book-recommendations

[gray gazelle]

the book of maths by clifford pickover

[sudden kindle]

Francis Su - Mathematics for Human Flourishing

[scenic rapids]

IDEAL GANIT BY Dr. Amal K Bhaumik

[gray gazelle]

Yea books like this one

[gray gazelle]

I couldnt find this one😔

[gray gazelle]

Great philosophical book called Think Again by Adam Grant

[hearty steppe]

How many mathematical physicists study the mathematics and physics of harmonic analysis

[forest sleet]

i'd imagine many use harmonic analysis but don't study it directly or for itself

[stable torrent]

Alright book.

[marble solar]

Not very many

[stable torrent]

Bill gates read book, book is categorically good

[gray gazelle]

Bestseller bad

[wooden sparrow]

Is it a maths book or self help?

Self help books are trash

[gray gazelle]

probably a mix

Since self help sells

[fresh rapids]

u guys should read project hail mary

[gray gazelle]

What's it about

I want a 300 word review

[fresh rapids]

bruh

[strong plank]

Hey, I’m reading this book : https://nms.kcl.ac.uk/ashwin.iyengar/df.pdf#page7 (on abstract algebra) and I was wondering if there is a pdf with the correction of the exercises ? I found that : https://www.gregkikola.com/dl/guides/dfsol.pdf#page7 but there is not every chapters. So my question is : is there a pdf (official or unofficial) with a correction of every exercise ?

[stable torrent]

bro wtf this shit taking long than expected.

bro how many pages in dis

945...

[strong plank]

^^” I agree it s a big book haha

But do u have an idea of where I can find a correction book / pdf

[foggy relic]

does the author have an errata or smth

[strong plank]

Yes, here : https://www.shsu.edu/ldg005/data/mth636/dummit-foote-errata_3rd_edition.pdf

[gusty smelt]

no bad book

dont read DF

[strong plank]

Why is it a bad book ?

And is there any other books on the same subject @gusty smelt ?

[gusty smelt]

I liked artins book on algebra

jacobson is also a pretty good book imo

[foggy relic]

oh its DF

[strong plank]

Ok I’ll check that

[gusty smelt]

https://discordapp.com/channels/268882317391429632/716264872018706443/718931426346795099

[foggy relic]

is DF not the standard aa book?

[gray gazelle]

I dont think bad book is a good enough reason tbf

[gusty smelt]

good post

[gray gazelle]

d&f is just verbose

[strong plank]

Ok thx, I’ll read that

It may help me lol

Btw, it looks like DF have more exercise than Jacobson, no ?

[gusty smelt]

probably

[strong plank]

Kk

[misty wyvern]

Stop using DF, start using Aluffi

[dapper root]

My man

[obsidian valley]

aluffi is painful

i will try aluffi again once i learn how to do algebra like a normal person

[hearty steppe]

you mean learn to do algebra like someone who is a graduate level math student :\

Still gotta work my way there lmao

[sudden kindle]

@sage python I'm going to participate in a reading group on automorphic forms in the fall

It looks like we are using Bump

@sage python Give me a automorphic forms book review

[sage python]

I know Goldfeld-Hundley better than Bump tbh

[marble solar]

Just don't learn algebra

That's what I did

[sage kelp]

What are good resources for static and dynamic optimization?

[timid vector]

Jacobson is alright but some of the exercises are just bizarre

[frail gyro]

Eh is it bad fr or are you being ironic?

[crystal cape]

Looking for a good algebra book. Preferably not an expensive one since my country's currency has depreciated a lot against US dollar. Any recommendations?

[gray gazelle]

Not lang

[outer stone]

[prisma snow]

Unbased list does not include Rotman

[brisk ice]

im noob at this stuff but how many books of the same topic do you have?

Do your classes use multiple books on 1 subject?

or do you just end up looking for help from other books and that is why you might have more experience with more 1-2 books in a given subject

i just assume most people learn a subject with 1-2 books and move on to the next class / subject

or are you able to get a good sense of the book just doing a quick glance over it (after having already done the subject or not) to see how well structured it is?

[gray gazelle]

i follow 1 and only 1 book, refer to multiple others for reference, questions, missed topics, something that was difficult in the main book etc.

[brisk ice]

see that is why i wondering if maybe people just went through a course with a specific book and know it is bad because of it or just through looking at it for help only to find it wasn't very useful

[gentle wharf]

Hey which book may you people recommend for learning about complex numbers and logarithms and limits for like a person who is looking at the subject for the first time and wants to do relatively deep studies given that I would be looking at the topic for the first time

[prisma snow]

Do you mean complex logarithms and limits of complex numbers? Or are you talking about those as three separate thing.

[gentle wharf]

No complex numbers

And all the topics which are related

[gentle wharf]

I mean only complex numbers

[polar flare]

hellooo can i ask you guys what books you recommend for contest math? Im at grade 11 (16-17 yo)

[gentle wharf]

brah I am just a 15_ your old kid

IDK

[gray gazelle]

go to #competition-math and see the description to join math olympiad server. (or just go to #old-network to select olympiad server)

they have a channel #538282967299260419 where you can find whatever you need

or you can even ask them

[polar flare]

okok

thanks!

[gentle wharf]

Hey which book may you people recommend for learning about complex numbers and logarithms and limits for like a person who is looking at the subject for the first time and wants to do relatively deep studies given that I would be looking at the topic for the first time
I am just a 15year old kid wants to know abt the topic so that I can learn other topics which use dat

Someone pls help

[gray gazelle]

for complex numbers, any high school algebra book usually has a chapter on it. Hall & Knight's Higher Algebra book for example.

Logarithms: Even the wiki works for this one, khan academy eh ?

limits: Any decent calculus book should and would have it, stewart's calculus book maybe

[crystal cape]

I am a logistics engineering major by the way. So, college level books are preferred

[cursive orbit]

Not a book recommendation, but some advice:
If you're looking to save money on a book, there are illegal websites out there like libgen that you definitely shouldn't use. (wink)

[crystal cape]

Well, I know there are some options as you said but it's not ethical from my point of view. So, if I have to pay, I will

[cursive orbit]

That being said, have you seen if Khanacademy (which is legal and free, but not a book) fits your requirements?

[crystal cape]

Yes! It's been really helpful for my introductory statistics courses. But since I want to dive deep into math this time, I want to get a book instead of watching videos. Of course, I will use some supplementary resources along the way but I want my main resource to be a book

[flint forge]

I would like to offer the following POV: the authors of these books rarely get any money when you buy them, they get paid upfront for writing the book. After that all proceeds go to some large publishing corporation. So if your concern is that you downloading a textbook hurts the author, this is not really true.

Anyway I am not sure if anyone here is well versed in the algebra scene as those textbooks are like, largely the same and mostly make their money by producing 27th editions with minor changes

OpenStax is a legal and free option, though, so maybe you'd like that?

[crystal cape]

Sure, I will check it right away

[flint forge]

https://openstax.org/details/books/college-algebra

[crystal cape]

Thanks a lot 🙏

[flint forge]

no problemo

[gray gazelle]

Complex Numbers from A to Z by Andreescu does a good job I think

[eager stump]

if you have a uni account you can prob get free electronic copies of anything published by springer

or at least do an inter-library request

[strong plank]

Is it worth it to buy Artin's Algebra or read it online is as well. I mean, is the "experience" of having the book irl better or not?

[gray gazelle]

that's a personal thing

you're still looking at the same text

[flint forge]

Physical book is nice if you plan to use it a lot

I always prefer physical given the option

[primal summit]

God physical is just a whole different experience imo

so much nicer

[flint forge]

I always forget that I actually own hatcher

It’s in my room

[bronze raven]

burn it

[primal summit]

^

[flint forge]

All the hatcher hate is so silly

Its a good book

[bronze raven]

ye hehe

[primal summit]

I disagree but I respect your opinion

[flint forge]

Its not a great book or anything

But like

[bronze raven]

im still resding but rotman is top tier

[primal summit]

it has good illustrations

[flint forge]

Taught properly its very nice

I don’t think it’s a good book for self learning

[bronze raven]

i probably wouldnt feel so bad if i had a lecture behind jy

[primal summit]

Ok I agree with that

[flint forge]

You need a guide

[primal summit]

i'd probably enjoy it if I were taught it

[bronze raven]

i shouldve watched the utube lectures

[flint forge]

Esp someone who can explain the visual@stuff

[primal summit]

we're probably gonna be following hatcher next sem

that or munkres

[bronze raven]

Hatcher just fails at that sometimes

[flint forge]

The exercises in hatcher are great imo

Well

Except ch0

Those suck

[gusty smelt]

I liked Hatcher for the most part kek

[bronze raven]

rotman goated

shin was correct

[flint forge]

Too old

[primal summit]

based and rotmanpilled

[flint forge]

Bad typography

Gross

[primal summit]

I love old books

[bronze raven]

a small price to pay for perfection

[flint forge]

I hate them with a passion

[primal summit]

The one I have borrowed was a gift from the author

last time it was checked out was in 2002

[gusty smelt]

I’m slowly reading Tom dieck, I like it

[flint forge]

Lmao

I fully

[primal summit]

but you're already categorypilled john

[flint forge]

Bc no one else had ever checked it out

[bronze raven]

based!

[primal summit]

nicew

[gusty smelt]

Lolol nice

[bronze raven]

im going to start stealing books too

shits too easy

[flint forge]

I mean I’m gonna have to pay for it

[bronze raven]

ive never seem anyone take math books from the shlef

[flint forge]

But like

Worth it

[primal summit]

what book was it

[bronze raven]

how do they know you stole a book though?

[flint forge]

Library

I just never returned it

[bronze raven]

if ur library has like 12 floors

[flint forge]

Toda’s book

[bronze raven]

toda?

[primal summit]

they probably have a system from tracking that

[flint forge]

He’s a famous mathematici

[primal summit]

'toda' means thanks in hebrew

[flint forge]

Mathematician*

I think Toda was Japanese

I could be wrong

[primal summit]

he was

still funny to me tho

[broken meadow]

Todaaaa

[bronze raven]

todaroki

from mha

[strong plank]

Ok, because I’ll probably use it a lot, I think I’ll get it for my birthday :)

[gray gazelle]

that what my parents taught me when growing up.

[gray gazelle]

Hey !

hey which book would you guys recommend for Olympiad problem solving? Something like Paul Zeits's book

Like is terrence tao's book good?

#competition-math check channel description to join math olympiad server, then you can find resources at #538282967299260419.

alright

the server is also linked in #old-network if you cannot find it

[gray gazelle]

i have only read the first chapter but I think that it falls short for "problem-solving", you will be better off with engel's book or the pasquale book

Alright

I can't use Paul Zeits' book because the letters are too small 😅

although the portion I could read was pretty good

this looks fine for me ?

I guess

wait

well

I guess I have the same copy

i see, if you have a physical copy then rip, else if it is a ebook then zoom i guess ?

I have a phone

oh

and zooming in isn't very optimal

opinions on Problem Solving Strategies (engel)?

Great book, good questions - difficult examples (i have only done 2 chapters from it so no idea in general)

you can get better review in the math olympiad server 😄

alright

I guess I will just go with that book

[halcyon hornet]

What level?

[gray gazelle]

Probably

IMO level

or smth

@halcyon hornet

[tranquil ocean]

Maybe try the books by Andreescu

[gray gazelle]

which ones?

From the training series?

the xyz ones are updated and are with tricks

but they are not available as pdfs

the old ones are nice

[tranquil ocean]

A lot of the problems series are pretty nice

[gray gazelle]

XYZ ones?

yeah that is the new series from XYZ press called awesomemath or something

[tranquil ocean]

One of the ones I read was 106 geometry problems I think

[gray gazelle]

103 trigonometry problems and complex numbers from a to z is also very nice

I wanna focus more on algebra rn

he has a algebra book i think as well

[tranquil ocean]

Andreescu has a 102 algebra problems or something

[gray gazelle]

hall & knight is also quite good for algebra

teaches you some minor tricks etc, very old book

Actually I have Hall & Knight

but I never bothered reading it cause I got it as a problem set, which is for the admissions tests here

[halcyon hornet]

Okay.

AoPs books.

Are too famous.

[gray gazelle]

I have completed them

[halcyon hornet]

Woah what!

Did you buy all of them?

[gray gazelle]

no

I mean

just the problem books series

the 2 vols

[halcyon hornet]

Oh.

Wait you are that guy....

[gray gazelle]

I guess

The Psychological Part of Paul Zeits was actually very good

[crude sable]

Books for Partial Differential Equation? should be interesting and intuitive to read, should not be full with calculation jargon

[hollow peak]

I like evans a lot, but it's pretty dry as are most pde texts

He's not chatty but presentation is clean and choice of topics is great

[willow pecan]

PDEs is a very unintuitive subject

[bitter raptor]

really? I would have thought completely otherwise

i mean cant most scenarios be compared with a physical interpretation?

[brisk ice]

maybe it is the notation?

that is weird

[willow pecan]

So

There is some physical interpretation

But once you get to the realm of like

Energy estimates

Where the L^4 norm of the solution is bounded

Or the L^15/13 norm of the solution is bounded

There is little intuition to be gained

Also

PDEs are interesting when they are hard to deal with

The pdes that are interesting also happen to be the ones that defy intuition

Like Navier-Stokes

[lament sage]

i'm looking for a linear algebra book

I think I have an overall good knowledge of the subject and I want to learn stuff that is more oriented towards computations

https://ocw.mit.edu/courses/mathematics/18-065-matrix-methods-in-data-analysis-signal-processing-and-machine-learning-spring-2018/

i've been trying to follow this course

[willow pecan]

Demmel's Numerical Linear Algebra

[crystal lion]

https://images-na.ssl-images-amazon.com/images/I/81VdxkLuaOL.jpg

[lament sage]

going to check this one

what is this cover

cursed

[gray gazelle]

I guess demmel has a sense of humor

[velvet briar]

This is what will happen to you if you study this book

[willow pecan]

The cover displays how jpeg works

Because jpeg is actually a low rank svd

So it displays what happens as you include more singular values

[misty wyvern]

recommend me the most unreadable math paper youve encountered so far

the more black magic it is the better

[crystal lion]

https://www.irif.fr/~berthe/Articles/generalization_3_gap.pdf

[quick hornet]

you realize that the cliche answer is a mochizuki paper

[crystal lion]

this is a paper i had to read

it's just super computation heavy

[thick python]

https://hal.inria.fr/hal-00802885/document

this is a paper I (tried) to read for my computer science about work-stealing for multithreaded programs

it has just the most cursed notation I've ever seen

[hearty steppe]

That is some terrible notation

[thick python]

This was to get extra credit on a threadpool program, and I just passed on it

not worth trying to wade through that notational garbage

[cursive orbit]

pp

[marble solar]

https://arxiv.org/pdf/1705.08490.pdf

This is one that I've read through pretty extensively and I still don't know what's going on here

It's really not that unreadable, but when you try to decipher the logic or details

It gets hard

[gray gazelle]

Anyone familiar with Keith Nicholson's abstract algebra?

If so, how is it?

[cunning copper]

book recs for algebra?

[quick hornet]

what algebra

[cunning copper]

intermediate/college algebra

[gray gazelle]

Serge Lang's Basic Mathematics supplemented with a few other texts should be good

[gray gazelle]

You can also use Khan Academy

[prime oak]

is lang the standard for LA in UG

[gray gazelle]

i think axler is the standard

https://www.researchgate.net/publication/340741384_Disagreeing_with_Ramanujan_Theory_of_infinity_numbers

Damn they give doi to everything nowadays

[primal summit]

I don't think axler is optimal for a first pass/first course

I like lang for a first course but people here disagree

[primal summit]

What the actual fuck is this

[gray gazelle]

Why, I found that interesting.

Just a Random kid I know but see his work.

[primal summit]

I'm sorry, it's utter nonsense

[gray gazelle]

I am sure you will understand this someday.

[primal summit]

Lmao ok

[gray gazelle]

But, It's Mathematically Correct

See, it.

Properly

[sage python]

Tbh I don't really believe in first and second pass

[primal summit]

Are you a troll? Or just like, really young?

[sage python]

Axler has a bad pov by the end

[cursive orbit]

Lmfao

I mean technically he's right

But he's also wrong

[gray gazelle]

Axler is based

[sage python]

Not really

[gray gazelle]

Even if you dislike his book, you have to give him that

[sage python]

Lang I don't know as well

[gray gazelle]

Like you said.

I am Wrong but right.

[primal summit]

He's not even technically right

[sage python]

So much for a random kid you know

[cursive orbit]

He's right that 1 + 2 + .... ≠ -1/12

That's about it though

[primal summit]

Obviously in the sense of regular convergence that doesn't hold, that's not the point tho. Any mathematically literate person knows this

[gray gazelle]

I just found it fascinating I never thought of ramanujan theory from this perspective

[cursive orbit]

I don't think he even solved the quadratic properly either

[gray gazelle]

I know that but think from another perspective.

[gray gazelle]

Let me check.

[primal summit]

Anyone can make up rules and say 'look i'm right' but that doesn't mean their results are worth anythint

The algebraic manipulations are wrong anyways

At some point he asserts that 6\infty+1=7\infty

[gray gazelle]

I know but just think.

can't you just imagine

[cursive orbit]

We are thinking

And we think it's wrong

[gray gazelle]

I think, therefore I am

[gray gazelle]

I know it's wrong.

but just like it's fascinating.

[cursive orbit]

I too, find it fascinating to do arithmetic with infinity, with a false premise

[gray gazelle]

I like to pretend I am innumerate and that adding positive integers can give me a negative fraction

[gray gazelle]

😆 😆 😆 😆 hahaha

true

[solemn rover]

i find most proof theory pretty unreadable, for a representative example check out feferman's paper "Formal Theories for Transfinite Iterations of Generalized Inductive Definitions and some Subsystems of Analysis" in here. Most stuff by Kreisel is pretty barbaric to try and understand. Bonus : this volume starts with a full fledged philosophical defense of ultrafinitism

[gray gazelle]

This paper is completly verified https://www.researchgate.net/publication/340234353_EMC_2_Explained.

[solemn rover]

LMAO

did you write this?

[gray gazelle]

No

I am korean and he is Indian I suppose.

[solemn rover]

ok. what do you mean by "verified"

[gray gazelle]

Like just in a funny way.

[primal summit]

Verified by the DN council

[gray gazelle]

haha

[solemn rover]

i see. yeah I guess anyone can upload anything they want to researchgate

so perhaps some moderation is important

[gray gazelle]

This looks like a based paper, but "based" in a bad way

[warm socket]

I suddenly wonder if my dad wrote stuff on researchgate

[valid moth]

Find out

The math server deserves an answer

[warm socket]

he didn't, the world is safe

[hasty turret]

What about quora

[sinful pewter]

quora should burn to the ground

[timid vector]

sus

[marble solar]

@sage python So I've been working through Ahlfors, S&S, and Marshall problems

I have to say that Marshall's problems are more well thought out, and specifically designed to get you to pass your quals

Although the presentation of the subject might be a nuisance (starting with analytic functions instead of derivatives or integral representations)

[gray gazelle]

what should i read after abbott analysis?

Would Munkres Topology be a good next step?

[willow pecan]

Sure

[bronze raven]

If you had ability to get any math textbook for free what would it be

[gray gazelle]

useless ability if I'm going to be honest... and I don't really know

yeah its useless when you got libgen and zlib

joking

[bronze raven]

Im talking hard copy

[gray gazelle]

no idea

[bronze raven]

And its not useless because its a reality for me

[gray gazelle]

you must have lots of books

Depends on what you're into etc

yeah what you're into and what you need

but i'm open to explore new areas

[bronze raven]

none actually

[gray gazelle]

I'd probably get Tao analysis 2 since that's what I'm working on at the moment

[bronze raven]

i was thinking of looking for most expensive math book

and then reselling it

[gray gazelle]

why would you wanna do that

[bronze raven]

money?

[gray gazelle]

The market is tiny though

The most expensive textbooks are like that because there's no demand

[bronze raven]

school is buying me a book

so i just have to choose which one

[gray gazelle]

I'd pick one I'll be consulting a lot

But if you wanna get an expensive one go for it

[small garden]

The princeton companion to mathematics

[bronze raven]

?

[bronze raven]

i wish lol

i can only choose one book

[flint forge]

Buy dummit and Foote

I think it’s one of the best books to have a physical copy of and also expensive

[primal summit]

Anyone have a good book for basic convex geometry?

[obsidian valley]

why would you want a physical copy of D&F

its like 1000 pages

are you referencing d&f often

[primal summit]

Probably as a reference book for introductory algebra

[obsidian valley]

i really hope there are better reference books for algebra

[gusty smelt]

literally just get lang

if u want a reference.

[primal summit]

isn't d&f really comprehensive tho

[gusty smelt]

lang is more comprehensive.

[ripe granite]

lang is not a good book to learn from

[gusty smelt]

yeah but if you want a reference

then DF is a waste of money imo

[ripe granite]

D&F is a goldmine

[gusty smelt]

why r u all brainwashed by DF smh

[willow pecan]

Lang is cancelled for being a HIV denier

[gusty smelt]

was he really damn lol

[obsidian valley]

i feel like d&f is good to learn from

but i dont think i would pull it off myshelf if i needed to like

[ripe granite]

d&f + aluffi is a good combo

[obsidian valley]

remember some algebra fact

[gusty smelt]

I think its bad to learn from and bad to use as reference.

[obsidian valley]

I have aluffi on my shelf. but i will never use it

[gusty smelt]

its a wierd inbetween abomination

[obsidian valley]

or well i wont use it for another few months or so

[gusty smelt]

that just makes me want to shoot myself

[obsidian valley]

aluffi is scary

[ripe granite]

learn from whatever

algebra takes a WHILE to get really good

[gusty smelt]

that last sentence tells me u learned from DF

[ripe granite]

this is the case with all algebra books lol

early algebra is just dry

and the "nontrivial" bit is in the definitions

not the theorems/exercises

the trick is to read about the weil conjectures and power through

[gusty smelt]

yeah early group memes was pretty dry

but the applications sections were very wet

[obsidian valley]

so when does algebra get wet

if i am using df or aluffi

aluffi made me feel really stupid

[ripe granite]

what

[obsidian valley]

what

when does algebra get wet.

[ripe granite]

why did aluffi make you feel stupid

[obsidian valley]

well i didnt really get the point of anything that was happeniong

it was just like.

this is the category of groups

[ripe granite]

when you start doing AG

[obsidian valley]

and here is some random fact about the lcm of the orders of groups or something

[gray gazelle]

is Artin's algebra good?

[sage python]

Probably the best entry point if you don't yet know linear algebra

[static crest]

this is why you dont use aluffi jesse

and use dumb foot instead

[flint forge]

Dummit is boring too

Honestly it starts getting good at group actions

And then ring theory

[sage python]

D&F is decent to teach a class out of

[flint forge]

Any reference book is decent to teach a class out of

But it’s a boring book

[sage python]

Yeah

I don't think it's a book to read/learn from

But it's good to teach a class out of

I don't know if it's good as a reference or not in the sense of, is it easy to look up results in?

[flint forge]

It is

Imo

I do it

Its very thorough

[sage python]

Like is it a book that's useful to have on your shelf after you've learned the material. If it's good for looking up then yeah that's good

[flint forge]

And has lots of good examples and counter examples

[flint forge]

Yes

I think it’s one of the few books I’d never take off my shelf

[sage python]

What are the good reference books hmm

Rudin, D&F, probably Munkres, Hatcher

Hartshorne

[gusty smelt]

why not lang over DF for reference tho

[sage python]

Lang could be good too tbh. I at one point just pulled it up to read through some of the "raw field theory"

[gusty smelt]

yeah i learned my field theory/galois theory from lang

[gray gazelle]

I have said this before, and I will say it again. Nobody shits on my favorite books on my watch. You say D&F is boring, I say your mom is a f*t b***h.

[broken meadow]

f*t

[gusty smelt]

using fat as an insult is pretty bad

[flint forge]

You are so, so cringe

[sage python]

8da you have issues

Like I'm all for having strong opinions and defending them to the death

But after that exchange I can get firmly conclude that uh... You need help

Anyway tone it down a notch

[gray gazelle]

Okay, I will tone it down

[static crest]

censoring fat kekw

unless they meant it as a compliment and it was "fit bitch"

[broken meadow]

8da hates healthy people

extermination of all fit people

pain

[gray gazelle]

8da actually likes seeing their favourite books hated on

[gusty smelt]

If df is ur fav book I don’t trust you.

[gray gazelle]

And will compliment your mother if you do

Oh I can't read so I don't have a fav book

[crystal lion]

8da's mom is a sm*rt individual

[flint forge]

Df should only be your favorite book if you’ve only read one book

[crystal lion]

Df should only be your favorite book if you’ve never read Gallian

[sudden kindle]

DF haters be like

[marble solar]

Algebra will be your favorite subject if you can't dot your epsilons and cross your deltas

[broken meadow]

i will simply get good at all math

[primal summit]

I refuse to get good at analysis

[broken meadow]

imagine hating any one subject

[marble solar]

Group theory fucking sucks

[gusty smelt]

True John is polymath

[primal summit]

Even though I'm literally taking 2 analysis courses next semester

[gusty smelt]

Oh so my chem class this sem

[primal summit]

3 if you count prob

[gusty smelt]

Uses group theory

[broken meadow]

(the musings of a young to be mathematician)

[gusty smelt]

MonkaS

[primal summit]

Are you talking about Crystallographic groups?

[broken meadow]

inorganic chem moment or something

[gusty smelt]

It’s like an inorganic chem class, idk the details but my understanding is groups to describe simitries of molecules

Might be what ur talking about

[crystal lion]

number of ways a molecule can be oriented?

[primal summit]

It's that or point groups or both I think

[sage python]

Metal literally the only based person here

[gray gazelle]

I am also based

[sage python]

This comment in particular

Truly a good student

[broken meadow]

😃

[analog lava]

df fucking sucks

[sage python]

DF is like

Boring to just read

But it has the info

And if you're patient enough to read it, you'll understand everything since it's basically ELI5 algebra

[gray gazelle]

😠 😠 😤 😤 😒 🙃 😇

[austere ledge]

Hey guys. I'd consider myself weak at math. I like math, and I do a lot of basic linear algebra day to day (gamedev), but fundamental stuff I suck with and more advanced stuff is out of reach. I have some questions about learning myself and which books to get.

I read somewhere a good way to learn is to go through all of Khan academy starting from 1st grade? Haha

And how much do advanced mathematicians memorize, trig identities for example, and how much is left to be looked up or redirived? I'm a programmer and do A LOT of looking up stuff. Like I don't remember exactly how to implement a red-black tree but I'm sure I could work it out knowing the constraints.

Where should I start if all of my math is kinda shaky up to and including calculus?

[cursive orbit]

I wouldn't suggest doing everything from the beginning for the sake of it

Just learn what you need to know, and as long as you have a general idea of what goes on in the prerequisites, you should be able to fill in the gaps pretty quickly

[woeful marsh]

first grade math is boring af

ik from experience cough cough 4th grade my trying to grind KA

[eager stump]

trig identities is fine to look up as long as you can immediately recall why it works

like imo it's not good to look up the sum and difference formulas if you haven't worked out or seen the proofs/visual representations for why they work

but if you've internalized it there's no need to rederive every time

[gray gazelle]

당신이 바보 모두를 의심

Anyo haseyo

[gray gazelle]

https://www.amazon.in/Ramanujans-Lost-Notebook-Part-I/dp/038725529X

[bitter raptor]

This is the second time I hear this why does everyone hate on DF

Maybe I only like it cause I haven’t tried other alternatives but I find it good

I prefer what I’ve done so far to Judson

Though I’ll end up referring back to Judson for applications

[sage python]

I mean idk if it's hate lol

I just find it a bit too drawn out and dry. I got bored lol

[crystal lion]

is there a munkres like topology book which isn’t super old

like the pdf isn’t scanned and you can highlight stuff and ctrl f

hatcher is cool (it’s all of the above) but it’s alg top and i have only worked through the first (topology) chapter worth of munkres

[gray gazelle]

What is df?

Deez fNuts

[sudden kindle]

DEEZ fAT NUTZ

[gray gazelle]

😫

Fr

[coral narwhal]

deez feet

[midnight cipher]

Is there a book recommendation on Calculus 1 and 2 for a beginner?

[gray gazelle]

Calculus for dummies

[coral narwhal]

dummit and foote

[gray gazelle]

Workbook*

[coral narwhal]

Keisler infinitesimal calculus its free and hosted on some site

https://people.math.wisc.edu/~keisler/calc.html here's the site

[midnight cipher]

Just the workbook? Thanks, ill check it out

[midnight cipher]

Interesting. Thanks, ill check it out too

[karmic thorn]

Munkres has a new edition

Like, not a new edition with changes, just one with LaTeX digital version

Look for the one published by Pearson and GTM cover

From you know where (Amazon obviously)

[crystal lion]

you are the greatest human to ever live (behind gallian but yea)

thank you

[karmic thorn]

[neat sonnet]

is serge lang basic mathematics supposed to be this hard? I'm having trouble understanding his basic proofs for rules of addition.

Would there be any books you guys would recommend before reading it? Or should I just keep going through it at such a slow pace to make sure I understand every bit.

I'm struggling to get the proofs he talks about, example such as

N5 = -(a + b) = -a - b

Proof. Remember that if x, y are integers, then x = -y and y = -x
mean that x + y = 0. Thus to prove our assertion, we must show that

(a + b) + (-a - b) = 0

Which when he mentions the x, y, hes referring to N3 which states

If a + b = 0, then b = -a and a = -b.

Note: I don't need anyone to explain this, I'm just giving it as an example of how I don't understand what he's trying to say.

I tried watching a video to go along with it, and his explanation for this part is even worse than the book.

https://youtu.be/iQ9KKohrD-Y?list=PLMcpDl1Pr-viA25VUkHNmcUkWx9usPgyb&t=923

I put it to the timestamp, it lasts for about 15 seconds.

[eager stump]

i think it's just getting used to observing the properties of numbers and operations, and all their implications

it's also important not to just read these in your head

but write out the narrative of what you think is being said (and why it's being said)

(at least until you get used to these proofs)

[neat sonnet]

I watched a video about learning math from the beginning, and the very first book he recommended was..

Discrete Mathematics with Applications

The video didn't mention lang at all though. I wonder if I'm just failing to understand the way he's explaining proofs, it's hard because I don't have a clear definition of proofs and how they relate to what hes saying I guess. Also the fact I don't have a teacher to ask these things. That's why I tried watching the video above, but as you can see his explanation of N5 is pretty bad.

"cuz if we can turn this one minus then we'll get that and this on the other side" like what?

[eager stump]

It's hard to be clear for everyone. What's clear to one person can be too obvious or totally unclear to another.

[neat sonnet]

https://www.reddit.com/r/learnmath/comments/p88kjx/trying_to_learn_math_basic_mathematics_by_serge/?

Anyway, I'll stop rambling about not understanding as this isn't the channel for that. This gives a lot more context about my situation and goal. If you think I should stick to lang then that is fine, I just need to be lead a bit here.

That post is by me, I figured it'd be better than flooding the channel.

[eager stump]

whoa i'm not attacking you

[neat sonnet]

Nono, I didn't think you were at all!

[eager stump]

i get it, it can be frustrating

[neat sonnet]

I just felt bad because it is the wrong channel to be typing about I think

Don't worry, I didn't mean to imply I was feeling attacked by any means

[eager stump]

I know proof books aren't always recommended, but since Hammack offers his for free electronically online you might want to check it to just see what proofs aim to do... it's not always obvious if you haven't done proofs before

[neat sonnet]

Why don't people recommend em if you don't mind me asking

[eager stump]

i can't speak for them, but i think the thinking goes if you're seriously studying math you have to work through proofs anyway (and in the process get a feel for their technique and structure)

which in a way is true

but different people have different aims, plus they also learn differently

[neat sonnet]

Book of proof? Or something else

[eager stump]

i will say it doesn't hurt to peruse through a proof book. yea that one works

at least all the logical setup, direct proofs, proof by contradiction, etc.

so when you run into something like the proof you linked, maybe you'll recognize the structure and be able to follow the thread right away

[neat sonnet]

Do I need any highschool math education to go through the whole book? If so I could probably just read like half of it.

[eager stump]

at least that's one way, not the way. there are many ways

[neat sonnet]

for book of proof

[eager stump]

i think you only need a few bits of it. you def don't need to go through the whole thing

it gets to some complicated stuff at different points

but in general it's supposed to be approachable

[neat sonnet]

So basically, you believe it would help if I can translate:

-(a + b) = -a - b

Proof. Remember that if x, y are integers, then x = -y and y = -x
mean that x + y = 0. Thus to prove our assertion, we must show that

(a + b) + (-a - b) = 0

Into a more structured proof format. And it might be easier to process what he is trying to explain?

[eager stump]

well, so for example here

you should immediately recognize that it's important to know why he says we must show that

and maybe also useful to recognize the logical structure of if A and B, then C

truth tables aren't that intuitive to the uninitiated

contrapositive and vacuously true statements can confuse people

[gray gazelle]

I have both, but I think the workbook is the best.

[neat sonnet]

I know that from programming I guess. if(a && b) execute something is how it works . Is it the same concept?

[gray gazelle]

the other book is more like for extra explanation and examples.

[eager stump]

yes but it can be tricky. for example: https://math.stackexchange.com/questions/48161/in-classical-logic-why-is-p-rightarrow-q-true-if-both-p-and-q-are-false

[neat sonnet]

I guess, maybe he's saying "we must show that" applying N3 to the inverse of N5 is equal to 0, and so because of how we understand additive inverse on the numberline, N5 must be true? idk.

I'll read that

[eager stump]

the "idk" of your reply is important. doubt is a catalyst in math. trying to remove the doubt can build a lot of intuition

embrace doubt lol

[neat sonnet]

I mean, to me it makes sense. Will others agree? Was that what he was trying to show me? That's where I don't know.

I Just read that post btw and yeah it makes sense to me. I get how its different from programming if statements now.

Anyhow, I'm going to start reading some book of proof and see if that helps me with reading lang. Thanks for the talk sir, appreciate all the insight.

[eager stump]

np, good luck

keep at it

[neat sonnet]

I will. I have the drive to learn, just need some outside confirmation and encouragement every now and then is all. Have a lovely day!

[signal hinge]

i’m taking a course next semester which uses real and functional analysis by lang—which chapters of baby rudin would be helpful to review in preparation for the course?

[sage python]

1-7 at least

[marble solar]

Isn't chapter 8 the fourier specialy stuff

That'd be nice to have going in

[sage python]

I think it's a weird collection of topics

Basically 7 gives you uniform convergence

So I think 8 kinda cashes in by defining fancy functions and shit

Exponential, logarithm, trig stuff

Fourier series

I think it proves that C is algebraically closed

[marble solar]

It's a good chapter

[gray gazelle]

hi guys, does anyone know where i can download a free math textbook pdf?

i have the title and ISBN but not sure where i can download it

Statistics for Engineers and Scientists 5th ed, by William Navidi

[brisk ice]

#rules not be that person but

I don't anyway is suppose to help you pirate a book

Although I'm sure people know some places where and how

[gray gazelle]

oh i cant post abt books?

sorry

[brisk ice]

Well you can

[gray gazelle]

i just am not sure how to use libgen

[brisk ice]

Just not about trying to get them for free or whatever

[gray gazelle]

ah ok

[gray gazelle]

Bro, are you a grandma?

lmao no, i entered it in and it didnt work.

so i wasnt sure if i did it wrong

Oh, that's surprising that LibGen doesn't have the book

I found it on z-lib

can u link me @gray gazelle >

Sure

[brisk ice]

Is it possible some books where never put to pdf

I had look for 2 of mine before and gave up but the one was only $7 so whatever

[gray gazelle]

I think google had a huge project once to put every book to pdf

So i think it’s unlikely for even remotely popular books that they arent available in pdf

[brisk ice]

Must have not been popular

[gray gazelle]

Yea they realized the legality of it and stopped lol

[brisk ice]

Some random circuit analysis book 0130616559

[gray gazelle]

But the archive is still somewhere locked away

Oh lol right

[brisk ice]

I think it such a general book topic it isn't noticable

Noteworthy enough*

[neat sonnet]

good example I just seen in lang after reading some of a proof/logic book.
Prove the cancellation law for addition:
If a + b = a + c, then b = c

That is a conditional statement? Not universal tho

[dapper root]

Pls do not instruct people on how to pirate things on the server, it’s a TOS violation

[broken meadow]

We do not endorse piracy

[marble solar]

Ah you mised the chance to do a evangelion reference

which would have been hilarious

[brisk ice]

Maybe someone that hates police but likes the helmet might....

Okay maybe not that

Wonder how much they get paid per book

Many of these authors

[quick hornet]

for textbooks? not much

the cut is invariably sub-20% and typically more like 10%

idk about other types of books but i dont think its much better

[brisk ice]

anyone know

ik they have a library and people might also upload their own stuff

[gray gazelle]

It does have some

[hearty steppe]

You mean booklickers

[crystal lion]

pinged for deez nuts

thank you to whoever reacted on my behalf

[sage python]

Lol Jesus

Should've anticipated that the children would get too caught up in this and use the jokes where they make no sense

[crystal lion]

yea you should’ve predicted my stupidity

[sage python]

At least now I know what to expect

[white flax]

grokking algorithms

[eager stump]

What about it

[strong plank]

Does anyone know if there is a pdf with the solution for algebra of artin ? I ve found a pdf but it s only chapter 6, and 13,14,15… so if anyone know where I can found the correction… ^^"

[novel solar]

A first introduction to probability book recommendation please

[marble solar]

Durrett

[gray gazelle]

books to love math?

or whatever math book thats not a textbook

[marble solar]

I like Boyer's history and development of Calculus

[stone storm]

Is Durrett's intro prob book good? I just read his Stochastic processes book and it had a ton of typos

[marble solar]

Ppl say it's good

I tried reading the first section but I was ok w/ not re-reading measure thoery

[gray gazelle]

Wazzap, I am going through understading analysis by abbott. How can I supplement it with spivak? Like read its theory?

[narrow talon]

It’s good, but long winded and poorly compartmentalized imo so it makes a poor reference

[marble solar]

How about for learning?

[marble solar]

any better recs then?

what is a strong analysis background

I'll probably go w/ durrett because that's the standard for quals

[patent flume]

anyone got a book for commutative algebra

ring stuff

[sage python]

If you like doing problems, Atiyah Macdonald

If you wanna have more of the material in the text and just want a standard smooth-ish book that's less geometric, Matsumura

If you want something hypercomprehensive and geometric, Eisenbud

[patent flume]

alrighty

cheers

[gray gazelle]

Someone can recommend me a college algebra book for introduce me in the subject?

[cursive orbit]

I'd just use KhanAcademy

[eager sandal]

I was wondering if anyone here would know about good books for me.
I am a physics student and learnt maths mainly the physics way.
I went through Paul's online notes for differential equations and stuff.
I was wondering if anyone know what book covers maths focusing on what physics courses miss out.

[misty wyvern]

Boas's Mathematical Methods

[brisk ice]

Is this book any good

I assume it's like a review/reference book

[neat sonnet]

Anyone read "how to prove it"? By velleman

How did you like it? Im finding it challenging, and boring/tedious to go through. Some of the exercise questions feel like the information to answer them wasn't all taught. That or I'm not soaking in the information as well.

[gray gazelle]

No

[neat sonnet]

No what

Gimme more : p

How about "Discrete Mathematics with Applications" by susanna epp

[eager stump]

It's ok. Not my fav but it does its thing

[smoky surge]

I have heard discrete math for ducks is wonderful

[smoky surge]

thats whats recommended on this server I went through book of proofs awhile ago and I liked it but its def more cute than a whole course

[eager stump]

I bet there's a pigeonhole pun somewhere in there

[smoky surge]

id still recommend tho

[eager stump]

Yea it's not bad

It's readable

And free, though the hard copy is cheap

[gray gazelle]

I think working through the first few chapters of Basic Mathematics will prepare you for the algebraic proofs Lang asks for better than a proof book.

My 2c.

I got some mileage from Book of Proof's first few sections, just to get familiar with notation, but I think a proof book is overkill, especially Velleman.

There's a YT series by John Gardner where he reads through BM which might be helpful

Also BM has a reputation for being hard. Maybe not among grad students on Discord but it's completely different from most HS level textbooks which is why it has the reputation it does. It's a treatment of HS mathematics in a mature (uni) way. Axler's Precalculus has some comparable exercises as open "problems" but Lang asks you to do things a lot of students struggle with in the absence of instruction, because he asks for creative applications of definitions, theorems and axioms and doesn't ask much in the way of computation. And Lang seems to have a polarizing expository style (I like it but it requires acclimatising).

I haven't worked through section 2 on plane geometry yet but it looks good to rectify poor geometric intuition (our education is mostly analytic) , our prof used neat geometric proofs in calculus and they seem like black magic at first.

[timid vector]

Is there a book which doesnt make point-set miserable

[gray gazelle]

munkres

[timid vector]

I didnt like it too much the first time i tried reading it

But maybe i should just bite the bullet

[gray gazelle]

is their a good book for differential geometry

lee

[lapis sundial]

People used it in my (physics) course in first year. It's probably decent for physics and stuff but don't expect much rigour or abstraction - it feels a bit more recipe-ish idk

[neat sonnet]

Thank you for this. It gives me hope! I do programming so I was assuming the logic part of the proof book would come naturally. Apparently, not.

I think the difference is that I'm not used to abstracting word play into a formula, and I'm not used to thinking "theoretically" if that makes sense.

Is your suggestion to read first few chapters of a proof book and then try lang again?

[frank matrix]

Looking for a solid matrix algebra book

[willow pecan]

What sort of matrix algebra?

[flint forge]

That is the opposite of matrix algebra lol

[brittle grotto]

XD

[flint forge]

i think you replied to the wrong user

[brittle grotto]

Omg

[flint forge]

Me: Condensed.pdf can't hurt me
Ultraproduct: reminds me of the reading group

[brittle grotto]

What do you want to focus on in matrix algebra

[brittle grotto]

Long day today

[brisk ice]

so i was looking for a list of books maybe k-12 up and commmon courses you would take in a math major. Could anyone look at this list of books and tell me which ones to remove and which ones to possible replace

[brittle grotto]

I could have a look yeah

[brisk ice]

it is kinda long and i have not much knowledge of them i just was kinda looking at common courses people take so i have a list and some are repeat topics

[frank matrix]

Not sure, really just looking for a good textbook for my class

We don’t have an official one

[brittle grotto]

Can I know what grade you are in? Just so I can narrow my research

[frank matrix]

Sophomore in University Mech Eng

[brittle grotto]

Ok, I will tell you if I find anything

[brisk ice]

some are probably redundant so let me know. Also some people might not like them

and idk if some are just super niche topics that i added on accident

[cursive orbit]

Lol

[brisk ice]

look idk

dont flame

[cursive orbit]

Gallian abstract algebra is gonna please 123four

[brisk ice]

i just added a bunch of books and need to trim it down

im not even sure if some of these books are the same topic with a slightly different name

[cursive orbit]

Well that's like

The whole list

There's like 5 introductory abstract alg books in there

[brisk ice]

well i dont know an "ideal" one

prefer more introductory for all of them i would say

[gray gazelle]

Throwing out this calculus and non-proof based linear algebra non-sense and just starting with analysis and linear algebra will save you a lot of time and misunderstanding.

[brisk ice]

time to make a hit-list of ones to eliminate

unless anyone just has a more ideal list

[cursive orbit]

You could get rid of Gallian and Farleigh abstract algebra

[brisk ice]

would it be easier to just say books to keep

[gray gazelle]

Is Gallian abstract algebra a bad book

[brisk ice]

[gray gazelle]

What about "A first course in abstract algebra with aplications" by Joseph Rotman

[brisk ice]

if any of this is directly towards me I won't know anything as I just lumped a bunch of books together

[subtle siren]

@brisk ice I think I'll just comment on the only thing I have any confidence in, and that is that the Ross probability book is the most standard among the 3 related ones:

1. S. Ross
2. Wackerly, Mendenhall & Scheaffer
3. Dobrow
   They probably come in different flavours so there's no direct comparison I guess, but Ross I think is most standard for starting, then somewhat graduate could be Wasserman's All of Statistics (which seems to competes with Wackerly)

[gray gazelle]

no itsnnot towards u

my bad

[cursive orbit]

Depends who you ask. Some people think it's too hand-holdy, but some people swear by it.

[gray gazelle]

I like hand holdy books

[brisk ice]

hand-holdy meaning what exactly?

[subtle siren]

Tell you everything, I suppose

[gray gazelle]

i guess books that explain and tell u everything

[brisk ice]

oh well i didn't know if that meant less proofs and stuff like that

[subtle siren]

There's definitely a sweet spot for that and it really depends on the author

[brisk ice]

and more just intuitive feel of ideas

[subtle siren]

I'm trying to take a look through Dobrow to see what level it expects

[subtle siren]

Right I just took at look at Dobrow (actually the 2nd ed, which is Wagaman & Dobrow) and it seems to be around the same as Ross in expected level at least at first. It does have a few examples in R which Ross wouldn't have.

As a purely pedagogical comment I think the textbook might need more figures from just quickly glancing through it, but if you do not require visuals that might not be important. It gets more illustrative nearer the end, but could help with more closer to the start

[slate quarry]

Hi guys. I remember a few months ago someone sent (I don't remember if was in this channel, or in the discussion channel) a really interesting image (at least interesting to me). The image was basically a roadmap of math textbooks. I only remember that the roadmap starts with some openstax books, and that there were many books by Lang. I've tried to find it, but I failed.

[slate quarry]

It was visually similar to that.

There were physics books too.

[brisk ice]

How good are the openstax books?

I remember doing a bit of one of them for some astronomy class and it was okay but idk about other classes

[hollow drum]

I'm taking a first year grad algebra course. The instructor said we could use lang or hungerford. Which would you guys recommend?

[eager stump]

They're decent enough

[sinful crag]

Does anyone here have opinions on the best reference texts (for a refresher, not first course) for ODES and PDEs? My undergrad ODE used Diprima and I really didn't care for it.

[willow pecan]

PDE reference should be Evans

No good ODE books unfortunately

[still jay]

Was it this?

[quick hornet]

wtf is that flowchart

why is proofs a prerequisite for fucking everything

why does it pay lip service to a "non-proofy path" through lang hs alg/calculus but suddenly hit you with the fucking do carmo

why is the only prerequisite to topology abstract algebra

did the chart maker choose textbooks solely for their names

[narrow echo]

yay I have a prof on the chart

[quick hornet]

what the hell is category theory doing... where it is

[narrow echo]

I can't decipher the biases of whoever made this yet

[quick hornet]

why learn about the independence of CH before reaching fucking jech

(or a similar book)

why are there 2 "geometric algebra" books on a non-physics path

man im so confused

also whys it recommend the hard shit right away for high school level stuff/calc/analysis

but its abstract algebra recommendation is pinter

at least be internally consistent with whether you expect your students to be good right away or not

[willow pecan]

Also riemannian geo and riemannian manifolds are not connected

[quick hornet]

like you can theoretically go straight from lang's calculus to spivak's CoM

which is possible, dont get me wrong

but like

why are students going down the algebra path spoonfed intro proofs, then pinter

whereas students going down the analysis path are like

straight into lang's calc and then spivak's CoM

[static crest]

proofs textbook 🤢

just do lin alg

[quick hornet]

it has lin alg after the proofs book

[static crest]

ya, I meant doing a proofs book is useless

just learn it as you do lin alg

[narrow echo]

where is this from pls ty

[quick hornet]

also yeah vakil is bizarrely positioned

you have 3 paths into vakil

[willow pecan]

Oh PDE is also in two places

Lol

[quick hornet]

• "Category theory (Awodey)"
• "Riemann Sufraces (Miranda)"
• "Modern Differential Geometry (Lee)"

imagine never taking an algebra course, but having read do carmo and lee

and then walking into vakil

[willow pecan]

Category theory comes from advanced abstract algebra though

[quick hornet]

no i misread

it comes from abstract analysis

no clue what that means

[dapper root]

What?

[willow pecan]

Anyways

Bad graph

[dapper root]

Are people suggesting ppl do the rising sea without an algebra class?

[willow pecan]

Don't use it

[quick hornet]

i suppose the rest of the analysis isnt abstract

[quick hornet]

thats one way you can navigate the above flowchart.

[dapper root]

Lmfao

[narrow echo]

aren't the lines prereqs and not paths

[dapper root]

Hurb

[quick hornet]

unless the implication of the arrows is they require ALL leadin arrows as prereqs

but thats even stupider

[spiral gust]

Is that list some actual course list in a university or is it just some meme?

[narrow echo]

it's high effort

[willow pecan]

It's bad

[dapper root]

Do you guys remember the /sci/ textbook images

[static crest]

🤨

[dapper root]

You can tell it’s from /sci/ because there’s always an anime girl

Saying “you can do this”

[static crest]

lmao

[quick hornet]

also

[dapper root]

And they always have like 4 proof books

2 set theory books

[quick hornet]

why is AG of curves nowhere near modern AG

like yeah they kinda talk about different things but

[dapper root]

And like 17 books in you do single variable calculus

[quick hornet]

theyre not even in a path

[static crest]

I mean I always had an anime girl on every cheat sheet I was allowed to use in uni and hs

although it wasn't motivational and all the anime girls had faces of disgust

[quick hornet]

it feels weird to me that these images attempt to lay out like

10 years of fucking coursework

like, teach them a roadmap for what they need to do right now and maybe what they need to do next year

[static crest]

ya, goals need to be realistic

[quick hornet]

anything beyond that is wayyyy too far forward to plan

its not even that the goals are unrealistic necessarily

its that goals change

if youre in prealgebra you should not be planning out how to read Rising Sea

[static crest]

gotta have SMART goals

[cursive orbit]

I think individualized flowcharts on areas of mathematics, i.e. complex variables, would be way more readable and way more helpful

[static crest]

I think using a flow chart at all for this is misguided

[willow pecan]

The Calculus

[sage python]

There's no real point in flowcharting that hard

[cursive orbit]

[sage python]

Do what's in front of your face

Future you does what's in front of their face

Etc

[cursive orbit]

read the preface of the books

[quick hornet]

i mean in fairness

every preface ever says

[sage python]

@sterile cedar what are you trying to learn now?

Like this month

[quick hornet]

"nothing is expected of the student beyond mathematical maturity and some basic [field]"

[crystal lion]

can I learn inter universal teichmuller theory right now?

on it

initial theta data

ok I give up

[cursive orbit]

can I learn Matrix-based Information Universe: Neverland Theory right now?

[sage python]

I don't think when you're early in math it makes a whole lot of sense to have long term goals. If you're about to take calculus it makes no sense to be like wow I'm doing all this to eventually learn AG. Like you don't even have a perspective on AG to suggest that it's a thing to want to learn

[quick hornet]

just read nlab for 8 hours a day until eventually it starts making sense

[crystal lion]

ok time to learn what a scheme is

time to learn AG in one day

every time I try learn the definition of sheaf on nlab I end up clicking through a bunch of terms until I'm back at sheaf

[crystal lion]

oh wait schemes and sheafs are two different things

what are the morphisms

oh that makes sense i guess

[quick hornet]

this is why topology is useless.

[crystal lion]

I should go learn more category theory first

well any category theory besides what a category is

no like contravariant functors

i don't know what those are

i think so

maps between cateogries

which preserve stuff

yeah

why would you want that

oh

dumb question and kinda unrelated, but you can only have functors between small categories?

oh i could imagine some twisted functor between large categories

I see

from the category of open sets of the topological space to itself?

oh ok

i will continue reading from there bc i have better foundations now

i don't understand what the "restriction" map is here

if U \subset V

ohh from F(V) to F(U), not V to U

ok so the map is possible

i don't know what "restriction" means here though

oh the domain of the functions should be in the topology?

yea that would make sense

[trim lagoon]

any books to introduce me into stadistics and probabiblity

???

[crystal lion]

oh so it's a category of rings of continuous functions and not a category of just continuous functions?

for our presheaf F on the topology T:
the morphism from the open sets U to V (where U \subset V) should go to F(V) to F(U), where F(V) is a continuous functions from V to T and likewise with U

now to set up the map from (U -> V) to (F(V) -> F(U))

Let a \in F(V) and b \in F(U)

hmm setting up a map of maps is hard

oh I just introduced them for brevity but I guess making them elements would aid in the proof

wait I'm going to work with just continuous functions and not rings because things are already too hard for me

[crystal lion]

so the k = (U -> V) map takes k(u) = u for u \in U

ok so what do we want to make the map so that ((F(V) - > F(U)) satisfies the contravariant functor conditions

F(id_U) = id_{F(U)}
and
F(g \circ f) = F(f) \circ F(g) for morphisms f: X -> Y and g: Y -> Z

the identity morphism for an open set U is f(u) = u for u \in U and f: U -> U

associativity for the morphisms on open sets checks out too

(all of the above work was a sanity check for me on why our original top space forms a category)

wait wtf does a map between functions even look like

if f: X -> C and g: Y -> C where X \subset Y, what does h: g -> f even look like (I can't even think of an example)

i don't want to ping ultra but it is very tempting

[crystal lion]

@sweet lotus sorry

i don't see why this is anything but a map between two functions

ok maybe the category our presheaf is mapping into isn't clear in my head

the objects are continuous functions X -> C

and the morphisms are ???

oh each object is a set of functions with domain U?

ohhhhhhhhhhhhhhhhhhhhhhhhhh I get it

so for every f \in F(V) where f: V -> C, you make it map to g: U -> C where f(u) = g(u) for u \in U

(for U \subset V)

ok now let me look at the point of this, which you already described I think

oh the gluing lemma thing isn't that surprising because i don't think i understand the gluing lemma rn anyway

[sudden kindle]

This is a graduate level complex analysis textbook formatted like a highschool math text book https://press.princeton.edu/books/hardcover/9780691207582/a-course-in-complex-analysis#preview

[crystal lion]

my favorite type of formatting

[brisk ice]

How do non highschool text books change?

Just less color?

And boxes around things

[sudden kindle]

yeah

the highlighting is gone

Axler's Lin Alg textbook has a lot of colorful formatting but it doesnt feel like a highschool textbook, aesthetically

[marble solar]

I like Marshalls

[quick hornet]

honestly that style is dope

would not complain if more math books used it

yeah yeah it wastes colour ink, whatever

the book costs $300, they can afford it

[valid moth]

yeah lol

i like how axler is formatted at any rate

[still jay]

I dislike axlers formatting tbh, the colors distract me

[gray gazelle]

is theory of equations important and can anyone recommend me a book on it

[sage python]

Wait

This is actually good

@sudden kindle

Or at least like

Relative to how corny it is

It's actually kinda serious

@marble solar lmao they should hire you to shill for it

[hearty jetty]

Hey guys
Which books should I use to practice linear Algebra!
I am a beginner, studying LA from Khan Academy.

[slate quarry]

Yes, that is. Thanks a lot 😄

[gray gazelle]

For those who want to get 💸

[gray gazelle]

My recommendation is to not learn LA from khan academy, or any subject rigorously for that matter, because it simply skips over too many core topics, such as the replacement theorem. If you want a more theory based book i suggest friedberg insel and spence's LA book, if you are looking for a more rigorous and computational based book i suggest hoffman and kunze