book-recommendations

[obsidian valley]

in case his latex editor gets lost, duh

[hollow jetty]

Jacob Lurie vs Ed Witten

[gray gazelle]

oh christ it's 216

sunk cost

[hollow jetty]

Math-olympics

[obsidian valley]

just found a mathematical logic text that doesn't mention definability once

Ebbinghaus

[gray gazelle]

post the pdf

so i can look at it

[obsidian valley]

they do mention "minimal models"

[ripe granite]

minimal model program looks dope

[obsidian valley]

Different sort of minimal model xd

[ripe granite]

(i am trying to move the conversation away from logic)

[obsidian valley]

M minimal iff every definable subset of M is finite or cofinite

I'm getting bullied

[ripe granite]

[gray gazelle]

sorry brofibration

if jesse and ultra are in the same channel it's logic time

just as if sham and i are in the same it's geometry time

[obsidian valley]

It's the only math i know tbh

[hollow jetty]

This is me but with geometry 😂

[gray gazelle]

(and by geometry i mean shamrock talking about lie groups and it all going over my head)

[obsidian valley]

I got about 2 pages into the Zilber paper before realizing I am not qualified to read it

Okay maybe 3

[ripe granite]

what kind of geometry?

[obsidian valley]

Well I'm also not sure if it would be entirely productive, I'm just looking for proofs that models are minimal

[gray gazelle]

kahler manifolds..........

[obsidian valley]

I assume I do induction on formula complexity but

[hollow jetty]

Complex and Kahler stuff

[ripe granite]

noice

[hollow jetty]

Because physics 😛

[ripe granite]

noice?

[gray gazelle]

more geometry for me to eventually learn

[hollow jetty]

Atiyah Singer ❤️

dies

[fast portal]

Why does this atiyah guy keep changing his last name

[hollow jetty]

That is used so much.

[fast portal]

lol

[dense pewter]

algebraic geometry when?

[marble solar]

that was me

yA that was dumb LOL

I thought it was one guy!

[hasty turret]

X Æ A-Xii

[hollow jetty]

BTW, not a book but The Moment Map and Equivariant Cohomology by Atiyah and Bott is one of my favourite papers and I have it pasted on my room door. ❤️

"THE PURPOSE of this note is to present a de Rham version of the localization theorems of
equivariant cohomology, and to point out their relation to a recent result of Duistermaat
and Heckman and also to a quite independent result of Witten. To a large extent all the
material that we use has been around for some time, although equivariant cohomology is
not perhaps familiar to analysts. Our contribution is therefore mainly an expository one
linking together various points of view. "

[ripe granite]

by equivariant cohomology do you mean the borel stuff

[hollow jetty]

Who calls their 28 page high-octane paper a note?

[ripe granite]

or the stuff with mackey functors

and RO(G) grading

[hollow jetty]

I guess? I think of it as "group action-valued" cohomology.

[ripe granite]

right

so Borel

[hollow jetty]

I don't know what Mackey functors are.

[ripe granite]

Well you can obtain an example of a mackey functor from any G-module

If you have a G-module A

then for all subgroups H you can look at the fixed points

if H<K you have the corresponding map on fixed points

but you can also go the other way by averaging over K/H

if you combine all that data together you get a mackey functor

and these sorta play the same role as abelian groups

you get cohomology theories valued in mackey functors

on G-spaces

and the cool part is there's a cohomology theory is graded over the representation ring of G

and you still have the usual suspension isomorphism

where you smash with a sphere with a G-action corresponding to a representation of G

apparently this stuff is of interest

turned up in the proof of the kervaire invariant problem

[hollow jetty]

Well, {subgroups of G} -> R-mod looks like something that would be interesting to a representation theorist

[ripe granite]

number theorists too ig

Neukirch had a couple of exercises on mackey functors

[hollow jetty]

I avoid number theory like the plague 😨

[ripe granite]

turns out we dont avoid the plague much

[hollow jetty]

Here in australia, we definitely did.

[ripe granite]

fair enough

I thought number theory was boring and dry too

neukirch chapter 4 changed my view

(i think that's the right chapter?)

the one on class field theory

[hollow jetty]

Maybe I don't have the bandwidth since I am half a physicist.

[valid moth]

physics? then why not do NT 🤔

https://en.wikipedia.org/wiki/Primon_gas

@hollow jetty

[calm crane]

i still dont get why care about this tbh

[ripe granite]

zeta functions?

[quick hornet]

physics

[calm crane]

[hollow jetty]

Haha. You've got me there. But the zeta function isn't necessarily owned by number theory, is it?

[stray veldt]

it always depends on your goal, certainly you have to do some exercises at least to understand, but velleman has a lot and doing all is not necessary to do other (more fun, imo) math

[hearty steppe]

Are there other intro level books you think are more interesting especially after Velleman level

[stray veldt]

you can just read an intro math book (real analysis, linear algebra, discrete stuff)

(even abstract algebra in theory)

[marble solar]

I think the next step is baby analysis + linear algebra

[stray veldt]

ye, thats the standard stuff

preparing for analysis is one of the reasons i included a short part about inequalities in my writeup

[marble solar]

I'm a champion of Spivak

Calculus, but it has detractors here

[hearty steppe]

Detractors?

[hearty steppe]

I am considering reading Spivak calculus even tho I already learned 3 semesters of calculus

[vernal pilot]

does anyone know any book for the study of discrete mathematics?

[velvet briar]

I liked Oscar Levin, which was a free pdf on Google

It's an intro so if you want deeper this ain't it.

But if you're looking to enter, the book is easy

[vernal pilot]

Yes, it's for introduction

thanks

[gray gazelle]

Intro - Discrete math and its applications by Kenneth Rosen
Advanced - Concrete math by Donald Knuth

[hearty steppe]

I used Rosen. But I mean if there is an easier book, go with Levin in that case. I remember Rosen being good too

[marble solar]

I like the schaum's outline to discrete mathematics

[broken meadow]

ooh im gonna be using rosen next semester

chad Donald Knuth tho..

[karmic thorn]

Is Discrete Math an essential course for math majors? I suppose its contents are covered implicitly/explicitly in other courses?

[stray veldt]

short answer: no

[sage python]

Discrete math isn't the most standardized class tbh

[sudden kindle]

I wish there were a cool intro combo course

At my school

But no

[sage python]

Definitely some topics like number theory are largely subsumed by algebra, others like graph theory aren't vital

[sudden kindle]

[sage python]

PTY: that's sad, combo was my favorite course in undergrad

Or at least tied for it, but it might just be standalone number 1

[sudden kindle]

Ikr

For me my fav undergrad course was Algebra 2

We did a little bit of galois theory a little bit of module theory and a little bit of rep theory

[sage python]

Ooh nice

Yeah my algebra class was eh tbh

[sudden kindle]

The prof used no text book, but pure Russian lecturing

[sage python]

I liked the subject going in but I think if that was my intro to algebra I would've been an analyst now no question

I mean I'm kind of an analyst but

I would've disliked algebra

Thing is I learned linear algebra from my combo prof who made it so much fun, and I had gotten real into group theory by then

[sudden kindle]

Oh that's cool

[sage python]

But yeah that algebra class had garbage pacing, and the TA was real bad

[karmic thorn]

Weird, my uni doesn't introduce Linear Algebra till the 5th semester.

[stray veldt]

[karmic thorn]

And the uni covers abstract algebra and much of real analysis, diff.equations by then.

[steel viper]

hurb

[sudden kindle]

I think linear Algebra is a good intro to math course

Linear algebra + intro to real analysis are good 1st year courses

[karmic thorn]

Mine are Calculus(a bit more rigrous compared to HS but not quite analysis, Thomas' Calc kinda stuff), Analytic Geometry and an elementary course on Set Theory and Number Theory.

[obsidian valley]

All before you do LA?

[karmic thorn]

Yeah

[obsidian valley]

God I keep reading analytic geometry and expecting some advanced field

but it's literally like pre-calc

lol

europeans smh

[karmic thorn]

It's a weird analytic geometry course

[stray veldt]

analytic geometry can be done in a intro linear algebra way

[karmic thorn]

Kinda goes into 3D so not precalc

But doesn't get into transformations, etc. so not advanced either

I like Coxeter's presentation of geometry

[odd oracle]

This guy Nielsen co-wrote "Quantum Computation and Quantum Information", and did a video series covering about to the end of Chapter 2.
https://youtu.be/X2q1PuI2RFI

[smoky surge]

If I’m interested in network analysis where do I start

[hearty steppe]

Probably graph theory

[rancid bobcat]

Is this book from #books-old
good way to get into discrete mathematics on my own?

Classic Set Theory: For Guided Independent Study

[limpid gazelle]

wrong channel

[heavy barn]

Wrong server

[soft terrace]

anyone know a good book for stochastic partial differential equations?

[fiery urchin]

Hi guys can anyone recommend a good book that covers grade 10-12 maths? I am currently an undergrad student but realise I dont have fundamentals learned well enough to progress due to lack of interest in maths in past years.

I have also looked at the recommended books section but they seem to be for more advanced topics

[gray gazelle]

Aops books are good for basics, you can have a look

[fiery urchin]

Ok thanks

[sterile pelican]

Books from Gelfand's, Algebra, Geometry, Trigonometry, Functions & Graphs, and Methods of Coordinates are great books to read (they are all fairly thin do not feel intimidated by their numbers). Another one is Serge Lang's Basic Mathematics, which reviews all the aforementioned concepts.

[gray gazelle]

Serge Lang Basic Mathematics is more like a lookup manual though

I wouldn´t go through that entire thing

[sterile pelican]

I agree it is a good for reviewing concepts but I did not do the entire thing (using it as a primary text is not really that good)

I'd prefer Gelfand if possible but Lang is still pretty neat

[fiery urchin]

Thanks guys very helpful much appreciated

[hollow jetty]

I am a fan of Tao's Analysis as an intro to maths. It goes back to the basics and talks about what a number is, what an axiom is, Peano, ZFC, how to write a proof, etc. One of his propositions is literally "4 is not equal to 0"

[obsidian basalt]

Really?

[karmic thorn]

I'm using it rn, I second the suggestion.

[obsidian basalt]

I am planning to start with analysis soon (once i am done with discrete maths or abstract algebra, whatever i finish first). I was going to start with Tom Apostol (that is the name?) Book for calculus

But i have also tao's analysis

Should i go for tao's analysis?

[karmic thorn]

Have you done some calculus before?

[obsidian basalt]

Yes

[karmic thorn]

Then you can definitely start with Tao's Analysis.

[obsidian basalt]

Never reached stuff like doing triple integrals or things like that :/

[karmic thorn]

Multivar calc isn't a prereq for volume 1 at the very least.

[obsidian basalt]

But pretty solid basic experience with limits, series, derivates and integration (basic calc 1 from a non math major career knowledge)

[karmic thorn]

Sounds good enough.

[obsidian basalt]

I am exciteeedd

[karmic thorn]

Even if you feel like you're lacking the background anywhere, use any standard calc textbook like Apostol to fill in the gaps.

[obsidian basalt]

Thanks for letting me know I can try tao's analysis

This makes me happy haha thanks

[gray gazelle]

our teacher has actually urged our batch to study Tao's analysis

[hollow jetty]

I would even go so far as to say that you could use it without having done much calculus.

I supplemented with Pugh's Real Mathematical Analysis and Spivak.

Spivak feels a bit more like preparing for a maths comp to me, in terms of the flavour of exercises.

Pugh is a bit more sophisticated. Does things like construct the reals with dedekind cuts (as opposed to Tao's limits and decimal expansions)

Which felt like a magic trick to me at first.

[mossy flume]

Are Dedekind completeness and cuts not the standard way to construct R?

[hollow jetty]

He has exercises taken out of Berkeley(? iirc) quals

[hollow jetty]

shrug it's just not how Tao does it I guess

[mossy flume]

Hm ok

idk I just learned about Dedekind completeness a couple days ago and how R is on the only set (up to isomorphism) that obeys certain properties related to Dedekind completeness

[stray veldt]

eh

tao uses cauchy completeness

that and dedekind cuts are standard

[mossy flume]

Hm ok

[stray veldt]

cauchy completeness is more general, because you can complete any metric space with it

[mossy flume]

Seems like some stuff to look forward to in real analysis

[molten wave]

there's like 2 widely accepted standard constructions

and then some more fringe ones

for example you can construct R without constructing Q, by talking about almost-linear functions on Z

[mossy flume]

Oh really? That's cool

[molten wave]

the set of functions whose nonlinearity is uniformy bounded

modulo difference being uniformly bounded

that's R

[mossy flume]

I don't fully understand Dedekind cuts but that's a question for another channel

[molten wave]

pointwise addition gives addition, composition gives multiplication

proving anything useful in this construction is very difficult though

[gray chasm]

Hi! One of my friends recently wrote an precise introduction to analytical number theory. I felt this is the right place to share his work. URL: https://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvYy8zLzljNDRkYmJkZmVlYmZkZTQyMTE3NWRkOThiYjliY2MyMzAyZjBlLnBkZg==&rn=QW5hbHl0aWNfTnVtYmVyX1RoZW9yeS5wZGY=

This handout focuses on problem-solving.

[wooden sparrow]

How's gilbert strang for intro to linear algebra?

compared to friedberg/insel/spence?

[quartz pawn]

Friedberg is more proofs-based

If you want a more theoretical understanding of LA, then it's the better book

[wooden sparrow]

Okay

What about halmos?

[quartz pawn]

Haven't used it.

[gray gazelle]

How is Hoffman and Kunze compared to Friedberg?

[polar tulip]

dont know anything about friedberg, but H&K is pretty comprehensive, i think it takes a bit of mathematical maturity to read

but it's an awesome book

[quartz pawn]

Friedberg takes some mathematical maturity to read, but you can probably pick it up along the way. If you've taken a course in basic proof methods then you won't have any problems really.

[dapper root]

Has anyone used Gortz and Wedhorn's Algebraic Geometry I? I've heard it doesn't treat cohomology which is supposed to be in the eventual sequel, but that it is very very thorough with the theory of schemes (more than Hartshorne) and has easier exercises. I'm thinking of getting it for Christmas as a companion to Hartshorne.

[bronze igloo]

haese mathematics methods

[grave egret]

I have good tip. Everyone recommends Rudin analysis book. That book is very hard. I suggest you use the book found in #books-old called "measures integrals and martingales". It goes fast enough but at the same time makes sure you understand it. For an introduction to real analysis, I'd say its very good unlike rudin's which is too advanced in my opinion.

[sterile pelican]

how about books like Tao's Analysis?

[gray gazelle]

good.

[unkempt grove]

does anyone know/is using this book?
"John Hubbard Barbara Burke Hubbard - Vector Calculus, Linear Algebra, and Differential Forms A Unified Approach 5th ed."
libgen doesnt have its solution manual and slader doesnt even have the book listed

[drifting elm]

my school website linked to this other website with free license text books https://open.umn.edu/opentextbooks

[quartz pawn]

@drifting elm thanks

[sudden granite]

does anyone have a pdf of calculus for the practical man

[gray gazelle]

check libgen

[drifting elm]

or $8 kindle

[gray gazelle]

why pay when you can get for free

[drifting elm]

you have options

if I promote people paying authors and publishers then I have done my best effort

but in the end only you can decide what you do

[gray gazelle]

i get what you mean

but they only get royalties

[drifting elm]

it is deeper than that

[gray gazelle]

so they are earning money eitherway

[sudden granite]

i found it

[drifting elm]

we are also pulling this place down every time we promote something with a liability

[sudden granite]

no worries

someone copied a version from a kansas library

[gray gazelle]

oh lol

[gray gazelle]

what smh?

i didnt understand what you are trying to convey pardon me

[drifting elm]

if you own a forum that allows distribution of copyright infringement then you the owner of the forum can be forced to pay legal expenses to defend your section 230 even if you are innocent.

or you can shut it down.

or default and pay for all the books even if you had no involvement

[gray gazelle]

i dont own the forum

[drifting elm]

exactly so what does it matter then

[gray gazelle]

so why should i be bothered

[sudden granite]

whats a good book for multivar

[drifting elm]

I could say something but I don't want to tell you that you are wrong. if you don't see the wisdom in what I said then there is nothing I can say that will change your mind

[gray gazelle]

actually speaking piracy is encouraged by anime/film agency

[drifting elm]

do you know why youtube is constantly removing content for copyright?

[gray gazelle]

cause business wise their business is in merchandising

[drifting elm]

because if they didn't they would be deleted from the internet

they would not exist

no more youtube

[gray gazelle]

youtube doesnt wanna die

[drifting elm]

the publishers are a hammer, every server is a nail

[sudden granite]

hi very quickly

[gray gazelle]

i dont really know

but shouldnt your age children be eating sand in your age(joke btw)

[drifting elm]

also, youtube does zero merchandising

[gray gazelle]

you are in 10th and trying multivar calc nice

[sudden granite]

eh for future reference

[drifting elm]

and if you think anime companies encourage piracy let me introduce the case of suzy lu

[sudden granite]

next yr i'll start

[gray gazelle]

ah has she even been striked

[drifting elm]

she has been sued big time

[gray gazelle]

https://lifehacker.com/how-piracy-benefits-companies-even-if-they-dont-admit-1649353452

[drifting elm]

maybe she just needs to tell them that it is ok and all the lawyers will agree with her? LOL. in reality there are laws.

[gray gazelle]

take old games in case

do you want them to be lost to time

are roms really bad

if they preserve history

[drifting elm]

that site says "piracy can sometimes have its benefits"

[gray gazelle]

cuz that is also a form of piracy

[drifting elm]

but it is not written by a lawyer and he fails to mention the other side

[gray gazelle]

i have only pirated a few books in the past

[drifting elm]

"piracy is a crime that could get you fined, sanctioned, fired, or indicted"

[gray gazelle]

and i agree it isnt an ethical thing

[drifting elm]

there is an interesting theory that ethics are made up

but laws are real

[gray gazelle]

galois actually it is the distributor that gets in trouble

not us

[drifting elm]

that is not true

[gray gazelle]

cuz distribution is a crime

[drifting elm]

you should ask a lawyer

do you even know what that is?

[gray gazelle]

anyways i agree it is illegal

[drifting elm]

and do you think that is the only crime that can happen?

there is also conspiracy, rico laws, DMCA, promotion, solicitation and many more

[gray gazelle]

anyways i dont pirate shit anymore

so i should not really worry

i have stopped it since 4 years

[drifting elm]

I'm not telling you what to do but if you love this place then don't make it a place for pirates to pirate

[gray gazelle]

ok

ok

[drifting elm]

we cool

[gray gazelle]

yup

@sudden granite how do you plan on studying multivar calc

before learning regular calc

[sudden granite]

im not learning it rn

[gray gazelle]

oh

[sudden granite]

i'll save for later learning

[gray gazelle]

i have to learn integration next year

[sudden granite]

probably this time next yr i'll start reading

[gray gazelle]

i have been putting it off for 1 and a half year

[sudden granite]

rn i am reading langs basic mathematics

[gray gazelle]

i am still ahead so i shouldnt be crying

[sudden granite]

once im done i'll read a calc book

[gray gazelle]

nice

calc limits and derivatives are fun

but i dont find integration fun

so i keep on putting it off

one day i will force my dad to sit with me and force me to learn

[sudden granite]

i could avoid integrals

[gray gazelle]

wdym?

[sudden granite]

there are 2 courses at my school

one with integrals

[gray gazelle]

how will you anti derive

[sudden granite]

one without

[gray gazelle]

and find areas

[sudden granite]

basically i could avoid integrals but that seems like a waste of time

because i'll need to basically do the same course again

+integrals

so i would rather do integrals next yr

[gray gazelle]

do derivative+integration

[sudden granite]

and do mulivar in 12th

yeah exactly

[gray gazelle]

trust me it is better

[sudden granite]

and in college i'll be doing differential equations/ linear algebra at first

[gray gazelle]

oh college i am dropping maths

i have no choice

[sudden granite]

i like engineering

[gray gazelle]

in bcom

[sudden granite]

oof

i think mechanical would be fun but i dont think there is a market for that where i live

i need to get into tech

so maybe i'll go into electrical engineering

[gray gazelle]

i am trying to get into fin tech

fin tech- financial technology

[sudden granite]

nice

that sounds fun

[gray gazelle]

it is gonna be hard

[sudden granite]

i like mechanical but at the same time i dont want to spend 30 yrs sitting at a desk designing stuff in CAD

[gray gazelle]

CAD?

[sudden granite]

computer aided design

[gray gazelle]

oh

[grave egret]

W o w

[sudden granite]

stupid embed

smh

[gray gazelle]

you created this

wow

[sudden granite]

no

its some random thing

this is for a motorcycle i think

i forget what its called

[gray gazelle]

CS is a good profession ngl

i dont know if you have learnt coding

[sudden granite]

Dad i want to spend my life designing car engines

🌝

[gray gazelle]

have you?

[sudden granite]

no

ive built a "motorcycle"

[gray gazelle]

not learnt coding

[sudden granite]

i know javascript

[gray gazelle]

oh wow

i know it too

[sudden granite]

and some c sharp

[gray gazelle]

i only know java basic

[gray gazelle]

like inheritance and shit

[sudden granite]

dude this is actually pretty cool

[gray gazelle]

have you learnt autoboxing unboxing

encapsulation

[sudden granite]

no

java things

different from js

[gray gazelle]

wait wait

[sudden granite]

js is for web

[gray gazelle]

i am confused

you mean applets

[sudden granite]

this is javascript

[gray gazelle]

nah this i dont know oops

[sudden granite]

java is by oracle

[gray gazelle]

i thought you meant web design

i meant java

have you learnt java?

[sudden granite]

no

my dad knows it tho

he worked at oracle

[gray gazelle]

is java script hard

[sudden granite]

no its ez

java is harder

[gray gazelle]

i find java easy

[sudden granite]

do c++ then

[gray gazelle]

oh no

i dont know how semi oops work

[sudden granite]

dude its 11

i have a ton of hw

gtg

cya nice talking to you

[gray gazelle]

oop-object oriented programming

same

bai

gtg too

[drifting elm]

java script is like assembler in a way. it runs close to the hardware. it has basic primitives.

but that is also the bad thing too because you need a framework to get anything done. simple languages depend on huge library

[hearty steppe]

Not exactly

[drifting elm]

node.js exists

[hearty steppe]

Yea but that runs off C++

[drifting elm]

so

[hearty steppe]

Which translates to C, then to assembler, then to machine code then to hardware

[drifting elm]

pretty much proves my point

if it was not high performance then node.js would not be a thing

[hearty steppe]

It doesn’t run close to hardware. It has to get through 5 levels of compilers

[drifting elm]

we don't gain much from web assembly

are into web assembly?

js is such a simple language that it doesn't suffer a lot of slow down when you compile it

I have looked at bench marks for this

[hearty steppe]

Situational at best

[drifting elm]

I am talking about no library

[hearty steppe]

If you utilize the potential of node js effectively perhaps

[drifting elm]

just basic bench marks in js

compared to web assembly the conclusion was that web assembly is a waste of time

[hearty steppe]

Who uses web assembly

[drifting elm]

and node.js is only slightly slower than java

exactly, web assembly is pointless

never got any big adoption

[hasty turret]

What about js being stupid?

[drifting elm]

simple is a better word for it

[hasty turret]

Or why do people hate js?

[drifting elm]

because you can't really do anything without a library

[hollow current]

js is not stupid but js is for frontend mainly

[drifting elm]

or you end up doing a lot of work

[hearty steppe]

most people that hate js don’t like dynamically typed languages

[hollow current]

dynamic typing is crap

[hearty steppe]

I don’t really see why I would use JavaScript anytime soon anyway which means I’ll probably end up getting a lot of headache using it again

[drifting elm]

I though they just don't like learning a new frame work every time they switch jobs

[hearty steppe]

The only languages I tend to use these days are Python and R

I don’t even use them often

[drifting elm]

I use python, java, mathematica

I have sage but never needed it

[hearty steppe]

I have experience with a lot of languages and frameworks but like

I don’t care for engineering, it kinda bores me

[drifting elm]

well since this is a math discord, check sage, geogebra, jupyter

[grave egret]

I love js.

[drifting elm]

and octave

but if you want jupyter get anaconda to install it for you.

there is an app on linux called basic calculator

it can do crazy huge numbers no limit

[hasty turret]

Why don't you just write a program

[drifting elm]

I have python libraries that replaced basic calculator

and sage also does the same

[hasty turret]

You do crypto, right?

[drifting elm]

but if you code shell scripts then it is awesome

[hasty turret]

How do you deal with huge numbers?

[drifting elm]

you can do it in any language

[hasty turret]

Like without a custom array

[drifting elm]

you need the right library

[stray veldt]

python has arbitrary precision integers

by default

[drifting elm]

these are new methods new data structures

there is a library for fixed point decimal in py

not floating point

but yeah he is right. integers are autosized

[gray gazelle]

What is more efficient in terms of computer power buffered reader or scanner class

My teacher used to hate when I used to use input stream reader

[molten wave]

that's such a niche question

[gray gazelle]

a java programmer would probably know

[lime parcel]

i don't know that that is correct. v8 node engine performs super well, to say js is just for front end is like saying scheme is just for recursion, or python is just for cleaning data. js informs stuff like react, angular etc etc.

[calm crane]

i hear crypto

oh god v8

someday

browser pwn

webasm is absolutely atrocious

[gray gazelle]

#❓how-to-get-help

[calm crane]

wtf nodejs translates to c++ translates to c to assembler to ...
what drugs are you high on

[calm crane]

isit how to get pstd help

[sterile pelican]

what do you guys think of Pinter's Abstract Algebra?

[static crest]

Pretty sure node.js just straight translates to machine code at runtime, and the compiler is written in C++

But no actual C++ is generated

And also js is mainly for front end, it results in hilariously bloated code at times, and node.js in particular is single thread only iirc

Which is not to say only for front end, but mainly

[drifting elm]

when you have something like that that is single threaded you just make it multi-process

for a node.js web server every request spawns a process

[calm crane]

node isnt so simple haha

or js

so right

there is this thing called jit

if you call your function once only, why bother compiling to machine code when you can execute it on spot

but if you call your function like 100 times, should probably compile

if you call your func 1M times, always give integer, can start to seriously optimise the compilation

ok this more describing v8

does this open up exploits? yes
are they terribly difficult to find? yes all the people who exploit these stuff are literally gods

nodejs is like

painfully async

like java is forced oop

nodejs is forced async

kinda is why i stopped using node

too much pain

[dapper root]

Why is this in book-discussion lol

[calm crane]

my pstd spilling out of my brain

[gray gazelle]

F

[stark creek]

how do i get books legally in pdf format

no one really seems to sell pdfs

[dapper root]

I mean often springer or whatever has like an ebook version

[stark creek]

yeah but they are the only ones i know of

[dapper root]

I think more generally the answer is that they don't exist

Well..

actually that's not true

through your school you might have access to an online thingymabob where you can access a huge library of textbooks

and I think theoretically you could subscribe to that service as an independent entity maybe??

I think the AMS stuff is on there

[stark creek]

hmm

[hearty steppe]

Don't worry about the legal ramifications about downloading pdf files or ebooks. Law enforcement doesn't really care so much about it anymore. They've tried to target plenty of sources that share ebooks openly. Short story is, they just keep putting proxys of the original server up. So honestly man, your good. Even if you told a cop that you download pdf files off libgen, they ain't gona do anything to you.

I'd be more concerned with other multimedia content like downloading movies/shows or video games off torrent sites

[raw herald]

And if its something like sci-hub well then fuck the academic publishers anyway

[sterile pelican]

amazon ebooks?

[drifting elm]

https://open.umn.edu/opentextbooks this is %100 free open licensed

you can rent or buy ebooks here https://redshelf.com/app/ecom/book/774196/discrete-mathematics-774196-9781439812815-rowan-garnier-john-taylor

https://www.chegg.com/books

some publishers only sell through chegg. I really don't like that idea because chegg can raise the price to $40 for a 3 month rental😫

or $160 for a book

[calm crane]

l i b g e n

[hasty turret]

Isn't libgen technically illegal?

[sudden granite]

🤫

dont trust the govt

[dense wren]

i mean its illegal to walk on the freeway but that don't stop me

[marble solar]

We all thought we were safe from icebergs on the freeway

but this guy will sink you car

[stark creek]

@drifting elm do you know in what format those digital books are on redshelf

ah they have their own reader 😫

[cobalt arch]

Has anyone read the three volumes of amann and escher's analysis? If so do you recommend them as an intro to analysis?

[gray gazelle]

lochverstarker has I think

[stray veldt]

ye, i did more or less

they are great books

maybe a bit hard for self study

depends on mathematical maturity

also if you read all of them it will take you at least a year

@cobalt arch

i read about up to chapter 7

which is halfway through the second book

i learned complex analysis elsewhere

and measure theory as well

manifold stuff too

but what i read is really good

[cobalt arch]

Hm thank you @stray veldt

[wooden sparrow]

How do you know that one book is better than the other? Like going though one UG book seems to take a lot of time. And also did anyone go through a different book of same topic again just to see how they compare?

Won't it take a lot of time just to analyse how one compares with other?

[stray veldt]

if you already know the topic, it's not too hard to compare 2 books

[wooden sparrow]

how many books did you go through about analysis?

[stray veldt]

i know at least 3 pretty well

[quartz pawn]

Ppl go through an undergrad course and then in grad school you do the "big boy/girls" version

So most graduate students in here have gone through at least two or some form of lecture notes and they draw on stuff from various books too

[stray veldt]

i used all those 3 books plus my professors script to actually learn analysis

and kept 1 book as a reference

that being said, i have read none of them cover to cover

[quartz pawn]

I'm using Zorich and amann

At least trying

Alot of stuff in Amann though I've skipped cause I'm mainly usin Zorich

[wooden sparrow]

it's just that I got recommended tao for analysis day before yesterday, and looking at different people recommending different stuff made me question this

[quartz pawn]

Like intro to proof methods

know all that stuff

I mean you can tell at first glance which ones are more difficult

[stray veldt]

different people will like different things for different reasons

[quartz pawn]

or require more mathematical maturity

[stray veldt]

just see if the book works for you

[quartz pawn]

^

[stray veldt]

at the end of the day the analysis curriculum is very standardized

[quartz pawn]

^

[stray veldt]

there isn't too much one book can do much different than another

[wooden sparrow]

ohh

[quartz pawn]

There's difference in the pedadogical style obviously. One thing that I've noticed about Amann and Escher it makes use of diagrams and pictures. Zorich doesn't use as many but also draws upon many real world examples at the same time being rigorous.

Amann doesn't seem to do that

from what I've read of the first volume.

But there's less applications for that type of stuff anyways so that may change later down the line.

But Zorich even finds real world examples for that stuff too

[karmic thorn]

Is it wise to consult multiple books(for the same topic) at the same time?

[quartz pawn]

I usually get new perspectives on stuff if I do this or if I need clarification because I can't really seem to grasp it from one text.

Works for me.

[wooden sparrow]

bruh won't that take a lot of your time though?

[quartz pawn]

I've got plenty lol.

[karmic thorn]

Yeah, time is an essential concern for me.

[karmic thorn]

Lucky.

[quartz pawn]

But I'm content to finish it at a pace I'm comfortable with too

[karmic thorn]

I need a very wordy and thorough second-reference for intro abstract algebra.

[quartz pawn]

I use mainly one so that'll get finished relatively soon.

but if it takes me about a year and half to two years to finish the other one then I'm cool with that too

[karmic thorn]

I see.

[stray veldt]

dummit and foote has all the words

[sterile pelican]

dummit and foote is a gigantic tome that is only good for doing the exercises

[karmic thorn]

[sterile pelican]

I would say Herstein's Topics on Algebra is a nicer approach

[karmic thorn]

I already have plenty of exercises to do lmao. I'm really looking for a text rambling on the underlying theory.

[hasty turret]

Like this?

[karmic thorn]

Hmmm, Dn'F does seem good haha.

I'll check out both and see what clicks with me.

[wooden sparrow]

Isn't wordy a bit weary?

Or is it more explanative?

[karmic thorn]

I need it as a second reference basically, so it seems good.

[wooden sparrow]

Oh wait that makes sense

I downloaded amann and escher after loch suggested that here. I hope that's a helpful second reference

[karmic thorn]

I think I'll take a look at Amann and Escher too, Loch's endorsement of that book made me curious haha.

[karmic thorn]

Holy shit, Amann-Escher goes into intro abstract algebra, linear algebra and construction of number systems in chapter 1 itself.

[stray veldt]

ye, its kinda weird

it is very self contained and will need all this stuff at some point

[karmic thorn]

This is the first book I've seen with a chapter 124 pages long.

[wooden sparrow]

wait, so this is a better read?

[karmic thorn]

Whatever floats the boat for you.

[wooden sparrow]

Umm.... I don't know what floats my boat now

tao seems nice, but that's the only analysis book I've read

[karmic thorn]

[wooden sparrow]

Okayy

amann escher starts with sets, whereas tao starts with natural numbers

oh wait,tao also has sets

forgot

[karmic thorn]

Ehh don't sweat too much about it, the construction of natural numebers from Peano Axioms really doesn't need much set theory at all.

Chapter 3 gives enough Set Theory for intro analysis anyway.

[wooden sparrow]

got it

[stray veldt]

i mean, amann escher basically does a short intro to proofs first

[wooden sparrow]

Oh, that seems to be a better thing

[stray veldt]

then it introduces real numbers

and alongside that groups, vector spaces, some ring stuff even

the latter is probably not needed, but 🤷

[wooden sparrow]

okayy

[molten wave]

how to talk about category theory without using the word category

[drifting elm]

I thought there were problems with peano axioms? is there some errata we should know about before reading the source material?

[molten wave]

"errata" probably not

[drifting elm]

objections?

[molten wave]

it's not like they were shown inconsistent or anything

not really

like what problems do you have in mind

[drifting elm]

this is just a rumor. I have no experience in this area. I read math forum discussions with objections. but I forget them.

[molten wave]

godel showed some problems with math in general, involving the peano arithmetic

wouldn't say it's peano axioms that are at fault here

[drifting elm]

yes probably that

[molten wave]

rather our expectations of

consistency and/or completeness

[drifting elm]

yes that was it. incompleteness of peano arithmatic

[molten wave]

again it's not because peano axioms are somehow faulty

[drifting elm]

or maybe it was the peano numbers?

[molten wave]

all complicated enough formal systems suffer from the same issue

[drifting elm]

ok so I don't need to get focused on these details as a beginner?

[molten wave]

that's the same thing?

definitely not

[drifting elm]

ok thanks

[molten wave]

I assure you the natural numbers that every normal mathematician uses are some version of peano numbers

probably not axiomatic, but instead constructed using sets

but they are a model of the peano arithmetic

subject to the same axioms-now-theorems

[drifting elm]

I have an old book on axiomatic set theory and it really really fried my brain

[molten wave]

and of course, this means that sets inherit the same consistency/completeness issues

axiomatic set theory might be a little hard to grasp before you get an intuition for sets

[drifting elm]

the book goes forever about russel's paradox thats how old it is

[dapper root]

My natural numbers are actually all sets formed by the union of the last one and the empty set

I don’t write numbers

I just write really big nested sets

It’s very intuitive

[drifting elm]

now on the forums people have a new definition for set theory that avoids the paradox?

[molten wave]

if by "forums" you mean mathematical society in the 1920's

and by "new defiition" you mean ZF(C)

then sure

[dapper root]

You get sround russel’s paradox by not allowing unrestricted uhhh

I forget the actual name but

To take a set by like “the set of x such that...”

[molten wave]

comprehension

[dapper root]

You have to work inside of a different set. So it’s “the set of x inside S such that...”

[hasty turret]

Are proper classes considered interesting?

[dapper root]

And I think you have another one which might have been for Russel’s which essentially says no set can contain itself

[molten wave]

basically the intution that sets are predicates --- has to break down ever so slightly

[dapper root]

But I forget if that’s for Russell’s paradox or something else

[molten wave]

@hasty turret hardly

[dapper root]

I mean, define interesting lol. Some people find foundations interesting, I sure don’t

[molten wave]

better study universes in general

[hasty turret]

Like,classes are just special sets

[dapper root]

If you care about set theoretic issues you certainly must come into contact with them

[molten wave]

I mean NBG has the property of being finitely axiomatizable I guess

[dapper root]

No

A class isn’t a set

err

Some are

Some aren’t

[hasty turret]

Nvm,"set"

[drifting elm]

I think I need to ditch this axiomatic set theory book for something modern

[dapper root]

Right

[hasty turret]

As in collection of objects

[dapper root]

It’s a “collecion@

[drifting elm]

I don't need the history if it has been solved

I just need the maths

[molten wave]

how are you describing the collection

[dapper root]

But set has a very strict meaning since you know you can do operations in them

[molten wave]

a rule that tells whether it's in or out?

[dapper root]

Mniip fuck that definition

It’s just stuff

Everyone knows what it is

Chmonkey foundations

[molten wave]

literally no

[dapper root]

Nope

Chmonkey foundations

You and I both know what R is who cares

[molten wave]

axiom of ch-oice

[dapper root]

Chmonkey foundations includes choice

[molten wave]

idk R seems pretty fake

[dapper root]

It’s even in the first two letters

[molten wave]

i've been to a seminar on constructive analysis yesterday

I'm really not sure I understand R anymore

[dapper root]

That’s because you listened to liars

You listened to the snakes in the garden and now you question that which you know to be true

[hasty turret]

Christian moment

[dapper root]

Chmonkey isn’t a Christian moment

But also yeah that was a specific reference

[molten wave]

I think it's really about the locale of real numbers

and not the set/topology

[dapper root]

🥱🥱🥱🥱
I like your funny words mr magic man

This is me admitting I don’t know what locale means in this context

[molten wave]

I think we scared the hsct away

real ugct hours

I'ma be real with you, I don't either

[dapper root]

[molten wave]

apparetly you consider CHey, the category of complete heyting lattices

[drifting elm]

I conformed to using a standard cat with santa hat as my avatar

[stark creek]

anyone read the analysis books by tao

[polar tulip]

yeah, they're good if you're still learning how to do proofs

if you're more advanced pick up pugh's book

[hollow current]

zorich is great book

i leared anal from zorich

[fossil island]

Thoughts on Casella and Berger (https://fsalamri.files.wordpress.com/2015/02/casella_berger_statistical_inference1.pdf) for graduate statistics book? Seems like we'll go over chapters 5 thru 10ish

[drifting elm]

thicc

[quartz pawn]

@hollow current yea it's been really good so far

[hasty eagle]

TheDon

[wide meteor]

best book for number theory?

[stray veldt]

at what level?

[wide meteor]

what levels are there

ive never learnt number theory formally

[stray veldt]

ok, do you know abstract algebra?

[wide meteor]

no

[stray veldt]

then i like "An introduction to the theory of numbers" by Hardy and Wright

[wide meteor]

ill check it out thanks

[stray veldt]

that book is kinda massive, so there are probably shorter, more modern (, better) choices

[drifting elm]

I actually had this problem with learning number theory. all the books had no introduction.

I then went back to the easiest book

[wide meteor]

@drifting elm oh whcih book

[drifting elm]

I used elementary introduction to number theory

calvin long

it makes you write out the sums as an exercise

[karmic thorn]

Elementary Number Theory by Burton is really good.

[drifting elm]

https://www.amazon.com/Elementary-Introduction-Number-Theory-Calvin/dp/0881338362/

[gray gazelle]

"firendly introduction to number theory" looks pretty good if you don't have a lot of math background

[drifting elm]

after you learn the basics, every number theory has %98 the same exact subjects

point here is you only need 1 mid level book on it

the higher level books are basically random selections of case studies in number theory or more obscure useless theorems

[wide meteor]

so many books to choose from

[gray gazelle]

what math background do you have?

[wide meteor]

umm

[gray gazelle]

high school lvl?

early undergrad?

[wide meteor]

early undergrad

[gray gazelle]

hardy,wright seems like a good start, the book I mentioned "firendly intr to NT" is easier and probably better for self studying if you're willing to actually do the exercises

[wide meteor]

hardy wright is 700 pages so im kinda reluctant to do that one lmao

ima start with elementary introduction to number theory by calvin i think

[gray gazelle]

it goes into more advanced topics, you dont need to read all of them

[wide meteor]

oh

ok

[drifting elm]

I can't comment on that other book since I don't have it.

this calvin long book even explains the notation which is missing from most other books

it really is the first book to get

[wide meteor]

ill check out a pdf of all of these and see what i like

[stark creek]

Why arent there any books on stochastics

In the book room i mean

[gray gazelle]

Yes

[hearty steppe]

Cuz most people in this server aren’t statisticians

[gray gazelle]

no

Stochastic processes is applied math

[timber mesa]

a ton of pure math research is done on random walks and other stochastic processes

[hearty steppe]

I mean I am always looking for more SP books, I am not familiar with that many

[gray gazelle]

Can you advise me some good books

[timber mesa]

about what?

or what are your interests, what level math are you doing, etc.

[gray gazelle]

math . i am a high school and i want to learn math more

just i want a book to begin right

[karmic thorn]

Begin with HS maths, explore maths from the point of view of someone in HS, or an introduction to undergraduate math?

[gray gazelle]

thanks

[karmic thorn]

[prisma snow]

LOL

Maybe they just read "Begin with HS maths" as your advice

[karmic thorn]

Lmao I sincerely hope not

[prisma snow]

Tldr

[karmic thorn]

@gray gazelle What kind of book are you looking for?

I think Art and Craft of Problem Solving by Paul Zeitz may be worth checking out.

[gray gazelle]

that kind what can give me a good basics

[karmic thorn]

Oh, okay. @wooden sparrow provide your recommendations.

[wooden sparrow]

Do you want to learn for olympiads or do you want to understand maths better?

[gray gazelle]

understand maths better

[wooden sparrow]

Start with Lang's basic mathematics

[gray gazelle]

thanks

[marble solar]

I really don't know why ppl go back to the basic mathematics

why not just learn geometry or calculus?

[soft terrace]

hey while im here thx for the book recommend a while ago on SDEs moonbear

just finished it and it was great ^_^

[marble solar]

SDEs?

What did I do

🤷

[soft terrace]

stochastic differential equations u ended the world

[marble solar]

oh evans?

[soft terrace]

yeah

[marble solar]

Was it good?

[soft terrace]

1 small annoyance with it but yeah it was good

[marble solar]

I have my copy of evans PDEs on my desk

[prisma snow]

Because calculus is a shit show when you can't factorize, don't understand trig, and think that 10/1 = 0 because you cancel the 1s

[soft terrace]

i think it went about proving it differently than other SDE books though

[marble solar]

So why not geometry @prisma snow

Not ready for calculus? Go to Euclid's geometry

Ready for calculus? Just go do that

[prisma snow]

Sure, you can learn geometry, but that also requires solving equations and then you can't really learn anything else lol

[karmic thorn]

I guess any reasonable study of geometry will start from basic maths taught at school, no?

[marble solar]

Euclid doesn't have equations

[prisma snow]

Idk why you'd say don't learn basic math, just learn geometry forever

[soft terrace]

u mean the literal euclids books?

[marble solar]

yA

[soft terrace]

i dont think i ever read them all the way through

[marble solar]

One of my closest friends started reading in 6th grade

[karmic thorn]

Euclidean geo is a part of the middle school curriculum at my place(I totally hated it).

[marble solar]

By the time he got to HS he was reading Dirichlet's papers on Analytic Number Theory

[soft terrace]

lol euclidean geometry was a college course at my place

[pine igloo]

[soft terrace]

i was mostly interested in physics in HS

[karmic thorn]

Same

[soft terrace]

i didnt actually start liking math obsessively till college

[prisma snow]

And in all that time, he never learned how to factorize or do arithmetic. Your friend is impressive.

[pine igloo]

is there anything more pure than Euclidean geometry? why you hate purity

[marble solar]

IDK I think doing basic math again is like a waste

[soft terrace]

set theory is more pure than geometry 🙂

[marble solar]

Just go do something interesting

[pine igloo]

well set theory is also pure

[soft terrace]

lol

im just being semantic i know what u meant

[pine igloo]

I would say more foundational, more important, but purity wise, both

[soft terrace]

honestly id argue that though more complicated generalizing geometry makes it more pure doesnt it?

[karmic thorn]

I tried going through Euclidean geometry after years again, I found it to be a better(not brilliant) experience now that I have a better appreciation for proofs.

[soft terrace]

hah

thats a recipe for a bad semester

[marble solar]

@gray gazelle now you're talking my lingo

idk, skipping pre-reqs is how you get good at picking up math

[pine igloo]

actually we're talking about my favorite two worlds in maths, foundations (set theory particularly) and geometry (Euclidean particularly, hence my profile picture)

[karmic thorn]

@wooden sparrow

[soft terrace]

i like riemann/finsler geometry

and manifold theory

[pine igloo]

you like the good stuff I see

[soft terrace]

i think the most interesting stuff happens when u bend stuff 😉

[prisma snow]

I think a lot of students I've seen follow Moonbears' advice. That's why they can't do basic math in analysis

[soft terrace]

"how do i sum a infinite series?"

[wooden sparrow]

wat

[soft terrace]

"ive never seen that before"

[pine igloo]

well topology and geometry (non-Euclidean, differential, symplectic, ...) are very interesting

[karmic thorn]

Kinda like being stuck in calculus because you don't know the trig/algebra.

[soft terrace]

yeah that would suck

[pine igloo]

tropical geometry !

[marble solar]

I skipped trig & calc 1

🤷

[wooden sparrow]

Won't that make you feel rushed?

[soft terrace]

i hated partial fraction decomp in calculus

[wooden sparrow]

trying to fill in the gaps?

[karmic thorn]

Ughhhh the pain

[marble solar]

Honestly, I think you can bring down measure theory to first year university

[pine igloo]

you should view it in arithmetic of polynomials and fractions, you'll like it then

[soft terrace]

i dont know how measure theory would be better lol

[karmic thorn]

What are the prereqs for measure theory?

[marble solar]

A stick

[pine igloo]

a ruler

[karmic thorn]

Gotcha

[marble solar]

You can teach intro measure over discrete spaces with weights

I mean, we teach probability

Also get the basic ideas going of what length is

[soft terrace]

yeah

[karmic thorn]

Is topology a prereq?

[soft terrace]

they taught measure theory in my intro to real analysis course

[marble solar]

Measure Theory can be done very simply, but it's most powerful when combined with integration

[soft terrace]

we made it to lebesgue integrals

[marble solar]

So usually ppl want to wait till after you know something about riemann integration

[pine igloo]

well you need some set theory, basic stuff, some topology, at least for the real line and metric spaces
you'll need some calculus for integration theory

[soft terrace]

lol

[marble solar]

I honestly think my year studying Rudin's principles was a waste of time

[soft terrace]

never read it myself

we used stephen abbott

[marble solar]

I knew that stuff going into University

[soft terrace]

ah

[marble solar]

My CC taught topology

calculus on manifolds

[prisma snow]

Yes, learning stuff you already know is a waste of time. Duh.

[soft terrace]

CC topology O_O

[marble solar]

Riemman-Stieltjes integrals

[wooden sparrow]

@marble solar why do you think skipping prereqs is a good way to pick up maths?

[marble solar]

Because one way or another you're not going to have a class on everything

[timber mesa]

hot take: baby Rudin is a waste of time

[soft terrace]

it forces u to get urself up to speed

[prisma snow]

And you do that by learning the prereqs lol

[marble solar]

You have to learn how to pick up things on your own - a great way to introduce this is by signing up for a course

I took sobolev spaces without PDEs

I took Random Matrix Theory without probability

[soft terrace]

ooo

[marble solar]

I took 3 manifold topology without alg. top./diff. top.

[soft terrace]

u know a good book on that moonbears?

[marble solar]

On what?

I just named 3 topics

[soft terrace]

random matrix theory

[marble solar]

Terry Tao's book is good

[soft terrace]

sounds interesting and im in a stochastic frenzy

[marble solar]

I'd recommend some passing familiarity with measure theory

[soft terrace]

yeah i can do that

[marble solar]

you can pick it up at the same time you learn RMT

[soft terrace]

ive integration theory

done*

[marble solar]

Ok, that's all you'd really need

I have some problem sets from my professor on RMT

This was the covid semester so he was not really grading us that harshly

Oh I took algebraic curves without taking the pre-requisite first semester grad algebra

What else did I skip

[soft terrace]

grad algebra is easy to fill yourself in on

[marble solar]

🤷

Wouldn't know

Didn't do that

[soft terrace]

thought that was a requirement in most masters

[marble solar]

Algebraic Curves was mainly self-contained

(It was, that's why I did algebraic curves so I can waive it)

[soft terrace]

ahhh

[marble solar]

I don't like wasting time on the core/elementary things

I like to do the fun stuff

[soft terrace]

yeah i know that feeling

[marble solar]

I did to intro to measure, and intro to topology for a 3rd time during my MS

cuz I couldn't get away with everything

[sudden kindle]

i do the exact opposite

I spent years on the core courses lol

[sudden kindle]

core core

my aesthetic is core-core

taking core courses

🤓

[sterile pelican]

nightcore?

has anyone read Larson's Problem solving through problems? I would like to do some problem solving books

[viral falcon]

Help

I'm reading Calculus for the Practical man and don't know where to go from there

It doesn't cover limits so I'll probably need a cal-II book that covers that. Then Cal-III

I also have Adv Calculus by Woods. Where does that fit in all this

[fast portal]

???

[obsidian valley]

it doesnt cover limits?

[fast portal]

You are supposed to cover limits before tackling anything even deserving of the name calc 2

Mate your foundation got fucked hard

[obsidian valley]

that is an axler level omission

[fast portal]

Try spivak

It isn't exactly easy but it starts from very simple stuff and goes up

[obsidian valley]

spivak is too proof heavy if he's doing a practical calc book I tihnk

[quick hornet]

omitting limits isnt as uncommon as y'all seem to think

[obsidian valley]

really

[quick hornet]

theyre not seen as that useful in application-oriented texts

[fast portal]

You are already familiar with some knowhow of calculus right @viral falcon

[obsidian valley]

i feel like the vague notion of a limit is useful at least but /shrug

[quick hornet]

and the vague notion is really easy to learn

[fast portal]

like derivative of e^z being e^z

[gray gazelle]

thing get small thing get big

[obsidian valley]

sometimes both

[fast portal]

(that usually doesn't converge)

[viral falcon]

I've covered high school cal

I'm doing this kind of my own self stufy

should I go for Spivak next?

[fast portal]

yea if you intend to go for a more mathematical route

[viral falcon]

how further till spivak covers, C2?

[robust palm]

calc 1 courses typically cover limits + differentiation, probably the fundamental theorem of calculus, maybe a few basic integration techniques

calc 2 courses typically cover more advanced integration techniques, sequences and series, taylor series and maybe some applications of integration

calc 1+2 focus on calculus of functions from R->R, and calc 3 roughly covers the same ideas but on more general functions, of the form R^m -> R^n

I suspect spivak might not be a good choice for @viral falcon

if you want to get intuition, see some applications, and know how to compute derivatives and integrals, you might as well go for a book like stewart

I find a lot of "advanced calc" books to be rigorous (obviously this is intentional) but lacking in intuition that a good prof would provide

[flint forge]

(this is in my opinion a general problem with learning purely from textbooks)

[robust palm]

fair