book-recommendations

[broken meadow]

ye they all look like R^n but what is the original ones tho

in the context for this differentiation stuff

im not worried about making things into coordinates yet

[marble solar]

R^n?

like you can do R^2 or R^3

That was the motivation

[broken meadow]

er

i suppose i should explain what i have in mind first

so i know currently only how to express taking the derivative for polynomials

so i can say Ok here is a space of polynomials up to degree n with ordered basis {1,x,x^2,...,x^n}

then differentiation is linear operator from polynomials up to degree n to polynomials up to degree n-1

similar ordered basis just knock off the last one

so then i can make the matrix by just considering taking derivatives of each item in the ordered basis and writing their coordinates into the matrix as columns

this is fine and good

but this is feeling a little different to seeing derivatives in the matrix itself?

[marble solar]

feels the same to me

I guess I don't quite understand what the issue is

with that is moon bed time

[broken meadow]

i am new to linear algebra so ig that is the main issue

😔

guess i will wait till i take a proper course or something to figure this out

[hasty turret]

Yea,You need to know PDE stuff

[broken meadow]

it will come hopefully

bruh looks like the book had an accessible proof already

i cry

its ok

but my interest is still here for this magical calc 3 but for real type stuff idk

[gray gazelle]

so I have a project coming up for english class and we have to choose a non-fiction book of our choice, i'm thinking of choosing something about math pedagogy

what would you guys reccomend?

i know up to single variable calc so something abt k-12 math

also must be >250 pages

for the project we'll have to make an annotation sheet and a video essay

[devout sphinx]

https://teacherprep.princeton.edu/sites/teacherprep/files/events/presentation_files/Bibliography - Mathy (v7).pdf

i remember someone showed me this list before

[gray gazelle]

Guys.

I'm looking for books for Discrete Structures.

Which one do you like?

or courses?

[willow pecan]

Don't past the same question in multiple channels

One is enough

[karmic thorn]

And I think someone suggested Rosen's book yesterday. Did you check it out?

[gray gazelle]

Didn't see it?

Jesus.

2240 Pages.

[untold knoll]

calc w/ analytical geometry by simmons. is it a good intro?

[upbeat vine]

The guy who wrote the amazing book "Visual Complex Analysis", Tristan Needham, is expected to release "Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts" on July 13.

[gray gazelle]

[static crest]

[broken meadow]

:cros:

[willow pecan]

cros

[broken meadow]

cros product

[narrow echo]

@upbeat vine thx for sharing

[true veldt]

POG

[fossil island]

Thoughts on Wiggin's introduction to dynamical systems? https://www.researchgate.net/publication/258629276_Introduction_To_Applied_Nonlinear_Dynamical_Systems_And_Chaos

[narrow talon]

Stochastic diffgeo book?

[upbeat vine]

Any recommendations for Intro to theory of ODEs?

[gray gazelle]

I liked Basics and Beyond by Cain,Schaeffer.

Arnold might be a better fit for you I suppose, but it wasn't for me.

[upbeat vine]

@gray gazelle This looked very good! Thanks!

[timber mesa]

haven't heard of it 'till now but it seems nice and very complete

• a good amount of exercises

[ornate brook]

Any opinions on calculus vol 1 by Tom Apostol?

[karmic thorn]

A lot of reviews seem to describe it as a dry and weird presentation(integration preceding differentiation). I'd suggest you to skim through the first few pages and see if it vibes.

[static crest]

don't really use it

for self learning

[ornate brook]

Its the course´s recommended book, I kinda like it so far but maybe someone would mention a deal breaker or something really positive that would make me exclusively use it

[ornate brook]

I think integration before differentiation is reasonable as long as you are not working with primitives

[static crest]

if it's used as a text to accompany a course

then it's fine

apostol just isnt that good for self learning

imo

[plucky hawk]

anyone know any online textbooks/courses for abstract algebra?

[hearty steppe]

Charles Pinter

[vivid brook]

artin is my favorite

pinter is more accessible but it isn't as illuminating or in depth

[hasty turret]

D&F

[marble solar]

Richard Elman

[storm sleet]

I second pinter and S&F

[karmic thorn]

Since OP also asked for online course recommendations, I think the Group Theory playlist by Richard Borcherds is great.

[storm sleet]

I also second this suggestion

[willow adder]

socratica has good visuals and good simple explanations that act as good review to understanding. Not very rigorous but still nice

[gray gazelle]

@ornate brook i did calc from apostol and i taught it to myself

i regret doing that book for the most part

but uh if you need a terse book which mostly feels like it's for engineering students then i recommend it

[gray gazelle]

after doing a good amount of precalc and calc, I am thinking of starting introductory Linear Algebra through self study and I would greatly appreciate any book recommendation on introductory LA
ofc I will be using the typical online video and practice resources like Khan Academy, brilliant, etc
i am planning to pursue Computer Science ultimately so it must be oriented around that

my current knowledge includes vectors and 3D geometry, dot, cross products and triple products of vectors and very little about matrices

[proper tundra]

contemporary linear algebra by Howard Anton. i liked it because it has many visuals in it. If you think pictorially then this book will be helpful.

when i was doing linear algebra i used it along with LA concepts and methods by martin anthony and michele harvey

[gray gazelle]

@proper tundra ty sir, will definitely give it a shot

[ornate brook]

Oh, yeah I'm an engineering student

[gray gazelle]

sure go for it then

[hasty turret]

Why not do spivak

[gray gazelle]

it's in most engineering colleges' curriculum

pretty simple and lots of problems

the guy even cracks a joke in the first chapter

[ornate brook]

Apostol one?

[gray gazelle]

yeah

[ornate brook]

Cant believe my university uses mainstream textbooks

thats on third world public universities

[gray gazelle]

uh

okay?

[wooden sparrow]

Calculus?

[gray gazelle]

i mean if you want some elite textbook that no mortal can get his hand on then you're in the wrong universe

[split bluff]

is there a list of math books aimed for self studying? i tried reading some of the books in #books-old but i always found myself looking for someone online to try to explain me something and couldn't "fast enough"

[hasty turret]

Which topic?

You could probably just pick a random (one not aimed at advanced undergrads or smt) undergrad text and use it for self learning

[karmic thorn]

Also, maths is inherently difficult a lot of times. You may not immediately "get it", but fiddling around with ideas and progressing further would help. You might have to be a bit patient as well.

[split bluff]

i'm still a beginner, learning calculus and i'm about halfway through this calculus book https://www.whitman.edu/mathematics/multivariable/ but before i was reading this book, i tried spivak's calculus and it was really hard making progress there in comparison to the one i'm reading now. in 2 or 3 months i may be looking for some other book keep studying math, maybe one of proofs or linear algebra which is what people have been recommending me after i learn calculus

i also have a background in programming, the reason i'm learning math is to see if it can improve my programming skills

[karmic thorn]

Linear algebra is fun.

[split bluff]

some people have told me that linear algebra is necessary mostly for multivariable calculus, that it doesn't make too much sense if you don't use linear algebra

[hasty turret]

Did you try calculus or com?

[split bluff]

calculus or com?

[hasty turret]

Spivak has 2 calc books

1st is called calculus and the other one is calculus on manifolds

[split bluff]

i guess the second is harder than the first?

[hasty turret]

Yes

[split bluff]

i tried the first

[hasty turret]

Spivak requires you to think a lot

[split bluff]

yeah i'm aware of that, but after i quit reading it i started with the one i'm reading right now and i'm making more progress now with it, also because the book suspiciously has the same progression on topics than 3blue1brown calculus videos

i don't think i'm having too many issues with calculus right now, i'm thinking more about the future, about where to go after calculus, some guy recommended me daniel's velleman book of proof after reading the calculus book i'm reading right now because he says it's great for self taught people and programmers

is that good advice?

[narrow talon]

I believe the 3b1b videos are heavily based on an older calculus book called “Calculus Made Easy” or something similar. Spivak is really best as a second book in calc in my opinion, coming from someone who self studied calculus from Spivak and regretted it (although I wouldn’t be doing math otherwise so it has its ups and downs)

[split bluff]

was thinking the same, revisit spivak after i'm done learning calculus with this book

maybe even later

[narrow talon]

Velleman, linear algebra, or even Spivak(!) are all good choices after calc IMO, depends on what you want to do. If it’s programming find a discrete math book or do linear algebra, doesn’t reaaaly make sense to do Spivak

Other than it’s really quite a fun book, at least as someone who isn’t painfully slogging through it anymore

[split bluff]

to be honest i'm learning math because its fun, and using it for programming is secondary, it's kind of waking that same feeling i had many years ago when i started learning programming

maybe i'll go for a discrete math book after calculus, but, don't you need to know linear algebra to understand some discrete math topics?

[gray gazelle]

no

[willow pecan]

It can help in some rare cases but not really

[gray gazelle]

most programmers don't know any math beyond high school

[narrow talon]

Depends how far you go. Graph theory in particular is one of those topics that attracts a lot of hobbiest mathematicians - and professional mathematicians as a hobby - because it’s really quite accessible and enormously fun

[willow pecan]

Graph theory also benefits substantially from linear algebra

[narrow talon]

And that does indeed use a lot of linear algebra, but it’s unnecessary to get started with it

[willow pecan]

Yeah intro graph theory doesn't need any linear algebra

But linear algebra gives a very nice perspective

[narrow talon]

Lots of work left to be done in graph theory too, it’s really an excellent subject

[willow pecan]

Graph theory, along with the rest of discrete math, has the thing where open problems are very easy for even non-math people to understand

But they end up being nightmarishly difficult to solve

[narrow talon]

Absolutely, if I could solve any problem in mathematics with the snap of a finger it’d be Collatz, just to see how it’s done

There’s a book all about the Collatz Conjecture btw, it’s called the 3x + 1 problem I believe

[static crest]

really? if I could snap to solve a problem in math, I'd probably go with rh

it's been around for a while

[sage python]

Did someone implicitly say spectral graph theory?

[static crest]

no

[willow pecan]

No

But trace formula

[sage python]

And yeah RH for me since it would just have so many consequences

[static crest]

collatz seems cool, but I don't personally know of its broader effects in math

[sage python]

Collatz feels cute but idk how important it is so much as

[static crest]

rh just seems so far reaching

[willow pecan]

I think that

Hmmm

[sage python]

I guess everyone's curious about why it's all of a sudden so hard

[willow pecan]

Be able to determine the extrema of any function

[narrow talon]

Spectral graph theory is sick

[static crest]

no

don't do it

don't excite dami

[narrow talon]

I know the Collatz connect is something of a toy, but I have a soft spot for it

Probably because it’s so tantalizingly simple

[sage python]

Too late Poros

🙂

[static crest]

rip

[sage python]

Have I shown you guys the coolest theorem in math?

[narrow talon]

Bruh, spectral graph theory is sick just for spectral clustering alone

Let alone how easy it is to derive with just basic results of spectral graph theory

[sage python]

Actually there's apparently even a link to automorphic forms

[willow pecan]

[sage python]

Pretty much if you take the set of lattices in Q_p^2, you can say L->L' if L is an index p subgroup of L'

This is called the Hecke tree

And apparently you can do stuff with automorphic forms to prove the existence of expander graphs

[sage python]

heck u

[gray gazelle]

hack you

hack your ip

[remote ginkgo]

question

is this considered a book?

[karmic thorn]

Yes

[remote ginkgo]

ok, thank you

[vivid brook]

yes.

[raw herald]

very excellent book

[gray gazelle]

throw that book in the bin.

[hasty turret]

/usr/bin moment

[gray gazelle]

let me be your root

[narrow talon]

Bruh, was looking at books on stochastic differential geometry and people on MSE said that it wasn’t even math and belongs on stats SE

[willow pecan]

[gray gazelle]

Topkek

[narrow talon]

Lie groups are not stats

[gray gazelle]

welcome to the collective MSE superiority complex

please recall that every person who actively and regularly uses MSE is mentally ill

[narrow talon]

Haha!

[willow pecan]

@gray gazelle

[narrow talon]

I used to use MSE for hw

[gray gazelle]

Is stochastic differential geometry generally done in the stats department instead of the math department?

[narrow talon]

Now the only class where I need any help for homework has a solution manual so suck it

[narrow talon]

Depends

[gray gazelle]

i use MSE if i want to watch someone pull a contour out of their ass and explain none of their computations

[narrow talon]

Probability as a subject is often not in the math department

If it is, then no it’s probably not in the stats department. It it’s just seen as ghetto stats then yeah it’s in the stats department

[sage python]

Actually what I've more often seen is that statistics is its own subject but probability is in the math department

[gray gazelle]

it's stats!!! not math 1!!1!!!!!!! get this off my pure math website! !!11 !!

[narrow talon]

Then we’ve looked at other departments lol

Probability is mostly just like a frame of reference ngl, basically just do measure theory but forget the set you’re mapping from

Unfortunately all the books on the topic are either as dry as thousand year old gum or old enough to be on the edge of relevance

Many of*

[hearty steppe]

Believe me man, I don’t want to post more stats stuff up on my blog but it’s all I can really do rn to get content on there

I don’t know enough math to do anything else useful :/

[narrow talon]

Eg, Revuz and Yor is an alright book with many interesting exercises, but far from motivated and interesting content. I feel like you’d have to already have to need stochastic analysis to enjoy it. Williams on the other hand is a blast, but not quite rigorous enough or abstract in the particular way that current probability is abstract

Using both is necessary, and also sub-optimal

[sage python]

Are you just describing intro to probability books?

[narrow talon]

Stochastic mostly because that’s what I deal with right now

But partially intro too, Durrett would kill many first semester grad students, especially along with a first course in real analysis at the same time. I think Jacod Protter would be the answer to this problem if it were longer

[gray gazelle]

i say, as i contemplate making an MSE post on something that's bothering me

so many of these contour integrals end up with answers like

pi * scalars * trig function(pi * scalars)

and it makes me think there are easy geometric ways to do them

like can i just draw a polygon and say "obvious from diagram"

[static crest]

it's been that way

for a while

[static crest]

[gray gazelle]

math department got back

about the illegal homework

they're not doing anything about it

[static crest]

nice

sometimes it's pi * scalar, where the scalar is some weird nested nth roots

as well

like this

[gray gazelle]

there's probably some stupid trig form for that

[static crest]

and lastly, there's also random factorials

that show up

[gray gazelle]

,w sqrt(sqrt(5) - 1)/(2 sqrt 2)

[hasty eagle]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by TTerra#5291

[gray gazelle]

[static crest]

the factorials usually show up when you have a power of a trig function

[gray gazelle]

@willow pecan put this integral into mathematica please

[static crest]

being integrated

[willow pecan]

Which one

[gray gazelle]

.

[static crest]

$\int_0^{2\pi} \sin^{2k} \theta \dd \theta = \frac{\pi (2 k)!}{(k!)^2 2^{2k - 1}}$

[hasty eagle]

F[x]-module

[gray gazelle]

cursed

[willow pecan]

Mathematica doesn't give a closed form solution

[gray gazelle]

[willow pecan]

W|A doesn't either

[static crest]

$\frac{1}{2\pi} \int_0^{2\pi} e^{e^{-i \theta}} e^{i n \theta} \dd \theta = \frac{1}{n!}$

[hasty eagle]

F[x]-module

[static crest]

the powers of trig functions

always give random factorials

[sage python]

@narrow talon tbh I felt Durrett wasn't that that hard? Idk

[static crest]

just what I've observed

[sage python]

Thing is I didn't really focus much in probability I just kinda winged it

But the book felt solid

Also I've heard nice things about these notes

[hollow peak]

fourier coefficients for those who forgot they were working with fourier series

1/n! 😎

[sage python]

http://galton.uchicago.edu/~lalley/Courses/381/index.html

http://galton.uchicago.edu/~lalley/Courses/383/index.html

Lawler has notes and also Lalley

Lawler's notes are like, he would teach grad analysis at UChicago

Either grad real or grad complex

And he would make about a third of the class into probability

Lalley would teach the measure theoretic probability courses in the stats department, full class

[gray gazelle]

any book recommendations for integration ( reimann integrale)

[sage python]

Any calculus book

If you're just trying to learn how to integrate then Stewart or something

If you're trying to learn theory then Spivak

[gray gazelle]

its theory thanks ill check that

also looking for books of "partial-differential-equations" !

[willow pecan]

Depending on how much background you have, Strauss or Evans

[gray gazelle]

I'm studying evans here and there (well, more like made some progress on 1 chapter), so if you are working on it too I may join you 🙂

Oh, nvm, I just read chat, I guess you are looking for probably looking for something not as advanced

[marble solar]

is there anything of value in chapter 1?

[gray gazelle]

Oh, I meant chapter 5 when I said 1 chapter

(well, I skimmed chapter 1, it was like 10 pages)

Ch2-4 basically look too PDE, I didn't want to do them

[willow pecan]

[gray gazelle]

Well, ch2-4 will probably be my next step after ch5, I said I want to study PDE after all, so I should actually do those chapters, no sense running away from them

[gray gazelle]

Nvm, I might just read ch6 after ch5

[empty plank]

For a fun mix of Functional Analysis and PDE, Brezis is quite nice. Nowhere as comprehensive as Evans though

[narrow talon]

Durrett isn’t that hard, Lawlers notes are great too! Idk I get the impression that there at grad students coming in at drastically different levels of mathematical sophistication and those coming in after having just taken algebra, analysis, topology I would struggle with Durrett

But I guess at that point it’s on them

[whole rain]

Hey. Any good elementary geometry book recommendation ?

[karmic thorn]

Coxeter?

[whole rain]

Oh, looks great, thanks !

[karmic thorn]

(Just to be clear, look for Introduction to Geometry and not Geometry Revisited)

[gray gazelle]

Elements of Geometry by Euclid

[storm sleet]

Is spivak calculus on manifolds a good read? Someone was recommending it for our multivariable real analysis course

[gray gazelle]

it is a very good book with many good exercises

it's rather terse at times which might be unappealing

but it has some very very good exercises to work through, and gets right to the important material

uhhh

[hollow peak]

don't level it up

because they suck

[gray gazelle]

cope

[hollow peak]

stay mad geometer

[gray gazelle]

[hollow peak]

i just wrote this

i am so proud

[willow pecan]

Oh my

Are you starting your presentation from weak solutions

And building all the way to trace operators

[gray gazelle]

i don't really know of any specific book which covers them well. you can probably open any decent complex analysis book and find the section

[willow pecan]

And trace inequalities

[hollow peak]

not the presentation, the write up

there's not much point introducing trace operators without explaining what a sobolev space is

the end goal is sobolev embeddings if I'm not mistaken

[gray gazelle]

[hollow peak]

it is surprisingly cogent tterra

this is some of the most tame analysis I've seen

[willow pecan]

Sobolev embeddings are good

[hollow peak]

I'm really enjoying this material so far

I'm definitely going to come back to this when I have more time to do sobolev stuff in detail

[cobalt arch]

Any exercise books with solutions on linear algebra that covers a lot of ground? I would prefer something akin to shaum's outlines but with more solved problems.

[storm sleet]

People often recommend Linear Algebra done Right, but I can't speak to that one

We used Linear Algebra done Wrong and it was solid

https://www.math.brown.edu/streil/papers/LADW/LADW.html

[willow adder]

linear algebra done okay

[broken meadow]

linear algebra done

[willow adder]

a program that automatically proves any linear algebra problem

[sage python]

Linear Algebra Done Right is bad

[static crest]

based

and correct

[storm sleet]

can you elaborate?

[sage python]

He has this anti-determinant philosophy which is straight up stupid

[storm sleet]

also in a similar vein, any opinions on Romans advance linear algebra?

[sage python]

And it screws up how he thinks of related concepts like characteristic polynomials

Roman is supposed to be quite hard, more like a second book on linear algebra I feel

[marble solar]

That's where you're wrong

It's a good book

[storm sleet]

I'm coming in with 2 terms of linear and a course in undergrad algebra, and a course in grad ring theory

[marble solar]

As long as you learn determinants elsewhere

[sage python]

NOpe

[willow adder]

linear algebra done somewhat okay

[sage python]

The problem is that he teaches you that characteristic polynomial is just, oh go to C

Upper triangularize

Which is incredibly stupid

[marble solar]

It's an upper division book on linear algebra

What do you expect?

[quick hornet]

if its meant to be upper division why doesnt it introduce vector spaces over general fields

[storm sleet]

our "upper division" linear course didn't

We have 3 linear classes, 2 "junior core" courses targeting 3rd years, and a senior course they don't let you take without approval, bc its essentially the quals prep course

[sage python]

Moonbears I'm not saying it's a bad way to think about it in the sense of

It's hard for beginners

[marble solar]

Quals prep class sounds nice

[willow adder]

what is the best linear algebra book

[storm sleet]

It teaches all you should need for linear algebra on our quals

[marble solar]

Schaum's outline for linear algebra

Don't know the thoery?

theory*?

It'll teach you

[sage python]

I'm saying that the idea that characteristic polynomials are supposed to be thought of by triangularizing the matrix first is dumb

[willow adder]

[marble solar]

Don't know how to solve problems?

It'll teach you

[willow adder]

I will examine

[sage python]

Here's the thing about Axler

He does functional analysis and I guess doesn't think at all about algebra or differential geometry/topology

[marble solar]

don't get the manga guide

[sage python]

So from that pov yeah determinants aren't that important, and the standard way they're taught is unmotivated. Like oh bash a bunch of numbers together in a matrix

But the problem is that there is a conceptual approach to determinants and they're not only useful for change of variables as Axler claims they are

So it's not about the level of the book. I actually think even first and second year undergrads should just suck it up and read Hoffman and Kunze or LADW on a first pass

[marble solar]

My CC prof is teaching out of H&K

Right now

The class is rioting over it

They're like this is too hard

[sage python]

It's that the book was written based on a philosophy that's moronic

@marble solar Tell them to stop being bitches and get good

[marble solar]

That's basically what I want to say

[storm sleet]

Damn a lot of LADR hate on this server

[marble solar]

You guys clearly didn't have a class where the prof should have used LADR

[storm sleet]

tbf I haven't read it at all, I just know a lot of people recommend it

[sage python]

The proofs being slow is fine

[marble solar]

and reading it was an unfair advantage

[willow pecan]

[sage python]

Or like idk that's like, less a quality thing and more a demographic thing if that makes sense

[willow adder]

what is a slow proof as opposed to a fast proof

[sage python]

Axler's a book for people who don't know proofs or really anything other than how to speak English, and for that the exposition is good

It's just that he thinks about characteristic polynomials like an idiot

I learned linear algebra first from this 5 week summer thing taught by a prof who does combinatorics and complexity theory, and then from my analysis professor assigning us around 200 problems from Hoffman-Kunze and telling us to read it

It was overall good except that

Somehow in that mix Jordan form just never got covered until algebra

[storm sleet]

Jordan form isn't touch until our senior/grad course

[sage python]

Once you learn ring/module theory, Jordan form will fall out of a more general theory

[storm sleet]

Rotman has a part of a chapter proving existence and uniqueness

[sage python]

Namely the structure theory of finitely generated modules over a PID

[storm sleet]

Right right

I plan on reading the chapter soon lol

[mossy flume]

For lin Alg I'm using the FIS textbook

I like it

[hearty steppe]

Yea FIS is solid

[marble solar]

Alright nerds, anybody have any of the following: A good open source Elementary Number Theory Text, Numerical Methods text?

@willow pecan I'm lookin' at you since you're the numerical person

[quasi remnant]

any recommendations for an abstract algebra book which has a lot of examples and questionswhich is also suitable for a beginner

[marble solar]

Pinter

[warm glen]

https://realnotcomplex.com

check this out maybe? it's supposed to have a bunch of free books and stuff for advanced math

[marble solar]

That's pretty good

[warm glen]

there is a number theory section

[marble solar]

Yeah, most of these I need

I'm creating a list of resources at my university

This'll go nicel y

[warm glen]

cool

[willow pecan]

Wait do you want numerical methods for NT

Or are those separate

[marble solar]

separate

[tropic lion]

What do y'all think of Serge Lang Algebra?

[gray gazelle]

I don't like it

[tropic lion]

yeah like I think it's cool that it has so much but it kinda defeats the purpose

like a lot of topics are covered in other books

It just seems to be comprehensive for the sake of comprehensive

even though you learn the stuff it covers in like algebraic topology or geometry

Do y'all have any recommendations for learning commutative algebra?

[willow pecan]

Ok

Depending on how much background you have

Demmel's book for numerical linear algebra

LeVeque has a book on finite difference methods for ODEs and PDEs

Iserles also has a book on numerical methods for diff eqs

LeVeque has another book that is a self-contained intro to the theory of conservation laws and numerical methods for them

[static crest]

numerical

crimg

[willow pecan]

[novel iris]

btw ange are you still planning to do the linear equation solving talk on saturday?

[willow pecan]

It'll be next Saturday

Not this Saturday

[novel iris]

ah ok, ty

[willow pecan]

<@&681260374879633482>

[static crest]

chmonkey is probably the best one to ask

I think

[willow pecan]

@dapper root

[static crest]

atiyah and macdonald is a common recommendation from what I know

[glad prairie]

a-m is painful i hear

i know a lot of people like eisenbud

[willow pecan]

Isn't Eisenbud an AG book and not a CA book

Or was it the other way around

[tropic lion]

I don't dislike old books but I do find them harder to read than newer books

Also you sometimes get strange notation and since this is self study (not that notation really matters) I'm not sure if it's the best resource

it seems pretty concise though so I like that\

However conciseness is a double-edged sword

It's nice if you understand something but horrible if you don't

[storm sleet]

Eisenbud is an enormous book

Eisenbud is a CA book, targeted at AG

[tropic lion]

yeah I don't think I'll have time to go through all of it

[sage python]

Commutative algebra books megathread from someone who doesn't know any commutative algebra

[warm glen]

"A Term of Commutative Algebra" is apparently like an expanded/less terse version of A-M's book, they even sorta say that's what they aim for in the preface

[sage python]

🙃

[uncut knoll]

@tropic lion Hi. A book that has everything in one text is usually iconic.

Lang's is a recent book with an oldish flavor.

Eisenbud's is overkill.

[sage python]

Atiyah-Macdonald: Pretty quick, the writing is quite smooth. Kind of out of date. A lot of the material is in the exercises so you have to do most of them here, which for me would make it a bit of a slog.

Altman-Kleiman: Atiyah-Macdonald but more modern. I think it has solutions so you're not gonna be completely stonewalled if you are stuck on an important problem (better to first try without solutions, then use solutions as hints)

Matsumura: If I ever decide to actually take commalg seriously this is probably where I'll do it. Seems like it's mostly got the material you want here, and what I think is a more reasonable distribution of material between text and problems.

Eisenbud: Apparently locally very readable but long enough to scare me. Probably a fair bit geometric

[storm sleet]

@sage python At this point we should make another thread of book recommendations and have a channel #advanced-books, following the subjects in the "advanced" channels

[manic cape]

Any suggestions for geometric algebra?

[storm sleet]

My Differential Geometry/Gen Rel teacher recommended Geometric Algebra for Physicists, but I can't really speak to it as a reference

[novel iris]

I've read bits of that

it's quite nice

also haven't read enough to make any definitive statements

but it's a nice read from what I've seen

[dapper root]

@tropic lion
CA textbooks:
A-M: the usual recommendation. Pretty short, but is mostly just a bunch of exercises. I can’t fucking stand the book.
Eisenbud: Probably the most expansive CA textbook besides the entire Bourbaki collection on CA. If you can stand the book, it also elucidates a lot of geometric reasoning for the algebra, which is helpful if you want to do AG. Too big for me personally, I might refer to it when I want to learn something specific.
Miles Reid Undergraduate Commutative Algebra: has about the same stuff as A-M. More friendly IMO, also has geometric intuition. Pretty nice source IMO.
Steps in Commutative Algebra: another softer intro to commutative algebra. I haven’t dealt with it too much, I think it’s alright.
Matsumura Commutative Algebra: Very old book. Requires more prereqs than the other ones. Very few exercises, has very old notation (epsilon for set membership.) Mostly obsolete because of the newer Matsumura.
Matsumura Commutative Ring Theory: My personal favorite. Requires a bit more knowledge, it won’t cover eg: homological algebra, tensor product, etc. Has some of this in the appendices, but it definitely helps if you’ve seen it before. None to very little intuition, but if you’ve already done some ANT or AG you’ll likely know where the things in it are useful.

Overall:
A lot of CA textbooks are very dry and have almost no intuition (IMO this is due in large part to Bourbaki being so influential in this area of math). If you want intuition, Undergraduate Commutative Algebra by Reid might be one of the best. If you are strong in algebra, I recommend Matsumura (the newer one, commutative ring theory), it’s my favorite by far.

Also I suppose it should be mentioned. If you’re a robot and want to know obscure random results do the commutative algebra books by Bourbaki

The latest ones are only in French

[gray gazelle]

Maybe I will read the reid book at some point

[sage python]

@dapper root do you know why Yohan likes old Matsumura better than new?

[dapper root]

Idk

Weirdo?

There’s some theorems only in the older one

But likewise in the new one

In particular the new one doesn’t cover Japanese rings, and some of the material at the end has proofs being off put to the first one

The former obviously doesn’t offput any proofs to the latter

[hearty steppe]

Hey guys my current probability and statistics book feels uninspired. Problem sets feel too trivial. I am considering going straight into mathematical statistics books, any recs?

[steel viper]

AM GOOD

[manic cape]

So far I'm loving the book. Thanks man

[storm sleet]

npnp

[tepid prairie]

This is the best book I've ever come across.

[open dove]

How is S.Epp Discrete Mathematics: Introduction to Mathematical Reasoning?

I have previously taken a discrete mathematics course, but I need a strong hold on the topics like number theory, graphs, etc. and I want to work on my logic for more mathematical maturity. Is this book good to start with?

[calm crane]

agree

idk my brain just shuts down when i see long detailed proofs lol small hints and "lol immediate" works better for me understanding

best suggestion is always download a few books and see what you like

[karmic thorn]

"just know everything already"
~slimvesus

[hearty steppe]

damn still no Math Stat recs

[gray gazelle]

Mathematical Statistics?

[hearty steppe]

ye

im bored of regular stats books

i want something that will make me cry

[gray gazelle]

i know the Hogg/Craig book

intro to mathematical statistics

[earnest gazelle]

hey whats a good book for learning computational complexity theory? was thinking sisper's 'theory of computation'?

or just a course lecture notes would be fine

[willow adder]

understanding analysis good?

or

[hearty steppe]

Oh yes it is

That’s what I’m mainly using

[willow adder]

by abbot

[hearty steppe]

Yea

[willow adder]

abbott

ye

[cobalt arch]

Is Rudin's principles of mathematical analysis a reasonable goal to learn real analysis from in 2 months?

[hearty steppe]

Uh no, try Abbott and work on it for 4 months and see where you go

Rudin was too hard for me and still is

[karmic thorn]

Rudin is a bad first text, and worse if you're studying on your own.

[hearty steppe]

I like the wording a lot but it’s too mature for my knowledge

It’s good for a revisit to analysis

Try rudin if you enjoy analysis and want to do more

[cobalt arch]

Some people recommend pugh as well for a first intro to real analysis so I guess it comes down to abbott and pugh. Which one do you prefer and why?

Zorich is another recommendation. Tao's two texts are also recommended. I just want a book that has a clear exposition and comprehensive theory and many exercises ranging from computational ones to conceptual ones from easy to difficult. I guess I will need more than one book but I would like to know which ones are the better ones for undergraduate real analysis.

So would it be a good idea to use zorich as a reference for theory, pugh for visual intuition and abbott for mathematical maturity acquisition? Or would be tao a good text instead replacing any of the above three?

[narrow talon]

@hearty steppe there’s Casella Berger statistical inference and Wasserman all of statistics. More advanced is Van der Vaart Asymptotic statistics and Casella Lehman theory of point estimation

The latter two are popular books for graduate programs in math stats

[night knot]

The Sipser book or the Automata book by Hoppcroft and Ullman would be good to get into the theory of computation

For computational complexity specifically, check out Papadimitriou or Sanjeev-Barak

[earnest gazelle]

thanks. Strangely, the sipser book seems to very different from other computability/complexity books in it's notation and presentation. Any reason for this?

[willow adder]

best topology book

[narrow echo]

read Boas

[storm sleet]

Munkres

[willow adder]

foundations of general topology?

[tribal kernel]

I think Hatcher has point set notes

Not sure how well celebrated those are but his book on algebraic topology is a standard

[quick hornet]

hatchers point set notes are a good summary

theyre not like, munkres level detailed

but you dont need munkres level for most things

[ripe granite]

why does everyone want to skip point-set lmao

[quick hornet]

cause its lame

i mean i enjoyed munkres when i read it

[willow pecan]

[quick hornet]

and dont regret having taken it

though i skipped some of the middle chapters that no one reads

[ripe granite]

point set has very nice ideas

and is a good way to introduce "finding right notions"

idk

[obsidian valley]

what are point set ideas

where is the line drawn between topology and point-set

[quick hornet]

although half of munkres blurs the line

let me rephrase

half of munkres is alg top but i wouldnt consider it sufficient for an alg top course

it doesnt deal with pi_n for n > 1

[sturdy sail]

Lmao loops from S^{-1} to a pointed topological space up to homotopy

[quick hornet]

arcpi

[sturdy sail]

Why isn't S^{-1} a thing

Things would be so much nicer

[gray gazelle]

[ripe granite]

you might be interested in the spanier-whitehead category

[marble solar]

I've met one

Someone that does research in point set to this day

[karmic thorn]

[gray gazelle]

is point set research about making more T_ spaces?

[quick hornet]

the height of point set topology is knowing what "finer" means immediately without having to think about it for 2 seconds first

[gray gazelle]

Yo are you a discrete topology? Cause you're the finest of them all 😎

[storm sleet]

Guess I'm the trivial topology 😔

[gray gazelle]

I hate sand... It's rough, irritating, and has the trivial topology

[sudden warren]

can someone suggest me a book for practicing integration, derivation, series, limits, functions, algebraic structures, relations, polynomials, matrices and determinants?

could be multiple books of course

I am preparing for my final exam in 2 weeks and need to go over those topics

[gray gazelle]

How to practice integrals
Step 1: write down a crazy function
Step 2: try to write down the integral of it
Step 3: if you can't do it, then commit it to memory as a non integrable function

[sudden warren]

that seems a bit too much like trial and error since I don't have too much time left to prepare

[snow dirge]

Nice

[snow dirge]

The bible perhaps?

[sudden warren]

not sure even that would help

[gray gazelle]

Quran.

[willow pecan]

[sudden warren]

didn't know this was a religion study discord server

[storm sleet]

Only during finals week

[sudden warren]

makes sense

so are there any good books with practice problems?

I currently have around 10 problems for each topic but don't think that is nearly enough

[gray gazelle]

Has anyone read the Terence Tao analysis I book?

[narrow talon]

A lot of people like it

[whole rain]

@karmic thorn is currently reading it iirc

[wide meteor]

Terrence Tao doesn’t have many problems

[karmic thorn]

It's a good book if you have the time to work through it.

It gives the impression of having a few problem because

1. It is split into 19 chapters over 2 volumes.
2. Each chapter is split into ~5 sections, and each section ends with ~5 exercises each.
   So the number of problems is actually decent(not like Pugh on steroids)

To save yourself some time, I advise to read and work through chapter 2, 4, 5, 6, 7, briefly skim 3, 8 and then the usual progression. In 2/3/4, you may skip any part since it doesn't radically affect the chapters ahead.

[haughty bane]

hahahhha

[warm glen]

if anyone's read alcock's how to study for a math degree, what did u think of it

[narrow talon]

I’m potentially interested in doing doing some stochastic analysis on Riemannian manifolds but don’t much much past very classical diffgeo, where should I begin you think?

Lee will of course get recommended, but something including more Riemannian geometry would be nice. asking about the geometry btw, I know texts for the stochastic part

[sturdy sail]

Do Carmo's has a nice book on the subject

Idk if it is the best or most standard recommendation on Riemannian Geometry

But is nice

[narrow talon]

Does it cover the necessary smooth manifold theory? That’s the part I’m worried about jumping straight into a Riemannian geometry book

[nova lance]

I'm about to finish my undergraduate in pure math, if I wanna level up my Linear Algebra game, what would be a good book to read? My advanced linear algebra course ended on singular value decomposition, so that's about where I am in terms of concepts. I'm also pretty well acquainted with the functional analysis and differential geometry side of vector spaces, having taken some independent studies in them.

[narrow talon]

Lab linear algebra

Lax *

[nova lance]

This?

[karmic thorn]

Yes

[nova lance]

Looks decent, thanks for the tip!

[narrow talon]

I have a review of it a long time ago on this chat if you search my name

[molten wave]

that book really lacks

[narrow talon]

This one I believe

[sturdy sail]

I mean

Not really

He covers really basic stuff about manifolds like its definition, smooth functions between smooth manifolds, tangent space and the tangent bundle, differential forms, oriantable manifolds and integration on differential forms

All of this

In chapter 0

But it is sort of a recap

Of all this stuff

And not the best way to properly learn it

Books like Tu, Lee and A Comprehensive Introduction to Differential Geometry by Spivak do a much better job at teaching the basics.

[narrow talon]

Yeah sort of what I anticipated. Many of the recs are tomes which feel more like differential topology than geometry

[sturdy sail]

Ok so

Sorry for this

But the version of the book I have is in portuguese

It's also available in english tho

But you see

He has a chapter 0

On "Smooth Manifolds"

Which in portuguese would translate to Variedades Diferenciáveis

And it covers all the stuff I just talked about

[gray gazelle]

portuguese

[sturdy sail]

Yeah

[gray gazelle]

i am portuguese

[sturdy sail]

[narrow talon]

Sort of a minimum viable presentation of smooth manifolds. What I'd really like is an intro to manifolds/geometry with an eye towards analysis

[sturdy sail]

That's nice

[sturdy sail]

I see

This one is in English

I really can't help then

I would say that

Maybe A Comprehensive Introduction to Differential Geometry

Does a better job

At teaching the basics of manifold theory

With a view towards differential geometry

[narrow talon]

volumes one and two right?

[sturdy sail]

Yup

[narrow talon]

I think at that point I'd just refer to Lee/Tu, those older books are super nice for intuition but I'll stick with something a little more modern

There's a course that I can take my first year at PhD on Riemannian geometry, but not smooth manifold theory so I'll leave RG alone for a little longer

[gray gazelle]

do carmo will make you cry with his notation abuse

[sturdy sail]

Hey TTerra

[gray gazelle]

[sturdy sail]

What book on RG would you recommend?

Do Carmo is the only one

I have read

[gray gazelle]

lee or tu

are the only ones i can comment on

[sturdy sail]

No

[gray gazelle]

oh rg

[sturdy sail]

I mean RG

Sorry lmao

[gray gazelle]

lee

do carmo is good but the first few chapters are kind of hard to read

everything after the connections chapter in do carmo is good

[narrow talon]

Warner?

[waxen temple]

I want to learn group theory, is the chapter in Herstein enough or should I look into something like Dummit&Foote?

[gray gazelle]

dummit foote

[static crest]

d&f

[sage python]

D&F probably better than Herstein

It's annoying to unlearn Herstein's notation and I think D&F does a couple more things? Plus later for ring/module/field theory Herstein is deficient

[broken meadow]

ignore yohan

lmao

[sage python]

Jacobson is cleaner basically, which I quite like

[prisma snow]

Graham's number + 1

Even if your copy was eaten by your dog and then peed on, it would still be better

[storm sleet]

I liked the first 2 parts of D&F, feels like they ran out of passion when they started modules

Jacobson felt a bit light on details for group theory, but I picked up Rotman and found that to be a much nicer presentation of group theory

Actually, I don’t think I’ve seen anyone here talk about Rotman

What’re y’all’s thoughts on it as a second group theory book?

[dapper root]

Idk, but you should use Isaacs finite group theory

[sage python]

Rotman group theory? I spedrun a bit of it and it was solid

[still jay]

How is this for group theory

[hushed flint]

o damn burnsides book

[stray veldt]

i think this book has an interesting intro

an early edition states:

It may then be asked why [...] a considerable space is devoted
to substitution groups; while other particular modes of representation, such as groups
of linear transformations, are not even referred to. My answer to this question is that
while, in the present state of our knowledge, many results in the pure theory are arrived
at most readily by dealing with properties of substitution groups, it would be difficult
to find a result that could be most directly obtained by the consideration of groups of
linear transformations.

this was in 1897

then this had to be changed for the 1911 edition

Very considerable advances in the theory of groups of finite order
have been made since the the appearance of the first edition of this book. In particular
the theory of groups of linear substitutions has been the subject of numerous and im-
portant investigations by several writers; and the reason given in the original preface
for omitting any account of it no longer holds good. In fact it is now more true to say that
for further advances in the abstract theory one must look largely to the representation
of a group as a group of linear substitutions. There is accordingly in the present edition
a large amount of new matter.

[sudden kindle]

Yeah bro linear reps are so good

[stray veldt]

yeah, but it took a while to notice

anyways, i do not recommend this book

that intro thing is funny though

[thorny spear]

any good book for geometry and trigonometry?

[gray gazelle]

level ?

like for geometry

[thorny spear]

basic, im 0

never done geometry

[gray gazelle]

Has anyone here worked out the IA Maron textbook?

yeah

bits of it

[gray gazelle]

@obsidian valley

[karmic thorn]

Sullying yourself

But anyway Jesse would recommend Enderton

It's not boring

It's a rather steady read, from the first few pages I read

[gray gazelle]

lol mirza

just read the basic stuff from wikipedia and derive everything else yourself

[storm sleet]

I liked Mendelson, but the open logic book is nice too

[gray gazelle]

Try Enderton or Ebbinghaus

If you want more "interesting" stuff you should at least know the basics

[obsidian valley]

@gray gazelle Enderton and just start at the last section of chapter 1 (where he proves compactness) and go from there

you’ll be fine and its not boring

i mean building up FOL theory is sort of boring but its tolerable

like theres a reason i barely talked about truth

[gray gazelle]

Wdym?

[obsidian valley]

i gave a talk yesterday about this stuff and skimmed over truth because building up a theory for truth in enderton (and ebbinghaus, etc.) is really tedious

mostly because you need to introduce truth assignments and witnesses etc so you can handle free variables

[gray gazelle]

Ebbinghaus handles truth well in my opinion.

[obsidian valley]

maybe

I only have a passing familiarity w/ that part of Ebbinghaus

theres no avoiding it if you want to learn logic well imo

[gray gazelle]

Yes it is absolutely vital for model theory

[obsidian valley]

i dont like ebbinghaus notation the most out of all the truth assignment notations though 😆

[gray gazelle]

You are referring to semantic truth, right?

[obsidian valley]

i think semantic truth is the only truth I know 😆

[storm sleet]

How do people feel about Zariski commutative algebra?

[warm glen]

sorry to ask something wen the previous question wasn't answered yet, but has anyone read eccles' intro to mathematical reasoning?

[dapper root]

Zariski-Samuel? It's kinda old, but still workable

[warm glen]

i used it for a class on proofs and i found the chapters on counting to be extremely confusing, so to this day i don't understand basic counting

because they came after the chapters on functions, injections, surjections, bijections, etc

and used those for proofs, which were very difficult to follow

so i was wondering if anyone knew of another book or set of notes that explains basic counting using functions

[karmic thorn]

See the olympiad server in #old-network ; you'll likely get better recommendations there.

[karmic thorn]

I think any discrete math book would suffice? Rosen seems to be recommended a lot.

[warm glen]

hm maybe i haven't looked at them long enough but books like velleman's and hammack's intro proofs books cover counting without using injections, bijections, or surjections, and that's specifically what i'd like to learn

but i'll peek at rosen's, and ive been thinking of looking at chartrand/zhang too

[gray gazelle]

prmo is a math olymp right ?

[hasty turret]

Yes

It's the equivalent of AMC

[gray gazelle]

sorry i forgot to reply , try kieslev's geometry vol 1 and 2 if you are starting from scratch

it covers all the basics you need to know iirc

[dapper root]

for logic?

You should look at the text by Hall
Full name: Robert Bryson Hall

[obsidian valley]

ebbinghaus bad

[karmic thorn]

Oh, so you're basically looking for a book on cardinal, ordinal arithmetic? Then take a look at the relevant section in a set theory book.

[warm glen]

damn, is that what it is

ive got halmos in my drawer so i'll try to take a look there

[obsidian valley]

cardinal and ordinal arithmetic would be overkill

functions/relations chapter in a set theory book prob fine

[karmic thorn]

They kept saying "counting with functions, injections, etc." despite being recommended discrete math book, so I thought they were looking for cardinal/ordinal arithmetic.

[stray veldt]

throwback to when the prof in the discrete class i was TAing accidentally proved cantor bernstein in like first lecture

[karmic thorn]

Tfw your set theory class doesn't prove CSB

I just had the statement on my exam today

[stray veldt]

how'd it go?

broke: prove theorem in class
woke: have students prove them in the exam

[karmic thorn]

[karmic thorn]

Great actually

They're going easy on us because this has been a terrible online semester

[gray gazelle]

[karmic thorn]

And the upcoming semester would likely be another terrible online semester

[hasty turret]

How much HW do you get?

[karmic thorn]

Not a lot

[karmic thorn]

Any textbook recommendations for a first course in differential equations?

[gray gazelle]

Did you say you have already read rudin? Some time ago I was curious about intro to ODE books that is not too engineeringy/is for readers that are reasonably comfortable with analysis. I came across the book by Hale, although I haven't really read any of it

[karmic thorn]

No, I haven't read Rudin and I'm currently working through Tao's Analysis.

Hale, I'll check that out. Thanks!

(Is it short for Hirsch-Smale-Devaney, or Hale is the author?)

[prisma snow]

Hirsch Smale = Hale 😂 😂

[gray gazelle]

Hale is the author, it's a dover book

[karmic thorn]

Ah, okay haha

[gray gazelle]

have any of you done hermite's calculus?

idek if a book by him exists

hold on

[karmic thorn]

Isn't Hermite some super old nerd who came up with Hermite functions and stuff

[gray gazelle]

hermite polynomials i think

no i was reading that article yohan sent

https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html\

[karmic thorn]

Oh

Arnold

[gray gazelle]

and at the end he mentions some books

i was able to find most of them

except the first one

perhaps a translation doesn't exist

"I remember well what a strong impression the calculus course by Hermite (which does exist in a Russian translation!) made on me in my school years. "

[karmic thorn]

Soviet maths is something different lmao

[gray gazelle]

lot of excercises in russian books

@gray gazelle if you can read french https://archive.org/details/coursdemhermite00andogoog

there indeed is a book

[gray gazelle]

if you prefer russian then

but yeah getting hands on something similar is english will prolly be very difficult

[gray gazelle]

on other news i managed to get my hands on both of nikolsky's analysis volumes

[stark creek]

can anyone recommend me a book on number theory

[whole rain]

#book-recommendations message

there's some recommendations here @stark creek

[stark creek]

thanks

[mossy flume]

Ooooo number theory

I'm taking that next sem

unless this professor gets back to me and recommends another course

[livid ermine]

we used elementary number theory by burton, and i really quite liked it. it was very very clearly written. it also gave 2-3 pages of historical accounts and developments before each chapter. made the material feel more motivated

[gray gazelle]

burton bad <- ignore this comment , this comment is biased and is only my perspective of it.

[livid ermine]

Why do you think its bad?

I get that its your opinion, I'd still like to hear why you dont like it.... Its the only number theory book i've read so if theres a better one it'd be cool to know

The only think I didn't like about it was that the exercises were quite computational. I think they could've been made slightly harder also, but the book is very beginner friendly I think.

[mossy flume]

I guess on topic of number theory books

James Strayer, Elementary Number Theory

anyone know anything about this book?

[gray gazelle]

@mossy flume just gave a quick look , pretty cool ! it also has the history before chapter thing like burton and many of the theorems are demonstrated with examples. nice one

[mossy flume]

Ok cool

So then I'll stick to that book for the class rather than finding another

[gray gazelle]

I am looking for this book

A graphical approach to Algebra and Trigonometry by Hornsby, Lial and Rockswold

If anyone has got it or can provide links to it, it would be extremely helpful.

[split bluff]

got the isbn code?

sometimes it's better to look online with the isbn code

[willow pecan]

9780134696515

Is the isbn

[gray gazelle]

I am looking for the pdf

[glossy parrot]

hi

[uncut zealot]

My school has a copy of Mordell's Diophantine Equations in its library. Is it worth picking up, or is the stuff in it outdated/treated better in other books? For reference, it's the edition from 1970.

[gray gazelle]

"All knowledge is worth having."
-some wise man

[uncut zealot]

I mean, I agree, but insofar as I have only a finite amount of time to learn things and there's more material to learn than I can learn in my lifetime, it would be beneficial to be selective in how I choose to learn so that I can learn as efficiently as possible and the most up-to-date information as possible.

Yes

I expect some of the stuff to be timeless - the solution to degree 1 equations will likely not have made many advancements in the past thousand years or so, for example - but it also has large sections on elliptic curves, for example, and I'm pretty sure it was published a couple years after the BSD conjecture was conjectured.

[gray gazelle]

What are some good books to learn calculus for beginners?

[hearty steppe]

use James Stewart or Ron Larson for exercise problems while going thru Professor Leonard youtube channel

@gray gazelle

[limber fable]

;-;

[split bluff]

i use this one and it's amazing https://www.whitman.edu/mathematics/calculus_online/

was told spivak's good as well but only if you are somewhat seasoned

[hearty steppe]

spivak I think is great for a revist when your doing real analysis

[gray gazelle]

@hearty steppe @split bluff Thank you both for the information!

[split bluff]

is it worth reading spivak after learning calculus from another book for a person like me that studies computer science?

was recommended to go for discrete math after calculus but i'm having fun with calc

[hearty steppe]

use spivak with real analysis, thats my recommendation based on skimming thru it

[gray gazelle]

very worth it

it is like one of the best books i have read for its treatment to various equations

and also it is defacto standard in some classes to study from it , or parts of it when dealing with diophantine equations

[gray gazelle]

there is a nice book pinned in #calculus channel pins by Ann . Along with other resources , solving that one is very recommended by me

[uncut zealot]

Good to know. I'll be sure to pick it up tomorrow (I mean, today, technically, given that it's half-past midnight, but surely you get my meaning).

[vocal hatch]

Can anyone recommend me a book on Game Theory? Preferably something for self study so something thorough but not like a reference

[vocal hatch]

Why'd you delete you recommendations? They seemed pretty good

[gray gazelle]

Rubinstein and Mascler books are what i see being recommended here

@vocal hatch

[still jay]

I just want to brag a bit, I picked these up at my local bookstore for $20 total

[karmic thorn]

[prisma snow]

Wtf

They don't have books like that at my local bookstores

[karmic thorn]

[gray gazelle]

like,share and subscribe

[gray gazelle]

reminds me of the

'advanced calculus problem solver' book

[marble solar]

You have to look around a lot. Sometimes schools have book sales

Multiple book stores, drive to ones an hour away

[vocal hatch]

thank you!

[gray gazelle]

there's also the

"Theory of Games and Economic Behavior"

[vocal hatch]

I remember someone pointing out it misses out on some modern game theory, is it still applicable?

[marble rock]

is this enough https://www.maths.usyd.edu.au/u/athomas/FunctionalAnalysis/daners-functional-analysis-2017.pdf supplementary for functional analysis

[sage python]

Seems decent at a glance

[unborn edge]

hi

i have a doubt

[karmic thorn]

Read #❓how-to-get-help

If you want to ask for book recommendations,

[autumn flower]

same. lots.

[unborn edge]

there is a mistake in the calculus book

[karmic thorn]

Check for errata online

Or ask in a questions channel

[unborn edge]

in the differentiation section

wait

IN ans 16 e)

[autumn flower]

what is the question corresponding to answer 16e?

[marble solar]

Just integrate it

see if that's it

[neon wadi]

can I read baby rudin with 1st year calc and lin alg knowledge ?

[hearty steppe]

No

[neon wadi]

oof ok

[hearty steppe]

Do you have any exposure to proofs

[neon wadi]

yes

ofc

have done 4 classes with proofs lol

[hearty steppe]

Try Abbott’s Understanding Analysis that’s the book I’m mainly focused on for analysis

[novel iris]

||not a pleasant read tho ||

[storm sleet]

I second the Abbott recommendation

I’m considering going back through rudin to make sure my undergrad RA is up to par before grad school, but honestly Abbott is a lot easier to use

Hence my statement of undergrad, at my college general metric spaces is covered in our first year grad sequence (that some seniors take) or in our multivariable real analysis course, which covers partial derivatives, etc

[hearty steppe]

isn't Abbott just focused on one semester of Analysis though?

Mind you I have compared plenty of intro to real analysis curriculums, including MIT's to Abbott's table of contents and it seems Abbott does indeed only cover an intro to real analysis curriculum which should be fine for most people?

I wouldn't recommend just doing Abbott tho. I am trying to juggle with Schroder and Apostol here and there

oh...

I am considering doing number theory while learning analysis. I am realizing I kind of have pretty poor intuition for some modular stuff

then again my general intuition for theoretical math was, more or less infantile going into Velleman for the most part minus some basic logic and set theory exposure

like some questions with modular arithmetic perplex me a little bit

i don't think its a normal thing, and maybe I may as well just jump into an elementary number theory book before I regret not doing so

cuz I don't think my exposure is that great tbh with you

seems like it would be very useful going into analysis

err well a decent chunk of problems in velleman are throwing modular arithemetic proofs at me

so it is an assumption

meh i haven't really been doing analysis other than reading some intro chapter stuff and I thought I wasn't ready for the psets yet

nah

proof writing

mind you it doesn't help having autism traits and trying to learn math through self study

its not that i don't understand it, I feel like maybe I need a little more exposure

[hearty steppe]

ahh ok good to know I won't worry too much then

[void sable]

thoughts on woman hating by dworkin

[uncut knoll]

Hi. How many of your grad courses can you find in Lang's Algebra?

[ripe granite]

all grad courses are a series of footnotes to Lang's Algebra

[storm sleet]

We're using Lang

[whole rain]

[storm sleet]

well, "using" its a thing we steal HW problems from

[whole rain]

Isn't it precisely what a course using a book means ?

[ripe granite]

I don't think any of my classes actually used a book

[warm glen]

how fast and in depth does grad algebra go w the material

our undergrad algebra sequence does group theory, ring theory, and field theory over 3 quarters aka one academic year

the grad sequence seems to go thru group and ring theory more in depth and it also does that in one quarter

[gray gazelle]

I'm not sure anyone here will be able to help you, this probably really depends on the school

[warm glen]

ah, i figured thered be a standard

maybe a better question is what are u expected to cover in grad algebra

surely every grad sequence goes beyond group, ring, and field and galois theory?

[dapper root]

You should cover module theory as well, including the structure theorem for fg modules over a PID

A lot of them do some amounts of representation theory, commutative algebra, homological algebra, maybe some basic AG

I think what gets covered among the above topics varies a lot, but group, ring, field, module, and Galois theory seem ridiculous to not include

Maybe some do some Lie Algebra stuff? I kinda doubt it’s common, but if you’re being taught by some person dealing with representation theory and Lie algebras and stuff I don’t see why it would be out of the question. I don’t think the standard books cover it tho, so it would mean another textbook (except like Lang lol)

[storm sleet]

Our sequence does a second treatment of group ring field and Galois theory, and in the final term we address modules, commutative algebra and basic AG

Our diff geo sequence is where we do all lie related stuff

[sudden kindle]

Galois theory is really cool

Did you know the category of covers of your base space is equivalent to the category of locally constant sheaves on your base space?

Yes this is relevant to galois theory

[crimson cipher]

they cover this for the 1st year grad algebra sequence here

[static crest]

grad?

[crimson cipher]

yeah

well you should know all of it by the end of the first year or most of it

[static crest]

oh that makes more sense

everything to the end of field theory just seemed more like undergrad algebra content

but could just be like a pseudo review

[crimson cipher]

yeee

[dapper root]

What university is this?

That seems almost exactly what my course covered, with a few of the topics having like 1 or 2 extra things

[storm sleet]

Wait you covered Sylow theorems and nilpotency in undergrad?

Our undergrad algebra covered up to normal groups and touched group actions, didn't do much ring theory, and since our teacher hated us, we did some Galois theory

[willow pecan]

My first abstract algebra course covered Sylow theorems but not nilpotency

[karmic thorn]

No group actions at my uni

faithful

Okay cat theorist

Idk what this course is

I'll learn it myself

[willow pecan]

I see

So that's where Manan goes to uni

[karmic thorn]

But anyway I've made that public dozens of time

Hell

Slimvesus is shrouded in mystery

[quick hornet]

lowmath hasnt caught on that im lying about my identity and actually go to

gasp

ut scarborough

i'm just that good.

[whole rain]

I mean even without group actions it's not that hard

g mapped to (x |-> gx), and you're done

but that's cleaner with group actions yeah

huh ?

Nah that's 2 line long lol even without group actions

[karmic thorn]

American unis with good undergrad programmes, maybe dabble around dynamics in later years 🤨

[ripe granite]

college university

[whole rain]

Let G be a group, and g € G, denote by phi_g the application that maps x to gx.
phi_g is a permutation, whose inverse is phi_g^{-1}.
Consider the maps f: G -> S_G, g |-> phi_g, it's an homomorphism, and it's injective 'cause the kernel is trivial

(obvsly if you want to check everything, it's a bit longer, but I mean it's the same with group actions)

[sage python]

Slim don't say it like that now people are gonna take it as a challenge lol

[whole rain]

It is still a challenge

[karmic thorn]

[steel viper]

but jacobian doesnt go to UT scarborough...

[marble solar]

huh where do I go huh

yA

No School 4 moon

[static crest]

utsc nami arc?

[obsidian valley]

its the better campus anyways

[static crest]

literally exactly 0 people think that

in total

[broken meadow]

jesse is not a person

Owned!

ultra is the logic wrong

i am in pain

[willow pecan]

Something something modus tollens

[glad prairie]

[storm sleet]

At least for actives

[sudden kindle]

WHY

why thiss reaction imean

[static crest]

inspired by nami's message

[analog pollen]

Is mathematic methods for physics and engineering a good book?

[karmic thorn]

Depends on what you want to do. Also, there are multiple books going by similar names.

[analog pollen]

Yeah I mean the blue book

I just want it for quick review on my calculus and learning some advanced stuff