book-recommendations

[molten mason]

nerds

[violet shuttle]

...i should really go back and finish my unfinished GR coding project

Differential Topology by Hirsch, while really fucking difficult, felt well written, and will be where I go when I go back to learning it.

[tribal crow]

do you have plans for grad school too?

[violet shuttle]

Yep, but in physics.

[tribal crow]

GR researcher?

[violet shuttle]

Nope!

solid state baby!

[tribal crow]

what, then?

ah

i know 0 things about solid state physics

[violet shuttle]

more undecided about where in that vast topic

lol GR was just a "hey, I learned all this DG anyways...you're telling me all I need is a metric to understand this?"

well, really it was a professor talking to me about what a connection was.

Ashcroft and Mermin is one of my favorite textbooks.

So well written.

Shankar's The Principles of Quantum Mechanics is my absolute favorite.

Baby Rudin will always have a place in my heart, even if it's objectively not the best pedagogical tool, it was the best for me at that specific time.

[tribal crow]

ok im downloading this lmao

[violet shuttle]

well...you should learn quantum mechanics first

[tribal crow]

i'd like to know some solid state/condensed matter stuff

[violet shuttle]

it assumed you know quantum mechanics

[tribal crow]

this is mandatory for me anyways

[violet shuttle]

you don't need all of Shankar, just the first half (so, like, you need to have solved the Schrodinger equation a couple times and see discrete energy levels)

[tribal crow]

i'm the type of person to download textbooks im not ready for in the hopes that i can one day read them lol

[violet shuttle]

I download more books than I would need. I would be able to read most of them, it just wouldn't be as high a priority.

Lots of math have relatively little literal knowledge prerequisites

[molten mason]

I also like to download books

[tribal crow]

just why

[molten mason]

[violet shuttle]

I gotta prioritize, you know?

[tribal crow]

of course

we all do

[violet shuttle]

isn't this a cocatthink, as opposed to a catcothink?

or, is the idea that it's a (co(cat))think

aka a (catco)think

[molten mason]

Questions to ask the creator of the emoji

[violet shuttle]

I thought you made the universe?

[lusty ermine]

which books are good introductions to galois theory?¡

[sudden kindle]

Sour drop recommend David Cox's book

[molten mason]

You've asked for topics from a dozen different courses in just a few days.

Are you collecting books for the future? What is your goal

[lusty ermine]

I am new to math but want/need to learn more about it. I get tired in the public transport so instead of doing something else, I would like to take a look at your recs, so I can assess and analyze the topics with discretion. @molten mason

I am soon to enter university so I dont want to be the worst students

[molten mason]

Ah okay, also what is your first language?

[lusty ermine]

sorry for my bad english, my main language is latinoamerican spanish

[dusk wind]

you'll be alright, authors have possibly worse english

[remote sparrow]

you may want to ask in #foundations too if you haven't already

[molten mason]

It's not bad, it just means I can also recommend books in your language, such as Spivak's Cálculo infinitesimal

[main hill]

Hey Guys! Anyone familiar with Louis Leithold books?

[dusk wind]

yea

[molten mason]

Hay un libro sobre álgebra lineal en español también... un momento

[dusk wind]

thats pretty good

[main hill]

I'm asking since I'm a bit a collector but one title evades me:

https://books.google.pl/books/about/Trigonometry.html?id=IdTZAAAAMAAJ&redir_esc=y

this one - just about trigonometry

[dusk wind]

besides the books I think they have some reviews/publications floating around

you want that book physically?

[main hill]

can someone confirm is it real? Or is this some version of the college algebra & trigonometry combined together

[dusk wind]

I think I tried looking for it before, I couldn't find it

It is real and does exist

however most of the meat is probably mixed with algebra and trig book

Its that they are so old and the fkin libraries have a hold on the book for some reason

I couldnt find it anywhere

[main hill]

Yes - I think I have them all - except the spanish editions since I don't need them but this book only on trigonometry is a mystery for me

[dusk wind]

You would need to reach out to a specialist

also, if you have TC7 in english, can you do us all a favor and scan it, thanks

[main hill]

finding a pdf or djvu is also impossible

[molten mason]

Para álgebra lineal, busca Álgebra lineal y Geometría de Eugenio Hernández Rodríguez
Además Algebra Lineal y Geometria de Juan de Burgos

[dusk wind]

just gonna have to be satisfied with how he put it in the algebra+trig book. But its fine, as there are so many trig books anyway
and it's not too tricky a subject to learn, most I find are 200 pages or less

[molten mason]

Calc and Linear Algebra should fill up a few months of your time. Calculus is 3 semesters worth of classes. Linear Algebra is 1-2 semesters. Mastering those two topics will be necessarily before moving on.

You could also add proofs and set theory but I wouldn't know in Spanish, maybe Alex would know

[lusty ermine]

thanks for the recommendations 🤠

I will take a look at them in the bus

[main hill]

This one can be found on archive.org

[molten mason]

De nada

[dusk wind]

no, only the small version, it's not the true TC7

[main hill]

Yes - there's a lot of other trig books but as a collector I would love to have this book from Leithold as well. I think I like his teaching style so having a book for trig by him would be neat.

[dusk wind]

unless you mean the crap scan in spanish

[main hill]

What do You mean it's the small version and not true TC7?

[dusk wind]

yes

there are two versions of TC7

he released a shorter book with less pages after

[main hill]

some material got cut down?

[dusk wind]

it even says it in the title 'single variable'

otherwise you might be talking about the spanish pdf el calculo

[main hill]

Jeezz! I see it now. On archive.org there's the single variable - 1048 pages book

[dusk wind]

thats the only one

and its basically useless

the good news though is that the content should be the same as original TC7, just removed chapters

[main hill]

is TC7 in any way superior to for example 5th, 3rd or 2nd edition?

[dusk wind]

I'm not sure, but I went back to the older editions to get the full treatment

typos and such, from what I saw there wasn't a real difference

the older editions might actually be better in some ways

[main hill]

I see. Thanks for the info and insight about this. I wasn't aware. I just got the older editions. Never chased the newer ones because from my expierience they always cut the material down and the remaining gets crippled in one way or another (based on schaum's series)

[dusk wind]

Well it was a bit different back then, publishers weren't as aggressive as they are now, one good thing about the newer editions is readability though

[main hill]

I think that is very subjective - I don't mind the old fonts and papertype used back then.

In the meantime I've searched for full version of tc7 somewhere - no luck

[dusk wind]

You can get the physical book anywhere, but the pdf doesnt exist

which is one good reason to use the nerfed TC7 or learn spanish lol

[sage kelp]

What is a good introductory book for covnex analysis?

[violet shuttle]

Rockafellar, I hear.

[violet shuttle]

(campanella, communist bloc)

[heady ember]

That rocks (?)

[thorn cloak]

Is a good intro book to stats "Intro to statistical learning." I have taken two semsesters of probaility but it hasnt really covered any "stats", but I also dont wanta stats book that will repeat what i learned in prob

[final goblet]

hello

[remote sparrow]

wackerly, mendenhall, and scheaffer is good. the first 7 chapters are probability. after that is the statistics material

casella and berger is also a good choice if you have real analysis under your belt (which i believe you do)

you should also ask the statistics server

[storm zinc]

ISLR is better for learning modelling and applied statistics but it won't built off your foundational probability in the way a more mathematical statistics book will like the ones Sour Drop recommended

[molten mason]

Weighing the Odds: A Course in Probability and Statistics by Williams
Introduction to Mathematical Statistics by Hogg, Mckean, and Craig
Statistics for Mathematicians: A Rigorous First Course by Panaretos

[remote sparrow]

@orchid mortar @misty wyvern

[misty wyvern]

What level of math are you at and what level do you want to learn stats at

[lusty ermine]

any recs on discrete mathematics from the ground up

thx.

[hallow oriole]

concrete by knuth

[dusk wind]

https://discrete.openmathbooks.org/dmoi3.html
https://discretemath.org/ads-latex/ads.pdf (alternative)
https://amazon.com/Discrete-Mathematics-Applications-Ali-Grami-ebook/dp/B09ZKXCZHL

this one is also an option https://amazon.com/Discrete-Mathematics-Computing-Peter-Grossman/dp/0230216110

[steel cloud]

Okay thank you

[livid minnow]

Who is Alex?

[lusty ermine]

no idea

[steel cloud]

And what background is needed for office hours with a geometric group theorist?

[livid minnow]

someone posted this earlier: You could also add proofs and set theory but I wouldn't know in Spanish, maybe Alex would know

Just couldnt ever figure out who they were talking about

[lusty ermine]

yeah, I dont know the fella, “””alex”””

the fella baymax was rambling about, ‘alex’ is unknown to me.

[livid minnow]

Oh well. Thank you for helping me.. I thought maybe I was losting my mind or something

[lusty ermine]

@molten mason

[molten mason]

@marsh ingot Do you know any books about set theory, mathematical logic, or proof writing in Spanish?

It's early morning Sunday for them, it might be a while before they respond.

[lusty ermine]

alex is from spain?

[molten mason]

Sí

[violet shuttle]

My evil twin.

(the joke is that everyone knows i'm the evil one)

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-031-40714-7

there is a new edition of this book

[hazy elk]

Some basic understanding of group theory is helpful, for initial sections you don't need much, but a bit later into the book you will need some topology

[torn crypt]

yes, specifically in the parts I deal with, and in the arrow orderings

[steel cloud]

Okay thank you

[hot dagger]

LOL I better be damned then cuz my analysis/calc course has 18ESPB meanwhile LA has 12ESPB (hole year has 60ESPB this is European system)

so half of my year is carried by analysis and la

meanwhile I have 8 other math/programming subjects that cover the rest of 30ESPB

[violet shuttle]

learning esp?

what am i thinking of right now

[hot dagger]

European standard

[violet shuttle]

incorrect

[hot dagger]

for Bologna system universities

[violet shuttle]

i was thinking of a bed

you don't pass

[hot dagger]

actually

its caled ECTS

European credit transfer system

[violet shuttle]

so...what's this curriculum?

[hot dagger]

basically you have 60 points per year you need to gather through various courses

[violet shuttle]

analysis and la for half a year is...quite little

[hot dagger]

??

theyre both in 2 semesters

but carry as much points as other 8 subjects combined

[violet shuttle]

are we talking analysis from calc 1 to calc3 + diffyq?

2 semesters > 1/2 year

[hot dagger]

idk what is the definition of calc1 and calc2 and calc3

[violet shuttle]

calc1: derivatives and integrals.
calc2: series
calc3: multivariable

[hot dagger]

we are doing sequences, series, functions, limits, differentiability, integrals, riemann integral etc

whats multivariable?

[violet shuttle]

The calculus of functions of multiple variables

[hot dagger]

Yeah I dont think we cover this

[violet shuttle]

Calc1 and Calc2 in the US don't mention partial derivatives.

[hot dagger]

but I might be wrong

Integrals are done in this semester so we might do it later or not do it at all

[violet shuttle]

are you saying that you never take a multivariable calculus class?

[hot dagger]

havent done it

[violet shuttle]

I am confused. Will you be doing like analysis with epsilons and deltas before seeing partial derivatives??

[hot dagger]

probably lol

we did partial integration tho

[violet shuttle]

this...is strange to me

[violet shuttle]

wat

...what's this "partial integration" thing

[hot dagger]

we probably did partial derivatives aswell but it was 1st semester

[hot dagger]

solving integral with multiple steps

u and v

dv

du

[violet shuttle]

...??

Oh

You mean integration by parts!

[hot dagger]

mb

its called that yeah

fuck me and my translation god damn

[violet shuttle]

Your description as "multiple steps" is super generic

It's the reverse product rule.

[hot dagger]

shifts in math if that makes any sense

[violet shuttle]

And it's also a "swap the derivatives as long as you flip the sign and put a boundary term"

[hot dagger]

you mean DI method?

[violet shuttle]

"solve an integral in multiple steps" could be describing one of a thousand methods for finding an integral

[hot dagger]

I know that but we havent learned about it

[violet shuttle]

...what?

[hot dagger]

basically faster integration by parts

shorter*

[violet shuttle]

$ \int_{a}^{b} u dv = uv|^{a}{b} - \int{a}^{b} v du $

[hot dagger]

bot doesnt wanna listen

[violet shuttle]

...is that not how you summon the latex bot?

[hot dagger]

yeah

but prob doesnt work in this channel

because its book recomm haha

[violet shuttle]

Now, if uv vanishes on the boundary, it's zero

Commonly, you are integrating against a test function that's from a space like the space of smooth and compactly supported functions

[hot dagger]

we havent done definite integrals yet

[violet shuttle]

...

[hot dagger]

so I kinda cant remember from high school

[violet shuttle]

how the fuck do you learn integration by parts before definite integrals

[hot dagger]

by doing indefinite integrals

[violet shuttle]

are the europeans okay?

[hot dagger]

no

[violet shuttle]

I always assumed the Americans were the not okay ones!

[hot dagger]

geography wise

maybe even in general

but the schooling systems are way different

they have to pay for schooling

[exotic belfry]

in what sense

actually

[violet shuttle]

So you're telling me you are learning methods for integration before the damn fundamental theorem of calculus?

[exotic belfry]

that question doesnt need to be asked

i agree

[hot dagger]

yes

[violet shuttle]

wha!

[hot dagger]

we will do it but probably later

[glad rampart]

i dont know calculus how insane is that

[hot dagger]

yeah its fucked up

[violet shuttle]

you better fucking do it

if you don't you should mutiny

[exotic belfry]

differention is fine

integration is a nightmare

[violet shuttle]

The fundamental theorem of calculus relates indefinite integrals to definite integrals. It expresses the way that integration is really just area under a curve.

[hot dagger]

bro so system here is like:

1. Professor giving theory lectures
2. Assistant giving practice lectures
   Assistant is on Integrals while Professor hasnt even covered first semester fully so we are late when it comes to theory background

[violet shuttle]

in analysis, integration is fine, but derivatives are a nightmare.

[exotic belfry]

huh i was thinking of the (f(x+h)-f(x))/h thing 💀

[violet shuttle]

That's not a theorem.

That is a definition.

[hot dagger]

we did area under curve in high school

[exotic belfry]

i mean yeah

its called the first principle of derivatives right

[hot dagger]

but thats without any theory

just calculating shit

[violet shuttle]

I'm not sure why anyone would call it anything besides "The definition of the derivative"

[violet shuttle]

...

[exotic belfry]

because you can use it to calculate derivatives

so its not just a definiton its a formula

[violet shuttle]

It's literally the definition

[hot dagger]

we are abusing this channel purpose...

[violet shuttle]

"derivative" of f at x is defined as the limit as h goes to 0 of (f(x+h)-f(x))/h.

[exotic belfry]

i agree

[glad rampart]

#math-discussion ?

[hot dagger]

sure

[gray gazelle]

What textbook should i read to review all stuff ive learnt from 7th to 12th to prepare for college in the near future?

[exotic belfry]

the textbooks that you used for school from 7th to 12th maybe?

[gray gazelle]

i need an english one

i want to get myself used to learning math and physics in english

also had probably lost 7th to 9th grade's book

[violet shuttle]

A calculus book should suffice

[marsh ingot]

Nope

[exotic belfry]

I always get confused when people say stuff like this

then I remember USA is weird

do you only learn calculus in math in year 11 and 12

[violet shuttle]

Why?

You'll certainly review the necessary algebra when working through the calculus book.

[violet shuttle]

most do, yes...

what do you do?

[glad rampart]

theyre getting their masters in topology of course /j

[exotic belfry]

idk I'm in year 10 and I'm in Australia but I'm sure the syllabus includes more than just calculus

like our year 10 syllabus has probability, polynomials, geometry etc

not just algebra 2 or whatever

[violet shuttle]

#advanced-algebra message

[violet shuttle]

...what facts about probability and polynomials do you learn that isn't just algebra?

polynomials are def algebra. still holds true when you get into the abstract algebraic study of them

[exotic belfry]

well
true I guess you can group most of the stuff under algebra that still makes sense

but why just calculus that seems oddly specific

[violet shuttle]

probability theory early on is just additivity and independence <=> multiplicativity. however i did those math competitions, so...

[violet shuttle]

...how is that oddly specific?

[exotic belfry]

because there's a lot of stuff in math that isn't calculus? like it's a broad topic but not as broad as algebra

[violet shuttle]

"Oh, one of the most most used parts of math, that is necessary for further math, that every other course will assume knowledge of, and that is the first course with any real rigor"

[exotic belfry]

for example I think half of the year 12 course is about complex numbers

that's not calculus

[violet shuttle]

yes it is

[exotic belfry]

how??

[violet shuttle]

complex analysis is usually where you learn to deal with them properly.

there's the algebraic study, in that they are algebraically complete

but complex analysis is a cornerstone of math! it's famously nice!

also they don't really teach complex numbers.

not for me, at least

[exotic belfry]

but as far as I know calculus is nostly about derivatives and integrals

[violet shuttle]

...

yes...

Look, someone doing math is doing at least one of something algebra like or something calculus like.

[exotic belfry]

geometry

[violet shuttle]

Note that I'm cheating a bit by including the definition of continuity

[violet shuttle]

broski

The only geometry that isn't as calculussy is algebra.

Oh, but even in algebra you get derivatives of polynomials being important for characterizing multiple roots

and you have the zariski topology. when continuity is included as "calculus", tada

[exotic belfry]

huh

[violet shuttle]

Differential geometry! Riemannian geometry!

[exotic belfry]

our geometry is mostly about like angles and side lengths and areas. actually mostly angles, not too algebra-like

[violet shuttle]

this is just some trig and torturing students with "proof"s, or something, I don't actually remember.

[exotic belfry]

I agree, but it's still taught

[violet shuttle]

...actually, what was it that I hated about those?

[exotic belfry]

I hate geometry too

drawing and stuff

it's too arbitrary

[violet shuttle]

good thing you'll have the area formulae in the calculus textbook! Good thing the calculus textbook will be a good trig review!

[violet shuttle]

this is...what?

this is not at all why I think the class has problems

[exotic belfry]

like

ok wrong word choicr

not arbitrary

just like

I don't know how to express it

[violet shuttle]

the grade school geometry is really just linear algebra

[exotic belfry]

I just don't enjoy geometry

[violet shuttle]

Have you done any geometry beyond that class?

If not, don't discard the field. It's so totally different.

[exotic belfry]

similar and congruent triangles, cyclic quadrilaterals

etc

I don't remember much

[violet shuttle]

So, geometry gets generalized into ~3 thinfs.

Firstly, we have the generalization of calculus to manifolds (spaces that are locally euclidean).

This is how one generalizes multivariable calculus, and then goes on and add a metric and handle curvature (if you like physics, General Relativity uses this).

Secondly, (well, this should've been first), we have Topology, which mathematicians won't think of as geometry.

I have yet to come up with a good way to describe topology to someone that doesn't know what a topological space is already without just defining it and giving examples.

[exotic belfry]

"to a topologist, a coffee cup and a donut are the same thing"

(or something like that)

[violet shuttle]

But, basically, we take as primitives the notion of open sets, and we may not necessarily have a metric. This is where Mobius strips and Klein bottles and holes come from.

[exotic belfry]

aaah ok sorry to interrupt but

this all seems very complex

and I don't understand most of it

[violet shuttle]

Understand...which part? One obviously won't understand all of a field that one has just heard about.

Thirdly, we have Algebraic Geometry, dealing with the zero sets of polynomials.

Two spaces are topologically equivalent (homeomorphic) if there is a continuous and continuously invertible function between them.

A space is "locally euclidean of dimension n" if every point has a neighborhood around it that is homeomorphic to R^n.

[exotic belfry]

well sure

but

is there a reason you are telling me about all the fields of geometry?

I didn't ask about this

[remote sparrow]

this isn't about books anymore

[exotic belfry]

tbf it never was

I asked my original question in the wrong place

mb

[narrow crown]

Hi, could someone help me find the solution book for this ISBN 9789390727353?

[hot dagger]

Is there a good free service for translating PDF/Word documents? Adobe Acrobat doesnt have translation option, Word doesnt have my language (atleast 2016 version I have) and google translate doesnt support documents over 300 pages and other scammy sites charge over 800$ for translation although marketed as free??

[remote sparrow]

it's rather late but @sleek canopy @spark kiln @lean pagoda can probably speak to their experiences with hinman

[livid minnow]

Enlightenment philosopher Denis Diderot (1713 – 1784) once observed that “Mankind have banned the
Divinity from their presence; they have relegated him to a sanctuary; the walls of the temple restrict
his view; he does not exist outside of it.”

[tribal crow]

fwiw, I started epsilon delta analysis before formally seeing a definite integral lmao

[barren epoch]

what books are recommended to learn multivariable undergraduate analysis?

I'm currently using fitzpatrick but I'm having a really tough time understanding partial derivatives and the general MVT

i looked at lang and rudin but those dont seem to have what im looking for

[gray gazelle]

spivak "calculus on manifolds"
munkres "analysis on manifolds"
folland "advanced calculus"

use one of the first two along with the third

[barren epoch]

👍

thank you

[gray gazelle]

munkres is kinda like a worse version of spivak that's easier to understand

it tries to correct spivak's terseness but it goes too far and the book is a bit of a slog

[barren epoch]

i see

[gray gazelle]

and the exercises suck

[barren epoch]

i think im moreso just looking for a proper definition and understanding of partial derivatives and mvt i guess if that makes sense

fitzpatrick doesnt make sense to me

[gray gazelle]

check out folland's book

he does the multivariable MVT well iirc

[barren epoch]

oh great to hear

i will check that one out first

[gray gazelle]

the short explanation is basically: in multivariable calculus you do a lot of reducing to the single-variable case by restricting to paths

partial derivatives are the single variable derivatives along coordinate paths

the MVT is obtained by applying the single variable MVT along a path

[barren epoch]

right

im just also really weak in parameterization

which is the notation that fitzpatrick heavily uses

[gray gazelle]

better practice! folland has a lot of computational exercises, but a good amount of proofy ones too

[barren epoch]

yeah i have an exam in like 2 days but ill try my best

[gray gazelle]

gl

[gray gazelle]

Can you please tell prerequisites for folland?

download the book and find out

uhhh.... single variable calculus and linear algebra

Okay. Btw downloading on half way.

and i mean mathy proofy single variable calculus and linear algebra

Ah I got it. Probably a certain amount of maturity too?

i guess so

whatever you'd get out of "mathy proofy single variable calculus and linear algebra"

[gray gazelle]

Do you mean Calc 1, rather than Real analysis 1?

i'm not american so these are hard to distinguish for me

something along the lines of spivak's calculus book

"proof based calculus"

(I am not American too)

[gray gazelle]

I got my answer

Thank you!

[molten mason]

Some people never take calculus, some take it was early as 9th grade. Majority is 10th-12th because AP Calculus will count as university credit but only if you're in at least 10th grade I believe

[molten mason]

Basic Mathematics by Serge Lang for pre-Calculus

Any Calculus textbook written in the last 70 years for Calculus

[molten mason]

Probability, polynomials, and geometry is 5th-8th grade in the US depending on the student

[molten mason]

Complex numbers are introduced in pre-calculus course (although idk why because we didn't use them at all in calculus)

[floral lantern]

you can get the credit for taking the AP exam anytime

you just can't get it as an AP class on your transcript

if you're below 9th

[floral lantern]

more like 5th - 10th tbh most people take a full geo class in 10th and cover polynomials in alg 2

[molten mason]

Oh is it 9th? I thought it was 10th.

I know locally we have a school that takes AP classes starting in 8th grade and I know they're all pissed because it doesn't count for university credit lol

[floral lantern]

don't the AP exams still count?

I thought it was just that you can't put like "AP Calculus on your transcript"

if below 9th

[molten mason]

As far as I knew has to be within 3 years of applying to college .

You can tale the exam and get a 5 and all that but it only counts for high school credit, you'll still have to retake the class in university because its not university credit

[floral lantern]

oh it might be a local university credit thing then

because it's AP scores for credit

I thought

but idk

shame though

[fleet solstice]

Does anyone have any tips on reading Math textbook, if you wanna self study certain topics in math.

Like Algebra, Precalc... etc

[lusty ermine]

which book is good with real analysis, if possible hard problems

[trail hemlock]

rudin's pma has lots of hard problems

[lusty ermine]

is this the goto, for hard problems? I will give it a look, very much thx

[trail hemlock]

i think the best way to self study stuff is not to rush it. most textbooks will have some worked out problems, so make sure that you understand the ins and outs of the solution, as well as HOW the author solved the problem. then, try to solve a couple practice problems but never look at solutions unless you have struggled for a few hours, or yo are just completly lost on where to start. thats how I usually go through textbooks.

[trail hemlock]

i think most analysis textbooks have p hard problems, im going thru rudin rn lmao. i think the tao has some hard problems, abbot's understanding analysis does as well. but yeah, the rudin has some hard ass problems lol

[tawny copper]

Andreescu has a book which is nice. The flavor compared to Rudin is very different.

Abbot also has easy problems (not all are easy), which is nice to get introduced to a subject

[molten mason]

Do all the problems. I normally do my first pass doing all of the odd problems. Then I'll go through a second time doing the even problems and see what I need to work on.

[violet shuttle]

I only do some of the problems.

Ideally, you'd do more

[novel obsidian]

There's a balance to be struck for sure. You can very easily spend a year working through chap 1-7 of rudin if you do all the problems urself, accompany it with video lectures and another book, doing the problems out of the other book, but I think it might be better to be a bit more efficient on a first pass then come back once you've developed more mathematical maturity.

everything will be easier then

As someone who spent way too long on chap 3 of rudin (like 6 weeks lmao)

[modern ruin]

lol

i have a tendency still to spend a long time on single sections of books

[lusty ermine]

struck?

[novel obsidian]

I've convinced myself it's okay to go a little faster than 6weeks a chapter because I'll be forced to relearn this in about 8months in uni lol

[novel obsidian]

past participle of "to strike"

wait. are you a native english speaker

[molten mason]

They said elementary algebra and pre calc... mostly arithmetic problems. Much easier to do all the problems than in advanced math like Rudin lmao

[molten mason]

No, they speak Spanish

[novel obsidian]

"to strike a balance" is an expression renato, meaning to balance two things

[novel obsidian]

I was adding to what xela said

[fleet solstice]

Wdym by doing all the odd and even problems. Like if their were 50 problems, you would jus do the odd numbered ones, like 1,3,5... etc?

[violet shuttle]

I spent a long time on Chapter 2 (maybe it was three).

That chapter is what made me mathematically mature. The rest of the book was much easier.

[lusty ermine]

usually odd ones have solutions in the back. . . . . . . .

[violet shuttle]

sorry that wasn't clear to me. I just assume that when people ask questions like that, they did it because they find advanced math textbooks and don't know what to do to learn the material.

[lusty ermine]

cheers

[molten mason]

Yes. The answers to the odd ones are normally in the back of the textbook.

[glad rampart]

some textbooks dont include answers to all the problems they include?

[tribal crow]

the tradition is to include solutions for only the odd numbered problems, if the textbook has solutions at all

[glad rampart]

thats weird

[tribal crow]

its common wdym

[left cloud]

most math textbooks beyond early undergrad content don’t include any solutions

[tribal crow]

i'm aware

[left cloud]

most being like, every single one i’ve seen

[glad rampart]

just feels weird to include problems without also including their solutions

[tribal crow]

i mean

is the author expected to include a detailed proof for every exercise?

[left cloud]

i wasn’t directing that towards you, i know you said “if the textbook has solutions at all” lol

[glad rampart]

maybe its just my dumb high school perspective talking

[tribal crow]

i dont think most high school textbooks contain many proof exercises

[glad rampart]

mine do

[tribal crow]

interesting

how do they provide solutions?

[glad rampart]

they have a seperate smaller solutions manual for the exercizes, and just print the solutions to the problems in the main text in the chapter of the problem

[tribal crow]

i see

do the solutions contain detailed proofs?

or like

a sketch

[glad rampart]

line by line proofs

keep in mind it is algebra 1 so the proofs arent the most complicated things in the world but they are there

[molten mason]

Normally there's a separate solutions manual or it's expected that your professor/class will grade your answers. A lot of texts aren't self-study friendly in that regard.

Most textbooks up to Calculus contain odd-number answers in the back of the textbook, the even-number are reserved for homework by the teacher.

Even Spivak and Apostol have answers in the back

Lang's Undergraduate Analysis and Linear Algebra have solutions manuals But I don't know any for anything else.

[tribal crow]

you can always search for a solutions manual to a text on the internet, and see what you find

[glad rampart]

true

i love reading textbooks

[molten mason]

Me too

[tribal crow]

someone has probably typed up solutions to most(?) of the more popular textbooks

[tribal crow]

what's the textbook's name

this sounds interesting to me

[glad rampart]

art of problem solving, introduction to algebra for the specific one im reading

i heard they were good and that seems to be the case

[tribal crow]

ah AoPS

that makes more sense lmao

[glad rampart]

in a good way or a bad way lol

[tribal crow]

in a good way!

[molten mason]

We all know AoPS, good stuff

[glad rampart]

hell yeah

im finishing up the intro to algebra one rn and will probably go to intro to number theory next

very excited

[remote sparrow]

hubbard and hubbard or shifrin

[remote sparrow]

whether ap exams give credit towards an equivalent class varies by university

older books seem to be less stingy with including solutions

[rancid aurora]

Did you read Ralph Vince's books?

[last sluice]

any complex analysis book recommendations? ive taken an undergrad real analysis class that used tao as a reference if that helps give my background

[heady ember]

Enderton took me a year. Maybe more like 7-8 months, because there was a couple months I didn't touch it (I was revising for exams).

[remote sparrow]

#book-recommendations message

[novel obsidian]

jesus.

[heady ember]

What

It's not like I have gotten that much faster since, either

I certainly have improved though

[dusk wind]

useful to kickstart pre-algebra https://mathguy.us/Handbooks/PreAlgebraHandbook.pdf

or even BAE really

[last sluice]

oo thanks ill have a look at both of those

[marble solar]

I think Donald Marshall's book is good. Stein & Shakarchi complex analysis is probably the standard rec

Schaum's outline to complex variables has lots & lots of examples

[last sluice]

thank you ill have a look at those too then :)

[heady ember]

Look in pinned

[molten mason]

We were talking earlier in #discussion about freitag and busam, good opinions all around.

It's what Dami recommends in his pin

[heady ember]

Yamin shills their profs's book: Saeed Zakeri's a course in complex analysis.

[last sluice]

holy cow so many recommendations thank you

[marble solar]

Mathematicians are passionately picky people about the "right" way to learn something

[molten mason]

Zakeri's physical textbook is on sale right now, normally $70, $17 + $5 shipping if you live in the United States

[marble solar]

However, there is no real canonical right away, although there are certainly wrong ways

[last sluice]

unfortunately i do not live in the united states but wow thats a big discount

[molten mason]

Yeah PtYamin likes Zakeri, but there's not much info online... I think I only found 2 things online about and they both said it's good for a second text not a first text... only reason why I'm wary of getting it.

[remote sparrow]

you should probably link to princeton university press' website

that's where the sale is

[molten mason]

Oh yeah that makes sense.

Zakeri's A Course in Complex Analysis:
https://press.princeton.edu/books/hardcover/9780691207582/a-course-in-complex-analysis

[dusk wind]

because there are most certainly wrong ways

[marble solar]

Did you see my message after that?

[marble solar]

Like right here?

[hallow oriole]

i do think there is an objective way to learn something for some things tho

in that it's the best way to learn for the largest number of people

[violet shuttle]

Just inject the knowledge into your veins.

What's the issue?

[hallow oriole]

me w heroin

[prime dune]

Hey chat, a lot of the theory I eventually want to get to has to do with shit like harmonic analysis and lie theory, which has a LOT of content to understand and learn. After Abbott should I pursue Topology, Manifold Theory, or functional analysis to handle that

Because that’s a FUCKTON of shit that I’m going to have to slog through to get there

I’m slowly trucking through Jacobson’s for the algebra aspect

Namely concepts like Pontryagin Duality and Haar measures just seem really interesting

[remote sparrow]

you should learn functional analysis for harmonic analysis

[prime dune]

Functional analysis seems like the most interesting

Though going to Rudin’s functional analysis after Abbott seems like a bit of a jump

[remote sparrow]

you can read Measure, Integration, and Real Analysis by sheldon axler for the basics of measure theory and functional analysis

you'll need another book after axler for more functional analysis content

[modern ruin]

holy shit axler made a real book other than that awful linear algebra one?

[prime dune]

I think I’ve been told Rudin’s functional analysis is a good route

[remote sparrow]

the 4th edition of LADR substantially changed the treatment of determinants

also, it's free online at https://linear.axler.net

feel free to evaluate for yourself

[modern ruin]

yar

[remote sparrow]

the determinant is now treated as the unique alternating multilinear function mapping the identity matrix to 1, like many other treatments

[prime dune]

Functional analysis seems like analysis for algebraicists in denial

[remote sparrow]

there is also some multilinear algebra in ladr

[modern ruin]

hmm okay maybe I will stop shitting on axler so much (I still hate the book, but now it's no longer reasonable to hate it)

i really like it though becuase I also just really like LADW

[prime dune]

How did he used to treat it

[remote sparrow]

some odd complexification of a vector space construction

[tribal crow]

everyone i hear either loves or hates axler geez

[lusty ermine]

LADR or LADW

[tribal crow]

i never hear a single moderate opinion on his book

[remote sparrow]

ladr isn't intended as a first course

[modern ruin]

niether of them are

[prime dune]

I might ask a local printing company to print out a copy of Axler once I finish Abbott

His func analysis

[magic spade]

Actually ladw is intended as a first course

[prime dune]

Not linear alg

[lusty ermine]

ladw what is it?

[magic spade]

Linear algebra done wrong

[prime dune]

I should probably do linear alg at some point because I’m a computer engineering major and that’ll actually benefit my college path more than Jacobson Algebra is

But whatever

[remote sparrow]

it's not a specialized functional analysis textbook

it should be understood as a measure theory textbook with some really basic functional analysis

[prime dune]

I mean there’s Rudin from there

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-319-58540-6

https://www.amazon.com/Functional-Analysis-Peter-D-Lax/dp/0471556041

https://www.amazon.com/Introductory-Functional-Analysis-Applications-Kreyszig/dp/0471504599

kreyzsig has the fewest prerequisites, only requiring real analysis and linear algebra (no measure theory)

you can read kreyzsig if you want

[prime dune]

I do want to do measure theory

But I’ll figure out what I want to do when I get there

[remote sparrow]

[crimson leaf]

You should know linear algebra before functional analysis

[prime dune]

The textbooks are for self study and I forgot I have to take an actual linear alg course for my major

[crimson leaf]

Really you should know linear algebra before Measure theory

[lusty ermine]

is it true that you need to know the in and outs of la for entering func analy

?

[prime dune]

A lot of measure theory content like L^p spaces I’d assume require good knowledge of lin alg but as far as I’m aware a lot of functional analysis is in the finite dimensional case

[crimson leaf]

In a finite dimensional case you still need good linear algebra to properly work with finite dimensional vector spaces

[lusty ermine]

ye

can I get started in func analy knowing just the basics of la?

[crimson leaf]

Define basics

[lusty ermine]

I know very few theorems, also I am certain of
eigenspaces, eigenvectors, eigenvalues, basic linear maps, nullspaces, Rank, basis idk, only basics.

[crimson leaf]

This also depends on the level of functional analysis you're jumping into. For a proper course I would say comfortability with proof based linear algebra, analysis, measure theory, and point set topology would be required ideally

[lusty ermine]

I know very few linear algebra. I have only learnt basics for now

[crimson leaf]

I more so meant did you learn it with or without proofs

[lusty ermine]

without.

only computationally

[crimson leaf]

Then I would read something proof based first

[lusty ermine]

what do you recommend.

[crimson leaf]

#book-recommendations message

[lusty ermine]

damn

this books have proof writing exercises for la?

[crimson leaf]

Personally I like Friedberg, Insel, and Spence but you can pick your favorite sounding one

I'm not sure what you mean but they have problems in there for you to complete

[lusty ermine]

computational problems?

[lusty ermine]

you said comfortability with proof based l.a.

[crimson leaf]

Depends on the book but the main focus will be proofs

[lusty ermine]

thx.

[marble solar]

I think Functional Analysis is good, but so is PDEs

Haim Brezis has a book that does a mixture of both

[prime dune]

foolish of you to assume I wasn’t jumpscared and also enthralled by Sobolev spaces which kickstarted my desire to learn functional analysis

[marble solar]

I'd say in general you don't need a whole lot of depth to start Harmonic

[prime dune]

Also seeing smooth functions of compact support… everywhere

Literally everywhere in functional analysis

[marble solar]

I'm assuming you've learned the basics of complex analysis

and real analysis at the level of Folland/Ahlfors or Papa Rudin

Looking through the chat, it seems you're not there yet

I'd recommend starting on Knowing Linear Algebra, Complex Analysis, and Measure Theoretic Real analysis

or learning rather

[prime dune]

Complex function, “ooh I wonder if you can map open sets to eachother comformally”, reimann mapping theorem, dirichlet principle, Sobolev jumpscare

[marble solar]

Ok, so you've read something equivalent to Ahlfors?

e.g. you know what a Poisson Kernel is

[prime dune]

Not really, looked into it before, but it was an engineering context in terms of circuitry and shit

[marble solar]

Ah

[prime dune]

Read into it a little bit, turns out Sobolev spaces are neat

I need to formally go off a textbook and work my way there

[marble solar]

Yeah if you're looking for a road map for you start with {Linear Algebra, Fourier Analysis, Complex Analysis}

[prime dune]

The only real stuff I know about functional analysis a priori is Arzela Ascoli but like, the metric space context one

[remote sparrow]

you can read stein & shakarchi's Fourier Analysis if you want right now, which restricts itself to riemann integration

[marble solar]

If you're coming from an engineering background, it's probably easier to go with Churchill & Brown

[remote sparrow]

he's already working through Understanding Analysis by abbott

if he finishes that, he'd be well-prepared to tackle something else

[marble solar]

Stein and Shakarchi's presentation tends to not sit well with engineering minded folks

[remote sparrow]

for complex analysis or fourier analysis

churchill and brown do have a book on fourier series

[marble solar]

I was recommending churchill and brown for both

Stein and Shakarchi Fourier/Complex Analysis are very challenging books, even for math majors

[remote sparrow]

gamelin is a very gentle introduction to complex analysis

[marble solar]

Gamelin is much more gentle

[remote sparrow]

bak and newman is a power series first book with lots of answers in the back

[marble solar]

I am partial to the power series first approach

I think it is the correct one

[prime dune]

I am very much a fan of rigor and I do want to get a good grounding of measure theory and topology in the meantime

Eventually I want to get to Sobolev theory but I want to get the rigorous background first

And it’s a hobby so I literally have no time limit to learn it

The huge point of interest for me is how the notions all come together.

One of my end goals was to basically work my way up to Generalized Stokes through measure theory and real analysis as formally as I can make it from the ground up

like constructing R, using it to define measure spaces & metric spaces (both ways of assessing structure through either measuring set size or distance of points), then defining orientable manifolds, tangent spaces, the exterior algebra on it, constructing the exterior derivative and then finally tackling it using partitions of unity

[marble solar]

If that's the case then go for Stein & Shakarchi Fourier/Complex Analysis

Those books are quite challenging however

[lusty ermine]

how to get started with category theory and commutative diagrams?

[tribal crow]

er, you've been asking for books on a lot of different topics lately

[trail hemlock]

my boy juss smart 🗣️

[violet shuttle]

You should learn linear algebra before [insert math subject here]

Perhaps the only exceptions are single variable introductory real analysis, introductory topology, and maybe some algebra if you reorder it and learn the definition of a field before seeing vector spaces (like I did - I knew groups and first isomorphism, knew the definition of a field, and then the definition of a vector space was simple for me).

[tribal crow]

do you really need an intro to category theory at this stage?

i dont quite know what your goal here is

[violet shuttle]

i understand it

[tribal crow]

apologies if i'm coming off as a bit harsh

[violet shuttle]

ooh, shiny! lemme get the reference now!

lemme peek and learn the first couple definitions!

what stage are they at?

[tribal crow]

afaik, they've been doing a lot of LA recently

given by their activity in #linear-algebra

also in the help channels

[tribal crow]

i understand this feeling too lmao

[violet shuttle]

personally category theory just felt like "...? who fucking...what why...what"

until algebraic topology

[tribal crow]

but they've been asking for recommendations on a billion subjects it feels like

[slender cargo]

Hey, the enthusiasm is great. But yeah, probably better to thoroughly learn the early foundational subjects first (which is what I’m currently doing)

[tribal crow]

i have no issues with the enthusiam either lol

i'm just wondering what the goal here is

[slender cargo]

This is what I’m doing, some Algebra first before LA due to how my schedule lined up. Glad to hear it works out okay

[violet shuttle]

Note that I did very little algebra first

As in, literally just enough to understand the first isomorphism theorem and then the definition of a field.

[slender cargo]

Ah I’m in an abstract algebra class that only assumes computational linear algebra

Will be going through proof based linear algebra over the summer

[tribal crow]

i know a grand total of (probably) 0 things about abstract algebra rn

while i'm in this channel, i might as well ask for some recommendations lol

my institution uses Dummit & Foote i believe, but i hear the book can be a bit dry to self-study from

[violet shuttle]

You want something that's probably drier?

Well, get Lang!

[tribal crow]

ah yes, Lang

[violet shuttle]

It's not just dry, it also has little explanation!

[tribal crow]

definitely suitable for a freshman

[slender cargo]

Been using Beachy Blair and I think it’s a great book (although, I’m not even a grad student yet). Has a strong early emphasis on elementary number theory and a lot of exposition

[tribal crow]

its also self-contained!

perfect

[violet shuttle]

...yes? as long as you are mathematically mature

[tribal crow]

i am not

[modern ruin]

real af

[violet shuttle]

Then it's a terrible idea!

It has less explanation than I remember Baby Rudin having

Baby Rudin taught me how to create intuition and explanation out of something that didn't give me it

I bounced off Dummit and Foote. Mostly because I didn't do Baby Rudin yet

Then I landed on Lang

[tribal crow]

...i wonder if it's possible to just brute force your way through Lang with very little mathematical maturity

[violet shuttle]

Well, probably

[tribal crow]

i'd imagine that at least somebody has done it

[violet shuttle]

If I liked algebra more than analysis initially, I would've probably done that with Dummit and Foote

[tribal crow]

i feel like i could never lmao

but who knows

maybe i just need to try something like that

[violet shuttle]

did you feel that way with baby Rudin?

[tribal crow]

i'm still doing intro analysis right now lmao

[violet shuttle]

ah! okay

using tao?

someone else?

rudin?

le bebe

le petite rudin

[tribal crow]

spivak

[violet shuttle]

ah, never used his books

i did look at calculus on manifolds once

[tribal crow]

i'm probably going to attempt to go through some of it soon (starting in about 2 months?)

i wanna get to DG as fast as i can, but not have a bad foundation

[violet shuttle]

see i was recommended it by someone after forgetting to divide by h on an exam that asked for the definition of the total derivative

so i stopped reading it once it turned out that i passed said exam

[tribal crow]

lmao

[violet shuttle]

it was a "shit, do i not know this? like sure i knew we need to divide by h and just fucked up on the test, and i know it's a linear operator but didn't write that and when shown my exam later was like 'parsing handwriting a function' while knowing it's a linear operator, but, maybe I don't actually understand this well enough?"

those fears vanished when I passed and could comprehend my class

[tribal crow]

how much was this exam worth

geez

[violet shuttle]

this was the written anal qualy

i don't remember my score, i think it was like 70% of the total points? I don't remember what the bar was to pass.

[tribal crow]

70% sucks

oh wait

you mean

[violet shuttle]

it was better than anyone else that took it that time.

[tribal crow]

70% on the exam

i thought you meant 70% of your final grade

my bad

sorry sorry

[violet shuttle]

all's good!

i definitely should've done better, but, eventually you realize that kicking yourself is not productive

[tribal crow]

agreed

my past few exams/tests have not gone the best lmao

i'm quite unhappy with the results actually

but i'm trying my best to improve one step at a time

hopefully, i'll get better with time

i like to think so, anyways

[molten mason]

That's what I have

[tribal crow]

physically, or in pdf?

[molten mason]

Both. If we're talking about abstract algebra specifically, I have Undergraduate Algebra physical and Algebra pdf

[tribal crow]

i see

[remote sparrow]

fun fact, the 300-level linear algebra class at the uni we go to uses LADR

the professor is some new guy

[molten mason]

Artin's Algebra and Jacobson's Basic Algebra are recommended a lot here.

[tribal crow]

i love the name "Basic Algebra" lmao

[molten mason]

Sour Drop has a ton of Algebra recommendations, that's more his thing than me

[tribal crow]

i'd imagine that most people who dont study math or math-adjacent fields would conclude that "algebra" is the only algebra they know

[molten mason]

My school uses Contemporary Abstract Algebra by Gallian

[tribal crow]

i see

i've read somewhere that Gallian is "too much like a calculus book"

[molten mason]

If you're a chad you'll use Lang though

[tribal crow]

but i havent read a page of it

so idk

[tribal crow]

i think i have the pdf actually

[molten mason]

I would wait for a more in depth answer from someone more knowledgeable. The books I wrote already I've heard by others but I personally haven't gone through. Dami's pin also briefly reviews a couple of them.

[tribal crow]

i just opened the pdf, scrolled down to a random page, and was instantly greeted with this

[molten mason]

But it's a starting point for you to look up

[slender cargo]

I have him for analysis and he is great. He told me what topics he’s teaching out of LADR for when I self study it

[molten mason]

I'm crying rn

@tribal crow
#book-recommendations message

#book-recommendations message

[crimson leaf]

Big fan of Hungerford personally

[remote sparrow]

graduate hungerford presumably?

[crimson leaf]

Yeah never read the undergrad one

But for undergrad I like Rotman's book

[gray gazelle]

His undergraduate algebra book? Or graduate level? Which one are you talking about?

[molten mason]

The joke is his graduate book, as it's generally considered unapproachable. A serious answer would always be his undergraduate version first.

Aren't you going through Farleigh's A First Course in Abstract Algebra?

[gray gazelle]

Ah i got the joke lol. I somewhere (ig on math stack exchange) I read, Lang's graduate algebra cannot be used for self-study.

I was using Farleigh's Algebra, that time I was studying 5 books (5 difficult subjects). But this was not benefiting me. After doing discussion with you all (i remember in this channel) I decided to study only 2 subjects for now. Real analysis (Abbott) and Proof writing (velleman).

[molten mason]

Those two books are a perfect choice, Abbot helps a lot with proofs and Analysis is great You should be able to breeze through Velleman though and then be able to focus 100% on Abbot.

[gray gazelle]

Thank you! I think spending 1 − 2 hours daily on velleman is enough. However I have studied half of chapter 3.
But I am finding Abbott more interesting. So unintentionally I am spending more time on abbott.

[molten mason]

That's fine, you're doing great.

[gray gazelle]

Thank you!

[robust island]

Hey everyone, I'm currently in my first year of university studying as a vocational training studen computer science. I decided to take this stanford course on mathematical thinking: https://online.stanford.edu/courses/hstar-y0001-introduction-mathematical-thinking

Anyone interested to work on the assignments of the course together in a weekly manner till we finish it? If more people are interested we can form a group and also advance from there.
Feel free to dm me or reply to this message if interested.

[gray gazelle]

I self-study math for fun, but on Christmas, I decided to take a break to spend some time with my family. As a result, my calculus skills got rusty. Do you guys have any recommendations for resources to help me get back to my calculus level?

[dusk wind]

Antons + Schaums

[gray gazelle]

https://www.amazon.com/Calculus-Combined-Howard-Anton/dp/0471153060 ? this one ?

[dusk wind]

yea

theres also the calculus books at https://mecmath.net

[dusk wind]

there should be a newer edition for antons https://www.amazon.com/Calculus-Early-Transcendentals-Howard-Anton/dp/1119778182

[gray gazelle]

thx

[molten mason]

I have his 4th edition and it's timeless. Any edition is fine. I'm sure you can google "Howard anton calculus" and you'll have a top result

[void gazelle]

I really like the McMullen workbooks

[wheat trout]

Why would you need cohomology for integration? That is quite a leap.

You first learn doing multivariable integration in Euclidean spaces (R^n), maybe see some multivariable calculus book.

Then you could learn measure theory or real analysis (it is about Lesbegue measure) to understand what is integration w.r.t a measure.

[dusk wind]

10th edition doesnt look too wileyfied https://archive.org/details/HowardAntonCalculus10thEdtion

[fierce hedge]

What's a good primary book for rings and modules. I currently have DnF and Rotman but from what I heard dnf is a slog starting from the modules section idk about Rotman.

From past discussions I saw people shilling Atiyah McDonald, Reid's ug commutative algebra and Ideals, Varieties and Algorithms. Do they cover the same stuff or are they intended for different audiences?

[keen depot]

i book that can make me love calculus or linear algebra?

i dont like maths

[finite gale]

see pins for linalg book

stewart for calculus if you haven't learned it with calculations yet

not responding to you

[fierce hedge]

Advanced Modern Algebra

They are 3 editions of the same book. I have the second edition

[crimson leaf]

A first course in abstract algebra

[dapper root]

Hi tubu

[fierce hedge]

Yo chmonkey

[finite gale]

Hi chmuwu

[molten mason]

Howard Anton has both a Calculus and a Linear Algebra textbook

[keen depot]

thank you

[remote sparrow]

you can read hubbard or shifrin

https://www.amazon.com/First-Course-Abstract-Algebra-3rd/dp/0131862677

[novel obsidian]

,A

[remote sparrow]

likely too basic, but you can have a look at aluffi's Algebra: Notes from the Underground, which has the progression rings > modules > groups > fields

[molten mason]

@tribal crow here are more algebra recs above

[shadow linden]

Is Vicks for prasolov’s book better for algebraic topology

[thorn hinge]

I'll do an algebra course and the teacher decides the book

I asked a friend of mine which book the teacher uses, and he said Hungerford

The thing is, hungerford wrote 2 algebra books

I wanna study before the course, do they start at the same level?

The course is going to cover Galois theory fundamental theorem and Solvability by radicals (I don't know if this is the correct translation)

[finite gale]

Translation is fine

But depends on how much algebra you already know

[molten mason]

Abstract Algebra: An Introduction is for undergraduate
Algebra is for graduate

[tepid garnet]

John E. Freund’s
Mathematical statistics with applications

Is a really nice book

But you do need to do calc I & calc II. Makes it much easier to understand things

[thorn hinge]

Thanks, sir

[molten mason]

Yeah stats is calc-heavy

[tepid garnet]

It pops up in places I would’ve not expected it to

[turbid osprey]

whats a book for holes

[remote sparrow]

https://www.amazon.com/Holes-Louis-Sachar/dp/0440414806

[turbid osprey]

thanks but

i meant mathematics

i read that 7 years ago lol

[trail hemlock]

goat book

[crimson leaf]

What kind of holes

[shadow linden]

Take it from someone in high school. WRONG

What was the consensus on prasolov vs Vick algebraic topology?

[tepid garnet]

Why

Calc pops up everywhere in stats

[trail hemlock]

“WRONG”😭😭💀

[modern ruin]

good book

[remote sparrow]

never read it

[modern ruin]

you should it’s really good

one of the best of all time ngl

[molten mason]

A 7yof died in Florida this week digging a 5-6ft hole in the sand when it collapsed and caved in. The dimensions are similar to the book and it made me think of it instantly

[molten mason]

The Halo series is definitely better tf you mean best of all time

[modern ruin]

[fierce hedge]

Hmm not a bad idea. I think Rotman 3rd edition also does that

[torn iris]

a cheap maths book that can make you so much better at maths?

[finite gale]

any reasonable book as long as you put in the time

[molten mason]

It's the time and work put in, not the book

[violet shuttle]

whatever makes you focus better and helps you learn

e.g. for me, to learn by myself: pen and paper, night and darkness, lack of people, diet soda/ soda zero, food if near hungry time, energy&well restedness

[earnest wolf]

that guy who studied with babi rudin from day 1

[molten mason]

[main hill]

Hey Guys! I we put together Leithold, Anton, Stewart and Thomas and compare them regarding their calculus textbook then which of them You would recommend ?

[hallow oriole]

my complete thoughts on books out there for integral evaluation:

Nahin's Inside Interesting Integrals: probably the canonical book to start with for this. not too rigorous, lots of really neat tricks, very fun integrals. imo the treatment of contour integration is very standard here, not great but not awful. not very difficult, although some of the later problems can be super hard.

Valean's Almost Impossible Integrals: my favorite. i heavily recommend getting both nahin and valean, reading through nahin first, and then going through valean. more of a book containing many problems and solutions than one like nahin, very very good as a problem resource. the integrals can mostly be solved elementarily and are incredibly difficult.

Gordon's Complex Integration: some people swear by this but tbh i'm not a fan. the notation is disquieting (\int dx f(x)) and the problems while okay are not my favorite. maybe better for physics majors?

Edward's Treatise on Integral Calculus 1 and 2: theoretically very good but oh man it's so boring. if you want a book with a lottt of problems then do this. a lot of them are actually fairly good tbf and it's definitely valuable as a reference. read the pdf to see if you like it.

Boros' Irresistible Integrals: it's a perfectly good book ofc but nahin takes this book and improves upon it in almost every aspect. they aren't too dissimilar, ofc. imo the problems, exposition, etc in nahin are all better but maybe you might like the prose in this one? could be personal preference.

i recommend the first two. some others can be good but these are the ones i've checked out personally. (why would you want to evaluate integrals?? idk c fun)

[dire torrent]

is Bass's Real Analysis textbook actually free online, as a pdf?

[remote sparrow]

yes

https://www.math.stonybrook.edu/~aknapp/books/b2-alg.html

@fierce hedge apparently the first edition of Basic Algebra has gone through two printings

the second printing is nearly identical to the digital pdf

i have a copy of the first printing, first edition

[dusk panther]

are there any proof books that are not targeted at undergraduates, and high school students can use to get an insight on how to prove things?

[remote sparrow]

although i think that one is probably nicer than dropping a bunch of money on the second printing

https://www.math.stonybrook.edu/~aknapp/books/basic-alg/b-alg-corrections20.pdf

there is a complete list of errata to the first printing

can you believe i only spent $32 dollars on a copy of knapp labeled "very good?" i'll send pictures later today

[remote sparrow]

kinda arbitrary distinction tbh. you don't even need to know calculus with these sorts of books

[dusk panther]

what book would you recommend as a starting point, then?

[remote sparrow]

#book-recommendations message

@dusk panther

[dusk panther]

I guess i will go with "Book of Proof" by Hammack, since that seems to be pretty popular.

[tough owl]

What every body is saying by ex fbi agent

its about body language but

i thought you people will like it

[fierce hedge]

I mean I can get it printed for like 5 dollars
I am currently thinking about which algebra book to get printed - artin, knapp or silverman

[remote sparrow]

all of them

well artin's international edition is actually missing a chapter and its index, so don't get that pdf printed

namely the one on galois theory i think

[fierce hedge]

this is one of the main reason I wanted to get the non int edition plus the international edition has very poor paper quality

(I have the international edition paperback)

[remote sparrow]

[heady ember]

Pretty Bass'ed

[quartz pawn]

Does anyone know of a book or article that has a sort of elementary introduction to moments and proofs about how they affect the distributions of random variables — or determine the shapes of functions, however you want to look at it.

It probably doesn't exist. I'm probably going to have to learn a bunch of stuff before I really get into them lol.

[gray gazelle]

+1
Its not in measure theoretic probability books thats for sure. Haven’t seen it in popular stat inference books either.

[molten linden]

looking for an introductory text to topology, does anyone have any recommendations?

[stray veldt]

i liked lees intro to topological manifolds

despite its name, its just a topology book

[shadow linden]

Jay Cummings principles of mathematical analysis is good for practicing proofs, but focuses on real analysis. It’s a good book to read, and gives proofs well, but that is not its main purpose

[uncut salmon]

I have a really specific question, if someone could answer me he would be so helpful he couldnt even imagine.
I am searching a lin alg book that, beside the classical topics, talks about: minimal polynomial of a matrix, Fitting decomposition, Witt index/ isotropic spaces and related, Riesz theorem, jacobi method for the signature and a lot of jordan related stuff. My lecturer will talk about this stuff, but the books I have found dont, or do it partially.

[remote sparrow]

he also has a proofs book

[molten mason]

They're all the same/in similar category. That's like asking if we would prefer a Fuji apple or a Gala apple, it's not like you're picking between an apple and a banana. Just look through them all, maybe one author speaks better to you or has better images for you or whatever. I like Anton, but Stewart has full walkthrough of every exercise both even and off on Quizlet for $8/mo, you can't go wrong with Leithold or Thomas either. Leithold might be a bit more difficult/less modern looking but that's it.

[lusty ermine]

do you recommend quizlet, with which other books are you using the answers provided from quizlet?

[molten mason]

Quizlet Plus is $8/mo USD, they have not just answers, but complete step-by-step walkthroughs of many textbooks. I know for sure Stewart's calculus textbook. I checked and saw other math textbooks. Unfortunately none of Lang's textbooks.

I'm checking right now

They have it for Anton, Stewart, and Thomas for sure

I see Larson too

Anton's LA textbook 11th and 12th edition

Clicking a random one on Anton's LA 11th edition....
Chapter 3: Section 3.1: Exercise 6: Page 140

[molten mason]

If you're self studying through these textbooks, and you can't figure out how they got the answer and you can't find it anywhere else and you've tried it a couple times. Sometimes glancing in the walkthrough will give you insight on what steps you missed or did wrong.

HAHA NO WAY

I need to look through these more often I wonder how many books are in here I've missed

[marble solar]

Yeah, I think there are people that get employed by these companies that are giant math nerds desperate for some income

[fast bane]

hey guys! recently i was looking for apistol calculus V 1 pdf but i only found bad copies of it , do any one have any good copy of it ?

[gray gazelle]

Quizlet

[slender cargo]

I looked up the price for Stewart's Calculus and holy hell it's expensive for the most recent edition

[molten mason]

Most of them just have one solution, but I've seen a few problems/chapters that have 2-5 solutions each. You can tell it's a completely different person each solution.

They'll have a "verified" too which means it was double checked for accuracy

[molten mason]

It's used by a lot of American universities, so I'm sure that drives up the price.

[molten mason]

Since students are mandatory to buy it

[slender cargo]

I can undestand that. Just... wow

[molten mason]

Don't forget the cengage fee On top of the textbook, students have to buy the digital cengage pass every semester in order to do homework.

[slender cargo]

It's interesting flipping back through Stewart's Calculus now. He actually proves a lot of the results (maybe all?). And if you did the extra problems in the book, you might get some decent education in Real Analysis from his book

But most universities of course are using the book for its computational problems

[marble solar]

Yeah, there's a lot of good stuff in there. I remember when I was working as a tutor at the local college, I opened the book and just started doing all the Calc 3 proof exercises

Which was fun practice

[molten mason]

Yeah it's just a time issue. Each section has... what... 70 exercises? Instructors only use about 20 of them for homework? And even then students struggle to keep up. They barely have time to read the chapters, just enough to finish their homework, let alone finish anything extra.

[marble solar]

In Thomas' University Calculus there's a test for series convergence that is rarely taught

[molten mason]

Yeah I don't think Stewart is bad per se, it's not my # 1 choice but when people ask for Calc books it's definitely a fine option

[marble solar]

Yeah, there are exercises on Gauss' test and Kummer's test

Which are kind of fun

[marble solar]

I think another issue is that so many exercises require the use of a calculator

[slender cargo]

I kinda wonder how Stewart would compare to Spivak if you tried assigning the meaty extra problems

[marble solar]

Which takes the student out of thinking

[torn rivet]

Hah I’m actually thinking about going through Stewart from the beginning, we never been through the whole text in class and I’ve been out of university for a long time lol

[molten mason]

Yeah like this, perfectly great idea.

[marble solar]

So the school I went to taught out of Spivak & Thomas' Calculus. They used Thomas for routine problems & showing techniques, but spivak for proofs

[torn rivet]

Thanks for the validation, was wondering if that was silly to do lol

[marble solar]

It was a good balance between the two

[molten mason]

Now that's pretty cool

[slender cargo]

Probably the right way to go. Even though a regular Calculus book would have some rigorous stuff, it's not the focus of the book

[molten mason]

My calc classes were all taught by like, engineers and what not, you couldn't even ask them what a proof was.

[slender cargo]

Although I feel like if you're using Spivak, you don't need another book. Spivak has a lot of computational problems

[marble solar]

Spivak has a lot of computational problems, but even then they tend to be at a higher level

You can see his chapter on integration

[remote sparrow]

yeah. although the book is intended to be used over three semesters, so it's not completely ridiculous.

[molten mason]

I think my biggest gripe with Stewart isn't... the math portions. It's having to learn stupid shit from other disciplines. Like instead of spending a good portion of time on a topic learning the concept, you spend a little portion on the topic, then the rest of the time memorizing a random formula from biology, one from econ, one from physics, etc because those formulas would be on the test.

[marble solar]

Are you talking of things like Newton's law of cooling

or population dynamic problems?

[remote sparrow]

i didn't have to learn that stuff for ap calc

[molten mason]

Have you looked into Advanced Linear Algebra by Roman?

[torn rivet]

I think the market pricing of textbooks in general works out to pretty insane prices.

Not much has changed in calculus over the last 100 years, and printing pages in paper doesn’t cost that much

[remote sparrow]

yeah, color printing isn't a great excuse either according to axler

[molten mason]

It was easily 1/3 my class. If we just brushed on it as "Here's an example of this used in real world" that would have been fine, but our exams worth ~30 of our final grade would pull from these.

[molten mason]

Yeah there's no reason for there to be ~10 editions in the last 3 decades lol

[marble solar]

When I spoke to people from the textbook publishing industry, they cited a number of factors, one of the reasons is that cash-cow books subsidize less popular books

Another big strain on their finances are pensions

[molten mason]

My 1994 Anton has very little differences from the 2016 version.

And that's Edition 4 vs Edition 11

[remote sparrow]

a hardcover of friedberg insel spence is ridiculously expensive

[slender cargo]

I have Calculus classes to thank for pure math books being cheaper, I see

[torn rivet]

Haha right, lucky me I’m not trying to pass a class, so I can just buy slightly older versions at discount prices

[molten mason]

Yeah I had to get the paperback international edition lmao such a huge price difference

[molten mason]

Pensions at a textbook publisher is wild to me.

[torn rivet]

Hahah y, is it a good linear algebra book?

I have a book of problems by lang, but if it’s actually worth it I might check it out.

[marble solar]

The industry has been around for a long time, and older generations are retiring & living longer

Doesn't seem that wild

[remote sparrow]

it's a popular recommendation

[molten mason]

Not wild in it existing, just wild in how different the world is today.

[torn rivet]

Good to know! Is that the book you’d recommend?

I also have Aluffi sitting around here

[marble solar]

Yeah, there are lots of things that change the costs of books. I do think books are cheaper and more widely available nowadays than they ever were before. If you don't like a particular book, you can pick from plenty of others at varying prices or even older editions

Markets are deeply fascinating

[molten mason]

I've heard of many universities using it, including mine. It seems pretty common/standard like Stewart/Thomas is for calculus. It's great for learning theory stuff, pretty modern.

Both Lang books are fine too

[remote sparrow]

i prefer meckes as a first book, then axler. hefferon is also a good first book. hoffman kunze is great to complement axler too.

[crimson leaf]

Funnily enough I was just talking book prices with a prof

[tribal crow]

FIS is sold for $350 at my university bookstore

It’s insane

[uncut salmon]

I have just checked it out, it has almost every topic I needed, thank you. Do you think that chapters on modules are skippable?

[torn rivet]

Noted, thanks!

[slender cargo]

I looked through a Lang book and it has less exposition than Rudin's PMA

[crimson leaf]

He has a chapter in a research monograph he just found out it's $40 for the chapter...

[remote sparrow]

it's like $180 on amazon

[torn rivet]

Also noted, thanks!

[molten mason]

That's why I like it Straight to the point, missed the point? Too bad the train is going without you.

[tribal crow]

That’s still too much imo

[slender cargo]

dear god

[molten mason]

I think my first semester of university back in the day my textbooks were the same cost as my semester's tuition, if I took one more class it would have been more than my tuition.

[crimson leaf]

Lang's proof of zassenhaus lemma hurt me

[molten mason]

[remote sparrow]

btw which aluffi

[molten mason]

Not all of them, his preface tells you which module chapters you can skip.

[torn rivet]

Algebra chapter 0

[remote sparrow]

he has another book geared to undergrads

[fickle gyro]

Hi does anyone have any recommendations for SAT math textbooks? Ones that have like a shit ton of practice problems because I need to get better at doing math fast cuz I am slow

[slender cargo]

As an aside: as a returning student, it's been an interesting experience learning how to do Calculus again through a Real Analysis class. I don't remember anything about integration

[molten mason]

I'm not there yet but I can't wait.

[torn rivet]

The book does hurt my brain lol, thought maybe I would go back through Stewart and do analysis from Tao first.

But FIS looks interesting if I can find a reasonably priced copy

[molten mason]

Yeah the used market is great for self study. My first time in school, the professors would write their own in-house textbooks, you were forced to buy for like $300 or whatever, then you would use them for a semester then you can't sell them because no other school uses them, so everyone would just pile it up on a HUGE pile on the grass by the admin building since it was trash. You would hopefully find a student who would be taking the class next semester that you could sell it to unless that was the time the professor/school released a new version which was the same text but just different problems.

Good times.

I haven't taken differential equations yet but that's still a 500 page in-house text, luckily I was able to procure the pdf and print it.

[molten mason]

5th edition hardcover is $156

5th edition paperback is $23

Just get the paperback

[torn rivet]

Oh wow what a difference! I like hardcovers better but at that difference 23 is tempting

[molten mason]

$23 for paperback

[tribal crow]

that’s quite good

[molten mason]

It's international version, the paper is quite thin. Very easy to rip on accident.

On amazon select the paperback version and you can see the change in cover.

Bruh how have I not looked for this before.
FIS 5th edition on Quizlet Plus

[tribal crow]

Unfortunately I was never able to use these

too broke to pay for quizlet

wasn’t quizlet free in the past?

[molten mason]

Quizlet flashcards = free
Quizlet Plus which has solutions to textbook exercuses = $8/mo

[tribal crow]

ah

ig it is what it is

[violet shuttle]

do you have a better proof?

i remember his (like all the rest) being uninspired

[remote sparrow]

you can look at the collegeboard's sat prep book. there are also lots of unofficial workbooks

[royal lark]

wait really?

I can look at sols for free then

[lusty ermine]

only flashcards for free

[royal lark]

check #chill

[indigo flax]

Hello everyone

As someone who has only completed high school math, but who plans to go into an engineering/physics discipline, what are some good books that I should consider reading?

[hallow oriole]

i got my copy for like 30 bucks used

lmao

of fis

[light carbon]

I'm super into ML, but feel like I have weak statistical background which I only took a class in high school. Any recommendations?

feel free to ping me.

[indigo flax]

ML?

[light carbon]

machine learning, my bad!

[gray gazelle]

TB depends on your goals really

And your current knowledge in analysis and probability

[light carbon]

Well I want to truly understand machine learning. Let's say my current knowledge of analysis/probability is minimal. is there an intro book you recommend?

[dusk wind]

Pml probably

[gray gazelle]

To truly understand ML you need to (imho) truly understand statistics and have more-than-basic Linear Algebra. These are prerequisites for ML at a higher level. Otherwise you will find yourself scaling up stat methods not knowing what you are doing. If you start from literal scratch, I would pick first a book that combines Probability with Stats that involves some Stat Inferences as well. I recommend the one by L.E. Mee F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä
A Modern Introduction to Probability and Statistics: Understanding Why and How

After that or in parallel do some rigorous Linear Algebra that is geared towards ML - that is, focus on Matrices, which is a power house in ML. I recommend:
Gilbert Strang
Linear Algebra and Learning from Data

Once you have this two in, you should move to ML proper, but I recommend that you in parallel deepen your Statistical Inference. Most ML books try to teach you this on the way and do a bad job at it.

[dusk wind]

Most ML books are just clickbait

The good ones are outdated