book-recommendations

[sick wigeon]

I see

But i think i will need it

[timber mesa]

aaaand his proof of Tychonoff's theorem suffers from a similar problem imo — it's needlessly unintuitive and horrible when you could've just introduced nets (which are an important-ish tool in topology)

[timber mesa]

it's not a bad book

chapters up to 4 are good actually

[sick wigeon]

What other topology book do you recommend if not Munkres

[timber mesa]

I just reaaally hate how he proves Tychonoff's lmao

[timber mesa]

I like Willard's textbook

[brittle breach]

Shifrin has YouTube video which is based on rudins proof

[brittle breach]

Yeah I like this one a lot

[brittle breach]

How much of it have you read

[mortal ore]

anyone know if i should learn multivar on khan academy or if theres a more fulfilling textbook for the concept

i just want to be able to understand ODEs and PDEs basically

and tensors

[timber mesa]

not much tbh since I already had a point-set course (which used Munkres)

I'm reading it now for review and to learn more about nets and stuff we didnt see

[brittle breach]

I just read that chapter

[timber mesa]

I think it's a nice book though, it's thorough and some exercises are interesting

[sick wigeon]

I will watch that ...cool

I have one douby

Like shifrin

He does generalized stokes theorem later

I am not convinced whether he proves them properly

[timber mesa]

I think you don't need too much of multivar for DEs, Khan will be fine for now

[mortal ore]

alright cool

[sick wigeon]

In the general setting or something

[mortal ore]

i just want to be able to understand physics and engineering concepts so hopefully khan will do enough of that

[timber mesa]

just get comfortable with the concepts and calculations

yeah

[mortal ore]

cool

[brittle breach]

I use his videos to get an idea
Watch until I can't bother then read rudin

[mortal ore]

multivar is already showing itself to be really cool so thats good

[frosty girder]

khan doesnt do much of multivariate tho
iirc there were 6 episodes

[sick wigeon]

Hmm

[timber mesa]

huh can't be that few

from what I recall most of the core things are there

[frosty girder]

lemme check again

ok no there is more, im dumb

its 6 of these, not just 6 videos

http://www.physics.miami.edu/~nearing/mathmethods/
btw i kinda liked these notes

[gray gazelle]

physic

[timber mesa]

yeah it's a pretty complete intro

[normal sandal]

Jesus just stewart's multivar is over 600 pages

[frosty girder]

i might as well learn multivariate analysis and not do mv calc and anal separately

[brittle breach]

How does the later chapters of Willard shows up in practice

[normal sandal]

this isn't even representative of difficulty there's just a lot of style stuff I think

[frosty girder]

Yeah but i would still prefer to do it from an analysis standpoint

[normal sandal]

Oh ok

[timber mesa]

I think that's the usual for engi calc books, they go way overboard with content

[timber mesa]

hmmm how so

lemme check my copy

... what exactly are you asking, like why the latter chapters are useful in maths?

[brittle breach]

Beyond chapter 4

[timber mesa]

compactness (chap 6) and connectedness (chap 8) are "nice" properties that are preserved by continuous functions

I say "nice" because e.g. it can be way easier to work with a topo. space if you know it's compact, or (path-)connected

the chapters about separation and countability (5), metrizability (7) and uniform spaces (9) are more like, problems that were historically important in topology

metric spaces are an important class of topo. spaces

with some additional properties

and it can be interesting to ask when a given topo. space is actually a metric space, like what's the least you could ask of it for it to be a nice space with a distance

the last chapter is about function spaces which are interesting in it's own right and useful in analysis

like, Ascoli's theorem and Stone-Weierstrass are useful tools in e.g. functional analysis etc

[timber mesa]

come to think of it, bit weird that Willard introduces connectedness so late in the book, it's a very important and central concept

[brittle breach]

I feel his book is aimed more towards analysis

[brittle breach]

Chapter 5,6,9
Are prerequisites for chapter 10 function spaces according to his guide

[timber mesa]

I see

chap 6 / compactness makes total sense, since Ascoli is about compactness in function spaces

not too sure about 5 or 9, maybe it's just a few sections

yeah I'm convinced the ordering in Willard is a bit odd

it's still a great reference and that's why I bought it in the first place

[brittle breach]

Yeah that.
Normal spaces and first half of 9

I know enough topology to understand what is used in Rudin analysis.
But would need to get some motivation to read more of Willard, love his writing though

[timber mesa]

my current motivation to learn nets properly is proving Tychonoff's theorem, and an expository text by Keith Conrad about finite-dimensional topological vector spaces

more like a "oh this looks cool" thing

[timber mesa]

esp. Conrad's text since I wasn't expecting nets to come up at all

dunno about motivation for the latter chapters though lol, I just kinda have an idea of why they're important and have used them at times in my analysis coursework

[brittle breach]

What tychonoff theorem

[timber mesa]

product of compact spaces is compact under the product topology

[brittle breach]

How useful is that

Something tossed around in analysis often?

[brittle breach]

I just looked at the proof, it seems trivial

Ok it is neat

[fluid bay]

as an application of tychonoff, sometimes you can show a space is compact by finding a closed embedding of the space in a suitably large product of compact spaces

[sick wigeon]

What was the intro manifolds book u used?

[frosty girder]

What would be the prereqs for manifolds?

[sick wigeon]

No idea

[frosty girder]

i was asking in general, not specifically asking u 😅

[keen flare]

Diff geo is so fun

[frosty girder]

idk man i havent done it

[keen flare]

I’m in an intro class rn but the general gist is like a good understanding of linear, some analysis, algebra, and topology

For diff geo at least

[frosty girder]

ic

i am doing 3 of those things

[gray gazelle]

how so pro

[frosty girder]

Im not able to do anything properly

and im still in hs so life is not so easy

[keen flare]

good on you lol

I’m a freshman in college right now so I feel behind already

[gray gazelle]

i am also in hs but just doing analysis is pain enough

cannot fathom how you manage three

[keen flare]

Analysis

measure theory class killing me rn

Especially since the probability class assumes you know how the lebesgue measure works

“I am willing to do anything with you during my office hours except the construction of the lebesgue measure, you should have seen that in analysis already”

Ok I’m done ranting sorry I hate this semester

[gray gazelle]

understandable

[sage python]

@keen flare read the appendix in Durrett's Probability Theory

That + chapter 1

[frosty girder]

[sage python]

Is a reasonably good treatment of measure theory iirc

[frosty girder]

[sage python]

@keen flare for what it's worth, I'm doing fairly well in math overall

And in my first year of college I was doing calculus lmfao

Thankfully my undergrad has a pretty good fast track program for people who don't have much background but are quick on the uptake, so even though I pretty much barely had the equivalent of Calculus AB in high school, I was able to start with Spivak Calculus

But the point is that you're already well ahead of the game by being where you're at now, if it's any help

[covert oxide]

Thanks, I’ll have a look

Okay

[keen flare]

Sure thanks I’ll give it a look

[lime sapphire]

has anyone had a look at velleman's calculus book? thoughts?

[gray gazelle]

i don't see the appeal to it (going by its contents and skimming through some questions)
If you want difficult questions, spivak or piskunov cover you well. If you want to just take a calculus course then your coursebook will suffice for the same.

If you want to see the sequences and deep(er) results then any well-written real analysis book will do.

(also I see that in the book, some theorems are proven in a non-obvious way and using results without citing what is being used, so i have my questions on the "rigorous first approach" claims, not that he defines what he means by "rigorous" though) @lime sapphire

Metro 2033

Played all the games and now reading the book

[lime sapphire]

ah i see, ye it seems very standard and indifferent to a lot of run of mill calculus books

[gray gazelle]

nvm i read it wrong

sorry lol!

[lime sapphire]

lol

np

[lime sapphire]

thanks for the piskunov recc though, this one looks like a nice read

[gray gazelle]

Yeah it is a very nice book, might seem like a bit terse but it gets better eventually

[compact owl]

I have hardy and wright

thanks for Serre arithmetic !

[proper lotus]

I, too, hate analysis in probabiility

[vernal steeple]

Hii,is there an easier proof book compared to How to prove it? I read through the introduction and gained nothing from the first 10 pages

[gray gazelle]

Why do you need a book to learn proofs btw ?

There is a document pinned in this channel for proofs and stuff, and there is Book of proof by Richard H. Hammack, another book which teaches the same.

But really, just jump into the subject and work through problems... You will eventually get the hang of proofs

The document mentioned

[vernal steeple]

I'm taking algebra in my first year of uni and it has a lot of proof | a+b|= |a|+|b| questions

[vernal steeple]

Thankss I'll go look into it

[rancid ivy]

Do you know a book that resumes basically all pre-universitary math ?

[gray gazelle]

How much was paused ?

[rancid ivy]

Wdym ?

[gray gazelle]

How much do you know ?

Like pre-calc, analytic geo, calc, linear algebra ?

[rancid ivy]

Just in general.

A book that resumes all pre unv math

Like I know all the HS math

[brittle breach]

I saw that in a number theory book.
That the p-adic ints are compact

[brittle breach]

Loring Tu intro to manifolds

[sick wigeon]

Nice

[rose comet]

Any recommendations for learning von Neumann algebra? A book that doesn't assume too much prerequisite knowledge would be a bonus

[pine trellis]

doing measure theory in first semester of undergrad
guys am I behind???

what math server does to a mf

[frosty girder]

whose doing that

[pine trellis]

fake tree?

[frosty girder]

oh yeah, fake tree is doing diff geo in first year of college as well

[pine trellis]

"guys I'm so behind"

[sage python]

tfw didn't do Langlands in high school

( ._.)

[timber garnet]

dam idk wtf is even measure theory

[pine trellis]

lies

propaganda meant to convince you that R is uncountable

[slim peak]

Does someone know a good reference for cohomology and existence of Harmonic forms on non compact (but complete) manifolds ?

[humble bluff]

if you havent done differential manifolds, algebraic topology and geometry, complex analysis and sheeve theory until age 8

you are probably not gonna become a good mathematician

[slim peak]

Should add, "If you didn't write your PhD Thesis before your 14th birthday."

[smoky zephyr]

if you aren’t regarded as a math legend by age 18 you’re worthless

[dapper root]

If you don’t become an emote on a math discord server before you’re 23, there’s no hope

btw

That’s me

[smoky zephyr]

how old are you though

[dapper root]

23

[smoky zephyr]

how old were you when that emote was added

[dapper root]

22

[smoky zephyr]

lucky

[humble bluff]

adjustment: 'a somewhat useful mathematician'

[timber mesa]

wouldn't say it's good to learn from those since (afaik) they're just a collection of theorems and facts without proof, and then some exercises. Hence the "outline". They might be good for review though.

[odd spade]

it's not about where you start but where you end up

unless you were publishing at 12 then good for you i guess

[quick hornet]

not really appropriate @autumn cargo

[autumn cargo]

its a vine

[quick hornet]

I'm aware.

[smoky zephyr]

are you aware of what this channel is for

[autumn cargo]

it was a book related vine

[quick hornet]

still not a book recommendation

and still not appropriate language

we tolerate some vulgarity but not when it's completely unrelated to the channel and/or discussion

[tulip blade]

this is just pretty dumb

how could you genuinely think you're behind

[tulip blade]

if you aren't coming out of high school with mastery of schemes and p-adic langlands then you should give up on being a mathematician tbh

[keen flare]

thank dude whoever recommended that Durret probability theory

Will probably use it til martingales cause it's more concise than lecture notes 🙂

[subtle mango]

thank dude whoever recommended Taylor Classical Mechanics

[sage python]

@keen flare 👍

[frosty girder]

i got 5 years, i can do this!

[frosty girder]

time for me to give up....

[glacial moat]

What's a good introductory (adv undergrad or early grad) book on differential geometry/tensor calculus/manifolds?

Essentially it's for the physics of general relativity but I'm looking for smth with more math and less hand-wavy explanations

[glad prairie]

[grand thistle]

anyone know the mathematical prereqs of david morin's classical mechanic's

it should be just calculus 1-3 right?

would linear algebra be part of those prerequisites

[lime sapphire]

this is from the preface of the book

The prerequisites for the book are solid high-school foundations in mechanics (no electricity and magnetism required) and single-variable calculus. There are two minor exceptions to this. First, a few sections rely on multivariable calculus, so I have given a review of this in Appendix B. The bulk of it comes in Section 5.3 (which involves the curl), but this section can easily be skipped on a first reading. Other than that, there are just some partial
derivatives, dot products, and cross products (all of which are reviewed in Appendix B) sprinkled throughout the book. Second, a few sections (4.5, 9.2–9.3, and Appendices D and E) rely on matrices and other elementary topics from linear algebra. But a basic understanding of matrices should suffice here.

[grand thistle]

ah right, if i were to be studying classical mechanics from morin or some other book like taylor, i should probably go through a calculus based university physics book (at least the mechanics part) right? or do you think an algebra based knowledge of high school physics is suffice? assuming that is i have the mathematical background down, since im going through calculus rn

the high school physics level im talking about is like the AP physics 1 level

[lime sapphire]

uhh ican't comment cus idk much about university physics, i just copy/pasted the paragraph from the book's preface lol

[cursive orbit]

AP Physics 1 should be fine. Most of what you learn in most calc-based high school mechanics classes is just a generalization of physics 1 (i.e. changing a few products to integrals and a few quotients to derivatives)

[grand thistle]

ah right, thanks anyway alphyte answered

[grand thistle]

i see, but it would be good to like maybe skim through it a bit, since im pretty sure they expect a good foundation and i should probably know at the very least things like the derivative of momentum times mass is force etc.

[brittle breach]

John Lee smooth manifolds Or
Loring Tu intro topological manifold

[glacial moat]

thanks! I was looking at Lee's earlier, it's a huge book tho

[teal crater]

Have you read Mardsen? Any idea how it compares?

[brittle breach]

Nope, no idea.

[fluid bay]

Warner is much more concise than Lee. Nicolaescu is a good in-between.

[gusty smelt]

If ur doing lee honestly just use it as a supplement to a lecture series or smth. It’s very easy to lose sight in that book

[gray gazelle]

Does anyone know of any good books or resources on how to get better with delta-epsilon proofs in analysis?

[fluid bay]

an analysis book

[gray gazelle]

Any that you recommend that explain that well?

[gray jungle]

i can send you some lecture notes by my professor if you're interested

[fluid bay]

a lot of people recommend abbot's analysis for this kind of thing. Haven't read it personally though.
I mean typically, you can avoid super tedious epsilon-delta arguments by applying limit theorems cleverly. So understanding how to avoid epsilon-delta is probably the more useful skill

[gray gazelle]

That would be fantastic, thanks! I've already done Calculus 1-2 a while ago, but my course never really covered delta-epsilon proofs that much (just the definition and one or two examples, no exercises) so I am trying to get better at it.

[gray gazelle]

Right I know all of those techniques (ie taylor, l'hopital, cauchy-d'lambert, stohl cesaro, etc.) but I want to bring things down to "brass tacks" if you know what I mean.

[gray jungle]

i have sent it in dms

hope it helps

[fluid bay]

yea the main thing is just to get comfortable with the formalism of epsilon-delta. Any analysis book should have practice proving basic things with epsilon-delta or epsilon-N. Also, I didn't mean limit theorems like those. I meant super basic stuff like sums, products, quotients of convergent sequences converge to the sums, products, and quotients of limits respectively. Limits commute with continuous functions and things like that

[gray gazelle]

OK, I'll look into that. Thanks, all!

[inner token]

I recommend a book called Understanding Analysis by Stephen Abbott for your first go around

If you're looking for one

[empty mortar]

[proven goblet]

I just finished reading "e the story of a number" by Eli Maor and it was a really interesting read, so i thought i'd reccomend it to you guys

[wicked summit]

What books should I study euclidean geometry from? I am a senior in high school and want to revise geometry and move to an advanced level

[quiet forge]

The Elements, by Euclid.

[rancid ivy]

Do you know a book that resumes all pre-universitary math ?

[quiet forge]

Nope.

[hollow shore]

Axler's PreCalculus and Lang's Basic Mathematics is what I used.

[rancid ivy]

Thanks !

[median salmon]

Can anyone suggest good books for studying trigonometry? I know the basic level till identities and wanna learn advanced while practising a LOT of questions, but i want the book to be interesting and descriptive instead of just listing down formulas to cram....

[marble solar]

Trigonometric Series

[median salmon]

I think that book is a little more on the higher level than I require…can u suggest something on the high school-Olympiad level?

[heady ember]

Baby rudin

Jk

[lime sapphire]

maybe just try lang's basic mathematics?

[hollow shore]

Axler's PreCalculus text has chapters dedicated to trig. You can check those out.

[median salmon]

Okk….thanks😊

[tulip blade]

Its fine

Most of it is standard undergrad material

[normal sandal]

I did not know Hatcher was freely available that's v cool

[rapid token]

Any recommendations for elementary number theory?

[timber mesa]

I really liked Burton's book

[craggy sapphire]

aops number theory.

[marble solar]

Apostol?

[craggy sapphire]

I need a euclidean geometry book that just has a lot of exercises to practice on

recommendations?

[brittle breach]

Hartshorne has a book on geometry, not sure how useful it might be to you

[dapper root]

Don’t sully him!

He literally has a book on Euclidean geometry

In addition to the one

[timber mesa]

and it's surprisingly decent

written for first year undergraduates iirc?

[sudden kindle]

Thats so epic

Dude has the hardest book on algebraic geometry for grad students and the an approachable book on Euclidean geometry for undergrads

Covered both sides of the textbook spectrum

[dapper root]

Dude just likes geometry

[surreal snow]

Anyone have free book about markov chains discrete and continuous with examples i have searched the internet and i cant find any real life examples :(

[surreal snow]

I can find examples on discrete time but on continuous i cant

[proper lotus]

https://www.probabilitycourse.com/chapter11/11_4_0_brownian_motion_wiener_process.php
Stock prices for continuous.
Though, they are a model more than anything

As to how good the model is, well, you can measure goodness of fit, probably

[surreal snow]

Ill check it thanks!

[gray gazelle]

Can anyone suggest a rigorous ode book ?

[sick wigeon]

Perko's dynamical systems
Or Arnold ode

[timber mesa]

there's Teschl's book too

I read an old one called Introduction to Linear Analysis, by D. Kreider

that's what my undergrad ODE course used

[humble bluff]

Bourbaki

Idk if its up to date though

Probably is

[dapper root]

Bro

No

Do not listen to this madman

[runic hatch]

is Bourbaki good for learning at all

[dapper root]

No

Lol

It’s a good reference book and if you are advanced and know specifically what you want

It’s fine

But you shouldn’t just read it cover to cover thinking you’re gonna use it like a normal textbook

[novel obsidian]

how socially unacceptable is it to skip spivak chapter 1

i already have some exposure to calc through khan

[karmic thorn]

Completely acceptable, but going through the exercises won't be a bad idea

[novel obsidian]

I'll do that then, thanks Manan

[karmic thorn]

[lime sapphire]

Wdym by reference book cus I've always heard people say that but no idea what it means

[dapper root]

"Shit, I need a result."
So you grab the book and comb over it to find the result, then reference that book for the proof

It's not a book you learn from, but something you go over when you need a specific result and need to know a proof, or if you recall there's some theorem vaguely like something you remember, and need a precise statement of it

[lime sapphire]

Hmm

I see

[humble bluff]

Bro bourbaki is great

Both as a ref book and reading book

[restive falcon]

what's a good book on differential forms and lebesgue integration

[lime sapphire]

ngl garling's vol3 of analysis looks good

[restive falcon]

i ask because according to #books pugh and rudin don't have a good treatment of the subject

does garling cover dufferential forms?

[timber garnet]

best video sites to learn undergraduate maths?

[frosty girder]

[gray gazelle]

Calculus on manifolds

Although I dont remember how he did lebesgue stuff

[lime sapphire]

if you mean stuff like differential manifolds then yea he does in volume 2

[hearty jungle]

professor leonard for calculus and diff equations

[hearty jungle]

for linear algebra khan academy and gilbert strang lectures

for real analysis :
https://www.youtube.com/playlist?list=PLLFpXNanTP9WGfbjxR5kCMXQgol4bGehz

for probability :
https://www.youtube.com/playlist?list=PLbMVogVj5nJQqGHrpAloTec_lOKsG-foc

nobody beats calculus when it comes to professor leonard

https://www.youtube.com/c/ProfessorLeonard

[pale fox]

i heard that name a lot but i never watched

[hearty jungle]

yeah he is damn good

[gray gazelle]

the MIT OCW course is good too

[torn belfry]

Im bored, could someone tell me a book about a niche topic thats actually very interesting

[gray gazelle]

it has noice exercises, (i have only used v1 so far though). If you are planning to read it then also get the errata files from here https://www.dpmms.cam.ac.uk/~djhg/

[lime sapphire]

yoo

thx

[slate mesa]

is there some field in statistic that focuses on finding signals given a time series? i mean, some sort of forecasting, but instead of focusing on the general forecast, it would predict whether the time series progresses one way or another or something

[slim peak]

Does someone have a nice reference about Hahn-Schur type theorems ?

Okay I got one

Here is a book about Black Magic

'Multiplier Convergent Series' by Charles Swartz

(this is NOT undergrad material)

[slim peak]

(I thought it was, that's why I advertise about it)

[covert oxide]

Hi, does anyone know a good book for practicing Olympiad-like questions? Maybe with an introduction as well but not necessary

[timber garnet]

@steel viper

[gray gazelle]

@karmic thorn

[steel viper]

Lmfao

B&

[torn belfry]

Pls

[gray gazelle]

Discrete Mathematics by Biggs is a really good book (so far, haven't finished the whole book yet)

[gray gazelle]

What do you think of introduction to calculus and analysis I and II of courant and john?

[brisk ice]

anyone ever use Cengage book and know what "mind tap" is

trying to understand the difference between just the book and "mind tap"

Is the unlimited thing because they use their online homework stuff through cengage?

[brisk ice]

Are these books good at what they are set out to do

[analog lava]

if your trying to learn linear algebra as a pure math major

[brisk ice]

1 is for linear algebra and other is for prob and stats class

[analog lava]

please learn from huffman kunze

[brisk ice]

well these are the books the uni is using for the 2 courses (linear algebra and prob/stats)

I take it none of these books are very note worthy

[analog lava]

then they would know better ig it really depends how u want to learn those topics

from what point of view i mean

[brisk ice]

so do you think the linear algebra book isn't very formal/ proof based?

[analog lava]

idk tbh i never read it before

but for me the best formal/proof based linear algebra book is definitely huffman kunze so i just suggested it

haha

[brisk ice]

oh I see

[analog lava]

idk if he is here anymore or not

thank you jacobian for recommending me this gem

haha

[runic hatch]

Spivak brushes up on some linear algebra and analysis in his first chapter; you could read that and see if you understand it well

(This is for calc on manifolds)

[fervent lava]

Nope, covers geometric stuff about determinants in the appendix but that pretty much it.

Wishing right now I didn’t gave away my only copy.

[stone agate]

What books do you recommend for these courses?
I'm just going to go in, look at these
courses

[marble solar]

It's ok

Nothing special

[brisk ice]

Thats what I assumed. Is it more so for teaching the processes involved in linear algebra than proving everything about it?

[marble solar]

It's a mixed bag

I wouldn't teach from it

Nor attempt to learn from it

[brisk ice]

:/ well that was the book my linear algebra class uses

most likely because of the online "MyLab" avaiable

but without having the class yet I'm not sure if the prof will teach without it and use the book and MyLab as a supplementary thing for problems and grading.

[hearty steppe]

I remember peeking at Lay and it kinda was meh

Your linear algebra class should use Friedberg et al and Janich

[sage python]

Prob depends on what kinda linear algebra class

Some linear algebra classes are geared at an audience which don't have much use for proofs

Tbf I do think linear algebra classes which aren't proofsy tend to do it wrong, they should just make everyone program stuff and then get to more advanced topics

[brisk ice]

wdym "program stuff and then get to more advanced topics"

you mean like actually program

leave the computation the the computer after you have done it a few times?

[sage python]

Yup

I think it's not very valuable to like, row reduce by hand 35 times

Just do it 4 times, get the idea, teach students how to code the algorithm

[hearty steppe]

Yea don’t math hole yourself into doing the same problem 35 times when you can get it the first 4-5 times. Friedberg you shouldn’t even have to do all the exercises in the chapter

But all the redundancy is there to idiot proof the concepts

[hearty steppe]

Hey just want to get a final opinion on recommended complex analysis books.

I have an interest for understanding analog processing a bit

[marble solar]

Marshall

Is the correct way to learn complex analysis

[marble solar]

Marshall complex is the best contemporary text, everyone else is wrong

This is the hill I choose to die on

[analog lava]

stein 😠

[sage python]

@marble solar defend Marshall compared to Narasimhan or Schlag

🔫 do it

[marble solar]

ok toy contour

[analog lava]

hahaha

it was so weird when i first read this term

hahaha

good one

[marble solar]

S&S is good for exercises & problems

But not so great for a lot of other things

[sage python]

Anf the other two?

[vivid solstice]

Huh so
can you recommend me a book for learning about geometry

High School Geometry*

[foggy relic]

euclids elements what level do you want?

Something like Khan Academy geometry vids should be enough for what you do in school but if you want something harder then I rec the Art of Problem Solving Intro to Geometry book

[vivid solstice]

Mostly about theorms related to circles and quads

for my exams

[foggy relic]

for exam prep i think khan should be fine

[vivid solstice]

ohok

So is it on yt?

[foggy relic]

its a website

search it up, the link should pop up

(their videos are on yt though also)

[vivid solstice]

Thanks

Got the website

[subtle mango]

"A Course in Modern Mathematical Physics" Szekeres vs Taylor "Classical Mechanics" (supplemented with Feynman lectures)?

[marble solar]

I don't have experience with them to say

[bronze obsidian]

is "A Mathematical Introduction to Logic" a good book to read im trying to get into math

im about to graduate hs i didnt take calculus or applied and wanna self educate myself in more fields of mathmatics just dont know where to start

[lime sapphire]

you can start with a book on proofs

How to prove it by Velleman

@bronze obsidian

[bronze obsidian]

ty

[heady ember]

Loch has a concised 30 pg proofs introduction which you can see in the pinned msg here or in #proofs-and-logic

[waxen tundra]

books for algebra?

[grand thistle]

i heard taylor was a classic but i’ve read a bit of morin and i like it the most

the problems on morin r also really good

both cover similar amounts of material iirc

[karmic thorn]

Is this a test?

[grand thistle]

.. you cant ask for help on a test and also wrong channel

[heady ember]

[subtle mango]

ic

[lime sapphire]

hi, can i dm you

[hearty steppe]

I’ll check them out thanks

So what’s the deal with Ahlfors

Narasimhan I might start with mainly cuz I’m reading Munkres

What about Needham?

Oh Schlag is a graduate level book?

[forest sleet]

Ahlfors is a classic

Just old

I think Needham is at a more beginning undergrad level (or maybe for non math majors)

[hearty steppe]

Ok I was thinking that. I think Narasimhan sounds perfect. I’ll still glimpse at the other texts. Schlag might go a little over my head, maybe not. We will see

I am curious about learning more about Riemann surfaces in depth. I still need to go thru baby rudin more at some point. But I want to progress more through the first main section of munkres and maybe get halfway or so before starting baby rudin chapter 2

Cuz munkres and baby rudin chapter 2 kinda work well together

Honestly probably 2-4 baby rudin you can use munkres as a buffer

[gray gazelle]

LADR is hated here

@jaunty sedge you can use the search function in this channel to see people's opinions

do you want a more theoretical book ?

or an application based book ?

if you're gonna use that book you can also study the MIT OCW by the same author

i didn't get much through it

but i took formal logic

and now im going through terry tao's lecture notes + Friedberg, Insel & Spence

and they are very good

terry tao's notes have very few prerequisites

as for the book i havent studied it as much

i honestly haven't read the recommended book

so i can't judge it

i am in the process of reading one right now

[proper lotus]

Amazon reviews treat this book like god.
And I have had other people tell me the same thing as written in the reviews
https://www.amazon.com/Linear-Algebra-Dover-Books-Mathematics/dp/048663518X

Specifically for independent-no-tutor study too

My final recommendation for books is, try them out

If you don't like LADR, you might like LADW

etc. etc. etc.

[gray gazelle]

linear algebra done wrong

[proper lotus]

And you might say wow, what a waste of time, I just want to learn about Column spaces

And to that I say, the only better alternative is to write your own notes

And that takes even more time

use 1 book, I think you get the style of the author pretty early on

Hoffman Kunze is the other favourite but I don't know if it's a first-timer book

[versed meteor]

hey, can anyone suggest me some good resource for putnam calculus

[sage python]

Do not do LADR

I should have a pin in this channel about that

He will teach you how to think about determinants and char/min poly in a very bad way

[keen flare]

have I been ruined if i was taught out of LADR mainly

[cursive orbit]

no

[marble solar]

Ahlfors is great, but slow build up and lots of geometry

[hearty steppe]

Ok

[marble solar]

I do think that Marshall is the "correct" viewpoint on complex analysis

although I'm a huge fan of others like Rudin, Ahlfors, Stein & Shakarchi, etc.

[marble solar]

Another underrated one is schaum's outline to complex variables

Lots & lots of solved examples for you

[sudden kindle]

LADR is good

Don't listen to dami

You can learn about determinants when you learn multidimensional analysis

You can learn about char poly when you do abstract algebra

[sage python]

PTY: "It's okay develop brainworms now and cure them later that's definitely better than not developing brainworms"

I should clarify it's not the delaying of the topics

It's that he makes you think thoughts you should never think in your lifetime

It makes you think the idea of the char poly comes from taking the matrix over C and upper triangularizing

The amount of time you spend believing this will be deducted from your lifespan

[smoky zephyr]

what if i just enjoy being taught incorrectly

[sudden kindle]

When I refer to LADR I am referring to the first 6 or 7 chapters

This is what most linear algebra courses cover when using the book

I never read past those chapters so I didn't see how Axler treats determinants or char poly at the end of his book

[subtle mango]

is learning set theory and proofs worth it for reading Hoffman & Kunze for LA? as opposed to not learning those for the sake of that textbook and going with something like Friedberg

assuming going in with no experience in set theory and limited proof

[sage python]

This is how he teaches you to think of char poly. Think of the matrix over C. Upper triangularize. Product of (t-diagonal)

He does connect it I think to generalized eigenspaces

But like bruhhhhhhhhhhhhhhhhhhhhh

Literal brainworms

[smoky zephyr]

this is exactly what i did lol, finishing up book of proof currently

[fluid bay]

no imo

[grand thistle]

i mean its good to know those things just in general, so if i were you i would

but its ur choice

idk how hoffman and kunze teach LA, but i think you'll be fine if it goes moderate pace

[subtle mango]

so far it is 2 yay 1 nay

[fluid bay]

hoffman and kunze is probably the most technical linear algebra book there is other than Halmos

[subtle mango]

did you do set theory then proof?

[fluid bay]

Just pick something slightly easier and learn the proofs as you go

[smoky zephyr]

sorry but what exactly do you mean

[smoky zephyr]

yes, i haven’t actually learned linear algebra yet though

[fluid bay]

I just mean the treatment, topics, and exposition is as abstract as any graduate level text.

[smoky zephyr]

oh wow

so i should probably go for an easier book?

[subtle mango]

that sound kinda fun tho

[grand thistle]

oh then you should learn proofs at least before

id do set theory as well

just read how to prove it

by velleman

[fluid bay]

i mean hoffman and kunze is a good book, and if you have the mathematical maturity to disect it, its probably worth reading. But if you have to intensely study intro-to-proofs stuff just to read it, then idk if its really worth it anymore. You can learn rigorous linear algebra faster from something a little easier

[hearty steppe]

I will try to get thru Schlag tho cuz I am interested in Riemann Surfaces. Do you recommend other books in case Schlag may be over my head? I might be able to handle Schlag but not sure if there are easier books especially for digesting the harder chapters

@sage python

[smoky zephyr]

what book would you recommend?

[sage python]

Schlag is probably very hard

[hearty steppe]

I def need to look back at Hoffman Kunze

[sage python]

It assumes you know every area of math aside from complex analysis lol

[hearty steppe]

Oh

I’ll still check it out to see what you mean by very hard

[fluid bay]

i like "linear algebra done wrong" by Sergei Treil. It was how i self-taught linear algebra. Some people like Axler, or friedberg, so those are other options

[hearty steppe]

I consider baby rudin very hard lol

[smoky zephyr]

ok thanks

[hearty steppe]

But I mean Rudin’s books are just hard in general

[grand thistle]

how rigorous is LADW?

its an introduction to LA right

[foggy relic]

btw, what makes marshall so good

[grand thistle]

since im thinking of going through an LA book after i finish the intro to LA part in apostol's calculus books

[foggy relic]

over like stein/shakarchi or needham,

[fluid bay]

yes. It is rigorous. The selection of topics and treatment is not quite as abstract as Axler for example. No infinite dim spaces, matrices introduced early on, etc... The exercises have a mix of proof and computation practice

[grand thistle]

ah i see

do you think it would be good to go through it after learning an intro to LA here

[grand thistle]

this book is pretty rigorous btw

or maybe i should go for a harder one? perhaps this covers most of the topics in LADW

[fluid bay]

I think this probably covers most topics you need to know most urgently for linear algebra

[grand thistle]

oh okay

what do you recommend doing from there?

a harder LA book?

if so, which one would you recommend

[fluid bay]

nah, i feel like once you know the basics, you can learn whatever LA you need as you go along with your other studies.

[grand thistle]

ah okay, thank you

[fluid bay]

np

[patent swallow]

which book should I pick for relearning precalculus? the art of problem solving or blitzer's

I would like to train my mathematical thinking and later study calculus (I am also very curious about graph theory and stats)

[daring quiver]

Khan academy

[smoky zephyr]

oops wrong channel

[halcyon hornet]

That Thing Got 17 Freaking upvotes.

I Love DemOcracy.

[tardy walrus]

i ToO loVe dEmocRacY.

[harsh jackal]

Hello I have started calculus recently and I need practice problems to solve. Do you know any books with a lot of practice problems ? Thank you!

[gray gazelle]

check the pins in #calculus, the link below will take you to it

#calculus message

[harsh jackal]

Thank you brother

But I am getting this

[gray gazelle]

ah

wait

https://archive.org/details/DemidovichEtAlProblemsInMathematicalAnalysisMir1970/page/n1/mode/2up

click on pdf below

scroll down

and click that pdf

[harsh jackal]

This ?

[gray gazelle]

yes

[harsh jackal]

OK thanks

Also is this for beginners ?

I have just started calculus

It is loading so thought of asking by the time

[gray gazelle]

the difficulty increases gradually

if you have a decent understanding of the subject matter, you should be fine. Just look for algebraic manipulations

you can ask for help here or any other forums any time

[harsh jackal]

Oh...

Oh...OK thanks

[gray gazelle]

Lmao wtf?

[gray gazelle]

sort of a weird one but are there any books (hs level- early undergrad level) that talk about connections of calculus with geometry ? Just in need of those types of problems

[halcyon hornet]

Yes.

[dapper root]

cope?

[empty mortar]

[subtle mango]

any significant difference between Velleman 2nd edition vs 3rd?

[fervent lava]

Nope.

Except maybe some number theory stuff.

[grand thistle]

stewart has a lot of problems

[gray gazelle]

Books on polynomials and how to deal with them in integrals?

Like a polynomial divided by another polynomial

[uncut zealot]

Like, rational functions? Most calculus textbooks should cover them in the chapter on partial fractions

[fervent lava]

Paul online math notes has a section on it.

[uncut zealot]

To double check, you mean integrals of the form $\int\frac{a_{n}x^{n}+\dots+a_{1}x+a_{0}}{b_{n}x^{n}+\dots+b_{1}x+b_{0}},dx$, right?

[gray gazelle]

Yup

[hasty eagle]

Zorn's Lemon

[gray gazelle]

@fervent lava I'll look it up

[uncut zealot]

Yeah most calculus textbooks should have something. The chapter you're looking for is "partial fractions".

[gray gazelle]

Does spivak have it

[uncut zealot]

Probably. I haven't read Spivak.

[fervent lava]

Yes, in elementary chapter.

[gray gazelle]

Alright

[fervent lava]

Something like that.

[gray gazelle]

Thank you both

[atomic stag]

I'm looking for a book that can explain Thorium reacter in detail detailed explanation for UG level

[karmic thorn]

Maybe try asking in the physics server in #old-network

[tranquil orbit]

List of books for number theory ?

[uncut zealot]

#books-old and #books both list a few. That said, number theory is such a large subject that there will be no complete list. Do you have a specific topic in number theory you want a recommendation for? (For instance, class field theory, L-functions, elliptic curves, etc.)?

[tranquil orbit]

Want to do elliptic curves but need to cover the basics first, is an introduction to the theory o-f numbers by hardy good for that or is something better

[uncut zealot]

If you want to do elliptic curves and already know a bit of algebra, try Rational Points on Elliptic Curves by Silverman and Tate. It's far more important to know a bit of algebra than a bit of elementary number theory going into elliptic curves, in my opinion.

If you've already taken like 3 different alg geo courses, try Arithmetic of Elliptic Curves by Silverman instead.

[north siren]

Idk if this is only math books but if not I highly recommend Hatchet, its a quick read and its rly good

[hollow peak]

My favorite algebraic topology book

[flint forge]

oh wait he actually meant hatchet

i assumed it was a typo at first

[sage python]

Hahahahaha

[north siren]

yes very amazing

[gray gazelle]

Any suggestion for a book to self-study calculus 3?

[robust heron]

I am utterly fascinated by mathematics, and I want to understand it better. What are some good resources for this?

It can be books or youtube channels or whatever

[fervent lava]

What do you know so far and what do you want to learn?

[robust heron]

My current level is calculus. Three out of the four classes I have this semester are calculus-based and I'm not doing as terribly as I thought I would. I want to make calculus easy the same way algebra eventually became easy for me, and then eventually get to more complicated concepts, such as Riemann hypothesis.

Theoretical physics, chaos theory, but again, for a bit later on.

Also I took logic a long time ago. It was an interesting topic but I haven't retained much information. Relearning it would be nice.

[dense hamlet]

RH

wait you are taking calculus after algebra???

that is very unusual at least in my opinion

[robust heron]

cmon bruh

[foggy relic]

calculus on manifolds

maybe try pauls online notes

or mit ocw mvc

[robust heron]

what are you talking about?

you took calculus in middle school or something?

[dense hamlet]

I thought you meant abstract algebra for a second, nevermind

[robust heron]

yeah I've never done abstract algebra in my life

[robust heron]

What does RH mean?

[dense hamlet]

riemann hypothesis

[robust heron]

ah ok

yeah just so you know I'm not interested in multiverse theory or simulation theory or any of that popsci stuff

I just used RH as an example of complicated mathematical concepts, I don't know much.

[robust heron]

but yeah some book reccs would be nice

[runic hatch]

well I guess you could go with the standard math major books

Maybe try Spivak's Calculus, or Apostol's Calculus, Vol. 1 + Calculus, Vol. 2

for abstract algebra I liked Artin's Algebra

[sick wigeon]

Gallian is a very nice book for abstract algebra

[hushed saddle]

Book Recommendation
To learn statistics using python (python 3)

[modern stone]

For beginners in Abstract Algebra, I’ve heard Pinter’s book is quite good

[modern stone]

I’ve heard Shiffrin is quite good

[gray gazelle]

I'll take a look, thank you!

[robust heron]

@runic hatch thanks

[wispy badge]

Hello

[fervent lava]

Hi.

[restive falcon]

for abstract algebra I'd highly recommend Algebra by godement

much of it is focused on re-examining linear algebra in a more intuitive, general way using modules

[fluid bay]

wow that sounds kinda cool

[robust heron]

I see

Thanks

[wise umbra]

The few times I opened this book it seemed like some part of it did not age very well

[dapper root]

I would be hesitant to believe a French book would be good pedagogically for an introduction

[slim peak]

Godement books on Analysis are pretty good

I never read Algebra one, but I trust him

[gray gazelle]

Anyone have an opinion on this book? https://link.springer.com/book/10.1007%2F978-1-4471-0613-5

I don't have any number theory experience and I want to self-study.

[sudden kindle]

Gareth Jones

Looks good

Actually looks like a good book for complete beginners in nt

[gray gazelle]

Ok, thanks. Looking for to learning how to be a prime number warlock.

[glacial tartan]

anyone have any good linear algebra textbook recommendations?

[marble solar]

Schaum's Outline is good

[split bluff]

thoughts on math philosophy books? are they worth the read to improve the way you think about math problems or they offer nothing in comparison to reading conventional math books?

[gray gazelle]

@split bluff I'm not sure if this qualifies as math philosophy, but for me, understanding that we can use different logics (eg, logic with and without law of excluded middle) to build mathematical theories was enlightening.

Also looking at the motivations and attempts to formalize set theory to do foundational math I find enlightening (eg, Russel's paradox).

And some treatment of questions like, "What is a number?", I found useful, since that question was banging around in my head.

Also, understanding the proposed differences between analytic and synthetic propositions was VERY enlightening for me. And that in some sense, mathematics is all tautological.

Highly recommend Language Truth & Logic by Ayer.

[restive falcon]

how so

[sick wigeon]

Has someone read the Manifolds part of shifrins multivariable calculus text?

How's it

[hasty turret]

What are some good textbooks for type theory ? I am looking to learn Haskell but I need type theory to rigorously talk about stuff

For example,I don't understand what it means for 2 functions to be equal when they can take in an argument of any type

[gray gazelle]

I think you should read Mathematical Circles(Russian Experience). It is a great way to build around concepts out of the syllabus, and an even better experience if u hv someone to discuss the problems in that book with.

[gray gazelle]

I loved the Cartoon Guide to Algebra!

RELATIVELY

but u can learn a lot from it

at any level from 6-10

class 6-10

even younger students can try it, but i recommend discussing the book with a teacher

if u r younger than 6th standard

[shadow tusk]

wow

[shadow tusk]

wait, they asked for a linear algebra book

does it cover linear algebra?

[grand thistle]

they meant college level linear algebra…

like vector spaces and stuff yk

not y=mx+b

unless ur talking about that one anime LA book that was on flammable math’s channel i don’t think that’s what they were looking for

[gray gazelle]

Can anyone recommend me any sublime books regarding calculus?

"sublime" ?

It's a synonym for excellent or anything that is of good quality.

Anyone?

Many people love spivak's text, mostly because of his A+ grade questions.
Piskunov's 2 part text is my personal favourite.
Other options that you can look into is Thomas' text, Strang's book (or the newer Openstax collection based on Strang)
Khan academy is also an option

Search this channel for more!

Thank you :D

[manic seal]

what's the go to book for real analysis

why delete

somebody wrote apostle and rudin, then deleted it, if anybody else wants to see the answer as well

I still look for more answers though

please reply

[gray gazelle]

Apart from apostle and rudin, check this https://www.math.ucdavis.edu/~hunter/intro_analysis_pdf/intro_analysis.html

[runic hatch]

At the end I’d recommend sticking to one or two analysis books tbh

There’s a lot of very good texts out there, and it can be easy to spend more time searching for a good book than actually studying the material

[gray gazelle]

Rd sharma book

[robust heron]

Be Extraordinary?

[gray gazelle]

The cartoon guide to calculus is good if u r starting with calculus or if u want to strengthen ur base

[gray gazelle]

What cartoon guide?

Is that a youtube channel?

[grand thistle]

uhh

is that a textbook?

[grand thistle]

i like apostol a lot tbh

its really nice to learn from and also rigorous

[gray gazelle]

Alr

ty

[grand thistle]

the only complaint i have is that its a bit confusing at the beginning

it kinda goes through unecessary trouble to define integrals before limits and continuity

but yeah it is what it is

still my fav

[gray gazelle]

The cartoon guide to calculus is a math book

Not really a textbook

U can find it on amazon

[restive falcon]

is a taste of topology good

[hearty steppe]

I enjoy munkres so far and I like Mendelson

[glacial tartan]

Doesn't cover linear algebra

[craggy dome]

Do you have recommendations on an analytic number theory book with a big emphasis on analysis?

[zenith oasis]

anyone have experience with Simmons's Differential Equations with Applications and Historical Notes or Hirsch and Smale's Differential equations, dynamical systems, and and an Introduction to Chaos
?

[gray gazelle]

I need a book for algebra 1 and 2

[nimble ledge]

Beginning and Intermediate Algebra by Tyler Wallace is good

[gray gazelle]

Thank you

Need to review and want to start algebra 2 soon

[nimble ledge]

nice

[gray gazelle]

Anything else

Also what do you think of Bob Miller

[marble solar]

How strong are you in analysis?

I like these notes a lot

http://www.math.byu.edu/~nick/ucla/205a/205a-notes.pdf

[craggy dome]

Had a grad courses on complex analysis, functional analysis, measure theory

Thank you so much :)

[marble solar]

If you're feeling more in for a challenge

You can follow Terry's notes

https://terrytao.wordpress.com/2014/11/23/254a-notes-1-elementary-multiplicative-number-theory/

[craggy dome]

Seems like exactly what l was looking for, thank you so much :)

[remote ginkgo]

this is very cool

[loud trail]

recommendations for books on multivariable calculus (specifically for exercises)? i'm currently using stewart's multivariable calculus 8th edition for my class, but i found the exercises to be quite lacking. need more practice because my midterm absolutely wrecked me

[remote ginkgo]

Shifrin's Multivariable Mathematics

skim table of contents for relevant sections

[modern stone]

Thoughts on this playlist about topology?

https://youtube.com/playlist?list=PLBEeOnR8lrBHNZWwk8-pHOQLQnP3u8bO8

[dense wren]

Would going through fulton’s algebraic curves in its entirety prepare one for hartshorne or vakil

[dapper root]

Honestly, preparation for Hartshorne is more just having a certain baseline level of algebra under your belt, and then being mentally (and/or emotionally) prepared to struggle a lot

That being said, I am a proponent of learning varieties first, and even just the case of curves probably introduces one to enough concepts to get an idea of what algebraic geometry is about, and hopefully gives you intuition to fall back on when you're struggling to grapple with schemes and all the associated crap that comes with that

[marble solar]

Berg's taking the same class I was, which was basically up to Fulton's treatment of Bezout

[dapper root]

So to summarize: I think the preparation for Hartshorne is kind of trivial / impossible. It's trivial in that you just go for it (assuming you have a certain level of algebra), impossible in the sense that no matter what you do it'll be hard as shit

But that being said, I think you'll profit from doing a classical book first, and curves is a great place to start, or even just only learn curves then move on to something like Hartshorne

[gray gazelle]

Can anyone recommend some good books for SASMO prep?

[dense wren]

@dapper root thank you for that I’ll keep it in mind, end goal for me is to get through hartshorne as a side project, so that’ll keep me busy for quite a while haha

[modern stone]

Is Khan Academy enough for multivar calc too or is it enough only for single variable calc?

[gray gazelle]

?

[grand thistle]

probably don't use khan academy past calculus bc

its fine for like

first time introductions

but its very

surface level

ive heard

[restive falcon]

is volker runde "a taste of topology" good

[gray gazelle]

lick it

[restive falcon]

i can't lick a digital copy

I'd just be licking an ssd

[gray gazelle]

lick it

Lol

[gray gazelle]

Ok can u say @restive falcon

[restive falcon]

looking for a good intro set theory book

[gray gazelle]

Yeah

[restive falcon]

minimal prereqs

[smoky zephyr]

@gray gazelle the set theory chapter in “book of proof” by richard hammack teaches it pretty well i’d say

https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf

[gray gazelle]

Oh ok

Thank you

[smoky zephyr]

mods the books is available for free online don’t say anything about me posting a link

[gray gazelle]

Past papers of the X-ENS exam for my pathways ("Maths Spé" - MP (Maths and Physics) in CPGE (in France))

For those interested, I have link to see other past papers of this exam or lessons in my pathways in CPGE :

Past papers :

https://concours-maths-cpge.fr/

Lessons :

https://cpge-paradise.com/MP4Math.php

École Normale Supérieure (whose the name is Ulm and with the maths exam of 6hours in X-ENS exam ):

https://www.ens.fr/une-formation-d-exception/admission-concours/concours-voie-cpge/concours-voie-cpge-sciences-0

École Polytechnique :

https://gargantua.polytechnique.fr/siatel-web/app/explorer/fVaJXpYYYK

I hope that pleases u

[odd shore]

Book recommendations huh

For biology or human anatomy lovers

[fervent lava]

eww.

[odd shore]

Yea i cant find the Biology server so i guess math will do

[fervent lava]

#old-network has a biology server.

[hearty steppe]

He’s looking for biocord

That’s the biggest biology server on discord

It’s not even a quarter of the size of our server

There is a medical professional server too but those people are kind of uptight

[solar cedar]

RSVP: https://forms.gle/dWwy66sQa7NJ5e6U9

[flint forge]

No

[frosty girder]

premeds

[gray gazelle]

Anyone got some free resources for learning Linear algebra to a decent level

I tried an edx course but didnt like it

[fervent lava]

Linear Algebra As An Introduction To Abstract Mathematics by Lankham.

[gray gazelle]

can I have a link and is it free

preferably online and free

[fervent lava]

Yes it a free online text. https://www.math.ucdavis.edu/~anne/linear_algebra/index.html. You find the pdf link around the bottom.

[gray gazelle]

thank you

[gray gazelle]

What's some cool stuff about topological groups

@flint forge you have any suggestions?

I know the book by Arhangielsky and Tkachenko

Not sure if that's solid

[flint forge]

Abelian pi1 and hopf algebra homology come to mind

[cyan prism]

any good free online statistics courses

like introductory level but goes past hs material

[foggy relic]

do you want calculus as a prereq for it or not

and by "hs material" do you mean kinda concepts based on intuition like sample, normal distrbutions, hypothesis kind of stuff?

or something more introductory/advanced

[cyan prism]

sure

ive only done single variable calculus tho

[cyan prism]

a little more advanced? idk

[foggy relic]

i recommend "All of Statistics: A Concise Course in Statistical Inference"

havent read the full thing but i read some portions and liked it

[cyan prism]

uh

anything a little less advacned

idk the content might be ok but its a little dense

[small socket]

@gray gazelle https://mtaylor.web.unc.edu/notes/linear-algebra-notes/

@cyan prism https://projects.iq.harvard.edu/stat110/home

@cyan prism http://julio.staff.ipb.ac.id/files/2015/02/Ross_8th_ed_English.pdf

[cyan prism]

looks good, thank you!

[outer ledge]

which book should i refer for multivariable calculus ?

[gray gazelle]

Can someone recommend a good trig textbook for practice?(I learnt a bit of trig on khan academy, but i wanna practice more)

[cyan prism]

um idk if there are better ones but

nsw cambridge math textbooks are pretty good

they have plenty of problems and good explanation

and there are different levels of practice problems

from easy to complex

[gray gazelle]

ok thank u

[grand thistle]

try the aops books

you'll pick up a lot more than just trig

from them

algebra vol 1-2

[gray gazelle]

aops?

can u say the full form?

[grand thistle]

oh

art of problem solving

[solid idol]

Trignometry books??

[gray gazelle]

ok thnks

[grave egret]

any books that contain enough graph theory to do gt research?

[shrewd dew]

Best book on fields and galois theory?

[stray veldt]

i like the one by morandi

[cedar eagle]

8

[dapper root]

How comprehensive is it?

I find myself needing facts about purely inseparable extensions and crap

[stray veldt]

it has a section on it

[dapper root]

Here’s an example of something I needed recently

https://stacks.math.columbia.edu/tag/030R

I just don’t know if any textbook has this level of generality and just really hurbed stuff on field extensions

[stray veldt]

this one doesnt

[dapper root]

ChmonkaS

[stray veldt]

its for teaching

[dapper root]

Bourbaki Algebra II it is

[stray veldt]

for a galois class that does slightly more than the average class

[dapper root]

I see

If only I could find a PHYSICAL COPY OF A HARDCOVER OF ALGEBRA II

Algebra I pops up every so often

But not Algwbra II 😔

[stray veldt]

does stacks project not have the stuff you need?

[dapper root]

Well

It probably does but I like book

[gray gazelle]

I would suggest using the book: "Precalculus concepts through functions a unit circle approach to trigonometry by Michael Sullivan"
It's complementary with KA Trig section. As you can see, it's table of contents

So I would say, video on KA or Prof Leonard, do the practice section on KA and after a topic go into the book and do the problems after each section, it usually has 1-100+ problems

[gray gazelle]

What kind of prereqs are there here?

I know the basics of linear algebra from the start of a course but I want to generally get into more advanced algebra

I have no idea where to start

I'm in year 9, the GCSE seems fine for me and I want to get into abstract and advanced and complex algebra

I can't decide between linear algebra or calculus or anything else, what would be a good option for me

calculus prehaps?

[split berry]

For those who haven’t done this:
Could you do me a favour for my school project please and thank you. It’s quick and shouldn’t take even 2 minutes. No email required!
Link: https://docs.google.com/forms/d/e/1FAIpQLScPvnacFTbZL6W6SpQlAIOpRPl9eRo2ivDzVf9uFL2BvThVzA/viewform?usp=sf_link

[wet spoke]

read(you can listen to the audiobook but read is better) Sierra Six

[wise umbra]

Probably Bourbaki haha

[wise umbra]

Oh nvm

There is also some stuff about inseparable extensions in Algebra by Lang but it might be too general for you

[dapper root]

Yeah hahaha

[dapper root]

I think it’s not general enough

[wise umbra]

Yeah I meant just the usual statements, not specific things

It's hard to find something more general than Bourbaki on these things, because the authors put in these books the most general theorems they could

[smoky furnace]

http://ebay.us/8AVgmK?cmpnId=5338273189

Anyone interested?

[small socket]

@gray gazelle A prerequisite is some familiarity with proofs and math notation (sets, functions, etc.). Also it helps to have seen calculus I and II, but it isn't necessary. The book is very thorough and does get to more advanced topics in algebra such as rings and modules.

[marble solar]

Trigonometric Series

[foggy pollen]

Is there good books about probability and statistic theory + measure theory (for some theoretical background) please ?

if possible available on google for free, otherwise i will check if my university library has it

[hearty steppe]

Oh I’m going that route @foggy pollen

Going thru Casella and Berger rn

[rapid token]

Is Pinter's "A Book of Abstract Algebra" too simple/basic for an undergraduate?

[flint forge]

some people think it is slow

i think they should read faster

[dense wren]

I think it’s good for someone who has no experience with abstract algebra and is looking for a gentle intro

[restive falcon]

artin is the gold standard for intro AA

[flint forge]

this is only true if one does not already know any linear algebra and wants to learn it

I don't think artin is particularly special otherwise

[tulip blade]

What do you think is good?

[flint forge]

Idk d&f is all I use

[gray gazelle]

Is apostle a good calculus textbook for absolute calc beginners?

[halcyon hornet]

It depends on prerequisites ig.

[gray gazelle]

Like people who only know about limits

And functions

In calc

[halcyon hornet]

Apostle is very rigorous and needs some knowledge of proofs.

[gray gazelle]

That’s fine

Any other choices with a more casual approach?

[runic hatch]

Spivak’s calculus also works, although it’s also pretty hard for a beginner

[gray gazelle]

Um im just a beginner so maybe not good for me

[runic hatch]

I feel like the best bet is to just pick one of those two and go through it in a slow but steady manner

[gray gazelle]

I only know this much

[gray gazelle]

Ok thnks

[runic hatch]

Well in terms of actual knowledge you don’t need any more than calc for either

[gray gazelle]

Then thanks

[runic hatch]

The hard part comes from grappling with a rather new way of thinking

Good luck

[gray gazelle]

Can you just name the apostle book

I can’t find anything on amazon with “apostle”

[gray gazelle]

I mean the calculus book by Apostle

[gray jungle]

stewart is the friendly book

[gray gazelle]

Is it this one

[gray gazelle]

Friendly?

[gray jungle]

you'll be fine reading it compared to something more challenging like spivak

[gray gazelle]

Im learning rn from a book called the cartoon guide to calculus

Im going for apostle for now

[gray gazelle]

Can someone confirm if this is the book im looking for

Anyone?

[gray jungle]

i think so

[gray gazelle]

Ok thank you!

[gray gazelle]

https://math.libretexts.org/Bookshelves/Calculus/Map:_Calculus__Early_Transcendentals_(Stewart) this one's also a good read for calc

[grand thistle]

btw its apostol

[grand thistle]

its that one, but my version has a blue cover

looks like this

and yeah its pretty great

but be prepared to be looking blankly at some proof then realizing what it means like the day after

also

might be good to go through a proof book like "how to prove it" by velleman first

idk if its very beginner friendly tho

might wanna go with stewart for a little bit

then

see if u wanna change to a more rigorous book

[gray gazelle]

How many books do you guys read at once?

Well looks like I won’t be getting apostol anytime soon

[grand thistle]

idk i rwad one at once

but that’s bc i can’t maintain like

two or more

i always end up focusing on one more than all the others

[frosty girder]

i plan to read like 3 at a time

[tranquil orbit]

Can someone give ve me a list of books building up to number theory of reiman hypothesis

Just want to understand it

[fervent lava]

2, with more time put in for one.

[rain hound]

I’m looking for an abstract algebra book that is very calculation based and visual and concrete, at either an advanced undergraduate or beginning graduate level. It can have rigor, but I’m preferably looking for something looser more akin to a math methods in physics/cs book, or a calculus book.

[flint forge]

I am not sure if you will find what you are looking for since most abstract algebra books aimed at undergrads+ are sort of proof based by necessity

But books like Dummit and Foote have a lot of calculational examples

[rain hound]

I’m fine with proof based, I just want a lot of calculations involved. The current one I’m reading has nice exposition but no calculations, Aluffi. Alternately I’d be happy with a category theory book that is very calculation based.

[steel viper]

What exactly does calculation based mean? Has a lot of examples?

Or are you looking for some kind of specific selection of results

[rain hound]

Works through select examples extensively and completely and thoroughly, it proves results, but either before or after will work through an example completely in a way that emphasizes intuition and problem solving over stating and proving abstract results. A really good text doing what I want here is Concrete Mathematics by Knuth. I’d really like something like that, but either for abstract algebra or category theory.

[steel viper]

D&F has a lot of computations like Max said

And some sections focused on things like

D_n and stuff

[rain hound]

Alright ty

[fleet aurora]

I am looking for a book which directly computes the dimension of the general affine group aff(V) for V being R^n or C^n and possibly provides some background on this. Do you have any recommendations?

[sudden kindle]

Just think about it

You can figure it out

Wikipedia explains this too iirc

aff(V) is a semidirect product of GL(V) and V itself (considered as an abelian group)

So the dimension of aff(V) should be dimension of GL(V) plus dim(V), which is n^2 + n

Check me if I'm wrong

[fleet aurora]

Yes, thats correct. But wikipedia for example never explicitly states n^2+n and I'd prefer some more serious reference

[marble solar]

Wikipedia math is unironically a serious reference. You can try nLab

[sudden kindle]

Well how are you considering aff(V) as a vector space? Its a group under composition sure, but whats the additive structure?

I don't think GL(V) is even a vector space. So I think my dimension, you mean dimension of the manifold/lie group

Is Aff(V) a lie group?

[fleet aurora]

Yes, by dimension I mean dimension of the manifold since it isnt a vector space.

[fleet aurora]

True, and I do not doubt the corresponding wikipedia article but still I do not want to use it as a reference when writing an article. I'd prefer some book or paper.

[marble solar]

Ah I see

[proper lotus]

Depends on how mature the article is. I'm sure there are many stubs

[sudden kindle]

I don't think you need to cite anything for this

Its just a computation

Dimension of a product of two manifolds is the sum of their dimensions

Here Aff(V) considered as a manifold is just GL(V) times V

GL(V) has dim n^2 and V has dim n if V =R^n

[flint forge]

Yeah there’s no need to cite this fact

[karmic thorn]

Introductory textbook for linear programming?

[brisk vapor]

can you recommend a book "for dummies" based on the contents of the second chapter of "handbook of applied cryptography" https://cacr.uwaterloo.ca/hac/about/chap2.pdf ? I need most of the information that is described in the chapter, but explained with more words and examples, and in a simple manner