book-recommendations

[wet sentinel]

if you check my profile and see my username you will know that i am a true pirate

[mortal iris]

Dear genius. By this logic, one person could buy anything and distribute it for free to everyone. This creates a massive loss for the creator and distributor of the product don't you think? And wouldn't you expect them to safeguard their financials?

Buying and owning a digital book does not give you rights to sell the book since you can make virtually infinite copies of it. You do however have rights to do this with a physical book but at the same time not with a scanned copy of it.

[winged ferry]

Does anyone have opinions on the Princeton lectures in analysis?

[slow roost]

Stein and Shakarchi right?

I don't like that they make me want to get 4 books

but the books seem very good

I only have the real analysis one

[frozen perch]

That’s the only one I know too, I like it

If the others are of similar quality, then I’d recommend them

[slow roost]

there's a math youtuber who says the first book on Fourier analysis is his favorite math textbook of all time

https://youtu.be/xWMCgg57MiA?si=mE9QBdZdEE8Jn4Oa

I had a look at the first chapter and frankly it didn't meet the level of hype he built up for it, for me

but I'd still like to have them all

[mighty pewter]

wow man im not reading all dis

holy yap

[mighty pewter]

https://tenor.com/view/one-piece-gold-roger-gol-d-roger-gif-2726255820708387963

[vital bane]

creating massive loss for massive corporations is always a massive win 🗣️

But yea dont discuss piracy in the server 🗿

[mortal iris]

Not really about right or wrong here. Just pointing out how stupid the guy was being.

[mortal iris]

Exactly why you're so smart 🙂

[mighty pewter]

Dude your a grown man worrying about pirating a math text book in a math discord server

Holy cortisol spike

https://tenor.com/view/what-solluminati-simple-thot-why-gif-9805666

I got the book for free regardless

[jolly dawn]

Good

[mortal iris]

Like I said. You're a genius with the utmost comprehension of everything that ever existed. It's not about being worried about piracy. It's about why what you claimed is not piracy actually is. Sometimes genius knows no bounds.

And as far as the server goes, it's existence could be in trouble if we violate it's tos. Pretty sure we all like that this place exists? Oh wait. Maybe geniuses like you couldn't care less.

[midnight gulch]

also pirating books is very easy, kind of a skill issue if you need to ask

[mortal iris]

Exactly lol

[mortal iris]

I used the complex analysis one. Very nice introduction to the subject.

[slow roost]

I ended up ordering Freitag & Busam's complex analysis for my big-boy text

looks like it covers modular forms and elliptic functions pretty thoroughly

excited to dive in

[tender cobalt]

what subjects can I move onto after finishing something like Hubbards Hubbards or Shifrin?

[slow roost]

Diff geo

McInerney's First Steps in Differential Geometry, which I just recently heard about here, looks like the best undergrad text for it I've seen, possibly

not sure yet if I like it more than Pressley

[daring wolf]

freitag? i know some of his books one is "etale cohomology and the weil conjecture"

[tender cobalt]

ooo

wait does Hubbards Hubbards cover the standard pure linear algebra course?

[slow roost]

oh, I'm not sure about that. For some reason I sort of assumed you've had some lin alg

[slow roost]

looks like it's the same Freitag

[daring wolf]

yeah

very based

[tender cobalt]

yes ive had, im just asking if it does

[slow roost]

ah. Yeah I'm not sure, but McInerney does review all the linear algebra needed for that book. It might be a little fast for someone who hadn't had that course

[tender cobalt]

interesting

does it cover diff geo in R^n

whats it about

[slow roost]

yeah. In fact it doesn't use manifolds at all. But it does cover Riemannian metrics, symplectic forms, and contact structures. A very interesting gambit

[tender cobalt]

wait whaat

riemannian metrics without manifolds?

that sounds interesting

[slow roost]

indeed! and it does cover tensors and differential forms leading up to that, but only in R^n

[tender cobalt]

oo

seems like a perfect transition book then

[slow roost]

yeah, I just started reading it and wish it were around back when I was first getting into this stuff

maybe it'll help me finally get down certain things well enough to get further in Tu and Lee

[tender cobalt]

just gave it a skim

It actually looks decent for a surface level overview of diff geo

it also seems like mostly computational stuff from what i see in the exercises

[slow roost]

yeah, that's usually the case in undergrad courses in diff geo

substantial theory results usually take a lot of building up to

[little yew]

Any recommendations on lattices and order theory? Or anything on combinatorial game theory?

[sacred thicket]

any recommendations on introduction to sheaves? (not in alg geo context)

[daring wolf]

Manifolds, Sheaves, and Cohomology by Wedhorn

Bredon has a sheaf theory book but idk if it's good

if you want something more general like grothendieck topoi then idk about it because I learned them from AG stuffs

[slow roost]

I think Mac Lane and Moerdijk, Sheaves in Geometry and Logic gets into that latter stuff

I’ve only skimmed it

[native cradle]

Chat, any book suggestions for Numerical analysis

it should have some coding problems in python/matlab too pls

https://link.springer.com/book/10.1007/978-0-387-21738-3

is this good?

[mortal iris]

You prefer coding heavy or math heavy?

Like there are different kinds of numerical analysis books. Coding heavy ones are better suited for application oriented stuff. Math heavy ones focus more on the numerical algorithms and their analysis and some deeper ones even require functional analysis.

[native cradle]

Slight problem , my course has coding

I prefer math heavy but I haven't done integration , series and power series in analysis

[mortal iris]

Then you cannot really use a math heavy one at all

[native cradle]

would

Tea Time
Numerical
Analysis
be a good read then>

[native cradle]

Fair enough

[mortal iris]

This is a good resource to use. Covers a lot of ground. Coding heavy but does cover the math reasonably well for an intro.

[native cradle]

Thanks!

[nocturne badge]

best decision ever made

[mortal iris]

This is also good if you want something mathematically richer. I would suppose you could use it as a complement to FNC

[nocturne badge]

make sure to read his second book too

[native cradle]

thanks!

I do want it to be mathematically rich 🥀 , I honstly wish this course were in my 3rd year instead

[mortal iris]

I kinda agree. I had numerical analysis and scientific computing in my first year as well but where I come from we already learn a bit of Calculus and matrix algebra in high school so it's alright-ish. Still think programming itself warrants a separate look with more insight than exploration into numerical analysis in a freshman course. You can always learn numerical analysis proper a little later.

[shadow vector]

🥹

[river token]

thoughts on RA by frank morgan guys

or way of analysis

[dry rune]

Does anyone have an introductory + in depth book on discrete mathematics?

I'd also appreciate if anyone knows some books where discrete mathematics is applied to other disciplines

[mortal iris]

Rosen's book is a good intro. Has plenty of applications in computer science

[dry rune]

Thanks! What about discrete maths into music theory?

[mortal iris]

Doubt you'll find that in books and even if you could it would be rare. Your best bet would be to look for courses that cover this kind of material online. Their notes and problem sets may be of help.

The only math and music related books ik are the Topos of Music volumes and they are not introductory at all.

[mighty pewter]

It wasn’t available on any website how is that a skill issue

[mighty pewter]

I never said I wouldn’t purchase the book from someone else you didn’t even read my original message get some hobbies man

https://tenor.com/view/gol-d-roger-one-piece-laugh-gif-21028191

[mortal iris]

My hobby is to have fun with geniuses such as you.

[viscid remnant]

@honest reef this is a follow up of the question you asked in the help channel. For Number Theory, there is an EGMO like book called Modern Olympiad Number Theory by Aditya Khrumi. Its the same style and Evan Chen also mentioned it. I do not know of like to like Combinatorics books but Evan recommends Counting Rocks! in his blog. Same for algebra but I think Hall and Knight is solid (Edit: though not really olympiad style as Killuminati pointed below)

But ig others might have more. Check out Evans blog too for his reccomendations.

[viscid remnant]

Having fun with geniuses is legitimately the best hobby. Its genuinely fun

[mortal iris]

Not really sure if Hall and Knight is good for Olympiad prep. All 3 volumes are great but it reads very differently to the likes of EGMO. That said I am outta context here and may be speaking out of line.

[gray gazelle]

guys where can I find workbooks for pre algebra and algebra ?

for free and with soloutions

[viscid remnant]

That's a fair point yeah but I don't really know any books that do algebra for olympiad specifically.

[burnt stag]

L take

[viscid remnant]

@honest reef and see this too https://artofproblemsolving.com/wiki/index.php/Olympiad_books

[honest reef]

thank you! ill check these out

[tiny crescent]

What

[normal crystal]

you can use the problems in the Openstax books

[half vigil]

is Contemporary Abstract Algebra by Joseph Gallian a good book?

[tiny crescent]

@half vigil

[half vigil]

thank you

[mortal iris]

Pretty good. We used it when I did Algebra 1 in uni.

[half vigil]

👍

ty

[mighty pewter]

“My hobby is to be a asshole in discord servers as an old man”

https://tenor.com/view/solluminati-solluminati-peace-solluminati-peace-sign-gif-11432900688091248344

[odd cargo]

killuminati meets solluminati

[mortal iris]

I love how ppl buy that I am old lol.

Also, I have to be extra kind to someone as kind as @mighty pewter

[molten gulch]

Piracy is illegal, piracy could get the discord server shut down, don't discuss it, don't encourage it. On an ethical level piracy is fine in my opinion FWIW, don't talk about it here

[mighty pewter]

When did I say I was going to pirate it bro YOU said that not me 😭😭😭🙏🏽

[mighty pewter]

It’s your whole schmeel man whatever it may be doesn’t change the fact that ur a bum

To my knowledge all I did was ask if anyone had the book

[mortal iris]

Of course, the genius has given an opinion.

[mighty pewter]

Wow man

https://tenor.com/view/flight-reacts-flightreacts-tongue-tongue-laugh-gif-13724048537815479089

[mortal iris]

This genius even reacts to his own texts. The pride on display is worthy of respect

[mighty pewter]

<@&268886789983436800>

Poor guy got logged

😭🙏🏽

[mighty pewter]

https://cdn.discordapp.com/attachments/1351238394528665792/1408458039345811537/attachment.gif

[barren pollen]

anyone got something I could read in an hour

[whole trail]

diary of wimpy kids

[whole trail]

yo shut up gng

[barren pollen]

I mean math related 😭 😭

[whole trail]

oh mb

shit ima be honest

idk bro like im in 8th grade

shi prolly mcgraw hill ngl

[barren pollen]

bro this is full circle moment

I joined this server when I was in 8th grade 😭

[whole trail]

yoo bro

that’s sick

its lit

[barren pollen]

looking back I'm so stupid

[whole trail]

why what happened bro

[barren pollen]

trying to grasp infinity and I can't even solve a quadratic

[whole trail]

hey man it’s all good

what type of maths do u wanna read abt

[barren pollen]

anything tbh

I'm open to new things

[whole trail]

which math r u taking right now sir

@barren pollen

[deft lava]

what's your math background?

[barren pollen]

I'm doing second year engineering uni done calc 1 2 and 3

and lin alg 1

[barren pollen]

if I could be anything I'd be a group theorist

3rd order logic

[mighty pewter]

on baby

[mortal ore]

yo i can agree with u on the biology shit but what did math majors do bruh

actually lowkey i probably already know the answer

[radiant marlin]

what book are you reading?

oh abbott?

good luck i suppose

you can always ask for help in #real-complex-analysis

[astral viper]

Hey, I'm looking to learn deeply about Algorithms, any books of your preferences? thank you!

[mighty pewter]

everything..

[molten gulch]

Clrs

[astral viper]

Already read it haha

[hollow epoch]

Introduction to Category Theory - Mac Lane or Riehl?

[astral viper]

will have a look on that one

[hollow epoch]

Sorry - I mean which is the better read to start?

[timber mesa]

personally I liked Riehl's writing more, it's also a more recent account of category theory

though this kinda thing is very subjective, skim both books a bit and then stick with one

would suggest you do that when you have many books for one subject generally

[slow roost]

1000% Riehl

Mac Lane isn’t a good introductory text

[mortal iris]

Another genius

[mortal iris]

I would say neither. Go with Lawvere

[dry rune]

I asked that question out of capricious whim, lol. When I first heard about discrete mathematics, I immediately thought of music theory due to the idea of discrete notes

I also feel the same sentiment. It seems very difficult to find books that relates mathematics to music and arts

[dry rune]

Thank you very much! This is a good one

[slow roost]

The Topos of Music by Mazzola is one. Fair warning though, it’s not very readable and of dubious usefulness

there’s Formalized Music: Thought and Mathematics in Composition by Iannis Xenakis, who was a badass composer

he discusses some of his own techniques in it, which were heavily influenced by math

[dry rune]

It's alright, I read metaphysics. My interests are anything but useful or practical

[slow roost]

and Harry Partch’s Genesis of a Music discusses the history of tuning systems and his own 43 notes per octave just intonation scale

great writing in that

he waxes philosophical about music a lot

[dry rune]

Thank you very much! I'll take up all of your recommendations :)

[slow roost]

sure one other one I haven’t read but looks interesting, Dmitri Tomoczko’s A Geometry of Music

here’s a short article he wrote that says orbifolds can be useful for modeling harmony https://dmitri.mycpanel.princeton.edu/files/publications/science.pdf

[dry rune]

Do you know any in depth book for music theory only?

I take up violin classes but I think I need to level up my music theory game further

[whole trail]

ty bro

[slow roost]

sure, well early on I took piano lessons and studied from a bunch of beginner books that taught how to read music, time signatures, key signature, dynamic markings, all that basic stuff.

Later on I wanted to learn more theory and how to play jazz, and The Jazz Theory Book by Mark Levine was very helpful

there's also Schoenberg's Theory of Harmony

and Fux's book on counterpoint

[daring wolf]

many such cases

[rotund ember]

Is nagel best for diff eq

[tender cobalt]

Same 😂

[midnight gulch]

what are the three for you right now?

[tender cobalt]

dont laugh bro

these arent just introductory books

if u are able to solve most problems from FIS and Abbott, you already have levelled up enough to start MOST other math books

just name one math subject

Diff geo? requires lin alg + analysis, so yes

measure theory? yes , requires linear algebra + analysis so you've got that covered too

algebra? yes, doesnt require linear algebra but helps with understanding the examples

so instead of thinking its just "introductory", think of it as a key

Key to unlock new levels of math

keep it up bro you can do it 🔥

[viscid remnant]

I rotate math and physics

[jolly dawn]

Honestly, that might as well be the best way to do it. I concentrated on Abbott's book for 6 months, and though I did mostly finish it (until chapter 7), it felt kinda hard doing the same thing every day

[dry rune]

You're so helpful, tysm

[jolly dawn]

This might not the place for it, but can anyone recommend more or less "rigorous" marketing strategy books, with detailed explanations of how specific advertisements succeeded/failed? I was reading "Positioning" by Al Ries & Jack Trout, but it feels like such a time waste....

[half void]

Spoken like a true undergrad

[violet quail]

Hello,

Could you guys/gals tell me if the book recommendations I have are good
-krishnamoorthy's challenge and thrill of pre college mathematics
-principals and techniques of combinatorics
-higher algebra hall and knights
-Calculus made easy- Mr. Silvanus Thompson
-the art and craft of problem solving, paul zeitz

[molten gulch]

FIS and sipser are a lot of fun, I still get use out of them

[mortal iris]

Hall and Knight is good. Thompson is a decent introduction but whether it's good or not depends on why you're learning Calculus. The rest idk much about to comment.

[violet quail]

thanks, killuminati.

[proper trout]

Do you guys recommend going through Pre-algebra books? (specifically AoPS Prealgebra). It just feels too big( or is this what I should expect with math textbooks? very new with this)

[normal crystal]

my gut reaction is this seems like an odd collection TOGETHER
I'm not sure what the goal is, so maybe consider that when picking the pieces

[mortal iris]

Depends on what level you're at. Some math textbooks do tend to be big. Some very concise. That is a matter of taste when it comes to exposition and writing. The bigger question is why if at all would you like to go through pre-algebra? What are you presently studying?

[violet quail]

actually, these are what I require lol, these are some concepts that I wanna dig deeper in before my next olympiad sooo, does that make sense?

[normal crystal]

no, not really
but I assumed you were thinking in the comp math direction

[desert oriole]

bs chatgpt writes at the end of every answer

[tender cobalt]

i didnt use chatgpt to write that 💀

oh ok thats good now

but fr introductory books are key

[desert oriole]

yeah obviously

but knowing first year math doesnt make most other math books approachable

[mortal iris]

It's like a key to your first pick of a door in the Monty Hall problem. Then some ppl come and show you what's in that second door (terribly written advanced math books) and while you could stick with the first one (introductory math books), it's more advantageous if you switch for a favourable outcome (well written advanced math texts).

[tender cobalt]

well ofc not the grad books ,but other subjects that typically require those as prerequisites and its a lot of stuff out there to learn thats what i mean

[tender cobalt]

right

[midnight gulch]

is analysis "first year math"?

[tiny lava]

is fitzpatrick's advanced calculus a suitable first read in real analysis

i'm willing to aid it with another book

but i would like to learn about multivariable analysis and fitzpatrick's table of contents captures basically everything i want to learn

[midnight gulch]

yeah definitely

[tiny lava]

i was thinking about reading abbott then fitzpatrick

because fitzpatrick seems to assume you have some analysis knowledge(?) from a quick skim of it

for background i've finished calc 3 and am almost done with ladr (reading it front to back)

[midnight gulch]

i think both books cover things at a similar pace

you could always get both to see which one suites you better

[tiny lava]

alright i'll look into both more carefully after i finish ladr

also should i read baby rudin

[midnight gulch]

also, fitzpatrick covers quite a bit more than abbott beyond the basics, so do with that what you will

[tiny lava]

yeah i want it because of it's multivariable analysis sections

[midnight gulch]

maybe, it has some good exercises

[formal estuary]

how are u finding LADR? I just got a copy 🙂

[tiny lava]

it's great so far (i'm only on ch7)! i like that it's abstract and focuses on vector spaces and linear maps

i'm taking an intro to linalg course at school and it's nice to switch between the two viewpoints and see how they connect

i started with close to zero proofwriting knowledge but the language isn't difficult and it was pretty welcoming for me

some of the exercises are pretty difficult though

[formal estuary]

no way! thats awesome

I found my intro to lin alg course to be really boring, I wasnt a hard working student at that time so Im sure that played a part, I think I would have enjoyed it a lot more had I been introduced to more abstract lin alg earlier

good stuff 🙂

[tiny lava]

i don't like it either, it's just useful for its computational purposes imo

a bunch of things in axler in my experience are slower because he strays from certain computational methods (i.e., showing dependence in vectors, computing eigenvalues/eigenvectors, etc.)

mainly he strays from gaussian elimination and determinants

also he doesn't necessarily avoid matrices but more often than not he uses linear maps when teaching things

[formal estuary]

yeah I read that he put determinants in the back of the book or something

[formal estuary]

very cool 🙂

[tiny lava]

indeed, i think it's better as a second read because determinants are pretty important computationally

[half void]

Dépends on country, school, and the level of preparation of the student coming in…

But yes; quite possibly

L1 in many schools in France, for example, are of the level of abott

[zealous jewel]

Is Calculus on Manifolds by Spivak the best 'next step' after Spivak's Calculus? I also read good things about Analysis on Manifolds by Munkres and An Introduction to Manifolds by Tu so I wasn't sure if any make more sense than the others.

[slow roost]

I've not read Spivak's Calculus on Manifolds or that Munkres book, but I can definitely recommend Tu

I think with this subject reading a lot of different books (at least a little bit) is really helpful

but I am that way with most subjects

the main ones I've studied from are Lee and Tu

[radiant marlin]

does Spivak's calculus book cover real analysis?

[slow roost]

it is a real analysis book

it's using "calculus" in an old fashioned sense used in UK classes where it was synonymous with real analysis

but it's a bit of an unusual real analysis book

[radiant marlin]

oh lol ok

between munkres and spivak, spivak is definitely the harder option. personally i would argue spivak is a better read but it honestly depends on how comfortable you were with real analysis, and whether you prefer routine exercises that just help you consolidate material or more challenging (and rewarding) ones

[slow roost]

I should clarify, Spivak's Calculus is really somewhere in between a typical calculus book and a full blown real analysis book like Rudin

it's probably misleading to call it straight up a real analysis book

[zealous jewel]

oh ok, Munkres is a more 'introductory [multivariable] real analysis'?

[muted shale]

Hello

@zealous jewel 👋

[radiant marlin]

they cover similar content but Munkres moves slower and "takes better care of the reader" lol, its exercises are also overall easier

but you should look at the table of contents of a real analysis book first and see that you are comfortable with most of the content before going to multivariable

[desert oriole]

afaik it is everywhere except in the us (but i thought it is also possible to do analysis first year in the us too)
(analysis as in baby rudin obviously and not measure theory or other)

[muted shale]

Is the channel related to math books only or books in general ?

[slow roost]

any books are fine, just people mainly ask about math books

[muted shale]

Okay
Is A journey through Olympiad Math good ?
Cuz my whole life I've been learning math in a non Latin language and I don't wanna be bound by school or teachers

[muted shale]

Quite understandable

[slow roost]

I’m not familiar with that book

[muted shale]

Wait what

Maybe I got the title wrong

[slow roost]

but I imagine it’s about math Olympiad competition problems

[muted shale]

Cuz There someone that was here that I know irl
mcplayer010
He suggested me the book
It's in English too so I supposed you might know of it

[slow roost]

Ive never been too interested in competitions, but there are probably people here who’ve heard of it

[muted shale]

I don't mean in an actual Olympiad aspect , but rather in the type of Math you'll find in an Olympiad

[muted shale]

Anyone here know the guy ?

[slow roost]

that’s basically all of high school math before calculus, and some number theory

[muted shale]

Oh , alright
Is the book good or above that ?

[slow roost]

what is your desire / goal from math books?

to understand better if that book will be good for you

and what’s your background?

[muted shale]

Yes
I want to go far beyond

[muted shale]

First year of high school
Teacher is straight up ahh
And I don't want to be bound by my age or level anymore
Plus I was already a math enthusiast
But the problem is I'd basically have to relearn math in English
Do you have any suggestions for that ?

[slow roost]

I’m afraid I don’t really have any particular good recommendation

you can try to start reading some more interesting math books, but you also have to learn the high school math curriculum well, and that should be your priority

and there aren’t really books on high school algebra, geometry, and precalculus that I’m especially fond of and recommend

pretty much any of them will do

look for stuff that’s available for free online

[midnight gulch]

it is certainly possible, but it is not the norm

[wet sentinel]

then i recommend that you avoid math olympiad tbh

its a better use of your time if you start studying towards higher math

because thats where the real fun lies

but first you should become familiar with hs math as ManifoldCuriosity recommended

[wet sentinel]

i hear that khan academy is good for this stuff

i dont really have recommendation for this tbh

but i have heard about khan academy too much that I would be really surprised if it turns out to be bad

the next step would be calculus

you can always open a calculus textbook and see if you can follow/if you are ready for it or not yet

and then decide what to do

[muted shale]

Yeah but the teacher does a horrible job + I wanna advance

[wet sentinel]

yea, then use khan academy ig

[muted shale]

I need something to teach me math from the start

In English

[wet sentinel]

well you need to explain what you mean by from the start

like hs math?

[muted shale]

Ah man :(
Gtg
Gn

[wet sentinel]

gn

when you wake up or something you can ask here again and explain what exactly you want

and then hopefully you will get help

[normal crystal]

"ok, explain what you mean"
....
"damn, will you look at the time...."

[wicked fractal]

I used it

It's really good

[wet sentinel]

yea then its good if you say so

[lofty lance]

Guys i am in highschool and am done with all of hs maths which book should i use to move ahead

[daring wolf]

depends on what you would like to learn lol

pure math? engineering? or what

[lofty lance]

Pure maths

[daring wolf]

do you have backgrounds on calculus right

[lofty lance]

Yeah

I have done ap calc and all

[daring wolf]

there are multiple choices like, calculus books that a lot of unis use (which cover up to multivariable calculus/some vector calculus)
instead you can start with linear algebra, and real analysis as well

[wet sentinel]

you could also do abstract algebra and (analytic) number theory if you want

[daring wolf]

no lol

start with linear algebra if you want abstract algebra

[wet sentinel]

i mean technically he can lmao

but yea it might not be the best thing to do

just stating the options he has

[daring wolf]

i mean yes but similarly one can technically do hartshorne in the same logic

[wet sentinel]

no

because intro AA doesnt need background ig

unlike hartshorne

which also doesnt need prereqs

[daring wolf]

just do it by force /j

[wet sentinel]

:chad:

[daring wolf]

and for number theory sure you can start with ENT but i dont like this

[wet sentinel]

yea i dont like ENT too thats why i said analytic

by analytic of course i mean apostol

other than that you would need CA lmao

[daring wolf]

I wanted to skip ENT in my uni but uhh like i need to take 72 points in maths but there aren't many courses to take instead

otherwise i need to take numerical shit

[wet sentinel]

but yea I would say start like normal people do. no need to start with analytic nt and shit

[daring wolf]

you can start in weird way but then you will end up with 3-IndCoh headass

[wet sentinel]

just go as a sane person, probably LA first

(of course proof based not computational/numerical)

[wet sentinel]

#book-recommendations message here is a list of LA books

[static gull]

What are some prerequisites to Hubbard and Hubbard’s book?

[molten gulch]

calculus and some linear algebra but that's about it

[static gull]

OK thanks

[minor venture]

Does anyone know a free geometry book for high school math that explains every term used and gives examples to solve for?

Is this book good for that? It has 800 pages though https://ia803106.us.archive.org/24/items/geometrytextbook/Geometry Textbook.pdf

[cunning elk]

that should be any halfway decent geometry book?

it does not matter which one you pick theyre all isomorphically bad if its a standard textbook

[minor venture]

Do you know a super short one but is also really good?

[cunning elk]

no

[radiant marlin]

do they let you take other (higher) NT without this as prereq

[daring wolf]

Idek if my uni has higher NT stuffs

at least i didn't see till now

[wet sentinel]

the right question is do they offer higher nt courses

[radiant marlin]

what about grad classes, if there are

[wet sentinel]

i want to comment but i wont

its the clopencry effect

[daring wolf]

I need to check this lol

[radiant marlin]

lolol

also if you have reading programs or a junior project/senior thesis, could just do that for number theory

i suppose

[vital bane]

Calculus? on Schemes?

[daring wolf]

this is real

lol

https://tjfonseca.github.io/teaching/calculus/

[vital bane]

I know lol that's what I was referencing

One day I will learn it

No matter what

[daring wolf]

just do this now by force

/j

[vital bane]

But first I need to learn QFT

[daring wolf]

i mean you can probably read some of the first paper because it deals with Kahler differentials which just requires ring/module theory

from the last chapter of the fist paper you need scheme theory but you can read before this appears

[wet sentinel]

this is truly calculus for those who already know it

[daring wolf]

stupid filtration

[static gull]

Is strang’s linear algebra enough for it?

and also calculus from aops

or is there anything else that i should do before it

[odd cargo]

what the hells going on here

[tame tree]

@static gull the book contains a coverage of linear algebra in R^n

[static gull]

oh, so i wouldn’t even need strang?

[tame tree]

no

[static gull]

alright tysm

[wicked fractal]

tfw stupid filtration turns out to be a marvelous idea

[daring wolf]

yeah

[chrome wasp]

Usually introductory books to analysis have first chapter on some naive set theory. Or maybe even algebra books have those, idk particular one.
(About sets, operations with sets, about mappings, image of map, inverse image, relations,...)
I would recommend to learn that absolutely needed concepts and statements from (lets call it naive) set theory (but be careful not to dig too deep into general set theory).
Would be good if some of those books introduce just a bits of proof writing logic, but you have probably covered some of basic logic statements in hs.
Then if you still have time to prepare ahead:

• in analysis I would focus on basic properties of real numbers as complete field (could skip construction of R, depends on book).
• intro to linear algebra (vector spaces, examples, linear dependence, subspaces, basis,...)

I just remembered Zorich mathematical analysis 1 has introduction I was thinking about, for example... but there are many more

[sage kelp]

Best books for a first introductory course in algebra?

[chrome wasp]

#book-recommendations message

[proper trout]

really? I had to choose whether to focus on my fundamentals or read ahead. I chose the former but now im skeptical. I'm halfway through AoPS introduction to algebra.

same situation as the previous 3 guys

[jolly dawn]

I also recommend picking up a real analysis book and reading it along side Hubbard's text. Although you can technically just jump straight into analysis in Rn in Hubbard, I feel like that may be confusing if you haven't met the concepts of epsilon delta proofs/uniform convergence/Riemann sums before. Also, as someone who's reading chapter 2 of Hubbard, I think linear algebra is not necessary AT ALL. Like, the authors introduce matrices and matrix multiplication with a beginner in mind (the same is harder to say for analysis: they state on the beginning paragraph of section 1.5 limits and continuity "we hope you have already begun your journey in real analysis")

[rough umbra]

i think groups/rings b4 linalg is nice bc u can learn linalg as transformations on fd vector spaces from the start

[daring wolf]

tfw you learn what linear transformations in abstract linear algebra book in the start

but yeah i get ur point

[pearl palm]

What order did you take your math courses in?

[daring wolf]

tbh I self-studied stuffs (while I'm taking courses in uni ofc)

at the start, I did rudin (analysis) and axler (linear algebra)

for latter stuffs i cant really describe in which order i did because this is somehow weird lol

[rough umbra]

u lose matrices as examples but if u do it in an ent oriented way it's fine

[pearl palm]

Another fellow self studier

[daring wolf]

what

i mean there are a lot of self-studiers here

[pearl palm]

Yes

I still assert it

[muted shale]

I'm here

[pearl palm]

Another fellow

[muted shale]

Back actually

[desert oriole]

courses having prereqs is stupid imo

[daring wolf]

this isn't related to prereqs lol

[tender cobalt]

any book for learning theory of ML ? (math based)

[desert oriole]

someone in that convo mentioned prereqs. i dont remember why i even wrote that though

[orchid vortex]

Kevin Murphy’s Probabilistic Machine Learning both intro and advanced, more advanced is Understanding Machine Learning and Foundation of Machine learning.

Also take a look at Learning theory from first principles.

[tame tree]

the linear algebra is definitely necessary

its how you make sense of things like implicit function theorem

[jolly dawn]

Well, idk all of it was introduced in the book so I thought that way

[tame tree]

as well as the determinant playing a role later on with integration

[tame tree]

oh yeah, what’s contained in the book is enough

[weary remnant]

Hello guys any book recommendations for coordinate geometry

[rough umbra]

Maybe like shifrin or one of lee’s books depending on what u mean?

[mortal iris]

Pogorelov's Analytical Geometry.

[mortal iris]

Typically the terms Co-ordinate Geometry are meant to be the study of conic sections, pairs of straight lines and quadric surfaces in a Co-ordinate basis. Typically Cartesian but with some polar forms and parametric equations wherever useful. Usually serves as a bridge between traditional Euclidean Geometry and Differential Geometry of Curves and Surfaces.

[normal crystal]

is it an indian curriculum thing that it keeps getting asked for

[rough umbra]

I see, thanks

[slow roost]

no, it's a unit, or sometimes units, of the US middle and/or high school math curriculum as well, concerned with things like the slope formula, midpoint formula, distance formula, coordinate formula of a circle, etc. It's typically not its own full course but parts of algebra and geometry (and precalculus)

[mortal iris]

Possibly. Its a part of the standard high school curriculum in India but quadric surfaces are not covered in much detail. The focus is more so on planes and conic sections in the Indian curriculum.

[odd cargo]

dont some countries teach conic sections as part of pre-calc

sort of makes sense in this context

[mortal iris]

Yeah but afaik places that have something called Precalc don't have what is called Co-ordinate Geometry as it's own thing.

[odd cargo]

yea i dont really remember ever hearing anything about "co-ordinate geometry" in school

transformations are a type of co-ordinate geometry aint it?

[mortal iris]

The Indian curriculum covers a lot of ground.

Grade 11: Discrete Math (Logic, Sets, Relations, Combinatorics, Probability) Algebra (Functions, Quadratic Equations, Complex Numbers), Trigonometry, Co-ordinate Geometry (Straight Lines, Conics, Vectors and Planes in 3D), Limits, Continuity and Differentiability.

Grade 12: Vector and Matrix Algebra (Linear Systems, Determinants), Differential and Integral Calculus (Plug and Chug stuff), First Order Linear ODEs, Combinatorial Probability and Statistics, Linear Regression and Linear Programming.

[odd cargo]

they teach that in pre-calc but never really call it co-ordinate geometry

[mortal iris]

Transformations is a rather vague term so idk really.

[odd cargo]

i meant horizontal and vertical shifting or stretching of a graph

[mortal iris]

Aah. Yes. That's part of it.

[slow roost]

some teachers may not mention it but that material is frequently called analytic or coordinate geometry in textbooks

[rich sun]

analytic geometry

[slow roost]

perhaps the best way to find out is just open up the HoTT book

I tried doing that once

I don’t remember it going very well though

curious to see other folks answer

I imagine it’s a good idea to be at least acquainted with homotopy in topology, and some type theory

the book does start by introducing type theory but I don’t know if it’s the best place to try to start learning that

[full pike]

i need a orietation, right now im want to study complex analysis, but i only have the courses of calculus on R and Rn, analysis on R and linear algebra, but im strugling in the book of the complex analysis, even though the book im reading is easy (stein and shakarchi)

[slow roost]

uhh

[full pike]

i go to study analysis on Rn or i continue in complex anlysis?

[slow roost]

who said Stein and Shakarchi is easy?!

[full pike]

xd

my friend have said

is not the best font lol

he have made complex analysis on rudin

[static cairn]

Hi, I'm looking for some books to learn combinatorics for a math olympiad, specifically in Poland, but most books in English probably cover the material. I really liked EGMO and MONT, and I'm looking for something similar from the basics?

[full pike]

you can indicate me a easier book?

[slow roost]

if you don’t mind sacrificing some rigor and depth, Saff & Snider is far more approachable

[full pike]

ok, thanks

[slow roost]

another option is Brown & Churchill

[remote sparrow]

https://complexanalysis.org/

this is good

[slow roost]

and Needham’s Visual Complex Analysis is extremely pleasant to read, though it’s a bit unusual and I recommend having it as a supplement to a more traditional reference

[odd cargo]

the cover photo on the book is hard as hell

[static cairn]

🙏 pls

[weary remnant]

I am no Indian but I use various resources to learn algebra analytic/cords geo and trig for calculus (I am doing a prep in Ipho)
Also our math curriculum here in the Philippines is really really easy you don’t even need to study for it

[wet sentinel]

if you want check "a course in complex analysis" by saeed zakeri tho i have no idea if its harder or easier than stein and shakarchi

[remote sparrow]

it's much harder

[wet sentinel]

ohhh i see

[radiant marlin]

what book is HoTT

[wild blaze]

analysis after baby rudin? no measure theory yet but want to get into functional analysis eventually. my uni does axler measure theory and conway functional analysis but was wondering what most ppl do thats more rigorous

also algebra after dummit / foote

[remote sparrow]

you can use folland for measure theory

[daring wolf]

algebra after dnf
there are a lot of ways to learn further algebra

[remote sparrow]

there are many paths you could take

[wild blaze]

what do u recommend after for functional analysis? and also, do most schools use folland as a 1 semester or 2 semester book

[remote sparrow]

depends whether pdes or operator algebras interests you more

i don't really know

[wild blaze]

alright ill probably come back once i finish folland then.

[remote sparrow]

you could also do probability

that doesn't really require functional analysis

[normal crystal]

I know, but it does seem requesting it here as a separate book has been a reflection of the Indian curriculum, even if it wasn't this time

[wild blaze]

should i do some CA before also?

if so any recs

[rough umbra]

skimming the preface rn -- if i've taken topology, real analysis, and some grad courses already, would u recommend this over, say, freitag and busam?

I currently know epsilon>0 CA and just want to pick up enough to be able to start doing stuff in complex geometry, for some more context

(ive read lee ISM and am reading vakil atm)

is it possible to read lee complex manifolds without having done CA lol

@cursive rivet hi bestie

[daring wolf]

I mean like you don't even need a full course on complex analysis to learn them, and it doesn't really take that much to know the minimum prerequisites for them
and IIRC books like Lee has a section on complex functions of multiple variables

(btw I would just read books e.g. voisin over Lee)

Lee just covers up to Hodge decomposition and the Kodaira embedding theorem, while voisin volume 1 includes much more interesting stuffs

[cursive rivet]

howdy gamer

no you need complex analysis

lee states in ch1 what you need, and it's basically a first course in it, and the proofs and techniques are important

[daring wolf]

yeah you need complex analysis but i mean like this doesn't require some unnecessary stuff which a lot of complex analysis book has inside

[cursive rivet]

in particular i do think a good understanding of complex variables, and the Wirtinger (del bar) derivative are actually super essential

like do you need to know the proof of morera's theorem, no, but you need a good understanding of the word "holomorphic" and fluency in switching between (x, y) and (z, zbar)

fwiw I like Lee's complex geometry book because it covers the basics in a good amount of detail entirely omitted from e.g. Huybrechts or Wells (haven't read Voisin)

though those books go into far more material that you should cover after

namely talking about being careful with sheaves and careful with "what parts of manifold theory do i need to be careful when i swap smooth with holomorphic" and go from real tensors to complex ones

(Wells does the sheaf theory but imo is not a very good source for it)

[daring wolf]

yea i think Lee is better than those two
voisin volume 1 deals with deeper stuffs, e.g. Hodge-de Rham spectral sequences, (abstract aspects) of Hodge structures and its polarizations, and variations of Hodge structures (i like it)

[cursive rivet]

yeah that is good stuff i gotta learn one day, the complex geometry i use day-to-day goes a completely different direction

[remote sparrow]

yeah

[remote sparrow]

you don't need to know complex analysis beforehand but it's good to learn at some point

[bright horizon]

yo is there an all in one kind of book for highschool math? cuz I wanna get to higher maths quickly

[slow roost]

I’m not aware of one book that attempts to cover all of high school math. It’s too much material

Lang’s Basic Mathematics is a good source for arithmetic, algebra, geometry, and trig / precalculus

but it doesn’t cover calculus, or statistics for that matter

and it doesn’t cover competition style problems

but one book isn’t needed for what you want to do

[bright horizon]

what about a curriculum or smth that I can follow easily

I found openstax and aops(idk what that means)

also im in 8th grade if im allowed to say that

[slow roost]

AopS is Art of Problem Solving

good resource for courses and books

Khan Academy is also good

[bright horizon]

howw much do openstax or AopS differ or either one is fine

[slow roost]

my impression is aops has a bit of a better reputation but I’m honestly not very familiar with either one

[normal crystal]

Openstax is basically intended to be a free version of the standard textbooks in the US college market, but the math texts start at prealgebra and cover HS math
except Geometry, I think
AOPS is intended for young math students with a comp math angle, and isn't free
but anyone, any age can use either

[static cairn]

Hi, I'm looking for some books to learn combinatorics for a math olympiad, specifically in Poland, but most books in English probably cover the material. I really liked EGMO and MONT, and I'm looking for something similar from the basics?

[wild blaze]

CA recommendations for someone with mathematical maturity of post baby rudin and working through folland for measure theory

Also, my friend is struggling in math and was wondering if there is a good college algebra-pre calc textbook and/or book that enhances critical thinking in mathematical/logical fields

[wispy bison]

axler measure theory is good, it’s also rigorous

[vestal dust]

over 1000 pages 💀

[tender cobalt]

Any good elementary geometry book?

[jolly dawn]

Depends on what you mean by elementary. If you're not super familiar with group theory and linear algebra, there's "geometry: a comprehensive course" by Pedoe. If you are able to work with those, there's Marcel Berger's influential text Geometry 1 &2

[tender cobalt]

by elementary i mean highschool geometry

like angles, circle theorems, bisectors , powers of points whatever etc

[jolly dawn]

Oh, idk then... 😅

[tender cobalt]

Ye not your fault, there's so much little resource on these 😭

Compared to linear algebra based affine /projective geometry books or whatever

[tender cobalt]

Altho thanks for the recommendation, the contents does look nice

[obtuse estuary]

check out AoPS's Introduction to Geometry text, it covers all of that

and more

[tender cobalt]

Thanks

[muted quest]

recommend books that are about explaining different ai models mathematically

[runic rover]

https://yufeizhao.com/olympiad/ but you can translate it into polish

[static cairn]

okay, thank you very much

[split portal]

Conway, ahlfors, newman and zakeri are all good for CA.

Newman covers less but is pretty gentle.

With conway I only mean the first volume of his complex book. I haven't looked much at the 2nd.

Zakeri seems to me like it assumes a bit more topology background than the others.

[runic rover]

yw

[lean wedge]

can any one suggest a better book for studying maths for beginners

[split portal]

It would probably help to have more info on what you know and what you want to learn

"Beginner" is sorta vague

[lean wedge]

quadratic equation

[split portal]

So, algebra and stuff?

Do you know trig yet?

[rough umbra]

Thank you

[wild blaze]

point set topology (some algebraic) and dummit/foote algebra is done as well

if that changes ur suggestions

[split portal]

Nope not really. I think they'd all be fine.

When I say conway though I just mean the vol 1 of his books for ca though

[wild blaze]

best CA that bridges to functional analysis?

[split portal]

I have not read the 2nd vol

I haven't done any functional so idk about that lol

[wild blaze]

okay awesome

thats fine

ill look at the ones u said thanks

[fluid harness]

Anyone here know about this one?

Wondering if it's worth it.

[molten gulch]

It's a good book, get an older edition, newer ones are awfully expensive

[fluid harness]

Bet. Thank you.

[rough umbra]

Sorry just confirming, ur saying yes to using zakeri over f&b?

I don’t have measure theory or functional analysis yet if that matters

[chrome wasp]

Is it for first course?

[remote sparrow]

yeah given ur goals

[chrome wasp]

If it is so, you can really start with any standard book (what I have in mind is content of part one from Lang's book)
And then pivot if you need something more specific. Cuz those 7-8 chapters are common in every intro book

[normal crystal]

<@&268886789983436800>

[steep yew]

Graduated a semester early and will be self studying before university. I’ve finished up to calc3 and elementary lin alg. I just bought the book of proof, wondering if anyone has any recommendations to learn alongside proofs.

[molten gulch]

real analysis

[steep yew]

Are there any books you’d recommend in specific for self study

[vital chasm]

Linear algebra is probably not a bad idea too, Linear Algebra Done Wrong is great and free on author's website

It goes more in depth than basic lin alg

Alternatively Axler or Friedberg, Insel, Spence seem to be well regarded

[shut grotto]

Understanding analysis by abbott

[steep yew]

Thanks

[steep yew]

Ok bet thanks. I self studied it kinda lightly over the summer and actually ended up covering more content myself than in my class lol

[heady ember]

Imo linear algebra is very dry so I'd recommend real analysis instead, which I found much joy in. But, analysis has also been much more energy intensive, in my experience.

[shut grotto]

Axlers LADR was pretty fun ngl

[heady ember]

From what I have heard, this sentiment about lin alg being dry is quite common so yeah.

[heady ember]

Nice! 👍

Idk why but lin alg just doesn't tickle my mind the same way analysis does.

Perhaps because there's less you can 'visualise'; ideas you can 'see' tend to be more fun to me.

[frozen perch]

You can never know too much linear algebra

[willow basin]

depending on what you think you'll end up doing, a self study in lin alg could have more utility in the long run. A good linear algebra book will have a gateway into cardinality stuff, could find a bit of metric space stuff, inner products, norms, which are all something you might find in an analysis text, and the proof techniques are kind of everywhere, even as you enter into analysis, but the converse isn't always true (that is to say, oftentimes a proof technique found in real analysis doesn't really show up much elsewhere, at least in my experience.) But a real analysis book is probably going to be more fun. I enjoy spivak's Calculus, though that one actually doesn't give you the metric space, norm, cardinality, etc like I mentioned...

that's a bad run-on

The series stuff and the bounding of quantities from real analysis sticks around, and almost always at the same time

[daring wolf]

homological algebra is just advanced linear algebra /hj

[alpine ridge]

Hi can anyone suggest a rigorous but introductory differential geometry book?

[slow roost]

manifolds, or classical theory of curves & surfaces?

[alpine ridge]

No not manifolds yet, just introductory with only vector calculus/calc3 as pre-requisite

[slow roost]

gotcha. In that case I recommend Pressley, Essential Differential Geometry, or McInerny, First Steps in Differential Geometry

both very accessible but they take fairly different trajectories

[alpine ridge]

Ahh got it, ill take a look. Thanks!

[slow roost]

sure. Also the standard text used in many courses is Do Carmo, Differential Geometry of Curves and Surfaces

I find it a tougher read but you may still enjoy it

[slow roost]

Do Carmo is full of statements that may be obvious to very clever people but aren't so obvious to me. For example,

"Let $\alpha: (a,b) \to \mathbb{R}^3$ be a curve parametrized by arc length $s$. Since the tangent vector $\alpha'(s)$ has unit length, the norm $|\alpha''(s)|$ of the second derivative measures the rate of change of the angle which neighboring tangents make with the tangent at $s$."

and it's like, at a glance I can more or less see what he's getting at, but I have to really stop and think hard to make sure I'm not just taking his word for it

[hasty eagle]

ManifoldCuriosity

[slow roost]

in this case, there's an important unmentioned fact that because $\alpha$ is unit speed, at all points its second derivative is orthogonal to its first derivative

[hasty eagle]

ManifoldCuriosity

[slow roost]

but sort of wrestling with a book and filling in details can be very fruitful, if you can handle some frustration

[runic heron]

is challanges and thrills of precollege mathematics 4th editon book is great option?.....

[slow roost]

thrills, eh?

[runic heron]

yeah

[slow roost]

is it a book you have to get for a class or are you looking to read for pleasure and self learning?

[runic heron]

option B

[slow roost]

gotcha. I can't say I'm familiar with it but having "thrill" in the title makes it sound exciting

looks like it has a lot of good reviews

[runic heron]

but still anyone actually reads it!?

[hybrid vapor]

Stewart or Spivak?

[willow basin]

They have the same title but the style couldn't be more different. Stewart's calculus is the most common college calculus textbook. There are some presented mostly rigorous proofs for various results, but it is certainly less logically rigorous than spivak. Also, for the exercises, most in Stewart are more or less calculations, meaning applying formulas and so on, whereas spivaks problems tend to be proofs, meaning you have to use previous results and reasoning to arrive at very general, abstract results (though in the world of pure math it is not considered to be too abstract.)

It depends on what your goal is. Spivak imo can be a great first rigorous math text, certainly better than rudin. If your goal is like be an engineer though, likely stewart, as much as I hate the book

[slow roost]

good summary

[alpine ridge]

Does this mean the second derivative measures how fast the unit tangent changes direction in respect to the curve?

[slow roost]

pretty much, yeah. How fast the curve deviates from being a straight line, or how fast the curve turns, at a point

it’s the curvature (for unit speed curves)

[alpine ridge]

Ah i see, the wording is also difficult for me sometimes

[slow roost]

yeah Ive just been skimming through it again. He presents some really interesting results quickly, but frequently makes use of various other results without proof, which I’m not the biggest fan of.. and he busts out all sorts of tricky formulas and stuff without motivation

he also calls the Frenet frame the Frenet “trihedron”, which Ive never seen anywhere else

[vital chasm]

Shifrin's notes are very good

For introductory differential geometry

[hybrid sigil]

I just found a blog that reviews tons of differential geometry textbooks including Pressley, do Carmo, O’Neill, Kreyszig, etc. Tge style of the reviews is funny and witty at times, I like it

[slow roost]

link please!

[hybrid sigil]

Here is a Pressley review, for example: https://theronhitchman.wordpress.com/2012/12/02/book-review-pressleys-elementary-differential-geometry-2nd-ed/

And this is his whole book list that he intended to review (not sure if finished):

https://theronhitchman.wordpress.com/2012/11/19/differential-geometry-book-list/

[slow roost]

very cool

[runic rover]

i wanna find some calculus, geometry and algebra books

[mortal iris]

Spivak, Spivak and not Spivak

[runic rover]

alr ty

[slow roost]

just cold recommending Spivak to someone who "wanna find some calculus"

naughty naughty

[runic rover]

someone's getting coal today...

wonder who it is

[slow roost]

Killuminaughty

[runic rover]

killuminati ⛔
killuminaughty ✅

[crimson swift]

Can anyone reccomend a good book to learn complex analysis? from like the basics of it

[willow basin]

This guy gets it

[viscid remnant]

Can I start working on Spivak's while working through Book of Proof by Richard Hammack. I have currently finished Logic and basic proving techniques (direct, contrapositive and contradiction). Or should I first complete Proofs?

[trail void]

you can do both or either

i did a few chaps from spivak and its better to know basic proof techniques atleast

[viscid remnant]

Yep, I completed the basic proof techniques part. I just asked because doing proofs only is feeling monotonous. It's kind of repititive and I like a little variety

[trail void]

then feel free ❤️

[willow basin]

Spivak has a meta line early in calculus when he's talking about the field axioms that did more for me than any logic type text or course ever did, lemme see if I can find it

I may also be imagining it

[willow basin]

I think I'm imagining it being a single sentence, but the first few chapters he gives some meta reasonings for why we have field axioms and ordered fields, (he is just calling them numbers) and it was really eye opening to me. Then he heads into his functions chapter, talks about the notation and how it's kinda weird, incredible exercises

[mortal iris]

It is the exercises that really sell Spivak as a Calc text (and his idiosyncratic writing)

And while his diff geo texts are also super well known, one that is not often talked about is his text on classical mechanics. It is one of the best introductions to mathematical physics as a discipline. He takes the time to point out using many examples how some of the intuitively obvious "easy physics" is actually quite difficult from a rigorous mathematical lens.

[mortal iris]

You're good to go. Spivak doesn't really expect you to have done a course on proofs but it's much more accessible if you have. Also, Hammack's later chapters do deal with proofs involving Calculus iirc.

[mortal iris]

Have you done real analysis?

[final vessel]

any documentaties/podcasts u lot recomend

[remote vortex]

I'm a big fan of Mike Duncan's Revolutions podcast

particularly the series on the French Revolution

[vital bane]

Is it on spotify?

[vital bane]

Or revolutions

[viscid remnant]

Like mathematical/technical or in general?

[floral lantern]

Beck is open access

[normal crystal]

nah, he's a scientologist

[remote vortex]

yep

[remote vortex]

Indeed, he covers like five French revolutions, but there's only one the French Revolution

(which in itself had at least two sub-revolutions not to mention a plethora of coups)

[final vessel]

mathematical

[faint jay]

I like Visual Complex Analysis by Needham

[rain wren]

this depends on your level

have you done measure theory and stuff?

or are you taking it striaght after intro real analysis

[final vessel]

yo

do u study at uni

[faint jay]

No
I self study

[final vessel]

A ok

cos i saw ur bio abt self studying

logic

nd i was curious on how u cld balance that w. uni

😅

[faint jay]

I keep a lotta books on math for the future
Rn I’m focused on logic and proofs

[gray gazelle]

Best choice is RD Sharma

according to me

[mortal iris]

No. Absolutely not. Not for anything.

[gray gazelle]

How

[mortal iris]

It is just poorly motivated writing with brain dead problem solving.

[gray gazelle]

Ok then i think you need tuitions

[mortal iris]

Also tries to do too much

[mortal iris]

Huh?

[gray gazelle]

yeah

in my country rd sharma is really good

[mortal iris]

Kid. I am mathematical physicist.

[mortal iris]

And I am from your country

It sucks

I used to think it was great some 10 years ago myself

It's not

[gray gazelle]

You are indian and you talk like this

that's not good

[mortal iris]

Anyone who thinks otherwise has the mathematical maturity of a peabrain

[gray gazelle]

sir

[mortal iris]

What's that got to do with being Indian?

It's a terrible book.

The Indian curriculum isn't designed to generate an interest in anything and it reflects in their books. The only pass I can give somewhat is to NCERT Physics.

And barely

[gray gazelle]

so is ncert good?

according to you

[mortal iris]

Read closely

If you wanna study math, pick up books on dedicated topics at your level rather than an all in one mess like RD Sharma or RS Aggarwal and the likes

[gray gazelle]

Pearson?

i prefer pearson too

[mortal iris]

That's a publisher

[gray gazelle]

IIT foundation

[mortal iris]

Not an author or a book

[mortal iris]

Nope. The math ones are a strict no no for these.

JEE math is like learning how to solve problems without understanding the math behind them

Not one good proof in there and it's all figure out the right trick

If you are in grade 11 and 12, use Hall and Knight Higher Algebra, Rosen's Discrete Mathematics, Stitz and Zeager's Precalculus coupled with Lang's Basic Mathematics and Pogorelov's Analytical Geometry. Finally Piskunov's Calculus when you get to it.

[vital bane]

b- b- but JEE is the hardest math in the world1!1!1!1!111

🥀

[mortal iris]

It sure is, for anyone who does math for getting into an institute as opposed to for the love of it.

[vital bane]

real

[vital bane]

You're doing a mathphys PhD?

[lavish radish]

Literally how math was for me in my k-12 years. I don't remember my math teachers even covering rational exponents. Here's the quadratic formula just plug in some numbers and you're good to go! NOT

It was 99% plug and chug

[mortal iris]

Potentially, focused on quantum foundations tho. Presently undecided and on a bit of a sabbatical exploring physics education cos that's something else I have an interest in. That said I have done a reasonable amount of work in the area to call myself that I would assume.

[vital bane]

Quantum foundations so stuff like hidden variable/non-local theory and Bell's theorem and stuff?

[mortal iris]

My work is more so on quasi probability distributions and characterising non-classicality, but yes around the same wheelhouse as those things.

[molten gulch]

I do not think people need to be re-educated because they dislike a given textbook. I personally cannot stand most of the "standard" textbooks as used within the Indian cirricula (for full disclosure, I am half Indian, never lived in India. I live in the US, however I have helped my cousins with studying for exams). Pearson is a textbook publisher. R.D. Sharma's books attempt to do too much in too little space. You also say that R.D. Sharma's books are the best for "everything", now does R.D. Sharma have a good book for real analysis? What about abstract algebra? Rigorous Number theory? Probability theory?

[normal crystal]

wait
wasn't this an argument days ago
why is it still going
I'm sure RD Sharma appreciates the glazing

[mortal iris]

Considering he now has ads for those hideous books, definitely.

[normal crystal]

instead of Stewart's Intgegral House, he can build the JEE Temple

[molten gulch]

I find it quite funny how many pages just advertize solutions to RD Sharma's textbook exercises

[hybrid sigil]

I wonder why there are so many textbooks for fundamental subjects like say abstract algebra, real analysis or linear algebra. There are tons of good books already, but people keep writing and publishing new ones every year. Is it because something is lacking in the existing literature? Or people aspire to create something new and unique? Or because many professors eventually convert their lecture notes to textbooks?

Not like it’s a bad thing, I am just thinking

[mortal iris]

From what I've seen it's mostly the converting of lecture notes

Though, some ppl like Cummings for instance do aspire to create something unique.

[hybrid sigil]

People keep writing textbooks in 2020s and Rudin aficionados still stand behind the book written in 1970s probably

[mortal iris]

Even Hubbard and Hubbard has a rather unique presentation

[hybrid sigil]

Does it mean that all those 50 years of book writing were in vain?

[mortal iris]

This is more so only because of its brevity. Practically no pedagogical value in such a book but definitely a lesson in pain for the masochists that mathematicians, particularly analysts tend to be.

Also there is this thing about academic inertia quite common in mathematics and physics. Ppl tend to refer to something too strongly in one generation and since they teach from it, it kinda takes root in the next and stays there. Most ppl do not appreciate the change when it comes to lecturing on certain more basic topics. Mathematicians are a little less prone to that than physicists though because many see writing proofs as an art and that shows among those with pedagogical skill.

[mortal iris]

These are the ones who probably write new books based on their lectures hoping it offers something different.

[hybrid sigil]

Apparently it won a prize in mathematical exposition:

It earned Rudin the Leroy P. Steele Prize for Mathematical Exposition in 1993.

[mortal iris]

Wow. That is a genuine shocker. That said idk what the prize's criteria is really. It might be awarded to books in a similar vein for the most part at least during some period of time.

[mortal ore]

I mean ive heard great things about rudin

[mortal iris]

It's not a bad book by any means. It's just not meant to be a book to learn from. It reads more like a monograph than a textbook.

I personally don't like it because I don't like dry exposition devoid of real world intuition.

[hybrid sigil]

Yeah, this inertia is quite clear. And even those recommendation resources like Reddit, math stack exchange and this very Discord: many people probably just recommend what they liked or used while studying. So I guess it’s difficult to enter the game and topple Rudin. Although some people apparently can achieve that and achieve that “recommended by default” status. Like Abbott or Axler

[mortal iris]

But it develops too much too quickly, even if properly and there is little room for a student to breathe.

[mortal iris]

Rudin has well been toppled today in Analysis for sure. It was never really that big in Europe afaik anyways. Most ppl also recommend Abbott and Cummings. Ppl into mathematical physics would always prefer Zorich. Rudin just hits the spot for the more masochist types today imho.

And there are far better texts already when it comes to Complex and Functional Analysis so really only Baby Rudin was half decent imo.

As far as Linear Algebra goes different texts do tend to take many different approaches and include certain special different highlights in their exposition. For instance it's Axler vs Determinants.

Or Shilov's physics heavy problems

Or Strang's lower level computation heavy text.

[hybrid sigil]

It’s interesting to look at other winners of that prize

J. S. Milne got it recently for all his freely available lecture notes

Aigner, Ziegler won it for “Proofs from THE BOOK”

And Cox et al. for “Ideals, Varieties and Algorithms”. Looks like they have good taste 🙂

https://en.wikipedia.org/wiki/Leroy_P._Steele_Prize?wprov=sfti1#Steele_Prize_for_Mathematical_Exposition

[tame tree]

rudin is actually goated for a second pass

abbott is too easy

the exercises are 🤌

rudin gives very generous hints that stop you from going down dead ends

also, with something like pugh theres a lot of exercises per chapter (and theyre all at the end of the chapter) which makes it hard to pick a balanced selection

rudin doesn’t have as much per chapter and if you do them all youve got a good handle on things

itll also make you develop and reprove some lemmas youve likely seen in topology

really the exercises i would say are like munkres level difficulty

his proofs are also very nice. the conciseness lets you focus on the key arguments of the proof without too much detail that serves to fill in gaps

also bergmans notes supplement rudin really well (even too much if you already know some analysis)

a useful feature is that the notes rate a rudin exercise by difficulty and offer some additional elaboration on rudin’s hints

[hybrid sigil]

Yeah, this is my problem in general: some books have tons of interesting exercises, but it’s difficult to know when to stop - also there is FOMO, who knows maybe some exercise is really important or gives some valuable insight?! So I tend to do most of them, but it’s slowing me down. Now I tend to budget the number of exercises in advance: like “Solve 15 exercises from Herstein”. This helps somewhat, at least I like that I stick to my own plan. Any better suggestions?

[tame tree]

i think giving yourself a set time frame to move on from a chapter can help

do exercises that seem interesting and try to work on ones that you think you have no idea how to do

[hybrid sigil]

Time limits are not very consistent: I may be more or less busy during particular week…

[tame tree]

true

give yourself some margin of error then

[hybrid sigil]

And I don’t want to start tracking time

[hybrid sigil]

Haha, yeah, but that may lead to another problem 🙂

Not knowing when to give up

I am often too stubborn and sometimes may spend days on a single proof!

I remember once solving a problem where I actually misunderstood the statement of the problem and was trying to prove a false statement for quite some time 🙂

Thankfully my friend noted the ambiguity in the statement and then I proved corrected version in minutes 🙂

And asked ChatGPT to find me a counter example for that wrong statement which turned out to be quite interesting in itself 🙂

[trail void]

im pretty sure theres even a cia document on pogerelov's geometry

oh look

https://www.cia.gov/readingroom/docs/CIA-RDP86-00513R001341610002-3.pdf

the internet is full of random suprises

[hybrid sigil]

Wow, what is the context here?

I.e. why is that on CIA site?

[trail void]

i have no particular clue but they have multiple documents on his works

mostly early 2000s though

oh there is a clue

they were simply trying to digitize and make this historical work accessible, im guessing its related to the cold war

the US did consider soviet mathematical works pretty good so it would make sense

https://www.cia.gov/readingroom/docs/CIA-RDP80-00809A000700180455-6.pdf

[wild blaze]

havent done any probability or stats or combinatorics whatsoever, but am interested

am doing measure theory rn

is there any probability / combinatorics things i should look at first

[ebon plinth]

They were sort of obsessed with the ussr you could say
Maybe someone referred to a content of this book in a coded message? Just speculation

[ebon plinth]

Simple game probabilities. Sum of two dices etc. convolution

[wild blaze]

what lvl is this for stat / probability

lower undergrad intro prob??

[ebon plinth]

Intro

[molten gulch]

<@&268886789983436800> piracy

[real marsh]

@ebon plinth pls don't send links to copyrighted books thanks

[ebon plinth]

This is a preview you absolute legend

[real marsh]

why do they post previews and then say in the book at the start "no part of this may be transmitted" 😭, okay if its like official that's fine

[ember karma]

To make our lives harder, of course

[dusk hemlock]

(i feel that this is kind of ambiguous due to some authors publishing the pdfs of copyrighted books)

[ebon plinth]

"Games, gambling, and probability : an introduction to mathematics / David G. Taylor, Roanoke College, Salem, VA." Without link . For the interest ed

[real marsh]

As a rule of thumb I do delete those. There's also a non trivial number of mathematicians who post copies of pirated books by other mathematicians to their website, which is great for me the mathematician, but not for me the mod

[dusk hemlock]

ok but what if i say clearly that the authors of this book have published it online?

[ebon plinth]

Idk man. I don't think much about copyright

It's ok if you delete just every link just to make sure

[ember karma]

That should be fine imo, from what I've seen, as long as it isn't directly shared on this server

[real marsh]

If its also copyrighted by the publishing house it is copyrighted, we don't know if the author is allowed to do that or not

[dusk hemlock]

wait what
the book is completely legal, the authors put the pdf online

[dusk hemlock]

it was self-published

[real marsh]

okay this is a completely different scenario

then its not a copyrighted text

[dusk hemlock]

well, wait, but it is

it's copyrighted

(sorry for starting this 😭)

[real marsh]

The author has seemingly then permitted distribution as long as you route to their site so its fine

[dusk hemlock]

(i actually kinda know the authors of this specific book )

[ember karma]

You're fine, it is a tough one, and there are situations where it's difficult, my view is that I want things to be as clear as possible so that there isn't any ambiguity, and then some things slip through and all of a sudden, server goes poof cause partnered and Discord big people angy

[dusk hemlock]

:thumpy:

[velvet briar]

Didn't we have a fixed "books" channel? Where did that go?

[dusk hemlock]

it was archived, #books

wait there's also #books-old

[velvet briar]

I can't access those

Well, I was thinking about trying logic. Let's say I know some pure math like topology and abstract algebra. Is there a good intro book for me?

[dusk hemlock]

select archivist in channels & roles

or just ,iam Archivist

[velvet briar]

That works! Thank you.

[obtuse ginkgo]

Hello , i am a pre-uni student with veryyyy basic knowledge of maths , like ABSOLUTELY BASIC - (Uhh like just know the basics of trig , ik barely anything about geometry , some very basic algebra stuff n all)
Pls guide me on how to start 🙏

[viscid remnant]

You want to do high school stuff?

[obtuse ginkgo]

Uhh i am guessing thats where I should be starting to do anything furthur?

[viscid remnant]

KhanAcademy then

[obtuse ginkgo]

Ic ic thx

[obtuse ginkgo]

But like is there any book , cz honestly i am faster learning with a book instead of lectures

[viscid remnant]

What exactly do you wish to study?

A good book can't do all of them. So we would need to be a bit more specific. I also assume you have done prealg since you started algebra

[cunning elk]

KA has plenty of written material too

online resources are insanely oversaturated at the precollege level

[tender cobalt]

what should i study after spivak calc on manifolds

[daring wolf]

depends on what do you want to learn and your background lol

[tender cobalt]

can i pick up something like Tu or Lee manifolds

but other than manifolds / diff geo , what can i pick up

[daring wolf]

tell your backgrounds

[tender cobalt]

linear algebra , analysis in R^n, and some topology

[daring wolf]

ok

[chrome wasp]

Have you done func anal & measure?

[daring wolf]

sure you can do these

[tender cobalt]

nope

anything else

something cool

[daring wolf]

some other stuff would be something like measure theory,functional analysis as said above
if you want something algebraic you need to do abstract algebra first

[tender cobalt]

ooo i see

so theres two ways to go, either algebraic or that analysis/diff geo type route

[chrome wasp]

Ugh...i dont think its that simple

[daring wolf]

yeah

[chrome wasp]

While you were reading CoM, what questions were you asking yourself the most, what was most interesting

[tender cobalt]

obviously differential forms and stokes theorem felt most interesting

[chrome wasp]

Yeah that is obv xD

[daring wolf]

X E.

[tender cobalt]

ye so the most natural followup would've been manifold theory and diff geo 😭

but i was wondering what other options i have

[chrome wasp]

Are you in uni? Or self learning

[tender cobalt]

self learning

[vital bane]

Self uni

[remote vortex]

The school of hard knocks

[chrome wasp]

Maybe you should continue with dif geo/topo as you mentioned or what feels cool to you. When you reach a point where you need something from other branch, you pause till you learn what you need.

[chrome wasp]

Complex analysis

[tender cobalt]

good idea

alrr

thanks

[chrome wasp]

Dont you dare show your name around here till you finish the proof

[real marsh]

@minor parrot don't advertise some random game lobby in half the channels in the server thanks

[tender cobalt]

yo do you have more recommendations on such books

[jolly dawn]

🤔 hmm

[jolly dawn]

Honestly I feel like elementary geometry is just a stepping stone for algebraic / differential geometry. If you do find elementary geometry interesting and want to go in like really deep, I can recommend "geometry revealed: a Jacob's ladder to modern higher geometry" by Marcel Berger, though it's more like a survey of open problems of the field. Idk much else to be honest

I haven't gotten doing the geometry books myself though. I've just read passages at random and thought the exposition was nice 🙂

[obtuse ginkgo]

Ye i have

[rough kettle]

What would you guys say the best textbook to order would be to learn calc 1 as a complete beginner?

[tender cobalt]

oooo

[mortal iris]

Depends on what you mean by "complete beginner"

[dense valley]

If you’re a complete beginner, start with covering college algebra and precalculus first or you’ll mess up in the algebra and geometry parts that calculus requires. As for books, I recommend Stewart or Thomas, those are very widely popular, lots of explanations online and they’re good at explaining concepts

If you’re not into that, you could try Sullivan

[dense valley]

Also, Stewart is used as the basis for a lot of university Calc 1 courses, which is what I assume you’re referring to?

[rough kettle]

Thankyou for this. I should’ve stated I have a basic understanding of algebra and trig as opposed to a complete beginner, I’ll check these books out

[cinder condor]

are there any book recommendations for beginner level integral? i have learned limits and derivative, and would like to learn integral next.

[mortal ore]

Khan academy

[cunning elk]

literally any standard calculus textbook

[dense valley]

yeah, integrals and integration is usually a chapter in calculus, so i’m not sure if there are any good books specifically for integrals

[viscid remnant]

I recommend Khan Academy upto alg/precalc level. At some point, you should shift to standard textbooks I think. Calculus is a good time to do that

[dense valley]

@wraith canopy

[mortal ore]

Linear algebra in my opinion

Calculus is still the point where theres really not enough tough theory to require a textbook imo

[viscid remnant]

But it serves as a good bridge I meant

[mortal ore]

Possibly, but khan academy is good for the practical-ness of calculus in my opinion

Calculus is only intended as a set of tools and some intuition

Rather than some actual powerhouse theory for proofs

[viscid remnant]

That's a fair way of looking at it

[tired echo]

the main things on my list of things to read are famous extremist manifestos

i think that those would help my chinese and german

[mortal ore]

Tell me when it switches from 20th century anarchism to 4chan chuddery

[tired echo]

LMAO

[mortal ore]

Assuming you read it chronologically ofc

[tired echo]

ofc ofc

maybe i should

alr lets see here communist manifesto, mein kampf, xiao hong shu, the industrial revolution blah blah,.... wtf is a chudjack

[tired echo]

what no extremist stuff should i read

non*

[mortal ore]

Brothers Karamazov was a good read

Widely claimed to be the best secular book ever

Hatcher might be a better work of fiction tho

[tired echo]

ty

[vital bane]

I finished it several days ago, it was extremely simple just like you said, literally just Cauchy-Schwarz

[north summit]

How's Conway Functional analysis? Any other recomendation ideally from springer(cause of discounts).

[wraith canopy]

Thanks That Stewart recommendation helped my basics a lot

[tiny crescent]

Is there a book explain sequential circuits?

[solar jewel]

you should perhaps try asking in the electrical engineering server #old-network

[tender cobalt]

what is the alg geo roadmap from zero

[mortal ore]

Prealgebra

[tender cobalt]

😭

[mortal ore]

What do u already know

[tender cobalt]

linear algebra analysis and some topology 🙃

[mortal ore]

Abstract algebra then

As for a starting book idrk

I used gallian to begin with and I ended out fine

But its so weak with group actions it hurts

Dummit and foote is the standard second read

It has its problems but its good

[barren pollen]

any1 know of a good platform to upload your books and read them on different devices?

i tried google books but with pdfs it blurs them 😭

[wild blaze]

adobe pdf, apple books, goodreads, pdf expert

some of the ones ive used

[warm sparrow]

What is the Calculus book I should use given that I am familliar with calc 1?

[wild blaze]

everyone usually likes james stewart

start at integration by parts or wherever you ended off

[warm sparrow]

thank you

[wild blaze]

have fun!

[hybrid sigil]

Dropbox?

I just put all pdfs and djvus there, properly tagged and then I can download and sync between devices

[mortal iris]

Einseidler and Ward

[mortal iris]

I used to think that too but no. It's entirely possible to strike a balance and thus Calculus should be as much about the intuition as a prelude to Analysis.

[mortal ore]

Well i did mention the intuition

But calculus is mostly for its tools since many non math students take it as well

[mortal iris]

Zorich's volumes on Mathematical Analysis and Arnold's ODE and PDE books are great examples of this but of course, one needs to tone down things a little while teaching given the nature of these texts. But most of these books are very much accessible to a first year and are heavily littered with applications particularly in physics while maintaining a high level of rigor.

[mortal iris]

The only pass for this is for engineering and economics students but a pen and paper Calculus course is useless for them in this day and age. They should be doing all this stuff on computers as opposed to sit and solve pointless integrals.

[mortal iris]

I think Artin does a pretty good job with group actions and isometries as well or maybe I am remembering things wrong.

[amber beacon]

algrbra noob to pro

[mortal ore]

Its moreso a test of competence and critical thinking

In the style of the kind of stuff they think about regularly

[remote sparrow]

because a lot of his "proofs" are fake?

[remote sparrow]

a little dry but straightforward

[north summit]

@mortal iris not in discount

[north summit]

The other option is bresis

[remote sparrow]

doesn't cover as much (notably missing is any coverage of distributions) but it has solutions in the back

it's a book designed to prepare you for pdes

it also assumes every vector space is real

[mortal ore]

Read my mind

[wild blaze]

hatcher isnt good??

[slow roost]

it is but it has a reputation for being loose

[mortal ore]

Hatcher is great for visual proofs but its not very rigorous