book-recommendations

[red wraith]

It's good and motivational you all should read

[dim pendant]

We should have the bot respond automatically with the .gg/books link whenever someone asks for a recommendation

that way nobody has to waste their time waiting, and nobody has to waste their time telling someone to use Khan Academy to learn trig for the 300th time

[molten gulch]

Which I believe could use with quite a few more entries

[dim pendant]

ye

[still panther]

https://mathematics.gg/books

[light jetty]

Hi, I'm a high school math student, I am looking for a book to learn about polynomials from which will also include proofs of theorems and stuff

I want to learn about the basics of polynomials with proofs

[cunning elk]

take… literally any high school algebra text?

[wraith cave]

😭 that’s literally me

[cunning elk]

AoPS intermediate algebra does a decent job proving most of the foundational results although a few of them (fundamental theorem of algebra, etc) do get handwaved bc you need much more advanced tools for it

[wraith cave]

every time i come here it’s always an algebra 1/2 request

instead of something interesting like pdes or complex analysis

[cunning elk]

and at such a low level the textbook market is even more oversaturated

that if you just spend 2 seconds looking

you’re more likely than not to find smth that works

also I’ve never heard of a high school algebra text focusing exclusively on polynomials wtf

you don’t know what you don’t know

??????????????????

you absolutely do need the techniques and basic knowledge from real analysis in order to be able to do complex

[naive lava]

if you are comfortable with epsilon delta proofs then no

you will use real analysis tools

but won't need to prove anything that real anaysy

everything either gets proven by the taylor expansion

or the cauchy integral formula

[cunning elk]

at least some basic familiarity with foundational techniques from real would be helpful tho no?

[naive lava]

oh of course

but you don't have to exactly know the constrution of riemann integral to prove anything about integrals in complex

that's what i meant

some schools offer something called, proof-based calculus

something like that should suffice for prereq

complex anal like complex anal

or just stating and using the theorems

cos there's a big difference

well is the main focus proofs or applications

[remote sparrow]

https://softwarefoundations.cis.upenn.edu/

[rigid trail]

applications

theres no way they can do the theorems without real analysis experience first 😭

[remote sparrow]

https://www.amazon.com/Complex-Variables-Applications-Brown-Churchill/dp/0073383171

notable counterexample

[rigid trail]

https://mathematics.gg/books/functional-measure-harmonic

it doesnt recommend any measure theory books bruh

[naive lava]

just use rudin

[rigid trail]

rudin dedicated like only one chapter to lebesgue theory 😭

[naive lava]

no it has 2 chapters

[rigid trail]

"its just common sense" ahh

[naive lava]

not that it's still good lol

[rigid trail]

you sure about that

the last two chapter are "integration of differential forms" then "the lebesgue theory"

It defines measure space in the final chapter on lebesgue theory

[naive lava]

oh i meant the big rudin

[restive granite]

Hello I am bhargava from India, I'm 13 (14 by this June) who has just arrived into high school. I have however plans of completing it before my summer holidays end, not only because I like thinking in depth of it but also because I don't like school and would rather work a ton to go to university instead directly.

but, my summer holidays end on may 31st , I am on a time crunch. I was academically poor with less marks than most people, but I do love thinking in depth and I can do it without getting distracted if it's a topic I love (i.e maths Or physics)

so what I really want someone to ask me to learn concepts each day and explain it when I finish my research and going indepth of that topic. and you'd ask questions so I actually understand what I'm talking about. And at the end of the month or sooner, I'd have learnt maths of 4 years of high school.

this feels like a better way for me to learn instead of reading books because It is something that I feel in command of and I like doing it. So please come if you can, I already spent over a month of my summer holidays trying to find a path.

[rigid trail]

oh

isnt papa rudin for complex

[rigid trail]

Don't avoid books

[restive granite]

I won't

but

I can't just focus on it if u say I read it

I wanna do it on my own

When someone gives me specific topics to research about

I see books and everything on it and go indepth while it still being fun to me

[proud osprey]

First section of big rudin is on measure theory at least

[rigid trail]

The specific topics should be high school math and maybe basic calculus

it seems

[rigid trail]

okay

[restive granite]

to give a context otherwise people wouldn't understand what they're tryna do

[restive granite]

no it can be higher

I can spent as much hours as it takes if it's something I love

but high school math should be covered by the end

[rigid trail]

Well at least get high school math first

You really cant go far without that

[restive granite]

yes but to do that properly without just turning pages

I shouldn't get bored by it

if u give me an advanced topic for example

[normal crystal]

he wants a personal (free) tutor for the next 27 days to "learn all of high school"

[restive granite]

I will spend hours on it to learn the ideas from basic maths

[rigid trail]

Books are great, they have high quality exercises. but if you want supplements, there is Khan Academy, lots of youtube series, and also https://tutorial.math.lamar.edu/

[restive granite]

no

I will repay when I get a job

or when I can

[rigid trail]

i don't think math books are "boring" unless you get bad ones

[normal crystal]

mhm
either way
that's not how it works on this server
you can ask questions in help
gl

[restive granite]

yes but there isn't an interest for me to just keep on reading them unless I want to learn a topic. which is why I want someone to ask topics each day that I'd go well into

and I would refer all those materials and understand it

[rigid trail]

Please learn high school math first

[restive granite]

I will but I want a motive to do so

[rigid trail]

it's very hard to do "research" into other topics if you dont even have that

[restive granite]

the motive is you giving me a topic

[rigid trail]

The motivation is so you can understand interesting math later

[restive granite]

not really, I wanted to develop a theory on structural infinities a few days ago

[rigid trail]

Preliminaries - Exponent Properties, Rational Exponents, Negative Exponents, Radicals, Polynomials, Factoring, Rational Expressions, Complex Numbers
Solving Equations and Inequalities - Linear Equations, Quadratic Equations, Completing the Square, Quadratic Formula, Applications of Linear and Quadratic Equations, Reducible to Quadratic Form, Equations with Radicals, Linear Inequalities, Polynomial & Rational Inequalities, Absolute Value Equations & Inequalities.
Graphing and Functions - Graphing Lines, Circles, and Piecewise Functions, Function Definition, Function Notation, Function Composition, Inverse Functions.
Common Graphs - Parabolas, Ellipses, Hyperbolas, Absolute Value, Square Root, Constant Function, Rational Functions, Shifts, Reflections, Symmetry.
Polynomial Functions - Dividing Polynomials, Zeroes/Roots of Polynomials, Finding Zeroes of Polynomials, Graphing Polynomials, Partial Fractions.
Exponential and Logarithm Functions - Exponential Functions, Logarithm Functions, Solving Exponential Functions, Solving Logarithm Functions, Applications.
Systems of Equations - Substitution Method, Elimination Method, Augmented Matrix, Nonlinear Systems.

start with that

[restive granite]

I studied a lot for it

[half void]

LMAO

[rigid trail]

thats plenty of topics

all very interesting

[restive granite]

and I've went pretty deep

[rigid trail]

what does that mean

[restive granite]

basically uh I had the idea of a function which

diverges using convergence

where it's a recursive self multiplying number

[normal crystal]

he will tell you
if you're his personal tutor of HS math for the next 27 days

[restive granite]

but each step depends on time

Half of the remaining

so

for example

a power a

takes 0.5 seconds

and a power a power a takes 0.25 seconds

[rigid trail]

what

[restive granite]

similarly it goes till the time is reached

[rigid trail]

What's a

and what does it have to do with seconds

[restive granite]

any number

and it depends on time

[rigid trail]

pls use math notation instead of explaining using seconds

[normal crystal]

#crank as a honeypot
mods need to try it

[restive granite]

each function results as: T(n) = 1/2 power (n+1)

[half void]

Isnt that just knuth up arrow

[rigid trail]

,, f(n) = \frac{1}{2^{n+1}} ?

[hasty eagle]

qiu

[half void]

https://en.m.wikipedia.org/wiki/Knuth's_up-arrow_notation

[restive granite]

no, that's T of n

f(n) = A {f(n-1)Number of knuths arrows)}

for example, if f0 is just a power a which is something like 3 power 3 , 9

then f1 is 3 power 3 power 3 ... 9 times

and f0 takes 0.5 seconds to complete

f(1) takes 0.25 seconds

[half void]

What does it mean that it takes a certain amount of seconds

[rigid trail]

Can someone else explain

idk what these seconds are

[proud osprey]

This sounds like that lightswitch paradox but without any paradox part

[normal crystal]

the seconds of your life you're losing to this explanation

[restive granite]

it doesn't really have a valid reason to depend on time which is why it failed as a theory when I realized that

I'm not trying to prove that here

I am just saying

I can dive into concepts

if someone gives me

I hope someone does

[half void]

Qiu already gave you

[restive granite]

yeah

[half void]

My friend

[restive granite]

I am gonna go through it

thank you for giving me that

appreciate the copy paste.

[rigid trail]

it is from https://tutorial.math.lamar.edu/

you can make it your motivation to complete pauls

[normal crystal]

you already came in hot with a goal of all your HS math in less than 4 weeks
you had the topics before you even typed
HS math

[rigid trail]

if you finish pauls then you will have up to calc 4 under your belt (mostly)

[restive granite]

wdym

yes

but I needed a different way to learn it

[normal crystal]

times like this I actually do wish I had image perms

[rigid trail]

or maybe you just need to start doing it

math isnt always about fun

but once you start learning then it becomes fun

yeah but it is necessary to get through

[half void]

All true

[normal crystal]

just pretend chatGPT is a member of this server
and each day ask it to tell you the next topic from your list

[restive granite]

math isn't, but I am. I can change how I percieve to learn math. Whether in a way I love it without getting bored or not.

[half void]

This is actually a good idea if this is what you are seeking

[half void]

Then change it

[rigid trail]

change yourself to perceive loving Pauls notes for the next 27 day

[restive granite]

it's gonna be the only option anyways in a day if no human agrees to my request

[rigid trail]

actually for the next couple of years

Pauls gonna serve you well through calc 4

so get cozy with it

[half void]

You don’t need a human

All you need is yourself

[rigid trail]

and a robot 🤖

[restive granite]

I don't need yes, I don't need tasty foods either, but I want someone so it feels better for me to learn it

[trail hemlock]

graphing stuff is fun wdym

[signal mountain]

whats your background, why do you so greatly feel the need to learn math if you seemingly dont acc want to 😭

[half void]

He’s 13

[signal mountain]

oh so its like school

[rigid trail]

you can just learn it from your high school like most people then

[trail hemlock]

u dont rly gotta listen tho

[rigid trail]

if you have the motivation to be way ahead, you gotta self study

[trail hemlock]

✌️😂

[signal mountain]

stop deeping it, just go to school, do some studying, youll be fine

[rigid trail]

no one is gonna hand hold you if you want to be ahead

[trail hemlock]

i mean i kinda understand where they are coming from

[normal crystal]

no you don't
you're just arriving late to be contrarian

[trail hemlock]

someone woke up on the wrong side of bed 😂 ✌️

[normal crystal]

🤡

[rigid trail]

🍿

[restive granite]

My background comes from an Indian family who absolutely fuckingly I believe to be blind soceital sheeps as in they don't understand the why of many things and just go on with their elders' way.

I am academically pretty poor and india is very competitive because a few hundred million chicks were fucked here. I wanna change my life though to be something which I'd want and like- to an extent atleast

[trail hemlock]

ok first of all, you did NOT need to phrase it that way

[half void]

Tf???

[signal mountain]

ok but why does it have to be math, there must be thing you acc enjoy that you could pursue instead

[rigid trail]

okay so you have a lot of motivation?

[half void]

Alright what the fuck

[restive granite]

I have already spent a month arguing on a lot of things, to receive no response

[rigid trail]

go study math with that motivation, pls

[restive granite]

yes

[rigid trail]

it will help you

[normal crystal]

tbh, I don't take any of this chat cereal
from the initial request
if I want a story with plot holes
I'll watch donghua

[restive granite]

I enjoy deep thinking, and math is a pretty similar thing

[trail hemlock]

shock value isnt gonna make MORE people give u an actual response

[rigid trail]

eat your veggies, learn highschool algebra

[restive granite]

no

[signal mountain]

deep thinking will assist you in any discipline

[half void]

I dont think you understand much either my friend

[restive granite]

I am not disciplined enough tho, I do agree it is important but I do not want to be disciplined to go somewhere and do 8 hours of nothing. if it was like a university, I could understand why I needed the discipline because of the importance of time there

[normal crystal]

fellow daoist

[signal mountain]

...what
i dont really see how that relates
im just saying why dont you take that enjoyment of deep thinking and apply it to say history or science or whatever else

[half void]

If you aren’t disciplined nobody will help you.

[restive granite]

no I don't, I question things I'm a skeptic. but the answers I get is somewhat of a nonsense

[rigid trail]

if you have the motivation you can build the discipline

[half void]

There is no nonsense it what we are trying to tell you—just study.

[restive granite]

yea it isn't nonsense but

[rigid trail]

you cant be saying "i wanna learn math i wanna learn math i wanna learn all high school math in 1 month" but also be not motivated enough to actually learn it

[restive granite]

I don't think it's the most efficient for me to study by seeing books

[remote sparrow]

some ppl wonder why im pretty much in this channel all the time instead of discussion

[restive granite]

only if I'm motivated by it I will learn it completely

[rigid trail]

books are very efficient

[restive granite]

yes they are

[rigid trail]

read the chapters, do the exercises

[remote sparrow]

#book-recommendations discourse > #discussion discourse

[restive granite]

but I won't be if u give me a book and say "ok read this and u be fine "

[rigid trail]

much much faster than high school courses

[half void]

Ooo new color

[trail hemlock]

your original question was asking people to ask you abt topics to go in depth, right? and you said you are willing to put a lot of work into smth that interests you. I dont see where this comes in

[normal crystal]

you guys still answering after the mass chick production line is something

[restive granite]

I wanna do that myself

[trail hemlock]

like are you willing to put in the work or not

[rigid trail]

damn pog

[trail hemlock]

if no, use some deep thinking to figure out why

[half void]

Yeah i know that line was actually crazy

[rigid trail]

that's how it works though

[trail hemlock]

if yes, follow peoples advice and use textbooks or khan academy or smth

[rigid trail]

Books, pauls notes, khan academy, youtube. you can ask questions on any math in this server. what else do you really need?

[remote sparrow]

i don't really read cultivation type stories, what's the appeal behind them?

[trail hemlock]

reading textbooks can be dry, sure

so use khan academy

[half void]

Motivation and discipline. But we cant give him that

[restive granite]

there are resources and I am willing to put the effort but if it's in a way self motivated, it would be efficient for me

[trail hemlock]

what are u on abt twin

[restive granite]

if someone gives me tasks about concepts

[rigid trail]

you arent willing to put in the effort if you need someone else to keep you motivated

[restive granite]

I feel self motivated enough

[restive granite]

well yes

[remote sparrow]

my dad watches a lot of wuxia movies

[restive granite]

no

I don't want someone to pamper

[trail hemlock]

???

[restive granite]

I want someone to just state concepts' names and leave

[half void]

Yo anyone got qft books

I’m bored

[restive granite]

And I'd explain them with my own research and indepth thinking

[rigid trail]

Okay, start with high school algebra concepts

It will help with literally all the rest of math

[trail hemlock]

what do u mean by "research"

[remote sparrow]

is crouching tiger hidden dragon like that?

i don't rly pay attention

[trail hemlock]

like afaik there arent many open problems in high school algebra

[restive granite]

Internet and searching and tryna understand the why of it then the how of it

by thinking

[remote sparrow]

almost all of the wuxia movies my dad watches have a crappy vietnamese dub

[half void]

Aight im out wth is this lmao

[trail hemlock]

its much better at least at the HS level to be more structured and use a textbook or khan academy, or smth

[rigid trail]

okay tbf there isnt a much of "why" and "how" in high school math, but also you're definitely going to need high school math before you get to that point so..

[trail hemlock]

you just dont have the background to be googling stuff and understanding it all

[tribal crow]

,ci

[hasty eagle]

Channel information for book-recommendations.

​ ​ ​ ​ ​ ​ Name: book-recommendations [#book-recommendations]
​ ​ ​ ​ ​ ​ Type: Text channel
​ ​ ​ ​ ​ ​ ​ ​ ID: 716264872018706443
​ ​ ​ ​ ​ ​ NSFW: No
​ ​ Category: Discussion (360643390594875392)
Created at: <t:1590841253:F>

Topic

Use this channel to ask for book recommendations. Tends to be mostly math but feel free to ask about other literature (YMMV). Check out https://mathematics.gg/books too!

[rigid trail]

send him to the nlab

[trail hemlock]

i love nlab

[normal crystal]

hmm, I don't read webnovels
but I do read some manhua and watch some donghua
some of them are interesting, some are just like comfort trash
the donghua produced in the last couple years with higher production values are night and day to a few years ago
for cultivator genre specifically, yea, most follow the same general path
but if you accept that, it can be enjoyable

[trail hemlock]

(this is the entire page)

[rigid trail]

bruhhhh

[trail hemlock]

LMFAO

ok ts is prob off topic

[remote sparrow]

https://www.royalroad.com/fiction/72771/depthless-hunger-underdog-xianxia-litrpg-monster

this is inspired by cultivation stories

i think this is good

[normal crystal]

definitely, especially in the lower budget, more trash ones

if you had those hours back
you could spend them being that guy's personal tutor this month
what a shame

I cannot
I'm not chinese heritage or even asian🤡
I would like to learn some mandarin though
on the Todo List
I would say my removed position is part of the appreciation for me
for the donghua

[cunning elk]

what the fuck did i miss

[normal crystal]

books not being recommended

[cunning elk]

immature 13 year old being immature?

shocker

[signal mountain]

nah tbf he was pretty reasonable

oh yh forgot abt that 💀

[trail hemlock]

a few hundred million 😭

[drowsy nacelle]

6'10 btw

[signal mountain]

ashdjasd

[trail hemlock]

same guy who was asking for feminist literature in here a few days back i think

[drowsy nacelle]

poor guy tripped over his ferrari cause he was too distracted reading feminist literature

hope he's doing alright

[trail hemlock]

that might be someone else, he sold the ferrari to help singlehandedly fund NPR

[drowsy nacelle]

yeah fair enough I mean he was too tall to fit in it anyways so win-win

[iron pulsar]

@silent roost i looked through your list. could you recommend me a personal finance book? i want to improve my money wisdom.

[broken bramble]

what did he say

[iron pulsar]

okay tysm!!

yes i have essentially 0 money smarts so i feel like all of these recs offer improvements for me

wow amazing!! tysm!!

i feel curious what your investment philosophy is

[normal crystal]

just skip to making those videos
that's how they made money too🤡

[iron pulsar]

hmm this all sounds very interesting. i'm not sure what it all means yet, but i can read more about it c:

who has shaped your investment philosophy the most?

[normal crystal]

sad day for Sabrina😢

he's retiring

[iron pulsar]

wow super interesting.

ig like, i could make a portfolio and put some money in it, even to get the feel of how it all works.

[normal crystal]

a real black swan event
an old, rich man grooming for good

[iron pulsar]

anyway, ty sabrina for your perspective! time to read.

do people regularly beat the SPY?

interesting. so it sounds wise to start with the SPY, read a lot, and then try to vary?

especially if i have like a simulator portfolio on the side to try my skills on

this might sound like a silly question, but is like storing money as cash considered an investment too?

[normal crystal]

if there is a negative real interest rate🤡

[iron pulsar]

mm interesting. so i'm learning to use SPY as the money grower and SGOV as like my bank account while i'm new to investments

i think i'll probably start with SPY and SGOV.
it sounds like that's like the minimum viable strategy for me right now.
and ig the percentage of my overall wealth that i store in SGOV depends on how accessible i want my money?

another possibly silly question, but like, what are the safe like portfolio services to invest through?

[shrewd talon]

Sabrina

[iron pulsar]

that sounds kinda complicated. so it sounds like if i were to copy your portfolio, then i'd likely not accurately reflect changes to it, and may do myself a disservice that way.

[shrewd talon]

Are you good at futures and options

If I use the black-scholes I think I’ll be set

[iron pulsar]

i think that makes the most sense for me

[shrewd talon]

Oh etfs are good

Yes I know because “America has a free exercise market or whatever”

It just gives a general price on what a option is worth

[iron pulsar]

okay ty again sabrina i really appreciated your wisdom

[shrewd talon]

So I use the heston model if I wanna account for a lot of volatility is this for options and futures?

Yeah I trade American

But I was told that black scholes is onlt calibrated at European markets

Then how do I calibrate it for free markers

The Heston seems to be a bit better though cause it takes into account the large amount of voltality.

Oh

Please teach me the ways of option trading

Can we use an example pls

On how I would use the Heston model

Okay yeah heston model works

For instance, can we take a look at a stock? So we can examine which method to use (black-scholes or Heston)

Can you dm me what resources I should look into so I can look into it and become a more proficient options trader?

I see the potential in so many things, such as the fact that Tesla stock oscillates quite frequently (very volatile) so I typically make a strangle and collect massive profits)

How does this relate to options trading

After I learn this volatility stuff how would I translate that into options trading

So learn this…?

Then analyze a 5 yr graph of a stock to determine the volatility, then use the Heston or black-scholes to gain insight and then execute the trade?

Options trading is interesting though

Can you dm me all the resources so I can understand more about volatility

And then ill use the volatility with the two equations/models

I might be fucked

But can’t it rake in a shit load of money?

Why do they not do it then

Wait cfa will definitley help for options trading

I just want to options trade lol

My porfilio is just index funds and I wanna start working on options

Why is the first volume 600 pages

I’m a mathematician at heart but these seems interesting

Are you a cfa

Isn’t cfa like economics

How long will it take me to get into the cfa

Like just finish all these fucking books

What the fuck

Bro I just want to options trade

Mhm

Fucking hate those premiums

Can you just dm me the resources

Yeah

It basically shows investors fear

The reason it’s so high is cause the tariffs

Sabrina, I buy options.

And then I sell them at like idk

Wait I still might need it

So make a call

And then make a strike accordingly?

CFA research aghgggg

[placid shuttle]

Anyone familiar with james stewart algebra and trig 4th edition ?

[iron pulsar]

how long does one of these take you? just curious

[vital bane]

what does CFA mean?

Computational Fluid Analysis?

[fresh skiff]

I thought complex functional analysis (idk if it exists)

[cunning elk]

use a different book

don’t support st*wart’s textbook industrial complex nonsense

[silk vault]

huh

[cunning elk]

did you know he got so rich from price gouging the shit out of his calculus textbook with its endless edition changes and whatnot

that he built this stupid ass mansion “integral house” as a vanity project?

[marble solar]

I mean, why not? If you got the money and can afford it, why not live the way you want to live? Stewarts Calculus book is pretty decent

[cunning elk]

https://www.amazon.com/review/R2IADID8E966E8 if you’re looking to actually understand the material surely there are better texts out there

[normal crystal]

he dead, dw

[cunning elk]

This attitude is found not only in the proofs but in the presentation generally. Stewart is basically a dog trainer. Sit! Roll over! Good boy! That is the spirit in which this calculus book treats you. You are taught to do tricks, rather than being led on an intellectual journey of exploration and discovery.
This can be seen in the many topics that are taught without any credible motivation provided for the reader. For one thing, the book is packed with supposedly "applied" or "real-world" problems designed to capture the reader's interest, which are easily seen to be intellectually bankrupt upon the slightest critical examination. Like a politician telling blatant lies and counting on people being too stupid to see through them, so also Stewart tries to fool you with cheap smokescreens into thinking that his problems have real-world relevance. Most ridiculously, of course, this is seen in the gratuitous full-colour stock photos that are peppered in various places. For instance, pre-med students constitute a significant portion of calculus students, so let's appease them with some problems about blood pressure and drug concentrations and so on, with some pointless stock photos of blood vessels and whatnot taking up a good chunk of the page, as if the book was not bloated and expensive enough without them. These problems, like so many other "real world" ones, consist of nothing but plugging numbers into formulas. The generic template for such problems is: "The function so-and-so represents something-or-other. What's the something-or-other when the value of the variable is 53?" The disastrous message to students is clear: applying mathematics means plugging numbers into formulas. It clearly does not involve thinking about why the formula is that way in the first place. It also clearly does not involve any kind of qualitative reasoning or any kind of conceptual conclusions. Applying mathematics simply means: when I plug this number in, that number comes out.

[normal crystal]

I don't disagree
but that's most undergrad (lower level) textbooks

[cunning elk]

the multivariable chapters get especially bad

so much shit gets handwaved and not properly motivated

I had to use it for a multivar class i took while still in high school

[cunning elk]

the same is true of the entire structure of the corresponding AP test

some random thing is given by extremely contrived function that we asspulled

[normal crystal]

richardo
sounds like you might regret the Stewart4Life forehead tattoo you got
live and learn

[cunning elk]

essentially isomorphic

all lower division calculus textbooks are basically identical in their utter lack of rigor and needless bloat

[normal crystal]

I prefer the tone of Thomas, there's something cloying about Stewart
but yea, all the major calc texts are similar by design

[cunning elk]

basically it doesn’t really matter which you pick

the market is oversaturated enough as is

paul’s online notes are a decent supplement if you want to see more worked computation examples

did your school not provide a book

😭

damn

yeah

larson/hostetler/edwards which was also terrible

idk when they bought those books but they must’ve been decades old

the district just cut >$1M from their budget for next year 😭 so must’ve been when they had a better financial situation

i graduated HS 3 years ago so that’s no longer my problem but

😔

I have a lot to say about how poorly designed APs are and how it’s facilitating k12 education’s race to the bottom

but i shall spare yall my rant

ok the spark notes version is:

• it’s what students should be covering in high school anyway (see for example the bullshit that is AP PRECALC)

• accordingly, it’s nowhere near actually being college level (also most APs besides like calc BC take a semester’s worth of material and then stretch it out to full year length)

• c*llegeb**rd’s monopoly on HS education self-perpetuates as people gravitate more towards APs while the non AP classes continue to nosedive in popularity and quality

that’s not college math

most schools count that as 000 level

ie non college level remedial courses

you can’t use it for actual credit anywhere

[normal crystal]

AP Precalc puzzles me because Precalc doesn't even count towards graduation at many universities

so it's like congrats! you got ahead
of what
idk

[cunning elk]

• the exams themselves have also continued to be dumbed down (all the exams post covid have been heavily nerfed and hollowed out of any challenge they could possibly have had)

[cunning elk]

• and continues to contribute to the needless toxic bullshit gamification of college admissions at the mid-high to high tiers

[normal crystal]

yea, I get that logic if it's already on the table

[cunning elk]

SEVENTEEN jfc 😭

I only took 10

yeah ew i hate gaming the system like that

lmao I was also salutatorian of my class

[normal crystal]

17
did you take AP in AP Studies🤡

[cunning elk]

AP lunch

AP recess

????

you can always transfer to a better school

look people won’t care how many APs you spammed in high school

make the best of your current situation

[cunning elk]

they usually stop caring by the end of first year

I know I did

[normal crystal]

I feel like your speech would've been YouTube gold
starts calm, ends with
"IT WAS JUST ONE F@&KING B IN AP CALCULUS, JUST ONE DAMMIT"

[rigid trail]

Fuck AP

[cunning elk]

anyway remember what channel this is lol?

[rigid trail]

All my homies hate collegeboard

Those fuckers gave me a 3 on ap calc bc because they didn't like the txt format I submitted for online exam 💀

I think I got a 0 on the frq

[cunning elk]

oh the covid years

[rigid trail]

Yeah man that was fucked up

[cunning elk]

seems like an eternity ago now im 1 year from finishing my undergrad

[rigid trail]

I was just a naive little 14yr old and they threw me off so hard with sudden online testing

[cunning elk]

real

[rigid trail]

the exam was so free man

I should have just handwritten frq and submit photo

[cunning elk]

I did my calc AB responses in latex 💀💀💀

[rigid trail]

Bro I wish I knew latex back then

Would've saved my ass

[normal crystal]

I like how Cleo just asked for intro financial literacy advice
and Sabrina was like "You are a CFA now, book your test date"

[rigid trail]

Okay now book related question

Arnold odes book

I took an ODEs course but this thing is still confusing for me

Am I mentally challenged

I had a negative experience with every single collegeboard exam I've taken. Usually with environment

With AP CS it was Java

[cunning elk]

have you looked at Simmons’ ODE book?

I haven’t read much of it but it’s supposed to be decent

[rigid trail]

Such a snooze fest writing getters and setters HANDWRITTEN

[rigid trail]

I'll look at it

At least ap CS is a free 5

Lmao

I dont think you really need to know java to get a 5 on AP cs

it's just common sense stuff

I literally watched the AP classroom videos the night before

I have never written a line of Java on a computer in my life

Funny I can say that but it is true

Same

Only Java written is hand written 💀

Dude I could not believe that they made people hand write getters and setters

That's the most npc stuff ever

They really should have the AP exam be like python or something idk

Much more relevant than Java for most ppl

I think a functional lang would be sick but I don't think many ppl would be happy with that

Actually I'm curious if any (non mathematician) ppl started programming with a functional language

I feel like everyone starts with python js java c/++ etc

[normal crystal]

sure
if that's what their school did

[rigid trail]

Thanks yeah it looks like what I need lol

I gotta review odes because I just hardcore memorized that bs instead of intuitively grasping

[cunning elk]

most lower division ODE courses are like that apparently

😔

just memorize endless list of disjointed techniques

[trail hemlock]

how is ts even possible, the class is taught in java

[rigid trail]

Yeah I was really disappointed

[cunning elk]

stupidly enough my uni doesn’t require ODE for math majors

which is

??????????????????

[trail hemlock]

LMFAO

howd he even get certified

[rigid trail]

I think a lot of stuff will be cleared up for me once I learn PDEs

[cunning elk]

oh that sounds like what happened at my HS

the AP CS “”””””””teacher””””””””

was TOTALLY INCOMPETENT

to the point that the STUDENTS were teaching the “TEACHER”

😭😭😭

[trail hemlock]

well mean it happens here too, my ap physics teacher has 0 physics education and is like genuinely incompetent

i love collegeboard

[rigid trail]

I was taking a programming elective purely because some of my friends were in it. I was helping the teacher with Python lol

[trail hemlock]

oh wtf ur right

well i mean that explains a lot

[cunning elk]

I still have not found the time to learn ODE

and I’m applying to grad school next year

halp

😭

[rigid trail]

LMAO

lowkey maybe skip to PDE

[cunning elk]

perhaps

[rigid trail]

all ODE's are PDE's 🗿

[cunning elk]

it’s just as mathy as anything else

[rigid trail]

Depends on the course. My course was super applied and lame

I don't understand anything conceptually except how to solve them

[cunning elk]

diffeq is the language of chemistry, physics, etc

without knowing ODE/PDE you can’t really do much in those fields

[rigid trail]

Well odes can be pretty cool but I think pde much more interesting in pure math sense

I kinda wish I was in EE for money

But I also love these math courses

if we switched places you'd be broke

pog

I'm just hoping that my lack of cs degree won't hold me back too much

it's just a piece of paper...I know the stuff but idk

Honestly

Yeah

But idk what else I'd do lowk

my only strengths are math and cs

please censor next time you say that

[cunning elk]

me, a music/math double major:

[trail hemlock]

whats wrong with liberal arts majors?

[rigid trail]

okay music is based

That's like the only exception

[normal crystal]

most people apply direct to Phd programs

[trail hemlock]

"i have black friends" ahh argument

[rigid trail]

I am NOT cut out for grad school 💀

[cunning elk]

gotta love the music side being completely unemployable

(classical piano 😭😭)

one of my piano classmates at one point was tripling in piano + flute + cognitive science

I think she eventually dropped to piano + flute double

[rigid trail]

Majors for individual instruments 😭

Hardest instrument

[cunning elk]

oh forgot to mention this is one of the top music schools in the US too 💀 but part of a larger university

[cunning elk]

strings (probably violin/cello imo)

[rigid trail]

No it is triangle

Piano is so good

piano compositions are goated

All the other instruments should fall off the face of the earth and I would be less devastated than if piano went

[cunning elk]

true and based

[placid shuttle]

What chapters do i need to focus in that book? I taking calculus in few months i dont got time for doing 1000 pages

[cunning elk]

chapters 1-11 or so should cover your standard single variable curriculum, calc 1 and 2

[rigid trail]

per the routine I will also mention Paul's online notes + Khan academy + Youtube (eg 3blue1brown calc series)

good supplements

3b1b good for before you start calculus or as you start

just for intuition sake

[cunning elk]

3b1b series in particular

is not meant to replace a full course

but to supplement it

same goes for his “essence of linear algebra” series

[remote sparrow]

yes, but that doesn't mean the methods for finding closed form solutions as is traditionally taught are useful outside of a small class of problems

anyone that's not doing a degree that's specific to a profession (e.g. engineering, law, or medicine) is a liberal arts major

math, physics, and bio majors are liberal arts students

boyce and diprima is fine

paul's notes can supplement it well

[rigid trail]

i really really like arnold ode but i feel a little bit dumb reading it

if you are more comfortable with physics than me then maybe it'll be easier

(a lot of the examples are physics intuition based)

[normal crystal]

this is free with video lectures
it's based on a free textbook that is meant to be similar to Boyce Diprima
https://web.uvic.ca/~tbazett/diffyqs/frontmatter-1.html

[mortal ore]

im guessing youve just never been good at them

like most mathematicians

ah

where does the disdain for the humanities come from then

[normal crystal]

oops, I forgot the link

[mortal ore]

i tend to find that people in STEM dont like humanities because they werent very good at them, but i suppose there can be other reasons

[last cipher]

Yes diprima is amazing. I can attest to this

[mortal ore]

oh thats the other reason

fair enough

but why look down

rather than simply not enjoy

[rigid trail]

i dont like analyzing or discussing history or literature, i just read it

i dont wanna have to talk to othesr about it if i dont want to

[mortal ore]

i see

[last cipher]

Reminder that theres a BA Mathematics degree 😌

Liberal arts with math

[rigid trail]

math major is BS at my uni 🗿

[mortal ore]

i can only get a BA in math where im at

a BS is for applied math

[last cipher]

At my Uni they offer both BA and BS

[rigid trail]

pure and applied both bs

[mortal ore]

pure math BS is interesting

[rigid trail]

yea

[mortal ore]

im double majoring in two fields both who have only BAs

im really choosing the academia life man

tho honestly i could get a fairly scientific job with pure math background

[normal crystal]

Chipper, I edited the link in if you didn't notice

[last cipher]

kind of want to work with physicists and such so im looking to go into applied. Not sure yet tho

[marble solar]

Ah yes, all those poor souls that were forced to buy a calculus book by....absolutely no one. Nobody makes anyone buy a book

[mortal ore]

my research next fall (if i end up doing it, which i should) will be physics related, and i study pure math

[marble solar]

Much less were they killed over it

[mortal ore]

math sorcerer cast a mind control spell on me to buy AI slop textbook

[rigid trail]

i hope you are joking

[mortal ore]

does this mean i would sooner be killed for proving sqrt(2) as irrational before getting killed for not buying a book

[last cipher]

any good introductory real anal. books???

[mortal ore]

syllabus saying you should get them != you should get them

[last cipher]

Ive thought about Understanding Analysis

[rigid trail]

abbott the normal rec

rudin if you wanna die like me

[mortal ore]

i mean if you want your uni to sucker you into buying shit you dont need

[normal crystal]

that's obviously false
books with access codes are a normal requirement for many, many classes
you don't have a choice

[mortal ore]

yeah this ones pretty good

[marble solar]

You're not required to buy a book for your class. You can be pushed to, but it's not like your life is on the line for buying the calculus book. Nobody is required to learn calculus. If you don't want to learn, then you don't have to!

[last cipher]

UTM is gold ngl

[mortal ore]

contrarian maxxing

[rigid trail]

my course also has Ross as a supplement analysis textbook

i think it is ok, some quirks but overall very clear

[mortal ore]

oh ts true

[last cipher]

I bet 9/10 times that these students dont even need to spend $100 on a calc textbook

Just go to a thrift store

[mortal ore]

damn i should lock in on my ethics paper

im so close to being done

[rigid trail]

no one should spent $100 on a calculus textbook

spend that on analysis instead 😭

you can get all of calc information online trivially

[mortal ore]

pirating is usually ethical

[normal crystal]

I hope you don't gamble

[mortal ore]

imo

[last cipher]

cant wait for my next paycheque. boutta hoard some texts from UTM 😭😭

[marble solar]

Your life isn't on the line to take a class with an online component. You can choose not to take such a class. You can also choose not to take any classes at all. Calling James Stewart's success blood money is ridiculous

[last cipher]

i dont

[normal crystal]

1, I didn't
2, you're arguing in bad faith for the opposite pov

[marble solar]

Multiple pieces for a moving conversation. My main point is it's not blood money, and you're not required to buy a book. If a particular class requires an access code, you can choose not to take that class

[rigid trail]

my uni has a math library which is rlly nice

i can just browse the books

i dont even check anything out

[last cipher]

is there any website other than amazon where i can get books

[rigid trail]

i just get an idea of what books are good then buy them myself or acquire pdf

[rigid trail]

i usually would get used books

[normal crystal]

you're just being silly or naive now, idk
but 👍

[rigid trail]

i dont see the point in getting brand new books ngl

lift the burden of another student instead 🗿

[marble solar]

Ah yes the "I don't like the way this class will be taught so I won't take it" silliness

[livid lintel]

Some people prefer the new book smell and aesthetics

[normal crystal]

I guess it's naive then, np

[rigid trail]

i see

[last cipher]

I wish some books are still compact like back then

instead of being massive

[rigid trail]

try harder

ok I got it for like $10 lightly used off Amazon and that is worth imo

but pdf nice too

[gray gazelle]

Would you recommend the stacks project as an intro textbook?

[fleet leaf]

The Stacks Project is not a textbook and it is definitely not meant to be an introductory textbook.

[vital bane]

That's just functional analysis

I think working over real and complex vector spaces is common in func anal

[stable flicker]

This book is open source so if you don't like anything you can change it yourself

Font isn't comic sans? You can make it comic sans

[fresh skiff]

I agree

[dim pendant]

It's not about what a new book is like, but rather what it is not like. Torn pages, writing in pen, and so on.

But I agree that most math students treat their books well enough to buy used every time

I've bought three used and the only book I would've possibly complained about had a slightly torn dust jacket

[dim pendant]

It reminds me of nlab lol

You have to be quite familiar with a lot of ideas to make efficient, practical use of it

[vital bane]

an open source textbook

false advertising

[vital bane]

@remote sparrow @merry sphinx 3Blue1Brown's math book shelf, Munkres, Stein and Shakarchi, Needham's VCA

@median fossil he even has QFT books, based

Anthony Zee's QFT book, but not Schwartz's book 😔

[median fossil]

I strongly dislike the first part of Schwartz

[vital bane]

the classical mech stuff?

and QED?

[median fossil]

The first 100 pages or so

[vital bane]

Surely it's the greatest QFT book of all time

[median fossil]

hesfalse

Tong and Harlow notes + Srednicki + Banks + Weinberg + P&S + Zinn-Justin ftw

This looks like an L + ratio copypasta

[naive lava]

you basically listed all other popular textbooks other than schwartz

[naive lava]

Do i see delgine??

[median fossil]

Yes that was on purpose

[gray gazelle]

Hi sir does anybody have good dpps or sheets for maths advanced level

[merry sphinx]

Makes sense

[rough umbra]

whatre your guys' favourite graph theory books

[mortal ore]

the one that ends the quickest!

https://tenor.com/view/hahaha-laugh-puppet-gif-17920416

[remote sparrow]

the three canonical graph theory books, diestel, bollobas, and bondy/murty are each biased towards different areas of graph theory

maybe skim through all of them!

[remote sparrow]

@gray gazelle i see topology and groupoids

[dim pendant]

Realist thing I ever heard

[rough umbra]

thank you :)

[rough umbra]

these r the ones my prof marked, dyk anything abt West if it's not one of the canonical ones?

[graceful moon]

Not a recommendation, actually a book to avoid, don’t recommend Wilson’s introduction to graph theory, it was what my class used and I hated it

Not poorly written or anything, just insultingly slow

[rough umbra]

Good to know, thank you

[mortal ore]

i used diestel for a bit, i should get back to it

it was pretty good

[graceful moon]

And I remember the 4th and 5th edition were quite different with one being significantly worse than the other, but I can’t remember which way around

[mortal ore]

at first it might seem like diestel isnt good because "man these theorems are very strange and their proofs are boring"

and then youll realize thats bc ur doing graph theory

[graceful moon]

Proof - If assumption A holds, this is trivial otherwise consider the following 137 cases:

[mortal ore]

i asked my favorite algebraist professor at my uni if he were willing to do a graph theory independent study with me

and he just straight up said "no way" because "its the most boring subject both to teach and to study"

[rough umbra]

chromatic polynomials r cool

i liked matroid stuff too

[mortal ore]

i mean yeah using graph theory for other means can be cool

my research this summer is somewhat graph theoretic

but like trying to do graph theory for its own sake just sucks

[rough umbra]

lol fair

[mortal ore]

you might as well just pick up a few basic graph theoretic tools and call it a day

[rough umbra]

yeah i didnt love the straight up graph theory stuff but stuff like using graph theoretic arguments in topology was neat

[remote sparrow]

west tries to be a survey

so i guess it's balanced, but doesn't go very deep in any particular direction

[rough umbra]

I see, thanks

[rough umbra]

Also, sorry to ask, I don't immediately see it from skimming their tables of content, which areas would these be?

[mortal ore]

i think a survey-type book is best for graph theory

[remote sparrow]

diestel - classification problems/structural graph theory
bollobas - extremal graph theory
bondy/murty - more topics relevant to computer science

[rough umbra]

🫡

Thank you

[lavish radish]

Spivak calculus

[tender river]

theres a List here https://realnotcomplex.com/analysis/calculus/

[remote sparrow]

doesn't cover multivariable calculus

you need to say calculus on manifolds instead

[stiff crow]

wdym by readable? I think Stewart calc is very easy to follow along

If you don’t understand a topic, you could always find it on Paul’s Online Math Notes

It’s pretty good

And perhaps that’ll help you

[rigid trail]

Paul's online notes saved my ass for multivariable

some goated stuff

[cunning elk]

studying physics alongside multivar should give you a fair bit more intuition

you need multivariable calculus to be able to fully describe E&M: vector fields, line/surface integrals, etc

curl and divergence operators also have very nice descriptions using physics

[rigid trail]

Mutlivar intuition is really satisfying

(im gonna eat my words so hard when I take analysis in several dimensions next sem)

[cunning elk]

my senior year of HS i took multivar alongside AP phys 2; while the AP obviously did not explicitly involve calculus in any way there was nonetheless a lot of overlap in the content they covered

[silver stirrup]

Was wondering if I could get a book recommendation for a linear algebra textbook

More specifically

I have taken a class in linear algebra, covering usual stuff like vector spaces, linear independence, basis, span, transformations, matrices, eigenvalues/eigwnvectors/diagonlizability, dual space, a little bit over R of normed/inner product spaces, adjoint stuff solely for the purpose of proving the spectral theorem, and some basic multivar stuff crammed in at the end

I feel like quite weak with matrices in general

I was looking for a book to really strengthen my knowledge (a good number of difficult/non trivial exercises) with good coverage of matrices

[cunning elk]

computational linalg books (ie most lower division treatments of it) focus a lot more on drilling matrix computations than actually doing proofs if that’s what you’re looking for

[remote sparrow]

https://www.amazon.com/Matrix-Mathematics-Cambridge-Mathematical-Textbooks/dp/1108837107

https://a.co/d/4U9rbe4

https://a.co/d/8NXEdN3

[shut grotto]

any reccomendations for proof based mvc books?

[rigid trail]

Spivak calculus on manifolds

[shut grotto]

thanks!

[remote sparrow]

hubbard or shifrin

[sharp goblet]

good if you want something fast to get into the topic

[shut grotto]

will look into those as well, thanks!

I mostly wanna formally learn a bit of mvc so i can do complex analysis, just putting that out there incase a specific book might work best for that

[normal crystal]

I saw a couple weeks ago
the Hubbard new DiffEq book that continues their Vector book is supposed to be published in December

[remote sparrow]

whoa

finally

[fresh skiff]

This December?

Wow

[remote sparrow]

https://matrixeditions.com/advancedcalculus.html

source above ^

you can check the tentative table of contents for it

[fresh skiff]

Cool

[soft lantern]

digital logic ?

[vital bane]

based pfp

[fresh skiff]

Almost same as mine but realistic

[still juniper]

Does anyone have book recommendations for Multivariable Calculus? I'm trying to study ahead during the summer for the class.
The University is using the weird Pearson access, and I'm not able to pay the ~120 dollars for the ebook access yet.

[vital bane]

Multivariable calculus?

https://www.khanacademy.org/math/multivariable-calculus

https://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx

http://www.damtp.cam.ac.uk/user/tong/vc.html

[analog shadow]

I'm currently going through Geometry\ (Basic and High-school) what are some good books? I feel pretty burnt out from videos being my only source of learning...

[dim pendant]

As long as you understand the logic behind what is happening, and you aren't just memorizing the algorithms, any resource should work to be honest. Especially because a lot of first courses in complex analysis assume that you're dumber than a real analysis student

[dim pendant]

In a math-specialized server, so few people interact with high school math that we simply don't know what books are good for that stuff, which is why we always recommend videos. In high school people are still trying to figure out how they need to go about understanding math, so it's harder to pick any one book and say "this". Usually all you need to do is internalize and practice patterns. So the best I can do is say "Basic Mathematics" by Lang, assuming he has content on geometry other than trig..

If there's geometry in that book, I suspect it will be at least somewhat more challenging than a video, but if I had to give someone a book for high school math, that would be it..

[shut grotto]

Yeah honestly I don't have a lot of motivation to properly do mvc right now and was thinking I'll pick it up on the side while doing complex analysis but I decided to ask and note down some books anyway just incase my plans change

[dim pendant]

Oh I mean fair

If you're interested in the geometry of curves and surfaces, that could also be a strong motivator

[shut grotto]

I see

I'll probably get into it at some point lmao

[vital bane]

Differential Geometry mentioned 🗣️🔥🔥🔥🔥

[vital bane]

also tbh you don't really need to learn it formally for complex analysis, iirc all you need to know are line integrals and green's theorem

The resources I've provided above should be more than enough

[shut grotto]

I see

[vital bane]

these

[shut grotto]

Alright that's nice

ah

I think I've already done mvc through khan once

[vital bane]

Oh nice

[vital bane]

then I think this might offer a newer perspective for you

[shut grotto]

I see

[dim pendant]

Btw we're not at all trying to beat you down, just save you time. Obviously don't rush the basics, but think like a grad student. Do what you think you need to do, not everything you could do.

[shut grotto]

will come back to this discussion when I'm done with my LA book :p

ty guys

[vital bane]

LA is quite important for MVC

[shut grotto]

makes sense

thanks

[vital bane]

This is scary I wanna learn all that I can but it seems in grad school it seems I'd need to focus on what I need to do

[shut grotto]

I know a bit of the computational side, I'm currently doing LADR though

[vital bane]

LADR

[shut grotto]

it's just fun in general

[vital bane]

4th edition is better, but I went through 3rd edition and imo it was a 6/10

I regret buying Axler

I should've bought FIS

FIS is based

[shut grotto]

What's FIS

[vernal pewter]

insel, spence, and I forget the first guy's name

[shut grotto]

Yeah I read the additions for the 4th edition, I'm glad I picked it up after the update

[vital bane]

Friedberg

[shut grotto]

I see

[vital bane]

it's great

[shut grotto]

That's nice

too deep into LADR to switch though

last 3 chapters left

[graceful moon]

I need to work out what it is I hate about LADR so much at some point

I think the descision to work over R and C is silly, but theres something much more broad about that book that I just do not fuck with

[shut grotto]

well I've only done a calc book and an real analysis book before this so I don't have any point of comparison

[vital bane]

fair

[graceful moon]

and I cant put my finger on quite what it is, possibly its just the way Axler writes

[vital bane]

it's not really silly

[shut grotto]

The lack of symbols maybe? idk

[vital bane]

it makes sense imo

[shut grotto]

That part is annoying to me

[vital bane]

beyond just algebra or coding theory you mostly don't care about arbitrary fields

[shut grotto]

Plus he does mention other fields when he finds necessary

[graceful moon]

More often than not you can just work over any field, or at worst any algebraicly closed field. I dont see any point in restricting yourself in a "second course"

[shut grotto]

For example one of the theorems given as an exercise wasn't true if you consider the field {0,1} with the binary kinda definition of addition and multiplication which he did mention

[graceful moon]

Beyond harmonic analysis you dont really care about fourier series, but they were still in my RA class. Its an algebra course, I think this is a non-argument

[vernal pewter]

ah right stuff like determininants get funny in characteristic 2, but as long as you point that trivia out when it happens it's fine

[graceful moon]

Everything gets funny in char 2

[vital bane]

that's a fair point, but inner products are only valid over R or C

general bilinear forms don't count

[graceful moon]

Not true but sure lol

[vital bane]

what do you mean?

[graceful moon]

Well you can define an inner product on continuous functions over some interval

Perfectly good inner product space

[vital bane]

continuous functions? from where to where?

[graceful moon]

Arguably youre always working over R or C, which ill give you, but you can just restrict to that when talking about inner products

[vital bane]

real/complex valued?

[vital bane]

that's what I mean

[graceful moon]

Dont have to no, \int_a^b f\overline{g} is the standard inner product there

[vital bane]

that's what I said?

but yeah I don't disagree with you I too would like to work over general fields like Hoffman and Kunze

[graceful moon]

But again, you have general bilinear forms and all the rest, inner products are a nice case for R and C which you can just mention when appropriate

[vital bane]

there is some neat algebraic facts that you miss out on when you restrict to R or C

[graceful moon]

This really isnt my issue with Axler anyway, its just not a choice I like

[vital bane]

But I guess different books for different audiences

[graceful moon]

Not that I really know what my issue with Axler is

[vital bane]

determinants

But I think he fixed his treatment in 4th ed

determinants and related topics like eigen-stuff in 3rd ed was abysmal

[graceful moon]

Yeah I consider anything before 4th ed to be a waste of time

Like it or not determinants are increcibly useful and you need to know how to use them, they need to be treated properly

[slender cargo]

just learn linear algebra through D&F

||jk don't do that||

Axler's treatment of determinants in his 4th edition though feels like something that's better deferred until after learning some abstract algebra. His treatment of it is the same (or nearly the same) as D&F's, but you have a way better grasp of what's going on with multilinear algebra, permutations, etc when you arrive at the chapter in D&F's book. But that takes significantly longer to get to, so..

[vernal pewter]

Yeah you should probably at least make sure the phrase "Linear Algebra" or "Vector Space" appears somewhere in the title of your book

ok now some guy is going to show up with a book titled topological vector spaces or some shit, my mistake

[manic cairn]

nah, the converse doesn’t hold

you’re likely still correct as stated

[manic cairn]

i don’t even think this is true.

fourier series are useful lots of places

not sure what counts as ‘algebra’ here, but number fields are also useful and aren’t R or C.

there’s also a ton of stuff on finite field representations

[mossy flume]

FIS my beloved

what a good text

that's my top LA rec

very well written, good treatment of determinants IMO (unique alternating multi-linear function from the set of linear transformations -> k which is 1 on the identity)

good coverage of topics

[graceful moon]

I agree that Fourier series show up elsewhere, my point is that even if R and C are the only fields non-algebraists care about (which isn’t true) it wouldn’t be an argument for only dealing with R and C

[floral lantern]

I used to like Axler in theory but after using it in class for a semester not so much 💀he takes a functional analyst’s perspective to the material and in my opinion doesn’t really emphasize the algebraic ideas going on under the surface?

It just doesn’t feel like an algebra book almost

And the proofs are very sort of analysis-y with choosing ordered bases and stuff

[dire stone]

is hungerford algebra good for reference

i want a book thats just like a list of concepts and definitions and theorems

also i liked axler as a book i read next to the class textbook

i cant imagine learning from it directly

but it was just cool as a different perspective

although im still mad about htat hting that he defined but did not name or say any of the properties at all of

i think it was the coimage

[remote sparrow]

i heard the galois theory chapter isn't that great

lang and jacobson make good references

[vital bane]

[fresh skiff]

GOAT

[vital bane]

🗣️🔥

can be used as a textbook, reference, pillow

anything!

[vital bane]

yea this is literally the only thing it'd be good for

[indigo notch]

People say Schaum's Outlines are "just problem books" but for some reason their style just clicks with me. I wish I'd known about them when I was in college and earlier. I could have been an astrophysicist!

[vital bane]

You still can be an astrophysicist

[normal crystal]

or at least an astroschaumsicist

[vital bane]

No

Not everyone wants the most rigorous treatment of a subject

[mortal ore]

thats why engineering exists

[vital bane]

your views are skewed because you've spent too much time in the math server

try the physics server in #old-network

that can be quite entertaining

I was

I temporarily left to focus on exams

[vital bane]

<@&268886789983436800>

[whole willow]

Has anyone read Mathematical Thinking by Douglas West and Paul D'Angelo?

It's meant as a fun introduction to proofs

How good is it? It's the only proofs book in India that isn't egregiously expensive

[vital bane]

<@&268886789983436800> ?

[vital bane]

Let's try pinging metal @broken meadow plz delete scam link, also happy birthday

[night gorge]

I got it, just finished work

[vital bane]

in #study-discussion as well btw

same scam link

[night gorge]

Easy, ta

[vital bane]

Now you look weird mq

[frosty kettle]

is barbeau's book on polynomials the only good book? I am trying to learn some theory for a regional math olympiad of sorts, and i find normal olympiad-style books a bit too fast paced. need to cover the main things like finding roots, vieta's, factor/remainder theorems, integer/rational root theorems, conjugate root theorem, symmetric polynomials, interpolation, the sum of squares, functional relations involving polynomials; that kind of stuff.

[wide geyser]

did you try the ones listed here? https://artofproblemsolving.com/wiki/index.php/Olympiad_books?srsltid=AfmBOoqYfMJMe9p_vZvCt8RUG6DoMgAO0somUOqajFFEou3w5fiUms6z#Polynomials

[jaunty loom]

Hello. I would like to self study following topics of undergraduate math:

Calculus (single-variable and multivariable)
Discrete mathematics
Probability and statistics
Linear algebra
Prerequisites for stochastic calculus
What books are the most recommended for these topics? I’m especially open to books used in other parts of the world, not only english literature used in the Americas. I’m fluent in english, spanish and german. I’m studying Chinese Mandarin.

For stochastic calculus, is studying analysis a prerequisite?

Thanks a lot in advance

[frosty kettle]

thats where i found it; looked to be the only decent one that also covers theory

[twilit pecan]

I dont myself work in stochastic calculus but seeing from a friend, I would say stochastic definitely has a hard analysis prereq

I would think you basically need real analysis fourier analysis and measure theory at the very least for stochastic

[vital bane]

@gray jungle same pfp as you James

[fresh skiff]

for a second i thought you James Ash

[wide geyser]

amir parvadi and 117 polynomials also cover theory, and the former is free

i think 117 polynomials is easier but not sure

[frosty kettle]

which one do you recommend? i'd like a book thats not insanely difficult and does some build up; so i get a decent treatment; this is prolly my first time doing olympiad math related to polynomials so.

[jaunty loom]

damn also a TCOAAL player

[fresh skiff]

Yeah lol

[vital bane]

TCOAAL?

[fresh skiff]

The Coffin of Andy and Leyley

The Coffin of Andy and Leyley

[remote vortex]

So good they named it twice

[fresh skiff]

internet issues

[wide geyser]

try 117 problems, you can see a preview here https://www.awesomemath.org/wp-pdf-files/xyz/look-inside/117-polynomial-problems-from-amsp-look-inside.pdf

[versed portal]

If I am interested in a quant career what areas of math should I focus on and what are good books for those areas. Right now I am reading apostal calculus volume 1 and plan to read volume 2 after but what next?

[half void]

I like jerrold marsden’s books, theyre available for free online.

https://www.cds.caltech.edu/~marsden/books/

[remote sparrow]

which ones?

doesn't seem like there are any pdfs for the student textbooks

does being able to view them on the caltech library website count?

i see you can download each chapter for some books

[acoustic cliff]

Huh, before one could have downloaded the PDF straight off the author's website

Things have changed

[remote sparrow]

but that's not the same as the full book in one pdf (although you could concatenate the pdfs)

[jaunty loom]

apostol calculus? damn

[normal crystal]

the full books are farther down the list
looks like only the Calc 3 volumes and SGs and Calc Unlimited are open

you can still download the open ones
Vector Calc was never free

but you can get them legit free from the links on his site anyway

that IS legitimate
that's my point
he's the author and made it open with agreement

oops, you said illegitimately
forget it, I'm done

[amber elm]

Hello.

What books are best for quadratic forms?

Introductory level.

[warm fiber]

I've heard that the AoPS books are pretty good and I'm thinking of reading one. What's your take on them?

[warm fiber]

And do you think any of them could be found for free?

[normal crystal]

you can't discuss the 2nd question here
people do tend to like them

[real stratus]

aops vol 1 is a great book

for whatever reason the way it teaches algebra is elite

[tulip lion]

what is a good book for doing group theory?

I want something short and fun

I did linear algebra from hoffman and enjoyed that and currently following rudin for analysis

something in the same lines would be appreciated

[real stratus]

linear algebra done right

@tulip lion

[sage python]

He's asking for a group theory book rather than a linear algebra book

[real stratus]

oh

nvm

i;m tired

[floral lantern]

Herstein’s group theory chapters are really good

The rest of the book as I understand is not as exceptional but

[tulip lion]

is there like nothing only about GT?

any clue about Armstrong's book

[remote sparrow]

rotman

also this: https://link.springer.com/book/10.1007/978-1-84882-889-6

there are online-only chapters for this book too

[tulip lion]

any pre reqs?

[full cairn]

Rotman's intro to group theory seems pretty decent as well: https://link.springer.com/book/10.1007/978-1-4612-4176-8

[half void]

Just look up marsden calculus pdf and you’ll find somethinf

[full cairn]

lol, just noticed you already said Rotman I'll make another suggestion then, Actions of Groups: https://www.cambridge.org/highereducation/books/actions-of-groups/9E2CF39D99D882E664FFAB8547B39469

[remote sparrow]

oh i linked that book in this channel some time ago

i don't really know anything about that book

just seemed cool

[full cairn]

I can't remember where I found that book, there's a decent chance I got it from you actually

[remote sparrow]

https://www.rxddit.com/r/math/comments/1kgrltk/your_recommended_exercise_books_with_solutions/

[rose oriole]

Okay so for canadian hs, Quadratics, Trigonometry and some functions

Iv always understood how to solve them but never really understood how it works if that makes sense

u guys know any books that can help me grasp the concepts?

[cunning elk]

try the aops books?

[vital bane]

Does this have group with operators?

[sage iron]

Government wanted people to go into STEM

[vital bane]

because it covered a large area and took credit for naturally occuring mathematicians

[sage iron]

So a lot of people went into stem

[mortal ore]

USSR was deadset on producing top tier scientists

if you look at some of the textbooks they had teenagers reading, its kinda insane

[vital bane]

Landau Lifshitz

[vital bane]

No

[normal crystal]

it was a combination of capacity and control

[remote sparrow]

what's the control exactly

[vital bane]

https://tenor.com/view/1984-gif-19260546

[remote sparrow]

well this was a real headline that ran: https://x.com/TheEconomist/status/1152408254435270656

The Economist (@TheEconomist) on X

In Soviet times, communist regimes pressed both men and women into scientific careers https://t.co/347mOJmHdv

X · Jul 20, 2019, 2:41 AM

[vital bane]

https://www.economist.com/europe/2019/07/18/why-half-the-scientists-in-some-eastern-european-countries-are-women

[remote sparrow]

the headline was definitely changed after backlash

https://www.facebook.com/TheEconomist/posts/in-soviet-times-communist-regimes-pressed-both-men-and-women-into-scientific-car/10157634370359060/

[strange tree]

Artin's Algebra

[cunning elk]

my algebra prof was a student of artin :o

but used herstein's book for our class instead