book-recommendations

[vital bane]

generating functions 🔥

[floral lantern]

this is not true for algebra/geometry

[still panther]

geometry is at Z tier

[tender cobalt]

is that bad or good 💀

[floral lantern]

oly moment

i should lock in next year for oly

[vital bane]

mfs trying to do research in algebraic geometry after getting a IMO gold medal:

[still panther]

i hated olympiad geometry and never even tried any of it on competitions

[floral lantern]

an alum from my school did an alg geo project and won an IMO gold

💀

[molten gulch]

integer tier

[still panther]

i loved computational geometry problems at programming contests though

[vital bane]

what does olympiad geometry entail?

[tender cobalt]

olympiadists my country are dumbfuck idiots, dudes dont even know epsilon delta proofs

[floral lantern]

💀

[vital bane]

ooh computational geometry is interesting

[tender cobalt]

all they do is spam problems and solve them WITHOUT EVEN learning any theory

[floral lantern]

there's nothing wrong with this

[tender cobalt]

there is wrong if you aspire to be an IMO medalist

how can you solve further problems if you dont even know theory

[molten gulch]

Not always, there is some theory at-least in some fields -James

[tender cobalt]

im talking about dudes from my country

[vital bane]

which fields? algebraically closed?

[floral lantern]

In my experience spending time on Olympiads and building problem solving skills is often more useful for many high schoolers than doing math by themselves without really understanding it or having structured programs to learn

It worked out fine for me but idk abt the avg person

[tender cobalt]

youre a different high schooler

not the average people

[floral lantern]

no I don't do oly

lmao

I did pure math all of high school

[vital bane]

olly olly oxen free

[still panther]

at high level there are like techiniques, like inverses, or you need to know Thales's, Menelaus's, Desargues'; Pappus's if you are really out there

[floral lantern]

but I was very privileged to have a strong math support structure that allowed me to do that

[cinder magnet]

we should discuss about rings as they are superior

[floral lantern]

and not fail

[tender cobalt]

"The IMO Compendium A Collection of Problems Suggested for the International Mathematical Olympiads: 1959–2004"

This book has some topics that appear in olympiad but guess what, these resources aren't even suggested to people from our coutnry lol

[vital bane]

interesting, so no metric tensors? sadge

[tender cobalt]

its all just elementary geometry mostly

[vital bane]

I should do some Euclidean Geometry some time

[still panther]

i wouldnt call it elementary but it is pretty boring

[vital bane]

I think Hartshorne has a book on it

[still panther]

he does yeah

but I would recommend anything else lol

[molten gulch]

he does

go read the elements kekw

[tender cobalt]

learn conics fr

[still panther]

it assumes you would read elements parallel to it

which thank you but i would rather not

[vital bane]

seems more like a systemic issue than the fault of the olympiad enthusiasts tbh

[vital bane]

let me learn greek real quick

[tender cobalt]

its the fault of the olympiad enthusiasts as well

they skip everything they see saying "it will not come in olympiad"

Little do they know that olympiad does not have a standard syllabus and whatever you learn to apply and solve problems can be beneficial

[still panther]

if you want to get a thorough course on the topic, i would read pamfilos instead

[tender cobalt]

my friend went to the national olympiad camp, and he solved a problem using calculus

[vital bane]

pamfilos?

[tender cobalt]

the instructor gave him side eye because of that 💀

it was like a minimum of a function

[vital bane]

Lectures on Euclidean Geometry - Volume 1

?

[still panther]

yea

its a two parter

[vital bane]

Volume 2 - Lectures on Non-Commutative Algebraic Geometry

[still panther]

a natural step in an adults life

[vital bane]

so this is an axiomatic approach to Euclidean geometry?

[molten gulch]

I've seen this mindet even go past the time of the olympiad in some cases

[vital bane]

much like Euclid's axioms I suppose

but I guess these are more modern using ZFC?

[mossy flume]

non-commutative algebraic geometry and commutative algebra is scary

[vital bane]

hm I don't even know if choice is required for Euclidean Geometry

[molten gulch]

looool

[still panther]

no, its just axiomatic euclidean geometry

i think

[vital bane]

the axioms are separate from ZFC?

[molten gulch]

Lectures on Euclidean Geometry - Volume 2: Circle measurement, Transformations, Space Geometry, Conics

[still panther]

i mean yeah euclids postulates or whatever

[vital bane]

Oh. My. God.

I have to get this book

[molten gulch]

LMAO

[molten gulch]

me when springerlink

[vital bane]

Why can't books be free 😔 like Axler's books

I guess they kind of are

[still panther]

athens has a leyline that spits out plane geometers

[vital bane]

and it's called a library

https://math.stackexchange.com/questions/823561/how-is-geometry-defined-using-zfc

[gilded shuttle]

thanks

[gray gazelle]

lmfao

<@&268886789983436800>

[dapper root]

Commutative algebra cozy

[mossy flume]

if the ring isn't Noetherian I don't wanna hear about it 🗣️ 🔥

there's been some use of noncommutative polynomial rings in algebraic complexity theory: https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2018.12

I want to learn more about some of that stuff

very interesting stuff, in the noncommutative setting the existance of linear non-commutative circuit lower bounds implies the existence of exponential non-commutative circuit lower bounds

and analogous things in the commutative setting don't exist (it'd be surprising if they did IMO)

[mellow wren]

mfw literally any counterexample nagata came up with

https://tenor.com/view/good-norming-good-morning-gif-good-morning-gif-pixmix-gif-11930298751610206899

[dapper root]

You can tell it’s complexity theory cuz they say “explicit”

[mossy flume]

pretty much yea

[novel obsidian]

I'm looking for a reference for quadratic and bilinear forms. Ideally something short so I can read Reid's Undergraduate Algebraic Geometry. Does anyone have any suggestions?

[loud onyx]

Can someone recommend me a good book covering multivariable calculus? I'm interested in the topic

I already have access to Stewart's Calculus: Early Transcenedtals, but if anyone has anything else i'm open to it

Just to add, i'm Croatian myself so if anyone has good piece literature in that language i'm also interested

[trail hemlock]

ask wilson

[loud onyx]

I can't, didn't you forget how the series ended?

[mellow wren]

you want it in croatian or english

[loud onyx]

Both are fine

[trail hemlock]

oh for english, Folland has a good book called "Advanced Calculus" that you may enjoy

[loud onyx]

Thank you my fellow croatian 🙏

[loud onyx]

Let me google it

I couldn't find at the moment, but i'll check it out tommorow

[loud onyx]

Sorry to bother, but i was wondering if I could dm you about something?

[mellow wren]

yeah sure

[gray gazelle]

hey @remote vortex sorry for pinging you but someone said you might be able to help with this and i saw you were on, you got anything to suggest?

[graceful moon]

I’ll DM you something for exactly that

[remote vortex]

Nothing other than Billingsley springs to mind, although it's arguable how introductory that one is.

Ostensibly it doesn't assume previous knowledge, but familiarity with the "classical" and less rigorous probability might be helpful

[gray gazelle]

I guess I'll give it a shot then, thanks.

[slender cargo]

Any rec for a "classical" and less rigorous probability book? I'm taking measure theory (using Axler's book) and have never learned probability theory..

[dapper root]

Blitzstein Hwang

Oh huh this ate my link

I’ll dm you

[slender cargo]

Thanks!

[sullen sorrel]

hii i am in elementary school and great at maths for my 7 grade so do smbd know some maths book for my level of maths it would really be helpful, maybe something for algebra?

[wraith cave]

how old are you?

[sullen sorrel]

14

in balkan is different grade system

[wraith cave]

i see 😭

try khan academy they have good videos on algebra 1 and 2

[sullen sorrel]

its from 1 to 8 then high school

[sullen sorrel]

where? on yt?

[wraith cave]

https://khanacademy.org/

[sullen sorrel]

thank you really much

[remote sparrow]

it's probably because your link contains the string that sounds like "eye cue"

[broken bramble]

is that not allowed?

[mortal ore]

yeah because people on here genuinely argue for eugenics whenever its brought up

[dapper root]

Oh yeah lmfaoooo

[broken bramble]

that's pretty funny

[vast jackal]

khan academy is great or basic mathematics by serge lang

[gray gazelle]

basic mathematics too good

[trail hemlock]

lang's basic mathematics is so dry and unmotivated i wouldnt blame someone for burning the book and not even recycling the ashes (imo). just use khan academy

[manic cairn]

ignore this man

basic mathematics is peak

[normal crystal]

now you see (above) what I was talking about, mhm

[gray gazelle]

right

[gray gazelle]

fr tho i don't think it is dry and unmotivated

i found it opposite

[real stratus]

can you check dm btw

[loud onyx]

What do you mean by algebra? Because algebra goes from 0 to 100 really fast

But for someone at your age who's interested in math topics, i suggest khan academy and 3blue1brown (maybe they're not 100% formally defining things at all times, but they do it intuitively which is better at pre-highschool level)

[vital bane]

also the formal definitions follow from intuition so if you develop the intuiton, you can follow it with formality

[loud onyx]

True

[final night]

@everyone I'm a year 10 from Australia trying to get accelerated/ahead of my class in mathematics. I was wondering is there any book recommendations I should do that can help me accelerate thank you 🙂

[fresh skiff]

what does it mean by year 10

[tender cobalt]

grade 10 probably

[fresh skiff]

oh makes sense

[loud onyx]

What is the last topic you covered in your math class?

[final night]

@loud onyx last topic was linear equation we are currently working on simultaneous equations

[loud onyx]

Okay so you haven't done functions or quadratic equation yet?

[final night]

no

[loud onyx]

Trigonometry is also a no?

[final night]

no

we are going to later in year but not now

[loud onyx]

The thing is, any type of higher maths requires some basic knowledge

For example, for calculus you need to understand functions well, and for linear algebra you need to understand vectors well. I don't know of any book that covers all those topic, maybe some pre-calculus book?
Do you know the curriculum for your next grade, if that's the topic(s) you want to advance in?

Khan Academy has good pre-calculus videos

[final night]

I know in year 11 in specs (specialists) and methods they do cover calculus but I don't know of any in between book that to cover before these years 10 and 11 in Australia.

[loud onyx]

What is your grade 10 curriculum after equations?

[final night]

I just in any mathematics whether it is trig, quadratic functions, calculus, etc. I just want to do mathematics that will get me ahead.

[final night]

I don't know

[loud onyx]

I'd suggest covering linear functions, quadratic equation and quadratic function next

And understand what a function is, try to understand (formal) definitions

[final night]

In Australia we don't get a mathematics year syllabus to follow.

[final night]

ok thank you do you have any books that you know or used that go over this.

[loud onyx]

I'm sorry, i did that back in high school so i only have my textbooks (they're not in english)

[final night]

ok but thank you for the help have a great day 🙂

[loud onyx]

Khan academy and 3blue1brown are the way to go at your level of math!

Those are youtube channels, if i didn't note it before

[warm river]

Are there any good books for early university math level? Like from the start

[loud onyx]

You mean like calculus and linear algebra?

[warm river]

yes

[final night]

I'm on khan academy website its asking pre-algebra, algebra 1 or algebra 2 which one is it we don't have this in Australia we just have different mathematics levels.

[loud onyx]

James Stewart's calculus book is pretty good and detailed

[warm river]

Does it have some good exercises and explains it from the beginning. I have the feeling some books like to jump from one topic to the next

[loud onyx]

Check out all of them, starting from pre-algebra and check if you already know the topics covered

[loud onyx]

I'd say it does, it even has some self-reflection at the beginning

Or like diagnostics test

Calculus: Early transcedentals

I think the book has around 1350 pages

[warm river]

There is a pdf version of it awesome gotta look at it

[loud onyx]

That's why i said all the things i said lmao

I'm not sure if it's frowned upon here to send some pdf versions since they might be illegal, but i personally believe that education and knowledge shouldn't be behind a payment

[vital bane]

Khan Academy is great! start at pre-algebra and work you way up to algebra 2 and pre-calculus and and calculus and then eventually de Rham cohomology

[final night]

What is de Rham cohomology?

@loud onyx I forgot to ask how much exercises do I do a day

[vital bane]

god's gift to this wonderful world 🙏

[final night]

lmfao

[loud onyx]

That's up to you

[final night]

okay 🙂

[deep moat]

https://cdn.discordapp.com/attachments/285066738863702016/1357581913090691132/petpetchick.gif

[woeful kite]

good book for finance ?

[tender cobalt]

is gamelin good for covering complex analysis?

[tender cobalt]

whats difference between ahlfors and gamelin

[vital bane]

well for one, they're written by different authors

[tender cobalt]

whats the difference in contents and coverage

and scope

[vital bane]

@naive lava is going through Ahlfors right now

he loves it

[gray gazelle]

another option is conway's functions of one complex variable

it's introductory but rigorous

[vital bane]

conway is good too

[molten gulch]

slender you've asked about CA books here like four times 😭

[tender cobalt]

idk what to do 😭

SO MANY CHOICES

[still panther]

just pick one

[molten gulch]

just close your eyes and pick one

[livid lintel]

There’s this thing called a spinning wheel

[tender cobalt]

okay

First i need to know the content coverage

of conway vs gamelin vs alfhors

if one covers less content i will just not select

[molten gulch]

sometimes ✨ it does not matter at your level ✨

[tender cobalt]

ill just go for gamelin then

since less prereq

[molten gulch]

yeah this is what you said last week 😭 please try to stick to it, now if it goes badly, try something else ofc

[tender cobalt]

okaky

[vital bane]

first you need to finish the books you're currently going through before coming to #book-recommendations

[tiny steppe]

No

[compact scarab]

Guys, would you recommend to read Introduction to Number Theory by Matthew Crowford, to get prepared for the math olympiad?

[slender cargo]

Don't you still have to learn elementary real analysis, and multivariable calculus as well? You have a while before you start complex analysis

And there's linear algebra, abstract algebra, etc...

[lunar pond]

The reckoners is an amazing series

[wraith cave]

any good books for pdes?

maybe a bit extra on fourier and laplace transforms as well if it allows

[naive lava]

goated book fr

i tried it, gamelin and churchill

ahlfors is by the best

[vital bane]

Churchill is for engineers

[naive lava]

I heard it's too slow

the thing i love about ahlfors over gamelin is that it actually makes sense

in a pedagocigal way

it starts out with defining functions with derivative

then develops everything one would need

every major problem

not too long, not too short

js enough coverage of the basics

[vital bane]

gamelin doesn't make sense in a pedagogical way?

[vital bane]

<@&268886789983436800>

in the other channels as well

Nice

[naive lava]

i mean

if u already have motivation

and know a little bit

[deep moat]

yes

[final night]

good morning everyone how has everyone's day been?

[rugged nimbus]

Pretty good so far

[rugged nimbus]

I have a course with the Churchill book and by the end of the semester we'll be through ch 7 on applications of residues
At that point should I consider continuing through ch 9 on conformal mappings or switch to a book like ahlfors?

[foggy quest]

I think you should just start with a more rigorous book like https://mtaylor.web.unc.edu/notes/complex-analysis-course/

I mean, Churchill is probably not that much less rigorous, but what's the point of it

[daring wolf]

Imagine churchill ☠️☠️☠️

[rugged nimbus]

Why the hate towards Churchill? I've had a positive experience as an introduction to complex Variables so far.
It obviously leaves things out, but it's nothing a second course or review wouldn't solve

[foggy quest]

A first course should be more advanced than Churchill. Churchill is for a zeroth course.

[rugged nimbus]

Ok, I'm just confused by how you said Churchill isn't much less rigorous than the textbook you provided.
Is that to say that it covers content more slowly than the book you provided? bc I see the immediate difference in how Taylor gets to the calcus instantly while Churchill takes his time

[rugged nimbus]

Also sorry if this is getting a bit discussiony

[vital bane]

check out both, both ch 9 and ahlfors and gamelin, see what suits you

[vital bane]

[vital bane]

imo it's not a bad book at all, it's just feels a bit too old for my tastes and of course it is just as rigorous as other CA books but it's a bit simplified and there is some details missing

[vast jackal]

there's no way the winston churchill himself?

oh nvm

I'm wrong..

[vital bane]

"Complex Analysis" by Winston Churchill

[wide dock]

any reference books for grade 12 olympiad

[serene flame]

BOOK REC - RS AGGARWAL GRADE 10

[viscid dome]

Can someome reccomend me a good book on order theory? I'm working through Rosensteins on Linear orders, and will soon explore one on universal algebra but it would be interesting to see it from a broader perspective of posets.

[remote sparrow]

https://www.amazon.com/Introduction-Lattices-Order-B-Davey/dp/0521784514

https://link.springer.com/book/10.1007/978-3-319-29788-0

https://link.springer.com/book/10.1007/978-3-0348-0018-1

https://link.springer.com/book/10.1007/978-0-387-78901-9

these are what i found online

[sullen sorrel]

Thank you so much everyone i tried khans academy and its really helpful, i had math olimpiad and won 3rd place because of algebra

[steel moth]

is twisted hate by ana huang worth reading? I usually dont read spice but most of my family members are recommending me that book.. Ive always known about ana huang though, but I'm not interested in reading her books

[hexed scarab]

Anyone have an integral book?

or diferential

[rugged nimbus]

Ok, gotcha thanks for the explanation

[molten gulch]

Hey does anyone have any recs for texts on the history of the formalization of calculus and analysis? One of our friends is looking for texts (multiple) in this vein that cover calculus in Newton's time, any ideas that would've been considered calculus today in the past such as methods for solving infinite series AS THEY EXISTED prior to Newton, etc...

[vital bane]

perhaps "A Radical Approach to Real Analysis" by David Bressoud?

[loud onyx]

Congrats

[stark turret]

why is "linear algebra done right" held in such high regard? I have no complaints about it, but it doesnt stand out to me as being much better than any other book. I guess the price helps

[broken bramble]

what other linear algebra books have you read?

[terse garnet]

Hello

how do I read books with proofs

especially when there is no answer to said proofs

[timber mesa]

answers?

[warm arrow]

i borrowed this book- "Modelling Mathematical Methods and Scientific Computation Book", kinda excited to look over before a class on modeling this next semester

[timber mesa]

not sure I understand the question, but in any case it helps to take notes and break down the actual proofs in the book into steps or filling in small details that the author omits

[terse garnet]

like for example serge lang

basic mathematics

[timber mesa]

if you mean instead how to do exercises that involve proving things that's another thing

[terse garnet]

has many exercises

where its asked to prove things

like the communative property

but theres no way of knowing whether your answer is correct

[timber mesa]

you know a proof is correct if every step makes logical sense and follows from things you already know, basically

if you need help or confirmation that your proofs are correct you can also ask here, it's fine if you ask in e.g. #math-discussion or #proofs-and-logic I guess

as for coming up with proofs it's kind of hard to just list "proof techniques" or things you should do, but some notes and books do just that

there's Hammack's https://richardhammack.github.io/BookOfProof/ which essentially has some basic logic and set theory and then a rundown on how you apply those things to write proofs

[terse garnet]

I c i c

[terse garnet]

whats your opinion on proof assistants in a programming language like lean 4

[timber mesa]

I don't have much of an opinion

been meaning to look into it sometime it's interesting if anything

[feral tusk]

Guys can you recommend a book for me

If there is no problem

[remote sparrow]

for what topic

oh they left

[slow roost]

then you need to read and do more proofs and correct more wrong proofs to hone your sense of if what you're doing is really legit or not

ideally getting help from people who know what they're doing better than you

[timber mesa]

that's a possibility as well

[timber mesa]

basically this, yes

maybe it'll look fine to you but you aren't 100% convinced, then someone else checks and realizes you assumed something or made a small mistake

[naive lava]

hartshorne

[remote sparrow]

this can't be a possibility, speaking noncolloquially. if your proof is wrong, then a thing you "already know" is false or applied incorrectly (so your step doesn't make logical sense).

[timber mesa]

I meant more like, the proof being wrong and you not realizing is something that can happen

[remote sparrow]

for sure

[timber mesa]

if you know with certainty that the proof is wrong then yeah

[gentle jasper]

Does anyone have a recommended text for point sets? Something to use to bridge the gap to Measure Theory by Axler. I feel like my knowledge of set theory is really hindering my understanding.

[naive lava]

halmos maybe

[velvet cove]

Book recommendations for "linear algebra and ordinary differential equations" ??

[naive lava]

if u find it too chatty jech or enderton are also reccommended afaik

[naive lava]

at what level

[still panther]

like, in the same book?

[velvet cove]

Early University level - doing bachelor of civil engineering- 2nd year

[naive lava]

schaums's outlines maybe?

[velvet cove]

Shaums has partial differential equations... can't find ordinary differential equations

[velvet cove]

Yes

@still panther ?

[limpid bear]

you could try that gil strang book https://math.mit.edu/~gs/dela/

[heady ember]

It seems Rautenberg's logic text is freely available on the Internet Archive:
https://archive.org/details/a-concise-introduction-to-mathematical-logic-3rd-ed-wolfgang-rautenberg-2009/page/1/mode/2up

Nice

[remote sparrow]

https://www.amazon.com/Differential-Equations-Linear-Algebra-4th/dp/0321964675

[broken bramble]

just set theory? or you want point set topology

[last cipher]

Has anyone used keith nicholson's linear algebra?

[patent canopy]

EGA by Grothendieck/Bourbaki

[patent canopy]

https://www.wiley-vch.de/de/fachgebiete/mathematik-und-statistik/advanced-engineering-mathematics-978-0-470-64613-7 try this

[remote sparrow]

https://www.youtube.com/watch?v=jpe3WVKbxbc

[small perch]

Typst is a new project. I believe, you can use it. I personally switched to typst tbh

[pine tundra]

I started by watching Federico Tartarini and Trefor Bazett on YouTube

[small perch]

I personally just google what I need. And there are plenty of documentation for something complex https://ctan.gust.org.pl/tex-archive/macros/latex/base/source2e.pdf

You can write anything you wish mostly with typst. But it still lacks some handy libraries, but still has something more low level, that will allow you to do so, just with some efforts

Typst is still under development, but you can do everything you see in textbooks

https://typst.app/universe/

[heady ember]

Imagine not using latex

Just start writing latex.

You can look up stuff as you go

[fresh skiff]

80 to 90% of my classmates don't know how to use LaTeX, they usy ppt (ms office) for presentation

[graceful moon]

I watched Dr Trefor Bazets videos to get started then I just used it a lot

[merry sphinx]

same

[fresh skiff]

The prof in university of Toronto?

[heady ember]

For math?

[fresh skiff]

Oh not really? I think he has written his introduction on YouTube as well.
Iirc he is a professor in university of Toronto and interested in Algebraic topology

I hope so i didn't misunderstood the prof lol

[fresh skiff]

For presentation

Math presentation

[old notch]

hi what's the go-to book for differential geometry? 👀

im new to the subject

[heady ember]

Common recs:

• John M Lee's series of three books on manifolds
• Jeffrey Lee's book on DG
• Toring Lu's books

[old notch]

is any of them more "beginner friendly" than others? or are they all good reccomendations for newbies?

[tender cobalt]

or if you want to learn basic differential geometry of curves and surfaces

you can check out Do Carmo's book or Pressley

[tender cobalt]

Loring Tu is very beginner friendly

his "introduction to manifolds" does not assume prerequisite in topology , covers the necessary in appendix

so if you know linear algebra and a bit analysis, you should be good to go with that

[old notch]

oke thanks

also is the guy's name Toring Lu or Loring Tu? just curious

[tender cobalt]

Loring W. Tu

[heady ember]

I always misspell his name

[heady ember]

I take that as a personal insult

You will only know why if you know me irl

Yet, I know what math is like
Boom, gottem.

~~I'm only still learning the basics ~~

[fresh skiff]

Oh maybe, haha i saw that intro like 2 or 3 years ago

[limpid monolith]

any recommendations for textbooks for ODE and PDE? Hopefully ones that contain solutions by Fourier Series Fourier Transforms and also Applying Green function

[graceful moon]

I believe he has retired from teaching to do YouTube full time but I’ve got no idea where he worked before then

I just used his LatTeX and multivarible videos when I started uni

[fresh skiff]

oh i got it

[normal crystal]

congrats, everyone remembered wrong🤡
not Toronto, not Australia, not retired
https://youtu.be/emDNbJX0-KA

[fresh skiff]

Damn

[slender cargo]

Wait. How do we use LaTex for presentations?? I must know. I use LaTex for writing up my assignments but I don't know what to do about ppt presentations..

[fresh skiff]

beamer

beamer classs

i will send link in few min

a lil busy

[remote vortex]

https://www.overleaf.com/learn/latex/Beamer

Overleaf has some examples

[sterile horizon]

Paper towns is a good book

So are Karin slaughter books, I probably should have been reading her books when I was young, but I read them regardless

[prime wigeon]

Hello everyone
I am learning about linear representations of finite groups. I am also interested in category theory but am at the start of it. I was wondering whether there are resources that would allow me to study representations through categories (and categories through representations) at an almost graduate level ? I would enjoy studying them both at the same time and it'd be convenient so I don't have to study them separately
I also take papers or university courses if those are available online

[dim pendant]

Are you taking a course on representation theory, or learning it on your own?

I've taken a look through some major books in the area and I don't see much category theory. I'm assuming it's either not very present, or it's just a bit down the line, closer to graduate and research level.

[dim pendant]

If you're taking a course, you could ask your professor.

Anyway, I doubt there will be any books on category theory that are motivated by the representation theory of finite groups.

[mellow wren]

imho the best way to learn category theory is through algebraic topology

it's what it was made for anyways

[prime wigeon]

I am learning it on my own !
Thank you for your help anyways !

[prime wigeon]

I take good note of this !

[dim pendant]

AT might actually be a goated gateway to category theory

there's a lot going on with higher category in the context of homotopy theory, for example

[gray gazelle]

Do you guys have any recommendations for books to learn coordinate geometry conic sections (like polar coords cartesian spherical and parabola circle straight lines hyperbola ellipses etc) and all from scratch to a uni level ig.

[dim pendant]

Khan Academy

This stuff isn't really studied in uni I mean there are geometry classes where this stuff is relevant but "up to a uni level" generally means "what I'd learn from a high school course in geometry and trig/precalc"

[cursive cradle]

Hello, trying to learn single variable calculus, never done it before. i am not a big fan of thousand pages filled with repetitive problems and not well-motivated. my geometric intuition is utterly shit.

i tried first few chapters of spivak, tao, and some other analysis/calculus books to get the basic taste (ofcourse; not doing calculus itself from these books severely limits my understanding), overall, i like tao more. its much more well written and avoids circular logic (that i find first few chapters of spivak suffer from), and doesent rely that heavily on geometry. the only downside... is well, i dont get the intuition for calculus. the problems are mostly proofs, and even those are relatively easy.

So i am looking for a calculus somewhere in between of spivak and tao; that does include proofs, but does not forget you to teach you intution, covers everything needed in a single variable course.

my benchmark for intution will be that after solving the book, i should be able to comfortably approach calculus problem books without lacking anything major. (for example, i.a maron's)

[molten gulch]

<@&268886789983436800>

[torn blade]

this is literally the situation im in rn

mfw my entire group wants to ise word/powerpoint for a mathematical report/presentation

[graceful moon]

If you’re making a presentation in Beamer you’ll likely want to install a new theme. The included ones are… dated to say the least

[broken bramble]

You can try "Real Analysis: A Long-Form Mathematics Textbook"

it's only around 400 pages

it has a kind of informal style, but i think it proves all of the basic results

[cursive cradle]

Jay Cummings one, right? thats more of an analysis book though, right? it doesent really cover everything you are taught in a standard single variable calculus course

i actually havent read it, so i might be wrong on that

[broken bramble]

Yes, well you made a reference to spivak which is basically an introductory real analysis book

honestly spivak is probably a harder read than the cummings book

[cursive cradle]

yeah but spivak covers much more. if i wanted to do analysis, i'd do tao's analysis or that green-german one "analysis 1"

but i really dont wanna mess up my intution and not know a lot of basic calc stuff that these books skim over

this will be my first proper exposure to calc

[broken bramble]

there's a series of modern, free calculus textbooks that you can find here: https://personal.math.ubc.ca/~CLP/

if i had to learn calculus all over again i'd probably go with those

if you're ok with a non standard approach there's also this book: https://www.amazon.com/Calculus-Set-Free-Infinitesimals-Rescue/dp/0192895605/

[cursive cradle]

alright, thanks. will check them out.

[fresh skiff]

So true ^

[slender cargo]

I’d personally keep going with Spivak. I’ve gone through his first few chapters, and yeah, not everything is completely rigorous, but that’s fine. Ch. 5 onwards is when the material starts in earnest.

Actually I think just about everything is rigorous aside from the geometry section. None of it is circular.

[restive falcon]

@pure kraken #book-recommendations message is a great overview of the available algebra textbooks if you're interested

[pure kraken]

what’s that

[marble solar]

There's always Apostol's Calculus

[pure kraken]

I never read books

[molten gulch]

One should read books

[marble solar]

But I think learning how to do calculus from a computational approach is not a mistake

[pure kraken]

I can do impassible stuff but not read btw

[molten gulch]

This is one of the main ways to study mathematics

[molten gulch]

??????

how

[marble solar]

At some point you do need to calculate some derivatives/integrals

[pure kraken]

Idk how to read unless we’ are in light mode discord

[pure kraken]

Yh

[pure kraken]

Lowkey blind

[molten gulch]

Books are on white paper

[pure kraken]

Yh

but

[molten gulch]

that should be bright enough

[pure kraken]

irl vision

is

like

[molten gulch]

Then use a screen reader?

[pure kraken]

na

[molten gulch]

There are tools for this

[past dust]

How’s the book on graphs by West ?

[remote sparrow]

are you legally blind? there may be braille renditions of certain books

are you unable to access an assistant who could help you read a book?

[tired glen]

https://youtube.com/playlist?list=PL590CCC2BC5AF3BC1&si=39Eqhwc1iOaVyuaD

It covers basic introductory calculus of single variable but its an online resource also search for MIT OCW 18.01 for worksheets and practice

[tired glen]

Spivak calculus is like introduction to real analysis

[brave topaz]

love it

[torn blade]

lectures + exercises are \cong to books

so like whats the matter

id say i have a pretty solid foundation on abstract algebra and ive never read an elementary abstract algebra book

[vital bane]

mfw lectures and books arent mutually exclusive

[torn blade]

i dont think either of us said that

i for one use both

[remote vortex]

I think they are, otherwise my students would have read the books

[past girder]

where yall get books without paying exorbitant cash

[remote sparrow]

you might get lucky while looking for used editions

[past girder]

i live in singapore its kinda hard to find

[remote sparrow]

international editions of some popular textbooks do exist

that are priced specially for people in your area

alternatively, you could have a print shop print and bind books for you

@heady ember

[past girder]

yeah theres this guy i found who does that

[heady ember]

Hello there

[past girder]

his paper is kinda cheap but for now it does what its supposed to

[fierce socket]

Can anyone can you suggest a book or pdf to help me cope up with the topic logarithms for engineering

maths

[heady ember]

You can use this to convert a PDF into signature form:
https://momijizukamori.github.io/bookbinder-js/
Then, print it out somewhere and follow this tutorial series
https://youtu.be/N6U8k2NaPMc?feature=shared
to bind your book.

[past girder]

great

[heady ember]

My own binding for Henry Cartan's Differential Calculus
#1059828221887135774 message

[past girder]

how hard is it to do?

i.e. should I wait until I find a book I really want

[heady ember]

Just takes a couple hours

Its not too hard

[past girder]

alright

thanks dude gonna try this out soon

are bookcovers judt cardboard?

[remote sparrow]

not the cardboard you might find in boxes, no

some are also made of leather or faux leather (e.g. bibles)

tbh i'm not quite sure

i will say most books don't have leather/faux leather covers

[coral narwhal]

Its a solid and comlete book, though fairly dense (atleast for undergrads). It was the reference text for my course and I liked the distribution of exercises across difficulty levels. If you're looking for a gentler alternative, I've heard Diestel is great.

[past girder]

how did you make yours?

is the best bet just making paperback

[remote sparrow]

i haven't made any books

[remote sparrow]

i guess, but you could easily have a print shop do that instead

[past girder]

oh wrong guy

i thought u were grass

[past girder]

true

[heady ember]

Take a couple cardboard backings (e.g. from foolscap pads or art paper stacks) and glue them together

Otherwise you can just buy some cardstock

[analog lava]

does anyone have an alternative for hatcher chapter 4?

something that is slightly more terse and covers the same ground

[weary iris]

Is there any good standalone books on calculus?
I've been recommended spivak and lang introductory course

[vital bane]

Stewart is good

so is Thomas

[tender cobalt]

Thomas based af

[merry sphinx]

how so

[vital bane]

@short sail 🗿

[short sail]

🗿

[vital bane]

bro is finally in the math server

this day will be marked in history

also green leaf, cringe

[weary iris]

Are all the recommended equal

[vital bane]

depends on what you're looking for

<@&268886789983436800> sus?

bro really tried to ping everyone in this server

[tender cobalt]

if youre a beginner, go for thomas

stewart is easier than thomas as a beginner book

[weary iris]

at risk of biting more than i can handle, i'd prefer no handholding and nothing too basic

[tender cobalt]

thomas is good in that

you should be good with that

and spivak is a challenge if you're feeling ambitious

[viscid valve]

I can advocate for Thomas being good for that too, yep. Just finished going through it myself, and it was just right for me

[weary iris]

i'll probably look into those two then thanks

[tender cobalt]

best recommendation is just start on something right away and switch if needed

[weary iris]

well idk it's still a book i'd have to buy

i have "found" the spivak calculus and so far it looks very ood

[tender cobalt]

just ordered Artin, Jacobson I, and Gamelin

[tender cobalt]

yes

[naive lava]

damn my mans serious about ts

but please check out ahlfors too

after gamelin

or whilst

[tender cobalt]

🫡

i intend to have two books for each subject, so definitely will get alfhors later too

[remote sparrow]

you could probably stand to read something more modern

[gray gazelle]

Topology & Groupoids covers homotopy quite well imo

It doesn’t cover any (co)homology though afaik

[broken bramble]

here is a very good free series of calculus textbooks: https://personal.math.ubc.ca/~CLP/

first books covers differential calculus, the second covers integral calculus, the third multivariable calculus and the last one is vector calculus

[grim ore]

fr die hard fan of T&G

But validly so

[naive lava]

what??

is the true?

I mean, sometimes things are wobbly but you see that clearly or he tells you them

[remote sparrow]

@marble solar

[gray gazelle]

is there an algebraic geometry book review or something like that where I can get info about different books and decide where to start? I see that there are a lot of books but I'm not sure which one I should try first

[cursive orbit]

there is a math.se thread with a lot of books (https://mathoverflow.net/questions/2446/best-algebraic-geometry-textbook-other-than-hartshorne), but I guess what book u should read depends on your background

[marble solar]

Ahlfors says correct things, but not precise things

very verbose, but when you try to write down maps, sets, or things exactly then it becomes a tad trickier than how Ahlfors presents it

I think Conway is probably the most precise Complex Analysis book, but everyone hates how dry it is

[old elk]

http://www.neverendingbooks.org/lets-spend-3k-on-mathbooks/

[vital bane]

have you finished Munkres?

[last cipher]

Thoughts on Charles Pinter's Abstract Algebra?

[broken bramble]

it's ok

there's nothing special about it

[remote sparrow]

it's good

[last cipher]

Im having trouble deciding between Balakrishnan's Intro. Discrete Maths and Oscar Levin's Intro. Discrete Maths

If anyones used these books please lmk what you think

[remote sparrow]

are you more interested in mathematical logic or philosophical logic?

#book-recommendations message

[tender cobalt]

Working through rn

[slender cargo]

Be sure to work through the problems. If you can't do the problems then you don't understand the material. Also I believe you should have finished an elementary real analysis text first (i.e. Abbott) before working through Munkres.

[tender cobalt]

Definitely, working through the problems is where learning happens

[tender cobalt]

I've gone through topology bits of analysis

Like topology of R and R^n

So I've got some idea

😁

[broken pecan]

Just want to share this is from Handbook of Mathematical Functions with formulas, Graphs, and Mathematical Tables by Abramowitz and Stegun in 1964. The age where computer wasn't even a thing

They are able to make these graphs, this is nuts to me. I don't know how they did it. Seems hand drawing. Beautiful

[naive lava]

ah yea i'd noticed that, especially in the integration chapter, it's kind of hard to recall thm's conditions

[vital bane]

So...Ahlfors + Conway is good?

Also dude you gotta check out Conway's "Functions of one complex variable - II" it's so sick 🔥

[naive lava]

should be

or narasimhan

what i did was just to write down every theorem in ahlfors in a piece of paper till i truly understood them all

but ahlfors is too good to pass on lol

everything flows so naturally

maybe too naturally that we miss the points lol

[vital bane]

I believe you

[heady ember]

I don't

[tender cobalt]

Tu vs Lee vs Spivak 🤔 (Diff geo)

[small loom]

Could someone recommend a good book that serves as an introduction to more advanced mathematics? I'm currently in 10th grade.

[tender cobalt]

you met me in the perfect timing, im in 10th grade as well, could guide you how i did it

what maths do you know right now ?

[small loom]

Everything on the curriculum for grade 10

[tender cobalt]

Which country? India?

[small loom]

Germany

Algebra:
Linear & quadratic equations, systems of equations, functions & graphs.
Geometry:
Pythagoras, trigonometry (sine, cosine, tangent), circle properties.
Statistics & Probability:
Averages, data interpretation, basic probability.
Logic & Reasoning:
Simple proofs, modeling problems.

[tender cobalt]

alright you can start with advanced trigonometry and calculus

"Precalculus" by James Stewart is a good place to start trigonometry

And you can use Thomas' Calculus for learning calculus

[small loom]

Thanks

[small loom]

That book costs 95$......

[molten gulch]

There are also freely available precalculus texts online

[remote sparrow]

feel free to buy used copies of previous editions

[wraith cave]

most math sites are free and pretty good

[vital bane]

Khan Academy is great

[hollow peak]

Tu for intro, Lee for reference, Spivak as a collectors item lol

[tender cobalt]

Spivak ain't good for learning? 😔

[molten gulch]

It just has way too much info

[hollow peak]

Yeah its very verbose

[tender cobalt]

D&F of diff geo?

[hollow peak]

Its like reading an encylopedia to learn history

[molten gulch]

Spivak diff geo (5 vols)

[hollow peak]

Unless youre referring to calc on manifolds?

[tender cobalt]

diff geo is what i mean

[vital bane]

D&F is 950 pages, Spivak all 5 volumes is 2200+ pages

every other author starting the book: uhh so let R_abc^d be the riemann curvature tensor of our 4-manifold 🤓☝️

spivak starting the book: this curves a lot, this curves a little 🗿

[tender cobalt]

does that mean its more pedagogical?

[heady ember]

What about Jeffrey Lee

[heady ember]

I heard vol 1 is good though, no?

[tender cobalt]

Is it good

[livid lintel]

Spivak likes to play and draw

[molten gulch]

Same, I haven't read any diff geo tho

[tender cobalt]

4.8/5 in amazon

can't be bad right?

[molten gulch]

We generally don't trust amazon reviews and prefer to go read MAA textbook reviews alongside asking people in or tangentially (no pun intended) in the field

[tender cobalt]

oo

[molten gulch]

Like amazon is one set of data points but you may notice that there it's common for a book with low quality reviews to commonly have physical quality issues and not much in the way of pedagogical or such issues

At-least that's what I've seen

[tender cobalt]

Yeah I saw these too

[molten gulch]

And then some people complaining about errata, which is fine, but annoys me when we know of the existence of errata sheets for the text that could've beenn refereneced (assuming they existed at the time the text was under review)

[remote sparrow]

errata sheets do not always exist

it also interrupts the flow of a text if there are way too many glaring errors

and of course, it hurts the book as a reference

[vital bane]

it also hurts the reader

financially

[dapper root]

<@&268886789983436800>

[molten gulch]

<@&268886789983436800>

[dapper root]

I win

[night gorge]

Thanks Ryan :)

[dapper root]

WTF

[molten gulch]

HAHAHHAHA

[dapper root]

What the Chmonkey

[night gorge]

Oh you both pinged LOL

Thank you both

[molten gulch]

LOOOOOOL

[night gorge]

I just saw the latest in my notifications

[molten gulch]

Hey dghost how goes it

[dapper root]

I even won

The race

[night gorge]

You did

[dapper root]

Chickenjockey

[night gorge]

Yeah good, tired, busy. 3rd week at the new job

[dapper root]

Oh cool

How is it

[night gorge]

flint and steel 📣

Yeah good, very different. Lots of people to learn the names of and levels of approval to go through for everything. Which is both annoying but a good skill to learn. And the project work itself is great and interesting because of what it all entails

lol

[dapper root]

Pull out $16374829293029 of free money here: www.scam.us.gov.org/virus

[molten gulch]

Ooh gl

[molten gulch]

@ modulators

[vital bane]

it was just a joke

[crimson halo]

Any algebraic geometry textbook recommendation for a graduate student with a background in algebraic and geometric topology and knowledge of homological and commutative algebra? I tend to enjoy lots of problems and attention to detail and completeness

P.s.: two years ago I took an undergraduate class using Fulton's algebraic curves, though I don't remember much

But I did enjoy it. However, I would like something that treats the subject in greater generality

Currently considering trying a Hartshorne+Vakil combo. Any thoughts?

[dapper root]

I don’t personally see a reason to do both

I think picking one and going with that is usually enough

Maybe supplement at times with the other as needed

¯_(ツ)_/¯

You could try using Görtz and Wedhorn, I like the books

They have more details than Hartshorne and the treatment is more modern

And I also want a data point of someone using it so you could become a test subject for the betterment of humankind. And by humankind, I kinda just mean myself

[crimson halo]

The reason I was considering both is because I kind of wanted to review classical stuff since I have forgotten most of what I covered in Fulton's book, but I also want to delve into the world of schemes and I know vakil is good for this

[dapper root]

Hartshorne is also schemes bro

[crimson halo]

Ye, but the first chapter is classical

[dapper root]

Yeah and nobody does it

[crimson halo]

oh

[dapper root]

Lol

[crimson halo]

lol

Welp

Any recommendations for the classical then? Görtz and Wedhorn?

[molten gulch]

Afaik most people do 2-4 but don't quote me on that

[dapper root]

Görtz and Wedhorn doesn’t have classical

[molten gulch]

This is pure unfiltered schemes

[dapper root]

I mean chapter 1 of Hartshorne is fine for a review

I ended up going back to it after doing chapter 2 and 3 and just blazed through it

[crimson halo]

Hm, aight

So basically then I have 3 contending books for schemes

I'll take a look at Görtz and Wedhorn. If they suit my style and are attentive to detail, I think I'd like it

[dapper root]

The only thing I’ll say is that there’s a huge errata. They did a 2nd edition to Vol1 which fixed a lot

But even then there’s some stuff

They have a thorough errata online tho

I think Görtz and Wedhorn is honestly really good though

[crimson halo]

Mind if I ask why you're a fan?

[dapper root]

The exercises are also more reasonable than Hartshorne

[crimson halo]

Just cause I know nothing about the book

[dapper root]

I think from this point in my life it’s because the treatment is more modern

[crimson halo]

yeah, that's not hard to believe lol

[dapper root]

And touches on the sophisticated way to look at these things which is how people actually view them

[crimson halo]

Okay, that sounds exactly like what I'm looking for

[dapper root]

Like they talk about representable functors and construct the grassmannian that way

Which is not strictly necessary, but for a lot of people will be how you will end up eventually thinking about things

[crimson halo]

Nice. I tend to like books that don't hold back on the categorical viewpoint too

[dapper root]

They are also more thorough in doing details for simpler things that Hartshorne just stated

Which when I look back, they’re really obvious

[molten gulch]

Afaik most of the errata I've seen on the page and in-text has been quite minor like missing capitalization, periods, etc...., though there is some bigger, to me it felt a bit like they were just documenting everything seen as errata

[dapper root]

But at the time when I had no idea was going on took me sometimes hours to figure out

[dapper root]

Yeah it isn’t categorical but it uses it where appropriate

More than Hartshorne or Vakil

[molten gulch]

Also chmonkey, was their book 2 (cohom of schemes) a 2nd edition too or totally new?

[dapper root]

I don’t know how to explain but they’re obviously German

[molten gulch]

Yeah

[dapper root]

When you get an understanding of what type of AG is big there

[remote sparrow]

i was about to ask you to compare the exercises between each, but then you essentially said you weren't really familiar with gortz and wedhorn

[crimson halo]

best compliment you can give

[dapper root]

And how they like to learn it, they’re German

[remote sparrow]

you want shafarevich for classical AG

[dapper root]

Görtz and Wedhorn is easier for exercises

And more is developed in text

[dapper root]

New

And it uses the derived category

Which is a plus IMO

[crimson halo]

yeah, I've considered it, but Idk if it would be a bit too slow

[molten gulch]

Are there any texts that bridge complex manifold stuff like what's done in, say, griffiths and harris, with modern AG? Afaik there are lots of relationships between manifold theory and modern ag via like serre's gaga theorem and such but idk how deep it goes

[dapper root]

Algebraic Geometry over the complex numbers by donu arapura

This is how I learned hodge theory

[molten gulch]

Ahhh nice

[dapper root]

And as part of it I learned like a bit of complex geometry I guess

It’s a really interesting treatment, but it’s the first time diff geo made any sense to me because I’m cooked in the brain

[molten gulch]

What are the prereqs for that? Hartshorne/gortz/etc... or anything on the manifolds side?

[remote sparrow]

do you need to be particularly good at analysis generally for AG

[dapper root]

You don’t need much AG background honestly

I think it developed it in text

Honestly I don’t think the prereqs were that high

It might be a good intro to these topics honestly

I think you need to have some knowledge of diff top

But if you’ve seen what manifolds are you should be okay?

[remote sparrow]

bump

[molten gulch]

Ahh

[remote sparrow]

there are connections between model theory and algebraic geometry so i'm somewhat curious about AG but not looking to specialize in AG

[dapper root]

No

You don’t need shit

[remote sparrow]

i'd probably work through my analysis books for fun, but i don't think i'll click with it

or be interested in pursuing analysis deeply

[crimson halo]

@dapper root any thoughts on Gathmann's notes?

[vital bane]

that's what you say now

[dapper root]

They’re for classical I think

They’re good

[crimson halo]

Cool, just asking cause I know my uni's course uses them

Thanks

[remote sparrow]

https://grossack.site/2021/12/22/qe-competition

inequalities begone

[crimson halo]

Does anyone know the prereqs for Hirzebruch's book?

[graceful moon]

I’ve never heard of it, but I’d be willing to bet it’s outlined at the very least implicitly in the preface or introduction

[crimson halo]

Couldn't find it there

[velvet yarrow]

have you guys got any recommendation on the best book of maths which has everything from the basic and goes to advance and even highers thinking problems, covering all the theorems (in various maths topics such as geometry calculus algebra etc) and the way to think them graphically.

series of books will also be accepted (P.S. - i hardly think that only 1 book will cover it all)

plus btw..hi i am new here

[molten gulch]

There is no single book that will achieve this

[graceful moon]

There’s no such book unfortunately. If you want to cover the basics up to calculus and the like in one place there is Khan academy

[molten gulch]

Beyond calculus, you'll probably want 1-2 books per subject to get diff viewpoints

[velvet yarrow]

yh thts why i said that a series will too work

[molten gulch]

There's a reason I have like 6 linear algebra books

[molten gulch]

Yeah no series by one author either

Sadly

[gray jungle]

I think there is this one book with a really large topic scope, but it also touches on it in a introductory/expository way iirc

[velvet yarrow]

ok suggest diff authors

[molten gulch]

The princeton mathematics guide?

Or maybe a handbook of some kind?

[gray jungle]

i think so yes

it can kinda give a overview on different field i suppose

[velvet yarrow]

for calculus what will you guys suggest

[wide geyser]

the napkin maybe

[velvet yarrow]

and may i ask u ppl qualification..if u dont mind

[gray jungle]

if you want to get into mathematics, i suggest spivak

stewarts book is fine too from what i heard

[velvet yarrow]

i am just a 12th grader

[velvet yarrow]

i have a basic idea what it is

[gray jungle]

Im finishing my masters degree if that comforts you

[velvet yarrow]

wow...major in maths

[wide geyser]

aops calculus (harder) or khan academy (easier)

[gray jungle]

you should start learning calculus from spivak or james stewart, later on you can jump into the basic university topics (Linear algebra, real analysis, discrete math, basic probability)

[velvet yarrow]

calculus is the base of all things...

[graceful moon]

Not so much in maths, but yeah it’s very important in general

[velvet yarrow]

michael spivak u say?

[gray jungle]

yep, thats my recommendation, but its not a easy book

for calculus students

[graceful moon]

Spivak is probably a hard place to jump in, Stewart would be a lot more gentle

Although it is an absolute tome

[velvet yarrow]

how long is it, its showing 70 pgs online

[graceful moon]

Yeah spivak is rather quick and light on details so it is a short book. Stewart which is the standard calculus book at a lot of universities is like 900 pages

[velvet cove]

Do You guys know about any online service that provides access to textbooks related to maths .?

[velvet yarrow]

i use library genesis for most of my needs...not promoting anything

[gray jungle]

To be clear you definitely wont be reading a full book on any math topic, even if the books are 500+ pages, you will usually be picking and choosing what to learn and solve.

[velvet yarrow]

yh

[graceful moon]

Especially Stewart, that book covers an ungodly amount

[velvet yarrow]

and by stewart u meant james stewart?

[graceful moon]

Yeah

[velvet yarrow]

k

[graceful moon]

It would be my recommendation if you’re self studying and new to maths

[velvet yarrow]

alryt gtg
u guys were a blast

[graceful moon]

I think you’d likely bounce off of spivak, but giving a go isn’t a bad idea

[gray gazelle]

yo so i read a lot of krugman and online stuff

and i wrote an article on it can someone give me feedback. its econ related but also a bit math related ig

https://medium.com/@hamsters/the-right-needs-better-tax-policy-a-case-for-land-value-tax-65b467041660

[gray jungle]

<@&268886789983436800>

[old elk]

Which differential geometry textbook do you think has everything you need to understand this area well, i.e., the best of all.

[sly jolt]

I liked Loring Tu

[cursive orbit]

Lees series is okay for beginner

[last cipher]

Do the editions of books really matter

I found rosen's discrete maths 5th edition in a thrift store, how does it compare to the most recent one?

[molten gulch]

It does not matter much

Maybe a few errata fixed, a few problems moved around

[last cipher]

Ahhh okay

Finding the book in a thrift store was such a great find

I was struggling to find a cheap discrete maths book

Looks like my prayers got answered

[naive lava]

sometimes

most authors list what changed on the preface

[dim pendant]

It only matters if the person who recommended or denounced a book mentioned an edition

Usually they just fix errors and add some content

[vital bane]

https://tenor.com/view/what-are-you-challenging-me-scooby-doo-shaggy-matthew-lillard-gif-17770189

[vital bane]

I see you have already posted this

[heady ember]

I'm 10000 years ahead of you

[tribal crow]

Neam and grass compete on who can take the longest to 100% their books

[heady ember]

Teach me O' master; how do I 100% my book fast?

[fresh skiff]

both are worthy opponents for eachother lol

[lusty perch]

Hey guys. I want to learn Lin. Algebra for AI research, so applied math essentially.

Would y'all recommend Friedberg-Spence-Insel's book, or Axler's? Or maybe smthn diff?

[vivid elm]

Grab before they remove it https://people.math.ethz.ch/~grsam/NCSE20/NumCSE_Lecture_Document.pdf

[heady ember]

How about you

[wide shale]

Fermat’s Last Theorem – Pierre de Fermat

x^n + y^n = z^n \quad \text{has no integer solutions for } n > 2
Fermat famously wrote he had a “truly marvelous proof” that didn’t fit in the margin.

[graceful moon]

So true

[mighty anvil]

hey, does anyone have any websites or apps that has textbooks

[graceful moon]

Openstax

[gray gazelle]

I need to touch you

[heady ember]

No I think you need some creativity. Blocked.

[gray gazelle]

The reactors 💀

[remote vortex]

I won't lie; I think of you everytime someone mentions "touching grass", but I'm very proud of myself for having resisted actually making the joke until now.

[gray gazelle]

Ok I am sitting on grass 👍😀

Feeling kinda itchy

[heady ember]

Well, I won't block you for that lol. You're my shitposting comrade . I just felt like blocking that random person for doing it, because it gets annoying sometimes

[gray gazelle]

......

[remote vortex]

I've frequently wondered just how often you get that line

[gray gazelle]

Whats wrong with the lame jokes

I like lame jokes

[heady ember]

Like I dunno every couple of weeks?

[gray gazelle]

Where do you live

How out side

[remote vortex]

In a rather nice house with my husband.

[gray gazelle]

I have realised one thing

[remote vortex]

Oh wait, this is #book-recommendations; I've just realized that

[gray gazelle]

In order to be successfully there is no shortcut in life

You have to work

You have to be dedicated

You have to put in the hours

[remote vortex]

...meanwhile instead you sit here making unoriginal jokes in the wrong channel of a discord server

[gray gazelle]

No fúçking motivation book can help you

That self help thing is bs

[gray gazelle]

I am leaving internet forever

This is prolly my last Convo

I have had enough lies

There is no need for internet for me to study

I have everything I need, that is a book, a notebook and a pen

And my teachers

This internet has taken like 5-6 years of my life

And I am 16

Ok not that much but like about 2 years

I played games in lockdown and did nothing

Last year was the same

This year I won't let it happen

I wasted 3 hrs today too

They are off of my life forever

No point in grabbing attention

The only point is to know the self and make myself the fullest of me

@remote vortex you there ?

Hmmm looks like you left

I am leaving this shít i recommend everyone to do the same for at least 21 days

That's 21 days of your life back to you

Good bye INTERNET 👋

[lusty perch]

Oh wow this is so helpful, tysm man!!

Like legit this is a crazy resource

[fresh skiff]

it depends what book you are talking about lol

[vivid elm]

Yeah lol. There is one on methods for PDEs too

[surreal flint]

I’m looking for information on zonohedra, symmetrohedra, and parallelohedra, anyone know where I can start looking

[vital bane]

people keep touching him, it's unbearable

[mellow wren]

Polytope discord

[frigid pumice]

which books are recommended for olympiad level maths preparation ??

[wide geyser]

evan chens egmo, modern olympiad number theory

[vital bane]

I read this as 4chan and was confused

[frigid pumice]

ill go through these books. thx for recommending

[muted patrol]

Does anyone have recommendations for books about problem solving, i don't do it much and I'm mainly interested in techniques and how to approach the questions

[strange tree]

problem solving strategies
art and craft of problem solving

[viral oracle]

hey guys, im looking for book on monte carlo methods (applications in physics), not too long (like introductory text, 200 pages max?). thanks

[autumn cargo]

Where is it ?

[molten gulch]

what text is this?

[manic cairn]

basic mathematics, serge lang

forgot that part was in there

[molten gulch]

ahh

[manic cairn]

just think about how based this take is for a high school/college algebra textbook

[trim kayak]

I want to study basic calculus and statistics just for fun. Which one should I start with first?

I have Stewart's 8th edition Calculus textbook that I want to use. Any recommendations for a good, basic statistics textbook?

[vital bane]

I think you should focus on Calculus first

meanwhile you can check out Khan Academy statistics course

[trim kayak]

Interesting, okay. Any recommendations for a good Stats book?

Oh okay. Thanks.

[vital bane]

https://www.khanacademy.org/math/statistics-probability

I don't really know any basics statistics books, the only statistics book that I know is All of Statistics by Larry Wasserman

I think that would be too advanced for you at the moment

Though he does say you don't need prior knowledge of probability and statistics

[vivid elm]

https://people.math.ethz.ch/~grsam/NUMPDEFL/NUMPDE.pdf

You can find them by searching "numpde/numcse lecture document" on google

[autumn cargo]

thank you very much

[ripe dock]

i want to pick up some math textbook but idk what topic i should
have a mostly hs-level education in it. i tried real analysis but idk whether i should go over the basics or skip to what i dont knowl

[vital bane]

Have you learnt calculus?

What about linear algebra? I think you would enjoy linear algebra it's quite fun and beautiful, try "Linear Algebra and Its Applications" by Gilbert Strang

[ripe dock]

ye thats what i meant

im thinking number theory though

[vital bane]

number theory is also cool, but I don't know any good number theory books for beginners

[mighty tartan]

i didnt see this, nice crashout

still on the server tho

[vital bane]

how is that a crashout

[brisk rapids]

Ireland Rosen?

[vital bane]

That's not really for beginners is it?

isn't that an algebraic number theory book?

you mean "Classical Introduction to Modern Number Theory"?

Unless you're refering to a different book by the same authors

[remote vortex]

People so rarely have the courage of their convictions

[covert vector]

maybe james k strayer’s elementary number theory might be up your alley?

elementary number theory i think has a lot of good concepts without many harsh prerequisites. maybe you’ll need some familiarization with proofs but shrug

[ripe dock]

Im actually fine with proofs i think

[brisk rapids]

The first few chapters should be accessible, right?

[molten gulch]

How much ENT does one need for AlgNT?

[twilit field]

algebra book recommendations except for hall and knight

[mellow wren]

ehhh not that much
It's more about knowing enough abstract algebra

if you know like

unique factorization of primes in Z

and how modular arithmetic works and some results regarding that

you're set essentially

[vital bane]

tbh you already need that just for regular abstract alg

Like you'll learn that while you're learning group and ring theory

so I guess you can just go AA -> AlgNT

AA -> AlgNT -> Arithmetic Geometry

[molten gulch]

ahh okay that's nice then

[fleet leaf]

yeah this is the closest we’ll ever be to pedagogic perfection

[ivory solstice]

do any of you know if there is a difference between "The Mathematical Olympiad Handbook: An Introduction to Problem Solving Based on the First 32 British Mathematical Olympiads 1965-1996 (Oxford Science Publications)" by A. Gardiner when the front cover is in red or purple?

[ivory solstice]

also, any book recomedations which are an interesting read and also would be good to put on a personal statement when applying for Uni?

[torn blade]

hollow knight?? i thought that mf was locked up

how is he writing algebra books

[rocky flicker]

try how to prove it by velleman. Its a pretty good intro to proofs

[vital bane]

@remote sparrow

[remote sparrow]

[warped saffron]

Any book recommendations Matrix analytic methods based on Markov Chains? Or Markov chains in general?

[remote sparrow]

for a general reference on markov chains, i heard levin peres wilmer is good

[warped saffron]

Thanks so much

[remote sparrow]

you might also have luck asking in #advanced-probability

[stuck fjord]

Anyone got fun books to read on differential geometry or topology?

[full cairn]

There's lots of options, there's Lee, which is too long to be fun, Milnor, which is too short, but Guillemin & Pollack is just the right length

There's also a pretty nice book called A Short Course in Differential Topology by Bjørn Dundas. I particularly like the example in the intro with the state space of a robot arm represented as a smooth manifold (he gives an illustration of regular values by looking at what happens to the state space when you restrict for example y to a particular length). It has lots of other good illustrations too

[stuck fjord]

these arent textbooks right?

[stuck fjord]

woahh

[full cairn]

Yeah they are. Lee has 3 or 4 books about manifolds, the one about differential topology is called Introduction to Smooth Manifold. Milnor has a book (or honestly more like a pamphlet) called Topology from the Differentiable Viewpoint, and Guillemin & Pollack's is just called Differential Topology

Lee and Milnor probably require some knowledge about topology beforehand, for G&P and Dundas it's not that important I think

[naive lava]

I'm almost done reading ahlfors and i was wondering where i can find some hard problems regarding CA, it doesn't necessarily have to be the same topics, just wanna see some hard problems to test out how well i did

[gray gazelle]

any recomendations on basic algebra
i need to learn matrixes 😭

[broken bramble]

khan academy

[gray gazelle]

do they make their video script publics

?

[remote sparrow]

try some qual problems

take another look at zakeri

https://link.springer.com/book/10.1007/978-3-319-42181-0

this book exists

[remote sparrow]

https://ww3.math.ucla.edu/past-qualifying-exams/

@naive lava try some of the ucla analysis qual problems from more recent years specifically

[tender river]

theres also this website for qual problems https://jonathanlove.info/qual/

[heady ember]

Indeed, it has a lot of other good illustrations. In particular, I find the following diagram especially enlightening!

[rose hinge]

first 15 lives of harry august is good

[torn blade]

Lee’s Intro to Topological Manifolds for topology and Lee’s Intro to Smooth Manifolds for differential geometry

[fleet ermine]

Hey guys I am looking for some resources with which i could go from basics, any recs?

[fresh skiff]

basics of what

[fleet ermine]

everything, i am just not sure where to start. We have no textbooks here

[acoustic sorrel]

everything ?

even basic arithmetic ?

[sly jolt]

pick up Stewart's singel variable calculus and if you struggle with that just look for some middle school level maths textbooks

[fleet ermine]

Sure i am willing to go from the very basics lol
I just wanna be sure i didnt miss anything
Education here is pretty messed up and we jump from one topic to another in all science subjects

with no rigid textbooks

[fleet ermine]

ill try

thank you

and if ill need to go over those middle school level ones? Is it okay to pick up any textbook out there

[sly jolt]

middle school is pretty much the same no matter where you are

some algebra, some geometry, some probability

[acoustic sorrel]

i still don't understand what you call "very basics"