book-recommendations

[narrow fiber]

Calling Lang more lucid than D&F too lol

[dapper root]

That list is garbage trash

[proper shale]

please someone reply me.

[dapper root]

Like 99% of these lists are garbage trash

[narrow fiber]

This fast track website is unbelievable lol

This is like half consisting of books that are dedicated to containing a wide breadth of material than presenting in a beginner-friendly way

Points for bott & tu though that book rules

[karmic thorn]

I'm omegasceptical of these elaborate pathways to learning esoteric math that start from basic calculus

I'm not sure I know anyone who has earnestly followed such a pre-determined path

[narrow fiber]

Yeah same here lol

[gray gazelle]

That list looks like it was produced by a high schooler lmao

[narrow fiber]

Like I get the allure of "wow check out my extremely detailed and ground-up learning path" but they all have such glaring pedagogical gaps and are so beginner-hostile it feels like the list author is showing off at a certain point

[dapper root]

Pretty sure it was made by Gristle

[narrow fiber]

Wait who's Gristle

[karmic thorn]

LMAO

[narrow fiber]

Oh no is this someone in here lol

[dapper root]

Sometimes here sometimes not

[karmic thorn]

I would be surprised if the author's intent was anything but showing-off

Maybe there's a wild chance someone wants to put it out there for the general audience the grounds one has to cover in order to reach mathematics closer to the research frontiers

But that intent is not conveyed, or at least I never interpreted it that way

All this just feels like Math Sorcerer in blogpost format

[narrow fiber]

I get the vague feeling someone could assemble this list just based off of looking up, in a series of google searches and stackexchange posts, "mathematics for theoretical physics" and then reading enough descriptions at a surface level to assemble them into what they feel is a coherent order

Nothing else justifies these book choices from the ones I'm actually familiar with

Idk any of the physics ones well

[karmic thorn]

Right

[karmic thorn]

I see, so this is where the pathbreaking Collatz papers on Vixra come from

[narrow fiber]

LOL

[onyx wren]

honestly i dont know how to feel about this

i have met people that invest a lot of ego into things like this and i sort of feel bad because it doesnt seem like they are actually interested in the math

[dapper root]

Skill diff

[onyx wren]

ye we can make fun of this but i think it is sad in a lot of ways especially if they dont know how they come off

because its not like they are trying to sell you something so there is no benefit outside of ego boost

[karmic thorn]

It can't be helped much if they consider legitimate feedback from qualified individuals as adversarial (worse, they cast anyone from "traditional" systems as automatically against their idea, like some conspiracy theorist of sorts)

Anyway, this is starting to go beyond the scope of the channel. Further discussion can be moved to one of the general discussion channels.

[crimson leaf]

It was yes

The other guy around grist used to peddle the portal one iirc

I don't want to misrepresent them but I believe their mentality is something like if you can't follow the fast track then you have no place in math and that following it will be make you smarter than most grad students (might be misrepresenting here will admit) etc

Also known for claiming things should take a ludicrous amount of time like calc 1 taking 1 day to learn all of shilov in 1 month

[gray gazelle]

Any books on calculus ?

Differential equations

I wanna study it ^°^

[strange crater]

Linear algebra is usually the next thing, you can read shilov's linear algebra

[unkempt scaffold]

https://www.youtube.com/watch?v=mnuAHa2pE8U

Can you guys recommend any book that focuses on Algebra and Trigonometry proofs? Wanted to help my 13 year daughter after watching that video, who is currently struggling to remember them.

[gray gazelle]

Differential Equations With Applications and Historical Notes by George Simmons.

[gray gazelle]

Thanks

[heady ember]

@gray gazelle

[molten mason]

I'm a fan of the person selling it for $890 on Amazon lol

[gray gazelle]

Internet exist

https://archive.org/details/g.f.simmonsdifferentialequations/page/n23/mode/2up

[molten mason]

Of course, but the $890 Amazon link was the first one to pop up on Google, and the first thing I noticed lol

[gray gazelle]

[molten mason]

Looks like a good book by the way, I'm skimming through it

[gray gazelle]

As far as I'm concerned, I'm looking for a recent version of Blitzer's college algebra.

[raven prawn]

im doing both igcse maths and additional maths

[raven prawn]

linear algebra as in matrices and vectors?

[heady ember]

You can also try Friedberg, but its proof-based

[raven prawn]

thanks, i’ll check it out

[heady ember]

Look at Dami's LA recs in pinned

[spare ridge]

based list

[onyx field]

for class 7 which book should I take

???

pls ping me

[subtle mango]

idk about textbooks, but theres good stuff on khan academy

see: “High School Geometry” and “Algebra 1”

[unkempt scaffold]

Thanks for the response. There is lot of content between the proofs. I am looking for a resource that will show one proof after another. Even a online article is fine, it doesn't have to be a book.

[sage python]

What a bad list lol

[alpine rover]

more math sorcerer:
https://youtu.be/didXE0HkSC8?t=324

not sure about algebra & trigonometry proofs because most algebra & trigonometry books are targeted at high schoolers

unless you mean proving trigonometric identities, which should be covered in every standard text

[gray gazelle]

Maths sorcerer is the best

[gray jungle]

Has anyone read chapter 8/9 of H&K 2nd ed, are they ok?

[fallow cypress]

yes all of hoffman+kunze is great

[silver herald]

^Agreed. Hoffman-Kunze are kind of like the canonical linear algebra text.

[loud cradle]

with the exception of one proof in the section on multilinear functions which is completely wrong

[fallow cypress]

wait which one xD

[novel obsidian]

I want to start learning number theory, and I came across borcherd's math 155 lectures on youtube, following niven, zuckerman and montgomery. Can anyone comment on how good a resource this is for a first pass on nt?

[sudden kindle]

What do you wanna learn in number theory

[novel obsidian]

I want to keep doors open, so if one day I decide to become an additive analytic number theorist then we'll be bueno

[sudden kindle]

Analytic -> Davenport 'Multiplicative Number Theory' (need to be comfortable with complex analysis)
Algebraic -> Marcus 'Number Fields' (need to be comfortable with abstract algebra, needs Galois theory for later chapters)

[novel obsidian]

is this after nzm?

[sudden kindle]

I don't know anything about additive number theory

[novel obsidian]

it was an example

[sudden kindle]

I never read NZM

Just started with Marcus

Already took Galois theory by then

[gray gazelle]

niven is good

[novel obsidian]

I don't have the background for those yet, maybe it'll be better to lay off the nt then

[gray gazelle]

probably the defacto standard for nt courses, for CS at least

[sudden kindle]

No thats not the message i intended to convey

Thats just the path I took to nt

Yours may be different

[solid wadi]

Hello! What can I read to understand mathematical theory of systems? Everyone says «systems», «systems» — I want a foundation to talk about this stuff.

[stray veldt]

its one of the standard elementary NT books

you cant go wrong with it

its a bit annoying, because there are (at least) two books with this name

[novel obsidian]

hm. Might just continue doing what I'm doing and later i'll revisit this

or i'll try nzm

i can't decide

i'll think about it tomorrow

[solid wadi]

Or else, explain to me why theory of systems is a pseudoscience and that I should study differential equations instead.

[loud cradle]

The lemma before theorem 7 in section 5.6 (page 170). The lemma is true but the proof is wrong if 2 is a zero divisor in K (the underlying ring). On page 144 there's a discussion where they carefully point out this issue, but then they seem to forget about it when they give the proof on page 170. 😁 Related MSE Q/A: https://math.stackexchange.com/questions/4197043/question-in-proof-of-lemma-before-theorem-7-of-section-5-6-of-hoffman-kunze-line

[narrow fiber]

Yeah they're fine

[gusty smelt]

lmao that list is something

[narrow fiber]

it rly is lol

[slender cargo]

"Lang's Algebra is more lucid than D&F" - I heard Lang is usually indecipherable to people who haven't learned abstract algebra

[gusty smelt]

yeah langs sections on group theory are like, laughably bad pedagogically (probably fine as reference though)

[narrow fiber]

even for reference I usually haven't had to check farther than Hungerford

[haughty vine]

bro no need to waste your time on khan academy, just spend some money for the good stuff

not free but mediocre

[orchid mountain]

Meanwhile Physicswallah laughing in the corner

[solemn rover]

you guys are so weird

who knows books by the first initials of their authors

H & K?

D & F

G a L

[remote sparrow]

G & L?

[still umbra]

Haha, this is how you know you've gone too far down the rabbit hole

[solemn rover]

get a life

[broken meadow]

DF and HK are common though

[delicate hemlock]

Yeah, it's a solid book

[sturdy shore]

the issue is this depends a lot on 1. what you know, 2. what those books are specifically

a book can be called "set theory" and either be introductory shit or the hardest book you'll ever glance at

[heady ember]

[sturdy shore]

no, I'm not committing myself to personalized help

but yeah, names of books reveal very little information beyond rough subject matter

need to know authors

how about uh

telling us your background first

most likely you'd only be able to tackle mathematical proofs or calculus if you don't know much math

if you are lacking in precalc knowledge, people either go towards khan academy or serge lang - basic mathematics

but you can also go through a proofs book, I assume it would be readable to you

but again, idk the author(s) so

[gray gazelle]

I think ill ask someone else thanks

[swift dome]

But is there any good proof book

[onyx wren]

yeah

Rudin is pretty good for intro to analysis

[heady ember]

[narrow fiber]

This isn't the most comprehensive resource for proofs but I like this one quite a lot https://deopurkar.github.io/teaching/algebra1/cheng.pdf

[broken meadow]

for proofs i took a course which used Hammack's book which was very small and to the point

[heady ember]

Loch has a summary of proofs pinned in #proofs-and-logic as well

[fallow cypress]

only the iconic ones

S & S

[sturdy shore]

stein shakarchi?

[remote sparrow]

#book-recommendations message

[crimson leaf]

Aren't those technically second or third initials though? Like Dummit's name is Richard M. Dummit so wouldn't the initials be R.M.D so D is third 🤔

[silver herald]

"Mathematical Systems Theory" tends to be name given to the study of Dynamical Systems and Control.

Honestly, if you have the background, Brin & Stuck's Dynamical Systems text is a common entry point

[hazy elk]

Just read "dynamics done with your bare hands" thank me later

Although it doesn't do the dynamics you need for control

[silver herald]

For Control from a Pure Math POV, Sontag is the standard

[mystic orbit]

LOL

omfg that's such a dumb statement

[gray gazelle]

[manic cairn]

I learned group theory from lang

[heady ember]

Username checks out

[grand thistle]

was it good tho

from a normal person perspective

not a sergelangfan pov

[foggy relic]

best method is reading Aluffi and doing exercises from Lang

[mystic orbit]

no

lang's graduate algebra is prolly the worst option for a first intro to algebra

it's literally mentioned in the preface that its target audience is graduates and lang expects the readers to have suitably covered some algebra in undergrad (or have read his book on algebra for undergrad)

the stupid thing is that it might actually be more lucid than D&F if it's you're second time covering its content

[mystic orbit]

I second this

[foggy relic]

+Borcherds lectures 🙂

[mystic orbit]

there are a million other options

thinking the most terse is the best for a first intro is idiotic

[mystic orbit]

[foggy relic]

based on Lang i think

[mystic orbit]

does borcherds have lectures on intro algebra?

[foggy relic]

yes

https://www.youtube.com/playlist?list=PL8yHsr3EFj51pjBvvCPipgAT3SYpIiIsJ

https://www.youtube.com/playlist?list=PL8yHsr3EFj53Zxu3iRGMYL_89GDMvdkgt

[mystic orbit]

oooo

[foggy relic]

also has commutative and homological algebraic series (what's the plural for this?) but I don't know if you would call that elementary or not

the great thing about lang is that each part is essentially a seperate book and the books are almost entirely self-contained

[mystic orbit]

those are at least introduced in a second course so prolly not very elementary

[mystic orbit]

yeah, he does mention that in the preface as well

@foggy relic do you think aluffi is enough to start tackling algebraic geometry?

(other than the pointset pre req ofc)

[foggy relic]

no clue, im definitely not someone you should ask for that

[mystic orbit]

why not? lel

[foggy relic]

because i dont know algebraic geometry

[mystic orbit]

I thought you were doing hartshorne, no?

[foggy relic]

nope

gave up+little time

ill try and come back to it later though

[mystic orbit]

I see

[foggy relic]

i wouldnt recommend aluffi alone though, the exercises are not very helpful lol

like alot of the time its just writing out stuff

[mystic orbit]

I know

a lot of them are just verifying the definitions

[foggy relic]

yup

[gray gazelle]

thoughts on this book?

[stray veldt]

interesting choice of cover

[molten mason]

1995 was a wild time

[gray gazelle]

the book is so thicc

[stray veldt]

wait

"the calculus 7"

i ... would suggest a more standard, modern book

[gray gazelle]

ye this is older than me

[gray gazelle]

like?

[stray veldt]

i am sure someone else can give a recommendation

spivak or something 🤷

[karmic thorn]

!calc when

There's also Paul's Online Math Notes

Khan Academy

[gray gazelle]

oh i use those already

[karmic thorn]

Thomas' Calculus (not free legally)

Math Libretexts

MIT OCW 18.01

OSU Ximera Calc 1

[heady ember]

Moth would shill Spivak too, probably

[gray gazelle]

okok ty////

[solid wadi]

Beautiful book!

[mystic orbit]

I second mit ocw

Especially if you're not used to books

[heady ember]

Hi DarQ

[mystic orbit]

Ello grass

[gray gazelle]

MIT OCW is a blessing ya

[mystic orbit]

Also, definitely check out 3b1b's essence of calculus

Tho that one is more of entertainment than a serious intro to the subject but it does a very good job of making a lot of stuff feel intuitive

[carmine cloud]

High-school math made understandable by Jeremy Martin ( you could probably find it on amazon)

[worn pecan]

learn intro analysis in high school

nowadays there are many books to do that

[remote sparrow]

jaime escalante used it, if you know who that is. legendary AP calc teacher in an inner-city neighborhood.

could very well have been dumbed down in later editions, though

[gray gazelle]

such as?

interesting route

[gray gazelle]

This book is amazing! It introduces limits straight with the epsilon-delta definition. That's so awesome

[solemn rover]

yes

I can't remember why I said first

idk

[calm pagoda]

is spivak calculus good for someone who never studied calculus before

[solemn rover]

It's probably doable, it's not necessarily overambitious, could be rough going.

Think of like, an "honors" calculus class in a college. Not necesssarily the best for everyone, but probably ok if you know what you're getting into

[calm pagoda]

maybe its more motivating to read when you already know what results youre working towards

from a high school class ?

[solemn rover]

Could be.

[calm pagoda]

just thikning for someone else

[solemn rover]

Hm I don't know. I took calculus for the first time in high school and then later in college, and I found college level calculus to be still somewhat challenging, I can imagine it would be more challenging without any prior knowledge of calculus and then doing it rigorously would be more challenging still. but on the other hand you never know, sometimes it's good to stretch a bit beyond your comfort zone

[calm pagoda]

I see what youre saying

i think you would have to be very ambitious

at which point youve probably already taken a calculus class

[remote sparrow]

ideally a university would teach it, but most schools do not begin with spivak's calculus. however, if you have absolutely no time pressure and average high school math prep, spivak is a good choice.

[heady ember]

Dami would suggest Schroder probably (for a friendly intro to real analysis)

[mystic orbit]

grass only suggests what other people suggest lel

[heady ember]

Me noob can't suggest anything myself

[mystic orbit]

how tf are you awake?

what kind of fucked up sleep schedule do you have?

[lapis sundial]

what is your local time lol

oh okay ouch

i was gonna say 4am isn't that bad but 5am

the fact i don't think it's that bad is evidence that my sleep schedule is also screwed

hope you uhhh will be okay

[narrow fiber]

my sleep schedule has been a mess

hoping that we're all able to get fulfilling rest soon lmao

I wish my sleep schedule was closer to this

[mystic orbit]

??????

mofo is nocturnal

[fallow cypress]

when do you sleep 😭

[gray gazelle]

this? with the german o?

who or what is dami?

or how

or why

[fallow cypress]

dami is one of the mods here, grass is talking about Bernd Schröder's book titled "Mathematical Analysis: A Concise Introduction"

for if you want to learn proof-based calculus

[heady ember]

Yeah

Congrats on the honorable eric!

[fallow cypress]

thank you!!!

[warm glen]

why can't all math books have covers this nice

[distant spear]

book recommendation for analysis on R^n?

[last spruce]

Anyone have any good math book recommendations that are not too heavy reads

[karmic thorn]

Spivak CoM? The take is more geometric but I think that's what anyone would also refer to as multivariable real analysis

There's also a two volume series by Duistermaat and Kolk

[karmic thorn]

Do you have any specific areas or interests in mind? And what mathematical background do you already have?

[last spruce]

Graduate level, algebra / number theory would be nice but willing to explore

[gray gazelle]

what are the prerequisites for studying pst?

(point set topology)
and what book would you recommend for a complete beginner

[mystic orbit]

literally nothing

[gray jungle]

Its hard to really define the prerequisites , just set theory is really all you "need" , but the ideas are rather abstract and one expects some " mathematical maturity"
Which is roughly speaking the ability to understand and work with mathematical definitions as well as manupilate sets ,functions and so on (as described in one pst syllabus).

[mystic orbit]

ig proof writing?

[mystic orbit]

hatcher's notes 100%

they're not too long and they're gonna be all you need for a loooong time

[mystic orbit]

not too heavy reads
graduate level

[last spruce]

I mean math books that I don’t have to sit with pencil and pad I guess

[mystic orbit]

also, I would imagine someone at the graduate level would at least be more particular in their interest than "algebra" and "number theory"

[hasty turret]

So you don't want to work out stuff?

[mystic orbit]

maybe ready about math history?

[last spruce]

Actually this is good thanks

[last spruce]

I mean he asked general area so

To be fair I have no idea what I’m doing

[gray jungle]

A classical book is munkres which is basically the bible of topology as my professor describes it (altho extreme)

I like simmons book but its a bit old school tbh

But if you just want the topology for other stuff (analysis /geo) then either hatcher or first chapter of bredon : Topology and geometry

[last spruce]

I can relate

[indigo mesa]

not necessarily tbh

i know several people about to graduate that are very vague about their interests

[mystic orbit]

[lapis sundial]

My interests are 12% and 27% depending on the kind of loan

[gray gazelle]

can i take a loan but with only 1% interest?

per annum

[dapper root]

Wtf

[gray gazelle]

Does anyone have textbook recommendations for the following topics:Further Differentiation and Integration Functions of Several Variables Linear Algebra Differential EquationsJust mainly want the practise questions and answer sheet tbh.

[mystic orbit]

???

a..

a year?

[distant spear]

[pseudo estuary]

any good books for IMO?

[mystic orbit]

the art and craft of problem solving

[gray gazelle]

also does this usually fall under calc 2 or 3

thoughts on Gallian for learning Field theory?

[fierce hedge]

Got these printed in Hardbound, the cover looks weird but the print quality is decent enough. Thanks @karmic thorn

[languid cypress]

Hey guys

What good books are there for differential equations?

[foggy relic]

You bonded them yourself?

[fierce hedge]

Nah, it's a company called Printster that prints and binds them

@foggy relic

[mystic orbit]

see #books-old or #books

[foggy relic]

Mfw cheaper to have Indian cousin buy and ship it to me than buy it legally

[fierce hedge]

It is what it is although I am surprised there isn't any service like that in US

[foggy relic]

There is lulu here

[fierce hedge]

I am guessing it is expensive @remote sparrow is it that?

[mystic orbit]

LOLLLLL

[foggy relic]

Not too bad, maybe $25 including shipping and all

The India one would be like $20

[karmic thorn]

Yeah they don't do a great job with covers, I think this is partly due to the fact that the source files are generally made for letter-sized page printing

[karmic thorn]

Since you later indicated an interest in math history, there's Mathematics and its History by Stillwell

For philosophy of math (which I believe is not actually comfortable to read ), there's Hamkins' Lectures on the Philosophy of Mathematics

[spare ridge]

lol

[night knot]

are you taking A-Level Further Mathematics??

[gray gazelle]

no this is a university level class

[night knot]

oh

and all of it is on just this one class?

[gray gazelle]

yes

[night knot]

I guess something like Kreyszig's Advanced Engineering Math would be a decent reference since it contains all you mention

[gray gazelle]

i'll look it up

[night knot]

There's also Mathematical Methods for Physics and Engineering by Riley, Hobson, and Bence

these two are fairly comprehensive and should cover what you need

[mystic orbit]

for a second I thought you guys were the same person monologuing lmfao

[night knot]

LOL

[karmic thorn]

See Apostol's calculus, volume 2

[gray gazelle]

thank you

[night knot]

no problem, hope they help!

[last spruce]

I’m going through Number theory: an approach from Hammurabi to Legendre by Andre Weil

[karmic thorn]

Interesting, let me know how it is!

[iron granite]

I need elementary combinatorics books which will prevent me from putting a pen through my eyehole.

[formal bronze]

What is it that you look for exactly? And what is elementary combinatorics?

[last spruce]

My class used the text by Brualdi iirc

[iron granite]

Books which will help me solve permutations and combinations problems.

[last spruce]

AoPS book if there is one is also probably good

[iron granite]

and not be filled with pointless bijections

[iron granite]

I'll look into that one

[last spruce]

Bijections are not pointless

[iron granite]

They are if you have an MCQ exam in 20 days.

[formal bronze]

What do you mean by pointless?

[iron granite]

They just want the result

[formal bronze]

JEE?

[iron granite]

Yup

[formal bronze]

Ah

[iron granite]

I'm banging my head against the wall and I'm not even making a dent

[formal bronze]

Are you done with past papers?

[iron granite]

I'm doing previous year questions alongside theory.

Does that count?

[formal bronze]

Those questions are the best representative of what you will see in the actual exam.

[formal bronze]

Also, I humbly urge that you do not rudely dismiss the usefulness of things that do not serve your narrow, immediate purpose. This is a math server.

[formal bronze]

I assume that it would.

[iron granite]

Jeez, okay. But you have to understand

It is discouraging to try and find books and have them be rigorous when I can't afford rigor.

I'd gladly read A Walk Through Combinatorics if it weren't for my deadlines.

[formal bronze]

We could discuss this on dm if you want to.

[iron granite]

Sure.

[near wagon]

Discrete Mathematics and its Applications isn’t bad. Solutions are in Quizlet also.

Also Probability for Enthusiastic Beginner has a chapter on Combinatorics.

[iron granite]

I'll check that one out

[swift dome]

#books-old and #books got some good stuff too

[remote sparrow]

lulu is cheap but apparently many pdfs are not up to its standards or "ready-to-print"

can't just drop them in and have them print for you

gotta fiddle around with stuff

if anyone knows how to make books lulu ready i would appreciate it

https://assets.lulu.com/media/guides/en/lulu-book-creation-guide.pdf

[night prairie]

Is it just me or does Hoffman Kunze get a bit confusing around section 2.6/2.7? There's just so much back and forth going on with the row/column stuff and it becomes hard to keep track of what exactly is going on. The theory is hard to fully follow at least index for index but the examples seem alright.

Should I be concerned or just keep reading and trying examples/problems until getting to chapter 3?

Any online videos or other resources that can help? It's about row spaces of matrices.

[loud cradle]

you could try gilbert strang's lectures, in particular look for the one involving the "four fundamental subspaces"

[sturdy shore]

it is a difficult book and will get more difficult, nobody said it's easy
I recommend looking into other books at the same time, always going to help seeing different perspectives

[loud cradle]

H&K is pretty dense in general (analogous to Baby Rudin for analysis), it's not unreasonable to expect to have to read some of the material multiple times for it to make sense

[sturdy shore]

and it's also normal to spend a lot of time on 1 page trying to parse the example, ^

[loud cradle]

btw, chapter 3 includes dual spaces... probably by the time you get there, you will look back fondly at how "easy" ch 2 was 😀

[night prairie]

I don't mind the abstraction for dual spaces (I think), it's just getting exhausting trying to keep track of all the indices, rows, columns lol

wondering if that will be an issue moving forward for later chapters

[sturdy shore]

yeah but you see getting comfortable with index shuffling and tracking is a very underrated skill

and yes you will see a lot of indices once you get to determinants

[loud cradle]

it does get more gnarly in some later chapters, particularly the ones with the determinant and multilinear algebra

there are a few confusing index typos here and there as well, just to keep you on your toes

[night prairie]

yeah I felt I had a good handle of everything all the theorem proofs, examples and problems up until the row space stuff around section 2.6

it just hit me out of nowhere

[sturdy shore]

I mean, the oddity is the former not the latter

[night prairie]

glad to hear, I just wanted to clear 3 pages an hour and I guess that's not realistic anymore

[sturdy shore]

hell no

[loud cradle]

oh double hell no

[sturdy shore]

some sections sure in general forget it

[night prairie]

yeah, I thought something was wrong with me, glad to hear this is a normal thing lol

[heady ember]

I don't remember the last time I cleared 3 pages of a math book in an hour

[night prairie]

3 pages an hour seemed fine until around page 57 or so

[loud cradle]

and surely not H&K, which is the hardest of the "basic" LA books

[sturdy shore]

there is the type of math book that is more chit chatty in which a faster pace is possible

h&k is not that

[loud cradle]

even LADR, which is considerably more chatty, the author tells you in the preface, if you're going faster than one page per hour you're going too fast

[sturdy shore]

have you seen linear algebra before?

if you haven't, that's very fast

[night prairie]

yeah I saw linear but don't have a good grasp of it, self studying using hk to learn it properly

[heady ember]

Oh yeah I saw that before lmao

[sturdy shore]

yeah so that's why right, you had some initial familiarity with LA which meant you were able to cover the initial sections in a faster pace

[night prairie]

yeah, I mean I have seen row space bla bla somewhere or another but no idea why it seems so hairy

don't recall seeing it like this

[sturdy shore]

well, a first course likely won't teach row spaces like h&k does

[loud cradle]

you might benefit from getting a second book with similar coverage, just to get a different exposition / approach.. you could try LADW which is a free download from the author

[heady ember]

Or pirate FIS

[night prairie]

would I be missing out on anything if I just watched GIlbert Strang's videos instead with pencil and paper? asking for a friend

[loud cradle]

i'm not sure i would advocate "instead" but it'd probably be a good supplement, at least for confusing topics

[hasty turret]

The HK section on determinants is very good imo

[loud cradle]

although i may be in the minority in finding strang a bit confusing, at least in his book "linear algebra and its applications", which is the only one i know.. his lectures might be clearer though

[night prairie]

yeah I think I'll check out all his videos and see if it helps, or just go through this row space stuff carefully

[hasty turret]

What's your goal exactly

[night prairie]

learn linear algebra I guess

actually understand it so I can be ready to handle linear algebra as presented in an algebra textbook

for Aluffi let's say

[hasty turret]

Just try to work out what HK actually means

[heady ember]

I guess im in a similar state, learning lin alg from FIS to read Jacobson's Basic Algebra I, and eventually, Lee's Introduction to Topological, and Smooth, Manifolds

[hasty turret]

It becomes clear when you try constructing some examples

[night prairie]

yeah I'll try that for simple examples

[sage python]

So we had to use this book in my undergrad analysis class

Like our prof would just assign a pset from chapter n and we'd have to read the associated section, along with our analysis pset

[hasty turret]

So, 2.6 is literally just "elementary row operations don't change the row space and if it were an RREF,it would be easier to describe"

[sage python]

When we got to dual spaces it was a bit tricky and one of my friends went to the prof's office hours asking about it

Well... we were taught about weak and weak* convergence in Banach spaces

[night prairie]

yeah I am wondering, do the specifics of 2.6 really matter later on or nah?

[sage python]

With linear algebra I'm team, understand everything tbh

[night prairie]

like I can read all the arguments and say yeah makes sense

I'm team? wot

[hasty turret]

Not really

[sage python]

It's not huge compared to some other sections but linear algebra is the most important topic in math imo

[hasty turret]

This is literally all the specifics you need. HK just writes this out

[novel obsidian]

Yes you would be missing out. Read the book @night prairie

[night prairie]

yeah, I am convinced of all that, Drake. I am just worried that I can't do the proofs myself

[sage python]

I'd say read through it and try to absorb the ideas contained within, such that later if you had to think about it you'd have some intuition about what to do

[night prairie]

yeah, I'll spend some more time on it, thanks guys

just have to be okay with having to go at a slower pace as needed

[novel obsidian]

Better to go at a slower pace than to not absorb the material

[loud cradle]

ha, is that also the class where they assigned some huge number of exercises for homework every week? like most of the problems in each chapter?

[sage python]

Yeah

[heady ember]

Did you manage to complete all your homework then

[sage python]

Lol no

[jagged panther]

what books are best for linear algebra?

[loud cradle]

there are some reviews in the pinned messages

[gray gazelle]

are you looking for theoretical or computational? a first or second course?

usually, a first course in linear algebra is computation-based

so if that's the case, I can recommend Introduction to Linear Algebra by Serge Lang

for a second course, Linear Algebra Done Right is a great text and is pretty much viewed as one of the best

however its treatment of determinants is pretty bad

[jagged panther]

oh ok thanks mate

[worn pecan]

i do abstract algebra since kindergarten

i do graph theory when 3 years old

but i study linear algebra at 15, and it's proof-based

[pure rune]

Can anyone recommend a dense complex analysis book? I've recently realised how useful those really dense books can be for refreshers if you're already familiar with the content, and I want something like that for complex analysis that I can flip through a few pages to cover everything important I've done in bachelors lmao.

[sturdy shore]

complex analysis books are pinned

[gray gazelle]

what are some books for introductory combinatoric?

books that lean on computer science is preferable

[gray gazelle]

Rudin?

[mystic orbit]

papa rudin

[dreamy matrix]

Can anyone recommend a book for me, (math used in cs)

[gray gazelle]

https://www.amazon.com/Discrete-Mathematics-Applications-Kenneth-author-dp-1260091996/dp/1260091996/ref=dp_ob_title_bk

@dreamy matrix

[dreamy matrix]

thanks man

[gray gazelle]

np

[dreamy matrix]

gonna read it through a pdf, since I can't be bothered waiting for it to arrive here

[gray gazelle]

😉

[pure rune]

Idk how I didn't think of rudin. It's pretty much exactly what I wanted cheers

[mystic orbit]

[pale kite]

Is there a book like this for analysis? (Encyclopedic breadth, not at an introductory level, lots of words, examples, problems)

[pure rune]

Rudin again?

[grand thistle]

amann and escher's 3 volume series i guess

for intro analysis*, it covers i think all the basics (i.e. stuff in baby and papa rudin), and has a lot of advanced topics like riemannian geometry and stuff i think

though i can only speak on the first volume

[pale kite]

oh, cool!!!

[grand thistle]

it's also pitched at a higher level, beginning with a lot of algebra stuff then going into the basic analysis theorems using a lot of topology and discussing banach spaces/ calculus on them pretty early on

[pale kite]

sounds perfect for me

[grand thistle]

yeah they're great books

i loved volume 1

[pale kite]

The pinned says Conway is like the dummit and foote for complex analysis, so I guess there's a rec there

[grand thistle]

no idea abt that, havent done much complex analysis at all myself

[oblique gust]

Yo anybody here has the a pdf of the algebra and geometry problem books for the training of the USA national imo team?

[night prairie]

this makes me so mad how clear it becomes when writing examples... why couldn't HK just give useful suggestions instead of relatively less useful text just taking up space

[whole cove]

any recs for

two things actually

1. mathematical logic

2. theory of computation

i lied its 3

3. programming language theory

[pale kite]

I am going to provide a recommendation - if you have not taken point set topology, but you're interested in algebra, a good motivation is to try and understand the Zariski topology.

[tawny copper]

Check the pinned comment of Diligent Clerk

[whole cove]

cheers

[night knot]

Introduction to the Theory of Computation by Michael Sipser

[night knot]

Types and Programming Languages by Benjamin Pierce
Structure and Interpretation of Computer Programs by Abelson and Sussman

[fervent mist]

Hi, hope you are having a happy new year, I want to ask which book or videos can you recommend me to study Affine space of n dimension, conics on the Affine space, Erlangen program :')

[karmic thorn]

I think the first two are addressed in Shaferavich's Linear Algebra and Geometry, I don't have a recommendation for Erlangen program though

Found this from a Math Stackexchange thread: https://bookstore.ams.org/view?ProductCode=STML/81

[worn pecan]

papa rudin is real analysis and the application of real analysis in complex analysis

[mystic orbit]

no, real analysis is baby rudin

papa rudin is complex analysis

[worn pecan]

in my country, measure theory and lebesgue integral count as undergraduate real analysis

baby rudin is "mathematical analysis"

[grand thistle]

no papa rudin begins with real analysis and measure theory then uses those to transition into complex analysis im pretty sure

it has both

[mystic orbit]

ah

I see

[worn pecan]

the complex analysis in papa rudin is not enough

you need another references

[mystic orbit]

I'm tempted to take a look

[grand thistle]

you should then

i have it on my desk rn

[mystic orbit]

no fucking way

you gonna do it?

[gray jungle]

Rca starts veeeery weirdly , immediately defines measurable functions before briefly discussing measures and then jumps into integration theory.
The proofs are really compact, this books feels more like a handy reference.

[lost nacelle]

@river holly https://craftinginterpreters.com/
would you find this interesting?

[river holly]

I have never found a book interesting.

[lost nacelle]

need to find better books

[river holly]

yeah well I’ve been given the best books according to people here

I need something to physically do in order to get investing in a thing.

[lost nacelle]

the books does have instructions to make your own programming language

maybe will like

[remote sparrow]

#book-recommendations message

[remote sparrow]

A Walk Through Combinatorics by Miklos Bona is one good choice

[remote sparrow]

https://4chan-science.fandom.com/wiki//sci/_Wiki

look through the computer science section

[lime sapphire]

books are overrated

people should start asking for which lecture notes are the best

[cursive orbit]

I mean a good reason one would prefer books is the presence of exercises

those are more useful that the content itself

[lime sapphire]

i was half sarcastic there lol

but yea i mean usually when you can find lecture notes online you can also find the course they were accompanying

[mystic orbit]

4chan-science

[sterile harness]

what’s the best book for intro abstract algebra

[remote sparrow]

pinter or judson are pretty good

[sterile harness]

I’ve seen “Dummit and Foote” a lot in this channel

Is that more advanced

[hasty turret]

The first half is pretty approachable

[sterile harness]

as an intro?

[hasty turret]

Yes

[sterile harness]

would you recommend the books sour drop recommended or should i get dummit and foote

[hasty turret]

I have done only DnF

And Aluffi

So can't say

[sterile harness]

alr

thx

[mystic orbit]

aluffi

[remote sparrow]

pinter and judson are both available as cheap paperbacks. judson is also legally free online

[foggy relic]

Good books are Jacobson, Lang, Artin

DnF makes u sleep

[mossy flume]

Can confirm

DnF was super super dry

I wonder what we'll use in my algebra class next sem

[sage kelp]

The Way of Analysis. Im actually going to go through it this year

[turbid mural]

i want to learn everything on differential geometry

[remote sparrow]

maybe spivak's five-volume series on differential geometry could work?

may not be everything but it sounds like a lot

[turbid mural]

alr

[remote sparrow]

although the simplest starting points would be do carmo or tapp's Differential Geometry of Curves and Surfaces (different authors, same title)

they are introductory undergrad treatments

i don't know anything much beyond that

spivak iirc is for advanced undergraduates or graduate

[sturdy shore]

you did not answer what your background is, which is by far the more important part of the question

[hollow peak]

I don't really like do carmo's geometry of curves and surfaces

I think you're better off just starting with smooth manifold theory and then learning general riemannian geometry

he spends a lot of time talking about "regular surfaces" which are really just immersions of two-dimensional manifolds iirc

this is much more motivated if you actually do manifold theory first to understand why we care about this setting specifically

(I recommend Tu's intro to manifolds, then either do carmo riemannian geo or lee's IRM if you're very comfortable with bundles)

alternatively Tu's differential geometry is a good prep for IRM

[swift dome]

[fast tangle]

does anybody know any calculus books that are actual books and not textbooks?

[hearty steppe]

Spivak? Apostol?

[karmic thorn]

What do you mean by actual books and not textbooks?

Are you looking for a monograph that has no exercises?

[fast tangle]

yes i think so

[hearty steppe]

You should just do real analysis

[dapper root]

Lol

[hearty steppe]

I mean I love it and I’m not even good at the problems

[fast tangle]

what is that sorry💀

[hearty steppe]

Give Schroder’s mathematical analysis a concise introduction a shot.

It’s not as terse as rudin and is friendlier than Apostol

I mean I really like baby rudin. I’m probably going to go back to it one day

I only did the first chapter and half the exercises 😂

Oh man those exercises are really hard too and they pick your brain

[dapper root]

This seems

Like it has absolutely no relevance to what they were asking for

[hearty steppe]

I assumed he didn’t want a standard textbook and wanted to learn the meat of calculus

[fast tangle]

it seems really cool and interesting thank you

ill look into it

[hearty steppe]

But I mean standard pure math textbook it is, instead of one of those university calculus class textbooks

Spivak might be a bit harder to read but Apostol calculus you should still check out I think

I liked what I saw in it at least

[karmic thorn]

So... what exactly are you looking for in a book like that? Definitions, theorems, proofs and some examples?

Plus history and references for further reading?

[fast tangle]

I mostly just want a book that’ll teach me calc in a concise way

[karmic thorn]

Why avoid a textbook, then?

I can understand if you'd like a concise textbook, one that doesn't have dozens of repetitive problems

But learning calculus will inevitably involve solving problems on your own

[fast tangle]

I wanna be able to read it on the train or just something like that

[novel obsidian]

you're not going to learn then

[fast tangle]

I was thinking I could practice on my own time

[karmic thorn]

That's not how math can be learnt, unfortunately

[swift dome]

You wanna read instead of solving

[fast tangle]

I did it with probability so I wanted to try it out with calculus

[karmic thorn]

If you do intend to write down and solve problems, use a textbook (there are many). Even more concise are lecture notes and problem sets combinations that several universities have on their websites.

You can check out MIT OCW 18.01 for instance

[swift dome]

https://archive.org/details/DemidovichEtAlProblemsInMathematicalAnalysisMir1970

[fast tangle]

Ooo okay thank you for the advice and recommendations I appreciate it

[terse echo]

do most books have solutions?

i cant find solutions to mine

[karmic thorn]

Uncommon for undergrad and beyond textbooks to contain solutions

At most they'll have solutions/hints to even/odd numbered exercises

And even that fades away

[gray gazelle]

where can i find the most difficult problems for conic sections aka coordinate geometry? (aside from imo stuff, i want problems in ellipse, hyperbola etc imo stuff doesnt have any problems relating to that) not sure if this qualifies as book rec

[lime sapphire]

lmao

[gray gazelle]

what

[lime sapphire]

its just a funny idea thinking of conic sections at IMO level

[gray gazelle]

😔 ik but

some very difficult problem sources

do you know any

[lime sapphire]

you most likely won't find much

[gray gazelle]

you can surely make conic sections at imo level (atleast i made 2 probs that are very difficult)

[gray gazelle]

hmm, atleast somewhat difficult problem sources?

do you know any

[lime sapphire]

maybe apendix 2 of spivak's calculus

[gray gazelle]

i want some practice but my present sources are just too damn easy

thats not difficult

and it doesnt really have much

[karmic thorn]

Does AoPS not have anything on it

[gray gazelle]

more of explanation

[gray gazelle]

Some problems scattered here and there

often varying greatly in difficulty and more of (oly) geometry problems from what i have seen

[karmic thorn]

Oh okay, so you're not looking for things from an olympiad perspective?

[lime sapphire]

maybe try past papers from the korean high school curriculum, iirc its filled with conics

[karmic thorn]

https://arxiv.org/pdf/1111.6521.pdf

See if this fits what you're looking for

[gray gazelle]

lemme, thanks!

[gray gazelle]

oh

thanks for this too

you know where i can find them? @lime sapphire on google?

[lime sapphire]

yh i think google will get you something

[gray gazelle]

russian book, highly likely 💀 thanks a lot

[lime sapphire]

worth a try

[gray gazelle]

alright

💀

[gray gazelle]

no problems 🙁

[karmic thorn]

Create problems by proving the main theorems yourself

[gray gazelle]

i've already done that

just got a lot of time for conic sections, thought if there was something i could practice

apparently there isnt so nevermind i guess

thanks tho

[karmic thorn]

There's a book called Geometry by Coxeter

Maybe Introduction to Geometry

I don't remember the exact title

[gray gazelle]

i know of that book

[lime sapphire]

why are you looking for material on conic sections anyway?

[karmic thorn]

I don't think there's more to the theory of conic sections

[gray gazelle]

jee 💀

[lime sapphire]

bruh

[karmic thorn]

If you find geometry interesting you should move on to more interesting topics

Oh JEE

[gray gazelle]

actually i dont do olympiads anymore so

I did a year ago and like maths a lot (and tough probs)

[karmic thorn]

Well any of the usual JEE coordinate geo books may have more than enough already

[lime sapphire]

just keep doing practice problems from jee prep books; if you're looking for more interesting maths its not going to be part of jee prep

[gray gazelle]

but they easy, for algebra, combinatorics, calculus there is a ton of hard material

[gray gazelle]

hmm will just ask my teacher for some probs ig

[karmic thorn]

I'm not sure if there's a lot of room to complicate it without introducing more advanced ideas and tools

[gray gazelle]

not a lot of room but can be done anyways

[lime sapphire]

like for the sake of purely doing harder problems just do something other than JEE
iirc CMI entrance test problems are p good

[gray gazelle]

hmm yeah, CMI entrance test is pretty good ISI too

[crisp idol]

Platypus police squad

[gray gazelle]

Anyone has a good online class/lectures that goes through most of Discrete Math by K. Rosen ?

[lime sapphire]

You could try STEP maths questions on conics @Stotram#9095

[crimson leaf]

They left the server

[lime sapphire]

Lol

[mental canyon]

any books for questions regarding complex numbers

[empty matrix]

jee

[lofty gale]

sure

[oblique acorn]

Hi everyone, I'm looking for a book about basic geometry. Which book would you recommend me?

[sudden kindle]

Geometry by David Esplen Gray

[granite viper]

Synthetic geometry?

[oblique acorn]

I think so. Im from Argentina, and I know it as basic geometry. It is the first geometry that we all learn in high school.

[granite viper]

Why not just follow the schools course

It's almost always better to start coordinate geometry then

[oblique acorn]

Im not in high school. I want to relearn some thing that didn't teach us well in my school, now that I have free time

[remote sparrow]

try kiselev's geometry volumes

[fleet void]

recommend the book Simplified Mathematics?

[granite viper]

Maybe try proving some things in Euclid's elements?

Unless you're looking to apply

[hollow shore]

need some recommendations on a good and comprehensive problem book of olympiad problems with solutions

if anyone knows any good books matching the above description, ping me :3

[swift dome]

Which topics you interested in ?

[hollow shore]

standard olympiad topics like algebra, number theory, combinatorics, functional equations, etc

[narrow fiber]

Anyone have suggestions around good books on general relativity from a mathematical perspective? My Riemannian geometry is solid and I'm curious if anyone here has strong feelings for/against certain resources since I've come across a few decently-recommended ones

[digital eagle]

Oh my god, it is songwriter and Radiohead frontman Thom Yorke

[tawny copper]

Stefan Lozanovski or Evan Chen. You can also read Agricola

[tawny copper]

you should visit the mathematical olympiads discord server (linked in #competition-math, there you will find a lot of resources). Recently I found a book of combinatorics by Soberon which is so nice. For inequalities, I also really like the one by Kim Hung. For functional equations, I like the notes of Vaderlind and of Evan Chen. There's also a book by Small.

In general, there are many good resources. In that discord server you will find more

uh you already there haha, I thought you would find there what you needed

[swift dome]

Any good resource for Combinatorics

[heady ember]

At what level?

[swift dome]

undergrad

[fickle granite]

Has anyone read Halmos's Finite-dimensional Vector Spaces book? I'm coming from linear algebra self-taught from Apostol, and wanted to see if this book is any good to review/expand what I know right now

[solemn rover]

not really what you asked but there's a youtube series on symplectic geometry in classical mechanics you might like https://www.youtube.com/watch?v=pXGTevGJ01o

I have heard "Geometry Topology and Physics" by Nakahara is good, although I have no idea if it covers special relativity

[sturdy shore]

a review is pinned, great book but very particular so I'd pair it with a more "traditional" LA book

[fickle granite]

Thank you

[gray gazelle]

hey

does anyone know a good book to learn the basics of fourier analysis?

[sudden kindle]

Stein and Shakarchi

[gray gazelle]

thanks!

[lime sapphire]

what r the prereqs for this if i may ask

[solemn rover]

it's a graduate level textbook but it's pretty easy to read for a graduate level textbook

You should know like, basic analysis and be comfortable with epsilon delta stuff probably. But you don't need to have a lot of analysis experience

[mental canyon]

any books for questions regarding complex numbers
NEW

Stotram
jee

[remote sparrow]

A Walk Through Combinatorics by Miklos Bona

[gray gazelle]

any recs for category theory that aren't Mac Lane or Awodey? i.e. an undergrad level text

[fallow cypress]

probably just being familiar with the definition of infimum, supremum, limit, derivative, riemann integral, etc.; some facts about sequences of functions (pointwise vs uniform convergence)

so the contents of a first-semester analysis class

[cursive orbit]

riehl?

[fallow cypress]

I've also been recommended riehl's book

[gray gazelle]

what would the prerequisites be?

[fallow cypress]

I've heard it has minimal prerequisites theoretically, but to understand why it's useful, you should take probably a year of abstract algebra

[remote sparrow]

try The Joy of Abstraction: An Exploration of Math, Category Theory, and Life by Eugenia Cheng

https://www.amazon.com/Joy-Abstraction-Exploration-Category-Theory/dp/1108477224

the reviews seemed favorable anyhow

[smoky zephyr]

mathematics of mathematics

[lean pagoda]

Goldblatt is pretty lucid, though it's not really a replacement for a traditional CT text (i.e. one not focused on Toposes)

[solemn rover]

Awodey is undergrad level imo

Have you tried it?

The Eugenia Cheng book is a pop math book you would buy in the airport if you had a long flight. it's not a textbook

Tom Leinster has an introductory category theory book

So does Samson Abramsky

[gray gazelle]

There are no prerequisites in theory, but you should probably be familiar to Algebra

[crimson leaf]

The authors state familiarity with the Riemann integral so first course in analysis topics

[honest lance]

any differential equation book online? will take this semester

[gray gazelle]

adkins

probably will go deeper than what you need though

can you show us the syllabus for your module?

[atomic hound]

Good book on euclidean geometry plane?

[tender cedar]

hello guys

anyone here familiar with machine learning

I wanted to ask about the book called Mathematics for Machine Learning

what do you guys think of it

[glacial crypt]

decent, an ml server im in recommends it a lot

[subtle mango]

iirc, @glad prairie said that Evans PDE is a more “classical” approach to PDEs — would it be better to read something like Brezis for PDEs then?

though i’m not sure what makes the evans approach “classical” (i havent really read it yet)

[glad prairie]

Evans still offers an important set of tools that need to be learned by someone who wants to do pdes. Brezis is fine too, but idk about learning brezis "for pdes"

The point is that evans does not go into the really heavy functional analysis side of PDEs involving distribution theory and hefty harmonic analysis

A lot of his proofs are more "raw" and "hands on", avoiding toolkits that hide some of the nasty analysis (that still happens, but with it's hidden a little better i'd say)

[karmic thorn]

What all does Evans assume in the way of background

[glad prairie]

Mostly just linear algebra, real analysis, a little ODEs, and multivariable calculus for chapters 1-4. For chapters 5-end, some basic functional analysis and measure theory is assumed

But stuff you could learn on the way

Chapter 5 is when the book switches from "really classical pdes" to "sorta modern pdes" (in the sense of using functional analysis)

[subtle mango]

gotcha ty

so evans to brezis is a decent path?

[glad prairie]

Sure

Or like

Ch 1-4 of evans, brezis, ch5-end of evans. The two halves of Evans are like different books

Whatever you want to do tbh

Evans is fairly standalone aside from those prereqs

[remote sparrow]

william trench's book is legally available for free online. there are two versions iirc: one with and one without boundary value problems.

[slim gate]

hey guys any good resources that focus on functions and limits?

i really need to learn this concept

[merry sphinx]

anyone know any good real analysis exercise books?

[gray jungle]

rudin has cool exercises

[misty geyser]

Hi, don't suppose anyone knows any good books for pre-A-level, or A-Level maths for those GCSE level but willing to learn?

[gray gazelle]

???

[fallow cypress]

yeah rudin has good exercises for real analysis

[novel obsidian]

Use Khanacademy. It's what I did

[sage kelp]

Any thoughts on Mathematical Analysis by Canuto?

[sharp timber]

Hall and Knight is good too

[remote sparrow]

https://4chan-science.fandom.com/wiki//sci/_Wiki

look in mathematics > problem books

[merry sphinx]

thanks!

[heady ember]

You could probably find free example sheets on Cambridge's website

[tawdry orbit]

If somebody’s wanted to learn mathematics from the ground up, what are some rigorous books to accomplish this? I’m currently doing Book of Proofs by Hammack, what would be the next logical step?

[crimson leaf]

Probably a linear algebra book like the ones in the pins

Then analysis, abstract algebra, and topology would be some standard topics following that not necessarily in that order though

[frosty yarrow]

starts at pre alg, ends at topology

[gray gazelle]

keep doing it, it's quite an amazing book

[blazing parcel]

I asked this several times but nobody answered. Is Joy of X by Steven Strogatz good?

[warped wave]

Hi can anyone recommend me a good Linear Algebra book for mathematicians? I thought Strang's was good, but people said the contents were rather more computation-based as he puts main focus on matrices instead of abstract and rigorous mathematics. Is this right, or is it wrong and I should find a better book than Strang's?

[crimson leaf]

Check the pins

[gray gazelle]

LADR - Linear Algebra Done Right

has an emphasis on abstract mathematical proofs rather than computational LA

it's the industry standard for a second course in LA

[gray gazelle]

the treatment of determinants is often criticised though

[silver herald]

Strang is kinda meh and has very computational matrix-y focus. I personally find something like Hoffman-Kunze or FIS to be much better (LADR is good until it starts eigenvalues and determinants; those are treated much worse than even Strang IMO)

[warped wave]

So is it a good idea to start with LADR then switch books when it goes into determinants and eigenvectors?

[gray gazelle]

yes

but expect to struggle if you haven't done proof-based linear algebra before

[silver herald]

Disclaimer - I think starting with row elimination is kinda eh and find a geometrical flavour of linear transforms to be much nicer

[grand thistle]

Morton curtis is good imo

it also covers determinants earlier unlike axler

it's going to be difficult if you arent acquainted with proofs though

[gray gazelle]

well Axler's whole doctrine is that linear algebra shouldn't rely solely on determinants - he even has a paper written where he builds up the entirety of LA without determinants

[silver herald]

Honestly, if one has seen couple of basic proof by contradiction and proof by induction before - it shouldn't be that hard.

[grand thistle]

right but again it also presents stuff in a way that might seem more advanced compared to i.e. strang, like it defines groups, fields and their characteristic and other algebraic stuff even before it gets to defining a vector space

[karmic thorn]

The no-determinant approach seems to be very bizarre because you literally don't learn how to actually compute eigenvalues after reading an entire chapter devoted to them... which is not ideal

I like his presentation of other material though

The definitions, theorems, proofs are all very neatly organized

And the exercises are very nice

[silver herald]

Also, determinants does hold meaning beyond just computations and has useful connections to say - calculus on R^n

[silver herald]

True. For a person first time reading a proof based math book, it does take time to get used to parsing through the book to find a way to digest information (Then again, most math students starting with anal. and algebra/linear algebra do face this as well)

[karmic thorn]

I agree

Axler is correct in that the usual treatment of determinants in a linear algebra class is abysmal

But the answer is not to run away from it

Lax treats determinants in his book on linear algebra very well

Where he pushes the geometry to the fore

And the properties fall out nicely

[whole cove]

metric space question book/source anywhere?

[vital bane]

doom is that you

[silver herald]

Yes

[vital bane]

Lol I never see you on the math server

@gray gazelle ask for a book like that here

[gray gazelle]

very very very very difficult calculus problems book

just added a few more very

just to be sure

[karmic thorn]

What is "calculus" for you? Are problem books on mathematical analysis on the table?

[karmic thorn]

There's a book by Searcold, another very old book by Copson

A set of lecture notes mixing some pointset topology and metric spaces by T.W. Koerner

https://www.dpmms.cam.ac.uk/~twk/Top.pdf

Also, plenty of standard textbooks on real analysis go through it

See chapter 2 of Pugh's Real Mathematical Analysis, or Rudin's Principles of Mathematical Analysis

[gray gazelle]

calculus 3

123

[shadow tusk]

try this out https://github.com/ossu/math

[karmic thorn]

Hmm, see Demidovich's Problems in Mathematical Analysis (despite the title, I think the material is closer to the spirit of standard calculus courses)

[gray gazelle]

by hard i mean cheap tricks and manipulations are fine

[gray gazelle]

whats a good book for a first course in analysis

[mossy flume]

I liked Rosenlicht

[gray gazelle]

i self taught myself some analysis some time ago but ive forgotten most of it by now

[mossy flume]

Used that for my analysis class this past fall

[gray gazelle]

so i wanna refresh my memory a little bit

[gray gazelle]

oo ill give it a try

thanks!

[mossy flume]

Good explanations and the problems are nice

[gray gazelle]

oh sweet

[wild fern]

Has anybody read this book? I'm writing an essay on this and was wondering if it's worthwhile reading it. I am hoping for a foundational knowledge on ZFC and Gödels Theorem's so that I am able to apply them to something more specific myself rather than just providing already existing proofs and what not (a requirement for the essay)

[warped wave]

I know I already asked earlier, sorry to ask again, I'm just trying to plan out what books to read and their prerequisites during my free time for this semester.

1. What are the prerequisites for introduction to real analysis (i.e. Baby Rudin/Bartle and the kind)? I have taken Calculus I and will be taking Calculus II and III this semester.

2. Should I already be able to do Spivak's problems before jumping into real analysis i.e. must I read Spivak before doing introductory real analysis (because frankly I have only been learning from Thomas' and Stewart's Calculus)? I just don't want to start reading a book only to find myself not having the right foundations and stopping midway.

[crimson leaf]

You really only need knowledge of proofs. Spivak helps but it might be more beneficial to just do analysis. It will be hard and you may feel like you're not going anywhere or that you can't do it but you have to push through that for a gentle introduction I recommend Schroeder or Tao though

[sage kelp]

Dude! This is beyond amazing!

[icy knot]

Yeah I have it, great book.

[twin ridge]

Hello guys. I'm an actuary currently working at a media agency and was ask to take on various projects concerning MMM, Atribution models, etc. From what I know this is basically Econometrics, but I was wondering if there were already books that tackles these models from Marketing lens. Any suggestion? Any source of information would be of much help.

[sturdy shore]

I don't think any of the actual content here is bad (that I've looked at), but man what a terrible way to describe analysis

[shadow tusk]

why is it terrible?

[sturdy shore]

analysis is not the "mathematics of mathematics"

that is metamathematics, a field which is far away from analysis as far as math fields go

analysis (specially real) is just rigorous calculus

ofc not a perfect description of the field but as good as you are gonna get when you are describing it to a layman

[shadow tusk]

put the original description to chatgpt and asking it to fix it, how does this sound?

"Intro to Analysis is a course that builds on the concepts of Calculus and provides a rigorous and formalized study of the foundations of Calculus. This course will cover advanced mathematical concepts and will use formal proofs to establish mathematical results. Starting by proving the existence of real numbers, this course will take a foundational approach and will build the foundation of single-variable Calculus from scratch."

[sturdy shore]

sure, seems like a chatgpt W to me

[shadow tusk]

tbf, their other curriculums aren't as polished as their computer science one and it's encouraged to make a contribution

[slender cargo]

I feel like there's a ton of opinions on how to approach math education

[bright swallow]

if someone hasn't put it here yet, Algebra Unplugged by Kenn Andahl and Jim Loats, Ph.D is an awesome book and totally changed my life

[slender cargo]

people will likely feel more comfortable just recommending books than a one-size-fits-all approach

[shadow tusk]

what about this? "Analysis is the mathematics of limits and functions. Intro to Analysis is a course that builds on the concepts of Calculus and provides a rigorous and formalized study of the foundations of Calculus. This course will use formal proofs to establish mathematical results, starting by proving the existence of real numbers and building the foundation of single-variable Calculus from scratch."

changed it since it follows the pattern of their other descriptions

[devout fossil]

Hi, I'm looking for supplemental resources for self-studying Amann and Escher's analysis book. I wasn't able to find any solution manuals or lecture notes online

[sturdy shore]

"mathematics of limits" is okay but of functions is innacurate. That's all of math.

you can say sequences and limits, maybe

[sturdy shore]

what kind of resource are you looking for? you may look up solutions to individual questions on stackexchange, probably as good as you are gonna get

or ask here, of course

[shadow tusk]

alright

[devout fossil]

maybe other books to supplement my understanding

would be nice if there were lecture notes, but none seem to be available

[sturdy shore]

if you were to find any lecture notes on amann escher, they'd probably be german
I'm not sure if they've ever been used in a course in english

[sturdy shore]

if you don't have much previous exposure to algebra, it would do you good to have books on linear algebra and abstract algebra on the side

some recommendations are pinned

in particular, knapp has books on both analysis and algebra that you could take a look at

[devout fossil]

alright, thanks for the reccomendation

I've also heard it's probably better to skip a portion of the first chapter?

not sure how soon I would need abstract algebra

[sturdy shore]

you need it within like the first 5 pages lol

it's impossible to skip the first chapter, amann escher is pretty hardcore

iirc by chapter 2.3 you learn what a banach space is

and chapter 2.2 has the phrases "algebra homomorphism" and "ideal"

[grand thistle]

tbf you can kinda skip the hardcore algebra stuff

i skipped it and i was fine

i just skimmed chapter 1

never really saw the word ‘ideal’

[sturdy shore]

seems like you also skimmed chapter 2, then!

[grand thistle]

but knowing some analysis before and some metric space theory really helps

[grand thistle]

wait when does it start actually doing analysis?

[sturdy shore]

chapter 2

[grand thistle]

because yeah i did skim all the parts that aren’t analysis

and like half the analysis parts

since i did baby rudin before

[grand thistle]

yeah but if i recall correctly it didn’t come out that much

[sturdy shore]

polynomials come up a lot, though, which is part of the ring chapter

so all I'm saying is skipping chapter 1 will probably hurt more than help

but it is fine if you don't understand everything about groups/rings/fields perfectly of course

which is why I recommend doing algebra on the side

[grand thistle]

yeah it refers to the ring of formal power series quite a lot

[devout fossil]

any idea how I would go about finding german lecture notes for amann?

might wanna google translate them and see if they're any use

[sturdy shore]

would have to ask a german individual for that

[gray gazelle]

can anyone express their thoughts on the contents of this book, or, alternatively, if they have read it, provide any thoughts? https://www.amazon.co.uk/All-Mathematics-You-Missed-Graduate/dp/0521797071

here are the topics

[frosty yarrow]

Hey, has anyone used shepley Ross (iirc the name) for DEs? If so, how'd it go?

[remote sparrow]

math sorcerer has some videos about this book

a friend of mine owns it and they like it

it's supposed to be a way to get the gist of some big ideas in various fields of math

it also lists references for further reading

[gray gazelle]

gotcha. thanks

[lament crater]

Does anyone have a recommendations on topology readings after Bert Mendelson's Introduction to Topology?

Not really looking for anything in particular. I just want a wider scope on the subject.

[sudden kindle]

nice picture

[gray gazelle]

Munkres, or Morris

[oblique dove]

thanks

[sullen spruce]

book suggestions for ioqm?

IOQM is an indian Olympiad qualifier in mathematics, one of the most competitive mathematics exams.

Syllabus:

Permutations and combination
Trigonometric Functions
Finite series and complex numbers
Sequence & Series
Mathematical Reasoning
Quadratic equations and expressions
Probability theory
Number theory
Factorization of polynomial

[pine merlin]

Hey, I'm a 16 year old student. This is off topic. Could someone please guide me as to how I can learn mathematics from scratch to the college level?

[foggy relic]

What do you know so far? If functionally none, Khan Academy and Lang's Basic Mathematics are a good start

[lament crater]

Is Murkres that good. Seem to have seen a lot of it. And how does Morris differ?

[oblique dove]

aops books

how much do you already know

[hollow shore]

the art and craft of problem solving by paul zeitz is a pretty solid resource for this

[final wasp]

can i get a recommendation for like drawing and stuff?

someone pls i want to get better at drawing 😭

[karmic thorn]

This is probably not the most useful place to ask about that

[split bluff]

@pine merlin precalc, calculus, read a book of proof then study some real analysis and that should be a good base for learning more advanced topics

[karmic thorn]

Maybe a dedicated art Discord will have better inputs

[split bluff]

All that i've mentioned can take you about 2 years if you have little experience, so, don't worry about a more extensive path

[final wasp]

there are like none.. 😭

oh well back to looking

[karmic thorn]

Maybe Reddit/YouTube channels and their communities

Also see if you can find dedicated blogs/websites

[sullen spruce]

I know trigonometry, sequences and series, quadratic and probability. acc to my research number theory has comparitvely more weightage

[sullen spruce]

"geometry for Americans" damn nice topic name

[heady ember]

Isn't blender considered one, for example

I heard some people do art projects there

[oblique dove]

hmm

first check out the MODS discord

they have good resources and more qualified people to answe question

[shadow tusk]

https://github.com/ossu/math, but since you wanna learn from scratch, check this out first https://github.com/ossu/math/blob/master/FAQ.md#how-can-i-review-the-math-prerequisites

[gray jungle]

Simmons topology and modern analysis is pretty cool but its a bit old school

[narrow fiber]

Are you still looking for largely point-set? or algebraic as well

[copper radish]

Hi, I need a recommendation on a good book for doing time series analysis (in particular correlation & relationships between different time-series). Any suggestions?

[misty geyser]

Any good book recommendations for a complete beginners introduction to analysis? Thank you!

[steep oak]

Real analysis, or analysis on metric spaces?

[misty geyser]

Preferably Real, but suggestions for the other welcome if possible :), thanks

[steep oak]

Bartle and Sherbert's Introduction to Real Analysis

I was taught from here

I quite like it

[misty geyser]

That's great, thanks so much!

[copper radish]

Do people like the Understanding Analysis book by Abbott?

I have it and got through the first chapter or two. Good & complicated for someone like me with casual interest in the subject.

[remote sparrow]

yes, people like it

[narrow fiber]

I think it's good

It jumps off of not much more than familiarity with calculus

[sage kelp]

Basic Analysis I by Lebl, and it’s actually free. I will go through it this year if you want to chat or something

[gray gazelle]

How's Douglas B West's book on graph theory ?

[warm sparrow]

Good number theory book recs pls

[gray gazelle]

David Burton, Joseph H silverman

Imo

I like silvermans approach a lot

[warm sparrow]

yeah i am doing david burton rn

thanks for the silverman rec tho

[gray gazelle]

David Burton's is a good elementary text too

If you're in Indian subcontinent

You can get cheap SEA version of silvermans book

[gray gazelle]

Anyone ?

[heady ember]

Just wait, its only been ~10 mins

[warm sparrow]

CBSE or olympiad?

[gray gazelle]

Ok

[warm sparrow]

rd and rs are more than enough

mtg foundation series if you wanna do some harder sums

[lament crater]

Old school?

[lament crater]

Also including Algebraic. I generally I want to be able to read most topology related papers

[narrow fiber]

I think if you're solid with your point-set it's worth moving to Hatcher's book then

[gray gazelle]

is it your first time giving the exam

i gave it last year

it was damn hard . i studied few topic from mtg, iit foundation and rd sharma and the rest from FIITIJEE material

[misty geyser]

Just wondering, any good book recommendations for those whose knowledge is at GCSE level for Maths and Further Maths, but wants to expand?

[turbid mural]

recommended integral equations books ?

[gray gazelle]

Is it like Pre-RMO