming for, but still a general pre requisite for most CS programs)

[sick wigeon]

Is it as nice as solving geometry problems or its a different thing altogether?

[gray gazelle]

What is AoPS? I am not anglo

[stray veldt]

synthetic geometry is a lot different

[gray gazelle]

you can google it, its Art of Problem Solving

[stray veldt]

its similar to how euclid argued about geometry

[frosty girder]

i wont recc aops, they feel too comp mathy to me

[sick wigeon]

I wanted to know how is hilbert's book on geometry

Has someone read it

Or have any other suggestions

[gray gazelle]

I mean this https://artofproblemsolving.com/alcumus @gray gazelle

[sick wigeon]

For a book

[frosty girder]

discrete maths calc, and lin alg are really useful yeah

[gray gazelle]

especially for CS,

I know them all 😎 except for Statistics

[gray gazelle]

Wait is this free?

yes

completely

infact for most of the things I mentioned in my para, there is a free replacement almost as good

[frosty girder]

u know linear algebra?

[gray gazelle]

enough for cs

upto eigenvalues

[frosty girder]

idk what kinda lin alg is that

eigenvalues?

[gray gazelle]

and a little bit beyond it

[frosty girder]

hmm

proof based?

[gray gazelle]

some proofs

not a lot

but some

[frosty girder]

[gray gazelle]

Is this better than khan academy? I am interested in learning how to do proofs that's why I was interested in going for those books

[frosty girder]

can you prove stuff like
dim(AV)<=dim(V) for A:V->V?

[gray gazelle]

I dont think so

[frosty girder]

[gray gazelle]

?

[frosty girder]

Alright

[stray veldt]

shyshu quizzing people

[gray gazelle]

Khan Academy is like extremely good

[frosty girder]

u wanna do proofs?

[stray veldt]

khan academy is fine

[frosty girder]

its a rare opportunity that i find someone that i can quiz

[gray gazelle]

but AoPS is like Competition Math based

[stray veldt]

after that you can read some intro proofs (maybe the one i have written) and then read actual math books

[frosty girder]

oh yeah loch u wrote an intro to proofs

[gray gazelle]

which is mostly proof based

[frosty girder]

i forget about it too much

[stray veldt]

[frosty girder]

:penzene:

[gray gazelle]

Yes, I tried an engineering degree but I disliked how everything was "learn this just because"

[frosty girder]

i see

a lot of people recc the book "How to prove it" by velleman

[gray gazelle]

you dont need to do proof based things for learn this because that

just go through the derivations

[frosty girder]

i have heard good things about it

i have never used a proof intro thing myself

[stray veldt]

😵‍💫

[frosty girder]

i just winged it

[gray gazelle]

same

[frosty girder]

and it worked (for some parts at least)

[gray gazelle]

and i dont know if it worked

because i dont care anymore

[frosty girder]

for me it worked a little

coz i can do some analysis problems here and there myself

and that makes me happy

[gray gazelle]

I learnt that stuff mostly for ML but the thing is

[frosty girder]

😌

[gray gazelle]

I almost never found it helpful

[frosty girder]

what?

proofs?

[gray gazelle]

proofs are obviously like counter productive for introductory ML

but I am speaking of all the pre requisites most courses mention

[frosty girder]

why so?

[gray gazelle]

for ML

[stray veldt]

this whats wrong with ML

[frosty girder]

i was told u need to do proof based things for ML

[stray veldt]

there are so many papers that are just

[frosty girder]

sadge

[gray gazelle]

Like the Olympiads?

yeah

but alcumus is basic stuff

[stray veldt]

we used a different way to train and get 1% better results on this test

[gray gazelle]

i used it when I was just getting into maths too, and it really helped me so yeah

[gray gazelle]

I havent read papers but I think that is very significant, like 98% is considered bad and 99% is good

[stray veldt]

i dont think its significant

and its not even a real result

[gray gazelle]

I dont know really but

speaking from personal experience

I've been roasted multiple times from my seniors

[stray veldt]

the whole field of ML grew very quickly (and still is)

[gray gazelle]

for not being able to achieve atleast 97% when I did 95%

[stray veldt]

there are lots of people in it who dont know a lot of math

and then there are people who know more math and fix the mistakes of others

[gray gazelle]

Theoretical CS and Grad level ML is just applying pure math in a way which is not applied very early

but the thing is I spent 3 months learning a shitton of math

and then none of that was useful in making my own models, like you need to know a lot more than the course says to actually code a model whose existence makes sense

[stray veldt]

i mean 3 months is not a lot

i spent 5 years getting a degree in mathematics

[gray gazelle]

considering I had only 7 months to do stuff, it is (just so you know, lord JEE was supposed to consume me after that period)

[frosty girder]

"a"? arent u a post grad

[stray veldt]

i have 2 bachelor degrees

and am currently finishing a masters

[frosty girder]

i honestly have no idea about ML things, like not at all

[stray veldt]

i dont know if this is postgrad

[frosty girder]

[frosty girder]

finishing a masters?

[stray veldt]

i am writing my thesis now

[gray gazelle]

I dont know a lot either, my experience totals to about 5 months i think

[stray veldt]

im done in ~6 months

[frosty girder]

that would be post grad ig

[frosty girder]

mine is 0

[gray gazelle]

masters thesis

[frosty girder]

i might have to learn ML stuff later on if i fail to get a job in academia

[gray gazelle]

i will be trying to do some robotics next year but incorporating it into jee grind will be hard idk

[stray veldt]

ML is very, very big rn

and a lot of math people can get into it

[gray gazelle]

yeah thats the thing

if you are a math person

[stray veldt]

because the standard CS undergrad doesnt teach enough math to do it

[gray gazelle]

you can get far very fast

[stray veldt]

currently unis are building new majors called something like "data science" to satisfy this demand

[gray gazelle]

this, and when the time comes to actually use the math they teach, most have forgot it

[stray veldt]

but honestly by the time you graduate, ML craze mightve slowed down a lot

[runic hatch]

Tbh it feels like there’s also a lot of scammy ML jobs out there too

[frosty girder]

😭

[stray veldt]

if you get a math degree, just try to get solid foundations

[frosty girder]

where will i get a job after my PhD then 😢

[gray gazelle]

what makes you think this, just curious

[stray veldt]

it will always be easy to go into a less math heavy career

[gray gazelle]

academia

[frosty girder]

im not doing foundations if i get the option

[stray veldt]

and hard to go into a more math heavy career

[frosty girder]

academia isnt easy to get a job in

[gray gazelle]

i mean shyushu, considering you are so picky about learning things math major is going to be hard (like it already is)

[frosty girder]

how am i picky

[gray gazelle]

combi? no, foundations for ML? no

[frosty girder]

foundations as in the math field

not the ML thing

and combi isnt very exciting to me

[gray gazelle]

replace "for ML" with ""

still makes sense

[frosty girder]

trust me the way i want to do maths, its anything but picky

[gray gazelle]

dayum

Shyushu, you gave KVPY last year?

[frosty girder]

Nope

i will give it this year

[gray gazelle]

nice

[frosty girder]

[gray gazelle]

So, is art of problem solving like https://www.codingame.com/start ?

[heady ember]

Wait what's ML

[proper lotus]

Usually because it is obvious why you are doing something. You want to design a stable retaining wall. Do you really need to ask why?

[proper lotus]

Are you doing TCS or ML

[gray gazelle]

It's really difficult for my brain to just memorize random formulas, it's not even me having bad memory considering I am studying 4 foreign languages simultaneously, I need to understand the core logic of everything I read otherwise I will forget it

[heady ember]

I just read Loch's short intro to proofs (in pinned msg) and went onto some set theory fun, i.e. getting bullied by basic set theory lol

[frosty girder]

[hearty ocean]

https://www.youtube.com/watch?v=QpQ0RH7Yl7k&ab_channel=TheMathSorcerer

Does anyone have any other recommended books for applied math / mathematical methods? 🙂

There are the Schaums books which are pretty good, and there is also BOAS and Riley Hobson & Benson (both of which I own)

Im a theoretical physics student (who loves math), self-studying pure math but im just looking for good problem books for mathematical methods

Possibly BOAS and RHB is enough and I should just work through those problems though

If you are able to answer thanks in advance 🙂

[heady ember]

Mathematical methods for Physics and Engineering is well liked I think

But you should check with others haha

[hearty ocean]

Mmm yeah thats Riley Hobsen & Benson (RHB), I think possibly RHB and BOAS is enough to work through, im just intimidated by the problems in them haha 😂 instead of looking for different book perhaps should just bite the bullet and work through these books to be fair

this is BOAS by the way if anyone else is interested / in need of recommendations for applied math https://www.amazon.co.uk/Mathematical-Methods-Physical-Sciences-Mary/dp/0471365807

[livid ermine]

Have anyone read the book Algebraic Curves and Riemann Surfaces by rick miranada? I've read munkres and aluffi, and have just started reading ahlfors, and really enjoy complex analysis and eventually wanna get into AG. I've heard this book is quite good. Do you need to know any differential geometry?

[sudden kindle]

I just started reading it

Its pretty good. It's good at being explicit.

[iron granite]

Any good introductory graph theory books?

[hearty ocean]

I picked up "Introduction to graph theory" by Richard J Trudeau

it covers

graphs, planar graphs, eulers formula, platonic graphs, colouring, the genus of a graph, and euler and hamiltonian walks 🙂

The first chapter is about pure mathematics in general and gives a nice description of how to think about pure maths

Ive only read the first chapter

Im not sure if this is the kind of book you are looking for

This is deffinitely an introductory book though, it covers just the basics of graph theory and the basic important topics

@iron granite youve also got this on youtube

https://www.youtube.com/watch?v=HkNdNpKUByM&ab_channel=TrevTutor

https://www.youtube.com/watch?v=h9wxtqoa1jY&list=PL6MpDZWD2gTF3mz26HSufmsIO-COKKb5j&ab_channel=MITOpenCourseWare

https://www.youtube.com/watch?v=C7YrMRdLkqo&ab_channel=Dr.TreforBazett

^_^

[frosty girder]

I came to ask, is there anything that has graph theory as its pre req?

shit memes go in #chill

[hollow shore]

[hearty ocean]

?

[frosty girder]

troll

nvm them

[hearty ocean]

ah okay

[lapis heart]

<@&268886789983436800> (deleted msgs)
688123744337920030
@big-d#0687

[frosty girder]

ok thats enough <@&268886789983436800>

[hollow shore]

nothing more than what you already know

[frosty girder]

Ooo

Noice

[lime bison]

done, thanks

[hollow shore]

@frosty girder I read your message wrong

I thought you meant to ask what are the pre reqs for graph theory

sorry

[frosty girder]

oh lol

[gray jungle]

btw graph theory has a wide variety of applications outside math
if you try to look it up you'll find out it comes up everywhere

as to within mathematics im not experienced enough to answer what domains would require it

i suppose something like knot theory

[frosty girder]

knot theory uses graph theory?

i thought it was more topological

[frosty girder]

i see

[hearty ocean]

These videos, combined with a book like the one by Trudeau, would probably be more than enough for an intro to graph theory, from there can move on to more advanced books and use wikipedia to see how the introductory topics you have covered relate to the more advanced topics:)

[iron granite]

Thanks for the recommendations.

[coral narwhal]

I am starting intro to graph theory by douglas b west, murty and bondy is the standard I believe.

[gray gazelle]

Dr. Trefor Bazett is kinda meh I think

Nothing beats a good book

[native spear]

just wondering what everyone's thoughts are on "Calculus" by Michael Spivak? I've tried to do some problems in it but they are quite difficult. Does anyone know of some resources that help guide you through this book?

[gusty gorge]

True, but is one better than the other in material, or do they contain the same level of material, and one just assumes prerequisite knowledge?

[hearty steppe]

honestly can't go wrong with Zhang's Graph Theory or Voloshin's. But if YOU REALLY want a challenge and a very insightful intro, try Bona's combo + graph theory

@iron granite

[iron granite]

Thanks for the recommendation.

[gusty gorge]

Gibbon's Algorithmic Graph theory is what I used for my graph theory course, would recommend @iron granite

[coral narwhal]

@iron granite

[worthy karma]

Any recommendations for a good book on starting Complex Analysis? In terms of courses that might be relevant, I've taken the intro calculus classes, two semesters of real analysis, and upper-div Linear Algebra.

[gray jungle]

@worthy karma

[untold bay]

Any good book on Euclid elements?

[wicked trout]

A lot of math can be expressed in those low level concepts. Function is a set of pairs, addition is an two argument function etc.. I need a book which talks about high level abstractions in low level manners. In set builder notation, quantifiers, predicates.

[wicked trout]

Yes Oliver Byrne's version. It has nice pictures.

[tight crag]

So a mathematical logic book?

[heady ember]

Enderton's elements of set theory might be a good place to start

But you can probably check out the pinned list

[glad prairie]

I have a physical copy of this, published by Taschen. Relatively cheap for a good hardcover. It's so cool

[heady ember]

Hi ryc!

[glad prairie]

Hello grass

[acoustic ridge]

Can anyone tell me the best math book for practice?

[flint forge]

practicing what?

[shell geyser]

That's too vague for anyone to make recommendations. What level are you at? What are you trying to achieve?

[iron granite]

Any books which will help me with understanding the methods used in Real Analysis?

[frosty girder]

methods used in real analysis?

what does that mean?

[karmic thorn]

A real analysis textbook with a lot of exercises I guess

Something like Pugh, maybe

[restive falcon]

complex cobordism and stable homotopy groups of spheres

my best guess without knowing what you want to practise

[smoky zephyr]

bruh

[smoky zephyr]

somewhere out there there’s a high schooler that understands this book

[flint forge]

I don't think anyone truly understands that book

Especially the end

No one but Ravenel, to my knowledge, has actually tried to carry out that technique since

[restive falcon]

i want to be able to understand it

it seems like a cool long-term goal

and then write a book more complicated

[acoustic ridge]

I want to practice tricky math problems.That book should also contain good solution and explanation

[restive falcon]

on which topic

there will be no book that covers everything

[acoustic ridge]

Algebra and geometry

[restive falcon]

ah I don't know any books

[acoustic ridge]

Oh do you know any good book on Equation and functions?

[livid ermine]

Have anyone here read Algebraic curves and riemann surfaces by rick miranda and know whether its good and what the prereqs are? I have read aluffi and munkres, and have started ahlfors, but don't know any differential geometry, is this enough?

[frosty girder]

what even is that

[restive falcon]

according to maxj, the hardest maths book ever written

[frosty girder]

that feels a little subjective, but if something has a name like that, i wont place it in anything less than hartshorne territory at all

[fluid skiff]

Can any one help why $n|Q^2$ here

[hasty eagle]

SSK

[lapis heart]

Wrong channel, read the description.

[hearty ocean]

"How to think about analysis" by Laura Alcock

Analysis is proof based mathematics the methods used are proofs

There are certain recurring themes in the proofs that are relevant to analysis

[cobalt maple]

Hello people. I'm currently studying analysis, but would like to pretty soon start some self-study of topology and measure-theory. I'll cover some basic topology in C.C. Pugh's Real Mathematical Analysis (my professor doesn't use this book, so I haven't gone through it yet), then I'd like to move on to Munkres' Topology.
I just need a good book for measure theory; I stand between a couple of choices: Terence Tao's book, Sheldon Axler's (I enjoyed his Linear Algebra book, so I'm considering also going through his measure theory book), and lastly, continuing in C.C. Pugh's book, which I also really like, but haven't gotten far into yet.

Could someone maybe give some pointers as to what they think and themselves enjoyed?

[brittle breach]

I say use Axler if you like his style

[cobalt maple]

Ok, thank you.

Oh, and if anyone has any other recommendations for books or handouts, I'd also appreciate and take them into account.

[karmic thorn]

I guess you can bypass introductory textbooks on pointset topology with the lecture notes and problems here: http://www.math.toronto.edu/ivan/mat327/?resources

[sage python]

I like Bass Real Analysis for Grad Students

Stein-Shakarchi, Royden, Folland, and Rudin are standard depending on who you ask lol

[brazen niche]

can anyone suggest a textbook on multivariable calculus that can smoothly introduce you to differential geometry, or contain some differential geometry

I just searched one looks good "Multivariate Calculus and Geometry"

[fervent lava]

Maybe the book called “Multivariable calculus and differential geometry by Walschap”.

[brazen niche]

I don't know about this book and you suggest it only because of it's title?

i mentioned the book Multivariate Calculus and Geometry because I have read some of it and it's easy to read

[fervent lava]

The book I mentioned looks a bit harder. Looking at the table of contents.

[shell geyser]

Assuming you mean all of high school math, then maybe take a look at Basic Mathematics by Serge Lang. It summarises everything taught at the high school level and the problems are decently challenging.

[gusty smelt]

Recommendations for riemannian geometry? I will have finished around 17 chapters of lee intro to smooth manifold by the end of the semester due to my class, and I have a hyperbolic geo class next sem and I eventually wanna learn kaehler manifolds, so that’s my motivation and background.

[hollow peak]

if you don't need any foundational manifold stuff (which I assume you won't), then you could probably jump straight into lee's IRM

[gusty smelt]

yeahh but its lee

[hollow peak]

the annoying part is that if you have any gaps then there are tons of weird exercises that will be annoying

I like Tu, but mostly because it's good for referencing a lot of basic constructions, but I would hardly call it comprehensive

do carmo is something that people say is good as well

[gusty smelt]

right ill look into these

ill probably end up with lie but

lee

[hollow peak]

[sage python]

Wait I thought Tu did a ton

Which Tu?

[novel iris]

do carmo

[cobalt maple]

Thank you, this looks really interesting. I had also considered Rudin as I had heard a lot of good stuff about it. I'll check them out.

[cobalt maple]

Thank you 🙂

[bold sonnet]

Hey! Looking for a book on linear programming , which explains basic variables and why we are equating zero for non basic variables ...

[gray gazelle]

Me too, if you get an answer ping me

[bold sonnet]

Yep, will do

[marble solar]

I'm a big fan of Spivak's books

Petersen's Riemannian Geometry text is pretty good, but very technical

[proper lotus]

This is the standard
http://athenasc.com/linoptbook.html

I have not read this in detail, but I would recommend it for the little I have read
https://www.amazon.com/Understanding-Using-Linear-Programming-Universitext/dp/3540306978

There is also https://vanderbei.princeton.edu/LPbook/

[distant bobcat]

looking for a book for self teaching calculus

idc if it's dense or too detailed i want something that'll help me learn what's going on and not just memorize and apply rules

[balmy flume]

3blue1brown vids are pretty good at explaining the intuition behind calculus

if you already know the computation of calculus and want to go more in-depth rigorously, there's always spivak

[balmy flume]

you might want to supplement this with khan academy practice too

[finite nova]

I am looking for a free pdf of this book

Tata McGraw-Hill 's by Vinay Kumar

[misty wyvern]

Have you tried Wikipedia

This server really likes Friedberg Insel Spence but compared to Roman they're basically babby

If you want a funny version of linear algebra maybe check out Horn and Johnson

Horn and Johnson is a real recommendation, so is FIS

Horn and Johnson is like uhh the linear algebra that underlies modern matrix analysis, FIS is probably too basic for someone going through Roman soon

HJ is a good reference it's just just purely matrix analysis. There have been recent open problems in physics and theoretical CS solved by people who just read HJ and applied theorems verbatim.

Honestly if you weren't working through Roman I'd recommend Roman, there's a big gap between basic linear algebra and that level of stuff.

Closest thing that will prepare you is abstract algebra's multilinear stuff.

[ornate shuttle]

what's the best textbook on algebra to use after gallians's contemporary algebra?

i really hate the way he treats the dihedral group

as a picture of a plane figure and its different positions in the plane

and the multiplication table

i recently found a definition of the dihedral group as the group generated by {x,y}

where x^n = e and y^2 = e and yxy = x^{-1}

this seemed like a much better definition

[karmic thorn]

I was reading chapter 26 on generators and relations just a while back, I think he does cover this aspect there.

Anyway, Dummit and Foote's Abstract Algebra is pretty extensive. If you are comfortable with Gallian you could also look into Basic Algebra by Knapp, or Basic Algebra 1 by Jacobson.

Here's a review for common abstract alg textbooks

[rocky nebula]

what's a good book to learn ordinary differential equations?

[gray gazelle]

What math textbook do american high school students use at school?

[gray gazelle]

@gray gazelle I do not recall using a textbook as much as listening to the teacher and doing online exercises. Textbooks only became a thing once I started doing pure math.

Interesting

At my school we use textbooks

here in Australia at least

[runic hatch]

I feel like high school texts generally aren’t very good

[gray gazelle]

I still want to try them

[runic hatch]

At least I don’t remember any texts that stood out to me

I got more mileage out of Paul’s Online Notes for calculus

Khan Academy is nice too

[gray gazelle]

I've tried paul online and khanacademy a long time ago, they're quite good

I should try some khanacademy practice problems

I forgot khanacademy existed

[grand thistle]

i prefer textbooks myself

but

i sometimes use like other sources like khan acadamy or wikipedia or smth similar as reference

[shell geyser]

I feel like most high school level texts follow basically the same format and there really isn't a "good" book. You can look up any books on precalculus for a good sample of what you'd do in high school.

It's basically all just introduce a concept and then do a bunch of practice problems and then move on to the next concept.

That being said, I do find textbook problems better than Khan Academy. KA is great if you want a lot of problems, but in my opinion most of them are a bit on the easy side.

[cyan prism]

do u use cambridge txtbooks

[gray gazelle]

Yes

[cyan prism]

nice

[gray gazelle]

How did you know that

[cyan prism]

bc like all of aus uses them lmao

all of aus except victoria, that is

[gray gazelle]

Mhmm

[cyan prism]

cambridge textbooks are great

especially the development and enrichment exercises

if you can do those you have a great grasp on the content

[gray gazelle]

Sometimes I do get bored doing the problems

They're good for exam preps but personally I don't find them too fun

[bold sonnet]

Thanks for your suggestion. I will take a look at them.

[bold sonnet]

.

[cyan prism]

i mean that's true for all of high school maths imo

olympiad is more fun

and uni stuff

although idk much

[gray gazelle]

Uni has fun math except olympiad math

actually I don't really much olympiad experience

[grand thistle]

i dont like olympiad math

[gray gazelle]

same

[cyan prism]

why

it's so much harder and more interesting than high school amth

[runic hatch]

Not much of a bar to clear there

[frosty girder]

based sean

[hollow vector]

it is and it isn't - it feels mostly artificial and arbitrary, but then again math works in strange ways

sometimes something which doesn't look all that interesting like lagranges theorem on squares is actually there, because of some fairly modern mathematics

i made that joke and noone has seemed to catch it

[mental flare]

hello guys, i'm gonna be participating in the national math olympics this thursday, are there any resources to help me understand and practice that kind of logic and proof problems?

[proud orbit]

u can go through these

[mental flare]

Thank you

Thursday will be phase 1

[gray gazelle]

Any book recommendations for learning functional equations with zero background?

[proud orbit]

good luck 👍

[gray gazelle]

how do you think of the book "from maxwell's equation to yang-mills theory"

[gray gazelle]

https://cemc.uwaterloo.ca/resources/courseware/courseware.html

shouldi use this

[cyan prism]

you see we don't know what lagrange's theorem of squares is

[cyan prism]

true

especially olympiad geometry

it's literally like 'see how many lines and circles you can fit into 1 config'

[hollow vector]

another example is inversive geometry

[cyan prism]

yes

[hollow vector]

secretly you can start with it and end up talking about riemann surfaces, hyperbolic spaces, discrete subgroups of PSL(2,R), special relativity, basic QM

all sorts of things

[cyan prism]

oh really

cool

[hollow vector]

yes, really you can

[cyan prism]

is that cuz in some geometries circles and lines are actually th same

[hollow vector]

Its basically because inversions are just z -> 1/z

lol

(cba to TeX complex conjugates)

[hearty steppe]

If your going to study QM, you might as well just study math mostly

Otherwise it’s just not really gona make sense

As much sense as it barely makes

[cyan prism]

whos going to study qm

not me

[hollow vector]

If? Just do it lol

[cyan prism]

one day maybe

[hearty steppe]

As long as you are spending 70% of the time studying math, QM will still be something else for that extra 30%

[cyan prism]

i'm still in grade 8 lmao

[hollow vector]

I feel like its just general education - everything is basically related to everything

[pale scarab]

Damn this is a good reminder of how little geometry I actually know.

Geometry is strange in that much of it is accessible to elementary age kids yet can offer challenges at the highest level.

[hollow vector]

Geometry is basically god

[foggy relic]

yet is very boring (euclidian)

[grand thistle]

isn't qm all about hilbert spaces or smth

[forest sleet]

QM happens on hilbert spaces but it isn't a main focus

like the hilbert space itself

isn't a main focus

[gray gazelle]

Hilbert spaces in themselves, there's an easy characterisation of them, their theory lies more in the maps between them

Is that what you mean? @forest sleet

[gray gazelle]

I'm currently going through the AS & AL math syllabus by cambridge international, and I want a proper and comprehensive book on their syllabus endorsed by them.

The subject I want is Probability and Statistics 1

I found three books - all for the same syllabus - is anyone familiar with them or can recommend one over the other?

[gray gazelle]

Im in high school, so TCS is way beyond me ngl, but I do ML

[hasty turret]

Oh,so you realised those courses are useless for anything more tha plug and chug?

If you want to learn real ML,I imagine you need a thorough understanding of stats

[gray gazelle]

I mean, basic (like very basic) linear algebra is very helpful but going very far in Linear Algebra I dont think is helpful in beginner things

stats ofcourse is needed but I kinda think I went too far with Linear Algebra and Calculus

[hasty turret]

All you need to know from Linear algebra is the definition of linear transform

And maybe rank nullity

[gray gazelle]

yeah and I finished the book by Gilbert Strang, and did some Multivariable Calculus before even trying to start ML

I think its more like my own fault spending so much time on the math, but almost everyone recommends you to finish these courses before starting with ML (Idk if this is true but when I was learning, atleast I Interpreted their advice as this, correct me if i am wrong)

[hasty turret]

Look if you want to do ML,do ML

Don't waste time on "math for ML" or something. You can google stuff for math you don't understand

[gray gazelle]

yes thats what I am saying

I also took that book Math for ML

but that was far too concise (or unreadable? like condensed?) for me

now when I was getting into robotics I considered "finishing the pre requisites" but nah I think I should learn from what I did wrong and just start doing stuff

[hasty turret]

I am still waiting for the "Quantum Computing" craze

[gray gazelle]

lol every now and then I get quantum stuff in my newsletters

[hasty turret]

If you are still planning on doing this,read a stats textbook

Even If you drop ML,it will be applicable for other fields

[gray gazelle]

I am not learning anything specifically, I am just studying physics and chemistry at the moment, but I spend my time thinking of some ideas, see if they are already implemented, if not then learn the stuff you need to make it, or if I already know the stuff, I just make it

ML might have to become a part of my next project

[hasty turret]

What's your next project

[gray gazelle]

I was actually studying fourier trasnforms when I decided to make something to convert mp3 to piano notes

now I want to do the same stuff but with guitar and its very difficult to think of a solution

[hasty turret]

ML sure doesn't seem like the solution for that

[gray gazelle]

it was very simple honestly, just a coincidence, yesterday mark rober did this thing with a real piano

[gray gazelle]

I researched a bit, found MuseNET and Magenta

both generate music randomly

I read their papers, but couldnt really think of a solution either

I will have to implement what they did and probably mess with it to figure it out, but I think because there are so many pitches you could probably map each part signal from the full signal to the notes on the guitar and this part is pretty easy

like if i play what it generates, it sounds like what the piano gives but weirder

the difficult part comes when you think of how a guitar is played (same thing is the problem with a piano too I think but they probably solve it by having multiple notes for each part like repeating the notes instead of grouping them), one stroke has to play several notes/strings (not always the case, but i am no expert on guitars)

I am a bassist

I mean I could read how a guitar works (I have played the guitar, very bad at it, but still i do know something about it), but that doesnt help a lot in accomplishing what I want too

not sure if magenta implemented the guitar but MuseNET sure did and actually there was a newer version whose name I forgot

any idea @hasty turret?

[livid ermine]

[hasty turret]

Ok,I have no idea about this stuff. Sorry

[gray gazelle]

nevermind, but you would like to have a look at jukebox,musenet and magenta (just for fun) its pretty cool

[hasty turret]

Ok,I have nothing better to do. So I will ig

Technically I am supposed to grind leetcode for interviews. But I don't want to do that

[gray gazelle]

sad

are you in the The Programmers Hangout too? I think I have seen you there

[hasty turret]

Yea

[gray gazelle]

oh nice

[hasty turret]

ML stuff seems like a safe option in case I really get bored with normal dev work

[gray gazelle]

try robots, its fun too

I kinda want to do more robotics but monee

[hasty turret]

But how practical/useful is robotics

I can see it being a thing in unis

But what about jobs

[gray gazelle]

depends, I am in High School so yeah it doesnt matter much

I forgot you are a adult

what category does that kind of stuff come in, like typing without keyboards (typing gloves?)

lemme find where i saw it

[hasty turret]

Like with a stylus?

[gray gazelle]

no wait I will show you

one second

this

[hasty turret]

Damn

[gray gazelle]

its very basic, like it works by trying to type and it pulls the strings sends bluetooth signal

[hasty turret]

Looks sick

[gray gazelle]

what category is this? Electronics engineering?

It probably is, probably not

[hasty turret]

Mechatronics ig?

[gray gazelle]

probably

yeah it is

that kinda stuff is lit too

I run out of money ever 1 month lol so cant get more into this stuff

[hasty turret]

If you are looking for this as a way to choose your degree, Don't. Most profs here are incompetent

And I heard you don't have access to labs as a student to do your cool stuff

[gray gazelle]

oh, no I am not

I just think its fun, I am from India and you probably have heard people cursing jee a lot

[hasty turret]

I know I passed jee

[gray gazelle]

what

you are from India?

[hasty turret]

Indeed

[gray gazelle]

nice

so you do understand my nick lmao

[gray gazelle]

what does this mean tho? Choose your degree?

[hasty turret]

I meant choosing your major

Don't tell me you don't know about the admission process

[gray gazelle]

I do

arent you assigned your major on the basis of your jee rank?

[hasty turret]

Well,You can choose certain majors depending on your rank

For example,AIR 50 can choose EEE,ECE or CSE in iitb

But AIR 100 can't choose CSE in iitb

[gray gazelle]

yeah

I do know about all that stuff

yeah, I am likely to choose CSE cause its pretty easy the curriculum and I already have a lot of experience with computer science stuff

[hasty turret]

True

[gray gazelle]

but how do professors come into this choosing major thing?

[hasty turret]

They don't

[gray gazelle]

oh

I still dont understand what you meant by that message

[hasty turret]

I meant this

[gray gazelle]

alright I think

I actually today itself gave the entrance to some coaching centre

I tried contacting/emailing some robotics clubs around me, but none of them responded

[hasty turret]

As in clubs part of a uni?

[gray gazelle]

uni, clubs in schools, student run clubs

[hasty turret]

I don't think they will take in people who are not from the uni

School clubs are usually not very developed,afaik

[gray gazelle]

the clubs arent but I went to a school last year, and most students had a lot of equipment, even though the school didnt lol

like they brought their own equipment

[hasty turret]

I remembered my uni has a robotics club

[gray gazelle]

damn

[hasty turret]

Apparently A club here made a car from scratch

[gray gazelle]

not even talking of a simple school lmao, it was the shri ram school (by and large the best school in all of delhi),

I think they started participating in FIRST robotics since 2021 and the school has spent some money since then

[gray gazelle]

oh and that isnt my school I just managed to get a student to invite me

[hasty turret]

I think schools are motivated by board results

Because that's what parents look for

[gray gazelle]

yeah

do you have any suggestions for some interesting stuff I could do with less budget (atmost 140 dollars or a bit more)

[hasty turret]

I am a pure theory guy,so no

[gray gazelle]

nevermind then

what do you do?

web dev? systems? ml?

[hasty turret]

@silver herald might be able to answer this

[gray gazelle]

then i think i should change the currency lol

[hasty turret]

Well, I have no clue really. I do whatever I feel like I have to do,which is mostly webdev

[gray gazelle]

I guessed so

[hasty turret]

I know a bit about low level stuff,but I suck at it rn

[gray gazelle]

low level stuff of? ML?

[hasty turret]

Like systems programming

The stuff you write with C,C++,Rust,Go ,etc

[gray gazelle]

yeah i understand

I tried to learn C++ but couldnt find how it was better than Python (except for speed) so I didnt continue after the basics

Im pretty good at web dev too but havent done much from 2-3 months

[hasty turret]

Python becomes unbearably slow in some cases where performance speed is critical. For the general use case, python is good enough

[gray gazelle]

Yeah I have seen some benchmarks of loops where python took 10 times more time, but others where it is more or less the same

you wouldnt want to use Python to run on a huge dataserver processing tons of data every second right? (im not sure)

[hasty turret]

Honestly, right now I am going through a existential crisis

[gray gazelle]

how, why?

web dev isnt fun?

[hasty turret]

I don't find it satisfying

[gray gazelle]

same

[hasty turret]

I want something more intellectually challenging

[gray gazelle]

same thing

Competitive Programming is challenging but not very useful either

[hasty turret]

Well, It's challenging but it's like a game more than something you want to study

[gray gazelle]

yeah

I like robotics stuff but that is also pretty easy

i mean obviously not the complex stuff

but basic robotics, plug in wires do some code boom and yeah debug

[hasty turret]

Actually, I think I might study topology

[livid ermine]

you should study combinatorics

[gray gazelle]

topology, interesting

why so?

[hasty turret]

It seems fundamental for a lot of subfields

[gray gazelle]

Combinatorics :lol:

[gray gazelle]

hmm

[gray gazelle]

i agree it is hard, but why

[livid ermine]

It is more useful than topology for most areas and is more problem solving oriented and thus more interesting to work with I think.

in cs related stuff at least

[hasty turret]

I am actually kind of familiar with combinatorics

[gray gazelle]

same

[gray gazelle]

I am only familiar with olympiad combinatorics

and I think Uni Combi and Olympiad combinatorics are pretty similar?

depends on your uni i expect?

No lol

[livid ermine]

I haven't seen that advanced Olympiad combinatorics, but to me those questions just seemed like very clever applications of quite elementary identities

like vandermonde and a bunch of binomial stuff

[gray gazelle]

yeah

[livid ermine]

I don't think it is all that related to the stuff you would study in a combinatorics class at a universtiy

[hasty turret]

Uni combi is less "haha random counting arguments go" and more generating functions

[gray gazelle]

I havent done much combinatorics

[gray gazelle]

hell yeah

olympiad combi is the former but harder I think

generating functions is something I see often but most people in the community dont prefer that as their first approach to the problems

I just realised I forgot a lot of combinatorics

[gray gazelle]

they are designed for the general public...

[cursive orbit]

I doubt most high school students use their textbook for anything other than problems.

[runic hatch]

Yeah they’re at best a decent source of exam-like problems

And I wouldn’t really say they’re designed for the general public

That’s more popmath territory

[forest sleet]

Yeah I mean that qm happens on L^2 but the interesting part is the operators on it

[gray gazelle]

try win binary exploitation, targets these days are hard 😄

[obsidian valley]

Does anyones school use Gallian's Algebra for problem sets & have some sort of public course page? I'm trying to find out which exercises are worth my time

Ideally for like Ch 17 - 21

So this would be a rings & fields course

I found one good one but if anyone else has one it would be appreciated https://cklixx.people.wm.edu/teaching/m430.html

[night nebula]

Anybody know any good competition math books? I just need something that has a wide variety of topics that are common in math contests. Individual books are cool too, I'm open to any suggestions

[cyan prism]

Problem Solving Tactics

EGMO by evan chen for geometry

[gentle arrow]

need good calc/linalg books
preferably ones that are nicer and simpler to understand

[smoky zephyr]

i used https://tutorial.math.lamar.edu/ for calculus

[candid sedge]

can anyone please suggest me a really good book for calculus,functions and graph, basically to study for Jee Mains and Advanced ( exams )
i have few books but they're only question packed whereas i need a book which has some good theory in it

so that i can understand it myself by reading it

[hollow shore]

https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/

https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/

[hallow oriole]

does anyone have a set theory textbook with calc or lower prereqs?

low calc

like starting Taylor series and only knows what a Fourier transform is from 3b1b calc

[karmic thorn]

Hammack's Book of Proof

[hallow oriole]

tyyyy there's even an official free version online 👀

[shell geyser]

Book of Proof is a great resource. Good choice!

[fervent lava]

It's available for free in his website, just type book of proof by Hammack online.

[heady ember]

You could try Enderton's Elements of Set Theory as well

[hard canopy]

Hello, i am a physics student and i want to study mathematical physics. So, I started to learn some pure math on my own. Rn im studying real analysis. I am taking differential geo class in school and also studying a little algebra on my own. My end goal is functional analysis for now. What kind of path would you recommend to reach to the functional analysis? Which topics should i study before that

[sage python]

Presumably you've got linear algebra down cold, especially Euclidean/Hermitian spaces, eigenstuff, and the spectral theorem.

Then yeah real analysis is good, diffgeo is less necessary but you're probably pursuing it out of independent interest in GR or smth. Algebra is good for health if not something that's likely to be explicitly referenced in functional analysis (unless you do some representation theory at all)

I'd say depending on how you go about things, measure theory may or may not be important. Brezis is the book I'm most familiar with for functional analysis post-measure theory, and that has a PDE angle. Kolmogorov-Fomin is the one I'm most familiar with pre-measure theory, it's pretty good foundationally.

If you're interested in links to quantum mechanics, I believe the idea of a C* algebra is particularly important for that purpose, so it may not be a bad idea to look for sources that zoom in on that in particular

Pretty sure C* algebras were an idea developed as mathematical formalism for quantum mechanics

[hard canopy]

Yes

[hard canopy]

I see thanks, I actually haven't seen linear algebra as a pure math course but i think i have a decent understanding on it but i can read a textbook ofc.

[hard canopy]

Yes i do, actually that's why i want to learn it. So I'll finish the real analysis lecture series frome somewhere, then i can look it up on some measure theory.

What about topology?

First time seeing the C* algebra, interesting

[sage python]

Ah true, I guess depending on how you go about the analysis you do you'll prob learn the topology needed on the way

[tame pivot]

what are some good rigorous calculus 3 textbooks?

ones that arent necessarily limited to R3 and has linear algebra as a pre-req

i've learned calc 3 in R3, but i want to understand it more rigorously

[cursive orbit]

Analysis II by Zorich

[tame pivot]

thanks, should I read analysis I by zorich before that?

or is it not necessary

[cursive orbit]

it shouldn't be necessary if you are familiar with calculus already

[tame pivot]

kk

[sage python]

Spivak Calc on Manifolds is good

Shifrin Multivariable Mathematics includes the linear algebra that it does

[tame pivot]

would i need to learn topology before going into spivak?

[sage python]

Nah

[tame pivot]

kk

[royal jay]

Anyone have recommendations for convex optimization? I already have Boyd. Having some trouble

[gray gazelle]

read diary of a wimpy kid

very good

[fluid bay]

is that your recommendation for convex optimization?

diary of a wimpy kid 2 was great for homological algebra. can confirm

[timber mesa]

great pop-sci novel

[plucky shell]

I would say that this topology book is also really good for beginners

Explains things easily

[fluid bay]

remember, topologies are glorified semi-lattices

[timber mesa]

I was just memeing I don't actually like Munkres

but yeah Mendelson is a nice-ish book

[dapper root]

That's an old one kxrider

[fluid bay]

oldy but a goody

[plucky shell]

Topology is stretchy geometry (Please don't attack me, I made that joke on twitter, I still haven't recovered)

[smoky zephyr]

i thought it was loose geometry

or something

[dapper root]

did you actually get owned on twitter for saying that??

[plucky shell]

Yeah

[dapper root]

Also topology is in a weird spot cuz, in a sense it's kind of just rubbery playdoh geometry sort of

[plucky shell]

yeah

[dapper root]

but that's like, after a while

and only if you like do low dim topology or something

so many fields use the basics of topology, but it's either just like euclidean stuff, or just kinda formal

if you pick up munkre's it will not look like that at all forever

[plucky shell]

sitting in intro to topology lectures is "doughnut and coffee cup same thing OwO"

[dapper root]

it's just axioms

blah blah sets inverse image

here is what Hausdorff mean

[fervent lava]

Are there other subfields of topology besides point set and algebraic topology?

[dapper root]

I mean

[timber mesa]

differential topology

[plucky shell]

yeah

[dapper root]

there's like low dim topology

[fervent lava]

Yeah, forgot that one.

[dapper root]

but I think as far as pure topology goes there isn't... a lot?

[plucky shell]

is there higher dimenisonal topolgoy?

[dapper root]

I think a lot of it is fused with other fields a bit

[plucky shell]

like for string theory

[dapper root]

I don't know the details but

my understadning is dim 0,1,2 are easy

[timber mesa]

also areas where a specific kind of topological space is studied, e.g. trees or Peano continua

[dapper root]

dim 3,4 which are low dim topolgoy are hard

[timber mesa]

but as active research yeah there isn't a ton

[dapper root]

and past that it becomes easy again for whatever reason

I think string theory focuses on geometry more

so like symplectic manifolds or something

[plucky shell]

I guess, yeah

[dapper root]

calabi-yau, Kahler, etc.

[fervent lava]

The topology used in first year analysis would be point set right?

[dapper root]

yeah

all this is pointless anyway, no intro point set class talks about sober spaces

irreducible sets

generic points

You have to develop that while you learn algebraic geometry

[plucky shell]

Yeah, I agree

[dapper root]

smh

also at a certain point you don't even use topological spaces, smh my head

[mint mountain]

Pointless topology

[mint mountain]

High dimensional topology generally means the topology of manifolds of dimension > 4. In dimension < 4 it is not so hard to prove that topological manifolds can be smoothed, reducing the problem to differential topology or combinatorial topology, but in high dimensions it is hard to prove even that there are only countably many compact manifold

[gray gazelle]

just found a good lecture notes for all the basic pure maths theoretical physics students should know, beyond that, the approach is good he linked things very wellhttps://knzhou.github.io/notes/mat.pdf

[misty wyvern]

cool notes, I'll be referring to them to ungrads

[marble solar]

It's almost solely LDT

That streches and plays with manifolds, like clay

[shy compass]

i thought symplectic stuff was more topology flavoured than geometry? since there are no local invariants (curvature, so on)

[dapper root]

I mean idk it’s still geometry

Or well

Some ppl call it symplectic topology

Some call it symplectic geometry

¯_(ツ)_/¯

[shy compass]

yeah I never found a reason for that divide

[flint forge]

ive heard people say symplectic is like

a weird middle ground

where its too structured to vibe like most topology

but too unstructured to be geometry

personally anything strong than homotopy is geometric

[stark stratus]

Nichodemean Ethics

[tiny stone]

guys dont you think stewarts precalc goes overboard kinda?
im recommending precalc resources for my friend, i wanna refer him to a yt series and an aops precalc book (what i used), but hes planning on doing stewarts precalc, i took a look and its 1k pages
i also dont know the content of some of the chapters

[fluid bay]

1k page books like that are not really designed for self-study. If its just precal, than yea, a yt series and/or khan academy is just fine

[shell geyser]

I think a lot of US high school textbooks do have a tendency of being very long. I did use Stewart and I thought it was pretty good, though it is arguable if it's necessary. Realistically, you probably don't need to do all the topics in Stewart to do calculus.

Though if your friend isn't very inclined towards mathematics, I think something like Stewart which explains and gives a crap load of examples is probably an easier read than an AOPS book.

[misty wyvern]

I'm happy to call symplectic geometry geometry, but the people who do boundary field theory stuff likely know it via alg top machinery.

[wintry current]

Hello guys, I know this isn’t a book recommandation request but I’m looking for some good blog that shares articles about maths (any advanced level) that would help me expand my knowledge (any field). Thanks !

[frosty girder]

wow, didnt know i have already done homological algebra

[robust heron]

[gray gazelle]

what is homological algebra?

[quick hornet]

do you know what homology is

[gray gazelle]

In topology?

[quick hornet]

youre a different person

[gray gazelle]

I just wondered what you meant

[quick hornet]

im probing whether the question is 'what is homology' or 'what sets homological algebra apart as a distinct topic rather than part of alg top'

[flint forge]

homological algebra is the process through which one computes homotopy groups of spheres

it has no other purpose

[quick hornet]

like the difference between "what does 'commutative' mean?" and "i studied commutative rings in abstract algebra, what makes commutative algebra different?"

[gray gazelle]

Not homology groups?

[flint forge]

the homology groups of the sphere require significantly less technology

[gray gazelle]

Also I thought there are different theory of homology, also outside of topology

[flint forge]

(i am mostly joking, by the way. homological algebra is very useful outside of what i use it for)

[candid sedge]

a book for calculus pls recoommend

im not in college yet

[flint forge]

pauls online math notes or khan academy are the most common recs here

[gray gazelle]

I've used paul's notes myself in high school, they are pretty nice

[candid sedge]

no like i have completed the calculus at school level

i guess

but i want to learn what they teach in college too

[flint forge]

You could try out the book Calculus by Spivak

[candid sedge]

but i also want a book which has theory in it

[flint forge]

Thats a much more advanced version of calculus

Yeah

it sounds like you'd enjoy spivak's book

[candid sedge]

not one where its just filled with question

[candid sedge]

oh

would i understand it by reading ?

[flint forge]

Yes. In theory you can read it without any calculus background at all

But its a little hard

compared to other things you've seen before, probably

It's much closer to proof based mathematics than normal calculus

[candid sedge]

oh

yes im interested in calculus

[wintry current]

Everybody ignored my request

[candid sedge]

like not that i know much about it yet

but am interested in learning it

[candid sedge]

you could see youtube videos instead

for good problems

[flint forge]

I'd need to know your interests and level first, probably.

[wintry current]

Oh, like?

[flint forge]

Quanta is a decent place to start

but also

[candid sedge]

3brown1blue or something like that

[flint forge]

quanta is kind of bad

[wintry current]

Mm

[flint forge]

I'd say take a look at spivak and see if you like it pigen

[wintry current]

I am at at the advanced level

[candid sedge]

sure i'll go with soft copy at first

[flint forge]

My university used it to bridge the gap between high school and more serious math

You can also find it online

[wintry current]

Okaay thanks a lott

[flint forge]

This could mean a lot of things.

Are you a Ph.D. student, for example?

[wintry current]

Umm

Middle university

[flint forge]

Gotcha

Okay, Akhil Mathew's blog climbing mount bourbaki, The Higher Geometers blog (idk his name), Terrence Tao's blog, and Qiaochu Yuan's blog all come to mind

Those are the ones I tend to come across anyway

If you're in university I'd recommend never looking at quanta

I should write a blog

he says for the 100th time

[wintry current]

Oh right

Thanks a lot

I’ll take a look at this

[candid sedge]

im from india and have completed the calculus they have till 12th standard @flint forge

so am i equipped with enough knowledge

to understand the book you recommended ?

or do i need to get better and then proceed

[flint forge]

I think you can give it a go

Maybe find an online version if you don't want to commit the money and then buy it later

I promise spivak won't mind 🙂

Worst case scenario you decide to come back to it later

[candid sedge]

yes im gonna do that first

thanks for the help

[frosty girder]

the number of indians here never seems to go down

anyways, yeah u probably are good enough for spivak

[tame pivot]

every day the number of JEE conversations increase

[frosty girder]

they will increase a lil more soon

[tame pivot]

is it jee season

[frosty girder]

since jee is next month (at least part of it)

yup

[tame pivot]

i see

[frosty girder]

it is prime jee season

and i will have to suffer through it 😢

[proud orbit]

book rec for number theory? i'm in 10th grade and i don't have any previous knowledge about it...so, a book with basics would be good

[stray veldt]

silverman a friendly introduction to number theory

[orchid musk]

I think Gareth jones elementary number theory is fantastic

[proud orbit]

is david m burton elementary number theory good?

[novel shell]

any multivariable/vector calc self study textbook recs?

[fervent lava]

Have you studied linear algebra?